U.S. patent application number 17/114421 was filed with the patent office on 2021-04-22 for system, apparatus and method for extracting three-dimensional information of an object from received electromagnetic radiation.
The applicant listed for this patent is CELLOPTIC, INC.. Invention is credited to Gary BROOKER, Joseph ROSEN.
Application Number | 20210116865 17/114421 |
Document ID | / |
Family ID | 1000005305881 |
Filed Date | 2021-04-22 |
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United States Patent
Application |
20210116865 |
Kind Code |
A1 |
ROSEN; Joseph ; et
al. |
April 22, 2021 |
SYSTEM, APPARATUS AND METHOD FOR EXTRACTING THREE-DIMENSIONAL
INFORMATION OF AN OBJECT FROM RECEIVED ELECTROMAGNETIC
RADIATION
Abstract
An apparatus and method to produce a hologram of an object
includes an electromagnetic radiation assembly configured to
receive a received electromagnetic radiation, such as light, from
the object. The electromagnetic radiation assembly is further
configured to diffract the received electromagnetic radiation and
transmit a diffracted electromagnetic radiation. An image capture
assembly is configured to capture an image of the diffracted
electromagnetic radiation and produce the hologram of the object
from the captured image.
Inventors: |
ROSEN; Joseph; (Omer,
IL) ; BROOKER; Gary; (Rockville, MD) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CELLOPTIC, INC. |
Rockville |
MD |
US |
|
|
Family ID: |
1000005305881 |
Appl. No.: |
17/114421 |
Filed: |
December 7, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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16459888 |
Jul 2, 2019 |
10859977 |
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17114421 |
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15704890 |
Sep 14, 2017 |
10379493 |
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16459888 |
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15014742 |
Feb 3, 2016 |
9804563 |
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15704890 |
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14727342 |
Jun 1, 2015 |
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15014742 |
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13970103 |
Aug 19, 2013 |
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14727342 |
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12515343 |
Feb 18, 2010 |
8542421 |
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PCT/US2007/085094 |
Nov 19, 2007 |
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13970103 |
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60869022 |
Dec 7, 2006 |
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60866358 |
Nov 17, 2006 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G03H 2001/0436 20130101;
G03H 1/0402 20130101; G03H 2240/23 20130101; G03H 1/0443 20130101;
G03H 2240/24 20130101; G03H 2001/0224 20130101; G03H 2240/13
20130101; G03H 2240/21 20130101; G03H 1/0841 20130101; G03H 2225/33
20130101; G03B 35/02 20130101; G03H 2001/0452 20130101; G03H 1/06
20130101; G03H 2001/085 20130101; G03H 2001/0458 20130101; G03H
2223/23 20130101; G03H 1/041 20130101; H04N 1/00827 20130101; G03H
1/08 20130101 |
International
Class: |
G03H 1/08 20060101
G03H001/08; G03H 1/04 20060101 G03H001/04; G03B 35/02 20060101
G03B035/02; H04N 1/00 20060101 H04N001/00; G03H 1/06 20060101
G03H001/06 |
Claims
1. (canceled)
2. An apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object and transmit a transmitted electromagnetic radiation based
on the received electromagnetic radiation; capture an image of the
transmitted electromagnetic radiation; and produce the hologram of
the object from the captured image, wherein the electromagnetic
radiation assembly is configured to simultaneously control more
than one phase of the transmitted electromagnetic radiation.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 14/727,342, filed Jun. 1, 2015 which is a
continuation of U.S. patent application Ser. No. 13/970,103, filed
Aug. 19, 2013 (now abandoned), which is a continuation of U.S.
patent application Ser. No. 12/515,343, filed Feb. 18, 2010 (U.S.
Pat. No. 8,542,421, issued Sep. 24, 2013), which is a national
stage of PCT/US07/85094, filed Nov. 19, 2007, and claims the
benefit of priority under 35 U.S.C. .sctn. 119(e) of U.S. Patent
Provisional Application No. 60/869,022, filed Dec. 7, 2006, and
U.S. Patent Provisional Application No. 60/866,358, filed Nov. 17,
2006. The contents of these applications are incorporated herein by
reference in their entirety.
BACKGROUND OF THE INVENTION
Field of the Invention
[0002] This invention relates to an apparatus for capturing
electromagnetic radiation, such as light or other forms of
electromagnetic radiation, from an object and extracting object
geometric information from the received radiation, in the field of
three-dimensional imaging and holography. The invention also
relates to a system and method of performing those functions.
Discussion of the Background
[0003] Conventional techniques for capturing three-dimensional
information from physical objects include holography,
range-finding, and tomography. However, conventional techniques may
disadvantageously require an active illumination source, or place
limitations on a light source (e.g., may require coherent light, a
point light source or a bandwidth limited light), place limitations
on movement of the object or the sensing apparatus (e.g., require
that the object and sensing device be stationary, or require that
they be moved in a predetermined fashion), may require complex
electromagnetic radiation assemblies (e.g., complex arrangement of
mirrors and lenses), and may produce poor quality three-dimensional
images having low resolution or low fidelity.
SUMMARY OF THE INVENTION
[0004] Accordingly, one object of this invention is to provide an
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, diffract the received electromagnetic radiation, and
transmit a diffracted electromagnetic radiation; and an image
capture assembly configured to capture an image of the diffracted
electromagnetic radiation, and produce the hologram of the object
from the captured image.
[0005] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation includes
light.
[0006] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation apparatus includes
only one radiation propagation axis and is configured to propagate
electromagnetic radiation only along the radiation propagation axis
in only one direction.
[0007] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly includes
plural electromagnetic radiation elements each having an axis of
symmetry arranged along a same straight line.
[0008] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly includes
plural electromagnetic radiation elements each having a geometric
center arranged along a same straight line.
[0009] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation received from the
object and the electromagnetic radiation diffracted by the
electromagnetic radiation assembly have a same radiation
propagation axis.
[0010] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation received from the
object includes incoherent light.
[0011] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation received from the
object is produced by the object.
[0012] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation received from the
object does not interfere with an electromagnetic radiation that is
not received from the object to produce the hologram of the
object.
[0013] Another object of this invention is to provide a novel
apparatus, wherein the object and the apparatus are configured to
remain stationary during the capture of the image.
[0014] Another object of this invention is to provide a novel
apparatus, wherein each portion of the electromagnetic apparatus is
configured to remain stationary during the capture of the
image.
[0015] Another object of this invention is to provide a novel
apparatus, wherein at least one of the object or the apparatus is
configured to be in motion during the capture of the image.
[0016] Another object of this invention is to provide a novel
apparatus, wherein the hologram is produced from a single captured
image.
[0017] Another object of this invention is to provide a novel
apparatus, wherein the hologram is produced from plural captured
images.
[0018] Another object of this invention is to provide a novel
apparatus, wherein the hologram includes a Fresnel hologram.
[0019] Another object of this invention is to provide a novel
apparatus, wherein the hologram includes an image hologram.
[0020] Another object of this invention is to provide a novel
apparatus, wherein a phase and intensity of the diffracted
electromagnetic radiation is described by a convolution of the
received electromagnetic radiation and a Fresnel Zone Plate.
[0021] Another object of this invention is to provide a novel
apparatus, wherein the hologram includes geometric information of
the object, and the geometric information includes, for each
electromagnetic radiation radiating surface of the object, (i) a
range distance between the electromagnetic radiation radiating
surface of the object and the electromagnetic radiation assembly,
(ii) a horizontal offset distance of the electromagnetic radiation
radiating surface of the object, and (iii) a vertical offset
distance of the electromagnetic radiation radiating surface of the
object.
[0022] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly is
configured to transmit the electromagnetic radiation including a
convolution of the received electromagnetic radiation and a complex
transmission function including a linear summation of a first
transformed pattern, a second transformed pattern and a third
transformed pattern, the first transformed pattern including a
first shifted concentric ring pattern, the second transformed
pattern including a second shifted concentric ring pattern, and the
third transformed pattern including a third shifted concentric ring
pattern.
[0023] Another object of this invention is to provide a novel
apparatus, wherein each of the first, second and third shifted
concentric ring patterns are shifted away from one another in a
same plane of the electromagnetic radiation assembly.
[0024] Another object of this invention is to provide a novel
apparatus, wherein each of the first, second and third shifted
concentric ring patterns includes a Fresnel Zone Pattern or a
portion of a Fresnel Zone Pattern.
[0025] Another object of this invention is to provide a novel
apparatus, wherein the portion of the Fresnel Zone Pattern includes
a Fresnel Zone Pattern having one or more rings removed, one or
more extra rings added, one or more rings having a varied width, or
one or more rings having a portion of the ring removed.
[0026] Another object of this invention is to provide a novel
apparatus, wherein a phase of the Fresnel Zone Pattern or the
portion of the Fresnel Zone Pattern in each of the first, second
and third shifted concentric ring pattern is different.
[0027] Another object of this invention is to provide a novel
apparatus, wherein a predetermined thickness and coefficients of
absorption or reflectance of the electromagnetic radiation assembly
is configured to control the phase and intensity of the diffracted
light.
[0028] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly is
configured to control at least one of the phase or intensity of the
transmitted electromagnetic radiation by varying a thickness of a
material through which electromagnetic radiation passes.
[0029] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly further
comprises: a first electromagnetic radiation assembly configured to
receive the received electromagnetic radiation from the object and
transmit a first transformed electromagnetic radiation; a complex
mask assembly configured to receive the first transformed
electromagnetic radiation from the first electromagnetic radiation
assembly, and transmit a complex masked electromagnetic radiation
according to a complex transmission function; and a second
electromagnetic radiation assembly configured to receive the
complex masked electromagnetic radiation from the mask assembly,
and transmit a second transformed electromagnetic radiation as the
diffracted electromagnetic radiation.
[0030] Another object of this invention is to provide a novel
apparatus, wherein the complex mask assembly further comprises: a
mask controller configured to vary the complex transmission
function of the electromagnetic radiation assembly over time, said
mask controller configured to vary the complex transmission
function to be based on a Fourier transform of a first Fresnel Zone
Pattern at a first time, a Fourier transform of a second Fresnel
Zone Pattern at a second time, and a Fourier transform of a third
Fresnel Zone Pattern at a third time.
[0031] Another object of this invention is to provide a novel
apparatus, wherein the image capture assembly further comprises: a
timing controller configured to capture a first partial image at
the first time, a second partial image at the second time, and a
third partial image at the third time; and a summing unit
configured to produce the hologram as a sum of the first partial
image captured at the first time, the second partial image captured
at the second time, and the third partial image captured at the
third time.
[0032] Another object of this invention is to provide a novel
apparatus, further comprising: an electromagnetic radiation
separating assembly configured to separate the electromagnetic
radiation received from the object into three object
electromagnetic radiation portions each including a different
frequency range; said first electromagnetic radiation assembly
including three first electromagnetic radiation subassemblies each
configured to receive one of the three object electromagnetic
radiation portions, and respectively transmit first, second and
third portions of the first transformed electromagnetic radiation;
said mask assembly including first, second and third mask
subassemblies respectively configured to receive the first, second
and third portions of the first transformed electromagnetic
radiation, and respectively transmit first, second and third
complex mask transformed electromagnetic radiation; and said second
electromagnetic radiation assembly including three second
electromagnetic radiation subassemblies respectively configured to
receive first, second and third complex mask transformed
electromagnetic radiation, and respectively transmit first, second
and third portions of transmitted electromagnetic radiation.
[0033] Another object of this invention is to provide a novel
apparatus, wherein the first mask subassembly is configured to
transmit the first complex mask transformed electromagnetic
radiation based on a Fourier transform of a first Fresnel Zone
Pattern, the second mask subassembly is configured to transmit the
second complex mask transformed electromagnetic radiation based on
a Fourier transform of a second Fresnel Zone Pattern, and the third
mask subassembly is configured to transmit the third complex mask
transformed electromagnetic radiation based on a Fourier transform
of a third Fresnel Zone Pattern.
[0034] Another object of this invention is to provide a novel
apparatus, wherein the image capture assembly includes at least one
of a CCD, a CMOS light sensitive device, another electronic camera,
a light sensitive emulsion, or another photosensitive device.
[0035] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly consists
of i) one diffractive electromagnetic radiation element and ii) one
converging lens or mirror.
[0036] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly consists
of i) one diffractive electromagnetic radiation element and ii) two
converging lenses or two mirrors.
[0037] Another object of this invention is to provide a novel
apparatus, further comprising: an objective assembly arranged
between the object and the electromagnetic radiation assembly and
configured to collimate, focus, invert or modify the
electromagnetic radiation from the object, prior to the received
electromagnetic radiation being received at the electromagnetic
radiation assembly.
[0038] Another object of this invention is to provide a novel
apparatus, wherein the objective assembly includes at least one of
an objective lens, a zoom lens, a macro lens, a microscope, a
telescope, a prism, a filter, a monochromatic filter, a dichroic
filter, a complex objective lens, a wide-angle lens, a camera, a
pin-hole, a light slit, or a mirror.
[0039] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation apparatus includes
a diffractive electromagnetic radiation element or two lenses
configured to produce an off-axis Fresnel Zone pattern when the two
lenses are illuminated by a coherent light.
[0040] Another object of this invention is to provide a novel
apparatus, wherein the two lenses are arranged in a same plane
perpendicular to an radiation propagation axis of the received
electromagnetic radiation and the two lenses have different focal
lengths.
[0041] Another object of this invention is to provide a novel
apparatus, wherein the two lenses are arranged in different planes
perpendicular to an radiation propagation axis of the received
electromagnetic radiation.
[0042] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation includes at least
one of an x-ray radiation, a microwave radiation, an infrared
light, a radio frequency signal or an ultraviolet light.
[0043] Another object of this invention is to provide a novel
apparatus, wherein the electromagnetic radiation assembly and the
image capture assembly do not include any reflective
electromagnetic radiation elements.
[0044] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object along a radiation axis in an electromagnetic radiation
receiving direction, transmit a transmitted electromagnetic
radiation along the radiation axis in the electromagnetic radiation
receiving direction, and interfere a first portion of the
transmitted electromagnetic radiation with a second portion of the
transmitted electromagnetic radiation the transmitted
electromagnetic radiation; and an image capture assembly configured
to capture an image of the transmitted electromagnetic radiation
transmitted along the optical axis in the electromagnetic radiation
receiving direction, and produce the hologram of the object from
the captured image, wherein the radiation axis is a straight
line.
[0045] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object and transmit a transmitted electromagnetic radiation based
on the received electromagnetic radiation, the transmitted
electromagnetic radiation including the hologram of the object; and
an image capture assembly configured to capture an image of the
transmitted electromagnetic radiation and produce the hologram of
the object from the captured image.
[0046] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, transmit a transmitted electromagnetic radiation based on
the received electromagnetic radiation, and interfere a first
portion of the transmitted electromagnetic radiation with a second
portion of the transmitted electromagnetic radiation; and an opaque
image capture assembly configured to capture an image of the
transmitted electromagnetic radiation produced by the interference
of at least the first and second portions of the transmitted
electromagnetic radiation, and produce the hologram of the object
from the captured image, wherein a center of the electromagnetic
radiation assembly and a center of the image capture assembly are
arranged along a same straight line.
[0047] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
consisting of one diffractive electromagnetic radiation element and
configured to receive a received electromagnetic radiation from the
object and transmit a transmitted electromagnetic radiation based
on the received electromagnetic radiation; and an image capture
assembly configured to capture an image of the transmitted
electromagnetic radiation, and produce the hologram of the object
from the captured image.
[0048] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, perform a transformation of the received electromagnetic
radiation, and transmit the transformed received electromagnetic
radiation, the transformation including a convolution of a function
representing an intensity distribution of the received
electromagnetic radiation and a concentric ring function; and an
image capture assembly configured to capture an image of the
transmitted electromagnetic radiation, and produce the hologram of
the object from the captured image.
[0049] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, perform a transformation of the received electromagnetic
radiation, and transmit the transformed received electromagnetic
radiation, the transformation including a convolution of i) an
intensity distribution of the received electromagnetic radiation
and ii) a function having regions of positive slope and negative
slope when evaluated between a center of the optical assembly and
an outer edge of the optical assembly; and an image capture
assembly configured to capture an image of the transmitted
electromagnetic radiation, and produce the hologram of the object
from the captured image.
[0050] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to convolve i) a received electromagnetic radiation
received from the object and ii) a curve having plural inflection
points between a center of the optical assembly and an edge of the
optical assembly, and transmit the convolved electromagnetic
radiation; and an image capture assembly configured to capture an
image of the convolved electromagnetic radiation, and produce the
hologram of the object from the captured image.
[0051] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, perform a transformation of the received electromagnetic
radiation, and transmit the transformed received electromagnetic
radiation, the transformation including a convolution of i) an
intensity distribution of the received electromagnetic radiation
and ii) a transformation function that is a linear combination of
three partial transformation functions, each including a concentric
ring pattern; and an image capture assembly configured to capture
an image of the transmitted electromagnetic radiation, and produce
the hologram of the object from the captured image.
[0052] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of a chemiluminescent
object, said apparatus comprising: an electromagnetic radiation
assembly configured to receive a received chemiluminescent
radiation from the object, and transmit a transmitted
electromagnetic radiation including the hologram of the object; and
an image capture assembly configured to capture an image of the
transmitted electromagnetic radiation, and produce the hologram of
the object from the captured image.
[0053] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a scattered electromagnetic radiation
scattered by the object, which scatters a source electromagnetic
radiation, and transmit a transmitted electromagnetic radiation
based on the received scattered electromagnetic radiation, the
transmitted electromagnetic radiation being independent of any
source electromagnetic radiation that is not scattered by the
object; and an image capture assembly configured to capture an
image of the transmitted electromagnetic radiation and produce the
hologram of the object from the captured image.
[0054] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to diffract an electromagnetic radiation received from
the object; and an image capture assembly configured to capture an
image of the diffracted electromagnetic radiation and produce the
hologram of the object from the captured image.
[0055] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: plural electromagnetic radiation sources
configured to radiate the object with plural electromagnetic
radiation signals; an electromagnetic radiation assembly configured
to receive a received electromagnetic radiation from the object and
transform the received electromagnetic radiation, the received
electromagnetic radiation including portions of the plural source
electromagnetic radiation signals scattered by the object; and a
capture assembly configured to capture an image of the transformed
electromagnetic radiation and produce the hologram of the object
from the captured image.
[0056] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of a fluorescent object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received fluorescent radiation from the
object and transmit a transmitted electromagnetic radiation based
on the received fluorescent radiation; and an image capture
assembly configured to capture an image of the transmitted
electromagnetic radiation and produce the hologram of the object
from the captured image.
[0057] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of a black body
radiation radiating object, said apparatus comprising: an
electromagnetic radiation assembly configured to receive a received
black body electromagnetic radiation from the object, and transmit
a transmitted electromagnetic radiation based on the received black
body electromagnetic radiation from the object; and an image
capture assembly configured to capture an image of the transmitted
electromagnetic radiation and produce the hologram of the object
from the captured image.
[0058] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, transmit a transmitted electromagnetic radiation based only
on the received electromagnetic radiation from the object, and
interfere a first portion of the transmitted electromagnetic
radiation with a second portion of the transmitted electromagnetic
radiation; and an image capture assembly configured to capture a
fringe pattern produced by the interference of at least the first
and second portions of the transmitted electromagnetic radiation
and produce the hologram of the object from the fringe pattern.
[0059] Another object of this invention is to provide a novel
electromagnetic radiation apparatus configured to produce a
hologram of an object, said apparatus configured to receive a
received electromagnetic radiation from the object, diffract the
received electromagnetic radiation, and transmit a diffracted
electromagnetic radiation including the hologram of the object.
[0060] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of a scene, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
scene, diffract the received electromagnetic radiation, and
transmit a diffracted electromagnetic radiation; and an image
capture assembly configured to capture an image of the diffracted
electromagnetic radiation, and produce the hologram of the scene
from the captured image.
[0061] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, transform the received electromagnetic radiation, and
transmit the transformed electromagnetic radiation including a
fringe pattern; and an image capture assembly configured to capture
an image of the fringe pattern and produce the hologram of the
scene from the captured fringe pattern.
[0062] Another object of this invention is to provide a novel
apparatus configured to produce a hologram of an object, said
apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object and transform the received electromagnetic radiation; and an
image capture assembly configured to capture the transformed
electromagnetic radiation including the hologram of the object,
said hologram includes fringe patterns produced by an interference
of the received electromagnetic radiation with itself, and said
hologram not including fringe patterns produced by an interference
of the received electromagnetic radiation with any other
electromagnetic radiation.
[0063] Another object of this invention is to provide a novel
method for producing a hologram of an object, said method
comprising steps of receiving a received electromagnetic radiation
from the object; transmitting a diffracted electromagnetic
radiation based on the received electromagnetic radiation;
capturing an image of the diffracted electromagnetic radiation; and
producing the hologram of the object from the captured image.
[0064] Another object of this invention is to provide a novel
apparatus, wherein the received electromagnetic radiation does not
include coherent light.
[0065] A new method of recording digital holograms under incoherent
illumination reflects light from a three-dimensional (3-D) object,
propagates through a diffractive optical element (DOE) and is
recorded by a digital camera. Three holograms are recorded
sequentially each for a different phase factor of the DOE. The
three holograms are superposed in the computer such that the result
is a complex valued Fresnel hologram. When this hologram is
reconstructed in the computer, the 3-D properties of the object are
revealed.
[0066] Another new imaging method records multicolor digital
holograms from objects emitting fluorescent light. The fluorescent
light specific to the emission wavelength of various fluorescent
dyes after excitation of three dimensional (3-D) objects is
recorded on a digital monochrome camera after reflection from a
diffractive optical element (DOE). For each wavelength of
fluorescent emission, the camera sequentially records three
holograms reflected from the DOE, each with a different phase
factor of the DOE's function. The three holograms are superposed in
a computer to create a complex valued Fresnel hologram of each
fluorescent emission. The holograms for each fluorescent color are
further combined in a computer to produce a multicolored
fluorescence hologram and 3-D color image.
BRIEF DESCRIPTION OF THE DRAWINGS
[0067] A more complete appreciation of the invention and many of
the attendant advantages thereof will be readily obtained as the
same becomes better understood by reference to the following
detailed description when considered in connection with the
accompanying drawings, wherein.
[0068] FIG. 1 is a block diagram of an optical apparatus according
to an embodiment of the present invention;
[0069] FIG. 2 is a block diagram that illustrates an example of
captured geometric information according to embodiments of the
present invention;
[0070] FIG. 3 is a block diagram of an incoherent correlator that
may be used as the optical assembly in the optical apparatus of
FIG. 1;
[0071] FIG. 4 is a block diagram of an embodiment of an optical
apparatus that includes an optical assembly;
[0072] FIG. 5A is a detailed front view of an embodiment of a mask
that includes a DOE having an array of plural transform
regions;
[0073] FIG. 5B is a cross-section view of a symmetrically arranged
volume modulated diffractive optical element structure;
[0074] FIG. 5C is a cross-section view of a volume modulated
diffractive optical element structure;
[0075] FIG. 5D is a cross-section view of an index modulated
diffractive optical element structure;
[0076] FIG. 5E is a cross-section view of a mixed mode diffractive
optical element structure;
[0077] FIG. 5F is a cross-section view of a reflective volume
modulated diffractive optical element; Figure SG is a cross-section
view of a reflective volume modulated diffractive optical
element;
[0078] FIG. 6A is a detailed front view of another embodiment of a
mask that includes a DOE having an array of plural transform
regions;
[0079] FIG. 6B is a cross-section view of a mask including a
transmission layer having varied transmissivity for regions
adjacent to corresponding transform regions;
[0080] FIG. 6C is a cross-section view of a mask having transform
regions configured to vary an amplitude of the received light;
[0081] FIG. 6D is a cross-section view of a mask having a printed
overlay;
[0082] FIG. 6E is another embodiment of a mask configured to vary
an amplitude of the received light;
[0083] FIG. 6F is a block diagram of an embodiment of a mask
including SLMs;
[0084] FIG. 6G is a block diagram of another embodiment of a mask
including SLMs;
[0085] FIG. 7 is an example of a binary Fresnel Zone Pattern;
[0086] FIG. 8A is an example of a sinusoidal FZP;
[0087] FIG. 8B is an example of another sinusoidal FZP;
[0088] FIG. 8C is an example of another sinusoidal FZP;
[0089] FIG. 9A is an example of a Fourier Transformed FZP
pattern;
[0090] FIG. 9B is another example of a Fourier Transformed FZP
pattern;
[0091] FIG. 9C is another example of a Fourier Transformed FZP
pattern;
[0092] FIG. 10A is the amplitude portion of a complex transmission
function that is a Fourier Transform of a linear combination of
three mask functions;
[0093] FIG. 10B is the phase portion of a complex transmission
function that is a Fourier Transform of a linear combination of
mask functions,
[0094] FIG. 10C is an example of a pattern on a CCD when a point
object is present at the input;
[0095] FIG. 11A is a block diagram of an embodiment of an image
capture assembly;
[0096] FIG. 11B is a block diagram of another embodiment of an
image capture assembly;
[0097] FIG. 12A is a view of an embodiment of a light intensity
capture device that includes a charge coupled device having three
distinct regions;
[0098] FIG. 12B is an example of a two-dimensional intensity image
including three partial images;
[0099] FIG. 13A is an example of an arrangement of distinct regions
in an embodiment of a light capturing device;
[0100] FIG. 13B is another example of an arrangement of distinct
regions in an embodiment of a light capturing device;
[0101] FIG. 13C is another example of an arrangement of distinct
regions in an embodiment of a light capturing device;
[0102] FIG. 14 is a block diagram of an embodiment of a capture
control unit that includes an image data processor that combines
the electronic image data;
[0103] FIG. 15 is a block diagram of an embodiment of an optical
apparatus that varies the mask over time;
[0104] FIG. 16 is a block diagram of a controllable mask that
includes a spatial light modulator under the control of a mask
controller;
[0105] FIG. 17 is a block diagram of another embodiment of an
optical apparatus in which the mask is varied over time,
[0106] FIG. 18 is a block diagram of another embodiment of an
optical apparatus;
[0107] FIG. 19 is a block diagram of another embodiment of an
optical apparatus;
[0108] FIG. 20A is a block diagram of an embodiment of an optical
apparatus having a first transforming optical assembly including a
reflective optical assembly;
[0109] FIG. 20B is a block diagram of another embodiment of an
optical apparatus having a first transforming optical assembly
including a reflective optical assembly;
[0110] FIG. 21A is a block diagram of another embodiment of an
optical apparatus;
[0111] FIG. 21B is a block diagram of another embodiment of an
optical apparatus;
[0112] FIG. 22A is a block diagram of an example of an optical
apparatus that does not require a second transforming optical
element;
[0113] FIG. 22B is a block diagram of an example of an optical
apparatus that does not require a first transforming optical
element;
[0114] FIG. 22C is a block diagram of an example of an optical
apparatus that does not require first and second transforming
optical elements;
[0115] FIG. 23 is a block diagram of an embodiment of an optical
apparatus including a reflective type diffractive optical
element;
[0116] FIG. 24A is a block diagram of another embodiment of an
optical apparatus;
[0117] FIG. 24B is a block diagram of another embodiment of an
optical apparatus;
[0118] FIG. 25 is a block diagram of another embodiment of an
optical apparatus;
[0119] FIG. 26 is an example of an off-axis Fresnel Zone
Pattern;
[0120] FIG. 27 is a block diagram of a portion of an optical
apparatus including a composite mask having lenses;
[0121] FIG. 28A is a side view of an embodiment of a composite
mask;
[0122] FIG. 28B is a side view of another embodiment of a composite
mask;
[0123] FIG. 28C is a side view of another embodiment of a composite
mask;
[0124] FIG. 28D is a side view of another embodiment of a composite
mask;
[0125] FIG. 29 is a block diagram of another embodiment of an
optical apparatus;
[0126] FIG. 30 is a detailed view of an embodiment of a grating
having low and high transmissivity regions;
[0127] FIG. 31A is a block diagram of an embodiment of an optical
apparatus that may be used with a lined transparency or
grating;
[0128] FIG. 31B is a block diagram of another embodiment of an
optical apparatus;
[0129] FIG. 32 is a block diagram of a conventional holographic
system;
[0130] FIG. 33 is a block diagram of another embodiment of an
optical apparatus;
[0131] FIG. 34A shows a phase distribution of the reflection masks
displayed on the SLM with .theta.=0.degree.;
[0132] FIG. 34B shows a phase distribution of the reflection masks
displayed on the SLM with .theta.=120.degree.;
[0133] FIG. 34C shows a phase distribution of the reflection masks
displayed on the SLM with .theta.=240.degree.;
[0134] FIG. 34D shows an enlarged portion of the reflection mask in
FIG. 34A indicating that half of the SLM's pixels (randomly chosen)
modulate light with constant phase;
[0135] FIG. 34E shows an enlarged portion of the reflection mask in
FIG. 34A indicating that half of the SLM's pixels (randomly chosen)
modulate light with constant magnitude;
[0136] FIG. 34F shows an enlarged portion of the reflection mask in
FIG. 34A indicating that half of the SLM's pixels (randomly chosen)
modulate light with phase of the final on-axis digital
hologram;
[0137] FIG. 34G shows a reconstruction of the hologram of the three
letters at the best focus distance of `O`;
[0138] FIG. 34H shows a reconstruction of the hologram of the three
letters at the best focus distance of `S`;
[0139] FIG. 34I shows a reconstruction of the hologram of the three
letters at the best focus distance of `A`;
[0140] FIG. 35 is a block diagram of another embodiment of an
optical apparatus;
[0141] FIG. 36A shows magnitude of a complex Fresnel hologram of
the dice,
[0142] FIG. 36B shows phase of a complex Fresnel hologram of the
dice;
[0143] FIG. 36C shows a digital reconstruction of a
non-fluorescence hologram at the face of the red-dots on the
die;
[0144] FIG. 36D shows a digital reconstruction of a
non-fluorescence hologram at the face of the green dots on the
die;
[0145] FIG. 36E shows magnitude of a complex Fresnel hologram of
the red dots;
[0146] FIG. 36F shows phase of a complex Fresnel hologram of the
red dots;
[0147] FIG. 36G shows a digital reconstruction of the red
fluorescence hologram at the face of the red-dots on the die;
[0148] FIG. 36H shows a digital reconstruction of the red
fluorescence hologram at the face of the green dots on the die;
[0149] FIG. 36I shows magnitude of a complex Fresnel hologram of
the green dots;
[0150] FIG. 36J shows phase of the complex Fresnel hologram of the
green dots;
[0151] FIG. 36K shows a digital reconstruction of a green
fluorescence hologram at the face of the red-dots on the die;
[0152] FIG. 36L shows a digital reconstruction of a green
fluorescence hologram at the face of the green dots on the die;
[0153] FIG. 36M shows a composition of the digital reconstructions
in FIGS. 36C, 36G, and 36K; and
[0154] FIG. 36N shows a composition of the digital reconstructions
in FIGS. 36D, 36H, and 36L.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0155] Conventional holographic techniques may include methods of
capturing a hologram of an object by capturing an interference
pattern that results when a first portion of a coherent laser light
beam (e.g., reference beam) interferes with a second portion of the
laser light beam reflected off the object (e.g., object beam). A
three-dimensional image of the object may be viewed by
appropriately illuminating the recorded interference pattern with
the reference beam.
[0156] FIG. 32 is a block diagram of a conventional holographic
system including a laser 9000 that shines a coherent laser light
beam along a first optical axis 9026 through a partially reflective
and transmissive mirror, such as a beam splitter 9002. A first
portion of the split laser beam is guided by lens 9004 and mirror
9008 to illuminate the object 9014 with the object beam 9010 along
a second optical axis 9024. A second portion of the split laser
beam is reflected by the beamsplitter 9002 along a third optical
axis 9018 and guided by lens 9006 and mirror 9028 to direct a
reference beam 9012 along a fourth optical axis 9020 to an image
capture device 9016 such as a photographic plate, a charge coupled
device (CCD) or a complementary metal oxide semiconductor sensor
(CMOS). The reference beam 9012 and the object beam 9010 reflected
from the object 9014 along a fifth optical axis 9022 interfere with
each other, producing an interference pattern that may be recorded
as a hologram on the image capture device 9016.
[0157] Conventional holography solutions that produce a hologram by
interfering two parts of a light source along different optical
paths or optical axes may be very sensitive to any change in
alignment of the optical paths or axes, because even minor changes
in the length or direction of the optical paths or axes will change
the phase relationship of the portions of light that interfere.
Such a change will result in a change to the resulting interference
pattern and hologram, and yield a distorted resulting image.
[0158] For example, in the holography system of FIG. 32, a factor
such as motion, vibration, component deterioration or distortion,
or thermal expansion, may cause a slight change in the length or
direction of one or more of the first, second, third, fourth or
fifth optical axes 9026, 9024, 9018, 9020 and 9022, respectively.
Even a slight change in one of the axes may cause a corresponding
change in the phase relationship of the reference beam 9012 and the
light reflected from the object 9014 along the fifth optical axis
9010, thereby causing a significant change in the resulting
interference pattern and hologram captured at the image capture
device 9016.
[0159] Such a sensitivity to axial variation in conventional
holographic systems may result in reduced resolution in the
resulting three-dimensional information.
[0160] Various conventional attempts to address such a sensitivity
to axial variation have had limited success. For example, attempts
have included using massive platforms and shock absorbers to dampen
vibration, high tolerance mechanical optical stages to reduce
positioning errors, and optical and structural materials having
reduced coefficients of thermal expansion to reduce thermal
expansion effects. However, these attempts generally increase the
cost, size and mass of conventional holography systems, and reduce
system portability and availability.
[0161] In addition, conventional holography systems may require an
active light source to illuminate the object and produce the
reference and object beams. Active solutions that require
illumination of the object by a particular light source may limit
the applicability and usefulness of the conventional holography
systems. For example, an active light source would not be useful in
stealth military targeting holographic systems where it would be
undesirable for the targeting device to give away its position by
producing light or other electromagnetic radiation. Alternatively,
an active radiation source would not be applicable in holographic
systems that observe objects that produce their own light, such as
a holographic system observing chemiluminescent, black body, or
infrared illuminating objects. Such a holographic technique may be
useful in observing objects such as ships by virtue of their
ability to block the chemiluminescence of background emissions in
certain bodies of water, such as the chemiluminescent Red Sea.
[0162] In addition, conventional holographic systems that rely on a
coherent light source, such as a monochromatic laser, may be unable
to capture color information from the object unless multiline
lasers or multiple lasers of different wavelengths are used.
Systems such as those are likely to be very complex. Further, such
systems may not be suitable for capturing three-dimensional
information regarding objects that should not be illuminated with
laser light (e.g., sensitive biological material).
[0163] Conventional holographic techniques using incoherent light
to illuminate an object rely on a simplifying assumption that
incoherent source objects may be considered to be composed of many
individual light source points, each of which is self coherent, and
each of which can therefore create an interference pattern with its
mirrored image. For the purposes of this document, incoherent light
is any temporally or spatially incoherent light for which any two
electromagnetic fields emitted from a same location at two
different times (in the case of temporal incoherence) or emitted
from two different locations at the same time (in the case of
spatial incoherence) do not create an interference grating or
pattern when the two fields are summed together. Various methods of
incoherent holography have been proposed using this principle, such
as methods described in A. W. Lohmann, "Wavefront Reconstruction
for Incoherent Objects," J. Opt. Soc. Am. 55, 1555-1556 (1964), G.
Cochran, "New method of making Fresnel transforms," J. Opt. Soc.
Am. 56, 1513-1517 (1966), P. J. Peters, "incoherent holography with
mercury light source," Appl. Phys. Lett. 8, 209-210 (1966), H. R.
Worthington, Jr., "Production of holograms with incoherent
illumination," J. Opt Soc Am. 56, 1397-1398 (1966), A S. Marathay,
"Noncoherent-object hologram its reconstruction and optical
processing," J. Opt. Soc. Am. A 4, 1861-1868 (1987), and G. Sirat,
D. Psaltis, "Conoscopic holography," Optics Letters, 10, 4-6
(1985), each of which is incorporated herein by reference.
[0164] However, the conventional incoherent holographic techniques
may require impractically high levels of light intensity. Thus,
conventional incoherent holographic systems require active
illumination of objects, and therefore may exhibit the resulting
problems and limitations described above.
[0165] In addition, conventional incoherent holographic systems may
rely on illuminating the object with a bandwidth limited source to
reduce sensitivity to length differences in the plural optical path
differences. For example, in a conventional incoherent holographic
system acceptable variations in the relative length of optical
paths may be limited to the inverse of the bandwidth multiplied by
the light velocity. Thus, a predetermined light source having a
limited bandwidth may be required, and the elimination of
extraneous illumination may be necessary in conventional incoherent
holographic systems.
[0166] Further, conventional incoherent holographic systems may
require optical arrangements having plural optical axes similar to
the example shown in FIG. 32. Thus, conventional incoherent
holographic systems may also be susceptible to variations in
direction or length of the optical axes, and attendant problems, as
described above.
[0167] In addition, conventional holographic techniques involve
splitting light into two channels using mirrors, which may have a
low transfer efficiency, and then recombining the split light. The
efficiency may be particularly low in the recombination where more
than 50% of the power gets lost.
[0168] Further, in a conventional Fourier hologram, each object
point is transformed to a linear grating throughout the entire
image plane (e.g., throughout an entire CCD plane). Thus, in
conventional incoherent methods of producing Fourier holograms,
light from each object point must disadvantageously be intense
enough to establish a high contrast grating or pattern over the
entire image plane.
[0169] Tomographic methods have been proposed to overcome the
limitations of conventional holographic techniques described above.
Such tomographic methods may involve capturing plural images of an
object from different points of view, for example by moving the
object, or the camera, or both, in between successive images, and
extracting three-dimensional object information by processing the
successive images. Conventional tomographic methods are described
in Y. Li, D. Abookasis and J. Rosen, "Computer-generated holograms
of three-dimensional realistic objects recorded without wave
interference," Appl. Opt. 40, 2864-2870 (2001), and Y. Sando, M.
Itoh, and T. Yatagai, "Holographic three-dimensional display
synthesized from three-dimensional Fourier spectra of real existing
objects," Opt. Lett 28, 2518-2520 (2003), each of which is
incorporated herein by reference.
[0170] Tomographic methods may be slow, however, as they may
require plural images to be captured before and after a relative
perspective between the object and camera is changed and thus may
not be able to capture objects which change during the time it
takes to capture the multiple images. Alternatively, tomographic
methods may require more expensive or physically large equipment
that includes the ability to simultaneously capture images of the
object from more than one perspective. Further, the methods may be
impractical for distant objects or immovable objects for which it
may be difficult to change a relative perspective from the camera.
In addition, if the object is moving in an unpredictable way, it
may be difficult to extract information from successive images
without having another source of information regarding the shape or
the movements of the object.
[0171] Range-finding methods involve measuring the distance between
an apparatus and various points on a surface of an object, and
constructing an image or model of the object based on the
distances. Further, some range-finding methods may include a
predetermined or controlled movement of the object or the apparatus
to predictably change the view of the object from the apparatus
over time. Thus, the conventional range-finding methods may also
include the predictable change in the view of the object to
determine an exterior three-dimensional shape of the object.
Conventional range-finding methods include systems that illuminate
points on an object with a laser, and measuring the amount of time
required for the laser light to travel between the object and the
laser source to determine a distance to the object based on the
travel time. Related methods include "painting" an object with a
laser stripe or grid and examining a deformation in the observed
grid to determine geometric information of the object.
[0172] However, such range-finding methods require active
illumination of the object by a coherent laser, and therefore are
not suitable for incoherently illuminated objects or for
fluorescent or luminescent emitting objects. When coherent light
sources can be used, they have the attendant problems and
limitations of active illumination and coherent light sources
described above. Further, the methods may be difficult to perform
if the object is moving in an unpredictable way, or if the object
is very close to the laser source.
[0173] Other range-finding methods may include using a camera with
a lens having a narrow depth of field and a calibrated automatic
focusing system. The automatic focus system automatically adjusts
the lens to focus on portions of the object, for example, by
maximizing contrast in resulting images. Then, a range to the
object is determined based on a mechanical position of the
calibrated lens. However, such a calibrated focus technique may not
be useful for objects having minimal optical contrast, or when
objects or the apparatus is in motion. Further, the accuracy of
such a system may be limited by the mechanical tolerances of the
calibrated lens.
[0174] Another conventional method includes extracting an object
distance from shadows in an image. For example, a conventional
shadow method includes capturing an image of shadows produced when
electromagnetic radiation (e.g., x-ray radiation or light) from an
object is blocked by a mask with a concentric ring pattern such as
a Fresnel Zone Pattern (FZP, a.k.a., Transmission Zone Plate, Zone
Plate, Zone Pattern, Fresnel Zone Plate, etc. . . . ) placed
between the object and an image plane.
[0175] For the purposes of this application, an FZP may be
understood to be a two-dimensional pattern of alternating light and
dark concentric rings in which a thickness (e.g., radial width) of
successive rings is inversely proportional to the distance from the
center of the rings. For example, the n.sup.th ring of an FZP may
transition (i.e., from dark to light or light to dark) at a radius
r described by the following equation (or by an approximation
thereof):
r.sub.n= {square root over (nf.lamda.)}
where n is an integer, .lamda. is the wavelength of the applied
light and f is the focal length of the FZP.
[0176] When used with scattered point light sources, such as stars,
the relative positions of the centers of the shadows in the image
may be extracted from the image, and distances to the corresponding
point light sources may be calculated from the shadow center
locations in the image. Such a method is described in L. Mertz and
N. O. Young, "Fresnel transformations of images," in Proceedings of
Conference on Optical Instruments and Techniques, K. J. Habell, ed.
(Chapman and Hall, London 1961) p.305, incorporated herein by
reference.
[0177] However, such conventional shadow ranging methods have a
limited usefulness for when the captured electromagnetic radiation
has a wavelength comparable to the distance between the rings of
the FZP, such as visible light. For example, the visible light may
be diffracted by the edges of rings in the FZP causing shadows in
the image to have poorly defined or smeared edges, thereby making
it difficult or impossible to isolate the centers of resulting
shadow patterns (e.g., see Mertz and Young at FIG. 2).
[0178] Conventional scanning holographic methods involve scanning
an object by illuminating a surface of the object with a moving a
pattern of Fresnel Zone Plates (FZPs), serially sensing the
intensity of reflected or transmitted light from the object (i.e.,
a one dimensional intensity signal) as the pattern moves across the
object, and integrating and processing the serially sensed light
intensities to generate three-dimensional information of the
object. In particular, a convolution between the object and the
moving Fresnel Zone Patterns is used to extract three-dimensional
information regarding the object Conventional scanning holographic
methods are described in Poon T.-C., "Three-dimensional image
processing and optical scanning holography," ADVANCES IN IMAGING
AND ELECTRON PHYSICS 126, 329-350 (2003), and G. Indebetouw, A. El
Maghnouji, R. Foster, "Scanning holographic microscopy with
transverse resolution exceeding the Rayleigh limit and extended
depth of focus," J. Opt. Soc. Am. A 22, 892-898 (2005), each of
which is incorporated herein by reference.
[0179] However, conventional scanning holographic methods require
that a pattern be moved across the object while the location of the
object is fixed, thereby limiting the usefulness of the method.
Alternatively, the pattern may be fixed and the object moved across
the pattern, resulting in similar limitations.
[0180] In addition, the scanning process may be a relatively slow
process requiring mechanical movements. Thus, scanning is
susceptible to problems produced by mechanical deterioration and
inaccuracy, such as reduced resolution as described above.
[0181] Further, since scanning holographic methods serially capture
a one-dimensional light intensity signal from the object and
integrate the serial signal to extract three-dimensional
information, such systems are highly susceptible to variations in
the relative positions of the scanning apparatus and the object
over the duration of the scan. For example, if such a system
captures a first intensity during a first part of the scan, and a
second intensity during a second part of the scan, any variation in
the relative positions of the object and the scanning apparatus (or
even minor changes in the internal arrangement of elements of the
scanning apparatus) may adversely introduce variations into the
captured second intensity, thereby reducing an accuracy, resolution
and usefulness of the system.
[0182] In addition, scanning holographic systems are generally
large and complex therefore they may not be suitable for
applications requiring portability or low cost. Further,
conventional scanning holographic systems may require an object to
be illuminated by an interference pattern produced by interfering
laser light, may include a very slow recording process that could
take several minutes or more for each object capture, and the
recording process may disadvantageously require significant
mechanical movement of recording device components and/or the
object during the recording process.
[0183] Holograms recorded by incoherent light open many new
applications like outdoor and astronomical holography (J. B.
Breckinridge, "Two-Dimensional White Light Coherence
Interferometer," Appl. Opt. 13, 2760 (1974)) and fluorescence
holographic microscopy (G. Indebetouw, A. El Maghnouji, R. Foster,
"Scanning holographic microscopy with transverse resolution
exceeding the Rayleigh limit and extended depth of focus," J. Opt.
Soc. Am. A 22, 892-898 (2005)). The oldest methods of recording
incoherent holograms have made use of the property that every
incoherent object is composed of many source points each of which
is self spatial coherent and therefore can create an interference
pattern with light coming from the point's mirrored image. Under
this general principle there are various types (J. B. Breckinridge,
"Two-Dimensional White Light Coherence Interferometer," Appl. Opt.
13, 2760 (1974)) (A. W. Lohmann, "Wavefront Reconstruction for
Incoherent Objects," J. Opt. Soc. Am. 55, 1555-1556 (1965)) (G.
Sirat, D. Psaltis, "Conoscopic holography," Optics Letters, 10, 4-6
(1985)) of holograms including Fourier (J. B. Breckinridge,
"Two-Dimensional White Light Coherence Interferometer," Appl. Opt.
13, 2760 (1974)) (G. W. Stroke and R. C. Restrick, "Holography with
Spatially Incoherent Light," Appl. Phys. Lett. 7, 229 (1965)) and
Fresnel holograms (G. Cochran, "New method of making Fresnel
transforms," J. Opt. Soc. Am. 56, 1513-1517 (1966)) (P. J. Peters,
"Incoherent holography with mercury light source," Appl. Phys.
Lett. 8, 209-210 (1966)). The process of beam interfering demands
high levels of light intensity, extreme stability of the optical
setup and relatively narrow bandwidth light source. These
limitations have prevented holograms from becoming widely used for
many practical applications.
[0184] More recently two groups of researchers have proposed to
compute holograms of 3-D incoherently illuminated objects from a
set of images taken from different points of view. (Y. Li, D.
Abookasis and J. Rosen, "Computer-generated holograms of
three-dimensional realistic objects recorded without wave
interference," Appl. Opt. 40, 2864-2870 (2001)) (Y. Sando, M. Itoh,
and T. Yatagai, "Holographic three-dimensional display synthesized
from three-dimensional Fourier spectra of real existing objects,"
Opt. Lett 28, 2518-2520 (2003)). This method, although it shows
promising prospects, is relatively slow since it is based on
capturing tens of images of the scene images from different view
angles.
[0185] Another method is called scanning holography (G. Indebetouw,
A. El Maghnouji, R. Foster, "Scanning holographic microscopy with
transverse resolution exceeding the Rayleigh limit and extended
depth of focus," J. Opt Soc. Am. A 22, 892-898 (2005)) (Poon T.-C.,
"Three-dimensional image processing and optical scanning
holography," Adv. in Imag. & Elec. Phys. 126, 329-350 (2003))
in which a pattern of Fresnel Zone Plate (FZP) scans the object
such that at each and every scanning position the light intensity
is integrated by a point detector. The overall process yields a
Fresnel hologram obtained as a convolution between the object and
FZP patterns. However the scanning process is relatively slow and
is done by mechanical movements. A similar convolution is actually
done also in the present work; however, unlike the case of scanning
holography, we propose here a convolution without movement.
[0186] Mertz and Young (L. Mertz and N. O. Young, "Fresnel
transformations of images," in Proceedings of Conference on Optical
Instruments and Techniques, K. J. Habell, ed. (Chapman and Hall,
London 1961) p.305) already proposed holographic photography based
on convolution without movement between object and FZPs. However,
their process relies on geometrical optics, which cannot yield good
imaging results in the optical regime. On the contrary, our
suggested correlator for implementing the holographic recording is
valid in the optical regime, since its operation principle is based
on the diffraction theory (J. Goodman, Introduction to Fourier
Optics, 2.sup.nd ed., McGraw-Hill, New York, 1996, pp. 63-95
(Chapter 4).
[0187] Referring now to the drawings, wherein like reference
numerals designate identical or corresponding parts throughout the
several views.
[0188] FIG. 1 is a block diagram of an optical apparatus 100
according to a first embodiment of the present invention. The
optical apparatus 100 is configured to capture a three-dimensional
information of an object 130, and the optical apparatus 100
includes an optical assembly 110 and an image capture assembly 120.
In particular, the optical assembly 110 receives light from the
object 130 along a receiving optical axis 140. For example, the
optical assembly may receive light from the sun 150 that is
reflected or scattered by reflecting surfaces on the object 130.
The received light may be polychromatic and incoherent light, such
as reflected sunlight, or may also include monochromatic light or
coherent light. In addition, the light from the object may be
fluorescent light or chemiluminescent light emitted by the object.
The optical apparatus 100, in this embodiment, does not illuminate
the object but passively receives light from the object.
[0189] The optical assembly 110 transforms the received light
according to a transformation described below, and transmits the
transformed light along the receiving optical axis 140. The image
capture assembly 120 receives the transformed light from the
optical assembly 110, and captures a two-dimensional intensity
image of the transformed light. The captured two-dimensional
intensity image includes three-dimensional or geometric information
regarding the portions of the object 130 from which light is
received at the optical assembly 110. The three-dimensional or
geometric information is encoded in the captured two-dimensional
intensity image as a Fresnel hologram. In other words, a hologram,
as discussed in this specification, is a two-dimensional image that
encodes three-dimensional information. In addition, the present
invention also applies to capturing a volume hologram, which is a
three-dimensional intensity image that encodes three-dimensional or
geometric information of an object. The image capture assembly 120
may extract the three-dimensional information from the captured
image. The image capture assembly may be an opaque light capturing
device. An opaque device is understood to mean a device that is not
transparent or translucent to electromagnetic radiation of relevant
frequencies and intensities, and therefore such a device does not
allow such electromagnetic radiation to pass through.
[0190] A Fresnel hologram is a real positive light intensity
distribution that encodes a complex valued wave-front distribution,
including three-dimensional information regarding the light
scattering surface of the object. Further, in a Fresnel hologram,
each point on the object is encoded into a portion of a sinusoidal
Fresnel zone plate with an entire range of spatial frequency
components present, as noted by Goodman, "Introduction to Fourier
Optics," 3rd Ed., Roberts & Company Publishers, 2005,
incorporated herein by reference. Thus, a three-dimensional image
of the object may be recreated optically, by appropriately
illuminating a transparency having the Fresnel hologram, or the
three-dimensional image of the object may be recreated by a
computer using an electronic image data of the Fresnel hologram.
The recreated three-dimensional image of the object includes
three-dimensional information regarding the shape and distance of
an observable surface of the object.
[0191] The optical apparatus 100 may advantageously capture the
three-dimensional object information without moving or being moved
(i.e., the spatial relationship between the optical apparatus 100
and the object 130 may remain unchanged from a time before an image
is captured to a time after the three-dimensional information is
extracted from the captured image by the image capture assembly
120). In addition, the optical apparatus 100 may advantageously
capture the three-dimensional object information while one or both
of the object and the optical apparatus 100 are in motion.
[0192] Moreover, the optical apparatus 100 does not project any
pattern on the object, such as is done in a conventional or
scanning holographic method. Further, the optical apparatus 100
does not include any parts that are required to move while the
light is being received from the object, such as a scanning
aperture used in scanning holography. Thus, without parts that move
during image capture, the optical apparatus 100 may be less
expensive to produce and use, more reliable, quieter, and faster,
for example, than an apparatus used for scanning holography.
Further, with respect to conventional holographic systems that
require active illumination (for example, illumination by a laser),
the present invention advantageously has a simpler design that may
be applied to more types of imaging.
[0193] In addition, the present invention does not require an
interference between a light from the illumination (i.e., not
scattered by the object) with a light scattered by the object.
Instead, the current approach diffracts light scattered by the
object, which may be understood as a mutual interference between
portions of electromagnetic radiation wavefronts coming from object
itself, and is not an interference between such scattered light and
another light from the source. Thus, as the mutual interference may
be performed by a few collinear electromagnetic elements (e.g.,
lenses and masks, or DOEs, as described below), or even a single
electromagnetic element (e.g., a single DOE, as described below),
the relative differences between optical paths of the interfering
wavefronts are easily controlled (e.g., all the optical paths pass
through the same electromagnetic elements) and therefore,
variations between the lengths of the paths may be more easily
controlled and minimized.
[0194] Further, the optical apparatus 100 may advantageously
capture the three-dimensional object information in a single image
(e.g., a single exposure).
[0195] Moreover, the optical apparatus 100 may advantageously be
able to capture images with very low levels of light intensity.
Conventional holographic systems may require beam splitters and/or
mirrors that may cause some received light to be lost or wasted. On
the other hand, the optical apparatus 100 does not require the use
of beam splitters or mirrors, and therefore may be able to capture
images with low levels of light intensity.
[0196] Further, conventional holographic systems may produce
Fourier holograms in which each object point contributes to
interference fringe patterns that are spread over the entire image
plane. Such conventional systems may require greater light
intensity than the optical apparatus 100, which translates each
object point using a Fresnel Zone Pattern, which may produce fringe
patterns for a particular object point in only a portion of the
image plane, thereby advantageously allowing for lower light
intensities.
[0197] In addition, the optical apparatus 100 advantageously
receives and transmits light only along a single axis, thereby
reducing susceptibility to axial variation and simplifying the
design, manufacture and use of the optical apparatus 100. Further,
the optical apparatus 100 is coaxial and self-interfering. In
particular, in the present embodiment light from separate light
paths is not interfered to produce an interference pattern or
hologram. Instead, the hologram is produced by diffraction of light
in the optical assembly 110. Although diffraction may be understood
as being produced by interference between each portion of a light
wavefront (i.e., each point along the wavefront being considered a
point source of light according to Huygens wave theory of light),
diffraction produced by a single coaxial assembly, as in the
present embodiment, is much less sensitive to variations in optical
paths between interfering light sources. In particular, light is
self-interfered, according to the present embodiment, because the
only interference is between light waves passing through various
portions of a same optical element (e.g., the optical assembly 110,
or the mask 304 in FIG. 3, described below), and it is much easier
to minimize path length and angle variations for paths passing
through a same optical element, as in the present embodiment, than
it is to control path variations between separate optical paths,
passing through separate optical elements, along separate optical
axes, as in the conventional holography systems. In addition, the
optical apparatus 100 may be used to advantageously capture
polychromatic incoherent light received from the object. Therefore,
a full color three-dimensional image may be recreated from the
Fresnel hologram recorded by the apparatus.
[0198] Although embodiments within this document are described as
transmitting and receiving light, capturing light images and
including optical assemblies, the invention is also applicable to
other types of electromagnetic radiation. Thus, the invention also
includes an electromagnetic radiation apparatus that includes an
electromagnetic radiation assembly that receives a received
electromagnetic radiation from an object.
[0199] FIG. 2 is a block diagram that illustrates an example of
captured geometric information according to embodiments of the
present invention. According to the example of FIG. 2, an object
200 is illuminated by a light source or sources (e.g., the sun 150)
causing light to be scattered or reflected by various light
radiating portions of the object 200. Three example light radiating
portions 206, 208 and 210 scatter light rays 216, 218 and 220,
respectively. These example light rays travel towards the optical
apparatus 100 (shown in FIG. 2 without the detail of FIG. 1). Light
captured by the optical apparatus 100, according to the present
invention, includes geometric information regarding the distance
between the object and the optical apparatus as well as the shape
of observable surfaces of the object 200 from which light is
received at the optical apparatus 100. For example, the captured
light includes information regarding a distance traveled by the ray
of light 218, and in particular, includes the distance between the
light radiating portion 208 and the optical apparatus 100. Further,
the captured light also includes geometric information regarding a
horizontal distance of the light radiating portion 208, for
example, a horizontal distance 212 between an edge of the object
200 and the light radiating portion 208. In addition, the captured
light also includes geometric information regarding a vertical
distance of the light radiating portion 208, for example, a
vertical distance 214 between an edge of the object 200 and the
light radiating portion 208. In this example, horizontal distance
212 and vertical distance 214 are distances measured in a
measurement plane 204 that passes through radiating portion
208.
[0200] Thus, an optical apparatus, according to the present
embodiment, may be configured to capture a light including
geometric information regarding each portion of each object from
which the light is received at the optical apparatus. Further, from
the geometric information, the size, shape and location of the
visible portions of each object may be determined. For example, in
FIG. 2, if light is scattered by each external surface of the
object 200, and at least a portion of the scattered light is
received at the optical apparatus 100, then the apparatus 100 may
capture light including geometric information regarding the
dimensions (e.g., height, width and depth) of each visible surface
of the object 200, as well as information regarding the distance
between the object 130 and the front surface of optical apparatus
100.
[0201] Although light is scattered by external surfaces in FIG. 2,
one of skill in the art will understand that such an optical
apparatus is also capable of capturing received light from an
internal surface of the object 130 that radiates light to the
optical assembly 100 through a translucent or transparent exterior
portion of the object 130. In that case, the captured geometric
information may include geometric information regarding an interior
portion of the object.
[0202] The optical assembly 110 includes any optical assembly
configured to control a complex amplitude of the transmitted light
according to the complex transformation function described below.
Thus, for example, optical assembly 110 may include one or more
refractive lenses, one or more diffractive optical elements (DOEs),
or one or more spatial light modulators (SLMs).
[0203] An incoherent correlator in the regime of diffraction theory
may include every system that produces a pattern of a Fourier
transform of the mask transparency on the system's aperture at an
output plane around a point that is linearly related to an input
point's location, when the incoherent correlator is illuminated by
a single point from some position on the input plane. Thus, the
incoherent correlator produces an output image including every
point in the input plane.
[0204] FIG. 3 is a block diagram of an incoherent correlator 300
that may be used as the optical assembly 110 in the optical
apparatus 100 shown in FIG. 1. The incoherent correlator 300 is an
optical assembly that includes a first transforming optical
assembly 302, a mask 304 and a second transforming optical assembly
306. Each of the first and second transforming optical assemblies
302/306 include the types of converging lenses that would perform a
two-dimensional Fourier transform of received light if they were
illuminated by coherent light (though coherent light is not
required during the operation of the present invention). When the
incoherent correlator 300 is illuminated by a single point light
source 308 from some position on a plane 318, the incoherent
correlator 300 produces a pattern of a Fourier transform of a mask
304 on an output plane 316. The plane 318 is located along and
perpendicular to an optical axis 320 of the incoherent correlator
300, at a distance (z+f.sub.1) from the first transforming optical
assembly 302, where f.sub.1 is a focal length of the first
transforming optical assembly 302 and z is a remaining distance
between the point light source 308 and the first transforming
optical assembly 302. The output plane is located along and
perpendicular to the optical axis 320 at a distance f.sub.2 from
the second transforming optical assembly 306, where f.sub.2 is a
focal length of the second transforming optical assembly 306, in a
direction away from the plane 318. Note that the Fourier transform
of a mask 304 on an output plane 316 is obtained only if z=0. When
z.noteq.0 the optical assembly 300 still performs a correlation
between the object, but with a different function than the Fourier
transform of mask 304. In other words, in the case that z.noteq.0,
the output plane 316 will include an output image that is different
than a Fourier transform of a mask 304.
[0205] FIG. 4 is a block diagram of an embodiment of an optical
apparatus 400 that includes an optical assembly 300. Optical
apparatus 300 includes a first transforming optical assembly 302, a
mask 304 and a second transforming optical assembly 306. Each of
the first and second transforming optical assemblies 302/306 are
the types of optical assemblies (e.g., converging Fourier lenses)
that would perform a two-dimensional Fourier transform operation on
a received coherent light (although the use of the apparatus does
not require coherent light). Light is received from object 130 at
the first transforming optical assembly 302, which transforms the
received light and transmits the transformed light. The mask 304
receives the transformed light, varies an amplitude and/or phase of
the received coherent transformed light as described below, and
transmits a portion of the received light as the masked light. The
masked light is received by the second transforming optical
assembly 306, which transforms the masked light and transmits a
second transformed light. The image capture assembly 120 receives
and captures the second transformed light, as described above. Note
that when the light received from the object is incoherent, the
transformations performed by the first and second transforming
optical assemblies 302/306 may not be Fourier transformations.
However, the first and second transforming optical assemblies
302/306 are the types of optical assemblies (e.g., converging
Fourier lenses) that would produce a Fourier transform of received
coherent light or received point source light.
[0206] The mask 304 includes any device or structure configured to
transform an amplitude and phase of a received light, according to
one or more predetermined complex transmission functions. For
example, the mask 304 may include one or more diffractive optical
elements (DOE), one or more amplitude filters, one or more lenses,
and/or one or more SLMs.
[0207] FIG. 5A is a detailed front view of an embodiment of mask
304 that includes a DOE having an array of plural transform regions
500-514. Each of the plural transform regions in the diffractive
optical element is configured to transform a phase and/or an
amplitude of a received light according to the transform equations
described below.
[0208] The diffractive optical element may include volume-modulated
diffractive optical elements that use a variation in the volume of
refractive material in each transform region to transform the phase
and/or amplitude of the received light and produce transformed
transmitted light. In addition, the diffractive optical element may
include index-modulated diffractive optical elements that use a
variation in a refractive index of refractive material in each
transform region to transform the phase and/or amplitude of the
received light and produce transformed transmitted light. In
addition, the diffractive optical element may include one or more
transmission layers of having a predetermined transmissivity to
thereby vary an amplitude of the received light. Further,
diffractive optical elements that combine one or more features of
volume-modulated, index-modulated and transmission layer
diffractive optical elements may also be included. Methods of
preparing the diffractive optical elements include, for example,
conventional methods such as those described in Salmio et al.,
"Graded-index diffractive structures fabricated by thermal ion
exchange," Applied Optics, Vol. 36, No. 10, 1 Apr. 1997, Carre et
al., "Customization of a self-processing polymer for obtaining
specific diffractive optical elements," Synthetic Metals 127 (2002)
291-294, and Nordman et al., "Diffractive phase elements by
electron-beam exposure of thin As.sub.2S.sub.3 films, Journal of
Applied Physics 80(7), 1 Oct. 1996, each of which is incorporated
herein by reference.
[0209] FIGS. 5B-5G show a view of cross-section AA' in FIG. 5A for
various embodiments of optical assembly 110. FIG. 5B is a
cross-section view of a symmetrically arranged volume modulated
diffractive optical element structure, in which the volume of
transform regions 500-514 are symmetrical with respect to a center
line 516.
[0210] In FIGS. 5C-5G, each of the transform regions corresponds to
a transform region in the embodiments of FIGS. 5A and 5B (e.g.,
transform regions 500C, 500D, 500E, 500F and 500G correspond to
transform region 500), however, with the properties of the relevant
embodiment.
[0211] FIG. 5C is a cross-section view of a volume modulated
diffractive optical element structure in which the volume of
transform regions 500C-514C are varied and arranged asymmetrically
with respect to a center line 516.
[0212] FIG. 5D is a cross-section view of an index modulated
diffractive optical element structure in which a refractive index
of transform regions 500D-514D is varied.
[0213] The optical assembly 110 is not limited to embodiments
including only volume or index modulated transform regions, but
also includes a mixture of volume and index modulated transform
regions, as well as transform regions that include both volume and
index modulation features.
[0214] Figure SE is a cross-section view of a mixed mode
diffractive optical element structure in which transform regions
500E, 506E, 508E and 512E include varied refractive indexes,
transform regions 502E, 510E and 514E include varied volumes and
transform region 504E includes both a varied refractive index and a
varied volume, for example.
[0215] The optical assembly 110 is not limited embodiments
including only a refractive-type diffractive optical assembly, in
which light passes from one side of the assembly to exit at another
side, but also includes embodiments having a reflective-type
diffractive optical assembly, in which light is reflected by a
surface prior to exiting the assembly.
[0216] FIG. 5F is a cross-section view of a reflective volume
modulated diffractive optical element including a reflective layer
518 and volume modulated transform regions 500F-514F. In this
embodiment, the received light enters through transform regions
500F-514F, is reflected by reflective layer 518 and passes again
through transform regions 500F-514F before exiting the diffractive
optical element.
[0217] The optical assembly 110 is not limited to embodiments
including transform regions having the shapes shown in the figures
above, but also includes embodiments in which the transform regions
have other shapes, for example a rounded shape.
[0218] FIG. 5G is a cross-section view of a reflective volume
modulated diffractive optical element in which the transform
regions 500G-514G have a different shape on an external edge and a
square shape on an internal edge adjacent to the reflective layer
518.
[0219] FIG. 6A is a detailed front view of an embodiment of mask
304 that includes a DOE having an array of plural transform regions
600-614, each of which may include features similar to those
described above regarding FIGS. 5A-5G. Further, each of the plural
transform regions in the diffractive optical element of this
embodiment is configured to transform an amplitude of a received
light using one or more transmission layers configured to reduce an
amplitude of received light by various predetermined amounts
according to the transmission equations below. In this embodiment,
transform region 614 is configured to include a transmission layer
including a material such as an absorbent ink or a reflective metal
configured to reduce an amplitude or intensity of transmitted light
by a relatively small amount, while transform regions 606, 610 and
602 are configured to reduce an amplitude or intensity of
transmitted by respectively increasing amounts. The varied
transmissivity may be produced by varying a number of layers of a
same material, varying a density of a same material, mixing various
concentrations of materials, or by any conventional method used to
vary an intensity of a received light.
[0220] Further, each transform region 600-614 may be configured to
apply different amounts of amplitude or intensity reduction over
different frequencies of the received light spectrum. Thus, each
transform region 600-614 may include an ability to differently
filter each color of the received light. For example, transform
region 606 may transmit a portion of received light having
frequencies close to the color red without reduction in amplitude
and may reduce the amplitude of all other frequencies of the
received light. Further, transform region 610 may reduce the
amplitude of received blue light by a first amount and may reduce
the amplitude of a received yellow or red light by a second amount.
All permutations of frequency attenuating profiles for each
transform region are included in the invention.
[0221] FIGS. 6B-6E show views of cross-section BB' in FIG. 6A for
various embodiments of mask 304. FIG. 6B is a cross-section view of
a mask including a transmission layer 620 having varied
transmissivity for regions adjacent to corresponding transform
regions 514F, 506F, 510F and 502F.
[0222] FIG. 6C is a cross-section view of a mask having transform
regions 614C, 606C, 610C and 602C configured to vary an amplitude
of the received light (e.g., for example, due to impurities added
to the transform region)
[0223] FIG. 6D is a cross-section view of a mask having a printed
overlay 622 attached to one side. The printed overlay 622 includes
printed regions 624 in which ink or other light absorbing or
reflecting material is deposited in regions adjacent to
corresponding transform regions 614D, 606D, 610D and 602D in
varying concentrations or amounts to vary an amplitude of the
received light. The printed overlay 622 may be printed prior to
being attached to the rest of the mask 304. Further, the printed
regions 624 may be printed directly on the DOE without using a
printed overlay 622, as shown in the mask 304 embodiment in FIG.
6E.
[0224] The DOE in the mask is not limited to DOEs having an array
of 64 transform regions as shown in the examples above, but also
includes DOEs having any other number of transform regions, and
includes transform regions arranged other than in an array, such as
with a radial arrangement of transform regions (not shown). Further
the transform regions may have any shape and be in any
arrangement.
[0225] The mask 304 may be configured to simultaneously perform one
or more complex transmission functions. In the present embodiment,
the mask includes three different transmission functions to produce
three different convoluted and transformed partial images within
each captured image. When particular transmission functions, as
described below, are included in the mask 304, the resulting three
different convoluted and transformed partial images in the captured
image may be combined as a Fresnel hologram of the object 130, from
which three-dimensional object information may be extracted.
[0226] FIG. 6F is a block diagram of an embodiment of mask 304
including an amplitude SLM 628 that is configured to controllably
modify an amplitude of a received light, and phase SLM 630 that is
configured to controllably modify a phase of the amplitude modified
light and that is mounted adjacent to the amplitude SLM 628.
[0227] FIG. 6G is a block diagram of an alternative embodiment of
mask 304 in which amplitude SLM 628 and phase SLM 630 are not
located next to each other, but have an intervening space. Further,
the SLMs may alternatively be placed in a different order with
respect to the light path (not show). Further, the invention may
include other SLMs that may be available now or in the future and
are configured to controllably modify both the amplitude and phase
of a received light.
[0228] The two-dimensional intensity image captured by the image
capture assembly is generally described by an intensity function
o(x,y), which describes the distribution of light intensities
captured at each point in the image capture plane (i.e., x, y
plane). The three intensity functions o(x,y) define the partial
contribution to the overall image intensity contributed by each
partial image, and is related to the overall image intensity
function as follows:
o ( , y ) = n = 1 3 B n o n ( , y ) ( 1 A ) ##EQU00001##
[0229] where B.sub.n is a complex constant.
[0230] The transmission functions that produce the three partial
images captured by the image capture assembly 120 are defined as
follows:
o.sub.n(x,y)=.intg..intg..intg.s(x',y',z')|h.sub.n(x-x',y-y',z')|.sup.2d-
x'dy'dz' (1B)
where s(x',y',z') is a function that describes the intensity at the
system input in the vicinity of the point (x',y',z')=(0,0,0). From
the function o(x,y), the geometric information regarding the light
scattering surface (i.e., the portions of the object facing the
optical apparatus 100 that scatter or emit light that is received
at the optical assembly 110) of the object may be determined in
terms of object referenced coordinates x', y' and z'.
[0231] The transformed light includes point spreading functions
(PSF) h.sub.n(x,y,z) contributed by each transmission function. In
the present embodiment, h(x,y,z) is a linear summation of point
spreading functions h.sub.1(x,y,z), h.sub.2(x,y,z) and h.sub.3,
which each perform a light spreading function with respect to the
image capture coordinates (i.e., x, y, z). PSF h(x,y,z) is defined
as follows:
h ( , y , z ) = n = 1 3 ( 1 2 exp { i .pi. 2 .lamda. .DELTA. ( z )
[ ( - n ) 2 + ( y - y n ) 2 ] + i .theta. n 2 } + 1 2 exp { - i
.pi. 2 .lamda. .DELTA. ( z ) [ ( - n ) 2 + ( y - y n ) 2 ] - i
.theta. n 2 } ) p z ( - n , y - y n ) , ( 2 ) ##EQU00002##
where p.sub.z(x-x.sub.n,y-y.sub.n) are two-dimensional disk
functions centered at points (x.sub.1,y.sub.1), (x.sub.2,y.sub.2)
and (x.sub.3,y.sub.3), respectively, in the image capture space, i
is the imaginary unit (i.e., i=(-1).sup.0.5), .lamda. is the
wavelength of the propagating light, and .DELTA.(z) is a parameter
monotonically related to the distance Z. Further, the disk function
p.sub.z has a diameter function d(z) that varies the diameter based
on the value of z and thereby limits the diameter of a
corresponding FZP. Further, each PSF is selected to have a
different constant phase value .theta..sub.n.
[0232] Although the equation above includes a single value .lamda.
for the wavelength of the propagating light, the above equation may
be used for polychromatic light by assuming that the captured
intensity image is a combination of intensities in plural portions
of the total captured spectrum, and for example, the captured
intensity image may be considered as a combination of captured red
light intensities, captured yellow light intensities, and captured
green light intensities. Further, the invention also includes using
other color models to represent the colored image, such as
CMYK.
[0233] Thus, in the image captured at the image capture device
(i.e., at z=0), the PSFs h.sub.1,2,3 are given by
h ( , y , 0 ) = n = 1 3 ( 1 2 exp { i .pi. 2 .lamda. .DELTA. ( 0 )
[ ( - n ) 2 + ( y - y n ) 2 ] + i .theta. n 2 } + 1 2 exp { - i
.pi. 2 .lamda. .DELTA. ( 0 ) [ ( - n ) 2 + ( y - y n ) 2 ] - i
.theta. n 2 } ) p o ( - n , y - y n ) , ( 3 ) ##EQU00003##
Therefore, the desired light transforming function of each partial
function H.sub.n(u,v) of the optical assembly 110 is the Fourier
transform of h.sub.n(x,y,0) in equation 3 above. Thus,
H.sub.n(u,v), corresponding to embodiments with the spatial
multiplexing of partial mask patterns as shown in Equation 3 and
FIGS. 9A-9C, 10A and 10B, is defined as follows:
H n ( u , v ) = { 1 2 exp [ i .pi. .lamda. .gamma. 1 ( u 2 + v 2 )
+ i 2 .pi. .lamda. f 2 ( n u + y n v ) + i .theta. n 2 ] + 1 2 exp
[ i .pi. .lamda. .gamma. 2 ( u 2 + v 2 ) - i 2 .pi. .lamda. f 2 ( n
u + y n v ) - i .theta. n 2 ] } * P ( u , v ) , n = 1 , 2 , 3 ( 4 A
) ##EQU00004##
[0234] In alternative time multiplexing embodiments, such as those
shown in FIGS. 15, 17 and 18, H.sub.n(u,v) may be defined as
follows:
H n ( u , v ) = { 1 2 exp [ i .pi. .lamda. .gamma. 1 ( u 2 + v 2 )
+ i .theta. n 2 ] + 1 2 exp [ i .pi. .lamda. .gamma. 2 ( u 2 + v 2
) - i .theta. n 2 ] } * P ( u , v ) , n = 1 , 2 , 3 ( 4 B )
##EQU00005##
where * represents a convolution operation.
[0235] Further, the overall transforming function of the mask
H(u,v) is defined as follows:
H ( u , v ) = n = 1 3 H n ( u , v ) ( 5 ) ##EQU00006##
where u and v are coordinates in the plane of the optical assembly
110 corresponding to the x and y coordinates in the image capture
plane (i.e., the u axis is parallel to the x axis and the v axis is
parallel to they axis), and P(u,v) is the Fourier transform of disk
function p.sub.o(x,y).
[0236] In the equations above .gamma..sub.1,2 may be defined
according to the following equation:
.gamma. 1 , 2 = .+-. 27 f 1 2 4 f 2 ( 6 ) ##EQU00007##
[0237] Note, however, that the invention is not limited to using
optical assemblies having a different focal length and that the
equations may be extended to allow same focal lengths for the two
optical assemblies. In other words, the parameters of mask
.gamma..sub.1,2=.+-..gamma. are determined according to Equation 6
when the parameters f.sub.1 and f.sub.2 are known f.sub.1 and
f.sub.2 may be chosen according to the resolution of the SLM or
DOE. For example, if the SLM area is D.times.D, with N.times.N
pixels, then the pixel size is .delta.=D/N. The minimal ring width
of FZP displayed on this SLM is well known as
.delta.=|.gamma.|.lamda./D. Therefore, from the equation
D/N=|.gamma.|.lamda./D one gets |.gamma.|=D.sup.2/N.lamda.. Then,
substituting |.gamma.| into Equation 6 yields the values of the
parameters f.sub.1 and f.sub.2. Note that this example illustrates
only one possible set of considerations, but the invention also
includes methods and resulting apparatuses produced with filter
parameters calculated based on other factors.
[0238] When the transform regions of a mask include a color
filtering capability configured to filter out or to pass light only
centered at particular frequencies, as described above with respect
to FIG. 6A. The masks do not have to change when illuminated by
various colors. The response of a mask transparency changes
according to the wavelength of the light, for example as shown in
Equation 27 below.
[0239] FIG. 7 shows an example of a binary Fresnel Zone Pattern
700, in which each of zone includes only one of two transmissivity
states: substantially transparent, and substantially opaque, with
respect to the light being transmitted. In this example, the FZP
700 is printed on a glass substrate 702 that transmits more than
90% of light within the visual light spectrum using an ink that
reflects or absorbs more than 90% of light within the relevant
light spectrum.
[0240] The invention is not limited to binary FZPs having
alternating zones of more than 90% transmission and more than 90%
absorption/reflection, but also includes FZPs having other levels
of transmission, and absorption/reflection, as known in the field
of FZPs. Further, the invention is not limited to FZPs having zones
having a consistent transmissivity throughout each zone (i.e.,
zones that are entirely substantially transparent or entirely
substantially opaque), but also includes FZPs having zones with
varying transmission levels within each zone. In addition, the
invention is not limited only to patterns of complete circular
rings, but also includes patterns of partial rings, such as an
off-axis FZP. Moreover, the invention also includes replacing the
FZP with a photon sieve, such as described in Kipp et. al.,
"Sharper images by focusing soft x-rays with photon sieves,"
Nature, vol. 414, 8 Nov. 2001, pp. 184-188, incorporated herein by
reference.
[0241] FIGS. 8A-8C show examples of sinusoidal FZPs 800, 802 and
804. In sinusoidal FZPs, transmissivity varies sinusoidally between
points of maximum transmissivity in substantially transmissive
zones and points of minimum transmissivity in less transmissive
zones, along a straight line radiating from the center of the FZP.
Further, the FZPs 800, 802 and 804 each have a different phase.
[0242] FIGS. 9A-9C show examples of Fourier Transformed FZP
patterns (FT-FZP) 900, 902 and 904 that are Fourier transforms of
FZPs 800, 802 and 804, respectively. Note that the FT-FZP patterns
may also have an FZP concentric pattern. However, where the FZPs in
FIGS. 8A-C produce an image having an intensity vs. radial
coordinate distribution having a uniform amplitude across the
radial coordinates, the FT-FZPs in FIGS. 9A-C have an intensity vs.
radial coordinate distribution similar to a bell curve with an
intensity peak at the centers of the rings in the ring patterns,
and reduced intensities at all other locations. The Fourier
transforms of Fresnel zone patterns may be used to produce the mask
functions according to Equation 4 above.
[0243] Further, H(u, v) of Equation 4 may be obtained by Fourier
transform of h(x,y,0) from Equation 3 multiplied by the quadratic
phase function. Note that an FZP may be a sum of two quadratic
phase functions with opposite signs in their arguments, and the
Fourier transform of a quadratic phase function is also a quadratic
phase function. Therefore, each quadratic phase of h(x,y,0) is
multiplied by a quadratic phase function and then Fourier
transformed to another quadratic phase function. The net result is
that H(u,v) is a sum of two quadratic phase functions. It is
possible to carefully choose h(x,y,0) to make sure that H(u,v) will
be a sum of two quadratic phase functions with arguments that are
equal in their absolute value and have opposite signs. In that
case, the sum of quadratic phase functions is a FZP with a bell
curve because h(x,y,0) has a disk shape. In particular, a disk
function may be transformed to what is called a Mexican-Hat
function, which is convolved with the infinite FZP as shown in
Equation 4 This convolution may gradually decrease the amplitude of
the FZP as radius values increase, thereby creating the bell curve
shape. According to the features of Fourier transforms the
restricted area on h(x,y,0) causes a convolution of H(u,v) with a
narrow function indicated in Equation 4 by P(u,v). This convolution
is responsible for the bell-like shape of envelope of H(u, v).
[0244] FIG. 10A is the amplitude portion of a complex transmission
function according to Equation 5, which is a linear combination of
three mask functions each according Equation 4B, and corresponding
to the Fourier transform of the three FZPs in FIG. 10C.
[0245] FIG. 10B is the phase portion of the complex transmission
function according to Equation 5, which is a linear combination of
mask functions according to Equation 4, and corresponding to the
Fourier transform of the three FZPs in FIG. 10C.
[0246] The complex transmission function of Equation 5 and examples
illustrated in FIGS. 10A and 10B may be implemented using a single
DOE or SLM or combinations of DOEs and/or SLMs, as described
above.
[0247] Note that the FT-FZPs (e.g., as shown in FIG. 9A-C) may be
an amplitude only real function, but the linear combination of
FT-FZPs is an amplitude and phase pattern (e.g., as shown in FIG.
10A-B). This is possible by a careful choice of h(x,y,0). When
h(x,y,0) is chosen to be two particular quadratic phase functions
that, when multiplied by the quadratic phase function of the lens
and performing a Fourier transform of the resulting product, the
obtained result is two quadratic phase functions having arguments
that are equal in their absolute values, but with opposite signs.
In that case, the sum is a purely real function. On the other hand
this property may not occur with the H(u,v) shown in FIGS. 10A-B,
because the combination of 3 FZPs together is not symmetric in the
sense that h(x,y,0).noteq.h(-x,-y,0). Further, it is well known
that a Fourier transform of non-symmetric functions can not be
purely real.
[0248] FIG. 10C is an example of the pattern that is generated on
the CCD when a point object is present at the input, as described
above during the process to produce mask patterns shown in FIGS.
10A and 10B.
[0249] FIG. 11A is a block diagram of an image capture assembly
1100 that includes a light intensity capture device 1102 and a
capture control unit 1104. The light intensity capture device 1102
of this embodiment is a conventional light capturing device, such
as a charge coupled device (CCD) as used in digital cameras, and is
configured to capture a two-dimensional array of light intensity
information (i.e., image of the received light) under the control
of the capture control unit 1104. The invention is not limited only
to CCDs but may also include other devices that capture light
intensity, such as a photographic film or a transparent film, an
X-ray detector, other electromagnetic radiation detectors, a CMOS
device, a diode array, or a photo-detector, etc. . . . .
[0250] The capture control unit 1104 controls the light capturing
functions of the light intensity capture device 1102 and is
configured to retrieve electronic image data information from the
light intensity capture device 1102. For example, in the present
embodiment, the light intensity capture device includes a CCD
connected to the capture control unit 1104, which is configured,
according to conventional means, to retrieve electronic image data
from the CCD image array. Alternatively, for example, if the light
intensity capture device included a photographic film, the image
capture control unit could include a conventional image scanning
function configured to scan the captured image from the
photographic film, and thereby retrieve the electronic image data.
The invention also includes other conventional methods of capturing
electronic image data, known to those of skill in this field.
[0251] The capture control unit 1104 controls the functions of the
CCD 1102, and may also include and provide control for conventional
photographic mechanical assemblies such as a shutter and/or a
controllable aperture (not shown) to control aspects of capturing
the image on the CCD 1102. Alternatively, one of skill in the image
capture field will understand that such mechanical assemblies
controlled by the capture control unit 1104 may be arranged in any
convenient location along the light path between the object and the
image capture assembly, or between the light source and the image
capture assembly.
[0252] According to the present embodiment, light is spread by the
pattern in the mask 304 which includes PSFs h (Equation 3) having
disk functions p.sub.1(x,y), p.sub.2(x,y) and p.sub.3(x,y) centered
at points (x.sub.1,y.sub.1), (x.sub.2,y.sub.2) and
(x.sub.3,y.sub.3), respectively, in the image capture space. Thus,
an image capture device may be configured to include three distinct
regions within a single light intensity capture device to receive
three distinct partial images produced by mask 304, such as the
light intensity capture device 1102 in FIG. 11A. Further, the image
capture device may include three separate light intensity capture
devices to receive the three distinct partial images produced by
mask 304, such as light intensity capture devices 1106, 1108 and
1110 in the embodiment of image capture assembly 1112 shown in FIG.
11B.
[0253] FIG. 12A is a view of an example of a light intensity
capture device 1200 that includes a charge coupled device 1202
having three distinct regions 1204, 1206 and 1208. A central
location in each region 1210, 1212 and 1214, respectively,
corresponds to a center of each of the three partial images
produced by the optical assembly 110. In particular, the
coordinates of the points 1210, 1212 and 1214 correspond to
(x.sub.1,y.sub.1), (x.sub.2,y.sub.2) and (x.sub.3,y.sub.3),
respectively, from Equation 3.
[0254] FIG. 12B is an example of a two-dimensional intensity image
according to Equation 1A captured by image capture assembly 120,
including three partial images 1216, 1218 and 1220 produced by
optical assembly 110. Such a two-dimensional intensity image is
converted into a three-dimensional image of the object by the image
capture assembly 120, as described below.
[0255] FIGS. 13A-13C show other examples of ways in which the
distinct regions of a light intensity capturing device may be
arranged, where each distinct region includes a center 1300. One of
skill in the art will understand that the light intensity capturing
device may be divided into three or more zones in any convenient
manner. For example, if the light intensity capturing device
includes a randomly addressable CCD, the boundaries of the zones
may be arranged along convenient address regions. Alternatively, if
the light intensity capturing device includes a photographic film,
the boundaries of the zones may be arranged according to the
geometries that are convenient for the dimensions and aspect ratio
of the film.
[0256] According to Equation 1A above, an image capture assembly
120 receives and captures light having a light intensity
distribution given by o(x,y). To extract the object geometric
information from the captured image, the image capture assembly
operates on the captured image (i.e., intensity function o(x,y))
according to Equation 1A. Thus, the object geometric information of
the object s(x',y',z') is given by the following equation:
s ( ' , y ' , z ' ) = O F ( , y ) * exp [ - i .pi. .lamda. .DELTA.
( z ) ( 2 + y 2 ) ] ( 7 ) ##EQU00008##
where O.sub.F(x,y) is a linear combination of the intensity
distributions in the partial images as follows:
O.sub.F(x,y)=o.sub.1(x,y)[exp(-i.theta..sub.3)-exp(-i.theta..sub.2)]+o.s-
ub.2(x,y)[exp(-i.theta..sub.1)-exp(-i.theta..sub.3)]+o.sub.3(x,y)[exp(-i.t-
heta..sub.2)-exp(-i.theta..sub.1)] (8).
The extraction of the geometric information may be performed using
methods from the field of digital holography, for example as
described in I. Yamaguchi, and T. Zhang, "Phase-shifting digital
holography," Opt. Lett. 22, 1268-1269 (1997), incorporated herein
by reference.
[0257] In addition, the capture control unit 1104 may include
functions for combining the electronic data for each of the three
partial images according to Equation 8, for extracting the object
geometric information according to Equation 7 and for providing the
resulting object geometric information in a desired format.
Alternatively, those functions may be performed in a general
purpose computer configured to receive the image data from the
image capture assembly.
[0258] The object geometric information may be extracted as surface
data, which may be suitable for use in applications such as
physical modeling (e.g., to create a computer model of the object)
or three-dimensional fabrication (e.g., to create a physical
three-dimensional copy of the object) applications. In addition,
the object geometric information may be displayed graphically, for
example using two-dimensional representations of three-dimensional
objects (e.g., a two-dimensional projection such as isometric
projection, or a two-dimensional representation of a
three-dimensional object that may be animated to rotate the object
around one or more axes to better illustrate the three-dimensional
object), or using direct three-dimensional representation of
three-dimensional objects (e.g., holographic display or
projection).
[0259] FIG. 14 is a block diagram of an example of a capture
control unit 1400 that includes an image data processor 1402 that
combines the electronic image data according to Equation 7 to
produce the object geometric information, and an object data output
device 1404 to output the object geometric information. The image
data processor 1402 may be implemented using a conventional
processor and conventional data processing software. The object
data output device 1404 may include any of a number of conventional
devices configured to utilize three-dimensional object geometric
data such as a visual holographic display, a virtual reality
environment display, a three-dimensional object fabrication device
(e.g., laser sintering fabrication device, a digitally controlled
lathe, etc. . . . ), a simulation model, a two-dimensional
animation of a moving three-dimensional object, etc. . . . . The
invention also includes a capture control unit (not shown) that is
configured to include an interface to an external control device,
such as a computer, which may replace image data processor 1402 and
object data output 1404, to flexibly perform the image data
processing functions in a separate device.
[0260] In the embodiments described above, three different mask
patterns having three different transmission functions (e.g.,
functions H.sub.1, H.sub.2, and H.sub.3 of equation (4B or 4A)) are
combined in a single mask, three partial images resulting from the
mask patterns are simultaneously captured, and the three partial
images are combined to obtain geometric object information.
However, if the image capture assembly of FIG. 11A is used, the
resulting resolution of the captured image may be reduced if the
pixel array size is not increased three times so that each of the
three images are the same resolution so that the three partial
images may be captured on a single light intensity capture device.
Alternatively, if the image capture assembly of FIG. 11B is used,
or if a single sensor with three times the area is used, the
resulting cost of the capture apparatus is increased by the cost of
two additional light intensity capture devices or the larger format
sensor.
[0261] Another embodiment that varies a mask over time may not
cause the possible resolution reduction or cost increase of the
preceding embodiment. In particular, in this embodiment, a mask may
be varied over time, resulting in three different partial images
that vary over time. The three different partial images may be
captured by an image capture assembly configured to capture images
over time, and the three partial images may be combined to extract
the geometric information of the object.
[0262] FIG. 15 is a block diagram of an embodiment of an optical
apparatus 1500 that varies the mask over time. Optical apparatus
1500 is similar to the embodiment of the optical apparatus 400 in
FIG. 4, however, the optical apparatus 1500 includes a controllable
incoherent correlator 1502 and a controllable image capture
assembly 1506 that are controlled by a timing controller 1508, and
the optical apparatus 1500 is configured to capture
three-dimensional or geometric information of object 130 using at
least three different images captured at different times.
[0263] The controllable incoherent correlator 1502 is similar to
the incoherent correlator 300 of the embodiment shown in FIG. 4.
However, the controllable incoherent correlator 1502 includes a
controllable mask 1504 having a mask that may be controlled by the
timing controller, to controllably transform the amplitude and
phase of light received from the object. One or more spatial light
modulators (SLMs), as described in FIGS. 6F and 6G, may be used in
such a controllable incoherent correlator.
[0264] Further, the controllable image capture assembly 1506 is
similar to the image capture assembly 120 in the embodiment shown
in FIG. 4. However, the controllable image capture assembly 1506 is
further configured to be controlled to capture and retrieve
electronic image data by the timing controller 1508.
[0265] FIG. 16 is a block diagram of controllable mask 1504 that
includes a spatial light modulator 1600 under the control of a mask
controller 1602. The mask controller 1602 controls the mask
controller 1602 to transform light according to complex transform
functions H.sub.1, H.sub.2 and H.sub.3 of Equation 4B, at times
t.sub.1, t.sub.2 and t.sub.3, as synchronized by the timing
controller 1508. In an alternative embodiment, the mask controller
1602 may be eliminated and the spatial light modulator 1600 may be
controlled directly by the timing controller 1508, or by another
external device not shown (e.g., an external computer operated
controller). Image capture assembly 1506, also under the control of
timing controller 1508 captures three partial images at times
t.sub.1, t.sub.2 and t.sub.3 and combines the partial images to
obtain geometric information for object 130, as described
previously.
[0266] FIG. 17 is a block diagram of another embodiment of an
optical apparatus in which the mask is varied over time. In this
embodiment, a mask controller 1700 controls a mechanical position
of a multimask 1712. The multimask 1712 includes three masks 1702,
1708 and 1710 corresponding to the masks H.sub.1, H.sub.2 and
H.sub.3 according to Equation 4B. The mask controller moves the
multimask 1712 in directions 1704 to place a corresponding mask
between optical transforming assemblies 302 and 306 at times
t.sub.1, t.sub.2, and t.sub.3, under the control of timing
controller 1508. Image capture assembly 1506, also under the
control of timing controller 1508 captures three partial images at
times t.sub.1, t.sub.2 and t.sub.3 and combines the partial images
to obtain geometric object information for object 130, as described
previously. The multimask 1712 may include masks in a linear
arrangement as shown in FIG. 17, or may include masks arranged in a
radial arrangement, or any other suitable arrangement.
[0267] The three partial images may also be produced and captured
simultaneously using an arrangement including three different
optical assemblies having different masks and arranged to each
receive a portion of the light received from the object.
[0268] FIG. 18 is a block diagram of an embodiment of an optical
apparatus 1800 having optical assemblies 1802, 1804 and 1806 that
are configured to each receive a portion of the received light from
the object by an arrangement of partially transmissive and
reflective mirrors 1808, 1810 and 1812 (e.g., "partially-silvered"
mirrors). An image capture assembly 120, such as the embodiments
shown in FIGS. 11A and 11B, captures and processes the received
partial images as described above.
[0269] Although the embodiments are described using only
transmissive optical elements (e.g., refractive lenses and
transmissive masks) one of skill in the art will understand that
the invention also includes alternative embodiments in which one or
more of the optical elements may be replace with a corresponding
reflective optical element, as desired.
[0270] FIG. 19 is an embodiment of an optical apparatus 1900 that
is similar to optical apparatus 400 shown in FIG. 4. However,
optical apparatus 1900 includes a reflective mask 1902 that is
configured to reflect unmasked light, instead of transmitting the
unmasked light as in mask 304. A beam splitter 1904 redirects the
light reflected by mask 1902 to the second transforming optical
assembly 306.
[0271] FIGS. 20A and 20B are block diagrams of embodiments of
optical apparatuses 2000 and 2008, respectively, in which the first
transforming optical assembly is implemented using a reflective
optical assembly. In FIG. 20A, a beam splitter 2004 directs a light
received from the object 130 to a reflective optical assembly 2002,
which transforms the received light and reflects the transformed
light towards mask 304 and second transforming optical assembly
306. In the present embodiment, light transmitted from the second
transforming optical assembly is reflected to the image capture
assembly 120 by a mirror 2006.
[0272] Similarly, in FIG. 20B, a reflective optical assembly 2010
receives a light from object 130, transforms the received light and
reflects the transformed light to a beam splitter 2012 which
directs the transformed light to mask 304, and so on.
[0273] Other arrangements of mirrors or beam splitters to
conveniently direct light are also included in the present
invention.
[0274] In the optical apparatus embodiments described above, when
the electromagnetic radiation received from the object includes a
wide bandwidth, it is possible to capture frequency information in
the image capture assembly. Thus, it is possible for the image
capture assembly to determine a corresponding electromagnetic
radiation frequency or frequencies for each portion of the object.
For example, when a white light is received at the optical assembly
from the object, the image capture assembly may determine the color
of each portion of the object from the image captured by the image
capture assembly.
[0275] In addition, it may be possible to increase the resolution
of the captured three-dimensional information by reducing the
bandwidth of the received light. For example, the resolution of the
captured three-dimensional information may be increased by limiting
the bandwidth of the received light to those frequencies of light
close to the color red. Such an increase in resolution may be
obtained by filtering received or transmitted light in the optical
assembly to have a reduced bandwidth using conventional filters, or
by irradiating the object with a reduced bandwidth light source,
using methods known by those of skill in the art.
[0276] However, images captured using a reduced light bandwidth may
not include a sufficient level of information regarding the various
colors of the received light, and therefore may not allow for the
image capture assembly to determine colors of the object to a
sufficiently high level of accuracy. Accordingly, other embodiments
of the invention may include plural channels each configured to
receive light and capture images within different portions of the
electromagnetic spectrum, and them to combine the separately
captured images to produce full spectrum three-dimensional
information regarding the object.
[0277] FIG. 21A is a block diagram of optical apparatus 2100 that
receives light from object 130. The received light is partitioned
into three light portions 2103, 2105 and 2107 by light partitioning
devices 2102, 2104 and 2106, respectively. The three light portions
2103, 2105 and 2107 each include a subset of the bandwidth of the
received light. For example, light portion 2103 may include only
light frequencies near the color red, light portion 2105 may
include only light frequencies near the color green and light
portion 2107 may include only light frequencies near the color
blue. The light partitioning devices 2102, 2104 and 2106 may
include any combination of dichroic mirrors, color filters, mirrors
or other partially transmissive frequency filtering devices known
to those of skill in the art.
[0278] The light portions 2103, 2105 and 2107 are received by
optical assemblies 2108, 2110 and 2112, respectively, which each
may be configured to transform the received light as described
above. That is, each of the optical assemblies 2108, 2110 and 2112
may transform a light portion of the received light as described
above (e.g., using three partial mask patterns or a time varying
pattern), and transmit the transformed light to an image capture
assembly 1112 that includes a separate light capture assembly for
each of the three partial mask patterns, or to an image capture
assembly 1100 (not shown) that includes a single light capture
assembly configured to capture different images over time or
different partial images within different regions of the
assembly.
[0279] In addition, the optical apparatus 2100 includes an image
combining apparatus 2113 configured to receive image data
representing the images captured at image capture assemblies 1100
and combine the image data to produce combined broadband
three-dimensional information regarding the object. For example,
the optical apparatus 2100 may be able to capture full-color
three-dimensional information with a higher resolution than the
embodiments described above.
[0280] FIG. 21B is a block diagram of an optical apparatus 2126
that receives light from object 130 and separates the received
light into three light portions 2115, 2117 and 2119 by light
partitioning devices 2114, 2116 and 2118, respectively. The three
light portions 2115, 2117 and 2119 each include the entire
bandwidth of the received light. For example, if the received light
includes a white light then each of the three light portions 2115,
2117 and 2119 also includes a white light. The light partitioning
devices 2114, 2116 and 2118 may include any combination of
polychromatic mirrors, beam splitters or wideband transmissive
devices known to those of skill in the art.
[0281] The light portions 2115, 2117 and 2119 are received by
optical assemblies 2120, 2122 and 2124, respectively, which each
may be configured to transform the received light as described
above. That is, each of the optical assemblies 2120, 2122 and 2124
may transform a light portion of the received light as described
above (e.g., using three partial mask patterns or a time varying
pattern).
[0282] Further, each of the optical assemblies 2120, 2122 and 2124
may be configured to selectively filter out some received light
frequencies. For example, the optical assemblies may include
conventional color filters (not shown) to filter out certain light
colors. Further, the mask in each optical assembly may include
light transforming regions having predetermined attenuation of
received light frequencies, as described above with respect to FIG.
6A. That is, each transform region 614 may be configured to apply
different amounts of amplitude reduction over different frequencies
of the received light spectrum.
[0283] Each of the optical assemblies 2120, 2122 and 2124 transmits
the transformed portion of received light to an image capture
assembly 1112 that includes a separate light capture assembly or
region of an assembly for each of the three partial mask patterns,
or to an image capture assembly 1100 (not shown) that includes a
single light capture assembly configured to capture different
images over time or different partial images within different
regions of the light capture assembly.
[0284] Although the embodiments of FIGS. 21A and 21B include
received light that is separated into three portions, other
embodiments in which light is separated into other numbers of
portions are also included.
[0285] An incoherent correlator may equivalently be implemented
with alternate optical apparatuses other than the lens/mask/lens
arrangements described above. For example, by applying the
well-known thin lens approximation for lenses, the incoherent
correlator may be implemented with a single optical transforming
element and a single mask, with either the mask or the optical
transforming element arranged to first receive light from the
object. In addition, the optical assembly 110 may be implemented
using a single diffractive optical element. The equations 1-5 above
therefore also apply to embodiments having a single transforming
optical assembly and a mask, and embodiments having an optical
assembly implemented using only a single diffractive optical
element.
[0286] FIG. 22A is a block diagram of an example of an optical
apparatus 2200 that is similar to the optical apparatus 400 shown
in FIG. 4. However, the optical apparatus 2200 does not require a
second transforming optical element. Instead light is received from
the object 130 by optical transforming element 2202, which
transforms the received light and transmits the transformed light.
The transformed light is received by mask 2204 which selectively
transmits a portion of the transformed light. Image capture
assembly 120 receives and captures an image of the selectively
transmitted light and obtains geometric information regarding
object 130 from the captured image, as described above.
[0287] FIG. 22B shows an example of an optical apparatus 2206 that
is similar to the optical apparatus 400 shown in FIG. 4. However,
the optical apparatus 2206 does not require a first transforming
optical element. Instead light is received from the object 130 by
mask 2208 which selectively transmits a portion of the received
light. The second optical transforming element 2210 receives the
selectively transmitted light, transforms the received light and
transmits the transformed light. Image capture assembly 120
receives and captures an image of the transformed light and obtains
geometric information regarding object 130 from the captured image,
as described above.
[0288] There may be a relatively high cost to manufacture optical
assemblies having a conventional incoherent correlator structure.
An alternative embodiment of the present invention the optical
assembly may be implemented using a single diffractive optical
element (DOE) in place of the incoherent correlator.
[0289] A single DOE may replace the incoherent correlator (e.g.,
incoherent correlator 300 including first and second transforming
optical assemblies 302/306 and mask 304 in the embodiment shown in
FIG. 4) described above. A DOE that is equivalent to the incoherent
correlator is the product of the mask filter function and the
transmission functions of the first and second transforming optical
assemblies, H.sub.DOE, defined as follows:
H DOE ( u , v ) = exp [ - i 2 .pi. .lamda. f ( u 2 + v 2 ) ] .intg.
.intg. h ( , y , 0 ) exp [ - i .pi. .lamda. f ( 2 + y 2 ) ] exp [ i
2 .pi. .lamda. f ( u + vy ) ] d dy ( 9 A ) ##EQU00009##
where f is the focal length of the first and second transforming
optical assemblies included in the DOE, h(x,y,0) is given above in
Equation 3, and other parameters are as described with respect to
Equation 4.
[0290] Further, the focal lengths of the lenses are not required to
be the same. When the focal lengths are different, the H.sub.DOE,
is defined as follows.
H DOE ( u , v ) = exp [ - i .pi. ( f 1 + f 2 ) .lamda. f 1 f 2 ( u
2 + v 2 ) ] .intg. .intg. h ( , y , 0 ) exp [ - i .pi. .lamda. f2 (
2 + y 2 ) ] exp [ i 2 .pi. .lamda. f 2 ( u + vy ) ] d dy ( 9 B )
##EQU00010##
Note that although Equations 9A and 9B do not include literal P
function terms, p.sub.o(x,y) is part of h(x,y,0), and when the
integral in Equations 9A and 9B are solved, the convolution with
P(u, v) is obtained.
[0291] FIG. 22C is a block diagram of an example of an optical
apparatus 2212 that is similar to the optical apparatus 400 shown
in FIG. 4. However, the optical apparatus 2212 does not require
first and second transforming optical elements. Instead light is
received from the object 130 by mask 2214 which transmits light
based on a complex transformation of the received light. Mask 2214
may be implemented using only a single diffractive optical element,
as described above. Image capture assembly 120 receives and
captures an image of the transformed light and obtains geometric
information regarding object 130 from the captured image, as
described above.
[0292] FIG. 23 is a block diagram of an embodiment of optical
apparatus 100 in which the optical element 110 includes a
reflective type diffractive optical element, for example, such as
the diffractive optical elements shown in FIGS. 5F and 5G. In this
embodiment, the optical apparatus 100 receives a light from object
130 along a receiving optical axis 2304. The optical apparatus 100
transforms and reflects the received light to produce a transmitted
light transmitted back along optical axis 2302. The transmitted
light is reflected by a beam splitter 2300 to an image capture
assembly 120 located along a capturing optical axis 2302 of the
optical apparatus. In the present embodiment, capturing optical
axis 2302 is arranged at an angle of approximately 90 degrees from
the receiving optical axis 2304. However, other angles between the
receiving and capturing optical axes are also included in the
invention.
[0293] With only two optical axes, the current embodiment may
advantageously reduce a size of the optical assembly 100, while
exhibiting less sensitivity to axial variations than in
conventional holography systems.
[0294] An objective-side optical assembly, such as an objective
lens, a zoom lens, a macro lens, a microscope, a telescope, a
prism, a filter, a monochromatic filter, a dichroic filter, a
complex objective lens, a wide-angle lens, a camera, a pin-hole, a
light slit, a mirror, or any other optical assembly may be placed
between the optical assembly and the object to collimate, focus,
invert or otherwise modify the light from the object, prior to the
light being received at the optical assembly. Such an arrangement
may advantageously allow light from objects or portions of objects
to be received, when it would not be possible or practical to
receive that light without the inclusion of the objective-side
optical assembly.
[0295] Further, an objective-side optical assembly may include
refractive or diffractive optical elements configured to at least
partially cancel any disadvantageous wavelength dispersal effects
that may be caused by the optical apparatus 100, as described by
Goodman, "Introduction to Fourier Optics," 3rd Ed., Roberts &
Company Publishers, 2005, at p. 212, incorporated herein by
reference.
[0296] FIG. 24A shows an alternative embodiment including the
features of the embodiment in FIG. 1, as well as an objective-side
optical assembly 2400 that receives light from the object and
transmits a received light to the optical assembly 110. The
objective-side optical assembly 2400 in the present embodiment
includes a magnifying refracting objective lens that produces a
magnified image of the object 130 centered on an image plane 2402.
Thus, the present embodiment may capture more detailed geometric
information regarding a magnified portion of the object.
[0297] The present invention may also operate in conjunction with
an existing sensor-less camera, which is understood herein to be
any camera from which the existing digital light sensor (e.g., CMOS
device or CCD) or light sensitive capture medium (e.g., film and
film transport mechanism) has been removed, or moved away from the
image plane of the camera to allow an apparatus according to the
present invention to be used with the remaining optical and
mechanical components of the camera. For example, film, film
transport mechanisms and the rear cover of an existing 35 mm film
camera may be removed and replaced with an optical assembly and
image capture device according to the present invention, thereby
making the existing camera capable of capturing three-dimensional
information. Such an arrangement advantageously allows the present
invention to conveniently take advantage of and operate with
existing photographic lenses, shutter systems and aperture control
systems of existing cameras.
[0298] FIG. 24B shows an example of an embodiment of an optical
apparatus 2404 including features similar to the optical apparatus
100 shown in FIG. 1. In addition, the optical apparatus 2404 is
configured to operate with an existing sensor-less camera 2406,
which receives light from the object 130 along an optical axis 140,
and manipulates the light using conventional camera features (e.g.,
lens, ground glass focusing screen, shutter and aperture of the
existing camera) to produce an image of the object centered at
image plane 2408. The optical apparatus 2404 includes a chassis
having mechanical and electrical attachment features suitable for
coupling the optical apparatus 2404 to a portion of the existing
sensor-less camera 2406 near the image plane produced by the optics
of the existing sensor-less camera 2406 (e.g., as a replaceable "3D
back" of the camera). The optical assembly 110 receives light from
the image of the object at the image plane 2408 and transmits a
transformed light, which may be received, captured and processed to
extract three-dimensional information of an object by the image
capture assembly 120, as described above.
[0299] The present invention may also operate in conjunction with
an existing camera. In particular, the optical assembly in the
embodiment described herein may be used in conjunction with a
conventional digital or film camera to illuminate the image plane
of the conventional camera with a Fresnel hologram or partial
Fresnel holograms of the observed object. The conventional camera
may be used to capture an image of the hologram fringe patterns
using the corresponding conventional means (e.g., light sensitive
film or digital sensor), and image data corresponding to the fringe
patterns may be converted into three-dimensional data of the object
using a general purpose computer.
[0300] The invention is not limited to a single DOE that includes a
transmission function based on a linear combination of three
transmission functions each having a Fourier transforms of a FZP.
On the other hand, the invention also includes receiving a portion
of the light from the object at each of three DOEs, which produce
three partial images that are combined.
[0301] FIG. 25 shows a block diagram of an embodiment of an optical
apparatus 2500 including partially reflective and transmissive
mirrors 1808, 1810 and 1812 that direct a light received from
object 130 to each of three diffractive optical elements 2502, 2504
and 2506, respectively, which each perform a transforming function
including a Fourier transform of a FZP. The image capture assembly
2508 extracts three-dimensional information from an image of the
light transmitted by the diffractive optical elements, similar to
the manner described above.
[0302] In addition, alternative embodiments of the optical assembly
110 may consist of a single SLM as shown in FIG. 6F or one or more
SLMs as shown in FIG. 6G.
[0303] Further, the invention is not restricted only to using three
mask patterns to produce three partial hologram images that are
combined. The invention also includes using an off-axis holographic
method that employs a single off-axis hologram instead of three
masks.
[0304] During reconstruction of an image from an off axis hologram
each term is diffracted toward a different direction and therefore
a desired angular separation can be achieved even from a single
hologram, by taking advantage of the fact that angular separation
in diffraction theory is directly translated to a spatial frequency
separation. This characteristic may be exploited based on the idea
that, when performing a convolution between functions f and g, it
is equivalent to transform f and g to the frequency domain by a
Fourier transform to obtain functions F and G, obtain a product of
F and G, and transform the product back by an inverse Fourier
transform. Thus, an optical apparatus that shifts a spatial
frequency spectrum of a received light may be advantageously used
to create a Fresnel hologram.
[0305] An optical apparatus that produces an off-axis Fresnel Zone
Pattern (OAFZP) in response to point input light source can be used
to convolve a received light rather than the FZPs in the
embodiments above, and convolution using the OAFZP based assembly
will allow for a convenient separation of terms in the frequency
domain.
[0306] FIG. 26 shows an example of an OAFZP 2600.
[0307] To synthesize the off-axis FZP we may introduce a linear
phase term to the equation for the on-axis FZPs described above, to
result in the following OAFZP transformation function
h ( , y , z ) = p z ( , y ) { 1 2 exp [ i .pi. ( 2 + y 2 ) 2
.lamda. .DELTA. ( z ) + i 2 .pi. ( .alpha. + .beta. y ) .lamda. ] +
1 2 exp [ - i .pi. ( 2 + y 2 ) 2 .lamda. .DELTA. ( z ) - i 2 .pi. (
.alpha. + .beta. y ) .lamda. ] } ( 10 ) ##EQU00011##
[0308] Further, it is not necessary to use a mask or a spatial
light modulator to create such an OAFZP producing optical assembly.
Alternatively, an arrangement of at least two lenses each shifted
away from an optical axis of an image plane and arranged so that
their focal points are at different distances from an image plane
may be used to produce an OAFZP.
[0309] FIG. 27 is a block diagram of a portion of an optical
apparatus including a composite mask 2720 having lenses 2714 and
2716. Light 2718 is received and refracted by lenses 2714 and 2716
towards lens 2702 having focal length f 2712. In this example,
lenses 2714 and 2716 are configured to have different focal
lengths. Spherical waves 2706 and 2704 produced by lenses 2714 and
2716, respectively, interfere with each other to produce OAFZP 2708
at image plane 2710.
[0310] Although the example of FIG. 27 includes convex and concave
lenses, the invention includes any combination or permutation of
convex and/or concave lenses. Further, the lenses may have
different focal lengths, and be arranged in a same plane, as shown
in FIG. 27, or alternatively, the lenses may have the same or
different focal lengths and be arranged in different planes.
[0311] FIGS. 28A-D show examples of composite masks 2800, 2802,
2804 and 2806. Further, although the lenses shown in the composite
mask examples described above are round lenses that cover only a
portion of the composite mask plane or planes, the invention also
includes other shaped lenses (e.g., cylindrical lenses) covering a
portion or the entirety of the composite mask plane or planes. In
addition, the invention includes replacing one or both of the
lenses in the composite mask with a corresponding diffractive
optical element, or with a FZP.
[0312] Therefore, a composite mask that produces a single off-axis
FZP may replace the masks or diffractive optical elements based on
Fourier transforms of FZPs in any of the optical apparatuses
described above. However, to achieve further separation of terms in
the frequency domain a pattern of lines may be projected on the
object, or an optical grating having an appropriate spatial
frequency may be placed between the object and the image capture
plane to add a pattern of lines to the image of the object.
[0313] FIG. 29 is a block diagram of an embodiment of an optical
apparatus 2900 that is configured to receive light from object 130
and extract three-dimensional information about object 130 from the
received light. Optical apparatus 2900 includes an objective
optical assembly 2902 that receives light from object 130 along an
optical axis 140. The objective optical assembly 2902 produces an
image of the object 130 at an image plane 2908. A grating 2904,
located on the image plane 2908, adds a pattern of lines to the
image of the object 130 which propagates to first transforming lens
302. Further, the optical apparatus 2900 includes a composite mask
2910 which transforms the light received from the first
transforming lens 302, and transmits a transformed light. Second
transforming lens 306 receives the transformed light and transmits
a further transformed light, and image capture assembly 120
captures an image of the light and extracts three-dimensional
information from the captured image, as described above.
[0314] FIG. 30 is a detailed view of an embodiment of grating 2904
that includes low transmissivity regions 3002 and high
transmissivity regions 3000. A width 3006 of the low transmissivity
regions 3002, and a width 3004 of the high transmissivity regions
3000 are selected so that contrasting dark and light areas are
observable in the resulting image at the image capture device 120.
Gratings including variable widths of high and low transmissive
regions may also be used.
[0315] As discussed above, the pattern of lines may also be applied
to the light illuminating the object or to the light received from
the object. For example, light illuminating the object may pass
through a lined transparency configured to produce shadow lines on
the object.
[0316] FIG. 31A is a block diagram of an embodiment of an optical
apparatus 3100 that may be used with a lined transparency 3102 to
obtain three-dimensional information of an object 130. Light from
light source 150 is shadowed by lines on the lined transparency
3102 to produce lined illumination on object 130. The lined
illumination reflects from the object 130 and is received by the
first transforming lens 302 in the optical apparatus 3100. Further,
the optical apparatus 3100 includes a composite mask 2910 which
transforms the light received from the first transforming lens 302,
and transmits a transformed light. Second transforming lens 306
receives the transformed light and transmits a further transformed
light, and image capture assembly 120 captures an image of the
light and extracts three-dimensional information from the captured
image, as described above.
[0317] Alternatively, it is not necessary to use the grating 2904.
Instead, the light coming from the object may be split into two
beams, each of which is transferred by a different off-axis lens
toward a different portion of the filter. The filter and the system
beyond the plane of the filter are similar to corresponding
portions of the previous embodiments described in FIGS. 27, 29 and
31A.
[0318] FIG. 31B is a block diagram of an embodiment of an optical
apparatus 3100 that includes two off-axis lenses 2901 and 2903 and
is configured to obtain three-dimensional information of an object
130. Optical apparatus 3100 includes an objective optical assembly
2902 that receives light from object 130 along an optical axis 140.
Beam splitter 2908 and mirror 2909 transmit portions of the
received light to mirrors 2907 and 2905, respectively. The light
reflected from mirrors 2905 and 2907 propagates to first
transforming lenses 2901 and 2903, respectively. Further, the
optical apparatus 3100 includes a composite mask 2910 which
transforms the light received from the first transforming lenses
2901 and 2903, and transmits a transformed light. Second
transforming lens 306 receives the transformed light and transmits
a further transformed light, and image capture assembly 120
captures an image of the light and extracts three-dimensional
information from the captured image, as described above.
[0319] One of skill in the art will understand that the optical
apparatuses described above are not limited to capturing only
reflected sunlight, but may also determine the shape and distance
of object portions that do not reflect light but instead emit a
fluorescent light, a black body radiation, a chemiluminescent light
or other light produced by the object, or objects that reflect or
scatter light from sources other than the sun. In addition, an
optical apparatus, according to the present embodiment, is not
limited to capturing only the external shape and distance of
objects, but may also capture information regarding internal
portions of an object that radiate (i.e., reflect or fluoresce)
light from an internal portion through a transparent or translucent
surface of the object to the optical apparatus.
[0320] The present invention is also not limited to capturing
geometric information regarding an object using a Cartesian
coordinate system (e.g., x, y, z), but also includes capturing
geometric information using any other coordinate system that may
fully describe the shape, size and location of the object, such as
a three-dimensional polar coordinate system (e.g., .phi., .theta.,
r), an earth referenced coordinate system such as the global
coordinate system (e.g., latitude, longitude, elevation), a
coordinate system incorporating an ellipsoid earth model reference
system such as WGS-84, an earth centered earth fixed Cartesian
coordinate system (ECEF) (e.g., x, y, z), Universal Transverse
Mercator (UTM), Military Grid Reference System (MGRS), or World
Geographic Reference System (GEOREF), etc. . . . . Further,
although Cartesian type measurement terms such as "vertical,"
"horizontal" and "range" are used throughout the present
description, those terms are intended to also include corresponding
measurement terms in other reference systems, but which are omitted
from the description herein for reasons of clarity and brevity.
[0321] The use of the apparatuses is not limited to the field of
three-dimensional imaging, but also includes uses in pattern
recognition, target acquisition, and object identification, etc. .
. . performed in three-dimensional space, for example as described
in Y. Li and J. Rosen, "Object recognition using three-dimensional
optical quasi-correlation," JOSA A 19, 1755-1762 (2002),
incorporated herein by reference.
[0322] Advantages of the present invention may make embodiments of
the invention suitable for three-dimensional imaging applications
that are impossible or impractical without the present invention.
For example, the present invention may be applied to capturing
three-dimensional movies/video/television images, performing
three-dimensional object recognition for moving objects or
stationary objects from a moving or stationary platform (e.g.,
military targeting applications, robotic sensing applications,
autonomous aid to vision impaired users, etc. . . . ), autonomous
navigation and safety functions (e.g., automatically guide an
automobile to stay on a road and avoid collisions with moving and
stationary objects), weather sensing (e.g., capture
three-dimensional information regarding clouds or air masses
detected with radar, visible light, or infrared and/or ultraviolet
light, etc. . . . ), security functions (e.g., monitor locations
and identity objects in a room, monitor identities and locations of
people in a building, three-dimensional synthetic radar, etc. . . .
), and three-dimensional environmental mapping for virtual reality
simulation (e.g., create three-dimensional model of tourist
destination for virtual visit), or three-dimensional models of
environments that are difficult or impossible to observe directly
(e.g., internal body cavities, microscopic environments, hazardous
environments, extraterrestrial environments, underground or sea
environments, remote environments, etc. . . . ).
[0323] Although examples described above deal with optical
components and visible light, the present invention also applies to
receiving other forms of electromagnetic radiation from an object
and determining three-dimensional information of the object based
on the received electromagnetic radiation, such as x-ray radiation,
microwave radiation, radio frequency radiation, and ultraviolet and
infrared light. For example, embodiments of the invention described
above may be modified to replace optical components (e.g., lenses,
mirrors, diffractive optical elements, SLMs) with corresponding
x-ray components, such as are known in the art and as described in
i) U.S. Pat. No. 6,385,291 to Takami, ii) Pereira et al., "Lithium
x-ray refractive lenses," Proc. SPIE 4502, 173 (2001)., and iii)
Beguiristain et al., "Compound x-ray refractive lenses made of
polyimide," Proc. SPIE, vol. 4144, pp. 155-164, each of which is
incorporated herein by reference.
[0324] Further, for example, the present invention may be
applicable as a replacement for existing x-ray imaging systems
(e.g., CT scanners). As the present approach does not require any
moving parts, x-ray imaging done using an embodiment of the present
invention advantageously may produce a scan more reliably, with
higher resolution, greater speed and less total radiation exposure
to the patient.
[0325] Each of the embodiments described above may be modified to
replace optical elements with equivalent x-ray elements known to
those of skill in the art to produce three-dimensional information
based on a received x-ray radiation from an object (i.e., a
three-dimensional x-ray image). For example, the present invention
may be applicable as a replacement for existing electron microscope
technology.
[0326] Further the invention also applies to other forms of
propagating energy waves, such as sound waves and may be applied to
produce three-dimension object information using passive or active
sonar.
[0327] Coherent light, which propagates according to the paraxial
approximation, is described mathematically as a convolution between
an input aperture and a quadratic phase function with an
appropriate parameter in a denominator of an exponent power
indicating a propagation distance of the wave from the input
aperture. Thus, the complex amplitude (i.e., the electrical field)
distribution O(x,y) on some transversal plane, in a distance z from
the input plane, may be given (in the Fresnel approximation) by
O ( , y ) = .intg. .intg. S ( ' , y ' ) exp { i .pi. .lamda. z [ (
- ' ) 2 + ( y - y ' ) 2 ] } d ' dy ' ( 11 ) ##EQU00012##
where S(x',y') is the complex amplitude on the input aperture at
the transverse plane z=0, .lamda. is the wavelength of the
propagating light and (x',y'), (x,y) are the coordinates of the
input and output planes, respectively. For 3D objects,
contributions from the object points are accumulated to the
following expression,
O z ( x , y ) = .intg. .intg. .intg. S ( x ' , y ' , z ' ) exp { i
.pi. .lamda. ( z - z ' ) [ ( x - x ' ) 2 + ( y - y ' ) 2 ] } dx '
dy ' dz ' ( 12 ) ##EQU00013##
where (x',y',z') are the coordinates of the input space. In a
conventional holography approach that produces a Fresnel hologram,
the complex amplitude O.sub.z(x,y) may be interfered with a
reference beam and the intensity of the resulting interference
pattern is recorded on a photographic plate or a digital camera.
However, according to the present invention, a convolution similar
to Equation 12 may be performed differently using incoherent light,
because the Fresnel propagation described in Equation 11 may be
valid only for coherent illumination.
[0328] For a two-dimensional (2D) input intensity function s(x,y)
and an intensity point spread function (PSF) |h(x,y)|.sup.2, a
correlator output intensity (e.g., of a correlator such as shown in
FIG. 3) distribution may be given by the following convolution,
o(x,y)=s(x,y)*|h(x,y)|.sup.2=.intg..intg.s(x',y')|h(x-x',y-y')|.sup.2dx'-
dy' (13)
where the asterisk denotes a 2D convolution, h(x,y) is the
amplitude PSF in the system, but under coherent illumination.
h(x,y) is related to the 2D inverse Fourier transform of the filter
function H(u,v) at plane P.sub.2, as the following,
h ( x , y ) = .intg. .intg. H ( u , v ) exp [ i 2 .pi. .lamda. f 2
( xu + yv ) ] dudv ( 14 ) ##EQU00014##
where f.sub.2 is the focal length of the second lens in the
correlator shown in FIG. 3. To solve for 3D objects rather 2D, a
response of the incoherent correlator to a 3D input function may be
determined. Further, although the input function is
three-dimensional, the output and the convolution remain
two-dimensional. In fact the correlator response for a 3D input
is,
o(x,y)=.intg.s(x,y,z)*|h(x,y,z)|.sup.2dz=.intg..intg..intg.s(x',y',z')|h-
(x-x',y-y',z')|.sup.2dz'dy'dz' (15)
To calculate the general 3D amplitude PSF h(x,y,z) of the system, a
response to a single point located at some point (x,y,z) in the
vicinity of the rear focal point of the correlator may be
determined. Such a calculation produces the 3D PSF of the system
which may be used to calculate the system response to any possible
3D input. Since the system is known as space invariant it is
correct to calculate the system response to a point on the optical
axis at some point (0,0,-z), and to generalize the response toward
a general location at (x,y,z). The input point is located a
distance f.sub.1+z from the lens 302 at the point 308 (i.e.,
0,0,-z), as shown in FIG. 3.
[0329] The Fresnel integrals in Equations 11 and 12 can be used to
calculate the light distribution because a single monochromatic
point source is by definition a spatial coherent source. By
substituting the representation of a single point source,
represented by a delta function .delta.(0,0,-z), into Equation 12
as the input S(x,y,z), the result on the plane of the first lens
302 is a diverging quadratic phase function as follows,
O L 1 ( x , y ) = .intg. .intg. .intg. .delta. ( x ' , y ' , z + z
) exp [ i .pi. .lamda. ( f 1 - z ' ) { ( x - x ' ) 2 + ( y - y ' )
2 } ] dx ' dy ' dz ' = exp [ i .pi. .lamda. ( f 1 + z ) ( x 2 + y 2
) ] ( 16 ) ##EQU00015##
where f.sub.1 is the focal length of the first lens in the
correlator shown in FIG. 3. This quadratic phase function is known
as the paraxial approximation of the spherical wave propagating in
the z direction, and the paraxial approximation of a concave
spherical lens transparency. This spherical wave propagates through
the incoherent correlator and beyond the correlator the beam
becomes a converging spherical wave. It may be shown that at the
plane where the beam is focused one gets the Fourier transform of
the transparency function of the mask H(u,v). This Fourier
transform is scaled according to the specific location of the focal
plane and is multiplied by a quadratic phase function.
[0330] Assuming that the three optical thin elements L.sub.1,
L.sub.2 and H(u,v) of the incoherent correlator (e.g., elements
302, 306 and 304, respectively, in FIG. 3) are all located at the
same plane, the diverging spherical wave and the two adjunct lenses
L.sub.1 and L.sub.2 can be replaced by a single equivalent lens
having a focal length f.sub.e, as follows:
f e = ( 1 f 1 + 1 f 2 - 1 f 1 + z ) - 1 = f 1 f 2 ( f 1 + z ) f 1 2
+ z ( f 1 + f 2 ) ( 17 ) ##EQU00016##
In a system having the equivalent lens in place of the correlator,
once the system is illuminated by a plane wave, the complex
amplitude on a back focal plane of equivalent lens L.sub.e is
related to the 2D Fourier transform of the transparency function
H(u,v). This means that the complex amplitude on the back focal
plane, at a distance f.sub.e from the equivalent lens L.sub.e
is
u ( x , y , z ) = A exp [ i .pi. .lamda. f e ( z ) ( x 2 + y 2 ) ]
.intg. .intg. H ( u , v ) exp [ - i 2 .pi. .lamda. f e ( z ) ( xu +
yv ) ] dudv ( 18 ) ##EQU00017##
Note that the incoherent system is analyzed above according to the
rules of coherent diffraction theory because the beams are
considered to have been emitted from a single infinitesimal point.
Since the output of the system is located a distance f.sub.2 from
the equivalent lens L.sub.e the output complex amplitude is
obtained after a free propagation beyond the back focal plane of
the equivalent lens L.sub.e.
[0331] Free propagation of coherent light may be obtained, as
mentioned above in Equation 11, as the result of convolution
between the complex amplitude in the starting plane and a quadratic
phase function. According to this, the output complex amplitude
is,
h ( x , y , z ) = u ( x , y , z ) * exp i .pi. .lamda. [ f 2 - f e
( z ) ] ( x 2 + y 2 ) = { exp [ i .pi. .lamda. f e ( z ) ( x 2 + y
2 ) ] .intg. .intg. H ( u , v ) exp [ - i 2 .pi. .lamda. f e ( z )
( xu + yv ) ] dudv } * exp [ i .pi. .lamda. [ f 2 - f e ( z ) ] ( x
2 + y 2 ) ] ( 19 ) ##EQU00018##
Note that although the function in Equation 19 deals with three
dimensions, the convolution is always in 2D. Equation 19 expresses
the general 3D amplitude Point Spreading Function (PSF) of the
system when it is illuminated by coherent light. Further, Equation
19 can be simplified by writing explicitly the convolution
integral, switching the order of integration and using the
well-known result of the Fourier transform of quadratic phase
function. Such a simplification reduces the four integrals of
Equation 19 to a double integral as follows:
h ( x , y , z ) = exp [ i .pi. .lamda. [ f 2 - f e ( z ) ] ( x 2 +
y 2 ) ] .times. .intg. .intg. H ( u , v ) exp [ - i .pi. [ f 2 - f
e ( z ) ] .lamda. f 2 f e ( z ) ( u 2 + v 2 ) ] exp [ - i 2 .pi.
.lamda. f 2 ( xu + yv ) ] dudv ( 20 ) ##EQU00019##
Another equation used to synthesize the filter in the system is the
expression of the amplitude PSF for any point at the plane z=0,
given by substituting f.sub.e(0)=f.sub.2 in Equation 20, as
follows,
h ( x , y , 0 ) = exp [ i .pi. .lamda. f 2 ( x 2 + y 2 ) ] .intg.
.intg. H ( u , v ) exp [ - i 2 .pi. .lamda. f 2 ( xu + yv ) ] dudv
. ( 21 ) ##EQU00020##
[0332] As described above, the intensity PSF for incoherent systems
and for intensity distributions on the input and output planes is
|h(x,y,z)|.sup.2. The intensity PSF represents the impulse response
of general incoherent systems. By taking the absolute square of
Equation 20 one finds that the 3D intensity PSF is,
h ( x , y , z ) 2 = .intg. .intg. H ( u , v ) exp [ - i .pi. [ f 2
- f e ( z ) ] .lamda. f 2 f e ( z ) ( u 2 + v 2 ) ] exp [ - i 2
.pi. .lamda. f 2 ( xu + yv ) ] dudv 2 ( 22 ) ##EQU00021##
The general expression of Equation 22 can be used to compute the
PSF for a given filter or the required filter for a given PSF.
[0333] According to Equation 17 the expression in the exponent of
Equation 22 is,
[ f 2 - f e ( z ) ] f 2 f e ( z ) = f 2 - f 1 f 2 ( f 1 + z ) f 1 2
+ z ( f 1 + f 2 ) f 1 f 2 2 ( f 1 + z ) f 1 2 + z ( f 1 + f 2 ) = z
f 1 ( f 1 + z ) ( 23 ) ##EQU00022##
Substituting Equation 23 into Equation 12 yields
h ( x , y , z ) 2 = .intg. .intg. H ( u , v ) exp [ - i .pi. z
.lamda. f 1 ( f 1 + z ) ( u 2 + v 2 ) ] exp [ - i 2 .pi. .lamda. f
2 ( xu + yv ) ] dudv 2 ( 24 ) ##EQU00023##
The general expression of Equation 24 can be used to compute the
PSF for a given filter or the required filter for a given PSF.
[0334] To obtain a Fresnel hologram, which is a convolution between
any object and a quadratic phase function, an incoherent intensity
PSF in a shape of a quadratic phase function with a number of
cycles (Fresnel number) dependent on the distance z is selected.
This may not be achieved directly because |h(x,y,z)|.sup.2 is a
positive real function while a quadratic phase function has
negative and imaginary values.
[0335] One method of selecting such a PSF is to compose the PSF
|h(x,y,z)|.sup.2 as a sum of three terms, one of them is the
required quadratic phase function, and their sum maintains the
condition that |h(x,y,z)|.sup.2 is a positive real function. Thus,
a PSF such as shown in Equation 25
h ( x , y , z ) 2 = p z ( x , y ) { 1 + 1 2 exp [ i .pi. .lamda.
.DELTA. ( z ) ( x 2 + y 2 ) ] + 1 2 exp [ - i .pi. .lamda. .DELTA.
( z ) ( x 2 + y 2 ) ] } ( 25 ) ##EQU00024##
satisfies this condition, where .DELTA.(z) is a parameter linearly
related to the distance z and p.sub.z(x,y) is a disk function with
the diameter d(z), different for different values of z, that
indicates the limiting aperture of a corresponding Fresnel Zone
Pattern (FZP). The amplitude PSF for this choice is
h ( x , y , z ) = p ( x , y ) { 1 + cos [ i .pi. .lamda. .DELTA. (
z ) ( x 2 + y 2 ) ] } = 2 p ( x , y ) cos [ i .pi. 2 .lamda.
.DELTA. ( z ) ( x 2 + y 2 ) ] = p z ( x , y ) { 1 2 exp [ i .pi. (
x 2 + y 2 ) 2 .lamda. .DELTA. ( z ) ] + 1 2 exp [ - i .pi. ( x 2 +
y 2 ) 2 .lamda. .DELTA. ( z ) ] } ( 26 ) ##EQU00025##
Note that a possible arbitrary pure phase term can multiply
h(x,y,z) without affecting the square magnitude of h(x,y,z) given
in Equation 25. However in order to get a Fresnel hologram of all
the object's points, it is preferred that h(x,y,z) remains as a sum
of two quadratic phase terms along the propagation axis. Of the
possible phase functions that can multiply h(x,y,z), only a
quadratic phase function may satisfy the condition that h(x,y,z) is
a sum of two quadratic phase terms after propagating a distance.
Accordingly, it is appropriate to assume that h(x,y,z) is a sum of
two quadratic waves with the same magnitude of Fresnel number but
with opposite signs, as given in Equation 26. Further, as described
below, two quadratic waves with different Fresnel numbers may be
used in an optimized solution.
[0336] Based on the desired h(x,y,z), H(u,v) may be calculated by
inversing Equation 21, to produce the following filter function in
Equation 27.
H ( u , v ) = .intg. .intg. h ( x , y , 0 ) exp [ - i .pi. .lamda.
f 2 ( x 2 + y 2 ) ] exp [ i 2 .pi. .lamda. f 2 ( xu + yv ) ] dxdy (
27 ) ##EQU00026##
Substituting Equation 26 into Equation 27 yields Equation 28
H ( u , v ) = { 1 2 exp [ i .pi. .lamda. .gamma. 1 ( u 2 + v 2 ) ]
+ 1 2 exp [ i .pi. .lamda. .gamma. 2 ( u 2 + v 2 ) ] } * P ( u , v
) ( 28 ) ##EQU00027##
where P(u, v) is the Fourier transform of p.sub.o(x,y). Note that
H(u, v) is 2D function which determines the dependency of h(x,y,z)
along the transverse coordinates (x,y). The dependency of h(x,y,z)
along the z axis is dictated by the location of input source
point.
[0337] The intensity PSF may be obtained by substituting the filter
function of Equation 28 into Equation 22. Substituting Equation 17
into the exponent expression of Equation 22 yields,
[ f 2 - f e ( z ) ] f 2 f e ( z ) = f 2 - f 1 f 2 ( f 1 + z ) f 1 2
+ z ( f 1 + f 2 ) f 1 f 2 2 ( f 1 + z ) f 1 2 + z ( f 1 + f 2 ) = z
f 1 ( f 1 + z ) ( 29 ) ##EQU00028##
Assuming that the filter function is
H ( u , v ) = { 1 2 exp [ i .pi. .lamda. .gamma. ( u 2 + v 2 ) ] +
1 2 exp [ - i .pi. .lamda. .gamma. ( u 2 + v 2 ) ] } * P O ( u , v
) ( 30 ) ##EQU00029##
therefore, Equation 22 becomes,
h ( x , y , z ) 2 = .intg. .intg. { 1 2 exp [ i .pi. .lamda.
.gamma. ( u 2 + v 2 ) ] + 1 2 exp [ - i .pi. .lamda..gamma. ( u 2 +
v 2 ) ] } * P o ( u , v ) .times. exp [ - i .pi. .lamda. z f 1 ( f
1 + z ) ( u 2 + v 2 ) ] exp [ - i 2 .pi. .lamda. f 2 ( xu + yv ) ]
dudv 2 ( 31 ) ##EQU00030##
After summation corresponding terms, the result is,
h ( x , y , z ) 2 = .intg. .intg. { 1 2 exp [ i .pi. ( f 1 2 + f 1
z - .gamma. z ) ( u 2 + v 2 ) .lamda. .gamma. f 1 ( f 1 + z ) ] + 1
2 exp [ - i .pi. ( f 1 2 + f 1 z + .gamma. z ) ( u 2 + v 2 )
.lamda. .gamma. f 1 ( f 1 + z ) ] } * P o ( u , v ) exp [ - i 2
.pi. .lamda. f 2 ( x u + y v ) ] dudv 2 ( 32 ) ##EQU00031##
Calculating the Fourier transform,
h ( x , y , z ) 2 = { 1 2 exp [ - i .pi. .gamma. f 1 ( f 1 + z ) (
x 2 + y 2 ) .lamda. f 2 2 ( f 1 2 .gamma. + f 1 z + .gamma. z ) ] +
1 2 exp [ i .pi. .gamma. f 1 ( f 1 + z ) ( x 2 + y 2 ) .lamda. f 2
2 ( f 1 2 .gamma. + f 1 z + .gamma. z ) ] } p o ( x , y ) 2 ( 33 )
##EQU00032##
Calculating the square magnitude yields,
h ( x , y , z ) 2 = 1 + 1 4 exp [ i 2 .pi. .gamma. f 1 2 ( f 1 + z
) 2 ( x 2 + y 2 ) .lamda. f 2 2 ( f 1 2 ( f 1 + z ) 2 - .gamma. 2 z
2 ) ] + 1 4 exp [ - i 2 .pi. .gamma. .intg. 1 2 ( f 1 + z ) 2 ( x 2
+ y 2 ) .lamda. f 2 2 ( f 1 2 ( f 1 + z ) 2 - .gamma. 2 z 2 ) ] (
34 ) ##EQU00033##
The parameter .DELTA.(z) is,
.DELTA. ( z ) = ( f 1 2 ( f 1 + z ) 2 - .gamma. 2 z 2 ) f 2 2 2
.gamma. f 1 2 ( f 1 + z ) 2 ( 35 ) ##EQU00034##
Equation 35 gives the value of .DELTA.(z), the distance of a
reconstructed image point as a function of the object point's
location on the z axis, for the general choice of
.gamma..sub.1,2=.+-..gamma..
[0338] The derivative of .DELTA.(z) yields the axial magnification
as a function of z. The derivative of .DELTA.(z) given in Equation
35 is,
d .DELTA. ( z ) dz = - z .gamma. f 2 2 f 1 ( f 1 + z ) 3 ( 36 )
##EQU00035##
Equation 36 indicates that there is a point at z=0, which is at the
front focal point in which the axial magnification is zero. This
point is also an extreme point of the function .DELTA.(z). This
means that for an object positioned at this location, points on one
side (e.g., object points where z<0) yield the same hologram as
other points from the other side (e.g., object points where
z>0). The result might be a reconstruction of an axially folded
image. Therefore, recording a hologram of an object located at this
point may be advantageously avoided.
[0339] The immediate conclusion from this curve is that one cannot
record a hologram of an object that has points from both sides of
the forbidden point. This is because every two points to the left
and to the right of z=induce the same hologram which is actually a
FZP with the same value of .DELTA.(z). In other words, from the
recorded hologram one cannot know whether the object is located at
z or at -z. A solution to this problem may be to record holograms
of objects that are all located only at one side of the point
z=0.
[0340] We also see from Equation 36 that .DELTA.(z) is not a linear
function of z. This phenomenon might introduce distortion of the
image if the object has considerable depth. However, this depth
distortion can be compensated during computer reconstruction of the
three-dimensional image based on the known curve of .DELTA.(z).
[0341] Equation 36 also shows that that in the region z>0 there
is a point where d.DELTA.(z)/dz gets its maximum value. This point
may be convenient for locating the object because in the vicinity
of this point the magnification may be maximal and approximately
linear. This point may be found by comparing a second derivative of
.DELTA.(z) to zero. The optimal point is at z.sub.o=f.sub.1/2.
Substituting the value of zo back into Equation 36 yields the
following axial magnification
M A = d .DELTA. ( z ) d z = - 4 .gamma. f 2 2 27 f 1 3 ( 37 )
##EQU00036##
Thus, Equation 37 provides a basis for selecting the value of
.gamma.. In any hologram without distortions during the
reconstruction the axial and the transverse magnifications are
equal. Therefore, the transverse magnification of the inventive
system is M.sub.T=-f.sub.2/f.sub.1. Substituting the non-distortion
constraint that M.sub.T=M.sub.A into Equation 37 yields the filter
parameter as follows,
.gamma. = 27 f 1 2 4 f 2 ( 38 ) ##EQU00037##
[0342] For example, when magnifications of the two lenses are -0.5
(i.e., f.sub.1=2f.sub.2) the filter parameter .gamma. is 27f.sub.2.
Thus, in the embodiment of FIG. 3, for the simpler case off
f.sub.1=2f.sub.2, one quadratic phase has a focal length resulting
in .gamma..sub.1=27f.sub.2. For symmetry, the other quadratic phase
may likewise be selected to have a focal length resulting in
.gamma..sub.2=-27f.sub.2. Substituting these values into Equation
30 yield the following filter function:
H ( u , v ) = { 1 2 exp [ i .pi. 27 .lamda. f 2 ( u 2 + v 2 ) ] + 1
2 exp [ - i .pi. 27 .lamda. f 2 ( u 2 + v 2 ) ] } * P o ( u , v ) (
39 ) ##EQU00038##
Note, that such a symmetric hologram has real values only, and this
property may be used to advantageously implement a mask.
Substituting the filter function of Equation 39 into Equation 22
yields intensity PSF of the form of Equation 25, where .DELTA.(z)
is given by Equation 35 as follows,
.DELTA. ( z ) = [ f 1 2 ( f 1 + z ) 2 - 27 2 4 f 1 2 z 2 ] 2 27 2 f
1 3 ( f 1 + z ) 2 = [ 4 ( f 1 + z ) 2 - 27 2 z 2 ] f 1 108 ( f 1 +
z ) 2 ( 40 ) ##EQU00039##
In the point z.sub.o=f.sub.1/2 of maximum, and almost linear,
magnification, .DELTA.(z.sub.o) is
.DELTA. ( z o ) = - 693 972 f 1 ( 41 ) ##EQU00040##
Note that when the hologram is reconstructed, twin images are
obtained along the z axis at the vicinity of the points
.+-..DELTA.(z) from the hologram plane Solving the twin image
reconstruction problem is further described below.
[0343] Following is an example of how parameters may be selected
for fabrication of a mask according to the present invention.
Assuming that an SLM used as the filter medium has N.times.N pixels
in a rectangle area of size D.times.D, a FZP with .+-..gamma.
parameters may be displayed on the SLM, where the width of a
thinnest possible ring is given by .delta.=|.gamma.|.lamda./D and
.delta.=D/N. Therefore, from the equation D/N=|.gamma.|.lamda./D
one gets .gamma.=D.sup.2/N.lamda.. For an SLM having D.apprxeq.2
cm, N.apprxeq.1000 pixels, the result is |.gamma.|.apprxeq.80 cm in
the visible light regime where .lamda..apprxeq.0.5 .mu.m. According
to Equation 22, and the discussion after that,
.gamma..sub.1,2=+27f.sub.2 and therefore f.sub.2.apprxeq.6 cm and
f.sub.1.apprxeq.f.sub.2/2=3 cm.
[0344] Equation 25 describes the intensity PSF captured by an image
capture device according to the present invention. This PSF has
three additive terms that are all concentrated in the center of the
image capture plane. Therefore, convolution of the object function
with such an intensity PSF yields three overlapped non-separated
terms. However, it is desired to extract only a desired convolution
term between the object and a single quadratic phase function among
the three convolutions with three terms of the intensity PSF. A
desired convolution between the object and a single quadratic phase
function among the three convolutions with three terms of Equation
22 may be extracted using methods similar to those in digital
holography, for example as described by I Yamaguchi, and T. Zhang,
"Phase-shifting digital holography," Opt. Lett. 22, 1268-1269
(1997), which is incorporated herein by reference.
[0345] The correlator may perform three operations of convolution
between the object and three PSFs equipped with three different
constant phase values. These PSFs may be synthesized by introducing
three filter masks with three different constant phase values as
follows,
H n ( u , v ) = { 1 2 exp [ i .pi. .lamda. .gamma. ( u 2 + v 2 ) +
i .theta. n 2 ] + 1 2 exp [ i .pi. .lamda. ( u 2 + v 2 ) - i
.theta. n 2 ] } * P ( u , v ) , n = 1 , 2 , 3 ( 42 )
##EQU00041##
By the relation of Equation 24, it can be shown that the three
filters induce three intensity PSFs as follows,
h n ( x , y , z ) 2 = p z ( x , y ) .times. { 1 + 1 2 exp [ i .pi.
.lamda. .DELTA. ( z ) ( x 2 + y 2 ) + i .theta. n ] } ( 43 )
##EQU00042##
Substituting the three PSFs of Equation 43 into Equation 15 yields
the output intensity images that may be recorded by a camera or
other suitable image capture device (e.g., CCD, CMOS, photographic
film, etc. . . . );
o n ( x , y ) = .intg. s ( x , y , z ) * h n ( x , y , z ) 2 dz =
.intg. [ s ( x , y , z ) * p z ( x , y ) ] dz + 1 2 exp ( i .theta.
n ) .intg. s ( x , y , z ) * p z ( x , y ) exp [ i .pi. .lamda.
.DELTA. ( z ) ( x 2 + y 2 ) ] dz + 1 2 exp ( - i .theta. n ) .intg.
s ( x , y , z ) * p z ( x , y ) exp [ - i .pi. .lamda. .DELTA. ( z
) ( x 2 + y 2 ) ] dz , n = 1 , 2 , 3 ( 42 ) ##EQU00043##
From these three images, a single term of convolution between the
object s(x,y) and one of the quadratic phases may be extracted. A
possible formula to isolate such a single convolution is
O.sub.F(x,y)=o.sub.1(x,y)[exp(-i.theta..sub.3)-exp(-i.theta..sub.2)]+o.s-
ub.2(x,y)[exp(-.theta..sub.1)-exp(-i.theta..sub.3)]+o.sub.3(x,y)[exp(-i.th-
eta..sub.2)-exp(-i.theta..sub.1)] (43)
O.sub.F(x,y) is a final complex valued hologram which satisfies the
relation
O F ( x , y ) = .intg. s ( x , y , z ) * p ( x , y ) exp [ i .pi.
.lamda..DELTA. ( z ) ( x 2 + y 2 ) ] dz ( 44 ) ##EQU00044##
The function O.sub.F(x,y) is the final hologram which contains
information on the one 3D image only. Such an image s(x,y,z) can be
reconstructed from O.sub.F(x,y) by calculating the inverse
operation to Equation 45, as follows,
s ( x , y ; z ) = O F ( x , y ) * exp [ - i .pi. .lamda. .DELTA. (
z ) ( x 2 + y 2 ) ] dz ( 45 ) ##EQU00045##
[0346] Subsequently, the process of obtaining a single hologram
with good separation between the three terms will be described.
However, practical aspects of performing the convolution with three
different PSFs are described first. There are several ways in which
the filters may be multiplexed to produce the three partial images.
For example, a time multiplexing system, such as the embodiment
shown in FIG. 15, multiplexes the filters over time. Alternatively,
the multiplexing may be done in the output plane of a single
channel, for example as in the embodiment shown in FIG. 4. When a
single point source is introduced at the point (0,0,0) the system's
PSF is a pattern of 3 FZP with 3 different phases, distributed at 3
separated locations on the output plane. This 2D amplitude PSF is
given by,
h ( x , y , 0 ) = n = 1 3 ( 1 2 exp { i .pi. 2 .lamda. .DELTA. ( 0
) [ ( x - x n ) 2 + ( y - y n ) 2 ] + i .theta. n 2 } + 1 2 exp { -
i .pi. 2 .lamda. .DELTA. ( 0 ) [ ( x - x n ) 2 + ( y - y n ) 2 ] -
i .theta. n 2 } ) p o ( x - x n , y - y n ) , ( 46 )
##EQU00046##
where (x.sub.n,y.sub.n) is the center point of the nth FZP.
h(x,y,0) of Equation 46 may be used to synthesize the filter H(u,v)
by Fourier transform of h(x,y,0). For synthesizing the diffractive
optical element (DOE) in a lensless system, for example the
embodiment shown in FIGS. 1 and 22C, one may multiply the filter
function by the transmission function of the two spherical lenses,
to identify the overall transmission function of the DOE as
follows,
H ( u , v ) - exp [ - i .pi. ( f 1 + f 2 ) .lamda. f 1 f 2 ( u 2 +
v 2 ) ] .intg. .intg. h ( x , y , 0 ) exp [ - i .pi. .lamda. f 2 (
x 2 + y 2 ) ] exp [ i 2 .pi. .lamda. f 2 ( x 2 + y 2 ) ] exp [ i 2
.pi. .lamda. f 2 ( xu + vy ) ] dxdy , ( 47 ) ##EQU00047##
where h(x,y,0) is given in Equation 46.
[0347] A further embodiment includes a method of recording digital
Fresnel holograms under incoherent illumination. According to this
embodiment, the reflected white light from a 3-D object propagates
through a diffractive optical element (DOE) and is recorded by a
digital camera. Three holograms are recorded sequentially each with
a different phase factor of the DOE. The three holograms are
superposed in the computer such that the result is a complex valued
Fresnel hologram. The 3-D properties of the object are revealed by
reconstructing this hologram in the computer. To the best of our
knowledge, the demonstrated hologram is the first digital hologram
recorded without using laser light.
[0348] A system according to this embodiment is shown in FIG. 33. A
white light source 3301 illuminates a 3-D object 3302 and the
reflected light 3303 from the object is captured by a CCD camera
3304 after passing through a lens L 3305 and a DOE displayed on a
spatial light modulator (SLM) 3306. The specific SLM in this
experiment operates in reflection mode, but it is well understood
that the same principles and analysis are valid for transmission
SLM as well. In general, such system can be analyzed as an
incoherent correlator, where the DOE function is considered as the
system's transfer function. However, in this work we find it easier
to regard the system as an incoherent interferometer, where the
grating displayed on the SLM is considered as a beam splitter. As
is common in such cases, we analyze the system by following its
response to an input object of a single infinitesimal point.
Knowing the system's point spread function (PSF), enables one to
realize the system operation for any general object. Analysis of a
beam originated from narrow band infinitesimal point source is done
using Fresnel diffraction theory (J. Goodman, Introduction to
Fourier Optics, 2.sup.nd ed., McGraw-Hill, New York, 1996, pp.
63-95 (Chapter 4)) since such a source is coherent by
definition.
[0349] A Fresnel hologram of a point object is obtained when the
two interfering beams are, for instance, plane and spherical beams.
Such a goal is achieved if the DOE's reflection function R(x,y) is
of the form,
R ( x D , y D ) = 1 2 + 1 2 exp [ - i .pi. .lamda. a ( x D 2 + y D
2 ) + i .theta. ] = 1 2 + 1 2 Q ( - 1 a ) exp ( i .theta. ) , ( 48
) ##EQU00048##
Where .lamda. is the central wavelength, and for the sake of
shortening, the quadratic phase function is designated by the
function Q such that Q(b)=exp[i.pi.b/.lamda.(x.sup.2+y.sup.2)]. The
constant term of 1/2 in Eq. (48) contributes the plane wave, and
the quadratic phase term is responsible on the spherical wave. The
angle .theta. plays an important rule later in the computation
process in order to get rid of the twin image and the bias
term.
[0350] A point source located at the point (0,0,z.sub.s) a distance
f-z.sub.s from a spherical positive lens, with f focal length,
induces on the lens plane a diverging spherical wave of the form of
Q(1/f-z.sub.s). Right after the lens, which has a transmission
function of Q(-1/f), the complex amplitude of the wave is
Q(1/f-z.sub.s)Q(-1/f)=Q[z.sub.s/(f-z.sub.s)]. After propagating
additional distance of d.sub.1 till the DOE plane, the complex
amplitude becomes Q{z.sub.s/[f(f-z.sub.s)+z.sub.sd.sub.1]}. Right
after the DOE, with the reflection function given in Eq. (1), the
complex amplitude is related to Q{z.sub.s/[f
(f-z.sub.s)+z.sub.sd.sub.1]}[1+Q(-1/a)exp(i.theta.)]. Finally, in
the CCD plane a distance d.sub.2 from the DOE, the intensity of the
recorded hologram is,
I P ( x , y ) = A Q [ ( f ( f - z ) z + d 1 + d 2 ) - 1 ] + Q [ (
af ( f - z ) + azd 1 za - f ( f - z ) - zd 1 + d 2 ) - 1 ] exp ( i
.theta. ) 2 , ( 49 ) ##EQU00049##
where A is a constant. The first term of Eq. (49) is now
approximated to a constant by assuming that z is much smaller than
f. Since the system is shift invariant the result of I.sub.P((x,y),
after calculating the square magnitude in Eq. (49), can be
generalized to a PSF for any source point located at any point
(x.sub.s,y.sub.s,z.sub.s), as follows,
I P ( x , y ) = A ( 2 + exp { i .pi. .lamda. .gamma. ( z ) [ ( x -
.gamma. ( z ) x s f ) 2 + ( y - .gamma. ( z ) y s f ) 2 ] + i
.theta. } + exp { - i .pi. .lamda. .gamma. ( z ) [ ( x - .gamma. (
z ) x s f ) 2 + ( y - .gamma. ( z ) y s f ) 2 ] - i .theta. } , (
50 ) ##EQU00050##
where,
.gamma.(z)=[d.sub.2-a-z(d.sub.1a+d.sub.2f-af+d.sub.2a-d.sub.1d.sub-
.2)/f.sup.2]/[1-z(a+f-d.sub.1)/f.sup.2]. For a general 3-D object
g(x.sub.s,y.sub.s,z.sub.s) illuminated by a narrowband incoherent
illumination, the intensity of the recorded hologram is an integral
of the entire PSFs given in Eq. (50), over all object points
g(x.sub.s,y.sub.s,z.sub.s), as follows
H ( x , y ) = A ( C + .intg. .intg. .intg. g ( x s , y s , z s )
exp { i .pi. .lamda. .gamma. ( z ) [ ( x - .gamma. x s f ) 2 + ( y
- .gamma. y s f ) 2 ] + i .theta. } dx s dy s dz s + .intg. .intg.
.intg. g ( x s , y s , z s ) exp { - i .pi. .lamda. .gamma. ( z ) [
( x - .gamma. x s f ) 2 + ( y - .gamma. y s f ) 2 ] - i .theta. }
dx s dy s dz s . ( 51 ) ##EQU00051##
Besides a constant term Eq. (51) contain two terms of convolution
between an object and a quadratic phase, z-dependent, function,
which means that the recorded hologram is indeed a Fresnel
hologram. In order to remain with a single convolution term out of
the three terms given in Eq. (51), we follow the usual procedure of
on-axis digital holography (I. Yamaguchi, and T. Zhang,
"Phase-shifting digital holography," Opt. Lett. 22, 1268-1269
(1997). commercial). Three holograms of the same object are
recorded each of which with a different phase constant .theta.. The
final hologram H.sub.F is a superposition according to the
following,
H.sub.F(x,y)=H.sub.1(x,y)[exp(-i.theta..sub.3)-exp(-i.theta..sub.2)]+H.s-
ub.2(x,y)[exp(-i.theta..sub.1)-exp(-i.theta..sub.3)]+H.sub.3(x,y)[exp(-i.t-
heta..sub.2)-exp(-i.theta..sub.1)]. (52)
where H.sub.k is the kth recorded hologram with the phase constant
.theta..sub.k. A 3D image s(x,y,z) can be reconstructed from
H.sub.F(x,y) by calculating the Fresnel propagation formula, as
follows,
s ( x , y , z ) = H F ( x , y ) * exp [ i .pi. .lamda. z ( x 2 + y
2 ) ] , ( 53 ) ##EQU00052##
where the asterisk denotes a 2D convolution.
[0351] The system shown in FIG. 33 has been used to record the
three holograms. The SLM (HOLOEYE HEO 1080P) is phase-only and as
so the desired function given by Eq. (48) cannot be directly
displayed on this SLM 3306. To overcome this obstacle, we chose to
display the phase function Q(-1/a) on only half of the SLM pixels.
The rest of the pixels were modulated with a constant phase, where
the pixels of each kind were selected randomly. By this method the
SLM function becomes a good approximation to R(x,y) of Eq. (48).
The SLM 3306 has 1920.times.1080 pixels in a display of
16.6.times.10.2 mm, where only 1024.times.1024 pixels were used for
implementing the DOE. The phase distribution of the three
reflection masks displayed on the SLM 3306, with phase constants of
0.degree., 120.degree. and 240.degree., are shown in FIGS. 34A-34C,
respectively. The other specifications of the system are: f=250 mm,
a=800 mm, d.sub.1=132 mm, d.sub.2=260 mm. The system also includes
beamsplitter BS 3307 and lens L 3305 is spherical with a focal
length f.
[0352] Three white on black letters each (U, S, and A), the 3D
object 3302 of the size 2.times.2 mm were located at the vicinity
of rear focal point of the lens. `O` was at z=-24 mm, `S` was at
z=-48 mm and `A` was at z=-72 mm. These letters were illuminated by
a mercury arc lamp (Zeiss-AttoArc 2, HBO 100W). A filter which
passed 574 to 725 nm light with a peak wavelength of 599 nm and a
bandwidth of 60 nm was positioned between the beamsplitter and the
lens L. The three holograms, each for a different phase constant of
the DOE, were recorded by a cooled CCD camera (HAMAMATSU DIGITAL
CAMERA C4742-95) and processed by a computer. The final hologram
H.sub.F(x,y) was calculated according to Eq. (52) and its magnitude
and phase distribution are depicted in FIGS. 34E and 34G,
respectively.
[0353] The hologram H.sub.F(x,y) was reconstructed in the computer
by calculating the Fresnel propagation toward various propagation
distances according to Eq. (53). Three different reconstruction
planes are shown in FIGS. 34G, 34H, and 34I. In each plane a
different letter is in focus as is indeed expected from a
holographic reconstruction of an object with a volume.
[0354] A process according to this invention may record holograms
of realistic 3-D objects illuminated by incoherent light. Since an
embodiment of the system may have only a single channel, it is not
affected by vibrations, it does not demand complicated alignment
and the bandwidth can be wider than conventional incoherent
interferometers. The concept of the present system can be applied
to the design for a portable and very simple holographic camera
which might be useful for various applications in the fields of
microscopy, still and video photography, astronomy and medical
imaging.
[0355] By this method, light is reflected from a 3-D object,
propagates through or is reflected from a diffractive optical
element (DOE) and is recorded by a digital camera. Each beam which
originates from any object point is split into two different,
mutually coherent, spherical waves. The beam splitting is done by
the DOE grating, which operates as if it were a composition of two
different diffractive spherical lenses. Therefore, the single
wave-front originated from a point-source is divided by the DOE to
two wave-fronts with different quadratic curves that propagate in
the same direction. The intensity of the two wave-front
interference, originated from the same point source, is accumulated
incoherently on the camera pixel array with the other interferences
from the entire object points to yield the complete hologram. In
order to get rid of the twin image and the bias beam resulting from
each single hologram which will be described later, three
incoherent holograms are recorded sequentially, each with a
different phase factor of the DOE. Using the common routines of
digital holography (J. Rosen, G. Indebetouw, G. Brooker, Opt. Exp.
14, 4280-4285 (2006)) (J. Rosen, and G. Brooker "Incoherent digital
holography," Submitted for publication in Opt. Lett. (November
2006)) (I. Yamaguchi, and T. Zhang, Opt. Lett. 22, 1268-1269
(1997)), the three holograms are superposed in the computer, such
that the result is a complex valued Fresnel hologram. When this
hologram is reconstructed in the computer, a single 3-D image of
the object appears in the digital reconstruction space.
[0356] The technique described above may also be used for color
fluorescence imaging. An example of such an embodiment produces a
color Fresnel hologram which reconstructs the 3-D object with its
original fluorescent colors. The 3D objects that are imaged, for
example "dice", may contain a fluorescent light source, such as
several spots of two fluorescent dyes each with different emission
wavelengths. The 3D objects are illuminated by an arc lamp source
with a bandpass filter to illuminate the specimen with incoherent
light of about 50 nm bandwidth and which can also excite
fluorescence in each of the fluorescent dyes. According to this
example, several digital holograms are generated for each of the
different fluorescent colors on the dice and for the dice
themselves. Each emission color is introduced into the recording
system by restricting the emission with a specific chromatic
filter. For each wavelength of the fluorescence emission and the
reflected non-fluorescent light image of the object, a different
Fresnel number is applied to the DOE's grating. For each
wavelength, three holograms are sequentially recorded, each with a
different phase factor of the DOE's function, such that the overall
number of captured holograms for M colors plus the complete
reflected non-fluorescent image of the object is 3(M+1). Every
three holograms of the same wavelength are superposed in a certain
way such that the result is a complex valued Fresnel hologram of
this wavelength. The digital reconstruction from each hologram is
added to the rest, yielding a complete color 3-D image of the
original object. To the best of our knowledge, the demonstrated
holograms are the first fluorescence holograms recorded without
scanning and the first fluorescence multiwave length emission color
holograms ever recorded.
[0357] An incoherent blue light source 3501 with a bandwidth of 56
nm illuminates a 3-D object 3502 as is shown in FIG. 35. The
object's fluorescent emission light 3503 is introduced into the
system after passing through one of the chromatic filters F.sub.2
3504. After passing through lens L.sub.1 3505, the beam is
reflected from a spatial light modulator (SLM) 3506 toward a
demagnification setup of two lenses L.sub.2 3507 and L.sub.3 3508,
which projects the holographic pattern onto a CCD camera 3509. To
understand the operational principle, we analyzed the system by
following its response to an input object of a single infinitesimal
point. Knowing the system's point spread function (PSF), enables
one to analyze the system operation for any general object.
[0358] A Fresnel hologram of a point object is obtained when the
two interfering beams are, for instance, plane and spherical beams.
Therefore, we choose the DOE's reflection function
R(x.sub.D,y.sub.D) displayed on the SLM to be of the form,
R ( x D , y D ) = 1 2 + 1 2 exp [ - i .pi. .lamda. a ( x D 2 + y D
2 ) = i .theta. ] , ( 54 ) ##EQU00053##
Where .lamda. is the central wavelength introduced to the system.
The constant term of 1/2 in Eq. (54) contributes the plane wave,
and the quadratic phase term is the paraxial approximation of the
spherical wave. The angle is the phase shift needed in order to get
rid of the twin image and the bias term.
[0359] The reflection function of the DOE given by Eq. (54) implies
that the system's outcome can be viewed as a sum of two overlap
imaging systems. Finding the location of each image is a key
concept for understanding this holographic recorder. In one system,
let's call it system A, the DOE is actually a converging
diffractive lens with a focal length of a, whereas in the other
system (system B) the DOE serves as a plane mirror. In system A, a
point source located at a distance d.sub.s=f.sub.1 from the lens
L.sub.1 is imaged to an image point at a distance
(a-d.sub.2)(f.sub.3/f.sub.2).sup.2 beyond the camera plane. In this
last expression we use the well-known fact that the axial
magnification of an ordinary imaging system is given by the
relation M.sub.A=M.sub.T.sup.2=(d.sub.o/d.sub.s).sup.2, where
M.sub.T is the transverse magnification, and d.sub.o is the
distance from the output aperture to the image. For any point at
(0,0,z.sub.s) located a distance d.sub.s=f.sub.1-z.sub.s from the
lens L.sub.1, assuming that z.sub.s<<f.sub.1, the distanced,
is approximately,
d o ( z s ) .apprxeq. ( a - d 2 ) ( f 3 f 2 ) 2 + M _ A z s = ( a -
d 2 ) ( f 3 f 2 ) 2 + ( f 3 a f 2 f 1 ) 2 z s = [ ( r 2 f 1 .lamda.
N ) 2 z s + r 2 .lamda. N - d 2 ] ( f 3 f 2 ) 2 ( 55 )
##EQU00054##
where the overall axial magnification M.sub.A is the product of
magnifications of the two consecutive imaging systems, r is the
DOE's radius and N is the DOE's Fresnel number given by
N=r.sup.2/.lamda.a.
[0360] In system B, assuming that d.sub.s.apprxeq.f.sub.1, the
object point is obtained far beyond the camera plane at a distance
that justifies approximating the location of the image point at
infinity. Therefore, for a point at (x.sub.s,y.sub.s,z.sub.s), the
intensity on the camera plane is the square magnitude of the
complex amplitude sum of the spherical wave converging at the
distance d beyond the CCD plane, together with a plane wave, as
follows,
I P ( x , y ) .ident. C 1 + exp { - i .pi. .lamda. d o ( z x ) [ (
x - M _ T x s ) 2 + ( y - M _ T y x ) 2 ] - i .theta. } 2 ( 56 )
##EQU00055##
where the overall transverse magnification is
M.sub.T=f.sub.3a/f.sub.2 f.sub.1=f.sub.3r.sup.2/.lamda.Nf.sub.2
f.sub.1. For a general 3-D object g(x.sub.s,y.sub.s,z.sub.s),
illuminated by a narrowband incoherent illumination, the intensity
of the recorded hologram is an integral over the entire PSFs, given
by Eq. (56), over all the object points, as follows
H ( x , y ) = A ( C ' + .intg. .intg. .intg. g ( x s , y s , z s )
exp { i .pi. .lamda. d u ( z s ) [ ( x - M _ T x s ) 2 + ( y - M _
T y s ) 2 ] + i .theta. } dx s dy s dz s + .intg. .intg. .intg. g (
x s , y s , z s ) exp { - i .pi. .lamda. d o ( z s ) [ ( x - M _ T
x s ) 2 + ( y - M _ T y s ) 2 ] - i .theta. } dx s dy s dz s ) . (
57 ) ##EQU00056##
Besides a constant term C', Eq. (57) contains two terms of
correlation between an object and a quadratic phase,
z.sub.s-dependent, function, which means that the recorded hologram
is indeed a Fresnel hologram. In order to remain with a single
correlation term out of the three terms given in Eq. (57), we
follow the procedure of on-axis digital holography (J. Rosen, G.
Indebetouw, G. Brooker, Opt. Exp. 14, 4280-4285 (2006)) (J. Rosen,
and G. Brooker "Incoherent digital holography," Submitted for
publication in Opt. Lett. (November 2006)). Three holograms of the
same object are recorded each of which with a different phase
constant .theta.. The final hologram H.sub.F is a superposition
according to the following,
H F ( x , y ) = H 1 ( x , y ) [ exp ( - i .theta. 3 ) - exp ( - i
.theta. 2 ) ] + H 2 ( x , y ) [ exp ( - i .theta. 1 ) - exp ( - i
.theta. 3 ) ] + H 3 ( x , y ) [ exp ( - i .theta. 2 ) - exp ( - i
.theta. 1 ) ] . = .intg. .intg. .intg. g ( x s , y s , z s ) exp {
- i .pi. .lamda. d o ( z s ) [ ( x - M _ T x s ) 2 + ( y - M _ T x
s ) 2 ] } dx s dy s dz s . ( 58 ) ##EQU00057##
where H.sub.k is the k-th recorded hologram with the phase constant
.theta..sub.k and k=1,2,3.
[0361] A 3-D image can be digitally reconstructed from H.sub.F(x,y)
by calculating the Fresnel propagation (J. Goodman, Introduction to
Fourier Optics, 2.sup.nd ed., McGraw-Hill, New York, 1996, pp.
63-95 (Chapter 4)). The reconstruction results of different
chromatic holograms are composed together to a complete color
figure. In order to get the same transverse and axial
magnifications for all the wavelengths we change the Fresnel number
of the DOE such that d.sub.o(z.sub.s), given by Eq. (55), remains
the same for all recorded wavelengths. In other words, the Fresnel
number of the (i+1)-th wavelength .lamda..sub.i+1 is
N.sub.i+1=N.sub.i.lamda..sub.i/.lamda..sub.i+1, where N.sub.i is
the Fresnel number of the i-th wavelength .lamda..sub.i.
[0362] An experiment showing the recording of a color fluorescence
hologram was carried out on the system shown in FIG. 35. The SLM
(HOLOEYE HEO 1080P) is phase-only, and as so, the desired function
given by Eq. (54) cannot be directly displayed on this SLM.
Instead, as a good approximation for Eq. (54), we chose to display
the required quadratic phase function on only half of the SLM
pixels. The rest of the pixels were modulated with a constant
phase, where the pixels of both types were selected randomly (J.
Rosen, and G. Brooker "Incoherent digital holography," Submitted
for publication in Opt. Lett. (November 2006)). The central
1024.times.1024 pixels of the SLM, on an area of 9.7 mm.times.9.7
mm, were used for displaying the DOE. The phase constants of
.theta..sub.1,2,3=0.degree., 120.degree., 240.degree. were
introduced into the three quadratic phase functions. The other
specifications of the system are: f.sub.1=250 mm, f.sub.2=150 mm,
f.sub.3=35 mm, d.sub.1=135 mm, d.sub.2=206 mm. L.sub.1, L.sub.2,
and L.sub.3 are spherical lenses, and F.sub.1 and F.sub.2 are
chromatic filters.
[0363] A pair of 8 mm.times.8 mm dice (i.e., the 3D object 3502)
(in which some of the dots were painted with either red or green
fluorescent paint) were positioned at the vicinity of the rear
focal point of lens L.sub.1 3505. The center of the die with red
fluorescent spots and the die with green fluorescent spots were at
a distance of 228 mm and 260 mm from L.sub.1 3505, respectively.
These dice were illuminated with a mercury arc lamp (ZESS-ATTOARC
2, HBO 100W) in which only light from 444 to 500 nm with a peak
wavelength of 472 nm and a bandwidth of 56 nm was allowed to pass
through bandpass filter F.sub.1 3510. All of the holograms were
recorded by a cooled CCD camera (HAMAMATSU DIGITAL CAMERA
C4742-95.12 bit, 1024.times.1280 pixels, bin 1) and processed by a
computer. The first three holograms (0, 120 and 240 degrees) of the
non-fluorescent surfaces on the dice were recorded with an
identical filter as the source's filter mentioned above placed in
the emission filter slider F.sub.2 3504. The Fresnel number for
these holograms was chosen to be N.sub.B=10 (based upon a center
wavelength of 472 nm). The magnitude and phase of the final complex
hologram, superposed from the first three holograms, is shown in
FIGS. 36(a) and (b), respectively. The reconstruction from the
final hologram was calculated using the Fresnel propagation
formula. (J. Goodman, Introduction to Fourier Optics, 2.sup.nd ed.,
McGraw-Hill, New York, 1996, pp. 63-95 (Chapter 4)) The results are
shown at the plane of the front face of the front die [36(c)], and
at the plane of the front face of the rear die [36(d)]. Note that
in each plane a different die face is in focus as is indeed
expected from a holographic reconstruction of an object with a
volume. The second set of three holograms was recorded via a red
filter in the emission filter slider F.sub.2 3504 which passed 614
to 640 nm fluorescent light with a peak wavelength of 626 nm and a
bandwidth of 11 nm. The Fresnel number during the recording of the
`red` holograms was N=7.8. The magnitude and phase of the final
complex hologram, superposed from the `red` set, is shown in FIGS.
36(e) and (f), respectively. The reconstruction results from this
final hologram are shown in FIGS. 36 (g) and (h) at the same planes
as in FIGS. 36 (c) and (d), respectively. Finally, an additional
set of three holograms was recorded with a green filter in emission
filter slider F.sub.2 3504 which passed 500 to 532 nm fluorescent
light with a peak wavelength of 516 nm and a bandwidth of 16 nm.
The Fresnel number during the recording of the `green` holograms
was N.sub.G=9.2. The magnitude and phase of the final complex
hologram, superposed from the `green` set, is shown in FIGS. 36(i)
and (j), respectively. The reconstruction results from this final
hologram are shown in FIGS. 36 (k) and (l) at the same planes as in
FIGS. 36 (c) and (d), respectively. Compositions of FIGS. 36(c),
(g) and (k) and FIGS. 36(d), (h) and (l) are depicted in FIGS.
36(m) and (n), respectively. Note that all the colors in FIG. 36
are pseudo-colors. These last results yield a complete color 3-D
holographic image of the object including the red and green
fluorescence. While the optical arrangement in this demonstration
has not been optimized for maximum resolution, it is important to
recognize that even with this simple optical arrangement, the
resolution is good enough to image the fluorescent emissions with
good fidelity and to obtain good reflected light images of the
dice. Furthermore, in the reflected light images in FIGS. 36(c) and
36(d) the system has been able to detect reflections of the
illumination on the dice.
[0364] Thus, this example shows a process of recording color
holograms of 3-D fluorescent objects. This example motionless
system is not affected by vibrations, it does not require
complicated alignment or a laser and the bandwidth can be wider
than conventional incoherent interferometers, entirely because this
holographic recorder is implemented on a single channel setup. The
proposed design might play an important role in many types of 3D
fluorescence applications (Patents pending) including fluorescence
microscopy so that multicolor 3-D structures and dynamic processes
could be imaged without any scanning, and therefore would be
expected to be faster then other methods.
[0365] Numerous modifications and variations of the present
invention are possible in light of the above teachings. It is
therefore to be understood that within the scope of the appended
claims, the invention may be practiced otherwise than as
specifically described herein.
* * * * *