The Effect of Sampling on FFT-Based Direct Integration Method in Digital Holography

摘要

The Rayleigh-Sommerfeld formula(RS) has proved accurate for evaluating diffraction of the optical field from a planar aperture. Thus the FFT based direct integration method for the RS(FFT-DIRS) can provide a more exact reconstructed image from sampling points of the diffraction field of the object than the numerical method for the Fresnel formula(FR) that is an approximation of the RS. Although the FFT-DIRS has been proposed and studied in some literatures, an important problem remains to be solved, that is the effect of sampling on it. Sampling of the object diffracted field leads to a periodic or quasi periodic shifting of the reconstructed image. If these spatial replicas overlap, the desired image can not be recovered without the aliasing noise. So the overlapping period plays an important role in employing the FFT-DIRS for the practical applications. In this paper, a formula of this overlapping period is obtained through the relationship between the RS and the FR. Then the validity of this formula at different distances is investigated by the experimental results.