Some Effects of Fourier-domain Phase Quantization

If the Fourier transform of a function g(x) is quantized, the function recovered by inverse transformation differs from g(x). By means of a biased limiter model, the effects of Fourier-domain phase quantization are studied. Amplitude information is assumed fully retained, while phase is quantized to N equally spaced levels. The recovered function is shown to consist of several different contributions, the relative strengths of which depend on the number of phase quantization levels. Several specific examples are given. Motivation and interpretation are presented in terms of digitally constructed holograms.