Multiresolution correlator analysis and filter design

The concept of multiresolution optical correlators is formally introduced. A mathematical analysis is performed for a generalized multiresolution correlator that emphasizes the roles of both input and filter spatial light modulator resolutions. Conditions are derived for overlapping and nonoverlapping correlation orders. A simulation is performed in which it is shown that the predicted performance of composite binary-phase-only filters designed by the conventional design procedure is different from the actual performance when they are implemented in a real optical correlator. The training of filters on multiresolution approximations of high-resolution discrete Fourier transforms generated by multiresolution wavelet analysis (MWA) techniques is proposed. An analysis is performed that shows that training on MWA approximations results in filters whose performance is the same in a real correlator as that predicted by the design procedure. This analysis is confirmed by simulation. Further simulations show that the performance of reduced-resolution filters designed by MWA techniques is markedly superior to the performance of those designed by conventional means. Finally, an analysis is performed that explains why the ratio of zero- to higher-order correlation peak intensities is much greater for the former than the latter.     

Serial transform optical correlator design principles

Optical correlators such as the 4f and VanderLugt optical systems have been an active area of research for many years; we refer to these types of optical system collectively as serial transform correlators (STCs). Despite being well known, misconceptions regarding the design of STCs are not uncommon. We show, for example, that one correlator configuration reported to suffer from a phase curvature problem in fact works correctly. We present and prove a simple set of rules to follow in the selection of a STC design that does not contain unnecessary constraints and that makes it easier to identify permissible optical systems. As examples, we discuss three representative types of correlator configuration, one of which is discussed in detail to highlight its practical advantages. A novel proof of the design rules is presented that does not depend on details such as what lenses or combination of lenses are used, what their focal lengths are, or what their locations are within the optical system. We also present a conventional Fourier optics proof.     

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.     

Distortion-invariant pattern recognition with Fourier-plane nonlinear filters

The use of nonlinear techniques in the Fourier plane of pattern-recognition correlators can improve the correlators' performance in terms of discrimination against objects similar to the target object, correlation-peak sharpness, and correlation noise robustness. Additionally, filter designs have been proposed that provide the linear correlator with invariance properties with respect to input-signal distortions and rotations. We propose simple modifications to presently known distortion-invariant correlator filters that enable these filter designs to be used in a nonlinear correlator architecture. These Fourier-plane nonlinear filters can be implemented electronically, or they may be implemented optically with a nonlinear joint transform correlator. Extensive simulation results are presented that illustrate the performance enhancements that are gained by the unification of nonlinear techniques with these filter designs.     

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     

Application of correlation filters for texture recognition

We propose a new statistical method to design spatial filters to recognize and to discriminate between various textures. Unlike existing correlation filters, the proposed filters are not meant to recognize specific shapes or objects. Rather, they discriminate between textures such as terrains, background surfaces, and random image fields. The filters do not require any on-line statistical computations for extracting texture information. Therefore optical (or digital) correlators can be used for fast real-time texture recognition without segmentation. The procedure is based on the assumption that textures can be modeled as stationary random processes over limited regions of an image. The optimum filter coefficients are determined by use of eigenvector analysis. Several examples are given to illustrate the proposed scheme.     

Computer-generated optical multiwavelet filters for hybrid image-classification systems

Optical coherent Fourier correlators are applicable in real-time image analysis such as image classification. The functionality of Fourier correlators can be increased by use of multifunctional filters, which have many spatially multiplexed impulse responses. The concept of multiresolution analysis on the basis of wavelet theory offers profitable methods to design multifunctional filters for image analysis. The applicability of such filters is demonstrated by an example in which different characteristic textures of medical images are extracted. The physical implementation of multiwavelet filters is restricted by modulation-domain constraints imposed by the use of spatial-light-modulator or of diffractive-element fabrication technology. Coding methods of diffractive optics are shown to be helpful to transform the original complex-valued distributions of multiwavelet filters into light-efficient quantized phase-only distributions by preservation of the original filter functionality. The quality of the designed diffractive phase filters is documented by computer experiments.     

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.     

All-optical pattern recognition for digital real-time information processing

To recognize digital streams of digital data, all-optical and passive techniques able to discriminate optical bit words in real time are presented. Discrimination capability of different correlators, both in free space architectures and in delay lines structures, is theoretically and experimentally analyzed. Experimental performances in word recognition are shown in the case of a volume holographic correlator, in the case of a lithographic phase-only-filter correlator, and in the case of a novel coherent delay lines correlator operating at the wavelength 1550 nm and at the bit rate of 2.5 Gbit/s.     

Anamorphic Multiple Matched Filter for Character Recognition,Performance with Signals of Equal Size

Abstract

The construction and performance of an anamorphic multiple matched filter for character recognition is presented, in the usual situation of characters of equal input size and having the same size in the target. So a simple anamorphic correlator can be employed to obtain the recognition of a given character. In order to avoid false alarms the characters in the target are rotated by different angles depending on the angular tolerance of the correlator, which is rotationally variant and smaller than in symmetrical systems within a certain angular region. Thus the number of signals to which the filter can be matched can be greater than with spherical optics correlators.     

Binary zone-plate array for a parallel joint transform correlator applied to face recognition

Taking advantage of small aberrations, high efficiency, and compactness, we developed a new, to our knowledge, design procedure for a binary zone-plate array (BZPA) and applied it to a parallel joint transform correlator for the recognition of the human face. Pairs of reference and unknown images of faces are displayed on a liquid-crystal spatial light modulator (SLM), Fourier transformed by the BZPA, intensity recorded on an optically addressable SLM, and inversely Fourier transformed to obtain correlation signals. Consideration of the bandwidth allows the relations among the channel number, the numerical aperture of the zone plates, and the pattern size to be determined. Experimentally a five-channel parallel correlator was implemented and tested successfully with a 100-person database. The design and the fabrication of a 20-channel BZPA for phonetic character recognition are also included.     

Improvement to human-face recognition in a volume holographic correlator by use of speckle modulation

We show that a speckle-modulation technique can improve the parallelism and the recognition accuracy of volume holographic correlators. The object patterns are modulated by a speckle pattern generated by a diffuser. These modulated patterns are stored as Fourier holograms by use of angular-fractal multiplexing. With the speckle modulation the sidelobes are completely suppressed, the cross talk is negligible, and the correlation peak becomes a bright sharp spot. Thus higher recognition accuracy is achieved. The angular separation between adjacent patterns in the multiplexing could be much smaller, resulting in larger capacity and higher parallelism of the correlator. Also, this technique can be combined with other methods such as wavelet filtering to achieve a large invariant tolerance range. Theoretical analysis, numerical evaluation, and experimental results are presented to confirm that sidelobes and cross talk are sharply suppressed by the speckle modulation.     

Comparison of analog continuum correlators for remote sensing andradio astronomy

Two different designs of analog correlators for radiometry are compared in this paper. A continuum correlator based on a microwave nonlinear device is a simple and inexpensive way to detect wide-band polarized signals. Analysis and extensive measurements including linearity, dynamic range, amplitude response, phase balance, and stability are presented, and the suitability of the designs for microwave radiometry is discussed. Both correlators showed nearly ideal performance. A novel method for determining the correlator degradation factor is applied     

Comparison of automatic target recognition system performance with full- and reduced-resolution correlators

The performance of an automatic target recognition (ATR) system with full- and reduced-resolution correlators was compared. In addition, the ATR system performance with reduced-resolution filter sets designed by use of multiresolution analyasis (MA) and downsampling (DS) techniques was also compared. It was discovered that results obtained at the optical correlator subsystem level, pertaining to the relative merits of the MA and the DS techniques, could not be extrapolated to the system level. This was because target signature differences between the test and the training imagery were discovered to have a greater influence on system performance than the choice of filter design technique. In addition, it was found that, for the case in which the target signature and the reduced-resolution filter were of the same size, there was some degradation in the receiver-operating-characteristic curve for reduced resolution compared with full. Nevertheless, this was deemed to have no practical significance, and thus the use of reduced-resolution optical correlators for ATR merits serious consideration.     

Spatial-domain implementation of optimal multicriteria correlation filters

We show that optimal regions of support for correlation filters in the frequency domain can be approximated by relatively small convolution kernels in the spatial domain. We present an optimal approach for generating regions of support, as well as a fast nonoptimal approach for conventional optical correlators. Because the convolution kernels are similar to low-pass filters, the resulting input image to a correlator is always positive valued. We show that the performance of the convolution-based approach is comparable with the optimal frequency-domain approach. An important advantage of our method is that it can be implemented on low-cost arithmetic frame grabbers that can perform convolution with small kernels in real time. In addition, our method can be used in conjunction with a filter spatial light modulator that cannot produce a zero state.     

Size Dependence in Optical Correlation for Pattern Recognition and Its Compensation by Wavelength Tuning

When optical correlation employing holographic Vander Lugt filters is applied to pattern recognition the detector output is easily influenced by size variations in the pattern. A method is proposed and tested to compensate these influences by tuning the light source to a different wavelength. The theoretical basis for this operation is developed and examples are presented where the correlator output has been evaluated quantitatively for changes in size and wavelength. It is demonstrated that the correlation functions agree well with theoretical expectations and that the correlation peak which is degraded by size variation may be restored by tuning to the appropriate wavelength.     

Direct sequence spread spectrum differential phase shift keying SAW correlator on GaAs

This paper presents the design, fabrication, and experimental results for a differential phase shift keying (DPSK) single SAW-based correlator on GaAs for direct sequence spread spectrum applications. The DPSK modulation format allows for noncoherent data demodulation; the SAW device correlator acts as the despreader. Unlike the conventional technique of using two parallel correlators and a one data bit delay element, this new system uses two inline correlators. When implemented on SAW devices, this in-line structure has the advantage of an inherent one data bit delay, lower insertion loss, and less signal distortion than the parallel structure. The DPSK correlator is fabricated on a {100} cut GaAs substrate with SAW propagation in the 110 direction, Using this cut, which is widely used in electronics, Rayleigh waves are generated with a piezoelectric coupling coefficient of the same order as ST-cut quartz. The piezoelectric semiconductor GaAs is of great interest because it is the only substrate that can be used to integrate SAW devices directly with electronics on the same chip, resulting in smaller packaging, reduction of packaging parasitics, lower cost, and greater system integration. This paper presents experimental results for SAW in-line correlator structures on GaAs along with their despreading system performances. Experimental measurements in both the time and frequency domains were performed and were found to be in good agreement with theoretical predictions.     

Statistical performance of cascaded linear shift-invariant processing

The cascaded correlator architecture comprises a series of traditional linear correlators separated by nonlinear threshold functions, trained with neural-network techniques. We investigate the shift-invariant classification performance of cascaded correlators in comparison with optimum Bayes classifiers. Inputs are formulated as randomly generated sample members of known statistical class distributions. It is shown that when the separability of true and false classes is varied in both the first and the second orders, the two-stage cascaded correlator shows performance similar to that of the optimum quadratic Bayes classifier throughout the studied range. It is shown that this is due to the similar decision boundaries implemented by the two nonlinear classifiers.     

Pattern recognition with an adaptive joint transform correlator

An adaptive joint transform correlator for real-time pattern recognition is presented. A reference image for the correlator is generated with a new iterative algorithm. The training algorithm is based on synthetic discriminant functions. The obtained reference image contains the information needed to reliably discriminate a target against known false objects and a cluttered background. Calibration lookup tables of all optoelectronics elements used are included in the design of the adaptive joint transform correlator. Two methods for the implementation of the proposed joint transform correlator in an optodigital setup are considered. Experimental results are provided and compared with those of computer simulations.     

Performance comparison of ferroelectric liquid-crystal-technology-based coherent optical multichannel correlators

Our purpose is to compare two architectures when implemented with ferroelectric liquid-crystal technology: the conventional VanderLugt and joint transform correlators. The architectures are compared in the single-correlation and multichannel cases. The analysis covers both theoretical aspects and practical considerations regarding implementation. Specifications for a multichannel correlator design, including considerations of both spatial light modulators and architecture configurations, are discussed. Experimental results are presented for both architectures. Finally, the benefit resulting from extension to multichannel operation is discussed in terms of both multiplexing and algorithmic capabilities.