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Description  |
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TECHNICAL FIELD
This invention relates to optical correlators and more particularly to
real-time edge-enhanced optical correlators utilizing the four-wave mixing
properties of photorefractive materials.
BACKGROUND ART
The main advantage of optical correlators, as compared with their digital
counterparts, is that high-resolution Fourier transform operation on the
input optical images may be rapidly executed, typically in nanoseconds by
simply transmitting the input image through a single lens. However, the
overall speed of an optical correlator is still limited by how fast the
information can be updated on the input devices (spatial light
modulators), the real-time holographic material, and the output device
(camera or detector array). The speeds of these three components are
equally important because the slowest component will determine the overall
speed of the system.
Gregory Gheen and Li-Jen Cheng have reported using photorefractive GaAs in
a paper titled "Optical correlators with fast updating speed using
photorefractive semiconductor materials," Applied Optics, Vol. 27, No. 13,
pp. 2756-2761, (1988). The objective was to improve the speed of real-time
optical correlators. In principle, all nonlinear optical materials can be
used as real-time holographic materials. However, although many nonlinear
optical materials have very short response times, they require too high an
intensity to yield a practical diffraction efficiency.
Photorefractive crystals are in general slower than other nonlinear optical
materials, but they can operate with a much lower power requirement. Among
all the photorefractive crystals, semiconductors such as GaAs, InP, and
CdTe are in general one to two orders of magnitude faster than
photorefractive oxides such as BaTiO.sub.3, SBN and BSO. They are,
therefore, more suitable for real-time applications.
In the GaAs based optical correlator reported by Gregory Gheen and Li-Jen
Cheng, the input image and the reference image were put on photographic
films only. That does not lend itself to real-time image correlation. What
is required is some means, such as a liquid crystal TV panel having a
thin-film transistor active matrix of MxN pixels where M and N are
integers, to serve the function of spatial light modulators to produce in
real time input and reference images. Consequently, an object of this
invention is to provide a real-time GaAs-based VanderLugt optical
correlator in which real-time input devices, i.e., liquid-crystal TVs
(LCTVs), are used. The output device is a vidicon camera. The speeds of
both the LCTVs and the vidicon camera are video rate, while that of the
GaAs may be much higher (as high as 1000 frames/sec). Therefore, the speed
bottleneck of the optical correlator is at both the input and the output
devices.
When the shape, size and orientation of the object in the input image and
the object in the reference image are the same, the correlator displays a
bright spot (autocorrelation peak) in the output image at an equivalent
location of the object in the input image. Therefore the autocorrelation
peak can be used not only to identify an object but also to track its
location. Edge-enhanced input and reference images yield a sharper
autocorrelation peak and thus a better defined position of the object in
the input image. Nevertheless, the autocorrelation peak intensity of edge
enhanced input and reference images is more sensitive to the relative size
and orientation of the object in the input image with respect to the
object in the reference image.
Edge enhancement of an image can be implemented by using the dependence of
the diffraction efficiency (or modulation depth) on the write-beam ratio
in four-wave mixing in the photorefractive crystal. J. P. Huignard and J.
P. Herriau, "Real-time coherent object edge reconstruction with Bi.sub.12
SiO.sub.20 crystals," Appl. Opt., Vol. 17, No. 17, pp. 2671-2672 (1978);
J. Feinberg, "Real-time edge enhancement using the photorefractive
effect," Opt. Lett., Vol. 5, pp. 330-332 (1980); and E. Ochoa, L.
Hesselink and J. W. Goodman, "Real-time intensity inversion using two-wave
and four-wave mixing photorefractive Bi.sub.12 GeO.sub.20," Appl. Opt.,
Vol. 24, pp. 1826-1832, (1985). The technique of real-time coherent object
edge reconstruction with Bi.sub.12 SiO.sub.20 reported by J. P. Huignard
and J. P. Herriau can be used to edge-enhance the input image, but it
cannot be used to edge-enhance the reference image. Consequently, another
object of this invention is to implement edge enhancement on the reference
image using the dependence of the index grating erasing, which reduces the
diffraction efficiency on the read beam intensity.
STATEMENT OF THE INVENTION
In accordance with the present invention, a laser beam is expanded,
collimated and split into three beams, namely write beam 1, write beam 2
and read beam, using polarizing beam splitters and half-wave plates,
although a separate laser may be used for the read beam. The half-wave
plates are used for adjusting the beam intensity ratios by rotating the
polarizations of the laser beams. Separate spatial light modulators, such
as liquid crystal TV panels, are placed in the paths of write beam 1 and
the read beam in order to introduce an input image and a reference image,
respectively. The input and reference images are then Fourier transformed
by separate lenses and directed onto opposite faces of a photorefractive
crystal, such as a photorefractive compound semiconductor crystal. The
write beam 2 is directed onto the same face of the semiconductor materials
as the write beam 1 which bears the input image.
A Dove prism is placed in the path of the read beam and caused to spin
about the axis of the read beam to rotate the reference image and thereby
produce a rotation invariant effect in order to provide for correlation
between the reference image and all angles of orientation of the input
image. The read beam which bears the reference image is subjected to the
Bragg diffraction process as it is transmitted through the semiconductor
material and then propagates along the path of write beam 1. In so doing
the diffracted beam is reverse Fourier transformed. Orientation of the
semiconductor material causes the diffracted beam (s-polarized) to be
polarized perpendicular to that of the read beam (p-polarized) so that a
polarizing beam splitter in the path of write beam 1 reflects only the
diffracted beam into a suitable readout means, such as a TV camera.
The power ratio of write beam 2 to write beam 1 is optimized so that the
input image is effectively edge enhanced by the photorefractive crystal
using the technique reported by J. P. Huignard and J. P. Herriau in the
paper cited above. What is new here is that the power ratio of the read
beam to the write beam 1 is optimized so that the object in the reference
image is also edge enhanced by the photorefractive crystal in accordance
with the present invention.
The novel features that are considered characteristic of this invention are
set forth with particularity in the appended claims. The invention will
best be understood from the following description when read in connection
with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a general block diagram of a correlation theorem-based
optical correlator.
FIGS. 2a and 2b illustrates two configurations of correlation-theorem based
optical correlators, namely (a) the VanderLugt configuration and (b) the
joint transform configuration, respectively.
FIG. 3 illustrates schematically an arrangement for a real-time optical
correlator utilizing the polarization properties of degenerate four-wave
mixing in a photorefractive semiconductor material in accordance with the
present invention.
FIGS. 4a and 4b illustrate schematically the experimental result of edge
enhancement of the input image and the reference image. FIG. 4b
illustrates in an idealized line drawing the result of cross correlation
of the small circular reference image with the large circular input image
shown in FIG. 4a.
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, an optical correlator is shown which implements a
correlation theorem given by
A.sub.1 A.sub.2 =F.sup.-1 [F(A.sub.1)F*(A.sub.2)] (1)
where A.sub.1 and A.sub.2 represent two two-dimensional images and A.sub.1
A.sub.2 represent the correlation function of A.sub.1 and A.sub.2 given by
##EQU1##
The significance of Equation (1) is that it contains only the Fourier
transforms of A.sub.1 and A.sub.2 which can be easily implemented
optically using lenses, while Equation (2) contains a double integral
which is not in an explicit form that can be implemented optically. The
time needed for a Fourier transform operation is as short as the time
needed for light to travel less than twice the focal length of the lens,
usually only a few nanoseconds.
The multiplication operation in the right side of Equation (1) is
implemented by holographic writing and reading. The result of
multiplication, F(A.sub.1)F*(A.sub.2), is proportional to the diffracted
beam. The inverse Fourier transform of F(A.sub.1)F*(A.sub.2) can be again
performed by a lens. Two optical correlator configurations will now be
discussed and compared with reference to FIGS. 2a and 2b.
In a nonreal-time implementation, writing and reading a hologram takes
place at different times, whereas in real-time implementation they are
required to take place simultaneously. That requires a four-wave mixing
process in which the write beam 1, the write beam 2, and the read beam may
interact with each other in the holographic medium according to nonlinear
coupled wave equations. In general, in a correlation-theorem based optical
correlator, there are two methods for writing and reading the holograms
using distinct configurations illustrated in FIGS. 2a and 2b, namely (a)
the VanderLugt configuration and (b) the joint transform configuration. In
the VanderLugt configuration, the hologram is written by the Fourier
transform of input image and write beam 2, usually a plane wave, and read
by the Fourier transform of reference image, while in the joint transform
configuration, the hologram is written by the Fourier transforms of both
images and read by a plane wave.
Mathematically, these two configurations are similar, but in real-time
implementations there is a difference in the system speed limitations.
Namely, in the VanderLugt configuration, the image in the read beam may be
changed faster than the speed of the holographic medium because the read
beam is not responsible for writing the hologram, whereas in the joint
transform configuration, none of the image beams can be changed faster
than the speed of the holographic medium, because they need to write the
hologram. This difference is important in achieving rotation variance and
size invariances as discussed below.
Correlation theorem-based optical correlators are not rotation- and
size-invariant, because they only perform template matching. Although
rotation invariance and size invariance can be achieved using certain
algorithms, these algorithms usually cannot be implemented optically;
instead, digital implementation is needed. However, size invariance and
rotation invariance can be implemented optically by rotating and varying
the size of the reference image continuously. This implementation is not
practical unless the reference image can be changed much faster than the
input image. Therefore, VanderLugt configuration is more adequate for
implementing rotation invariance and size invariance. However, one should
note that the frame rate of the system will be decreased if the reference
image is rotated on the spatial light modulator electronically. A
potential solution to this problem is to rotate the image
optomechanically. For example, the image in the optical beam may be
rotated by a Dove prism.
The nonlinear optical process involved in the real-time optical correlator
is four-wave mixing because there are four beams, i.e., three input beams
and one output beam mixed in the nonlinear optical medium. Degenerate
four-wave mixing (DFWM) refers here to the four-wave mixing process in
which the wavelengths of all the beams are the same, whereas non-DFWM
refers to the one in which the wavelengths of the read beam and the write
beam are different. (Note that in nonlinear optics, non-DFWM may also
refer to the process in which the wavelengths of the two write beams are
different.) A fundamental issue that occurs in volume holographic medium
based correlator is the view angle limitation imposed by the Bragg
diffraction process in which the diffraction angle cannot be arbitrary as
in the non-Bragg diffraction process.
The Bragg limitation is different for optical correlators using DFWM and
non-DFWM. In DFWM, Bragg diffraction only limits the view angle of the
read beam, whereas in non-DFWM it limits the view angles of both the read
beam and write beam 1. Thus, for optical correlators using DFWM, it is
possible to have a full translation invariance (by putting the input image
in write beam 1), whereas for optical correlators using non-DFWM, only
partial translation invariance exists.
Bragg diffraction does limit the view angle of the read beam or the write
beam 2 in both DFWM and non-DFWM. However, because the position of the
reference image can be fixed and centered to the read beam (in the
VanderLugt configuration) or to the write beam 2 (in the joint transform
configuration), this Bragg limitation usually does not create a problem
unless the reference image is too large; even so, the size of the
reference image can always be reduced to be within the view angle using a
lens imaging system.
Another difference between DFWM and non-DFWM in the photorefractive crystal
is the diffraction efficiency. In DFWM, because the wavelength of the read
beam is the same as that of the write beam, the hologram will be partially
erased and so the diffraction efficiency will be reduced, whereas in
non-DFWM the wavelength of the read beam can be chosen such that the
photorefractive crystal is not sensitive to that wavelength. Therefore, in
general, the diffraction efficiency in non-DFWM is higher than that in
DFWM, but because of the advantage of translation invariance discussed
above and edge enhancement discussed below, DFWM is selected for the
present invention.
Image Edge Enhancement
Edge enhancement is an image processing technique that erases the body (or
DC component in the Fourier domain) of an image so that only the edge (or
AC component) is kept. Edge-enhanced optical correlation refers to the
kind of correlator in which the input image and the reference image are
edge-enhanced. The advantage of an edge-enhanced correlator is that the
autocorrelation peak of an edge enhanced image is sharper than that of the
original image. However, the tradeoff is that the peak intensity is
relatively sensitive to angular shifts and size difference between the
input image and the reference image. The size sensitivity problem is more
difficult to solve than the angular sensitivity problem. Nevertheless, in
certain applications, the size of the input image is fixed and always the
same as that of the reference image.
The angular sensitivity problem can be solved by rotating the reference
image continuously, such as by spinning a Dove prism. Edge enhancement of
an image can be implemented holographically by using the dependence of the
diffraction efficiency on the writebeam ratio, as in the prior art
referred to hereinbefore. However, this prior-art technique can only be
used to edge enhance the input image. In accordance with the present
invention, the reference image in the read beam can also be edge enhanced
in a manner which will now be described in detail. With DFWM in a
photorefractive crystal, the index grating can be partially erased by the
read beam. The erased amount increases with the read beam power. Note that
the beam power equals the beam intensity times the cross-section area of
the main laser beam, typically about 1 cm.sup.2. Consequently, the beam
power ratios for edge enhancement may be adjusted by adjustment of light
intensity since the cross sections of both write beams and the read are
substantially equal. But to be technically correct, it is the power ratios
of the write beams and the read beam that are optimized for input image
edge enhancement in the first instance and then output image edge
enhancement, although adjustment of intensity is sometimes used
hereinafter.
Since in the Fourier domain, the DC component (body of the image) usually
has a higher intensity than the AC component (edge of the image), the
diffraction efficiency of the DC component is lower than that of the AC
component. The intensity ratio of the read beam to the write beams is
optimized so that the object in the reference image is effectively edge
enhanced by the photorefractive crystal. The required adjustment for this
may be determined empirically by placing the same input image in the read
beam as placed in write beam 1 and, after adjusting the intensity ratio of
the write beam 1 to the write beam 2, adjusting the intensity ratio of the
read beam to the write beams until optimum edge enhancement is achieved.
Thus, the combination of Fourier lenses and the photorefractive crystal in
the present invention functions effectively like a high-pass filter which
allows only the edges of the input image and the reference image to pass.
This unique and simple process for simultaneous double-edge enhancement in
a photorefractive crystal based optical correlator can save the otherwise
needed additional computer time for achieving edge enhancement.
Example
In one example of the present invention illustrated in FIG. 3, GaAs
photorefractive crystal PRC is used as the degenerate four-wave mixing
(DFWM) material in the VanderLugt (transmission-hologram) configuration,
because obtaining a higher speed in the GaAs material and a full
translation invariance was desired. The tradeoff in this configuration is
a smaller diffraction efficiency. However, the read-out signals obtained
were still strong enough to saturate a TV camera 10 (vidicom) or the
equivalent (e.g., a Ge detector array). With a diffraction efficiency less
than 0.1% (estimated from previous experiments), background noise can be
easily stronger than the signal. The only way of obtaining a clean output
was to eliminate as much background noise as possible. A high
signal-to-noise ratio was achieved by selecting the crystal orientation
indicated above the GaAs crystal PRC in FIG. 3. That orientation can yield
a cross-polarization readout, and in so doing, the polarization of the
diffracted beam was caused to be perpendicular to that of the read beam as
well as the background noise as indicated in FIG. 3, so that the noise
could be eliminated by a polarizing beam splitter PB3.
The main laser beam 11 from an Na:YAG laser 12 was expanded and collimated
by lenses L1 and L2 and then split into three beams, namely WRITE BEAM 1,
WRITE BEAM 2, and READ BEAM by polarizing beam splitters PB1 and PB2.
Mirrors M1 through M7 are provided as needed to route the split beams onto
the photorefractive crystal PRC at the appropriate angles with faces of
the crystal, as shown. Half-wave plates H1 and H2 were used in conjunction
with the beam splitters PB1 and PB2, respectively, to adjust the beam
power (intensity) ratios referred to hereinbefore. Spatial light
modulators implemented with liquid crystal TV panels, LCTV1 and LCTV2,
were put in the respective paths of the WRITE BEAM 1 and the READ BEAM to
introduce the input image and the reference image, respectively, under
control of a personal computer PC. However, since the READ BEAM need not
be coherent with WRITE BEAM 1 and WRITE BEAM 2, a separate laser could
have been used to generate the READ BEAM directed through the spatial
light modulator implemented with the liquid crystal TV panel LCTV2.
As mentioned earlier, the Bragg diffraction process will limit the
horizontal size of the reference image modulated in the READ BEAM. To
reduce this limitation, the images on the two liquid crystal TV panels are
demagnified by lenses L3, L4 and L7, L8, respectively. The images are then
Fourier transformed by lenses L5 and L6, respectively. The diffracted beam
propagates from the GaAs crystal PRC along the WRITE BEAM 1 and passes
through Fourier lens L5 in a direction opposite WRITE BEAM 1. By doing so,
the diffracted beam in the path of WRITE BEAM 1 is inverse Fourier
transformed.
The orientation of the GaAs crystal PRC is indicated in FIG. 3 directly
over the crystal allows cross-polarization readout, i.e., the polarization
of the diffracted beam passed through the lens L5 is perpendicular to that
of the READ BEAM. As a result, polarizing beam splitter PB3 reflects only
the diffracted beam (s-polarized) into the camera 10, because other beams
are p-polarized. This not only yields a higher signal-to-noise ratio, but
also allows most of the WRITE BEAM 1 to be transmitted through and most of
the diffracted beam to be reflected by the polarizing beam splitter PB3.
In order to produce an input image and a reference image in the respective
WRITE BEAM 1 and READ BEAM, the personal computer PC was installed with
image frame grabbers 13 and 14. In general, an image frame grabber can
take real-time video input, freeze one frame and digitize it for storing
in a disk in the computer. In reverse, it can convert the digitized image
to standard analog video signal for separately driving the liquid crystal
TV panels LCTV1 and LCTV2. Using image manipulation software in the
computer, it is possible to do many things to the digitized image, such as
"cut and paste," move image detail from one area to another, and even
create an image from scratch. In the example, the input and reference
images were entered through the separate image frame grabbers 13 and 14
synchronized by the personal computer. The reference image was kept fixed
in the frame grabber 14 to drive the spatial light modulator panel LCTV2,
while the input image entered through the spatial light modulator LCTV1
contained fixed and moving objects at different times. The movement of an
input image was simulated by using the moving function of the image
manipulation software. It was contemplated that in actual applications,
the input image would be from a TV camera 15, hence the need for the frame
grabber 13, and the reference image would be from the computer PC
installed with the required software for synchronizing operation of the
frame grabber 13 with the frame grabber 14, while continually entering
input and reference images.
Experiments performed with this arrangement included a successful video
demonstration of real-time image correlation, response time measurement,
characterization of the spatial light modulator for panels LCTV1 and LCTV2
and edge enhancement. In all the experiments, the diameter of the
collimated main laser beam was about 0.4" which covers about 1/3 of the
spatial light modulator panel (1.1".times.0.8"). The laser beam was not
expanded to cover the full spatial light modulator (liquid crystal TV
panel), because a higher intensity at the crystal was desired for yielding
a shorter response time. (Note that the response time of a photorefractive
crystal is basically inversely proportional to the laser intensity.)
The spatial light modulators LCTV1 and LCTV2 used were obtained from a
color projection TV sold by Epson, together with the pixel drive
circuitry.
One projection TV contains three spatial light modulator panels (LCTVs)
modulating three (red, green, and blue) beams, separately. The device
technology of the LCTVs is the thin film transistor (TFT) active matrix
which can yield a relatively higher contrast ratio than earlier
technology. The resolution of each LCTV is 320.times.220 and the measured
contrast ratio at 1.06 micron was 100:1. Due to the pixel structure of the
panel, the transmitted image is diffracted into many orders. The maximum
transmittance of an LCTV was experimentally checked at 1.06 micron
wavelength and a value of about 8%. The LCTVs were operated at a TV video
frame rate which is slower than the frame rate that could be used for
correlation of images directed onto the GaAs. That TV frame rate was thus
the maximum speed at which the correlator could be operated.
The GaAs sample used was undoped, polished, and antireflection coated. The
dimension was 11.times.10.times.5 mm. No external electric field was
applied to enhance the diffraction efficiency, because the applied
electric field would increase the response time of GaAs. The response time
of GaAs was measured by a Ge detector with WRITE BEAM 1 being chopped. The
rise time of GaAs in the correlator setup was measured as a function of
the total laser intensity for READ BEAM: WRITE BEAM 1 : WRITE BEAM
2=100:70:1 (measured before the beams were transmitted through LCTVs). The
shortest response time measured was 0.8 msec at a total laser intensity of
about 1.5 W/cm.sup.2 and a grating spacing of about 6 microns (angle
between write beams=11.degree. ). In general, at this intensity level an
order of magnitude shorter response time should be obtained, but, in
practice, the spatial light modulator LCTV1 and LCTV2 could cut down the
light intensity and thus the speed significantly. Nevertheless, the
experimental data indicate that even at 200 mW/cm.sup.2 the response time
(10 msec) is still comparable to the video rate.
The maximum total beam power just before the beams entered the crystal was
about 100 mW, which was only about 6% of the total laser power. Thus, to
reduce the power requirement, it is necessary to find a spatial light
modulator that has a higher transmission. Nevertheless, for a frame rate
between 100 and 1000 frames/sec using LCTVs, very compact commercial
laser-diode pumped single frequency solid state lasers (0.5 W) may satisfy
this power requirement.
Note that because the READ BEAM does not have to be coherent with WRITE
BEAM 1 and WRITE BEAM 2, two separate lasers can be used as noted
hereinbefore, one for the READ BEAM and one for WRITE BEAM 1 and WRITE
BEAM 2. Thus, the effective available total laser power of these compact
lasers is 1 W. With such lasers, it is possible to build a very compact
and fast GaAs based optical correlator.
As mentioned earlier, it is possible to perform edge enhancement on both
the input image and the reference image in the present invention. In this
experiment, two circular images shown in FIG. 4a were used, one a large
filled circle and the other a small filled circle. FIG. 4b shows that the
correlation pattern between the large filled circle and the small filled
circle (dot) is an unfilled circle, i.e., an edge enhanced image. This is
true for either when the dot is in the input image via LCTV1 or in the
reference image via LCTV2.
The correlation output shown in FIG. 4b actually contains two circles with
the inner circle stronger than the outer one. This is because the dot is
actually a small filled circle which was also edge enhanced in the
wave-mixing process, and that the correlation between a small circle and a
big circle is two circles. The difference in radius of the two circles is
equal to the diameter of the small filled circle, because in FIG. 4b, the
inner circle corresponds to the overlap between the two circles as the
small input circle is moving and touching the inside edge of the big input
circle, while the outer circle corresponds to the overlap between the two
circles as the small reference circle is moving and touching the outside
edge of the big input circle. In both cases, there is edge enhancement of
the correlation between two circular images, but the inner circle edge
enhancement is greater.
As noted hereinbefore, the edge enhancement technique of this invention
requires adjustment of not only the power ratio of the WRITE BEAM 1 to the
WRITE BEAM 2 but also of the WRITE BEAM 1 to the READ BEAM, and, since the
cross sections of the beams are equal, it is possible to adjust power
ratios by adjusting intensity ratios. That is done by adjusting the
intensity of the WRITE BEAM 1 by providing a polarizer P1 and adjusting
the angular orientation of a half-wave plate H3 in its path to adjust the
intensity of the WRITE BEAM 1 relative to WRITE BEAM 2. Similarly, by
providing a polarizer P2 and a half-wave plate H4 in the path of the READ
BEAM, the angular orientation of the half-wave plate H2 is adjusted to
adjust the intensity of the READ BEAM relative to the WRITE BEAM 1.
It should be noted that a DOVE PRISM may be placed in the READ BEAM path
and caused to spin about the axis of the READ BEAM to rotate the reference
image during correlation with an input image. That produces a rotation
invariant effect for correlation between the input image and all angles of
orientation of the reference image. There would be no advantage in the
special case of correlating two circular images, but except for that
special case, such a DOVE PRISM should be included.
Although particular embodiments of the invention have been described and
illustrated herein, it is recognized that modifications and variations may
readily occur to those skilled in the art. Consequently, it is intended
that the claims be interpreted to over such modifications and equivalents.
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