Compact phase-conjugating correlator: simulation and experimental analysis

A simulation and experimental investigation of a recently proposed, compact, phase-conjugating correlator is undertaken. The effects of noise and other distortions in the input image and in the correlator filter plane are considered. As with other phase-only designs, the phase-conjugating correlator is sensitive to distortion of the input image while being robust in the presence of filter-plane distortions; this robustness is enhanced by the phase-conjugating property of the design.     

Four-plane space-variant Fresnel-transform optical processor with a random phase encoder

We introduce a four-plane Fresnel-transform space-variant optical processor consisting of an input plane and two filter planes. One filter mask is programmable with a spatial light modulator. The second filter mask is a fixed random binary phase array with a known pseudorandom distribution of pixels. The order of the masks can be interchanged, giving different output characteristics. In one case the Horner efficiency of the correlator increases dramatically. In the other case the edge enhancement of the output image is removed. We discuss the theory for this general processor and its implementation with phase-only masks. We present experimental results when a binary magneto-optic spatial light modulator was used.     

Analysis of spatial light modulator contrast ratios and optical correlation

We have performed a general analysis of optical correlators with spatal light modulators (SLM's) whose primary defect is a finite contrast ratio (CR). Our mathematical analysis identifies three noise terms that appear in addition to the correlation term. The filter SLM contains either a phase-only filter (POF) or a binary-phase-only filter (BPOF). Insertion of a dc block at the center of the filter SLM decreases the noise background in the correlator plane; this dc block is larger than that required for the same level of performance in a correlator whose SLM's have transmissive (or reflective) dead zones. With a noise-free input and the dc block, our computer simulations that show the peak intensity falling off as the CR decreases are in quantitative agreement with the correlation term of the mathematical model. For a cluttered, disjoint noise input this agreement is only qualitative, and at low CR's the dc block is definitely required for the BPOF correlator if the secondary peaks in the output are to be brought below the correlation peak.     

Adaptive phase-input joint transform correlator

An adaptive phase-input joint transform correlator for pattern recognition is presented. The input of the system is two phase-only images: input scene and reference. The reference image is generated with a new iterative algorithm using phase-only synthetic discriminant functions. The algorithm takes into account calibration lookup tables of all optoelectronics elements used in optodigital experiments. The designed adaptive phase-input joint transform correlator is able to reliably detect a target and its distorted versions embedded into a cluttered background. Computer simulations are provided and compared with those of various existing joint transform correlators in terms of discrimination capability, tolerance to input additive noise, and to small geometric image distortions. Experimental optodigital results are also provided and discussed.     

Fresnel transform-based correlator

We present a new technique for information processing using Fresnel transform-based correlation. The main emphasis is on the design of a correlator involving the reference object and its near-field diffraction pattern at an optimized distance. The input-scene image and its diffraction pattern constitute the input pattern of the new correlator. The new technique shows a significant increase in discrimination ability and optical efficiency. Moreover, different encoding methods, such as the phase-only filter or the matched filter, can be used in conjunction with this method. A theoretical analysis as well as examples are given.     

Optical wavelet transform by the phase-only joint-transform correlator

A method is presented that performs the optical wavelet transform with liquid-crystal televisions as spatial light modulators operating only on the phase of the incident coherent light. The architecture is the joint-transform correlator, and the wavelets and the image to be transformed are encoded in the input plane of the system. The mathematical formalism describing the adaptation of the joint-transform correlator to the wavelet transform is given and extended to the operation of the phase-only joint-transform correlator. A new wavelet is described for two-dimensional image processing, and experimental results are presented for optical wavelet transforms done in real time by use of this wavelet in the phase-only joint-transform-correlator architecture. The analysis is extended to multiwavelet (multispectral) analysis by the joint-transform correlator, and simulation results are given. Finally experimental results with the phase-only joint-transform correlator applied to multi-wavelet analysis are presented.     

Spectral optimized asymmetric segmented phase-only correlation filter

We suggest a new type of optimized composite filter, i.e., the asymmetric segmented phase-only filter (ASPOF), for improving the effectiveness of a VanderLugt correlator (VLC) when used for face identification. Basically, it consists in merging several reference images after application of a specific spectral optimization method. After segmentation of the spectral filter plane to several areas, each area is assigned to a single winner reference according to a new optimized criterion. The point of the paper is to show that this method offers a significant performance improvement on standard composite filters for face identification. We first briefly revisit composite filters [adapted, phase-only, inverse, compromise optimal, segmented, minimum average correlation energy, optimal trade-off maximum average correlation, and amplitude-modulated phase-only (AMPOF)], which are tools of choice for face recognition based on correlation techniques, and compare their performances with those of the ASPOF. We illustrate some of the drawbacks of current filters for several binary and grayscale image identifications. Next, we describe the optimization steps and introduce the ASPOF that can overcome these technical issues to improve the quality and the reliability of the correlation-based decision. We derive performance measures, i.e., PCE values and receiver operating characteristic curves, to confirm consistency of the results. We numerically find that this filter increases the recognition rate and decreases the false alarm rate. The results show that the discrimination of the ASPOF is comparable to that of the AMPOF, but the ASPOF is more robust than the trade-off maximum average correlation height against rotation and various types of noise sources. Our method has several features that make it amenable to experimental implementation using a VLC.     

Multilevel phase- and amplitude-encoded modified-filter synthetic-discriminant-function filters

The performance of the modified-filter synthetic-discriminant-function (MfSDF) filter with multilevel phase and amplitude (MLAP) constraints is investigated with various in-plane rotated images from an in-class Bradley armored personnel carrier vehicle and an out-of-class Abram MI tank; this is of interest because of the commercial availability of liquid-crystal televisions, which are able to encode the gray-level amplitude and/or the discrete multilevel phase information. The evaluation is performed to explain better the image-distortion range that can be covered effectively by MLAP/MfSDF filters. The results show that the MLAP/MfSDF filter offers much-improved correlator system performance with a greater allowable image-distortion range while maintaining 100% discrimination between in-class and out-ofclass images; furthermore, it shows an improved ability to accommodate the input image noise when compared with the MfSDF filter with a binary phase-only constraint. Thus the MLAP/MfSDF can be implemented effectively by a hybrid optical/digital correlator system to track a vehicle or a tank dynamically as it moves along a random trajectory across the input field.     

Analysis of the dual discrimination ability of the two-port photorefractive joint transform correlator

An all-optical joint transform correlator featuring two operative correlation planes(ports) with complementary performance is presented. We present the theory of operation, derive the input-output characteristics, and demonstrate computer simulations and experimental results. The two-port joint transform correlator is based on simultaneous use of two photorefractive wave-mixing architectures. The first port uses two-beam coupling, and the second port uses four-wave mixing. The performance of the two ports depends on an experimentally controlled beam intensity ratio and the photorefractive coupling coefficient. With appropriate selection of these parameters, the first port is capable of high discrimination, while simultaneously the second offers a low discrimination output. Our results show that the two-beam coupling port can achieve peak-to-noise and signal-to-noise ratio values better than the phase-only correlator, whereas the four-wave-mixing port performs similarly to the classical joint transform correlator. This leads to a potential application in which the correlator could be set up so that in one port a general class is detected (interclass) and, in the other, the specific item in a class is detected (intraclass).     

Optical Security System with Fourier Plane encoding

We propose a new technique for security verification of personal documents and other forms of personal identifications such as ID cards, passports, or credit cards. In this technique a primary pattern that might be a phase-encoded image is convolved by a random code. The information is phase encoded on the personal document. Therefore the information cannot be reproduced by an intensity detector such as a CCD camera. An optical processor based on the nonlinear joint transform correlator is used to perform the verification and the validation of documents with this technique. By verification of the biometrics information and the random code simultaneously, the proposed optical system determines whether a card is authentic or is being used by an authorized person. We tested the performance of the optical system for security and validation in the presence of input noise and in the presence of distortion of the information on the card. The performance of the proposed method is evaluated by use of a number of metrics. Statistical analysis of the system is performed to investigate the noise tolerance and the discrimination against false inputs for security verification.     

Synthetic circular-harmonic phase-only filter for shift, rotation, and scaling-invariant correlation

A synthetic circular-harmonic phase-only filter is described. With this filter and a Fourier-transform correlator it is possible to obtain shift, rotation, and scaling-invariant correlations.     

Single-channel polychromatic pattern recognition by the use of a joint-transform correlator

We present a single-channel system for color image recognition that is based on a joint-transform correlator setup. The color images are encoded as phase and amplitude functions, inspired from the Munsell color representation. A real-time implementation of the new codification method can be achieved by the use of a spatial light modulator operating in phase-only modulation mode. We determine the optimal codification for a linear color-phase code. Its performance is compared with a conventional multichannel correlator by means of computer simulations. Experimental results are also presented.     

Analysis of image detection based on fourier plane nonlinear filtering in a joint transform correlator

Signal and image and detection systems based on nonlinear operations of Fourier-transformed data often exhibit greater selectivity than standard matched-filtering techniques. One such system is the joint transform correlator. We analyze the performance of the nonlinear joint transform correlator in terms of the output signal-to-noise ratio; this signal-to-noise ratio is evaluated in terms of both output contrast (peak-to-noise floor) and output variability (peak-to-peak standard deviation). The main assumption used is that the signal energy is small relative to that of the additive noise; this assumption is defensible in practice owing to the generally small spatial extent of target images relative to scenes. With respect to the first performance measure, this study is an extension of that in an earlier paper [Appl. Opt. 34, 5218 (1995)]. The previous analysis was carried out under a restriction that the signal and noise spectra were to be similar (actually multiples of one another). In the current study there is no such constraint, and all analysis of the second measure is new. The analysis is supported by simulation. A benefit of analytical rather than simulational study is that conclusions can be drawn with greater confidence. One of the most interesting of these is that the smooth square-root Fourier plane nonlinearity, more usually known as the k-law processor with k = 0.5, offers extremely robust performance with respect to relative noise bandwidth.     

Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators

We describe a nonlinear joint transform correlator-based two-layer neural network that uses a supervised learning algorithm for real-time face recognition. The system is trained with a sequence of facial images and is able to classify an input face image in real time. Computer simulations and optical experimental results are presented. The processor can be manufactured into a compact low-cost optoelectronic system. The use of the nonlinear joint transform correlator provides good noise robustness and good image discrimination.     

Complex encoding of rotation-invariant filters onto a single phase-only spatial light modulator

The accuracy and flexibility of the technique proposed by Davis et al. [Appl. Opt. 35, 2488 (1996)] for the encoding of the amplitude and the phase of a filter onto a single liquid-crystal spatial light modulator operating in a phase-only regime has been exploited to implement several filter designs in a convergent optical correlator. We have selected some filters, that given their mathematical structure showing some degree of rotational invariance, or having a parameter to regulate their behavior, require amore precise encoding. We present correlation results of outstanding quality for various rotationally invariant filter designs that have never been previously implemented with a real-time optical correlator.     

Scale-invariant optical correlators using ferroelectric liquid-crystal spatial light modulators

New experimental results for scale-invariant implementations of the binary phase-only matched filter and the nonlinear joint transform correlator using ferroelectric liquid-crystal spatial light modulators are presented. We provide a comparative study of both architectures for real-time road-sign recognition. Signal-to-peak-noise ratios in excess of 5 dB over a scale range of 1.0 to 2.0 are achieved under realistic conditions of clutter.     

Differential phase shift keying direct sequence spread spectrum single SAW based correlator receiver

This paper presents the design and measurement of a SAW device to be used in a correlator receiver for a differential phase shift keying direct sequence spread spectrum (DPSK/DSSS) system. The DPSK modulation format allows noncoherent data demodulation while the SAW device correlator acts as the despreading operator. In a conventional DPSK receiver, the received signal is normally split into a lower and upper path. One of the paths contains a correlator, and the other path contains a one data bit delay element and another correlator. The outputs of both paths are then fed to a noncoherent data demodulator. The device presented in this paper combines both the delay element and the two correlators in a single SAW device; therefore, a better temperature tracking mechanism, simplicity, as well as the elimination of the broadband SAW delay line are achieved. The SAW structure contains a broadband SAW transducer, and two serially coded pseudo noise (PN) DPSK filters. The SAW based correlator was built on lithium tantalate. The center frequency was set to 150 MHz, with a 63 chip PN spreading code and a data rate of 300 Kbps. Experimental measurements of the SAW device autocorrelation results are presented.     

Fractional joint transform correlator

We combine two concepts: the joint transform correlator and the fractional Fourier transform. This combination is almost as convenient experimentally as the classical joint transform correlator. As a processor it is as versatile as the standard fractional Fourier correlator.     

A comparison of two correlation schemes

Processes involving the cross-correlation of two noisy data streams are frequently encountered in signal processing. The performances of two commonly used correlators, the simple and complex correlators, are examined. The conventional view is that the complex correlator is superior to the simple correlator by a factor of the square root of two in output signal-to-noise ratio (SNR). However, by modifying the simple correlator to utilize all the available information, its performance is improved. The development of the modified correlator is explained, and a computer simulation shows that this modified correlator is approximately equivalent to the complex correlator in noise performance     

Bessel function output from an optical correlator with a phase-only encoded inverse filter

We report on a technique for producing a Bessel function correlation output for an arbitrary input pattern. The central dark spot at the center of the Bessel function correlator output is narrower than the width of the normal correlation spot and can be extremely useful for locating the center of the correlation signal. The Bessel function is produced by convolution of the extremely sharp correlation produced by an inverse filter with the Bessel function and is encoded with a single phase-only liquid-crystal spatial light modulator. To encode amplitude information on the filter, we spatially modulate the phase encoded on the filter. Amplitude modulation is obtained by modulation of the diffraction efficiency of the phase grating. Experimental results are presented.