Contrast optimisation of coherent images

Contrast optimisation is a method that can be used to correct phase errors in coherent images such as SAS images. However, the contrast measure of a given coherent image is a random variable due to the speckle present in coherent images. The variance of this measure puts a limit on the ability of contrast optimisation to focus an image. This paper derives probability distribution statistics of the most common contrast measure, the sum of the pixel intensities squared. These statistics are then verified by a number of speckle simulations. The developed statistics can be used as a tool to understand and improve the method of contrast optimisation.