Cross talk between holograms of finite contrast in a phase-code multiplexing system

The cross talk between holograms recorded in a phase-code multiplexing system is analyzed. The signal-to-noise ratio (SNR) is derived for the original image of a finite contrast ratio in the presence of a phase-shift error of the reference beam. It is shown that one particular code in the Walsh-Hadamard code set can be the dominant cross-talk noise source. We experimentally measured the SNR of the holograms recorded in an 8-bit phase-code multiplexing system by varying the contrast ratio of the original image. We show good agreement between experiment and theory. The existence of one bad code is also shown experimentally.