Optical wavelet transform by the phase-only joint-transform correlator

Abstract

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.

Subband mutiresolution by multi-object phase-only joint transform correlator

“…However, realization of filter coefficients and pixel values are a problem for amplitude-only JTC due to consisted negative values. To alleviate this problem, the phaseonly JTC technique has been reported, recently, in which both the input and Fourier planes are phaseencoded [9][10][11]. The phase-only JTC yields similar results as the amplitude only JTC as shown in Fig.…”

Image feature extraction by dynamic neural filtering and phase-only joint transform correlation

“…To alleviate this problem, POJTC technique has been reported recently, in which both the input and Fourier planes are phase-encoded [11][12][13]. The POJTC yields similar results as the amplitude-only JTC.…”

<title>Practical considerations for wavelet transforms obtained using a phase-only joint transform optical correlator</title>

“…H(u) is required to have a zero d.c. Fourier component for admissibility and thus it behaves as a band pass filter in the Fourier transform plane. The WT ofthe spatially dependent signal s(x) is defined mathematically as W,(a,b) = (s(x), hab(X)) = h(-dx = x) ® ha(X) (2) in the space domain or, in the frequency domain, W,(a,b) = (S(u),Hab(u)) = F{S(u)Hao(u)} = X)®ha(X) (3) and can be seen as the correlation of s(x) with the dilated wavelet function ha(X), where the symbol ® represents the correlation. The W,(a,b) is known as the continuous WT coefficient.…”