Necessity analyses of phase masks in joint fractional Fourier transform correlator

In this paper, the mathematical expressions and the particularities of the joint fractional Fourier transform correlator (JFRTC) are detailedly analyzed. In a JFRTC, the distance between the two fractional correlation peaks can be adjusted flexibly by shifting the fractional orders. However, the intensity of the fractional correlation peaks decreases rapidly as the first fractional order p₁ drops. The former property is very useful in a practical recognition system, but the latter one seriously reduces the recognition sensitivity of a JFRTC. For this reason, phase masks should be added at the input plane of the JFRTC to enhance the intensities of the fractional correlation peaks and effectively overcome the default. Compared with the existing JFRTC with single phase modulation, a JFRTC with double phase modulation is suggested to more flexibly improve the performance of a JFRTC.