A Monte Carlo framework for rendering speckle statistics in scattering media

Abstract

Speckle image Scattering Medium Coherent IlluminationMonte Carlo Rendering 0°0.0025°0.0075°g = 0 g = 0.9

Interferometric transmission probing with coded mutual intensity

“…Many of these techniques have long prior history in optics and biomedical imaging [Bertolotti et al 2012;Katz et al 2014;Popoff et al 2010b;Vellekoop et al 2012;Vellekoop and Mosk 2007]. In particular, the structure of the transmission matrix for different types of scenes has been studied extensively using analytical approximations to coherent light propagation [Judkewitz et al 2015;Osnabrugge et al 2017], physically-accurate simulations [Bar et al 2019], as well as measurements that allow directly visualizing both its spatial-domain and frequency-domain forms [Waller et al 2012]. Both the memory effect and the transmission matrix are highly-relevant to our work: We rely on properties of the former for some of our derivations, and we show how our technique can Fig.…”

“…This diagonal band corresponds to the memory effect of speckle [Goodman 2007, Section 5]; therefore, the extent of the memory effect introduces a limit on the resolution at which we can perform incoherent probing. The memory effect of speckle has recently been used in computer vision and graphics for motion tracking and non-line-of-sight imaging [Smith et al 2017[Smith et al , 2018, and has been extensively modeled using Monte Carlo rendering algorithms [Bar et al 2019]. We note that these works focus on far-field speckle correlations (directional sources and sensors), whereas the correlation and memory effect relevant for Proposition 4 are for the near-field case (point sources and sensors) [Judkewitz et al 2015;Osnabrugge et al 2017].…”

Exploiting speckle statistics in random media beyond the diffusion limit

“…In Fig. 1(d) we show the result of this reconstruction applied to speckle images rendered with our algorithm [5] with two illuminator arrangements. As the angular range used in the second simulation is wider than the range at which the classical memory effect is valid, the reconstruction fails.…”

“…Moreover, other types of speckle correlations beyond the angular range of the memory effect are not well studied. In a recent research [5], we suggest a computationally efficient Monte-Carlo (MC) simulator that can evaluate speckle statistics as a function of bulk material parameters, whose accuracy was verified against an exact yet computationally heavy wave solver. Here we show how such a numerical approach opens the door for new ways of studying speckle statistics.…”

Rendering near-field speckle statistics in scattering media

“…For this, we draw inspiration from Bar et al [2019], who introduced a Monte Carlo framework for simulating speckle correlations in a way that combines physical accuracy and computational efficiency. Unfortunately, despite offering orders-of-magnitude acceleration compared to previous physically-accurate simulation techniques (e.g., wave equation solvers), the algorithms of Bar et al [2019] are primarily intended for simulating far-field speckle statistics, and remain impractical for the near-field case. For example, as we show in our experiments, using their framework to simulate current techniques for focusing inside scattering [Judkewitz et al 2014] can take several days on a large cluster.…”