AND TIME SEQUENTIAL FOR PATTERN
M. KOCK and G. RABE * Philips Forschungslaboratorium
Hamburg GmbH, 2 Hamburg 54, Germany
Two optical multiplex arrangements for pattern recognition are compared. In the first system the Fourier spectrum of an object transparency is optically multiplied for parallel processing with a matrix of different holographic Fourier filters. In the other arrangement the spectrum of the object transparency is switched time sequentially by means of a light beam deflector onto different filters in the Fourier plane. In comparison the time sequential method appears better adapted for high information content.
1. Introduction In the well known technique of matched spatial filtering as first described by Vander Lugt [I] the Fourier transform of an object transparency is multiplied by a holographically recorded filter function, so that the back transform of this product leads to a two-dimensional correlation in the response plane. In its most simple form each object can be compared with one filter only at a time and processing speed is governed by the exchange of filters. Several attempts have been made to overcome this limitation. A well known technique is the coherent or incoherent superposition of several filters at the same place of the storage medium. The response of different filters can be separated by various methods such as coded reference waves [2-61, rotating the photographic plate during each exposure , rotating gratings or similar techniques [8-l 0] . In another method a number of filters is spatially separated in the storage plane and addressed simultaneously by means of a multiplexing device. This method was first proposed by Groh [ 1 11, using a point hologram for multiplexing. Experimental results using such a parallel processing system will be reported in section 2. * Elektro
The recent development of fast light beam deflectors now allows a still different approach, where each of the spatially separated filters is addressed time sequentially. Such a system is described in section 3, and in section 4 results are compared with those obtained by using a parallel processing system.
2. Parallel multiplex
Our experimental arrangement for the parallel processor is sketched in fig. 1. In order to record the matrix of Fourier filters in the storage plane and to multiply the object spectrum we have used a so-called synthetic multiple phase hologram. as described by Dammann and Gortler (121 In contrast to the point hologram suggested earlier, this multiplexing component allows in-line operation combined with high efficiency for multiplication rates up to 30 X 30. In the actual experiment we have used a 40 X 40 mm2 phase plate exhibiting 7 X 7 beams of equal intensity at 50% diffraction efficiency. In principle, also phase plates giving different intensities for the central images can be used for introducing, e.g., a kind of weighting function for the correlation signals. In the system (fig. 1) the point source, i.e., a suitably illuminated pinhole, is imaged by lens L, into the filter plane. The multiple phase hologram behind 73
IPi& 1. Optical
The matrix of reference with dotted lines.
L, multiplies this image point into a matrix of 49 identical points. The spectrum of the object transparency .f’(x,~j) behind the phase plate is thus convolved with the point matrix. Lens L? accomplishes the back transform of all products in p&tllel. In order to avoid overlapping of the correlation functions reference
the filters have to be recorded with coded waves, or in other words, each holographic
filter has lo have a particular
and could bc displayed
:m oscillos~ope.lJsittg the crab> correlations practically
onto a monitor
only the true auto-corrclatioii
of the information
the object plane. The upper limit is roughly given by the bit-t-ate which can be processed by L2 divided by the number of f’iltt’t functions. As art additional handprocessing
a high re-
ple input data. whet-c the rcqutred rcsolutic~ti within each correlation field I> Iiot too stringent.
3. Time-sequential as
:I ~lnall and bright light dot. The spatial position. i.e., Ihc spccil.ic cot relation field. \tf the corrclatiott dot i:, tclatcd to the kind of ohiect which is posttioned III the Input plant. As an example we have used alphanumerics 01‘ the OC‘R-A rypc. The grouptng and the kind of Ictterx \tc~iecl in the filter plane is shown in the left part ot’ t‘lg. 7. The other pictures arc photograph5 01 the nsci-eeti showing auto-correlatiotis of the letters C; anil ‘I‘. ‘lk
Lens L1 is the bottleneck of the system. The total information has to be transtnitted by this lens. That
threshold so that appt‘ared
multiplex ~ystenis appear useful mostly for charactel recognition pobl~nis or smiilar applications wtth sim-
that all tort-c-
a variable elt‘ctrtcul could be suppressed
the Cilteru are indlcatcd
i;olutton detection d~vicc because of the multiplicity of ttrc individual tort-elation fields. Thcrcfore parallel
latiotts can be observed sitnultaneously in a tnatt-ix of spatially sepal-ated correlation fields. The output signals wcrc detected bq, an Image 01 thtcon
part of fig. 2. Herein
S/W-ratio of about 90 dB. The right pictures show the effect of an electronic threshold, suppressing all background light resulting from noise. cross correl:ttions, arid non-linearities.
icap the parallel
with its rcspcctive rcfct-ettce apertures. I:or simplicity’s
sake a multiple phase hologram of equal properties was used to generate this bundle of ~eferertct‘ waves. In reconstructton
leads to a restriction
That can be achieved with, e.g.. a matrix of point sources as schematically shown in fig. 1. Each filter was recorded separately wave by use of movable
ill the nliddle
Fig. 2. Experimental
Left side picture the autocorrelations
tances (Ax,,, Ay,) and selected, e.g., by means of a light deflection device. However, as Vander Lugt [ 131 has shown, any displacement of the filter in relation to the Fourier spectrum or vice versa intrinsically decreases the correlation spot, so that only variations of few microns in alignment are tolerable. Hence the high precision requires a digital light beam deflector, DLD. Such a device has been developed by Schmidt and coworkers (see, e.g., [ 141) offering up to lo6 positions with ran-
shows the grouping is about 20 dB.
and the kind of objects
S/N ratio of
dom access times of < 1 psec. For the present experiments a unit with ten stages, corresponding to about 1O3 positions was available. Fig. 3 shows the arrangement of the sequential correlator using the principle of spatially separated and sequentially addressed point sources. A laser beam is switched by the DLD into a particular direction and is then suitably focussed by a lens system L, onto one element of a matrix of Selfoc fiber optics. The focal spot produced by the lenticule serves as a point source
single correlation field
Fig. 3. Optical
of the time-sequential
using a digital
light beam deflector
from which a divergent spherical wave more or less inclined to the optical axis illuminates lens L, which acts as an imaging lens for the focal spot. For our first experiments a matrix of 7 X 7 Selfoc lenticules was available, so that only part of the 32 X 32 possible positions of the DLD could be used. For the production of the filter matrix, the reference wave indicated with dotted lines is the only carrier. Now the correlation between object transparency f(x,y) and all functions stored in the filter plane can be displayed time-sequentially by lens L, in a single correlation field. So far we have carried out experiments with the same set of OCR-A characters and comparable geometrical arrangement as in the parallel system. In this case the experimental results for both techniques are practically identical, so that the results shown in fig. 2 represent also the response of the time-sequential system.
lustrated case the response in the correlation plane is the same for both techniques. Nevertheless there are differences in the requirements on the various components: (i) for comparable input data, the time-sequential system allows one to use a simpler detector matrix, (ii) for a given detection device, the time-sequential system alows one to process objects or patterns with N-times higher information content. Other differences arise for the optical components. These can best be discussed in terms of the spacebandwidth product: in both cases there are N spatially separated filters in the Fourier plane each occupying a bandwidth W. Lens L2 (see figs. 1 and 3) then has to transmit a total bandwidth of NW. In the case of parallel processing the responses of the filters are displayed in N non-overlapping correlation fields of size A. Thus, L, must have a space-bandwidth product *
Lens L, has only to transmit the input data A W. For the case of time-sequential processing the responses
Fig. 4 illustrates the different operation of both systems for a particular case of character recognition: in the parallel processor (a) a single character is compared with the total filter set; in the time-sequential system (b) a whole picture frame (here a set of characters) is compared with one of the filters. In the il-
+ +++ +++
data Fig. 4. Example
* It should be noticed that the requirements for Lz can be reduced by a factor of N, if a matrix of lenses is used, where each small lens has to transmit only A W. But this, for optical, mechanical, and economical reasons appears as a less attractive solution.
input of different
response (a) and time-sequential
appear in a single correlation field A at different times, so that the space-bandwidth product of L2 (and of L, too) has to be SWt =NAW. This means for the latter system, that either a simpler lens L, can be used or the input data can be increased by a factor of N thus allowing to correlate more complex data as required for the more general case of pattern recognition. Because of the high switching speed of the DLD the total filter set can be scanned in a matter of microseconds. Alternatively, if the system is applied for recognizing single characters several filters can be superimposed as shown in refs. [2-lo], thus combining features of sequential and parallel processing. In conclusion it can be said, that the time-sequential system is preferable in those cases where the correlator has to handle high input data, whereas the parallel system is better adapted for simple character recognition where it offers economic advantages because of the simplicity and cheapness of the optical multiplexer.
We would like to thank H. Dammann, G. Groh and H.J. Schmitt for fruitful discussions. Part of the work was supported by Bundesministerium der Verteidigung, Bonn, Germany. References [l J A. Vander Lugt, IEEE Trans. Inf. Theory (1964) 139.  D. Gabor, Nature 208 (1965) 422.  A. Vander Lugt, Appl. Opt. 5 (1966) 1760. (4) R.F. van Ligton and KC. Iawton, J. Appl. Phys. 38 (1967) 1994.  J.T. Ia Macchia and D.L. White, Appl. Opt. 7 (1968) 91.  J.Ch. Vienot, J. Bulabois and L.R. Guy, Opt. Commun. 2 (1971) 431.  E.N. Leith, A. Kozma, J. Upatnieks, J. Marks and N. Massey, Appl. Opt. 5 (1966) 1303.  J.D. Armitage and A.W. Lohmann, Appl. Opt. 4 (1965) 399.  F. Bestenreiner and R. Deml, Optik 28 (1968169) 263. [lo] P.F. Mueller, Appl. Opt. 8 (1969) 267. [ll] G. Groh, Opt. Commun. 1 (1970) 454.  H. Dammann and K. GBrtler, Opt. Commun. 3 (1971) 312.  A. Vander Lugt, Appl. Opt. 6 (1967) 1221.  U. Schmidt and W. Thust, IEEE J. Quantum Electron. QE-5 (1969) 351.