Random Phase Data Masks: Fabrication Tolerances and Advantages of Four Phase Level Masks

An analysis is presented of the intensity variations in the Fourier transform plane resulting from the use of a bilevel random phase mask for holographic data recording as suggested by Burckhardt. To maintain a fixed ratio of peak intensities between in-phase amplitude components and out-of-phase components for an imperfect phase mask, the permissible error in the phase shift varies as 1/N, where N is the number of apertures in the data mask. A factor of $2^{\frac{1}{2}}$ reduction in the rms intensity fluctuations in both the Fourier transform plane where the hologram is recorded and in the retrieved image may be obtained by using four levels of phase shift. No further improvement is obtained with additional levels.