Speckle noise arising from coherently illuminated polydisperse and continuous size distributions of discs

Abstract

An existing model of the speckle noise affecting images in far-field in-line holographic imaging is extended to distributions of disc-shaped particles which are no longer of uniform diameter. In this model the signal-to-noise ratio in replayed images from ideal in-line holograms in the Fraunhofer regime is limited by the speckle field arising from the overlapping Airy patterns. The original study was motivated by holographic particle image velocimetry and assumed that all the particles were of uniform diameter. We extend this model to cover polydisperse, power-law, exponential and Gaussian distribution functions and include an explicit limit on our maximum particle diameter to ensure that the hologram is recorded in the far-field of all the particles.