Analysis on the focal spot characteristics of random Gauss phase plate

Gaussian phase plate (GPP) is a special kind of continuous phase plate, which surface figure can be described as a Gaussian random process. In this paper we propose an analysis model to discuss the statistical characteristics of GPP's focal spot. Using the gradient histogram instead of the diffract integral, the variance of the focus light intensity is analyzed. And the variance reflects the stability of the intensity envelope of the focal spot. Both the deducing process and the numerical simulation are presented. And the results show that the stability of intensity distribution in the focal spot is directly proportional to the correlation length of the phase plate.