Generalized joint fractional fourier transform correlators: a compact approach

Fractional correlation was introduced recently. We generalize the architecture of a joint (Fourier) transform correlator (JTC) to achieve the joint fractional (Fourier) transform correlator (JFrTC) such that fractional correlation can be obtained. Here the Fourier transform in the JTC is replaced by the fractional Fourier transform, and four different JFrTC architectures can be implemented. The mathematical derivations for these JFrTC architectures are given, together with the simulation verifications. The JFrTC can provide a correlation signal similar to a delta function but with a small discrimination ratio, such that it is insensitive to additive noise. In a conventional JTC the distance between the two desired correlation signals at the output plane is fixed and depends on the distance between the input and the reference signals. However, with a given fractional order and an additional phase mask the separation distance between the two correlation signals at the output plane of a JFrTC can be larger or smaller than that of a JTC. This property is useful for the applications of real-time target tracking. Unlike in a previous approach [Appl. Opt. 36, 7402 (1997)], we need only two fractional Fourier transformations instead of three to achieve fractional correlation.     

Nonlinear joint fractional transform correlator

An important tool in optical pattern recognition, the joint fractional transform correlator (JFTC), was introduced recently. We analyze the peak properties of fractional correlation (FC) by symbolic derivation and computer simulation. We show that the FC has a maximum correlation peak when the second fractional Fourier transform is reduced to the conventional Fourier transform. We introduce nonlinear operations in a joint fractional transform power spectrum and propose a differential JFTC and a binary differential JFTC. Numerical simulations show that such nonlinear JFTCs exhibit remarkable improvement in correlation peak intensity, discrimination capability, and signal-to-noise ratio. An optoelectronic setup that can implement such nonlinear JFTCs is also proposed.     

Optical wavelet-matched filtering with bacteriorhodopsin films

We present here the experimental and numerical results to demonstrate the superior performance of optical wavelet-matched filtering over conventional matched filtering. For this purpose, the biomolecule material bacteriorhodopsin (bR) as the recording media and the improved dual-axis joint transform correlator configuration as the preferred optical setup have been used. Compared with the dual-axis joint Fourier transform correlator, the dual-axis joint wavelet transform correlator provides better correlation performance.     

Fractional correlation operation: performance analysis

The fractional correlation is a new tool related to the fractional Fourier transform. It is useful for comparison and recognition, especially for shift-variant cases. The performances of such a correlator are analyzed according to the standard criteria of signal-to-noise ratio, correlation sharpness (peak-to-correlation energy), and Horner efficiency. The conclusions are that the performance is object dependent and that for nonwhite noise, compared with the conventional correlator, improved performances are possible. In addition we show that for a white-noise spectrum the fractional correlation has performances similar to the conventional correlator.     

Space-variant simultaneous detection of several objects by the use of multiple anamorphic fractional-Fourier-transform filters

A fractional correlator that is based on the anamorphic fractional Fourier transform is defined. This new, to our knowledge, correlator has been extended to work with multiple filters. The novelty introduced by the suggested system is the possibility of the simultaneous detection of several objects in different parts of the input scene (when anamorphic optics are dealt with), thereby permitting an independent degree of space invariance in two perpendicular directions. Computer experiments as well as experimental optical implementation are presented.     

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.     

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。     

散斑分数傅里叶联合变换相关测量研究

提出数字散斑联合变换分数相关测量方法,利用分数相关可以锐化相关峰的作用,在数字散斑联合变换相关运算中用分数傅里叶变换代替傅里叶变换,提高测量精度。通过对散斑图像进行相位调制,有效地解决了分数傅里叶变换的移变性带来的谱移问题。编程模拟和对拉伸试件位移场测量的结果表明,只要选择合适的分数傅里叶变换级次和相位调制函数,可以使相关峰的半宽度从4～5pixel锐化到仅1pixel,得到优于傅里叶变换相关的理想输出。     

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.     

Space-variant optical correlator based on the fractional Fourier transform: implementation by the use of a photorefractive Bi(12)GeO(2(a)) (BGO) holographic filter

A space-variant optical correlator is proposed on the basis of the fractional Fourier transform. The optical device uses as a recording medium for the holographic filter a photorefractive Bi(12)GeO(2) (BGO) crystal. The experimental results confirm the shift-variance properties. Some limitations that arise from the volume diffraction are also considered.     

Distortion-invariant fringe-adjusted joint transform correlation

A distortion-invariant joint transform correlator based on the concepts of the fringe-adjusted joint transform correlator and the synthetic discriminant function is presented. Computer-simulation results show that the proposed joint transform correlator is distortion-invariant for the target image from the training set and produces sharper correlation peaks and lower sidelobes compared with the classical joint transform correlator.     

Filter-feature-based rotation-invariant joint Fourier transform correlator

Rotation-invariant target detection using a trained filter-feature-based joint Fourier transform (JFT) correlator is investigated. First, a composite reference image is obtained from a training set of targets. An optimum filter formulation is then applied on this composite image to come up with a new feature that we refer to as a filter feature. This feature is then used in a JFT correlator, which results in a simple and robust rotation-invariant target recognition system.     

Characterization of an Optimized Nonlinear Joint Transform Correlator

Abstract

The performance of a nonlinear joint transform correlator which employs a GEC-Marconi optically addressed spatial light modulator in the Fourier plane is investigated in terms of the device operating conditions and other system parameters. We discuss the optimum performance characteristics of the correlator and the sensitivity to changes in the rotation, scale and separation of the objects in the input plane.     

抗噪性联合变换相关器

我们对联合变换相关器的输入图象进行Roberts梯度处理,同时对参考图象采取相移技术,并在频域中将功率谱二值化。与传统的联合变换相关器（CJTC）相比,新型的联合变换相关器（NJTC）消除了功率谱的直流分量,锐化了相关峰强度,提高了衍射效率和识别能力,同时增强了联合变换相关器的抗噪性能。用计算机模拟出预言结果。     

Fourier-plane windowing in the binary joint transform correlator for multiple target detection

With recent advances in state-of-the-art spatial light modulators, the optical joint transform correlator (JTC) and the binary joint transform correlator (BJTC) are becoming practical signal-processing tools. The performance of these devices is limited by the difficulty of separating the cross correlation between the reference and the targets in the scene from signals resulting from cross correlations between objects in the target scene. One technique that reduces this problem is to use a sliding window in the Fourier plane as a convolution mask filter to set an adaptive binarization threshold. This suppresses the autocorrelation response and reduces the dynamic range of the Fourier-plane signal. This results in correlation performance improvement by a factor of 2 to 4. A mathematical model is developed to describe the windowing process for both the JTC and BJTC for the case in which the scene contains multiple targets and background clutter. The derivation of the windowing process is general and includes any spatial high-pass or bandpass filtering in the Fourier plane. The results are supported with experimental data.     

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.     

Efficient computation of joint fractional Fourier domain signal representation

A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains.     

All-optical subtracted joint transform correlator with a holographic interferometer

A new, to our knowledge, subtracted joint transform correlator (SJTC) is proposed that has no digital processing in a computer. All processing for obtaining correlation signals between an object and multiple reference patterns were treated optically by use of a joint transform correlator with a holographic interferometer similar to the Mach-Zehnder one. The joint power spectrum of the reference patterns was subtracted from that of the input image (the object pattern plus the reference patterns), and the spurious correlation signals between the different reference patterns were removed. Because of the optical parallel computations of the Fourier spectra and the subtraction, the real-time SJTC is possible to achieve by use of only an optical system. An experimental arrangement of the system and system performances of the shift-invariant characteristics and discriminability are described. The results show the good performance of this system.     

Incoherent-to-coherent conversion and square-law transmission based on photoinduced birefringence in bacteriorhodopsin films

We review the main optical properties of bacteriorhodopsin that are relevant to its use as a spatial light modulator. A model is described for the transmittance of a film placed between crossed polarizers in which photoinduced birefringence occurs. We show when the transmittance is proportional to the write intensity. We use this property in a joint transform correlator for incoherent-to-coherent conversion and effective square-law modulation in the Fourier plane.     

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.