Nonconventional joint-transform correlator

Broadband space-variant Fresnel processor

We present a radically new class of optical setup working with white-light illumination, namely, a chromatically compensated processor operating in the Fresnel domain. The optical configuration is a hybrid (diffractive-refractive) three-lens system that exhibits an intermediate achromatic Fresnel plane and an output image plane without chromatic distortion. As a first application of this optical arrangement we develop a parallel space-variant color pattern-recognition experiment with white light.

On-axis joint transform correlation based on a four-level power spectrum

We propose a method to obtain a single centered correlation with use of a joint transform correlator. We analyze the required setup to carry out the whole process optically, and we also present experimental results.

Fractional correlator with real-time control of the space-invariance property

In pattern recognition, it happens that the amount of space variance should be controlled. This may be achieved by use of a partially space-variant correlator. We present a novel configuration for achieving a partially controlled space-variant correlator. In this configuration the lenses are fixed in their focal lengths and locations. The filter function is also fixed. To change the amount of space variance, we need change only the longitudinal location of the filter without reencoding it. It is also shown that this type of correlator provides improved correlation peaks according to correlation-sharpness criteria.

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.

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.

Joint-transform correlation under varying illumination

The effect of varying the illumination of the target scene on the performance of classical, binary, and fringe-adjusted joint-transform correlators is investigated. Simulation results show that the fringeadjusted joint-transform correlator yields better correlation output than the classical or the binary joint-transform correlator under all illumination conditions of the target scene.