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We present a Monte Carlo rendering framework for the physically-accuratesimulation of speckle patterns arising from volumetric scattering of coherentwaves. These noise-like patterns are characterized by strong statisticalproperties, such as the so-called memory effect, which are at the core ofimaging techniques for applications as diverse as tissue imaging, motiontracking, and non-line-of-sight imaging. Our framework allows for theseproperties to be replicated computationally, in a way that is orders ofmagnitude more efficient than alternatives based on directly solving the waveequations. At the core of our framework is a path-space formulation for thecovariance of speckle patterns arising from a scattering volume, which wederive from first principles. We use this formulation to develop two MonteCarlo rendering algorithms, for computing speckle covariance as well asdirectly speckle fields. While approaches based on wave equation solversrequire knowing the microscopic position of wavelength-sized scatterers, ourapproach takes as input only bulk parameters describing the statisticaldistribution of these scatterers inside a volume. We validate the accuracy ofour framework by comparing against speckle patterns simulated using waveequation solvers, use it to simulate memory effect observations that werepreviously only possible through lab measurements, and demonstrate itsapplicability for computational imaging tasks.

A Monte Carlo Framework for Rendering Speckle Statistics in Scattering Media