Investigations Of Joint Fractional Fourier Transform Correlator

The joint transform correlator (JTC) is paid more attention by researchers than the Vander Lugt correlator (VLC) with its advantages, such as high spatial bandwidth product, without integrated filtering and real-time operation etc. Fractional Fourier transform (FRFT) is a generalization of the conventional Fourier transform (FT). Its properties are more extensive and flexible than those of a conventional Fourier transform, which leads a much wider applications. We exert both advantages by combining the fractional Fourier transform with the joint transform correlator. Properties of the joint fractional Fourier transform correlator (JFRTC) are investigated detailedly in this thesis.First, the numerical simulation system of the fractional Fourier transform written by the MATLAB language is set up on the basis of the Namias's fractional Fourier transform theory and the diffraction angular spectrum theory. Then, the numerical simulation systems of the joint fractional Fourier transform correlator and the fractional Vander Lugt correlator are assembled based on the numerical simulation system of the fractional Fourier transform. Second, the properties of the joint fractional Fourier transform correlator are studied in two aspects of theory analysis and numerical simulation, and the conclusions are as follows: ? The distance of the correlation peaks can be adjusted by shifting the fractional orders p\ and P₂; â‘¡ Not only the distance between the correlation peaks but also the intensity of the correlation peaks is influenced by the value of p₁. When p₁ drops, the distance between the correlation peaks increases, meanwhile the intensity of the correlation peaks declines. (3) The value of P₂ influence only the distance between the correlation peaks. The distance decreases while p₂ drops. Besides, the necessity of phase-modulation in a joint fractional Fourier transform correlator is analyzed in detail. By adding two certain phase masks to the object and the reference images at the input plane, the intensities of the correlation peaks are greatly enhanced, and the quality of the correlation peaks are obviously improved. Last, the distortion-invariant property of the fractional Vander Lugt correlator and the joint fractional Fourier transform correlator is studied respectively. From the study we can make a conclusion that the fractional correlator has the capability of distortion-invariant pattern recognition when a series of nonlinear methods are adopted.