Hexagonal sampling techniques applied to Fourier and Fresnel digital holograms

Abstract

Hexagonal sampling offers substantial computational efficiency in processing circularly band-limited and/or circularly symmetric functions and also offers a significant reduction of required data storage compared with rectangular sampling. Both Fraunhofer and Fresnel computer-generated holograms utilizing hexagonal sampling are capable of exploiting these properties. Hexagonal fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) algorithms have been developed along with efficient algorithms for generating the lens transmittance and free-space-transfer matrices that comprise software packages designed to accept hexagonally sampled input arrays and generate hexagonally sampled output arrays suitable for direct encoding into digital holograms.