A new method for obtaining higher-order optical correlation/convolution using a spatial light modulator with extended phase modulation

In this work we present a new method to optically obtain the convolution / correlation between two functions. The technique is based on obtaining higher powers of a properly designed phase-only hologram. The approach combines some of the advantages of the classical 4f and the JFTC correlator systems. These higher powers of the hologram transmission function can be obtained easily using a spatial light modulator (SLM) with an extended phase modulation of various cycles of 2π radians. SLMs with such extended phase modulation present useful unusual diffraction properties that can be exploited to surpass some limits of SLM technology. In this case we exploit them to obtain higher order optical correlation terms. Computational simulations and experimental results agree with theory.