Shift and scale-invariant correlator using a radially stretched phase-only filter

A radial stretching of the phase only filter depending on the energy angular distribution of the target spectrum is used to perform shift and scale invariant pattern recognition. The complex conjugate of a basic size target Fourier transform and the cumulative energy angular distribution are calculated. Then the radially stretched filter providing the same energy contribution to the correlation peak independent on the target size is prepared and used in a conventional correlator, with spherical-wave illumination. The maximum scale ratio of recognizable objects equals 1:1.5. Computer simulations and experimental results, showing the performance of the filter are presented.