Simulating speckle with Mathematica® The speckle phenomenon is ubiquitous occurring in all regions of the electromagnetic spectrum as well as in both ultrasound and synthetic aperture radar imaging. Speckle occurs whenever radiation is reflected from a surface that is rough on the scale of a wavelength or is passed through a diffusing surface that introduces random path length delays on the scale of a wavelength. This book is devoted to simulation of speckle phenomena using the software package Mathematica®. Various techniques for simulating speckle are discussed. Simulation topics include first order amplitude and intensity statistics speckle phenomena in both imaging and free space propagation speckle at low light levels polarization speckle phase vortices in speckle and speckle metrology methods.