Speckle statistics and depth discrimination in the confocal scanning optical microscope

Abstract

Expressions for the mean intensity, speckle contrast and intensity covariance of the speckle patterns produced in the confocal scanning optical microscope (CSOM) are derived. It is assumed that the lenses have gaussian pupil transmission functions and that the fluctuations introduced by the thin phase screen are gaussian distributed with a gaussian autocorrelation function. The calculations are limited to cases in which the central limit theorem can be invoked. The results are analysed and their dependence on the statistics of the phase screen is illustrated by examples in which the formula are evaluated numerically. The relevance and implications of these results on the depth discrimination property of the CSOM are also discussed.