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January 15, 1997 / Vol. 22, No. 2 / OPTICS LETTERS 87
Pure phase correlator with photorefractive filter memory
M. Duelli, A. R. Pourzand, N. Collings, and R. D¨andliker
Institute of Microtechnology, University of Neuchˆatel, Rue A.-L. Breguet 2, CH-2000 Neuch ˆatel, Switzerland
Received June 10, 1996
We report on the investigation of a new compact configuration of an inverted VanderLugt-type correlator system.
The phase of the Fourier transform of the image to be recognized is displayed on a phase-modulating electrically
addressed spatial light modulator. This phase display is compared with the phase of the Fourier transforms
of a reference library recorded in a photorefractive LiNbO
3
crystal. Angular hologram multiplexing permits
fast data access, and the use of the conjugated replica of the stored templates leads to an elimination of phase
distortions introduced by the optical system. With such a configuration, the correlator is fully shift invariant
in spite of the photorefractive crystal thickness and has good discrimination with sharp correlation peaks.
1997 Optical Society of America
Pure phase correlation
1
uses only the phase informa-
tion of the object and a template; i.e., it takes the phase
distribution of the Fourier transform of the object to be
recognized and correlates it with the phase-only filter
defined by Horner and Gianino.
2
This type of corre-
lator shows sharp correlation peaks, a high light ef-
ficiency, and a high discrimination capability. It is
mathematically equivalent to inverse filtering.
3
The
phase distributions are implemented with twisted ne-
matic liquid-crystal television (LCTV) screens that can
be updated within a few tens of microseconds. How-
ever, the correlation of a single input image with a
single filter at video rate limits the correlation speed.
Previously high-capacity optical memories were com-
bined with correlators where reference objects were
stored on optical disks
4
or as phase holograms in pho-
torefractive crystals
5
and sequentially loaded into the
correlator, permitting a fast search through the refer-
ence library.
We built a compact hybrid digital–optical correlator
system that performs pure phase correlation. A com-
mercially available LCTV is used as a phase-only input
device for the phase distribution of the Fourier trans-
form of the input object, and a photorefractive crystal
serves as a holographic memory for the storage of a li-
brary of reference objects. Thus the real-time perfor-
mance of spatial light modulators (SLM’s) is combined
with the high storage capacity and the fast data access
of volume holographic memories. It is also possible to
update or refresh the holographic memory.
In classical 4-f correlator systems the size of the fil-
ter has to be matched to the size of the Fourier trans-
form of the input image. If a SLM is used in the filter
plane this requirement leads most often to a large fo-
cal length of the Fourier-transform lens and thus to a
large overall size of the whole system. A high-quality
lens and SLM must be used to minimize aberrations.
An adjustment sensitivity of a few micrometers perpen-
dicular to the optic axis and a few tens of micrometers
along the optic axis has to be fulfilled to yield correct
results. Moreover, for a nonquadratic pixel size of the
SLM an anamorphic imaging system must be built or
the filter changed electronically to correct for the as-
pect ratio. To avoid these requirements we use the
same optical setup for the storage of the reference ob-
jects and for the correlation of the input image with the
stored reference objects.
The experimental setup of our system is shown in
Fig. 1. During storage of the reference objects in the
photorefractive crystal, Shutter 1 is open and Shut-
ter 2 is closed. The beam from an Ar
1
laser (wave-
length l 488 nm) is split into an object beam,
which illuminates the LCTV, and a plane-wave refer-
ence beam. The phase function fsu, vd of the Fourier
transform of the object to be stored is calculated by
software as a 512 3 512 matrix from the original
object, which is also given as a 512 3 512 matrix. It
is displayed on the LCTV, which works in the phase-
modulation regime.
6
The transmitted light is then
collected by a lens and interferes with the reference
beam in the photorefractive LiNbO
3
:
Fe s.0.1 mol. %d
crystal, where a phase hologram is written. We use
the 90
±
geometry; i.e., the crystal is a 45
±
cut with a
size of 10 mm 3 10 mm 3 7 mm. Its low dark con-
ductivity leads to a storage time of a few weeks in the
dark. For hologram multiplexing the angular encod-
ing scheme is utilized by rotation of the storage crystal
by Du 0.025
±
for each consecutive hologram. The
holograms were recorded with 30 cycles in the incre-
Fig. 1. Experimental setup of the phase-only correlator
system: BS’s, beam splitters; SF’s, spatial filters consist-
ing of a 203 microscope objective and a 10-mm pinhole; M’s
mirrors, L
1
,L
2
, lenses; f ’s, 200 mm; PS, point stop, with
diameter mm; FFT, fast Fourier transformer; c, direction of
the c axis.
0146-9592/97/020087-03$10.00/0 1997 Optical Society of America
88 OPTICS LETTERS / Vol. 22, No. 2 / January 15, 1997
mental recording schedule
7,8
and a writing time of 5 s
per image per cycle. The writing intensities of the
modulated object wave I
ob
and the plane reference wave
I
ref
are approximately I
obj
I
ref
9 mWycm
2
. Be-
cause a defocused edge-enhanced image is stored in the
photorefractive crystal, there is no dynamic range limi-
tation as is the case in the storage of Fourier trans-
forms, in which the amplitudes of the object and of the
reference beams are equal only over a narrow range of
spatial frequencies.
The SLM consists of a liquid-crystal display taken
from an Epson VPJ700 video projector. The resolution
is 320 3 220 pixels, with a pixel size of 80 mm 3 90 mm.
The screen acts as a multilevel phase hologram that
generates superimposed diffraction orders.
9
The coef-
ficients of the diffraction orders depend on the phase
matching and the coupled amplitude modulation. The
first order is the ideal phase-only response but with
reduced light efficiency (typically 70%); i.e., an edge-
enhanced object is reconstructed by the high-pass
filtering effect if only the phase information of a
Fourier-transformed object is considered. The zero or-
der yields a central spot situated at the optic axis of the
system, and the minus first order corresponds to the
ghost image. An object that is reconstructed from
the displayed phase function in the focal plane of lens
L
2
is shown in Fig. 2. The zero and first orders are
clearly visible; higher diffraction orders appear as noise
in the edge-enhanced object. The rectangular pixel
shape leads to an aspect ratio of the reconstructed ob-
ject that is different from that of the original. During
recording of the reference library a point stop blocks
the central spot at the focal plane of lens L
2
. A rect-
angular aperture at the same place eliminates the
higher diffraction orders that arise from the pixellation
of the LCTV.
To perform pure phase correlation we set the crystal
at the angle corresponding to the first stored filter.
Shutter 1 is closed, and Shutter 2 is opened. The
crystal is illuminated with the reference beam, and
the transmitted beam is retroreflected by a simple
mirror. A phase-conjugated replica of the wave that
has been stored at this angle is diffracted and returns
to the LCTV. The phase function expff
input
su, vdg of
the Fourier-transformed object to be recognized, which
is again calculated by software, is displayed on the
LCTV. The displayed phase function expff
input
su, vdg
and the retrieved and conjugated phase function
expf2f
i
su, vdg are multiplied in the LCTV plane. The
Fourier transformation of this phase distribution,
which is performed by lens L
1
, results in correlation
between the edge-enhanced reference object and the
edge-enhanced input object. The intensity distribu-
tion I sx, yd that is observed in the correlation plane,
i.e., the focal plane of lens L
1
, when the ith stored
object is retrieved is given by
Isx, yd jFThexpf jf
input
su, vdgexpf2jf
i
su, vdgjj
2
,
(1)
where FT denotes the Fourier transformation.
The autocorrelation gives a delta function; there-
fore we expect to detect sharp correlation peaks. The
correlation plane is imaged onto a CCD camera. By
rotating the crystal we sequentially retrieve the refer-
ence objects and correlate them with the input object.
In order not to erase the holograms during readout, we
strongly decrease the intensity of the reference plane
wave compared with the recording intensity. The in-
tensity of the incident light at the crystal is approxi-
mately I 140 mWycm
2
. Alternatively, holograms
could be thermally fixed in the crystal. Because a
conjugated wave is used, phase distortions introduced
by the nonflatness of the LCTV and the Fourier-
transform lenses are canceled, and simple lenses can
be used. Moreover, there is no need to correct for the
aspect ratio, and the system is compact and easily
adjusted.
The experimental results of the autocorrelation and
the cross-correlation of an input object composed of
the three stored objects are shown in Fig. 3. The
surface plot of the interesting region of the correlation
plane covers only 10% of the whole correlation plane.
Because of the pure phase correlation, we obtain a good
discrimination capability with sharp autocorrelation
peaks. The noise in the surface plots arises from
the part of the reconstructed edge-enhanced object
that is not coupled into the correlation peak. Thus
for a heavily covered input object the noise is the
greatest. It should be noted that the noise in this
system is reduced because we filtered out the zero-
order component when recording the library in the
crystal.
The number of input objects that can be recog-
nized per second in this system depends on the
update rate of the SLM. Currently the phase trans-
formation of the Fourier-transformed input object
is performed with software. However, a real-time
electronic fast-Fourier-transform board
10
would permit
an update of the LCTV at video rate. The correlation
speed is determined by the time required for the
presentation of a new filter. This access time of the
holographic memory depends on the rotation speed of
the photorefractive crystal and the angular separation
of the holograms. With the crystal mounted upon
a stepper-motor-driven rotation state we can read
out approximately 1000 hologramsys in a continuous
movement. An increase in crystal length increases
the number of templates per angle and thus the
Fig. 2. Reconstructed object from the phase-only filter
observed in the focal plane of lens L
2
. The LCTV acts
as a multilevel phase hologram, leading to superimposed
diffraction orders.
January 15, 1997 / Vol. 22, No. 2 / OPTICS LETTERS 89
Fig. 3. Three phase filters that had been calculated from
the three objects shown were stored in the photorefractive
crystal. The surface plots show the intensity distribution
obtained in the correlation plane when the phase filter
of the input object was displayed on the LCTV and the
corresponding filter was read out from the holographic
memory. The surface plot covers only 10% of the whole
correlation plane.
number of correlations that can be performed per
second at the same angular velocity of the storage
crystal. At present, the number of correlations per
second is limited by electronic and electromechanical
components.
In conclusion, the system combines a holographic
volume memory for fast and parallel data access and
a real-time updatable liquid-crystal television in an
optical correlator. Shift-invariant pattern recognition
with sharp correlation peaks and high discrimination
can be performed owing to the pure phase correlation.
This study was carried out in the context of the Brite-
Euram II program ‘‘A hybrid opticalydigital correlator
for high speed pattern recognition.’’ We thank the
Swiss Federal Office for Education and Science for
financial support and the Department of Mechanical
Engineering, Glasgow University, for supplying the
image data and the photorefractive crystal. Oxidation
treatment of the crystal by M. Ewart and polishing by
J. Hajf ler of the Swiss Federal Institute of Technology
(Z
¨
urich) are gratefully acknowledged.
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