A Monte Carlo Framework for Rendering Speckle Statistics in Scattering Media

TL;DR

This paper introduces a Monte Carlo rendering framework that efficiently simulates realistic speckle patterns in scattering media, capturing key statistical properties for imaging applications without solving complex wave equations.

Contribution

It develops a novel path-space formulation for speckle covariance and introduces two algorithms for simulating speckle patterns from bulk scattering parameters.

Findings

Framework accurately replicates speckle statistics compared to wave equation simulations.

Enables simulation of memory effects previously only observed experimentally.

Applicable to computational imaging tasks with improved efficiency.

Abstract

We present a Monte Carlo rendering framework for the physically-accurate simulation of speckle patterns arising from volumetric scattering of coherent waves. These noise-like patterns are characterized by strong statistical properties, such as the so-called memory effect, which are at the core of imaging techniques for applications as diverse as tissue imaging, motion tracking, and non-line-of-sight imaging. Our framework allows for these properties to be replicated computationally, in a way that is orders of magnitude more efficient than alternatives based on directly solving the wave equations. At the core of our framework is a path-space formulation for the covariance of speckle patterns arising from a scattering volume, which we derive from first principles. We use this formulation to develop two Monte Carlo rendering algorithms, for computing speckle covariance as well as directly speckle fields. While approaches based on wave equation solvers require knowing the microscopic position of wavelength-sized scatterers, our approach takes as input only bulk parameters describing the statistical distribution of these scatterers inside a volume. We validate the accuracy of our framework by comparing against speckle patterns simulated using wave equation solvers, use it to simulate memory effect observations that were previously only possible through lab measurements, and demonstrate its applicability for computational imaging tasks.