Triplicator phase-only hologram and its use as a snapshot optical convolver and correlator

In this work we extend the optimum phase triplicator diffraction grating profile to a phase-only hologram. This modified hologram generates three equally-energetic orders with the highest diffraction efficiency, yielding a direct version and an inverted complex conjugate version of the target pattern in the ±1st orders, respectively, and a delta function in the DC zero order. When combined with another phase-only function, the resulting hologram yields convolution and correlation terms in the ±1st orders, respectively, while the target function encoded in the added phase appears in the zero order. Experimental results obtained with a high-resolution liquid-crystal phase-only spatial light modulator (SLM) demonstrate the proposed design.