Average amplitude matched filter

Abstract

We propose a simple method of determining whether an unknown object is a member of a class of objects. We modify the standard 4f optical correlator by inserting an amplitude mask in front of the phaseonly filter (POF) in the Fourier transform plane. Our computer simulations show that this changes the output from a POF correlation response to a classical matched filter (CMF) response. The CMF is less sensitive to an exact pattern match than the POF, which can be an advantage in detecting a class of objects. We took the Fourier transform of an ensemble average of five similar input images to make the amplitude mask, thus creating an average amplitude matched filter (AAMF). The AAMF emulated the response ofthe CMF in all autocorrelation and cross-correlation simulations. We also simulated binary phase-only versions of the CMF and AAMF. Again, in all cases the binary AAMF (BAMF) emulated the correlation response of the binary CMF (BCMF). A binary POF contains both a correlation and a convolution component. In the correlation plane, the correlation response of the binary POF is much larger than the convolution response. Both the BCMF and the BAMF correlation response contain a marked convolution as well as correlation response. The amplitude function forces more energy into the convolution response. The result is that the convolution component of the output is nearly as large as the correlation component.