The goal of this work is to apply previous method [1-3] developed for matched filtering of VL[4] to JTC[5] experiment. Method allows to avoid most of ...
The goal of this work is to apply previous method [1-3] developed for matched filtering of VL[4] to JTC[5] experiment. Method allows to avoid most of complications and limits inherent in usual recognition methods. The main point of the proposed method consists in that instead of real objects (incoming on the input of the recognition system) there are some synthesized phase ones with random phase distribution and unambiguously related to them, which undergo the recognition procedure. These object-dependent phase masks (ODPMs) are to be calculated in the digital part of the pattern recognition system over the known scheme of Fourier-transform (IFT) algorithm (Fig.1). The base for use of ODPMs instead of real ones is the property of mutual statistic independence of ODPMs corresponding to real objects not correlating between them.
To the initial objects fk was supplemented an additive statistic noise and defined its influence upon the correlation signals fkn Дfk and jkn(N) Дjk(N) (the upper index “n” means that to the initial object fk, was supplemented the noise, in parentheses there is the number of iterations up to which the ODPM is calculated). On the Fig.12 are given curves of dependence of the correlation signal amplitude on the level of noise for the object f2 and also for the corresponding to it ODPMs calculated for different number of iterations. As we can see in all cases curves for ODPMs lies below the curve (1) obtained for the initial object. It means that the proposed method is more sensitive to the influence of noises as the conventional one. The last can play as well as positive as negative part by recognition depending on the character of the posed problem. It is important to note that unlike to the traditional one the proposed method is a method with adjustable sensitivity in respect of the noise. With increase of the number of iterations by ODPM calculation the sensitivity increases too (see curves 2,3,4).
For the purpose of experiments we have taken ten amplitude objects, among which there were binary ones as well as halftone ones. For these objects there were calculated auto-correlation and cross functions fk Дfm, k,m =1,2…10. For each object fk on the iteration scheme Fig.1.there is calculated ODPM jk. Since the degree of interrelation jk with fk, defining degree of appropriateness for use of jk instead of fk was only to be defined, so we obtained jk for different number of iterations N increasing gradually this number. As it will be evident further the number of iterations N by calculation of the ODPM serves as a main parameter defining the degree of its relation with the real object. In cases where the object had a sufficiently complicated structure the use of initial distribution of random phases j0(x,y) (Fig.1) at the beginning of iterations was not necessary. In the absence of influence of j0(x,y) upon the iteration process the ODPM jk acquired the necessary relation with the object fk already during first iterations. When the distribution j0(x,y) was used, then the same for all objects. By the fixed number of iterations N, for the whole totality {jk} there were calculated auto-correlation and crossfunctions jk(N)Дjm(N), k,m =1,2….10. There were of interest also the behavior of correlation functions jk(1)Дjk(N) with increasing of N, which demonstrate the interrelation of ODPM related to the same object fk but synthesized at different number of iterations. Let us present some results we obtained. On the Fig.2 there are presented some objects used in our experiments, on the Fig.3 there are Fourier-spectra of these objects respectively. The used dimension in all cases amounted to 64Х64. On the Fig.4a,b there are ODPM s calculated for the object f2 by j0(x,y)=const, for the 1st and 150th iterations respectively. On the Fig.5a,b there are histograms demonstrating the specific weight of concrete values of phases in the general distribution of phases of ODPMs, the Fig.6a,b represents Fourier spectra of ODPMs for the same ordinal number of iterations. Results analog to results presented on the figures 4-6 were obtained also for objects f1, f3, f4.
Object
ODPM
Fourier-spectrum
Auto-correlation signal
Noise
Fig.5. Namber of sampling points for each of 100 phase levels of ODPM on the 1st (a) and 150th(b) iterations (for the object f2). Obiects Analyzer
SLM Bs
Data processing
CCD Joint power spectrum
Corr. signal A F P Rh.F
Fourier lens aperture
laser
CCD
k D1
The pattern recognition procedure in the optical-digital 4F correlator by the example of the VanderLugt correlator (Fig.7) can look in the following way: 1. The image of the reference object (P1) by means of the ССD 1 camera is inserted in the computer. For it using the IFT algorithm the reference ODPM (jref.) is calculated. 2. Using the purely phase SLM jref. from the computer is given into the input plane of the correlator (P 2); 3. On the holographic medium the matched filter for jref. (P 3) is recorded. 4. The image of the object to be recognized by means of the ССD 1 camera is inserted in the computer. For it using the IFT algorithm the comparison ODPM (jk) is calculated. 5. Using the same SLM j k from the computer is given into the input plane of the correlator (P 2) instead of jref. 6. There is carried out the matched filtering, registration of the correlation signal by means of the ССD 2 camera in the output plane of the correlator (P 4) and the analysis of the obtained result in the PC. It is necessary to note that a similare procedure can be applied also for the joint Fourier-transform correlator. It is evident that the both recognition procedure can be realized also in a purely digital form in the computer.
LC-R 2500
PC
D Mr He-Cd Rh. Fr. Analyser Analyser Sh
Table 1. Maximums of auto-correlation signals for objects and ODPMs Д
Pt
PC CCD
Д
-1 order
DC peak
RD
Bsp
Laser
SLM
+1 order
* +2 order
-2 order
In the result of numerical simulation and optical experiments on pattern recognition, using ODPM – method for VL and JT correlators we defined following pecularities: 1) phase distributions of ODPMs only depend on the object characteristics; 2) in the case that objects do not have cross-correlation signal, their ODPMs also do not have the signals; 3) optical and statistical characteristics of ODPMs are similar to ones of binary phase masks with randomly distributed rectangular pixels, phase values of which are “0” or “p”. 4)We save, also feature of increasing of sensitivity of propose method to degree of objects damages for ODPM calculated for different iterations (Fig.10). In the experiments of optical-digital JTC using a phaseonly spatial light modulator HEO1080, we demonstrate some advantages of proposed methods than those of conventional JTC, namely: modulus of Fourier spectra of ODPMs do not have local peaks, in most cases, and ODPM posses more uniform distribution of light intensity in Fourier domain than that of conventional JTC methods which use recognized objects; ii) their cross- and auto-correlation signals in the output plane have d-like form without other components, in most cases; iii) signal to noise ratio (SNR) of 3 correlation signal of ODPM is much higher ( > 10 times) than that of SNR in JTC using real objects.
