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.     

Multichannel single-output color pattern recognition by use of a joint-transform correlator

A novel method for performing color image recognition by the use of the coherent joint-transform correlator is introduced. The input plane of the proposed method is a spatial rearrangement of the separation into color channels of both the color input scene and the color target. This input plane is gray scaled and monochromatic, thus it can be displayed by the use of amplitude spatial light modulators to achieve real-time operation. The system provides a single output-plane result of the optical coherent addition of the separate channels' correlation outputs. At the output plane no electronic postprocessing is needed, and the detection decision is achieved simply by the application of threshold detection. Experimental results and computer simulations are presented to demonstrate the abilities of this system.     

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.     

Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques

The implementation of non-zero-order joint-transform correlators (JTC's) is presented. The zero-order spectra (i.e., the autocorrelation power spectra) are removed from the joint-transform power spectrum by use of phase-shifting techniques by which the output diffraction and input spatial domain can more efficiently be utilized. Applications of the phase-shifting techniques to both conventional JTC's and phase-transformed input JTC's (PJTC's) are discussed. Compared with the conventional JTC, the PJTC has the advantages of higher light efficiency, a better signal-to-clutter ratio, and the simplicity to realize phase shifting. We anticipate that the proposed non-zero-order JTC's should have a significant impact on the future development of more efficient JTC's.     

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.     

Polychromatic target identification with a color liquid-crystal-TV-based joint-transform correlator

A real-time polychromatic target-detection technique that uses a computer-addressable color liquid-crystal- TV-based joint-transform correlator (JTC) is presented. One of the major features of the polychromatic JTC is that the spectra content of the object can be exploited. Since the liquid-crystal-TV panel is computer addressable, the JTC system can be made adaptive, by which the joint-transform power spectrum can be manipulated. Experimental demonstration of the proposed polychromatic JTC is provided, in which we show that the spatial and the spectral content of targets can be detected.     

Reduction of the effect of aberrations in a joint-transform correlator

We report the study of the influence of optical aberrations in a joint-transform correlator: The wave aberration of the optical system is computed from data obtained by ray tracing. Three situations are explored: We consider the aberration only in the first diffraction stage (generation of power spectrum), then only in the second (transformation of the power spectrum into correlation), and finally in both stages simultaneously. The results show that the quality of the correlation is determined mostly by the aberrations of the first diffraction stage and that we can optimize the setup by moving the cameras along the optical axis to a suitable position. The good agreement between the predicted data and the experimental results shows that the method explains well the behavior of optical diffraction systems when aberrations are taken into account.     

Phase-only joint-transform correlator: analysis and experimental results

An analysis of the popular joint-transform optical correlator is presented for architectures employing spatial light modulators that operate only on the phase of the coherent light. Experimental results are also presented, for simple scenes that produce analytic solutions, which support the analysis.     

Joint transform correlator subtracting a modified Fourier spectrum

The optically generated joint Fourier transform (JFT) of a test image and a reference image is processed using a new method: the JFT is recorded twice. In the second recording the reference image is phase shifted by π with respect to the first recording. The two JFT's are subtracted and binarized with a threshold of zero. Strong correlation peaks are obtained, and correlations within the test image are suppressed. Some results of optical implementation are presented, using a ferroelectric liquid crystal display with 128 × 128 pixels for data input. The phase shift of the reference was implemented by the contrast-inverted reference input on the binary light-modulating device. Processing of the JFT is done by a CCD camera, a frame grabber, and a personal computer.     

Multiple-target detection with use of a modified amplitude-modulated joint transform correlator

Multiple-target detection with a modified amplitude-modulated joint transform correlator is proposed. With this technique the joint power spectrum is first modified by the subtraction of the power spectrum of the input scene only and of the reference image from it; the resultant modified joint power spectrum is next multiplied by the amplitude-modulated filter function. The effect of noise in the input scene on the performance of the joint transform correlator is analyzed and quantified. This technique is found to deliver a correlation output and the capacity to accommodate noise in the input scene better than both the fringe-adjusted filter-based joint transform correlator and the modified fringe-adjusted filter-based joint transform correlator.     

Optical wavelet processor by holographic bipolar encoding and joint-transform correlation

A novel optical wavelet processor based on the techniques of the joint-transform correlator and computer-generated holograms is proposed. A coding technique that is a simplified version of Lee's hologram [Appl. Opt. 9, 639 (1970)] is used to represent positive and negative values for the object signal and wavelet functions. We experimentally demonstrate that wavelet transforms of two different daughter wavelet functions can be simultaneously obtained by the appropriate arrangement of the daughter wavelet functions and the object signal on the input plane.     

Aperture tapering in a coherent optical correlator

Sharp edges located in an optical correlator input beam cause unwanted edge effects. A 1-D analysis is used to demonstrate this effect and how edge tapers can reduce this effect. Then an aperture made on film approximating the best taper is used to reduce the spurious signals in a matched filter correlator.     

Active contour segmentation by use of a multichannel incoherent optical correlator

We describe an optoelectronic incoherent multichannel processor that is able to segment an object in a real image. The process is based on an active contour algorithm that has been transposed to optical signal processing to accelerate image processing. This implementation requires exact-valued correlations and thus opens attractive perspectives in terms of optical analog computation. Furthermore, this optical multichannel processor setup encourages incoherent processing with high-resolution images.     

Controlled-intensity detection peaks in a binary joint transform correlator

In multiobject pattern recognition the height of the correlation peaks should be controlled when the power spectrum of ajoint transform correlator is binarized. In this paper a method to predetermine the value of detection peaks is demonstrated. The technique is based on a frequency-variant threshold in order to remove the intraclass terms and on a suitable factor to normalize the binary joint power spectrum. Digital simulations and experimental hybrid implementation of this method were carried out.     

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.     

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.     

Optical correlation of spatial-frequency-shifted images in a photorefractive BSO correlator

The optical cross correlation of an image with another image that was spatial-frequency shifted in one dimension was demonstrated in a photorefractive VanderLugt correlator. The first image was stored as a Fourier-transform hologram in a photorefractive Bi12SiO20 crystal (BSO) and was successively correlated with different spatial-frequency-shifted versions of a second image. We implemented the spatial-frequency shift by rotating a galvanometer mirror in an image plane, causing the Fourier transform to be shifted laterally in the BSO. We verified that the resulting operation in the BSO was an accurate complex multiplication of the shifted and the stored Fourier transforms. As many as 20 successive readouts were conducted without measurable erasure of the stored hologram. The dynamic range, saturation behavior, and other performance parameters were measured and are discussed.     

Color image recognition by use of a joint transform correlator of three liquid-crystal televisions

We present a joint transform correlator for color image recognition by using three liquid-crystal spatial light modulators. A method for simultaneously obtaining the correlation peaks of red, green, and blue is proposed and experimentally demonstrated.