Joint Wavelet-Fractional Fourier Transform

Based on Dirac＇s representation theory and the technique of integration within an ordered product of operators, we put forward the joint wavelet-fractional Fourier transform in the context of quantum mechanics. Its corresponding transformation operator is found and the normally ordered form is deduced. This kind of transformation may be applied to analyzing and identifying quantum states.

Design of a Modified Cassegrain System Used in Joint Transform Correlator

In order to detect and recognize infrared target with joint transform correlator,a modified Cassegrain optical system is designed.The main advantages of the system are large field-of-view,infrared dual-band common optical path and compact structure.In the modified Cassegrain optical system,the working wavelengths are 3.7~4.8μm and 8~12μm,the field-of-view is 4° and the aperture is 240mm.The paraboloidal primary mirror and hyperboloidal secondary mirror are all replaced by spherical surfaces.So the problems of high machining accuracy and alignment become much easier.In order to balance the aberrations,three compensating lenses are used in the system.The total length of the system is 183mm,and the ratio of the total length to focal length is 0.68.Moreover,the system has a good performance of athermalization between negative 40℃ and positive 60℃.The design results of the system show that the MTF value of each field is greater than 0.72 when the cut-off frequency is 11lp/mm.Due to the excellent image quality of the modified optical system,the ability of Joint transform correlator(JTC)applied in target tracking and identification has been improved for further.

Phase-only Correlation Measurement with Computer-controlled LCD and CCD Image Processing System

Using computer-controlled liquid crystal display (LCD) as an image processor and a CCD camera as a detector, phase-only correlation measurement is performed with the aid of joint transform correlation method (JTC). This computer -controlled LCD-CCD image processing system may be a powerful tool for defect detection, position control and pattern recognition. It enables new possibilities in analog real-time image processing. This is of great interest in microelectronic manufacturing today and in the future.

Multiple Targets Recognition for Highly-Compressed Color Images in a Joint Transform Correlator

In this paper, we are proposing a compression-based multiple color target detection for practical near real-time optical pattern recognition applications. By reducing the size of the color images to its utmost compression, the speed and the storage of the system are greatly increased. We have used the powerful Fringe-adjusted joint transform correlation technique to successfully detect compression-based multiple targets in colored images. The colored image is decomposed into three fundamental color components images (Red, Green, Blue) and they are separately processed by three-channel correlators. The outputs of the three channels are then combined into a single correlation output. To eliminate the false alarms and zero-order terms due to multiple desired and undesired targets in a scene, we have used the reference shifted phase-encoded and the reference phase-encoded techniques. The performance of the proposed compression-based technique is assessed through many computer simulation tests for images polluted by strong additive Gaussian and Salt & Pepper noises as well as reference occluded images. The robustness of the scheme is demonstrated for severely compressed images (up to 94% ratio), strong noise densities (up to 0.5), and large reference occlusion images (up to 75%).