Joint Transform Correlator Research Articles

Phase encoding the input scene of an optical correlator in the presence of nonoverlapping noise

We study the influence of phase encoding the input image of an optical correlator. We show that if the object to be located is perturbed by nonoverlapping noise, phase encoding can improve the correlation performance compared to amplitude encoding. We provide a phenomenological interpretation of this fact, taking into account the graylevel histograms of the target and of the noisy background. Using numerical simulations, we show that in some realistic situations, phase encoding can significantly improve the probability of correct location of a nonlinear joint-transform correlator (NLJTC).

Performances of an all-optical subtracted joint transform correlator that uses a photorefractive crystal

An all-optical subtracted joint transform correlator (JTC) was proposed and it was experimentally shown that the correlator successfully performs the pattern recognition with the number of reference patterns. In the correlator, an optical interferometer was introduced to remove the additional correlation signals between the reference patterns themselves from the output plane and a photorefractive crystal was also introduced to record the joint power spectra as volume holograms. The processing for removing the additional correlation signals was performed by the parallel computations in the interferometer in real time. In this study it has been found that the correlator yields significantly better correlation results than the classical joint transform correlator does and the recording of the volume hologram corresponds to a nonlinear processing of the joint power spectrum in the fringe-adjusted joint transform correlator. However the volume hologram has angular selectivity for matching the Bragg condition. It would restrict the shift-invariant area of the input image plane. This restriction has been investigated experimentally.

Color pattern recognition in white-light joint transform correlation

We first discuss the restriction on the incoherent source and the color filters in a joint transform correlation (JTC) system for white-light color pattern recognition and then report on a novel, to our knowledge, solution of channeling in a white-light JTC system, using a tricolor grating to encode the color patterns in real time. The theoretical analyses and the experimental results show not only that the restriction on the experimental condition is relieved but also that parallel channeling of the power spectra of the encoded pattern is easily performed. In addition, the zero-order power spectrum also forms a useful channel for the shape-only correlation.

A non-zero order joint transform correlator for space-variant pattern recognition

We propose a space-variant correlator using a joint transform correlator (JTC) architecture. The reference and target images of a JTC are modulated by a random phase function which is the sample of a stationary white process ergodic in mean and variance. The degree of shift-variance can be varied by changing the variance of the random phase function. The joint power spectrum (JPS) is a sinusoidally varying function with a spatially nonvarying average value. This property is advantageous in optical implementations when the JPS is captured by devices such as CCD with a limited dynamic range. The zero-order and the correlations approach delta functions in the correlation plane. By subtracting a constant value equal to its spatial average from the JPS, the undesirable zero-order can be eliminated.

Defect Detection in Fabrics with a Joint Transform Correlation Technique: Theoretical Basis and Simulation

The theoretical basis of a technique for real time defect detection in fabrics is presented using a joint transform correlator. This correlation technique is an extension of Fourier transform analysis and is extremely useful for real time pattern recognition. The regular periodic nature of a woven fabric makes it possible to use the Fourier transform technique to detect defects. However, classifying various defect types is difficult from the Fourier analytical and experimental results. A solution to this problem is to use a joint Fourier transform of a reference pattern and the test pattern, and the joint power spectrum is further processed. Cross- and auto-correlation peaks, generated after the execution of the second Fourier transform on the filtered joint power spectrum, indicate the existence of a particular defect type. Because of the parallel processing ability of the optical system, implementing the joint transform correlation technique in an optical domain is advanta geous. A fractional power fringe adjusted filter is used for efficient detection of defects. The mathematical formulation of the technique is supported by the simulated results for identifying some defects such as the existence of thick yarns, knots, and missing yarns.

Performance of binary joint transform correlator using linear combination threshold function

A linear combination threshold function, which is defined as the linear combination of input and reference power spectra, is proposed to binarize the joint power spectrum of a joint transform correlator (JTC). The performance of binary JTC depends on the linear combination coefficients of input and reference power spectra. This relationship is investigated and an optimal linear combination threshold function is determined to get a trade-off between some of performance criteria for character recognition. The theory analysis and verification by computer simulation are described. The proposed technique is also investigated by a hybrid optoelectronic system.

Three-dimensional object recognition by Fourier transform profilometry

An automatic method for three-dimensional (3-D) shape recognition is proposed. It combines the Fourier transform profilometry technique with a real-time recognition setup such as the joint transform correlator (JTC). A grating is projected onto the object surface resulting in a distorted grating pattern. Since this pattern carries information about the depth and the shape of the object, their comparison provides a method for recognizing 3-D objects in real time. A two-cycle JTC is used for this purpose. Experimental results demonstrate the theory and show the utility of the new proposed method.

Space integrating joint transform correlator using a moving grating

A new one-step joint transform correlator (JTC) is presented, in which the joint transform of the images to be correlated is filtered by a moving Ronchi ruling. An alternative JTC architecture without moving parts using two Ronchi rulings is also suggested. A lens produces the spatial integral of the product of the joint transform image and the trans- mission factor of the Ronchi ruling, and a single element detector is used to capture the integral. The amplitude of the light modulation on the detector gives the cross-correlation function of the input images at coor- dinates (0,0) without major processing. Therefore, in principle this tech- nique significantly reduces the time required to evaluate the cross- correlation function, compared to that for usual JTCs. Experimental validation of the proposed one-step architecture is presented. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)01807-3)

Photorefractive Fe:LiNbO_3 crystal thin plates for optical information processing

The effects of the donor acceptor concentration ratio in iron-doped lithium niobate (Fe:LiNbO3) crystal plates on photorefractive response time and on grating diffraction efficiency are studied both theoretically and experimentally. The results provide a useful guide for designing photorefractive plates for optical information-processing applications. Two devices for real-time image recognition have been demonstrated: a photorefractive joint-transform correlator and a VanderLugt correlator. The former emphasizes fast response time, and the latter emphasizes high diffraction efficiency. By appropriate adjustment of the dopant concentration and the ratio of the donor acceptor levels, photorefractive Fe:LiNbO3 crystals that facilitate specific applications have been designed and fabricated. Shift-invariant image correlations have been achieved.

Cellular neural network implementation using a phase-only joint transform correlator

A phase-only joint transform correlator (JTC) is used to realize cellular neural networks (CNNs). The operation of summing cross-correlations of bipolar data in CNNs can be realized in parallel by phase-encoding bipolar data. Compared to other optical systems for implementing CNNs, the proposed method offers the advantages of easier implementation and robustness in terms of system alignment, and requires neither electronic precalculation nor data rearrangement. Simulation results of the proposed optical CNNs for edge detection are provided.

Pattern recognition with variable discrimination capability by dual non-linear optical correlation

The discrimination capability requirements of pattern recognition systems may vary from one given purpose to another. In this work a recognition system with variable and selective discrimination capability is obtained by applying a dual non-linear correlation (DNC) model to a joint-transform correlator. DNC is obtained by means of two non-linear operators that are applied to both the reference and input channels. A particular DNC is given by the values taken by two real control parameters that determine the non-linear operators. In comparison with conventional filtering methods, an increased and variable discrimination capability is achieved by varying the parameters values. Thus, variable tolerances are introduced in the recognition process. Specifically, tolerances to slight shape variations and intensity variations of the objects (alphabetic characters) are analysed in this work. Ranges for the two control parameters are found in each case in order to achieve either an increase or a relaxation in the system's discrimination capability. The developed application is extended to colour pattern recognition by multichannel correlation. In this case, four further applications with selective discrimination capability are developed: pattern recognition with high discrimination capability for shape variations and some tolerance to colour variations and, vice versa, pattern recognition with high discrimination capability for colour variations and some tolerance to slight shape variations; pattern recognition with high discrimination for both shape and colour, and, finally, a tolerance to slight variations in both shape and colour.

Bayesian theory for target location in noise with unknown spectral density

A Bayesian approach adapted to practical detection and location tasks of a target in additive Gaussian noise with unknown spectral density is developed and studied. The relevance of this theory is first discussed in comparison with a maximum a posteriori solution that has been recently developed [J. Opt. Soc. Am. A15, 61 (1998)]. The analysis is first performed without considering a particular prior for the spectral density of the noise. General results of the Bayesian approach are thus provided as well as properties of its first-order development, which corresponds to the so-called nonlinear joint-transform correlation frequently used in optical correlators. It is demonstrated that the kernel of the nonlinear filtering is an increasing function of the sum of the spectral density of the reference object and of the input image. Furthermore, it is shown that a power-law mathematical form of the nonlinear filtering is directly related to assumptions on the asymptotic behavior of the prior density probabilities of the unknown spectral density of the noise. These properties constitute new theoretical results in the context of statistical theory concerning the use of nonlinearities in optical correlators.

Real-time digital optical matrix multiplication with a joint-transform correlator

Joint-transform correlation architecture is employed for digital matrix multiplication. Real-valued matrix-vector, complex-valued matrix-vector, real-valued matrix-matrix, and complex-valued matrix-matrix multiplication operations can all be realized simply by programming of the data arrangement in the input plane of a multiple-input joint-transform correlator. The proposed method benefits from the advantages of speed because of the real-time processing capability of the joint-transform correlator and of high accuracy because of the digital representation of the multiplied numbers. Computer-simulation results are provided in which the negative binary encoding method is used to encode matrix elements.

Laser-diode-based joint transform correlator for fingerprint identification

A laser-diode-based joint transform correlator (JTC) is re- ported here for the identification and discrimination of fingerprints. The system employs compact and inexpensive laser diodes as the light sources and a bacteriorhodopsin (BR) film in the Fourier plane, which can record the joint power spectrum without the need for expensive spa- tial light modulators or CCD cameras. The BR film also introduces non- linearities in the Fourier plane which can improve JTC performance. In addition, real-time, all-optical programmable spatial filtering is demon- strated to improve the discrimination of the system. We present com- puter modeling and experimental results of this optical correlator, which shows excellent potential for the identification and discrimination of fin- gerprints. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)00701-1)

Novel implementation of nonlinear joint transform correlators in optical security and validation

Emblems using holograms or other diffractive devices have long been used to mark cards and other objects as a means of authentication. The effectiveness of such emblems as a security device is ultimately determined by the inspection system. Due to the expense and highly variable performance of the human inspector, automated machine reading devices are an attractive alternative for performing the verification task. An additional advantage of the machine reader is that information regarding the card or its holder may be stored covertly. A security verification system is presented consisting of a holographic security emblem in which information is covertly stored, and an automated reader based on a joint transform correlator (JTC). A holographic encoding method is used to produce an emblem that stores the required phase and/or amplitude information in the form of a complex, 3-D diffraction pattern that can only be interpreted through the use of a second 'key' hologram. The reader incorporates the use of the non-linear material, Bacteriorhodopsin, as a means of miniaturizing the system, reducing system cost, and improving system performance. Experimental results are presented that demonstrate the feasibility of the approach for security applications.

Micro-displacement by Means of Optoelectronic Nonlinear Joint Transform Correlation of Speckle Pattern

Two objective speckle patterns are obtained—one before and one after the object has been moved—and are placed in the input plane of an optoelectronic nonlinear joint transform correlator.Nonlinear transformation of the joint power spectrum permits a sharper correlation peak and a high signal-to-noise ratio. The autocorrelation peak coordinates of the first pattern are set as a reference for measuring displacements of the cross-correlation peak, and also, the calibration of the measurement system is performed.It is well known that speckle can be regarded as a random spatial carrier in which information on the shape and position of the diffusing surface is encoded. The correlation of speckle patterns is highly appropriate for measuring displacements of tens of micrometers.1,2 In this work, an alternative technique based on the correlation between two speckle patterns by means of a digital bipolar joint transform correlator3 is presented. Initially the technique is described and then experimental results are shown.

Performance Improvement of a Phase-Shifting Joint Transform Correlator by use of Phase-Iterative Techniques

We propose a new technique to improve the performance of the joint transform correlator (JTC). In this technique we have applied the phase-iterative algorithm to a phase-shifting JTC (PSJTC). By doing so, we restrain the noise that is contained in the recovered phase of the joint transform power spectra for the input images with background and additive noise. In the case in which the input image is embedded in the input noise, we find that, by using the phase-iterative techniques with the PSJTC, one can get a higher cross-correlation peak and signal-to-noise ratio than with a PSJTC alone. From the computer-simulation results, one can conclude that the proposed algorithm successfully enhances PSJTC performance, especially for an input image with large noise.

Phase-Encoded Joint Transform Correlator to Reduce the Influence of Extraneous Signals

A technique to reduce the influence of the dc and the complex-conjugate correlation signals that are inherent in a joint transform correlator is proposed. The key part of this technique is the use of a phase mask. The mask contributes only extraneous signals, so the influence of the signals is reduced. The desirable correlation signal is not affected, and its shape is retained. Computer simulations confirm the performance of the proposed phase-encoded joint transform correlator.

Photorefractive joint-transform correlator using incoherent-erasure in two-wave-mixing geometry

We propose and investigate a photorefractive joint-transform correlator that uses an incoherent erasure beam in a two-wave-mixing arrangement. Computer simulation and experimental results are presented showing its performance in terms of discrimination ability and noise robustness. Simulation studies show that this JTC can exploit a nonlinear transfer characteristic inherent to the energy transfer process.

Optical wavelet feature extraction using a multiple-input phase-only encoded joint-transform correlator

We describe an optical joint-transform correlator (JTC) that uses phase-only encoded inputs for multi-scale wavelet feature extraction. The analysis of the JTC is extended to multiple phase-only encoded inputs which allowed combinations of cross-correlations between input images to produce a multi-scale wavelet transform under certain conditions. In addition, we compare the results of phase-encoding to that of amplitude-encoding. Using multiple-input phase encoding allows feature extraction to be performed with wavelets described in the spatial domain.