U.S. patent application number 15/605179 was filed with the patent office on 2017-11-16 for apparatus for producing a hologram.
The applicant listed for this patent is CELLOPTIC, INC.. Invention is credited to Gary BROOKER, Joseph ROSEN, Nisan SIEGEL.
Application Number | 20170329280 15/605179 |
Document ID | / |
Family ID | 48574924 |
Filed Date | 2017-11-16 |
United States Patent
Application |
20170329280 |
Kind Code |
A1 |
ROSEN; Joseph ; et
al. |
November 16, 2017 |
APPARATUS FOR PRODUCING A HOLOGRAM
Abstract
An apparatus for producing a hologram includes a collimation
lens configured to receive incoherent light emitted from an object;
a spatial light modulator (SLM) that includes at least one
diffractive lens which is configured to receive the incoherent
light from the collimation lens and split the incoherent light into
two beams that interfere with each other; and a camera configured
to record the interference pattern of the two beams to create a
hologram, wherein a ratio between a distance from the SLM to the
camera and a focal length of the diffractive lens is greater than
1.
Inventors: |
ROSEN; Joseph; (Omer,
IL) ; BROOKER; Gary; (Rockville, MD) ; SIEGEL;
Nisan; (Silver Spring, MD) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CELLOPTIC, INC. |
Rockville |
MD |
US |
|
|
Family ID: |
48574924 |
Appl. No.: |
15/605179 |
Filed: |
May 25, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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14363380 |
Jun 6, 2014 |
9678473 |
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PCT/US2012/068486 |
Dec 7, 2012 |
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15605179 |
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61567930 |
Dec 7, 2011 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G03H 2001/0452 20130101;
G03H 1/041 20130101; G03H 2001/0224 20130101; G03H 1/06 20130101;
G03H 1/0005 20130101; G03H 1/0443 20130101; G03H 2001/0447
20130101; G03H 2001/005 20130101; G03H 2223/23 20130101 |
International
Class: |
G03H 1/00 20060101
G03H001/00; G03H 1/06 20060101 G03H001/06; G03H 1/04 20060101
G03H001/04; G03H 1/04 20060101 G03H001/04 |
Goverment Interests
GOVERNMENT RIGHTS
[0002] This invention was made with U.S. government support under
grant 60NANB10D008 awarded by the National Institute of Standards
and Technology (NIST). The U.S. government has certain rights in
the invention.
Claims
1. (canceled)
2. A system configured to examine a sample by both regular
microscopy and Fresnel Incoherent Correlation Holography (FINCH),
the system comprising: a mirror slider configured to position a
reflective mirror into a path of light emitted from an object when
the system is set to perform regular microscopy, and to remove the
reflective mirror from the path when the system is set for FINCH; a
beam splitter configured to receive the light emitted from the
object and reflected off the reflective mirror when the system is
set to perform regular microscopy; an imaging camera configured to
record an image formed at the system output; a reflective spatial
light modulator (SLM) configured to receive the light emitted from
the object when the system is set for FINCH, and to split the light
into two beams that interfere with each other; and a holography
camera configured to record the interference pattern of the
interfering light beams to create a hologram, wherein the SLM is
configured at an angle with respect to the image slide.
3. The system according to claim 2, wherein the SLM is transmissive
in-line in the optical path with respect to the image slide.
4. The system according to claim 2, wherein the SLM is configured
at an angle of 45 degrees with respect to the image slide.
5. The system according to claim 2, further comprising an output
polarizer between the SLM and the holography camera such that the
two beams pass through the output polarizer.
6. The system according to claim 2, wherein the beam splitter is
arranged to split the light reflected off the reflective mirror in
to a first light beam directed to an imaging camera and a second
light beam directed to a monocular viewing port.
7. The system according to claim 2, further comprising a tube lens
arranged between the reflective mirror and the beam splitter.
8. The system according to claim 2, further comprising an input
polarizer slider that is controllable to move an input polarizer
into the path of light emitted from an object.
9. The system according to claim 8, wherein the input polarizer is
arranged in the path between the dichroic mirror and the SLM.
10. The system according to claim 9, wherein when the system is set
for FINCH the reflective mirror is not in the path and the input
polarizer is in the path, and when the system is set to perform
regular microscopy the reflective mirror is in the path and the
input polarizer is not in the path.
11. The system according to claim 2, wherein the system is
configurable, by changing a position of the reflective mirror by
manipulating the mirror slider, to compare FINCH to standard
fluorescence microscopy on the same identical sample without change
in position or focus.
12. The system according to claim 11, wherein imaging of the sample
using the SLM as a tube lens is performed by moving the input
polarizer and the reflective mirror out of the path and displaying
a diffractive lens pattern with a focal length equivalent to the
distance between the SLM and the holographic camera.
13. The system according to claim 2, wherein the SLM is configured
to have a positive lens mask over the whole SLM and the two beams
with two mutually orthogonal polarization components, one of which
is parallel to the polarization of the SLM and the other which is
orthogonal to it, so that the interference happens between the
projections of each polarization component of the beams on the
crossing angle between the two orthogonal polarizations.
14. The system according to claim 2, wherein firmware of the SLM is
modified to give a 27.pi. phase shift over its range at a
45.degree. angle and Fresnel patterns displayed on the SLM are
adjusted for the 45.degree. angle.
15. The system according to claim 14, wherein an input polarizer
and an output polarizer are rotated 45.degree. along the optical
axis for improved resolution, so that all pixels on the SLM are
utilized to create two interfering wavefronts.
16. An apparatus for producing a hologram, comprising: a tube lens
configured to receive light emitted from an object; a first mirror;
a second mirror; a beam splitting cube configured to receive light
emitted from the object via the tube lens and to split the light in
two directions towards the first mirror and the second mirror; a
first lens positioned in the pathway between the beam splitting
cube and the first mirror; a second lens position in the pathway
between the beam splitting cube and the second mirror; and a
hologram plane configured to receive light emitted from the beam
splitting cube after it is reflected off the first mirror and the
second mirror to produce a hologram, the beam splitting cube being
disposed between the hologram plane and each of the first mirror
and second mirror with respect to the light that is reflected by
the beam splitting cube towards the hologram plane.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is related to and claims the benefit of
priority to U.S. Provisional Application Ser. No. 61/567,930, filed
Dec. 7, 2011, the contents of which are hereby incorporated herein
by reference.
BACKGROUND
1. Field
[0003] The present specification relates to Fresnel Incoherent
Correlation Holography (FINCH).
2. Description of the Related Art
[0004] Digital coherent holography has unique advantages for many
imaging applications. In some applications the recorded holograms
contain three dimensional (3D) information of the observed scene,
in others the holograms are capable of imaging phase objects.
Holography also enables implementing super resolution techniques
and even makes it possible to image objects covered by a scattering
medium. Because of these advantages, digital holography has become
important in optical microscopy. Examples of utilizing digital
holography as the basis for optical microscopes are the recently
published studies of lensless compact holography-based microscopes
(T.-W. Su, S. O. Isikman, W. Bishara, D. Tseng, A. Erlinger, and A.
Ozcan, "Multi-angle lensless digital holography for depth resolved
imaging on a chip," Opt. Express 18, 9690-9711 (2010); M. Lee, O.
Yaglidere, and A. Ozcan, "Field-portable reflection and
transmission microscopy based on lensless holography," Biomed. Opt.
Express 2, 2721-2730 (2011); O. Mudanyali, Bishara, and A. Ozcan,
"Lensfree super-resolution holographic microscopy using wetting
films on a chip," Opt. Express 19, 17378-17389 (2011)). Another
example of using digital holography in microscopy is the
holographic coherent anti-Stokes Raman microscope. In the present
study we extend our investigation of Fresnel Incoherent Correlation
Holography (FINCH), a way to utilize holography with incoherent
light, and which is another example of using digital holography in
microscopy.
[0005] The setup of FINCH includes a collimation lens (objective in
case of a microscope), a spatial light modulator (SLM) and a
digital camera (CCD or CMOS). The principle of operation is that
incoherent light emitted from each point in the object being imaged
is split by a diffractive element displayed on the SLM into two
beams that interfere with each other. The camera records the entire
interference pattern of all the beam pairs emitted from every
object point, creating a hologram. Typically three holograms, each
with a different phase constant in the pattern of the diffractive
element, are recoded sequentially and are superposed in order to
eliminate the unnecessary parts (the bias and the twin image) from
the reconstructed scene. The resulting complex-valued Fresnel
hologram of the 3D scene is then reconstructed on the computer
screen by the standard Fresnel back propagation algorithm (see J.
W. Goodman, Introduction to Fourier optics, 3rd Ed., (Roberts and
Company Publishers, 2005)). Unlike other techniques of incoherent
digital holography, like scanning holography, or multiple view
projection holography, FINCH is a non-scanning and motionless
method of capturing holograms. Acquiring only three holograms is
enough to reconstruct the entire 3D observed scene such that at
every depth along the z-axis every object is in focus in its image
plane. FINCH is a method of incoherent holography that can operate
with a wide variety of light sources besides laser light. Because
of this flexibility to practice high resolution holography with
FINCH, it can be used to implement holographic applications which
could not be realized in the past because they were limited by the
need for coherent laser-light. Applicants have recognized
additional properties of FINCH relating to resolution.
[0006] Recently two other research groups reported studies about
FINCH. In one publication (Y. Tone, K. Nitta, O. Matoba, and Y.
Awatsuji, "Analysis of reconstruction characteristics in
fluorescence digital holography," in Digital Holography and
Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical
Society of America, 2011), paper DTuC13), the authors investigated
the influence of the degree of spatial coherence of light on the
quality of the reconstructed 3D profiles in FINCH. In the other
publication (P. Bouchal, J. Kapitan, R. Chmelik, and Z. Bouchal,
"Point spread function and two-point resolution in Fresnel
incoherent correlation holography," Opt. Express 19, 1 5603-1 5620
(2011)), the authors proposed the conditions for optimal resolution
with FINCH. They concluded that resolution in FINCH imaging cannot
exceed that of a classical imaging system.
[0007] In this specification, the Applicants have come to different
conclusions and show that indeed, FINCH imaging can exceed standard
optical imaging system resolution. In the present specification,
Applicants bring a more complete analysis of FINCH as an imaging
system. Particularly, this specification addresses the question of
which of the systems, FINCH or a conventional glass-lens-based
imaging system, can resolve better. There is not an obvious answer
to this question because FINCH has unique properties that do not
exist in conventional optical imaging systems; on one hand, the
FINCH hologram is recorded by incoherent illumination, but on the
other hand this hologram is reconstructed by the Fresnel
back-propagation process, exactly as is done with a typical
coherent Fresnel hologram. So the question is whether FINCH behaves
like a coherent or incoherent system, or whether it has its own
unique behavior. Knowing that the difference between coherent and
incoherent imaging systems is expressed, among others, by their
different modulation transfer function (MTF), the more specific
question is what kind of MTF characterizes FINCH. Does FINCH have
an MTF of a coherent or incoherent imaging system, or does it have
its own typical MTF? The answer to this last question can determine
the answer to the resolution question. This specification analyzes
the transverse resolution of FINCH and show here, both
theoretically and experimentally, that FINCH imaging significantly
exceeds the resolution of a conventional microscope optical imaging
system.
BRIEF SUMMARY
[0008] In one embodiment, an apparatus for producing a hologram
includes a collimation lens configured to receive incoherent light
emitted from an object; a spatial light modulator (SLM) that
includes at least one diffractive lens which is configured to
receive the incoherent light from the collimation lens and split
the incoherent light into two beams that interfere with each other;
and a camera configured to record the interference pattern of the
two beams to create a hologram, wherein a ratio between a distance
from the SLM to the camera and a focal length of the diffractive
lens is greater than 1.
[0009] In another embodiment, a system configured to examine a
sample by both regular microscopy and Fresnel Incoherent
Correlation Holography (FINCH) includes a mirror slider configured
to position a mirror into a path of light emitted from an object
when the system is set to perform regular microscopy, and to remove
the mirror from the path when the system is set for FINCH; a beam
splitter configured to receive the light emitted from the object
and reflected off the mirror when the system is set to perform
regular microscopy; an imaging camera configured to record an image
formed at the system output; a reflective spatial light modulator
(SLM) configured to receive the light emitted from the object when
the system is set for FINCH, and to split the light into two beams
that interfere with each other; and a holography camera configured
to record the interference pattern of the interfering light beams
to create a hologram.
[0010] In yet another embodiment, an apparatus for producing a
hologram includes a tube lens configured to receive the light
emitted from an object; a first mirror; a second mirror; a beam
splitting cube configured to receive light emitted from the tube
lens and to split the light in two directions towards the first
mirror and the second mirror; a first lens positioned in the
pathway between the beam splitting cube and the first mirror; a
second lens position in the pathway between the beam splitting cube
and the second mirror; and a hologram plane configured to receive
light emitted from the beam splitting cube after it is reflected
off the first mirror and the second mirror to produce a
hologram.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 shows comparisons of the optical configuration for
(a) FINCH with only one diffractive lens and (b) A regular optical
imaging system with the same parameters used in (a).
[0012] FIG. 2 shows a summary of the main features of the three
linear systems discussed in the text. A.sub.s and I.sub.s stand for
a complex amplitude and intensity of the input object,
respectively. x and fx are the space and the spatial frequency
coordinate, respectively.
[0013] FIG. 3 shows (a) FINCH with two diffractive lenses, one is
positive and the other is negative; (b) FINCH with two diffractive
lenses, both are positive; and (c) a practical setup that emulates
the setup of (b), with one positive diffractive lens displayed on
the SLM and one positive glass lens placed near to the SLM.
[0014] FIG. 4 shows a schematic representation of the microscope
for comparison of FINCH to standard fluorescence microscopy on the
same identical sample without change in position or focus. The
position of the two sliders and the diffractive lens pattern
displayed on the SLM determines the imaging mode selected. The
position of the sliders is shown for FINCH. In this configuration
the increased efficiency for the separation of the reference and
sample beams is accomplished by capitalizing on the polarization
properties of the SLM. Input and output polarizers were rotated
45.degree. along the optical axis to separate the reference and
sample beams so that all the pixels on the SLM were utilized to
create the two interfering wavefronts.
[0015] Imaging of the sample using the SLM as a tube lens was
possible by moving the input polarizer to the open position and
displaying a diffractive lens pattern with a focal length
equivalent to the distance between the SLM and camera. Reversing
the position of the two sliders shown in the schematic allowed
direction of the fluorescent emission to pass through a standard
microscope NIKON tube lens to the monocular viewing port and
associated imaging camera for conventional fluorescence
microscopy.
[0016] FIG. 5 shows representative full field USAF slide images
captured in standard microscope operating mode (left panel). The
middle panel of FIG. 5 shows zoomed-in group 8 and 9 features from
full field standard microscope image. The right panel of FIG. 5
shows digitally linear reconstructed FINCH image of the small
central pattern shown in the middle image, slightly cropped to
match the middle image. All images were taken with a 5 mm aperture
placed at the back plane of the objective.
[0017] FIG. 6 shows cropped sections of images taken with: standard
Nikon tube lens configured for standard fluorescence microscopy
(first column); with the SLM acting as a tube lens (second column);
and with either the linear and non-linear reconstruction of FINCH
holograms. The FINCH images were recorded with a z-ratio of 1.8.
Images with the SLM as the tube lens or with the FINCH method were
taken at a SLM-camera distance of 1380 mm. The four sets of images
were taken with varying apertures in the back plane of the
objective as indicated on each row.
[0018] FIG. 7 shows that the visibility of the three smallest
features of the USAF test pattern in three imaging modes as a
function of the size of the aperture placed on the back plane of
the objective. Data with the Nikon tube lens was taken with the
lens and camera configured for standard fluorescence microscopy.
Data for the SLM as the tube lens or with the FINCH method (z-ratio
1.8) were taken at a SLM-camera distance of 1380 mm. Data for the
FINCH images are shown for both linear and non-linear
reconstructions.
[0019] FIG. 8 shows linear reconstructions of FINCH images taken at
varying z-ratios. At low z-ratio below 1, the SLM is focusing
behind the camera while at high z-ratio above 1, it is focusing in
front of the camera. Images were taken with a 5 mm aperture at the
back plane of the objective, with a zh of 1380 mm.
[0020] FIG. 9 shows non-linear reconstructions of FINCH images
taken at varying z-ratios. At low z-ratio below 1, the SLM is
focusing behind the camera while at high z-ratio above 1, it is
focusing in front of the camera. Images were taken with a 5 mm
aperture at the back plane of the objective, with a z.sub.h of 1380
mm.
[0021] FIG. 10 shows plots of the visibility of the three smallest
USAF features in FINCH as a function of the z-ratio, taken with a 5
mm aperture in the back plane of the objective. Data for both
linear and non-linear reconstructions are shown. These data were
taken with a z.sub.h of 1380 mm. For comparison, the visibility in
standard microscopy is approximately 0.1 when the aperture is 5 mm
(see FIG. 7). The lines are a polynomial fit of the data. For FINCH
Non-linear, y=-0.5769x.sup.2+2.1313x-1.1801 R.sup.2=0.8074 and for
FINCH Linear, y=-0.4848x.sup.2+1.7946x-1.1604 R.sup.2=0.7866.
[0022] FIG. 11 shows another configuration to obtain perfect
overlap between reference and sample beams that yields high
holographic efficiency. In this configuration the F3 and F4 lenses
were configured in a "4f" configuration with the respective mirrors
creating two respective "4f" lens systems with lenses of focal
lengths f3 and f4. The optical paths were adjusted so that the
optical paths were identical for the F3 and F4 arm at the hologram
plane to create complete overlap of the two spherical waves created
by the F3 and F4 arm and perfect and efficient holograms of the
objects imaged by the microscope objective at the sample plane.
[0023] FIG. 12 shows the results of a FINCH experiment to resolve
fluorescent beads beyond conventional microscope optical limits.
The FWHM (full width half max) of 100 nm Tetraspec beads was
measured by conventional fluorescence microscopy and "FINCH" with a
100.times. 1.4 NA objective at .lamda.=590 nm. The Abbe criteria
(0.5.lamda./NA)=optical resolution limit (0.5.times.590 nm/1.4=211
nm) but FINCH resolves better than the Abbe limit wherein a 100 nm
bead measured with FINCH had a FWHM of 130 nm under these
conditions.
DETAILED DESCRIPTION
[0024] FINCH, in the present model, creates holograms in a single
channel system as a result of interference between two waves
originating from every object point located in front of a
collimating lens. The following analysis refers to the system
scheme shown in FIG. 1(a), where it is assumed that the object is
an infinitesimal point and therefore the result of this analysis is
considered as a point spread function (PSF). For simplicity, we
assume that the object point is located at r.sub.s=(x.sub.s,
y.sub.s) on the front focal plane of the collimating lens L.sub.1
(an objective lens in the case of an infinity corrected microscope
system). For an infinitesimal object point with the complex
amplitude {square root over (I.sub.s)}, the intensity of the
recorded hologram is,
I H ( u , v ) = I s C ( r _ s ) L ( - r _ s f o ) Q ( 1 f o ) Q ( -
1 f o ) * Q ( 1 d ) [ B + B ' exp ( i .theta. ) Q ( - 1 f d ) ] * Q
( 1 z h ) P ( R H ) 2 . ( 1 ) ##EQU00001##
where f.sub.o is the focal length of lens L.sub.1, d is the
distance between the lens L.sub.1 and the SLM, z.sub.h is the
distance between the SLM and the camera, .rho.=(u,v) are the
coordinates of the camera plane and B, B' are constants. For the
sake of shortening, the quadratic phase function is designated by
the function Q, such that
Q(b)=exp[i.pi.b.lamda..sup.-1(x.sup.2+y.sup.2)], where .lamda. is
the central wavelength of the light. L denotes the linear phase
function, such that L(s)=exp[i2.pi..lamda..sup.-1
(s.sub.xx+s.sub.yy)], and C(r.sub.s) is a complex constant
dependent on the source point's location. The function P(R.sub.H)
stands for the limiting aperture of the system, where it is assumed
that the aperture is a clear disk of radius R.sub.H determined by
the overlap area of the two interfering beams on the camera plane.
The expression in the square brackets of Eq. (1) describes the
transparency of the SLM. This transparency is a combination of a
constant valued mask with a diffractive positive spherical lens of
focal length f.sub.d. In the past we presented two methods to
display these two masks on the same SLM. The older, and less
efficient, method is to randomly allocate half of the SLM pixels to
each of the two masks. Lately the inventors have learned that a
better way is by use of a positive lens mask over the whole SLM and
light with two mutually orthogonal polarization components, one of
which is parallel to the polarization of the SLM and the other
which is orthogonal to it, so that the interference happens between
the projections of each polarization component of the light beam on
the crossing angle between the two orthogonal polarizations. The
angle .theta. is one of the three angles used in the phase shift
procedure in order to eliminate the bias term and the twin image
from the final hologram. The asterisk in Eq. (1) denotes a two
dimensional convolution. The explanation of Eq. (1) is as follows:
the four left-most terms {square root over
(I.sub.s)}C(r.sub.s)L(-r.sub.s/f.sub.o))Q(1/f.sub.o) describe the
point source wave as is seen from the plane of lens L1. This wave
is multiplied by the lens L1 [multiplied by Q(-1/f.sub.o)],
propagates a distance d [convolved with Q(1/d)] and meets the SLM
where its transparency is in the square brackets of Eq. (1). Beyond
the SLM there are two different beams propagating an additional
distance z.sub.h till the camera [convolved with Q(1/z.sub.h)]. On
the camera detector, only the area of the beam overlap, denoted by
the area of P(R.sub.H), is considered as part of the hologram.
Finally, the magnitude of the interference is squared to yield the
intensity distribution of the recoded hologram. It is easy to see
from FIG. 1(a) and by calculating Eq. (1), that as long as the
source point is located on the front focal plane of L1, the
interference occurs between a plane and a spherical (in the
paraxial approximation) wave.
[0025] Three holograms of the form of Eq. (1) with three different
values of the angle .theta. are recorded and superposed in order to
obtain a complex hologram of the object point, given by,
H ( .rho. _ ) = C ' I s P ( R H ) L ( r _ r z r ) Q ( 1 z p ) , ( 2
) ##EQU00002##
where C' is a constant and z.sub.r is the reconstruction distance
from the hologram plane to the image plane calculated to be,
z.sub.r=.+-.|z.sub.h-f.sub.d|. (3)
[0026] The .+-. indicates that there are twin possible
reconstructed images although only one of them is chosen to be
reconstructed, as desired. r.sub.r is the transverse location of
the reconstructed image point calculated to be,
r _ r = ( x r , y r ) = r _ s z h f o . ( 4 ) ##EQU00003##
[0027] From Eq. (4) it is clear that the transverse magnification
is M.sub.T=z.sub.h/f.sub.o. The PSF of the system is obtained by
reconstructing digitally the Fresnel hologram given in Eq. (2) at a
distance z.sub.r from the hologram plane. The expression of the
hologram in Eq. (2) contains a transparency of a positive lens with
focal distance zr and hence, according to Fourier optics theory,
the reconstructed image is,
h F ( r _ ) = C ' I s v [ 1 .lamda. z r ] F { L ( r _ r z r ) P ( R
H ) } = C '' I s Jinc ( 2 .pi. R H .lamda. z r ( x - M T x s ) 2 +
( y - M T y s ) 2 ) , ( 5 ) ##EQU00004##
where C'' is a constant, F denotes Fourier transform, v is the
scaling operator such that v[a]f(s)=f(ax), r=(x,y) are the
coordinates of the reconstruction plane, Jinc is defined as
Jinc(r)=J.sub.1(r)/r and J.sub.1(r) is the Bessel function of the
first kind, of order one.
[0028] Eq. (5) describes the two dimensional PSF of FINCH.
Recalling that the object is a collection of infinitesimal
incoherent light points which cannot interfere with each other, we
realize that each independent object point is imaged to an image of
the form of Eq. (5). The complete image of many object points is a
convolution integral between the object denoted by intensity
distribution I.sub.s(r) with the PSF shown in Eq. (5), as
follows,
I.sub.i.sup.L(r)=I.sub.s(r)*h.sub.F(r). (6)
Eq. (6) indicates that FINCH is a linear invariant system for the
quantity of light intensity. However, since h.sub.F is in general a
complex valued function, I.sub.i.sup.L might be a complex valued
function as well. This observation does not contradict any physical
law because the reconstruction is done digitally by the numerical
algorithm of the Fresnel back propagation. The superscript L is
added to the intensity obtained by Eq. (6) in order to distinguish
it from the non-linear reconstruction discussed next.
[0029] In case the hologram is reconstructed optically by
illuminating the hologram with a coherent plane wave, the output
intensity is
I.sub.i.sup.N(r)=|I.sub.s(r)*h.sub.F(r)|.sup.2. (7)
I.sub.i.sup.N denotes intensity of the optical reconstruction, or
non-linear digital reconstruction as is demonstrated in the
experimental part of this study. This image is not linear in
relation to the gray levels of I.sub.s(r), but in some cases, for
instance, binary objects whose images are not distorted by the
non-linear operation, I.sub.i.sup.N preferred over I.sub.i.sup.L
because the side lobes of h.sub.F are suppressed by the square
operation, which results in improved image contrast.
[0030] The width of the PSF in every imaging system determines the
resolution of the system. The width of the PSF is chosen herein as
the diameter of the circle created by the first zero of the Jinc
function of Eq. (5). This diameter remains the same for both the
linear and non-linear reconstructions, and is equal to
1.22.lamda.z.sub.r/R.sub.H. According to Eq. (3), zr=|zh-fd| and
therefore, based on a simple geometrical consideration, the radius
of the hologram, which is the radius of the overlap area between
the plane and the spherical beams, is,
R H = { R o z h - f d f d f d .gtoreq. z h 2 R o otherwise , ( 8 )
##EQU00005##
where R.sub.o is the radius of the smallest aperture in the system
up to, and including, the SLM. For f.sub.d<z.sub.h/2 the
projection of the spherical wave exceeds beyond the plane wave
projection and therefore the radius of the overlap remains as
R.sub.o. Consequently, the width of the PSF for the regime off
f.sub.d.gtoreq.z.sub.h/2 is
.DELTA. = 1.22 .lamda. z r R H = 1.22 .lamda. z h - f d f d R o z h
- f d = 1.22 .lamda. f d R o . ( 9 ) ##EQU00006##
This PSF has exactly the size one would expect to see in the output
of a regular imaging system shown in FIG. 1(b). At first glance,
one might conclude that since the two systems have the same PSF,
with the same width, their resolving power is the same. However Eq.
(4) indicates that the location of the image point in the output
plane of FINCH is at r.sub.sz.sub.h.f.sub.o. This is in general
different than the location of the image point of the imaging
system of FIG. 1(b), which is r.sub.sf.sub.d/f.sub.o. In other
words, if the two systems observe the same two object points, the
size of all the image points in the two systems is the same, but
the gap between the two image points differs between the two
compared systems. The two point gap of FINCH and of the regular
imaging system differs by the ratio of z.sub.h/f.sub.d. Recalling
that resolution is related to the gap between image points, as is
manifested by the well known Rayleigh criterion, we realize that if
z.sub.h/f.sub.d>1, then FINCH can resolve better than a regular
system. This is because in FINCH, the gap between every two image
points is larger by a factor z.sub.h/f.sub.d of compared to the two
point gap of a regular imaging system with the same numerical
aperture. Moreover, increasing the ratio z.sub.h/f.sub.d in FINCH
increases the resolution, where the maximum resolving power is
achieved for the ratio z.sub.h/f.sub.d=2. Beyond this limit the
radius of the hologram is not increased further and keeps the
maximum radius of R.sub.o. That is again because the size of the
spherical wave projection on the detector exceeds the plane wave
projection, so the overlap area remains within the same circle with
the radius of R.sub.o.
[0031] To further investigate the properties of FINCH in comparison
to a regular imaging system, one needs to equalize the size of both
overall output images. Recall that the FINCH's overall image of
many points is bigger by the factor z.sub.h/f.sub.d>1, hence the
output image with FINCH should be shrunk by this factor. So, when
the FINCH image is shrunk by the factor of z.sub.h/f.sub.d the
overall image of both systems is the same and therefore can be
compared on an equal basis. However, the result of shrinking the
entire image causes the PSF size of FINCH to be narrower by the
factor of z.sub.h/f.sub.d in comparison to that of a regular
imaging system.
[0032] Therefore, the effective width of the PSF of FINCH is
.DELTA. e = { 1.22 .lamda. z r f d R H z h = 1.22 .lamda. f d 2 R o
z h f d .gtoreq. 1 2 z h 1.22 .lamda. z r f d R o z h = 1.22
.lamda. f d ( 1 - f d / z h ) R o 0 < f d < 1 2 z h . ( 10 )
##EQU00007##
[0033] According to Eq. (10) the PSF width and consequently the
resolution are dependent on the ratio z.sub.h/fdd for all values of
f.sub.d. Note that this dependence of the resolution to the ratio
z.sub.h/f.sub.d is different from the conclusion of previous
studies (see Bouchal et al., cited above), where the authors there
have claimed that above z.sub.h/f.sub.d>1 the resolution is
constant and is equal to that of a regular imaging system. The
minimum width of the PSF is obtained for z.sub.h/f.sub.d=2, and
this width is .DELTA..sub.e=0.61.lamda.f.sub.d/R.sub.o (or
0.61.lamda.f.sub.d/R.sub.o in the object domain), which is half the
width of the PSF of a regular imaging system [shown in FIG. 1(b)]
with the same numerical aperture. The effective PSF of FINCH for
the ratio z.sub.h/f.sub.d=2 is now,
h F ( r _ ) = C * I s Jinc ( 4 .pi. R o .lamda. f d ( x - M T x s /
2 ) 2 + ( y - M T y s / 2 ) 2 ) . ( 11 ) ##EQU00008##
[0034] In terms of resolution, the improvement of FINCH in
comparison to a regular incoherent microscope is more than a factor
of 1 but somewhat less than a factor of 2 because the PSF of FINCH
shown in Eq. (11) has the shape of that of a coherent system. To
estimate the resolution improvement we recall that according to the
Rayleigh criterion, two points are resolved if the dip between
their images is more than approximately 27% of the maximum
intensity. A simple numerical calculation indicates that in order
to create a dip of not less that 27% between two functions of the
form of Eq. (11), the minimal distance between them should be no
less than 0.61.lamda.f.sub.d/(1.4R.sub.o) and
0.61.lamda.f.sub.d/(1.5R.sub.o) in cases of linear and non-linear
reconstruction, respectively. Therefore the resolution improvement
of FINCH over a regular incoherent microscope is about a factor of
1.4 and 1.5 for linear and non-linear reconstruction, respectively.
The FINCH's resolution improvement over a coherent imaging system
is a factor of 2.
[0035] According to Eq. (5), the PSF of FINCH is obtained as the
scaled Fourier transform of the system aperture, exactly as is the
case of a coherent imaging system. Therefore the shape of the MTF
of FINCH is similar to the shape of the system aperture, i.e. a
uniform clear disc shape. However the cut-off frequency of FINCH is
different by the ratio of z.sub.h/f.sub.d than that of a regular
coherent imaging system, and can be twice as high in the optimal
setup of z.sub.h/f.sub.d=2. Moreover, FINCH with the ratio
z.sub.h/f.sub.d=2, has the same cut-off frequency as an incoherent
imaging system, but unlike the later system, the MTF of FINCH is
uniform over all the frequencies up to the cut-off frequency.
[0036] The present inventors conclude that FINCH is superior in
terms of resolution over both coherent and incoherent imaging
systems. In fact, FINCH enjoys the best of both worlds; it has a
cut-off frequency of an incoherent system with the same numerical
aperture, and a uniform MTF like a coherent system. FIG. 2
summarizes the main properties of FINCH in comparison to either
coherent or incoherent imaging systems. Looking at FIG. 2, one can
conclude that, in addition to the two well known types of imaging
systems, coherent and incoherent, there is a third type which can
be denoted as a hybrid imaging system characterized by FINCH, since
it associates incoherent recording with coherent reconstruction.
The hybrid imaging system is linear in the intensity but its PSF is
in general a complex valued function. Its MTF has the shape of the
system aperture with a cut-off frequency that can be twice as large
as that of a coherent imaging system with the same numerical
aperture. In comparison to an incoherent system we see that both
systems have the same bandwidth but FINCH does not attenuate the
intensity of spatial frequencies greater than zero, as the
incoherent imaging system does.
[0037] The superiority of FINCH in the resolution aspect is
explained by the fact that the hologram of each object point is an
interference result between two beams, both originated from this
same point. The information about the point location is stored in
the phase of both beams. During the wave interference, under the
condition z.sub.h/f.sub.d>1, the two phases have the same sign
and therefore they are summed such that the resulting linear phase
function has a higher slope than in case of recording a coherent
hologram with a non-informative reference beam. Therefore, as a
result of the phase gaining, the image point location is farther
from some arbitrary reference point than in the case of a regular
imaging system, and therefore the image magnification is higher in
FINCH. As the result, the separation between points is larger in
FINCH and this feature is translated to better overall resolution.
In the regime of z.sub.h/f.sub.d<1 the two summed phases have an
opposite sign such that the resulting overall phase is
de-magnified, the gap between various image points, and
consequently the resolution, are smaller in comparison to a
conventional imaging system with the same numerical aperture.
[0038] In this study we compare the transverse resolution of two 2D
imaging systems; the conventional incoherent imaging system and
FINCH. For both systems we analyzed the resolution at the front
focal plane of the objective in which a comparison could be made
because conventional incoherent imaging only resolves a single
plane of focus. While FINCH can resolve multiple planes in an
image, an analysis of FINCH resolution was limited to the front
focal plane in this study for comparison purposes. In the future,
theoretical and experimental analysis of the resolution properties
of a more general FINCH, in which the location of the object is not
limited to the front focal plane of the objective, should be very
interesting and may offer additional opportunities for high
resolution 3D imaging. Because FINCH utilizes an SLM it is possible
to modify the diffractive lenses in the system and therefore to
optimize the imaging resolution at different object planes.
[0039] All the above mentioned analysis is based on the assumption
that FINCH is diffraction limited and the pixel size of the camera
does not limit the system resolution. This assumption is fulfilled
if the finest fringe of the hologram can be correctly sampled by
the camera. Referring to FIG. 1(a) with the condition
z.sub.h/f.sub.d=2, and recalling that the finest fringe is created
by the interfered beams with the largest angle difference between
them, the condition that should be satisfied is
tan .PHI. = 2 R o z h .ltoreq. .lamda. 2 .delta. , ( 12 )
##EQU00009##
where .phi. is the largest angle difference between the interfered
beams in the system and .delta. is the camera pixel size. For a
given SLM and digital camera, the only free variable is z.sub.h.
Therefore, in order to keep the system as diffraction limited as
possible, the distance between the SLM and the camera should
satisfy the condition z.sub.h>4R.sub.o .delta./.lamda..
Increasing the distance z.sub.h, while keeping the optimal
condition z.sub.h/f.sub.d=2, narrows the field of view. Based on
geometrical considerations, the radius R.sub.v of the observed disk
which can be recorded into the hologram is
R.sub.v=2f.sub.o/R.sub.o/z.sub.h.
[0040] Based on the discussion above, it is clear that the optimal
ratio in sense of resolution between z.sub.h and f.sub.d is
z.sub.h/f.sub.d=2. However this optimal ratio is obtained in the
specific setup shown in FIG. 1(a) and the question is whether there
is a more general configuration of FINCH in which the same
resolution can be achieved. In the following subsection we answer
this question.
[Alternative FINCH Configurations]
[0041] According to Eq. (10) the effective resolution of FINCH
is
.DELTA. e = 1.22 .lamda. z r f d R H z h . ( 13 ) ##EQU00010##
In order to improve resolution one should look for a configuration
with higher R.sub.H and z.sub.h/f.sub.d and with a z.sub.r that
grows less than the other two factors. Such configuration might be
the one shown in FIG. 3(a), in which the FINCH is generalized in
the sense that the constant phase on the SLM is replaced with a
negative lens with f.sub.2 focal distance. When the various
parameters are chosen such that there is a perfect overlap between
the two spherical waves on the camera plane, R.sub.H and the ratio
z.sub.h/f.sub.d indeed become higher. The new z.sub.r is calculated
from a similar equation to Eq. (1), in which in addition to the
constant B there is a transfer function of a negative lens as the
following,
I H ( u , v ) = I s C ( r _ s ) L ( - r _ s f o ) Q ( 1 f o ) Q ( -
1 f o ) * Q ( 1 d ) .times. [ BQ ( 1 f 2 ) + B ' exp ( i .theta. )
Q ( - 1 f d ) ] * Q ( 1 z h ) P ( R H ) 2 . ( 14 ) ##EQU00011##
z.sub.r calculated from Eq. (14) is
z r = .+-. ( z h - f d ) ( z h + f 2 ) f d + f 2 . ( 15 )
##EQU00012##
The transverse magnification remains M.sub.T=z.sub.h/f.sub.o as
before. Next, we make use of the fact that the two spherical waves
perfectly overlap on the camera plane, and based on simple
geometrical considerations, the following two relations are
obtained,
R H = R o z h - f d f d , ( 16 ) z h - f d f d = z h + f 2 f 2 . (
17 ) ##EQU00013##
Substituting Eqs. (15)-(17) into Eq. (13) yields that effective
width of FINCH's PSF in the general configuration is
.DELTA. e = 0.61 .lamda. f d R o . ( 18 ) ##EQU00014##
This is the same result obtained with the configuration of FIG.
1(a) for z.sub.h/f.sub.d=2. The conclusions are the following: 1)
FINCH resolution in any configuration is limited by the value of
.DELTA..sub.e given in Eq. (18). This conclusion is expected since
any configuration of FINCH does not enable any new information, or
more spatial frequencies, to enter into the system, and therefore
there is no reason for any further resolution improvement beyond
the superior result given in Eq. (18). 2) The optimal configuration
can be obtained in many forms as long as the overlap between the
two different beams on the camera plane is perfect. This conclusion
is true even if both diffractive lenses on the SLM are positive,
where one is focused before the camera and the other beyond it, as
is shown in FIG. 3(b). In that case the z.sub.r is calculated by
the same method to be
z r = .+-. ( z h - f d ) ( z h - f 2 ) f d - f 2 , ( 19 )
##EQU00015##
and the radius of the hologram under the perfect overlap condition
is the same as is given in Eq. (16), where the following relation
also exists:
f 2 - z h f 2 = z h - f d f d . ( 20 ) ##EQU00016##
Substituting Eqs. (16), (19), (20) into Eq. (13) yields again the
same effective resolution as is given in Eq. (18). Here again the
optimal resolution can be achieved. Note that displaying two
different diffractive lenses on randomly distributed pixels of the
same SLM could result in reduced efficiency from both lenses,
because only half of the SLM pixels are available for each lens (J.
Rosen, and G. Brooker, "Fluorescence incoherent color holography,"
Opt. Express 15, 2244-2250 (2007); J. Rosen, and G. Brooker,
"Non-scanning motionless fluorescence three-dimensional holographic
microscopy," Nat. Photonics 2, 190-195 (2008)). Therefore a glass
spherical lens should be added to the system which together with
the SLM (on which the pattern of a sum of constant and quadratic
phase functions are displayed) creates an equivalent system of FIG.
3(b). This system is depicted in FIG. 3(c). The purpose of the
additional glass lens is to convert the plane wave, reflected from
the SLM, into a converging spherical wave which interferes with the
other spherical wave in order to create the hologram.
[Experimental Methods]
[0042] The purpose of these experiments was to test the theoretical
predictions. Specifically, we wanted to determine the relationship
between z.sub.h/f.sub.d and FINCH resolution and to compare the
resolution of FINCH microscopy at optimal z.sub.h/f.sub.d to that
of optical microscopy. Implementing FINCH holography in a
microscope (FINCHSCOPE) only requires that the fluorescence
microscope be changed in the way fluorescence emission is detected.
The infinity beam of the sample imaged with a microscope objective
is directed to an SLM and is split into two beams which interfere
at a camera to create a hologram. The microscope configuration
schematically shown in FIG. 4 used for these experiments was built
upon our laboratory's previous concepts and designs for
implementing FINCH in a microscope with some important additions
and modifications. In the experiments presented here, the identical
smallest features on the highest resolution USAF chart were imaged
at the plane of focus by three methods and compared; 1)
conventional high resolution fluorescence microscopy with all glass
optics including a matched and properly configured microscope tube
lens, 2) microscopy which utilized the SLM as a tube lens to focus
the image upon the camera and 3) holograms captured with FINCII and
reconstructed at the best plane of focus.
[0043] In order to simplify analysis and be able to compare image
resolution between conventional fluorescence microscopy (which only
resolves a single focal plane) and FINCH, a USAF negative test
slide (Max Levy Autograph) with a single plane of focus that
contained group 9 features as small as 645 lp/mm (0.78 .mu.m
feature size) was used and was much smaller than the smallest
features used previously. The slide was placed upon a fluorescent
plastic slide (Chroma) so that the negative features were
fluorescent. A No. 1 coverslip was placed on the slide with
microscope immersion oil between the coverslip and the test slide.
There was an air interface between the objective and the top of the
coverslip. The USAF pattern was adjusted to the plane of focus of
the objective and kept in that position for all of the imaging
experiments.
[0044] An important difference in the configuration from previous
designs is that the SLM was positioned at a 45.degree. angle and
the system was designed for ready switching between ocular or
camera viewing of the sample fluorescence and holography without
disturbing the position or focus of the sample. This new microscope
configuration was constructed on the stand of an upright Zeiss
Axiophot fluorescence microscope. The binocular head with camera
port and tube lens of the microscope was removed and the components
needed for FINCH holography and viewing of the sample were attached
to the microscope in its place. The remaining components of the
microscope were not altered. An AttoArc 100 watt mercury arc lamp
was used as the excitation source and the excitation was controlled
by an electronic shutter. In these experiments, an air Nikon Plan
Apo 20.times., 0.75 NA objective was used. The epifluorcscence
dichroic and excitation filter were Semrock Cy3 filters, and the
emission filters were a 570 nm center .lamda., 10 nm bandpass
filter (Thorlabs) for the FINCH images and the images taken with
the SLM as a tube lens. A Semrock Cy3 emission filter was used for
the glass tube lens ocular viewing and camera images. In
experiments not shown, as expected, the resolving power of the
objective-tube lens combination was confirmed to be the same with
the Cy3 emission filter as with the 10 nm bandpass filter. This is
because the Nikon Plan Apo objective--tube lens combination is
achromatic. A major improvement in light transmission was achieved
by placing the SLM at a 45.degree. angle and eliminating the beam
splitting cube used in previous work (G. Brooker, N. Siegel, V.
Wang and J. Rosen, "Optimal resolution in Fresnel incoherent
correlation holographic fluorescence microscopy," Opt. Express 19,
5047-5062 (2011)). Careful alignment of the SLM (Holoeyc HEO 1080P,
1080.times.1920 pixels, 8 um pixel pitch, phase only) in all
directions was essential to prevent any image degradation.
Furthermore the SLM firmware was modified to give a 2.pi. phase
shift over its range at a 45.degree. angle and the Fresnel patterns
displayed on the SLM were adjusted for the 45.degree. angle. Input
and output polarizers were rotated 45.degree. along the optical
axis for improved resolution, so that all the pixels on the SLM
were utilized to create the two interfering wavefronts. The 8 meter
physical curvature of the SLM substrate was accounted for in the
lens parameters used to generate the desired focal lengths created
by the diffractive Fresnel lens patterns that were displayed on the
SLM. A multi-axis micrometer controlled mount was constructed so
that the SLM could be adjusted to be precisely centered on the
optical axis and so that there was no rotational misalignment of
the SLM about the optical axis. A calibrated iris was attached to
the back aperture of the objective so that the back aperture could
be varied from 3 mm to 12 mm to reduce the resolution of the
objective so that FINCH imaging could be directly compared to
optical microscopy at different effective objective NAs. Removal of
the iris enabled imaging with the full 16 mm back aperture of the
objective. In order to compare imaging performance between regular
microscopy with that of FINCH, the microscope was configured so
that a precision mirror on a roller-ball bearing slider could be
inserted into the emission beam path without disturbing the
location or focus of the sample or the setting of the back aperture
of the objective. Once the mirror was in place, the emission light
was simultaneously directed through a Nikon tube lens and beam
splitting cube to another of the same model camera that was used
for holography. Furthermore, an ocular positioned on the beam
splitting cube allowed direct viewing of the sample under
observation. Both the ocular and both cameras were aligned and
positioned to be precisely parfocal (all at the same focus) under
imaging conditions at the correct focus position between the
objective and sample. An in focus image on the camera used for
holography was obtained when the focal length of the diffractive
lens pattern displayed on the SLM was equivalent to the distance
between the SLM and camera. The two CCD cameras were Qlmaging
Retiga 4000R, cooled 2048.times.2048 pixel, 7.4 .mu.m pixel pitch,
12 bit.
[0045] The operation of the microscope was controlled by software
written in LabView. Three phase shifted holograms were taken for
each FINCH image and calculated.
[Experimental Results]
[0046] The ability of the camera to resolve the fine fringes of the
hologram has a significant effect on the ability of FINCH to
resolve small objects. Because of this, we moved the camera away
from the SLM until we reached a z.sub.h position of 1380 mm at
which we were able to resolve the smallest features in the USAF
pattern using FINCH with z.sub.h/f.sub.d=2. The size of the
acquired hologram is equal to the size of the diffractive Fresnel
lens displayed on the SLM. As shown in the left panel of FIG. 5,
the microscope image of the small features in groups 8 and 9 (shown
in the red box) under standard imaging conditions with a tube lens
and with a 5 mm aperture over the back of the objective lens, was
quite small and needed to be zoomed in to see them as shown in the
middle image of FIG. 5, while the FINCH images needed to be zoomed
and cropped much less due to the magnification imposed by the long
SLM-CCD distance. As can be seen, the small features were not well
resolved by regular microscopy, however imaging with FINCH clearly
resolved the small features as shown in the right panel of FIG.
5.
[0047] The USAF resolution target used in these experiments
contains the smallest features available. In order to compare FINCH
resolution in a very controlled manner to standard microscopic
imaging, we imaged this target with the Nikon 20.times. 0.75 NA
objective which had a 16 mm back aperture. We then installed a
calibrated iris (Thorlabs) on the back aperture of the objective
and systematically reduced the aperture from 12 mm to 3 mm. At each
reduction in the back aperture, we took standard microscope images,
images using the SLM as the tube lens and FINCH holographic images
which were reconstructed as either linear or non-linear images as
described above. Results from using 3, 5, 8 and 16 mm (no iris)
back apertures are shown in FIG. 6.
[0048] Additional apertures of 4, 6, 10 and 12 mm were used with
results intermediate to the images shown here. An analysis of this
experiment is shown in FIG. 7. The plot of FIG. 7 shows the
visibility in the smallest group of lines versus the diameter of
the back aperture, where the visibility defined as
(I.sub.max--I.sub.min)/(I.sub.max+I.sub.min) is a standard quantity
used to characterize resolution. In this work, we examined
visibility of the horizontal features in group 9, element 3, i.e.
the smallest features. To define I.sub.max, we located the row of
pixels in each of the three features that had the highest summed
intensity. We then averaged all the pixel values from those rows.
To define I.sub.min, we located the row of pixels in each of the
gaps between the features that had the lowest summed intensity, and
then averaged the pixel values from those rows. Visual inspection
of the images and the visibility calculations demonstrate that
FINCH images resolve the smallest features better than images from
the comparable standard microscope configuration at all effective
NAs of the objective. Using the SLM as a tube lens produced images
which had similar resolution to the glass tube lens up to an
aperture of 8 mm, the approximate minimum size of the aperture of
the SLM when viewed at a 45.degree. angle in our setup.
[0049] We then investigated the relationship between resolution and
z.sub.h/f.sub.d, which we call z-ratio, using a reduced aperture of
5 mm since this dramatically reduced the imaging resolution of the
objective under normal microscope conditions. Images at varying
z-ratios from 0.85 to 2.4 were recorded and are shown in FIGS. 8
and 9. Visual inspection of the images shows that the resolution
continues to improve as z-ratio increases from 0.85 and reaches a
peak around z-ratio=1.8 t 0.2. Visibility data is presented in FIG.
10. The maximum is not exactly at z.sub.h/f.sub.d=2 because the SLM
has inherent spherical-like curvature which introduces an effective
positive spherical lens of about 8 meter focal length. In other
words, instead of a system of the type shown in FIG. 1(a) in which
the maximum resolution is obtained at z.sub.h/f.sub.d=2,
effectively there is a system of the type shown in FIG. 3(c) in
which there is an additional lens in the system (the inherent 8
meter curvature of the SLM) and the maximum resolution is obtained
at about z.sub.h/f.sub.d=1.8. Note that although the focal length
of the diffractive lens displayed on the SLM is corrected to
account for the inherent curvature of the SLM, the constant phase
mask cannot be corrected, and therefore the model shown in FIG.
3(c) is valid here. This system behavior is in contrast to the
report by other investigators that there was no change in
resolution between z-ratio of 1 and 2. Note that at z-ratio=0.85
the visibility in the smallest group of lines is zero and therefore
this point of data is not included in the plot of FIG. 10. However
this result fits the prediction that the resolution of FINCH for
z-ratio<1 is lower than that of a regular microscope; as seen in
FIG. 7, the visibility of the smallest group of lines, with
objective back aperture of 5 mm, is 0.1.
[Perfect Overlap Requirements for Finch]
[0050] Increased FINCH efficiency can be accomplished by
interfering two spherical waves to reduce the optical path
differences, yet maintain complete overlap between the two waves.
Under these conditions the camera can be placed quite close to the
SLM. This dramatically reduces exposure time, reduces noise and
creates much higher quality images. Perfect overlap between two
spherical beams originating from each image point (reference and
sample) creates the most efficient incoherent hologram and best
images.
[0051] To ensure perfect overlap of sample and reference beams and
therefore optimal holograms of all points in the object, each pair
of sample and reference beams must be concentric. This can be
achieved in the following ways.
[0052] 1. Telecentric arrangement of tube lens. [0053] a. Place a
tube lens at a distance away from the objective that is equal to
the tube lens focal length plus the microscope objective focal
length. [0054] b. Split the beam from the tube lens into two arms,
the F3 arm and the F4 arm. [0055] c. Into each arm place relay
lenses in a 4f configuration with unit magnification. The focal
length of the lens in the F3 arm must be different from the focal
length of the lens in the F4 arm. [0056] d. Recombine the arms into
a single beam path. [0057] e. This can be achieved in a Michelson
or Mach-Zehnder interferometer arrangement.
[0058] 2. Bring the hologram forming lens/assembly/SLM optically
into contact with the microscope objective. For example, with
reference to FIG. 3, set d=0. If d is not zero but is less than 20
mm, the sample and reference beams will be nearly concentric and
have almost perfect overlap.
[0059] FIG. 11 shows another FINCH configuration which can create a
perfect overlap between reference and sample beams that yields high
holographic efficiency. This configuration is also telecentric so
that the two different focal lengths used to create the two beams
needed for interference are coincident over the complete field of
view. This occurs because the tube lens fg is positioned fg
distance from the back focal length of the microscope objective
lens and makes the system telecentric. The optical distance
relationships for this configuration are as follows:
fg=Z1+2Z2+Z3
fg=Z1+2Z4+Z5
2f3+Z2=2f4+Z4
f3.noteq.f4
Z1 is a distance from the center of the beam splitting cube to the
center of the tube lens; Z2 is a distance from the center of the
beam splitting cube to the end of a focal length f3 of the first
lens; Z3 is a distance from the center of the beam splitting cube
to the focus of the light emitted from the first lens in the
direction of the beam splitting cube (the portion of light emitted
from the first lens is also known as the "F3 arm" in FIG. 11); Z4
is a distance from the center of the beam splitting cube to the end
of a focal length f4 of the second lens; Z5 is a distance from the
center of the beam splitting cube to the focus of the light emitted
from the second lens in the direction of the beam splitting cube
(the portion of light emitted from the second lens is also known as
the "F4 arm" in FIG. 11).
[0060] The "Z" distances are adjusted according to the equations to
create telecentricity and to ensure perfect interference between
the Z3 and Z4 arms of the interferometer. The mirrors in each arm
create a "4f" imaging condition causing the image to pass twice
through either the f3 or f4 lenses. The piezo device in one arm
(shown in the F4 arm) is used to alter the optical path length in
one arm of the interferometer to change the phase in either the
reference or sample beam path. During image capture, the phase is
changed for example by 2.pi./3 three times to obtain the three
phase-shiftedimages which create the complex hologram used for
further processing. The conditions for best interference require
that the optical distances of both arms of the interferometer be
equal. The CCD or CMOS camera is placed at the hologram plane. The
lenses f3 and f4 are selected to be high quality imaging lenses
such as achromats or composite lenses selected for their high
quality imaging resolution.
[0061] In the embodiments shown in FIGS. 3 and 4, the purpose of
the SLM is to separate the two beams and to change the phase on one
of the beams Changing the phase in the configuration of FIG. 11 is
done by moving the piezo device three times to create a 2.pi.
change for the three holograms which are normally captured. Also in
that configuration the phase change could be accomplished with a
SLM or liquid crystal device or by any other means for changing the
phase of a light beam.
[0062] The ultimate test of the super-resolving capabilities of an
optical system to resolve beyond established optical limits is the
ability to image objects which are smaller than can be resolved by
classical optical imaging systems. In that regard, 100 nm
fluorescent beads are well beyond the limits which can be resolved
by optical means. According to the Abbe criteria (0.5.lamda./NA),
with a 100.times.1.4 NA objective, the optical resolution limit at
590 nm would be 0.5.times.590 nm/1.4=211 nm. FINCH resolves better
than the Abbe limit wherein a 100 nm bead measured 130 nm as shown
in FIG. 12.
CONCLUSIONS
[0063] The present specification shows an analysis of FINCH with
the tools of the linear system theory. The theoretical conclusions
are supported well by experiments described herein. Applicants
conclude that FINCH is a hybrid system in the sense that its MTF
has the shape of a coherent imaging system but in the optimal
conditions, its spatial bandwidth is equal to that of an incoherent
system. The width of the PSF of FINCH, and accordingly its
resolution, is dependent on its configuration and on the ratio
between the distance from the SLM to the camera and the focal
length of the diffractive lens. In all the possible configurations,
the condition to obtain maximum resolution occurs when there is a
perfect overlap between the projections of the two different
interfering beams (originating from the same point source) on the
camera sensing plane. Under the optimal condition described above,
FINCH can resolve better than a regular glass-lenses-based imaging
system with the same numerical aperture. In terms of Rayleigh
criterion the improvement is between 1.5 and 2 fold in comparison
to incoherent and coherent systems, respectively.
* * * * *