All-optical nonlinear joint Fourier transform correlator

We present the first all-optical nonlinear joint transform correlator based on a square-law receiver in the Fourier plane. Our device uses a photorefractive limiting quadratic processor. The compressional nonlinearity associated with the transfer function of the limiting quadratic processor enables the correlator to detect signals embedded in Gaussian and non-Gaussian noise. In the limiting region this device correlates the phase-only information of the input. This is the first time to our knowledge that photorefractives or real-time holography has been used in the correlation of the phase-only information. We demonstrate the operation of this device experimentally, and we evaluate its performance throughcomputer simulation for various forms of noise.     

Binary joint transform correlator based on differential processing of the joint transform power spectrum

A novel binary joint transform correlator with differential processing in the joint transform power spectrum is proposed. The new model of the binary joint transform correlator can eliminate the dc component and sharpen the correlation intensity peaks, hence increasing its discrimination ability but with a lower complexity of computation. Preliminary results are shown by computer simulations.     

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.     

Approximate performance of the nonlinear joint transform correlator in signallike noise

We present a statistical-analysis technique for a nonlinear joint transform correlator (JTC) based on two assumptions: the noise and the signal spectra are identical, and the signal energy is small relative to the noise energy. The first assumption, while admittedly convenient, is also defensible in that it is a worst case and in that image and scene noise can be similar in texture. The second is also reasonable, given that even a clearly visible signal may have small energy compared with the scene noise if it is of limited extent; in any case, the results appear moderately faithful even for the case that signal and noise energies are equal. We discover that the optimal Fourier-plane transformation is spatially variant and tends to remove the Fourier amplitudes of the input image, and indeed functions in a way very similar to the spatially variant binary JTC. We also see that the classic (or spatially invariant linear) JTC is a very inferior technique for signallike noise, that the best spatially variant binary JTC uses a threshold proportional to the noise power spectrum, and that, if a spatially invariant binary-thresholded JTC is desired, then the median Fourier-plane value is an excellent choice of threshold. The performance predictions are verified by simulation and appear to be reasonable even for the highly nonlinear binary schemes.     

Hybrid nonlinear joint transform correlator that operates at a high frame rate

A joint transform correlator has been constructed by a spatial light modulator that uses the electroabsorption effect of GaAs crystal and operates at a high frame rate a TV camera with logarithmic response and a personal computer. In the system, logarithmic values of joint power spectra generated in an optical system were electrically digitized and inverse-Fourier transformed. The system has accomplished the operation of correlation with a throughput time smaller than 10 ms per an input image.     

Image rotation and translation measurement based on double phase-encoded joint transform correlator

An image rotation and translation measurement technology based on a double phase-encoded joint transform correlator (DPEJTC) is proposed. The reference and the target images are Fourier transformed. Then the magnitude of the Fourier-transformed reference (MFR) and target (MFT) images are multiplied with a high-pass emphasis filter and transformed from Cartesian space into polar space. Rotation between the reference and the target image is obtained by measuring the emphasized MFR and MFT in polar coordinates by the DPEJTC. The target image is rotated by the rotation angle in the inverse orientation to get the rotation-correction target image. Finally, translation between the reference and the target image is obtained through measuring the reference and the rotation-correction target image by the DPEJTC. Results based on digital computation are given to verify our proposal. A possible optical setup is suggested.     

Application of a wire-grid-mirror liquid-crystal light valve in a nonlinear joint transform correlator

We describe the operation of a wire-grid-mirror liquid-crystal light valve and its use for optical pattern recognition. The nonlinear characteristic of the wire-grid-mirror liquid-crystal light valve is used to implement the nonlinear joint transform correlator. Experimental results and computer simulations show that the nonlinear characteristic of the wire-grid-mirror liquid-crystal light valve can produce a well-defined correlation peak and low output background. The performance of the nonlinear joint transform correlator obtained when the wire-grid-mirror liquid-crystal light valve is used is compared with that of the binary joint transform correlator.     

基于液晶光阀微分处理的实时联合变换相关器

提出了一种用液晶光阀实现对输入图像的微分预处理和对功率谱微分处理的实时联合变换相关器。两个液晶光阀均处于非线性变换态,分别在输入面和频谱面上实现对输入图像和联合功率谱的微分处理。微分功率谱经傅里叶透镜变换后得到相关输出。实验表明,该相关器采用全光方式不仅保证了实时性,而且锐化了相关峰;经该相关器微分后的图像,其相关性能明显优于常规联合变换相关器输出的结果。     

Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination conditions

The correlation performance of binary joint transform correlators with unknown input-image light illumination is investigated for different thresholding methods used in the Fourier plane. It is shown that a binary joint transform correlator that uses a spatial frequency dependent threshold function for binarization of the joint power spectrum is invariant to uniform input-image illumination. Computer simulations and optical experimental results are provided.     

A novel secret sharing with two users based on joint transform correlator and compressive sensing

Recently, joint transform correlator (JTC) has been widely applied to image encryption and authentication. This paper presents a novel secret sharing scheme with two users based on JTC. Two users must be present during the decryption that the system has high security and reliability. In the scheme, two users use their fingerprints to encrypt plaintext, and they can decrypt only if both of them provide the fingerprints which are successfully authenticated. The linear relationship between the plaintext and ciphertext is broken using the compressive sensing, which can resist existing attacks on JTC. The results of the theoretical analysis and numerical simulation confirm the validity of the system.     

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.     

二元联合变换相关器的实现方法研究

采用中值取阈，局部取阈，参考图像功率谱取阈和联合功率谱（JPS）取阈四种方法对传统联合变换相关器的功率谱二值化，从而将振幅调制的功率谱转化为脉冲调制的功率谱。计算机模拟结果表明二值化可以获得更清晰更尖锐的相关峰，其中联合功率谱取阈法的识别效果最佳。     

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.     

Convergent optical correlator aligment based on frequency filtering

The convergent correlator is widely used but it presents the drawback of the alignment requirements: fine focusing of the input scene Fourier transform on the filter plane, filter centering, scaling the scene Fourier transform to match the filter size, and azimuth matching of the filter with the input scene. We propose a set of tests to obtain a precise alignment of the convergent correlator. These methods are based on frequency filtering properties and they are applicable either for amplitude input or for phase-encoded input. The tests we present allow us to fulfill all the alignment requirements. The theory on which these tests are based is explained. The experimental results obtained during the alignment procedure are presented. We show some additional verifications of the correct alignment of the convergent correlator.     

Partial rotation-invariant pattern matching and face recognition with a joint transform correlator

We describe the circular-harmonic (CH) image CH(mr), which is based on CH components for rotationally invariant pattern recognition. CH components of the order m, derived from an image in polar coordinates, are used to form a two-dimensional space together with the radial variable r. Filtering the CH(mr) image leads to a reference image with some rotational invariance. For a narrow-pass filter we have a single CH component with full rotation invariance; for an all-pass filter we have the original image with no rotational invariance; for a low-pass filter we form a reference image containing multiple circular harmonics with partial rotation invariance. Results of numerical simulations and optical experiments with a joint transform correlator are given that illustrate partial-rotation-invariant recognition for human face images.     

Secure optical data storage with random phase key codes by use of a configuration of a joint transform correlator

A secure optical storage based on a configuration of a joint transform correlator by use of a photorefractive material is presented. A key code designed through the use of an optimized algorithm so that its Fourier transform has a uniform amplitude distribution and a uniformly random phase distribution is introduced. Original two-dimensional data and the key code are placed side-by-side at the input plane. Both of them are stored in a photorefractive material as a joint power spectrum. The retrieval of the original data can be achieved with the same key code. We can record multiple two-dimensional data in the same crystal by angular multiplexing and/or key code multiplexing.     

High-efficiency hybrid joint transform correlator with pre-processed input image and replicated binary spectrum array

Abstract

The performance of a hybrid joint transform correlator (JTC) is improved by the input image pre-processing method and our proposed spectrum binarizing and replicating technique. The input image pre-processing can enhance the correlation discrimination ability of a JTC system, and the replication of the binary spectrum under an appropriate condition can further substantially increase the light efficiency, the maximum correlation peak intensity, the peak sharpness and the signal-to-noise ratio of the system at the same time by the mechanics of constructive interference. Theoretical analyses are presented. Both the computer simulation and optical experiment verifying the effectiveness of this technique are also given.     

Image hiding in Fourier domain by use of joint transform correlator architecture and holographic technique

Based on joint transform correlator (JTC) architecture and holographic techniques, a new method for image hiding is presented. A hidden image encrypted by JTC architecture is embedded in the Fourier hologram of the host image. Inverse Fourier transform can be used to obtain the watermarked image, and JTC architecture is used to decode the hidden image from the watermarked hologram. Unlike other watermarking techniques, by prechoosing information, the noise added to the recovered hidden image by the host can be reduced. Unlike other watermarking systems based on double random-phase encoding, no conjugate key is used to recover the hidden image. Theoretical analyses have shown the system's feasibility. Computer simulations are presented to verify the system's validity and efficiency. Numerical simulations also show that the proposed system is robust enough to resist attacks, such as occlusion, noise, and filtering.     

Joint transform optical correlator designed and analyzed by use of two- and one-dimensional hilbert transforms

Novel real-time joint transform, Hilbert transform optical correlators are proposed in which only a half or a quarter of the Fourier plane is written onto an optically addressable spatial light modulator. A point source is used to recover the result for the whole plane. As a result, images with a two- or four-times larger space-bandwidth product can be matched in amplitude and phase. The effect of truncating the transform plane is explained with two- and one-dimensional Hilbert transform analysis. Results of computer simulation are shown.