All optical image processing and pattern recognition apparatus using stimulated photon echoes

An image processing apparatus having a third-order nonlinear stimulated photon echo medium (1). The photon echo medium (1) can store large numbers of images in the form of a Fourier transformed pattern by spectral modulation. The spectral modulation is carried out by sending optical pulses in an optical pulse train having (or not having) image information to the medium (1) so that the population in the ground and excited states are modulated after the passage of the pulse trains and pulses. The Fourier transformed pattern is converted back to temporal modulation, consisting of a sequence of echo pulses that reproduce the original data pulse train. By using the apparatus, ultrafast operation such as convolution and correlation between a number of reference images and a test image can be achieved.

BACKGROUND OF THE INVENTION 
1. Technical Field 
The present invention relates to an optical, high-speed image processing 
apparatus, and more particularly to an all optical image processing and 
pattern recognition apparatus using stimulated photon echoes, which can 
process quickly a number of pieces of image information in real time. 
2Background Art 
High-speed real time processing of two-dimensional images has a variety of 
applications in which large numbers of images must be stored and analyzed. 
These include robotic vision, satellite remote sensing, medical image 
analysis, artificial intelligence and pattern recognition. Optical image 
processing is promising for two principal reasons: parallel processing 
capability and potentially ultrafast speed. Among the existing techniques 
for two-dimensional image processing is a stimulated photon echo technique 
in conjunction with optical Fourier transformation. 
(1) Stimulated Photon Echo 
Stimulated photon echo is achieved when optical pulses are sequentially 
incident into a stimulated photon echo medium, the line shape function 
(absorption characteristic) of which is illustrated in FIG. 2. FIG. 2 
shows that a photon echo medium (a rare earth ion doped dielectric 
crystal) includes many atoms having a narrow homogeneous broadening 
.DELTA..nu..sub.H, and such atoms integrally constitute an inhomogeneous 
broadening .DELTA..nu..sub.IH. When optical pulses P1, P2 and P3 (see 
FIGS. 1 and 3), the energy of which is within the stable absorption range 
corresponding to the inhomogeneous broadening are incident into such a 
medium at time t.sub.1, t.sub.2 and t.sub.3, respectively, a photon echo 
Pe occurs at time t.sub.4 subsequent to the time t.sub.3 (see FIG. 3). 
Time t.sub.4 which the photon echo Pe occurs, is .DELTA.t (=t.sub.2 
-t.sub.1) after t.sub.3, and hence, t.sub.4 -t.sub.3 =t.sub.2 -t.sub.1. 
The width .DELTA..tau. of the pulses incident to the photon echo medium 
has the following relationship with the inhomogeneous broadening 
.DELTA..nu..sub.IH and the homogeneous broadening .DELTA..nu..sub.H : 
EQU 1/.DELTA..nu..sub.IH &lt;.DELTA..tau.&lt;1/.DELTA..nu..sub.H. (1) 
The optical pulse P2 must be incident within time T.sub.2 (T.sub.2 
=1/.DELTA..nu..sub.H) after the incident of the optical pulse P1. The time 
T.sub.2 is the coherence-decay time of absorption transition during which 
the photon echo medium keeps coherency of the incident light. On the other 
hand, the optical pulse P3 must be incident within time T.sub.1 after the 
incidence of the optical pulse P2. The time T.sub.1 is the 
population-decay time of the absorption transition in which the photon 
echo medium returns to its thermal equilibrium state. Thus, the incident 
time of the optical pulses P1 to P3 must satisfy the relationship 
EQU t.sub.2 -t.sub.1 &lt;T.sub.2, t.sub.3 -t.sub.2 &lt;T.sub.1. (2) 
In general, T.sub.1 &gt;&gt;T.sub.2, and the optical pulse P2 is stored in the 
photon echo medium during the population-decay time T.sub.1. 
In this condition, time quadrature .theta.e of the amplitude of the photon 
echo pulse Pe is given by the following equation when the incident pulse 
intensity is weak: 
EQU .theta.e=.mu./.intg..epsilon.(t)dt.varies..theta..sub.1, .theta..sub.2, 
.theta..sub.3, (3) 
where .theta.i=.mu./h.intg..epsilon..sub.i (t)dt (i=1.about.3), .epsilon. 
and .epsilon..sub.i are the electric fields of respective optical pulses, 
and .mu. is the electric dipole moment of the ion in the photon echo 
medium. The intensity of the photon echo pulse Pe is proportional to the 
product of the incident pulses P1, P2 and P3 because the photon echo 
occurs in the third-order nonlinear interaction. Furthermore, it is seen 
that the optical echo signal the waveform of which is similar to that of 
the optical pulse P2 can be obtained when the optical pulses P1 and P3 are 
similar to the delta function having no image information. Thus, the 
photon echo pulse similar to the optical pulse P2 stored in the photon 
echo medium can be read out at time t.sub.4. The optical pulses P1, P2 and 
P3, and the echo pulse Pe must satisfy the phase-matching condition 
(momentum conservation equation) expressed by 
EQU -K.sub.1 +K.sub.2 +K.sub.3 -K.sub.e =0 (4) 
where K.sub.i (i=1, 2 or 3) and Ke are wave-number vectors of respective 
pulses. The echo pulse Pe takes place in the direction to satisfy the 
phase-matching condition. 
Examples of media having a wide inhomogeneous broadening of the absorption 
transition are shown in FIG. 4 and the following Table: 
TABLE 
______________________________________ 
Population-decay time (T.sub.1) and coherence-decay time 
(T.sub.2) for rare earth ion doped materials 
Material Transition 
.lambda.(.ANG.) 
T.sub.1 
T.sub.2 
Ref. 
______________________________________ 
Pr.sup.3+ :LaF.sub.3 
.sup.1 D.sub.2 -.sup.3 H.sub.4 
5925 500 .mu.s 
6 .mu.s 
a) 
.sup.3 P.sub.0 -.sup.3 H.sub.4 
4778 75 .mu.s 
2.4 .mu.s 
c) 
Pr.sup.3+ :YAlO.sub.3 
.sup.1 D.sub.2 -.sup.3 H.sub.4 
6105 180 .mu.s 
35 .mu.s 
a) 
Pr.sup.3+ :CaF.sub.3 
.sup.1 D.sub.2 -.sup.3 H.sub.4 
5941 506 .mu.s 
720 ns d) 
Pr.sup.3+ :LaCl.sub.3 
.sup.1 D.sub.2 -.sup.3 H.sub.4 
6011 195 .mu.s 
.81 .mu.s 
e) 
Pr.sup.3+ :LaBr.sub.3 
.sup.1 D.sub.2 -.sup.3 H.sub.4 
6033 162 .mu.s e) 
Pr.sup.3+ :YAG 
.sup.1 D.sub.2 -.sup.3 H.sub.4 
6096 230 .mu.s 
20 .mu.s 
f) 
.sup.3 P.sub.0 -.sup.3 H.sub.4 
4870 3 .mu.s 
g) 
Eu.sup.3+ :YAlO.sub.3 
.sup.5 D.sub.0 -.sup.7 F.sub.0 
5816 3 ms 58 .mu.s 
h) 
Eu.sup.3+ :Y.sub.2 O.sub.3 
.sup.5 D.sub.0 -.sup.7 F.sub.0 
5808 860 .mu.s 
419 .mu.s 
i) 
Eu.sup.3+ :CaF.sub.2 
.sup.5 D.sub.0 -.sup.7 H.sub.0 
5736 1.8 ms j) 
Nd.sup.3+ :LaF.sub.3 
.sup.4 F.sub.3/2 -.sup.4 I.sub.9/2 
8626 .12 .mu.s 
g) 
.sup.4 G.sub.7/2 -.sup.4 I.sub.9/2 
5221 g) 
Nd.sup.3+ :YAG 
.sup.4 F.sub.3/2 -.sup.4 I.sub.9/2 
8749 .09 .mu.s 
g) 
Sm.sup.3+ :LaF.sub.3 
.sup.4 G.sub.5/2 -.sup.6 H.sub.5/2 
5598 7.7 ms 110 ns k) 
Er.sup.3+ :LaF.sub.3 
.sup.4 S.sub.3/2 -.sup.4 I.sub.15/2 
5388 1.2 ms 12 ns l) 
Ho.sup.3+ :LaF.sub.3 
.sup.5 S.sub.2 -.sup.5 I.sub.8 
5376 .93 ms .66 .mu.s 
5375 .67 .mu.s 
.sup.5 F.sub.5 -.sup.5 I.sub.8 
6411 .55 ms .38 .mu.s 
______________________________________ 
a) Macfarlane et al., Phys. Rev. Lett. 43, 1726 (1979). 
b) Rand et al., Phys. Rev. Lett. 43, 1868 (1979). 
c) Chen et al., Phys. Rev. B21, 40 (1980). 
d) Macfarlane et al., Phys. Rev. B29, 2390 (1984). 
e) Genack et al., Phys. Rev. Lett. 45, 438 (1980). 
f) Shelby et al., Opt. Lett. 8, 304 (1983). 
g) Kachru et al., Private communication. 
h) Shelby et al., Phys. Rev. Lett. 45, 1098 (1980). 
i) Macfarlane et al., Opt. Commun. 39, 169 (1981). 
j) Gustafson et al., Anal. Chem. 51, 1762 (1979). 
k) Macfarlane et al., Phys. Lett. A116, 299 (1986). 
l) Macfarlane et al., Opt. Commun. 42, 346 (1982). 
FIG. 4 is an energy-level diagram of Pr.sup.3+ ion doped into a dielectric 
crystal LaF.sub.3, and the Table is a list of decay characteristics of 
various rare earth ion doped materials. As seen from the Table, decay 
times corresponding to typical absorption transitions greatly differ 
according to the host crystal into which rare earth ions are doped even if 
the rare earth ion is identical. The coherence-decay time T.sub.2 in a 
solid has a large temperature dependence, and is very short at room 
temperature (less than 10.sup.-13 sec.). The population-decay time T.sub.1 
is no more than several milliseconds. However, at an ultra-low 
temperature, the information is stored in the ground state hyperfilm 
levels as non-thermal population modulation which can last up to many 
hours. 
For example, decay times of Eu: YAlO.sub.3 absorption transition (.sup.7 
F.sub.0.sup.-5 D.sub.0 transition; wavelength of 581.6 nm) are as follows: 
coherence-decay time T.sub.2 at 6K is 58 .mu.s, population-decay time 
T.sub.1 is 3 ms, and population-decay decay time in the ground state 
hyperfine levels is approximately 3.8 hours. The inhomogeneous broadening 
is approximately 10 GHz. Consequently, the narrowest optical pulse width 
is approximately 100 ps, and about 10.sup.5 pulses (bits) can be incident 
into the photo echo medium during the coherence-decay time T.sub.2. These 
pulses can be stored nearly 4 hours. 
Similar photon echoes can be observed when one or more optical pulses P1-P3 
are analog optical signals including two-dimensional image information. 
For example, the optical pulse P2 including two-dimensional image 
information can be stored in the photon echo medium during the 
population-decay time T.sub.1, and can be retrieved by the incidence of 
the optical pulse P3. 
(2) Fourier processing of the optical signal 
FIG. 5 shows a Fourier processing system for the optical signal using a 
third-order nonlinear medium. A pair of lenses L.sub.1 and L.sub.2 of 
focal length f are placed on either side of the third-order nonlinear 
medium S, the distance from each lens to the medium being f. As shown in 
FIG. 5, images E.sub.1, E.sub.2 and E.sub.3 are located in the outer focal 
planes of the lenses, respectively. These images are irradiated by laser 
beams, the angular frequency of which is .omega.. The images E.sub.1, 
E.sub.2 and E.sub.3 are expressed by 
EQU E.sub.i =1/2A.sub.i (x,y,z)exp(i(kz-.omega.t))+c.c.(i=1.about.3) (5) 
where A.sub.i is the amplitude of the image E.sub.i, 
k is a wave number vector of E.sub.i (i=1, 2 or 3), and c.c. is an acronym 
for "complex conjugate". Here, the origin of the z-axis is defined at the 
leftmost point as shown in FIG. 5, and u.sub.1, u.sub.2 and u.sub.3 are 
defined as follows: 
EQU A.sub.1,3 (x,y,0)=u.sub.1,3 (x,y), A.sub.2 (x,y,4f)=u.sub.2 (x,y) (6) 
The angular frequencies of the incident beams are identical. The amplitude 
of A.sub.1 transmitted through lens L.sub.1 is subjected to Fourier 
transform in the Fresnel approximation and is expressed by 
##EQU1## 
where exp(ikn.DELTA.)exp(-ik(x.sup.2 +y.sup.2 /2f) is the transfer 
function of the lens L.sub.1, and "F" represents the Fourier transform. At 
the focal plane of the lens we have Z=2f in which case equation (7) 
simplifies and shows that the lens takes a perfect Fourier transformation. 
Similarly, A.sub.2 and A.sub.3 are transformed by the Fourier transform 
lenses L.sub.1 and L.sub.2. When the optical images thus transformed are 
incident into the photon echo medium S, nonlinear polarization Pn.sub.L 
occurs and is expressed by 
EQU Pn.sub.L =.chi..sub.ijkL.sup.(3) A.sub.1j A.sub.2K A.sub.3L * (8) 
where .chi..sub.ijkL.sup.(3) is a third-order tensor representing nonlinear 
optical susceptibility. Optical signal A.sub.4 produced by the nonlinear 
polarization counterpropagates with respect to E.sub.3 to satisfy 
conservation of energy and phase-matching condition (conservation of 
momentum) corresponding to the third-order nonlinear interaction. The 
A.sub.4 wave at z=0 is expressed by 
EQU A.sub.4 (x.sub.0, y.sub.0, 0)=Cu.sub.1 (-x, -y)*u.sub.2 
(x,y).multidot.u.sub.3 (-x, -y) (9) 
where C is a constant of proportionally determined by a nonlinear 
coefficient, "*" represents a convolution, and "." represents a 
correlation. It is seen from the above relationship that when u.sub.3 is a 
point source, A.sub.4 is a convolution image of u.sub.1 and u.sub.2, and 
when u.sub.1 is a point source, A.sub.4 is a correlation image of u.sub.2 
and u.sub.3. Thus, the Fourier optical system shown in FIG. 5 can achieve 
various image processings by using a third-order nonlinear medium S. 
In this case, the maximum spatial frequency can be obtained as follows. 
First, the maximum spatial frequency fms in the Fresnel approximation is 
given by 
EQU fms&lt;(4/.pi..lambda..sup.3 f).sup.174 ( 10) 
The upper limit of the input field spot size d is given by 
EQU d&lt;(4.lambda.f.sup.3 /.pi.).sup.1/4 ( 11) 
Hence, the maximum resolution Nmax is derived through the above two 
equations, yielding 
EQU Nmax=16 f/.pi..lambda. (12) 
When the focal length is 10 cm and the wavelength .lambda. is 0.5 .mu.m, 
the maximum spatial frequency is 10.sup.3 cm.sup.-1, which is sufficient 
for image processing. 
SUMMARY OF THE INVENTION 
In the above technique, each input pulse P1, P2, and P3 of the photon echo 
system presents a single image, and therefore, it is impossible to achieve 
Fourier image processing between more than three images by a single photon 
echo processing. This hinders high-speed processing necessary for 
industrial applications where a number of matching processings are 
required between a test image to be analyzed and many reference images. 
Therefore, the object of the present invention is to provide an optical 
image processing apparatus which can carry out image processing such as 
correlation processing between a test image and many reference images by 
an optical Fourier transform using a third-order nonlinear medium. 
To accomplish this object, the present invention combines the stimulated 
photon echo and Fourier image processing using a third-order nonlinear 
medium, being provided with a multiple image storing function by using a 
pulse train including a series of optical pulses instead of the first 
pulse P1 or the second pulse P2. 
More specifically, the present invention provides all optical image 
processing and pattern recognition apparatus using stimulated photon 
echoes comprising: a stimulated photon echo medium having an inhomogeneous 
broadening line shape function; first incident means for launching a first 
optical pulse into the photon echo medium; second incident means for 
launching a second optical pulse train including two or more optical 
pulses into the photon echo medium from a direction different from the 
incident direction of the first optical pulse in the coherence-delay time 
of the photon echo medium after the incidence of the first optical pulse; 
third incident means for launching a third optical pulse into the photon 
echo medium in the population-decay time of the photon echo medium after 
the incidence of the second optical pulse train, the population-decay time 
being defined as time during which the medium returns to its thermal 
equilibrium state from its excited state; and optical detecting means for 
detecting photon echoes emitted from the photon echo medium, wherein the 
second optical pulse train includes a plurality of pieces of image 
information. 
Furthermore, the present invention provides all optical image processing 
and pattern recognition apparatus using stimulated photon echoes 
comprising: a stimulated photon echo medium having an inhomogeneous 
broadening line shape function; first incident means for launching a first 
optical pulse train including two or more optical pulses into the photon 
echo medium; second incident means for launching a second optical pulse 
into the photon echo medium from a direction of the first optical pulse 
train in the coherence-decay time of the photon echo medium after the 
incidence of the first optical pulse train; third incident means for 
launching a third optical pulse into the photon echo medium in the 
population-decay time of the photon echo medium after the incidence of the 
second optical pulse, the population-decay time being defined as the time 
during which the medium returns to its thermal equilibrium state from its 
excited state; and optical detecting means for detecting photon echoes 
emitted from the photon echo medium, wherein the first optical pulse train 
includes a plurality of pieces of image information. 
In the preceding explanation of the stimulated photon echoes, each of the 
first and second optical pulses P1 and P2 is a single pulse. The present 
invention, however, uses a pulse train consisting of a series of pulses or 
an analog optical waveform as a second input instead of the second pulse 
P2 to generate a series of echo pulses or an analog optical waveform 
similar to the second input. 
Alternatively, a pulse train can be used instead of the first input pulse 
P1 because the first and the second pulses have similar effect. In this 
case, however, the resultant photon echoes have time reversed waveform as 
is understood from the principle of the stimulated photon echoes. 
Thus, the apparatus of the present invention has functions for storing and 
retrieving optical information. The storing capacity C of the apparatus is 
determined by the number of optical pulses that can be incident in the 
coherence-decay time T.sub.2. Since the narrowest width of the optical 
pulse is .DELTA..tau., 
EQU C=.DELTA..nu..sub.IH /.DELTA..nu..sub.H ( 13) 
The memory span, on the other hand, is determined by the population-decay 
time T.sub.1.

PREFERRED EMBODIMENTS OF THE INVENTION 
FIG. 6 shows an arrangement of an embodiment of the stimulated photon echo 
image processing apparatus of the present invention, which performs the 
image processing between a first image and the third or second image by 
the stimulated photon echo. In FIG. 6, a rare earth doped crystal 1 (0.1% 
Pr.sup.3+ : LaF.sub.3) cooled by liquid helium is used as a stimulated 
photon echo medium. The crystal 1 exhibits the .sup.3 P.sub.0 --.sup.3 
H.sub.4 absorption transition (wavelength of 477.8 nm), for which a pulsed 
dye laser 2 with 2 GHz linewidth is tuned. The crystal 1 (photon echo 
medium) can store large numbers of images in the form of a Fourier 
transformed pattern by spectral modulation. The spectral modulation is 
carried out by sending optical pulses and an optical pulse train having 
(or not having) image information to the medium so that the population in 
the ground and excited states are modulated after the passage of the pulse 
train and pulses. 
The pulsed dye laser 2 is pumped by the third harmonic of a YAG laser 3. 
The beam from the pulsed dye laser 2 is transmitted through a spatial 
filter 4 which is used to improve the spatial beam profile of the laser 
beam, and is reflected by a mirror 5. Two beam splitters 6 and 7 divide 
the laser beam into three beams B1, B2, and B3. 
The first beam B1 is expanded by a collimator 8 to illuminate uniformly the 
entire pattern of a first mask 9 uniformly. The first mask 9 is made of 
thin aluminum plates with small holes. The pattern was cut on aluminum 
foil, which was then attached to a microscope slide. The first beam B1 
passing through the first mask 9 is called the first image and is 
reflected by a beam splitter 10, and is focused by a Fourier-transform 
lens 11 into the crystal 1. The first mask 9 and the Fourier-transform 
lens 11 are f apart, the f being the focal length of the Fourier transform 
lens 11. Large numbers of first images can be generated in the 
coherence-decay T.sub.2 of the crystal 1 by using a spatial modulator (not 
shown). The coherence-decay time T.sub.2 for the crystal 1 is about 2.4 
.mu.sec as seen from the Table and the first images must be sequentially 
switched in the time T.sub.2. An example of a device satisfying such a 
condition is a spatial light modulator (SLM) described in SPIE Proc. Vol. 
634, 352-371 (1986). Increasing number of first images can be processed by 
using an SLM having a faster switching operation 
The second beam B2, which is split by the beam splitter 6, optically 
delayed by .DELTA.t.sub.1 through an optical delay line 12, split by the 
beam splitter 7, and is reflected by a mirror 13, is expanded by a 
collimator 14 to illuminate uniformly the entire pattern of a second mask 
15. The second beam B2, encoded with the second pattern 15 and reflected 
by a mirror 16, is focused by another Fourier-transform lens 17, entering 
the crystal 1 from the opposite direction with regard to the beam B1. The 
two lenses 11 and 17 share a common focal plane. 
The third beam B3, which is split by the beam splitter 6, delayed by the 
optical delay line 12, and further split by the beam splitter 7, is 
delayed by (.DELTA.t.sub.2 -.DELTA.t.sub.1) by an optical delay line 18, 
and is reflected by the mirror 19, thus counterpropagating with respect to 
the second beam B2. 
The echo image Be emitted .DELTA.t later than the incidence of the third 
beam B3 (see FIG. 7), counterpropagates with respect to the first beam B1 
and is detected by an optical detector 20 separated by the focal length f 
from the lens 11. The detector 20 is, for example, a vidicon camera or 
optical detecting array. Between the optical detector 20 and the beam 
splitter 10, is provided a Pockels cell 21 which functions as an optical 
shutter that transmits the echo while blocking scattered light from the 
input pulses. The echo image Be is the phase conjugate of the first image 
B1. 
When the third beam B3 is a plane wave, spatial convolution operation 
between the first image B1 and the second image B2 is achieved. To perform 
the convolution correctly, the thickness of the crystal 1 has to be within 
the "good focal plane" of the lenses 11 and 17, defined as the depth of 
focus of the lens, where the intensity distribution is a faithful Fourier 
transform of the original image. This thickness is given as Z.sub.0 
&lt;&lt;.lambda.f.sup.2 /(.pi.d.sup.2) where f is the focal length and d is the 
beam aperture diameter. In this case, Z.sub.0 is 1.5 mm, and the crystal 1 
was cut to less than a 1 mm thickness to avoid this length aberration. 
In another configuration, the third beam B3 carries the spatial image while 
the second beam B2 is a plane wave (to achieve this, the collimator 14 and 
the second mask 15 in FIG. 6 must be placed between the mirror 19 and the 
crystal 1). In this case, the photon echo image Be is the correlation 
between the first image B1 and the third image B3. This makes it possible 
to test the agreement of the two images B1 and B3. Accordingly, ultrafast 
pattern matching between large numbers of first images and the third image 
can be achieved. The first images B1 are given by switching many 
two-dimensional images previously made by a computer or the like by using 
the above-mentioned spatial modulator in the coherence-decay time T.sub.2. 
Each image is incident into the crystal 1 by a pulse in the pulse train 
constituting the first beam B1 as shown in FIG. 6, and the data entering 
the crystal 1 are stored in the form of a spatial Fourier transformed 
pattern. By entering the third image B3 to the crystal 1 as shown in FIG. 
7, the Fourier transformed pattern is converted back to temporal echo 
pulses be which represent the correlation images between the first images 
B1 and the third image B3. 
Echo images thus obtained are recorded with the optical detector 20. 
FIGS. 8A-8E show the stimulated photon echo image processing results with 
five different experimental configurations. 
FIG. 8A is a reproduction of the first image B1 with plane wave inputs of 
second and third beams B2 and B3. 
FIG. 8B is an image convolution case with one "x" and two dots yielding two 
"x"s. 
FIGS. 8C-8E are correlation operations between the first image B1 and the 
third image B3. When the first image B1 rotates by 90 degrees as shown in 
FIG. 8E, so does the echo image Be. The haze around the echo dots are the 
second pulse leakage through the Pockels cell 21. The dots in the first 
image are typically 5 mm apart. In some echo images, the edges are blocked 
by the 1 cm Pockels cell aperture. 
The experiments shown in FIGS. 8A-8E indicates that clear photon echo 
images can be obtained. 
Although the experiments are performed between two images, a number of 
first images or second images can be used as reference images by using a 
spatial light modulator for switching the first or second images and by 
using a pulse train as the first beam B1 or the second beam B2. The number 
of reference images is determined by the ratio of the inhomogeneous 
broadening to the homogeneous broadening of the rare earth ion, and is 
typically 10.sup.5 as described above. Thus, spatial convolution and 
correlation of input images can be performed on a nanosecond time scale. 
INDUSTRIAL APPLICABILITY 
According to the invention, spatial convolution and correlation of the 
input images in nanosecond time scale are performed by combining the 
nanosecond processing capability with the ultrafast high intensity storage 
potential of the stimulated photon echo medium. Thus, the present 
invention can be applied to two-dimensional image processing and pattern 
recognition which are required, for instance, in robotic vision, satellite 
remote sensing, medical image analysis, and artificial intelligence. 
While the present invention has been described in detail with respect to 
preferred embodiments, it will be understood that numerous modifications, 
changes, variations and equivalents will be made by those skilled in the 
art without departing from the spirit and scope of the invention. 
Accordingly, it is intended that the invention herein be limited only by 
the scope of the appended claims.