Rendering of Subjective Speckle Formed by Rough Statistical Surfaces

Shlomi Steinberg
ACM Transactions on Graphics

Publication date: February 1st, 2022
doi: 10.1145/3472293

A Stanford Dragon made of chromium rendered under a D65 illuminant. The light source is moderately coherent with a coherence radius of roughly $\sim30$ μm on average when incident upon the Dragon’s surface. The surface was modelled statistically only, therefore the scattered intensity, $I$, can be considered as a stochastic process. In order to render this scattered intensity we decompose it, in a physically and mathematically consistent manner, into its ensemble average, $\langle I\rangle$, and a fluctuating intensity, $\mathfrak{I}$: (left) The ensemble average of the process, $\langle I\rangle$, dominates the scattered energy and is the averaged scattered intensity over all possible realizations of the surface. (middle) The fluctuating intensity is a zero-mean process (only positive values were visualised) that gives rise to diffraction patterns—known as subjective optical speckle—that depend on the statistical properties of the light, surface and the imaging device. (right) The final intensity is then the superposition of the ensemble averaged lobe and fluctuating field.



 	author = {Steinberg, Shlomi and Yan, Ling-Qi},
 	title = {Rendering of Subjective Speckle Formed by Rough Statistical Surfaces},
 	year = {2022},
 	issue_date = {February 2022},
 	publisher = {Association for Computing Machinery},
 	address = {New York, NY, USA},
 	volume = {41},
 	number = {1},
 	issn = {0730-0301},
 	url = {},
 	doi = {10.1145/3472293},
 	journal = {ACM Trans. Graph.},
 	month = {feb},
 	articleno = {2},
 	numpages = {23},
 	keywords = {appearance reproduction, statistical surfaces, iridescence, scatter, speckle, monte carlo, wave optics, Diffractions, coherence}