Abstract

Spatial phase modulation using gratings, arrays, and patterns inserted into the reference beam during holographic recording can be used to multiplex numerous data fields in the same volume of a photorefractive material. We present a basically simple but general formalism for analyzing these schemes, where encoding is achieved by spatial frequency multiplexing. Spatial frequency analysis is used to evaluate and compare various approaches and configurations. The encoding elements are analyzed in the Raman-Nath diffraction regime to determine the amplitude and relative phase of their spatial frequency components. The harmonically related terms are represented as Dirac delta functions in reciprocal space (a spatial frequency representation). The propagation phase differences are determined by using a space transmission operator (a Fresnel propagator) that is a function of spatial frequency and displacement. Dirac "kets" are used as bookkeeping aids to represent the beams. Encoding elements and holograms are represented as operators. Results of the recording and reading of holograms with various encoding devices are discussed by using this formalism.

© 1992 Optical Society of America