Monte Carlo for Rendering Speckle Statistics

Physically Accurate Rendering of Speckle

We present a Monte Carlo rendering framework for the physically-accurate simulation of speckle patterns arising from the 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 effcient than alternatives based on directly solving the wave equations.

Physically Accurate

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Simulations generated with our Monte Carlo approach closely match solutions of the wave equation, reproducing known physical phenomena such as memory effect and coherent backscattering.

Computational Efficiency

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Our approach outperforms wave equation solvers by orders of magnitude


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Our approach uses only bulk macroscopic parameters of a volume, instead of requiring knowledge of its microscopic structure

Path-space Formulation for the Covariance of Speckle

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.


Chen Bar



Marina Alterman



Ioannis Gkioulekas



Anat Levin