U.S. patent application number 12/728528 was filed with the patent office on 2011-09-22 for computer implemented method for generating binary holograms.
This patent application is currently assigned to CITY UNIVERSITY OF HONG KONG. Invention is credited to Wai Keung Cheung, Wai Ming Tsang.
Application Number | 20110228365 12/728528 |
Document ID | / |
Family ID | 44647049 |
Filed Date | 2011-09-22 |
United States Patent
Application |
20110228365 |
Kind Code |
A1 |
Tsang; Wai Ming ; et
al. |
September 22, 2011 |
COMPUTER IMPLEMENTED METHOD FOR GENERATING BINARY HOLOGRAMS
Abstract
A numerical method of recording a two or three dimensional
object scene in a binary hologram. When the binary hologram is
illuminated with a reference beam, the original object scene can be
reconstructed and observed by a viewer. As the hologram is binary,
i.e. composed of black or white pixels, it can be printed with
commodity printers. The process is simple, fast, and economical,
hence decreasing the cost and time for hologram design and
production. In addition, with binary holograms, the ability to
store the holograms is enhanced and binary holograms facilitate
efficient transmission of the holograms.
Inventors: |
Tsang; Wai Ming; (Hong Kong,
HK) ; Cheung; Wai Keung; (Hong Kong, HK) |
Assignee: |
CITY UNIVERSITY OF HONG
KONG
Kowloon Tong
HK
|
Family ID: |
44647049 |
Appl. No.: |
12/728528 |
Filed: |
March 22, 2010 |
Current U.S.
Class: |
359/9 |
Current CPC
Class: |
G03H 1/26 20130101; G03H
2240/21 20130101; G03H 1/22 20130101; G03H 1/0808 20130101; G03H
2240/62 20130101; G03H 1/0891 20130101; G03H 2240/41 20130101; G03H
2001/0478 20130101; G03H 2210/30 20130101; G03H 1/0011 20130101;
G03H 1/0841 20130101; G03H 1/08 20130101 |
Class at
Publication: |
359/9 |
International
Class: |
G03H 1/08 20060101
G03H001/08 |
Claims
1. A method for creating a computer-generated binary hologram of an
object scene, the method comprising: downsampling an object scene
by sampling the object scene along two or more lines defined in
each of a plurality of image planes of the object scene to provide
a plurality of downsampled images, generating a hologram comprising
a computed two-dimensional interference fringe pattern of the
downsampled images with a reference light; and binarizing the
hologram to provide a binary hologram from which the object scene
can be reproduced when the binary hologram is irradiated with a
reference light.
2. The method of claim 1, wherein the hologram comprises hologram
pixels having respective phases, and binarizing comprises assigning
binary values according to the phases of the hologram pixels.
3. The method of claim 2, wherein binarizing comprises assigning
white and black levels to positive and negative polarized hologram
pixels, respectively.
4. The method of claim 1, further comprising printing the binary
hologram on a surface of a light transmissive and/or a light
reflective medium.
5. The method of claim 4, further comprising projecting a reference
light beam onto a surface of the medium on which the binary
hologram is printed, or projecting a reference light beam from
behind and through the medium on which the binary hologram is
printed.
6. The method of claim 1, further comprising projecting the binary
hologram onto a surface of a light transmissive and/or a light
reflective medium.
7. The method of claim 6, further comprising projecting a reference
light beam onto a surface of the medium on which the binary
hologram is being projected, or projecting a reference light beam
from behind and through the medium on which the binary hologram is
being projected.
8. The method of claim 7, further comprising projecting a series of
time-sequenced binary holograms onto the surface of a light
transmissive and/or a light reflective medium and generating a
three-dimensional moving image.
9. The method of claim 1, wherein the two or more lines intersect
each other.
10. The method of claim 1, wherein the two or more lines comprises
two or more sets of spaced apart lines.
11. The method of claim 10, wherein the lines of one set intersect
the lines of at least one other set.
12. The method of claim 10, wherein the two or more sets of lines
comprise sets of non-uniformly spaced lines.
13. The method of claim 10, wherein the two or more sets of lines
comprise sets of uniformly spaced lines.
14. The method of claim 10, wherein the two or more sets of lines
comprise four sets of intersecting lines.
15. The method of claim 14, wherein the four sets of lines comprise
a first set of lines passing horizontally through a respective
image plane, a second set of lines passing vertically through the
image plane, a third set of lines passing diagonally downwards from
left to right through the image plane, and a fourth set of lines
passing diagonally upwards from left to right through the image
plane.
16. A system for creating a computer-generated binary hologram of
an object scene, the system comprising: means for downsampling an
object scene by sampling each of a plurality of image planes of the
object scene along two or more lines defined in each image plane of
the object scene to provide a plurality of downsampled images,
means for generating a hologram comprising a computed
two-dimensional interference fringe pattern of the plurality of
downsampled images with a reference light; and means for binarizing
the hologram to provide a binary hologram from which the object
scene can be reproduced when the binary hologram is irradiated with
a reference light.
17. A method for reproducing an object scene recorded in a
computer-generated binary hologram, wherein the computer-generated
binary hologram has been created using the method of claim 1, the
method comprising: printing or projecting the binary hologram on a
surface of a light transmissive and/or a light reflective medium;
and projecting a reference light beam onto a surface of the medium
on which the binary hologram is printed or projected, or projecting
a reference light beam from behind and through the medium on which
the binary hologram is printed or projected.
18. The method of claim 17, further comprising projecting a series
of times-sequenced binary holograms onto said surface of a light
transmissive and/or a light reflective medium and generating a
three-dimensional moving image.
19. A system for reproducing an object scene recorded in a
computer-generated binary hologram, wherein the computer-generated
binary hologram has been created using the method of claim 1, the
system comprising: means for printing or projecting the binary
hologram on a surface of a light transmissive and/or a light
reflective medium; and means for projecting a reference light beam
onto a surface of the medium on which the binary hologram is
printed or projected, or projecting a reference light beam from
behind and through the medium on which the binary hologram is
printed or projected.
Description
FIELD OF THE INVENTION
[0001] The invention relates to a computer implemented method for
generating binary holograms and, in particular, to a method of
generating binary holograms that does not make use of thresholding
or injecting noise signals into the holograms in order to binarize
them.
BACKGROUND OF THE INVENTION
[0002] In holography, some of the light scattered from an object or
a set of objects falls on a recording medium. A second light beam,
known as the reference beam, also illuminates the recording medium,
so that interference occurs between the two beams. The resulting
light field is an apparent fringe pattern of varying intensity
which is the hologram. It can be shown that if the hologram is
illuminated by the original reference beam, a light field is
diffracted by the reference beam which is identical to the light
field which was scattered by the object or objects. Thus, someone
looking into the hologram "sees" the objects even though they are
no longer present. There are a variety of recording materials which
can be used, including photographic film. Holograms can also be
computer generated.
[0003] In the past holograms have usually been binarized by
thresholding, or injecting noise signals into the holograms using
methods such as the random phase or the error diffusion (or
similar) methods. These approaches either result in poor and/or
noisy reconstructed images, or the structural content is degraded,
sometimes to the degree that no discernable image can be
reproduced.
[0004] It has previously been shown through computer generated
holography (CGH) that a three-dimensional object scene can be
recorded as, or represented by, a binary hologram instead of a
gray-scale hologram, i.e. the pixels forming the hologram comprise
binary values rather than eight or sixteen bit grey scale values,
for example. Binary encapsulation of holograms therefore allows the
holograms to be recorded with much smaller data sizes, and enables
the swift production of printed holographic images on suitable
mediums using commodity printers which are only capable of
outputting black and white dots. For static object scenes, this
means of production is substantially lower in cost than the
conventional use of a spatial light modulator, and also enables
printing or display of very large holograms on suitable media. When
a binary hologram is displayed on an electronically accessed
display device, such as a spatial light modulator, the
reconstructed image of the object scene recorded by the hologram is
not affected by the non-linear characteristics of the display
device. In addition, with binary holograms, the storage capacity of
the binary holograms is enhanced and this facilitates much more
efficient transmission of holograms over transmission media.
[0005] Investigations have been conducted to understand the causes
of and address the distortions caused by quantization or digitizing
of grey-scale holograms, but little, if anything, appears to have
been done to address problems encountered with binary computer
generated holograms which have been found to produce severe
distortion upon reconstruction. In particular, if the original
object is complicated, there may be no discernable reconstruction
of the recorded image possible or the hologram will not allow the
original object scene to be reproduced for viewing.
OBJECTS OF THE INVENTION
[0006] An object of the invention is to mitigate or obviate to some
degree one or more problems associated with known methods of
computer generated binary holograms.
[0007] The above object is met by the combination of features of
the main claim; the sub-claims disclose further advantageous
embodiments of the invention.
[0008] One skilled in the art will derive from the following
description other objects of the invention. Therefore, the
foregoing statement of object is not exhaustive and serves merely
to illustrate some of the many objects of the present
invention.
SUMMARY OF THE INVENTION
[0009] In a first main aspect of the invention, there is provided a
method for creating a computer generated binary hologram of an
object scene, said method comprising the steps of: downsampling an
object scene by sampling said object scene along two or more lines
defined in each of a plurality of image planes of said object scene
to provide a plurality of downsampled images, generating a hologram
comprising a computed two-dimensional interference fringe pattern
of said downsampled images with a reference light; and binarizing
said hologram to provide a binary hologram from which the object
scene can be reproduced when irradiated with a reference light.
[0010] The step of binarizing comprises assigning binary values
according to the phases of the hologram pixels. This may involve
assigning white and black levels respectively to positive and
negative polarized hologram pixels.
[0011] The method may comprise the step of printing the binary
hologram on a surface of a light transmissive and/or a light
reflective medium, preferably using a conventional black/white
printer. The method may also comprise the step of projecting a
reference light beam onto a surface of the medium on which the
binary hologram is printed, or projecting a reference light beam
from behind and through the medium on which the binary hologram is
printed, thus enabling the original object scene to be reproduced
for viewing by a viewer.
[0012] Additionally or alternatively, the method of may comprise
the step of projecting the binary hologram onto a surface of a
light transmissive and/or a light reflective medium. This may also
include the step of projecting a reference light beam onto a
surface of the medium on which the binary hologram is being
projected, or projecting a reference light beam from behind and
through the medium on which the binary hologram is being projected.
It may also include step of projecting a series of times-sequenced
binary holograms onto said surface of a light transmissive and/or a
light reflective medium in order to generate a three-dimensional
moving image.
[0013] The method may involve using two or more lines which
intersect each other. The two or more lines may comprise two or
more sets of spaced apart lines where the lines of one set may
intersect the lines of at least one other set. The two or more set
of lines may comprise sets of non-uniformly spaced lines or
uniformly spaced lines. The two or more set of lines may comprise
four sets of intersecting lines which may include a first set of
lines passing horizontally through the respective image plane, a
second set of lines passing vertically through said image plane, a
third set of lines passing diagonally downwards from left to right
through the image plane, and a fourth set of lines passing
diagonally upwards from left to right through the image plane.
[0014] In a second main aspect of the invention, there is provided
a system for creating a computer generated binary hologram of an
object scene, said system comprising: means for downsampling an
object scene by sampling said object scene along two or more lines
defined in a plurality of image planes of said object scene to
provide a corresponding plurality of downsampled images, means for
generating a hologram comprising a computed two-dimensional
interference fringe pattern of said plurality of downsampled images
with a reference light; and means for binarizing said hologram to
provide a binary hologram from which the object scene can be
reproduced when irradiated with a reference light.
[0015] In a third main aspect of the invention, there is provided a
method for reproducing an object scene recorded in a computer
generated binary hologram, where said computer generated binary
hologram has been created using the method of the first main
aspect, said method comprising the steps of: printing or projecting
the binary hologram on a surface of a light transmissive and/or a
light reflective medium; and projecting a reference light beam onto
a surface of the medium on which the binary hologram is printed or
projected, or projecting a reference light beam from behind and
through the medium on which the binary hologram is printed or
projected.
[0016] The method may comprise the step of projecting a series of
time-sequenced binary holograms onto said surface of a light
transmissive and/or a light reflective medium in order to generate
a three-dimensional moving image.
[0017] In a fourth main aspect of the invention, there is provided
a system for reproducing an object scene recorded in a computer
generated binary hologram, where said computer generated binary
hologram has been created using the method of the first main
aspect, said system comprising: means for printing or projecting
the binary hologram on a surface of a light transmissive and/or a
light reflective medium; and means for projecting a reference light
beam onto a surface of the medium on which the binary hologram is
printed or projected, or projecting a reference light beam from
behind and through the medium on which the binary hologram is
printed or projected.
[0018] The summary of the invention does not necessarily disclose
all the features essential for defining the invention; the
invention may reside in a sub-combination of the disclosed
features.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The foregoing and further features of the present invention
will be apparent from the following description of preferred
embodiments which are provided by way of example only in connection
with the accompanying figures, of which:
[0020] FIG. 1 is a diagram showing a general hologram creation
method using an optical technique;
[0021] FIG. 2 is a diagram showing a general hologram creation
method using a computer implemented method;
[0022] FIGS. 3a to c illustrate a solid square, its on-axis
hologram before binarization, and its on-axis hologram after
binarization, respectively;
[0023] FIG. 3d is an intensity profile along the horizontal dotted
line of the hologram in FIG. 3b;
[0024] FIG. 3e is an intensity profile along the horizontal dotted
line of the hologram in FIG. 3c;
[0025] FIG. 3f is a reconstruction of the binarized hologram in
FIG. 3c;
[0026] FIG. 4a is an image "CTU";
[0027] FIG. 4b is an image referred to as "Lenna";
[0028] FIG. 4c is a reconstruction of a binary hologram formed by a
known technique of the image "CTU" in FIG. 4a;
[0029] FIG. 4d is a reconstruction of a binary hologram formed by a
known technique of the image "Lenna" in FIG. 4b;
[0030] FIG. 5 is a flowchart of the method of generating a
binarized hologram in accordance with the method of the
invention;
[0031] FIG. 6a shows the original oversampled signal I;
[0032] FIG. 6b shows the original oversampled signal of FIG. 6a's
spectrum with f.sub.s as a sampling frequency;
[0033] FIG. 6c shows the downsampled signal I;
[0034] FIG. 6d shows the downsampled signal of FIG. 6c's spectrum
with f.sub.s as a sampling frequency;
[0035] FIG. 7a is a line trace across the center of the hologram of
the solid square in FIG. 3a after down-sampling by 16 times in
accordance with the method of the invention;
[0036] FIG. 7b is a line trace across the center of the binarized
hologram of the solid square in FIG. 3a after down-sampling by 16
times in accordance with the method of the invention;
[0037] FIG. 8a is a reconstruction of hologram of a white square
after down-sampling by 16 times in accordance with the method of
the invention;
[0038] FIG. 8b is a reconstruction of hologram of the image "CTU"
after down-sampling by 16 times in accordance with the method of
the invention;
[0039] FIG. 8c is a reconstruction of hologram of the image "Lenna"
after down-sampling by 16 times in accordance with the method of
the invention;
[0040] FIG. 9a is an optical reconstruction of the hologram of a
white square using conventional techniques;
[0041] FIG. 9b is an optical reconstruction of the hologram of the
image "CTU" using conventional techniques;
[0042] FIG. 9c is an optical reconstruction of the hologram of a
white square after down-sampling by 16 times in accordance with the
method of the invention;
[0043] FIG. 9d is an optical reconstruction of the hologram of the
image "CTU" after down-sampling by 16 times in accordance with the
method of the invention;
[0044] FIG. 9e is an optical reconstruction of the hologram of the
image "Lenna" after down-sampling by 16 times in accordance with
the method of the invention; and
[0045] FIG. 10 is a block schematic diagram of a binary hologram
generation and reproduction system according to the invention.
DESCRIPTION OF PREFERRED EMBODIMENTS
[0046] The following description is of a preferred embodiment by
way of example only and without limitation to the combination of
features necessary for carrying the invention into effect.
[0047] In order to understand the novel method disclosed herein, it
is firstly useful to understand some general techniques relating to
the generation of holograms and to understand how distortion occurs
in binary holograms generated using conventional techniques.
[0048] FIG. 1 is a diagram showing a general hologram creation
method using an optical method, in which a method for recording an
object scene 10, i.e. an original image, on a recording surface 20
as interference fringes is shown. An XYZ three-dimensional
coordinate system is defined as illustrated, and the recording
surface 20 is placed on an XY plane. An object scene to be a
recording target is prepared as the original image 10. An object
light O emitted from an arbitrary point P on the original image 10
proceeds toward the entire surface of the recording surface 20. A
reference light R is irradiated onto the recording surface 20.
Consequently, interference fringes of the object light O and
reference light R are recorded on the recording surface 20. From
the hologram recorded on the recording surface 20, it is possible
by use of the reference signal to reproduce the original image for
viewing by a user, although a spatial light modulator as known in
the art may be required for image viewing.
[0049] Referring to FIG. 2, in order to create a computer generated
hologram at the position of the recording surface 20, the object
scene (original image) 10, recording surface 20, and reference
light R are respectively defined as data on a computer, and
interference wave intensities at respective positions on the
recording surface 20 are calculated using processor means of the
computer and suitably encoded processor executable instructions
stored in a memory of the computer. As shown in FIG. 2, the
original image 10 may be considered as comprising a matrix of N
point light sources P1, P2, P3, . . . , Pi, . . . , P.sub.N. In
theory, there would be an infinite number of such point light
sources, but, in practice, the number is determined according to
factors such as the capabilities of the computer processor and the
desired resolution of reproduced images. From the multiple point
light sources, it can be considered that these provide respective
object lights O1, O2, O3, . . . , Oi, . . . , O.sub.N proceeding to
a calculation point Q(x, y). The reference light R is irradiated
toward the calculation point Q(x, y), and a calculation is carried
out to determine amplitude intensity of an interference wave caused
by an interference between these N object lights O1 to O.sub.N and
reference light R at the point of the calculation point Q(x, y).
The object lights and reference light are considered as
monochromatic lights to carry out the calculation. On the recording
surface 20, a large number of calculation points are defined at a
predetermined pitch, and for each of the calculation points,
amplitude intensity is calculated, whereby an intensity
distribution of interference waves can be obtained on the recording
surface 20. From the computer generated hologram calculated for the
recording surface 20, it is possible to reproduce the original
image for viewing by a user. Reference is made herein to
US2008/0225359. It will be appreciated that this comprises one
computer implemented mathematical method for generating a hologram
using a computer, but that other computer implemented method are
known.
[0050] In either case, the recorded holograms can be binarized
using known techniques.
[0051] One way to produce a physical binary hologram from a
computer generated hologram is to create a binary pattern on an
actual medium based on image data comprising the intensity
distribution of the recorded hologram. By this means a binary
hologram for which the original image 10 has been computed by
processing means as interference fringes can be created. With
existing techniques, however, the use of a spatial light modulator
may be necessary for reproducing the original image from the
hologram.
[0052] As already indicated, known binary holograms have been found
to produce severe distortion upon image reproduction such that the
hologram will not reproduce the original object scene to any
discernible degree. The reasons for this may be understood from the
following.
[0053] A generic way of binarization is to assign white and black
levels to positive and negative hologram pixels, respectively. The
process also reduces the data size of the hologram as each pixel is
only represented with 1 bit. To illustrate the binarization effect,
a solid square, and its on-axis hologram before and after
binarization are shown in FIGS. 3a) to 3c), respectively. The
intensity profile along the horizontal dotted line of the hologram
is shown in FIG. 3d) while in FIG. 3e) is shown a line trace across
the center of the binarized hologram. Finally, in FIG. 3f), there
is shown the reconstruction of the binarized hologram in which it
can be seen that severe distortion occurs which renders the
reproduced binary image almost indiscernible. The reconstruction
does show, however, an interesting edge extraction of the original
object. This may be explained by noticing that the small high
frequency fringes (away from the center of the hologram) in the
intensity profile of FIG. 3d) have been emphasized, thereby
creating highpass-type filtering on the original un-binarized
hologram.
[0054] In FIGS. 4a) and b), shown is a binary image "CTU" and a
picture of "Lenna," respectively. Their respective reconstructions
after binarization of their holograms are shown in FIGS. 4c and
4d). Again, note that for the binary object as in "CTU", the
binarized hologram shows an effective edge extracted
reconstruction, although the reproduced image is of poor quality.
However, for the more complicated grey-scale image such as that of
Lenna, there is much more severe distortion, namely of the interior
content, which is due to the nonlinearity created by binarization.
In fact, no discernable reconstructed image can be observed.
[0055] In accordance with the novel method of the invention, the
object scene shown in FIG. 2, which may be considered as comprising
a matrix of N point light sources P1, P2, P3, . . . , Pi, . . . ,
P.sub.N, can be represented as a sequence of discrete image planes
which are parallel to the hologram plane. Each image plane I(u,v;
z.sub.j) contains the point light sources that are at a depth of
z.sub.j from a holographic recording plate. On the image plane
I(u,v; z.sub.j), if a location contains a point light source, the
corresponding pixel intensity is set to the intensity of the said
point light source. Otherwise, the intensity of the pixel is set to
zero. Given a discrete object scene which can be represented by a
sequence of planar images I(u,v; z.sub.j) each located at a depth
z.sub.j from a holographic recording plane, a Fresnel hologram
H(m,n) can be generated numerically as the real part of the product
of the object O(m,n) and a planar reference R(m,n) waves.
H(m,n)=Re{O(m,n)R*(m,n)}, (1)
where Re{.} represents the real part of a complex number. The
object wave is given by
O ( m , n ) = j = 0 J - 1 O ( m , n ; z j ) ( 2 a )
##EQU00001##
where J is the total number of image planes, and
O ( m , n ; z j ) = u = 0 X - 1 v = 0 Y - 1 I ( u , v ; z j ) exp (
kr ( m - u , n - v ; z j ) ) r ( m - u , n - v ; z j ) , ( 2 b )
##EQU00002##
where m, u and n, v are the discrete coordinate points along the
vertical and horizontal directions, respectively. The term
r(m-u,n-v;z.sub.j)= {square root over
((m-u).sup.2+(n-v)+z.sub.j.sup.2)}{square root over
((m-u).sup.2+(n-v)+z.sub.j.sup.2)} represents the Euclidean
distance between an object point at (u,v) on the image plane I(u,v;
z.sub.j) and the location (m,n) on the plane of the hologram. X and
Y are the vertical and horizontal extents of the image,
k=2.pi./.lamda. is the wave-number and .lamda. is the wavelength of
the optical beam. All pixels in the image are assumed to be self
illuminating with intensity I(u,v; z.sub.j). The reference wave
R(m,n) is assumed to be a plane wave or a spherical wave incident
at an angle .theta. with respect to the normal of the hologram. If
the reference wave is a plane wave, it can be represented by R(m)
for simpler optical geometry.
[0056] Eq. (2b) can be encapsulated as the two dimensional
convolution of the source image with the Fresnel Zone Plate F(m,n;
z.sub.j).
O(m,n;z.sub.j)=I(m,n;z.sub.j)*F(m,n;z.sub.j) (3)
where F(m,n; z.sub.j)=exp(ikr(m,n;z.sub.j))/r(m,n;z.sub.j).
Adopting the convolution operation in Eq. (3) in place of Eq. (2b),
the source image is expressed as a function of m and n (i.e. I(m,n;
z.sub.j)).
[0057] In the foregoing, it is assumed that the parallel images
planes are informly spaced from each other. However, it will be
understood that the parallel image planes may be non-uniformly
spaced. In general, an image plane is included for downsampling
whenever it contains one or more point light source(s) in the
object scene. There is no limit on the number of image planes that
may be downsampled. However, in practical implementations of the
method, it is simpler to assume a sequence of regularly spaced
parallel image planes. For any such image planes that do not
contain any point light sources, all the pixels are set to zero
intensity and will not therefore contribute to the computer
generation of the hologram.
[0058] It is envisaged that the object scene will, in most
implementations of the method, comprise a virtual object scene,
i.e. a computer generated object scene. However, if it comprises a
real scene, it will firstly be converted into a digital
representation OBJ(x,y,z) by an imaging means such as a digital
camera or a camera with associated digital processing means, where
x, y, z are the discrete rectangular coordinates of the three
dimensional object scene space. OBJ(x,y,z) denotes the amplitude of
an object point (if any) at position (x,y,z). If OBJ(x,y,z)=0, it
means that there is no object point at (x,y,z). Each point
OBJ(x,y,z) will be taken as a point light source in the calculation
of the hologram.
[0059] The novel method for generating binary holograms according
to the invention is illustrated by FIG. 5. The method comprises the
steps of downsampling 100 each of a plurality of images planes of
the object scene along multiple directions, generating 110 a
hologram from the plurality of downsampled object scene image
planes, binarizing 120 the hologram according to the polarities of
the hologram pixels, and printing or displaying 130 the binary
hologram using a printer or an electronically accessed display. The
method involves down-sampling the object scene by sampling each
image plane I(m,n; z.sub.j) of the said object scene along two or
more lines defined in each image plane of said object scene to
provide a sequence of downsampled images. Preferably, downsampling
involves using a matrix of spaced part horizontal, vertical, and
diagonal grid lines before binarization, where the grid lines may
be uniformly spaced. However, the down-sampling may use non-uniform
spaced grid lines. As such, the novel method of the invention does
not make use of thresholding or injecting noise signals into the
holograms in order to binarize them.
[0060] The following description of the novel method is based on
using uniformly spaced grid lines by way of example only, but it
will be understood that the method can use non-uniformly spaced
lines or even just a plurality of single lines in various
orientations with respect to the image plane.
[0061] For uniform spaced grid lines, each down-sampled image plane
I.sub.D(m,n; z.sub.j) is represented as follows:
I D ( m , z ; z j ) = I 1 ( m , n ; z j ) I 2 ( m , n ; z j ) I 3 (
m , n ; z j ) I 4 ( m , n ; z j ) where I 1 ( m , n ; z j ) = { I (
m , n ; z j ) m = .tau. M 0 otherwise , I 2 ( m , n ; z j ) = { I (
m , n ; z j ) n .tau. M 0 otherwise , I 3 ( m , n ; z j ) = { I ( m
, n ; z j ) m = n = .tau. M 0 otherwise I 4 ( m , n ; z j ) = { I (
m , n ; z j ) m = .tau. M , n = - .tau. M 0 otherwise ( 4 )
##EQU00003##
.tau. is an integer running from 0, .+-.1, .+-.2, . . . . M is an
integer denoting the spacing between adjacent grid lines. The
operator u denotes the union of the multiple sets of data
I.sub.1(m,n; z.sub.j) to I.sub.4(m,n; z.sub.j), representing
sub-sampling of the image I(m,n; z.sub.j) along the vertical,
horizontal, and diagonal directions. Sub-sampling tends to fill in
or strengthen some frequency contents of the hologram before
binarization.
[0062] For non-uniformly spaced lines, the foregoing relationships
may be adapted to include a random number factor operating on the
line spacing M. For example, for I.sub.1(m,n; z.sub.j)) the
relationship m=.tau.M may be amended to m=a.tau.M, where a, is a
random number which may have a value>zero and which is
preferably in the range from 0.5 to 1.5, although other ranges may
be preferred based on empirical measurements.
[0063] In respect of uniformly spaced lines, to clarify further,
I.sub.1 is formulated mathematically in one dimension in terms of
I. Thus, the sub-sampled signal can be written along the
m-direction as
I 1 ( m ) = I ( m ) r = - .infin. .infin. .delta. ( m - rM ) ( 5 )
##EQU00004##
[0064] For illustration, m is treated as a time variable t and the
spectrums of I with f as a frequency variable. FIG. 6a) shows the
original oversampled signal I and its spectrum with f.sub.s as a
sampling frequency, which is shown in FIG. 6b). f.sub.A denotes the
bandwidth of I. Assuming that the original signal is band-limited
to avoid aliasing error, the sub-sampling of the original signal
I.sub.1 and its spectrum are shown in FIGS. 6c) and 6d),
respectively for M=4. Note that for M=4, the sub-sampled signal has
four repeated spectra within the range from 0 to f.sub.s.
[0065] Returning to the equation of the hologram in Eq. (3), if the
Fresnel zone plate F(m,n; z.sub.j) is regarded as an input with
I(m,n; z.sub.j) being an impulse response then, since I(m,n;
z.sub.j) is a non-negative function, it can be considered that it
performs low-pass filtering (see the spectrum of the original
signal on FIG. 6b) on the fringes (Fresnel zone plates) presented
on the hologram. After sub-sampling, since the lowpass filter now
has been repeated along f as shown in FIG. 6d), this has the effect
of filling in some of the missing frequencies, namely those
frequencies around f.sub.s/M, 2f.sub.S/M, etc. as shown in FIG.
6d).
[0066] To illustrate the effect of sub-sampling, the square in FIG.
3a) is down-sampled by 16 times according to Eq. (5). Line traces
across the center of the holograms before and after binarization
are shown in FIGS. 7a) and 7b). These line traces can be compared
with FIGS. 3d) and 3e), respectively. It is observed that in FIG.
7b), there are now some fringes, albeit binarized, in the center
portion of the figure, which are responsible for bringing some of
the contents or details back into the original image.
[0067] FIGS. 8a), b) and c) show the reconstructions of the
proposed method. The source images are down-sampled based on Eq.
(4) or (5) with a factor M=16 before binarization. The factor is
selected as it results in good visual quality for all the
reconstructed images. In comparison with the results in FIGS. 3f),
4c) and 4d), respectively, it can be seen that the interior regions
of the images are preserved with better quality.
[0068] To further substantiate the novel method according to the
invention, computer generated holograms (CGHs) were prepared for
optical reconstruction. Each such hologram size was about 25 mm by
25 mm with 1024 by 1024 points/pixels. The holograms were
computer-generated with the following parameters:
.lamda.=0.65 .mu.m, z.sub.0=0.4 m with off-axis incident angle of
.theta.=1.2.degree.. All holograms were printed with a printer with
2400 dpi on Agfa Red Sensitive films, and illuminated by a laser
beam (reference light) for optical reconstruction. FIGS. 9a) and b)
show the optical reconstructions for the "square" and "CTU" using
conventional techniques which can be compared directly with
computer simulation results of FIGS. 3f) and 4c), respectively,
showing extensive distortion. Optical reconstructions using the
method of the invention based on the proposed downsampled images
are shown in FIGS. 9c) to 9e), which show basically the same
observations as obtained in FIGS. 8a) to 8c), respectively, namely
that the reproduced 3D image is less distorted and more complete,
i.e. fuller, than the images (FIGS. 9a and 9b) optically reproduced
from computer generated holograms formed using known methods.
[0069] It can be inferred from Eq. (5) that the higher the
down-sampling factor M, the larger will be the proportion of the
pass-band in the transfer function between the frequency range from
0 to f.sub.s as seen from FIG. 6d). As a result, this will decrease
the resolution of the source image I(m,n; z.sub.j), constituting to
certain degree of distortion. However, the increase of M will lead
to high diffraction efficiency for optical reconstruction. The
optimal choice of M varies between different object scenes and is
determined empirically (e.g., via simulation) prior to printing.
However a down-sampling factor between 8 to 20 generally results in
acceptable visual quality. Finally, as sub-sampling is merely a
pixel selection process, the additional amount of arithmetic
operations involved in the computation of the hologram is
negligible, which is desirable in the generation of CGHs.
[0070] Form the foregoing it can be seen that the invention
provides a method for creating a computer generated binary hologram
of an object scene. The method comprises the steps of: downsampling
the object scene by sampling said object scene along two or more
lines defined in each of a plurality of image planes of said object
scene to provide a plurality of corresponding downsampled images
and generating a hologram comprising a computed two-dimensional
interference fringe pattern of said plurality of downsampled images
with a reference light. The hologram is then binarized to provide a
binary hologram from which the object scene can be reproduced when
irradiated with a reference light.
[0071] The step of binarizing comprises assigning binary values
according to the phases of the hologram pixels. This may involve
assigning white and black levels respectively to positive and
negative polarized hologram pixels.
[0072] The method may comprise the step of printing the binary
hologram on a surface of a light transmissive and/or a light
reflective medium, preferably using a conventional black/white
printer. The method may also comprise the step of projecting a
reference light beam onto a surface of the medium on which the
binary hologram is printed, or projecting a reference light beam
from behind and through the medium on which the binary hologram is
printed, thus enabling the original object scene to be reproduced
for viewing by a viewer.
[0073] Additionally or alternatively, the method of may comprise
the step of projecting the binary hologram onto a surface of a
light transmissive and/or a light reflective medium. This may
include the step of projecting a reference light beam onto a
surface of the medium on which the binary hologram is being
projected, or projecting a reference light beam from behind and
through the medium on which the binary hologram is being projected.
It may also include step of projecting a series of times-sequenced
binary hologram onto said surface of a light transmissive and/or a
light reflective medium in order to generate a three-dimensional
moving image.
[0074] The method may involve using two or more lines which
intersect each other. The two or more lines may comprise two or
more sets of spaced apart lines where the lines of one set may
intersect the lines of at least one other set. The two or more set
of lines may comprise sets of non-uniformly spaced lines or
uniformly spaced lines. The two or more set of lines may comprise
four sets of intersecting lines which may include a first set of
lines passing horizontally through the respective image plane, a
second set of lines passing vertically through said image plane, a
third set of lines passing diagonally downwards from left to right
through the image plane, and a fourth set of lines passing
diagonally upwards from left to right through the image plane.
[0075] The invention also provides a system 200 for creating a
computer generated binary hologram as illustrated in FIG. 10. The
system comprises a memory 210 storing processor executable
instructions and a processor 220 adapted to execute said
instructions in order to implement the method of the invention. The
processor is also adapted to downsample the object scene in
accordance with the method as described above. The system may
include an object imaging scene means 225 such as a digital camera
or a camera with associated processing means for capturing a
digital image of the object scene where the object scene is a real
scene. In such case, the processor 220 is adapted to generate from
the captured digital image the plurality of image planes for the
object scene. The system 200 may also be adapted as a system for
producing physical holograms by being connected to a printer 230
for printing said holograms onto a suitable light transmissive or
light reflective medium as a black and white image. Additionally or
alternatively, the system 200 may be adapted to display the
hologram by projecting it onto a suitable screen or medium. The
system includes light irradiating means 240 for directing or
projecting a reference light onto a printed or displayed hologram
in order to reproduce the original object scene for viewing by a
viewer. The system 200 may also be adapted to project a times
sequence of holograms onto said screen to enable a moving image in
3D to be reproduced for viewing by users.
[0076] It is possible with the method of the invention to store a
plurality of holograms on the same recording medium by using
different wavelengths for the reference light or different angles
of incidence of the reference light in generation of the respective
holograms. This enhances the storage efficiency of the holograms as
well as providing a useful security feature on bank cards, bank
notes, etc. In fact, holograms generated according to the method of
the invention are particularly suited as security devices as they
can be printed using conventional printers, but are such that they
cannot be reproduced in a photocopy of a medium carrying one of the
holograms generated according to the invention and printed using a
conventional printer. This has the advantage of enabling security
holograms to be easily printed on less valuable items than bank
cards or bank notes or at least making available more widely the
use of holograms as a security feature at low cost. For example,
the hologram could be printed using conventional printers on say
product labels of goods such as perfume or even less high value
goods than this.
[0077] In general, the invention describes a novel numerical method
of recording a two or three dimensional (2D or 3D) object scene in
a binary hologram. When the latter is illuminated with a reference
beam the original object scene can be reconstructed and observed by
a viewer. As the hologram is binary, i.e. composed of black or
white pixels, it can be printed with commodity printers. The
process is simple, fast, and economical, hence decreasing the cost
and time in hologram design and production. In addition, with
binarized holograms, the storage capacity of digital holograms is
enhanced and it facilitates more efficient transmission of the
holograms.
[0078] With the method discussed herein, the reconstructed image is
less noisy in shaded areas. Moreover sharp edges and structural
content are preserved. It can be viewed easily with different kinds
of visible light sources (such as LEDs, spot light, and tungsten
lamp) as the reference light. The information recorded in the
hologram is also more resistant to damage than existing hologram
recording and display approaches.
[0079] While the invention has been illustrated and described in
detail in the drawings and foregoing description, the same is to be
considered as illustrative and not restrictive in character, it
being understood that only exemplary embodiments have been shown
and described and do not limit the scope of the invention in any
manner. It can be appreciated that any of the features described
herein may be used with any embodiment. The illustrative
embodiments are not exclusive of each other or of other embodiments
not recited herein. Accordingly, the invention also provides
embodiments that comprise combinations of one or more of the
illustrative embodiments described above. Modifications and
variations of the invention as herein set forth can be made without
departing from the spirit and scope thereof, and, therefore, only
such limitations should be imposed as are indicated by the appended
claims.
[0080] In the claims which follow and in the preceding description
of the invention, except where the context requires otherwise due
to express language or necessary implication, the word "comprise"
or variations such as "comprises" or "comprising" is used in an
inclusive sense, i.e. to specify the presence of the stated
features but not to preclude the presence or addition of further
features in various embodiments of the invention.
[0081] It is to be understood that, if any prior art publication is
referred to herein, such reference does not constitute an admission
that the publication forms a part of the common general knowledge
in the art, in Australia or any other country.
* * * * *