Optimization of the amplitude-modulated inverse filter for pattern-recognition applications

Abstract

An amplitude-modulated phase-only filter1, referred to here as an amplitude-modulated inverse filter (AMIF). The AMIF function is given by (1) where D and A can be constants or functions of both u and v, |R(u,v)| is the amplitude of Fourier spectrum of the reference function r(x,y), and (u,v) is the phase factor of R(u,v). The constraint D |R(u,v)| min+A guarantees that the gain of an AMIF based correlator is less than or equal to unity for all frequency values. When A < |R(u,v)|, AMIF is found to have a good correlation discrimination (CD) just as that of an IF and when A > |R(u,v) |, it is found to have a good optical efficiency (OE) as that of a phase-only filter (POF). By choosing values for A between the limits A < |R(u,v)| and A > |R(u,v)|, all the transition states between a POF and IF can be obtained. POF delivers nearly 100% OE and IF delivers the best CD. The AMIF allows for a trade-off between OE and CD and is shown to be very flexible to meet the pattern recognition applications. Our results show that AMIF has a better CD performance than that of a POF in the absence and presence of noise.