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ACM Transactions on Graphics · 2022

Rendering of Subjective Speckle Formed by Rough Statistical Surfaces

Shlomi Steinberg iD , Ling-Qi Yan

First published 1 February 2022DOI: 10.1145/3472293

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Abstract

Tremendous effort has been extended by the Computer Graphics community to advance the level of realism of material appearance reproduction by incorporating increasingly more advanced techniques. We are now able to re-enact the complicated interplay between light and microscopic surface features—scratches, bumps and other imperfections—in a visually convincing fashion. However, diffractive patterns arise even when no explicitly defined features are present: Any random surface will act as a diffracting aperture and its statistics heavily influence the statistics of the diffracted wave fields. Nonetheless, the problem of rendering diffractions induced by surfaces that are defined purely statistically remains wholly unexplored. We present a thorough derivation, from core optical principles, of the intensity of the scattered fields that arise when a natural, partially coherent light source illuminates a random surface. We follow with a probability theory analysis of the statistics of those fields and present our rendering algorithm. All of our derivations are formally proven and verified numerically as well. Our method is the first to render diffractions that produced by a surface described statistically only and bridges the theoretical gap between contemporary surface modelling and rendering. Finally, we also present intuitive artistic control parameters that allow rendering of physical and non-physical diffraction patterns using our method.
A Stanford Dragon made of chromium rendered under a D65 illuminant.
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.

Corrigendum

  • In Eq. 55 (Appendix D), all instances of $\eta$ should be $\eta^2$. The square is missing.

Cite this work

Shlomi Steinberg, Ling-Qi Yan. 2022. Rendering of Subjective Speckle Formed by Rough Statistical Surfaces. ACM Transactions on Graphics, 41(1), Article 2. https://doi.org/10.1145/3472293

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@article{Steinberg_Speckle_2021,
  address = {New York, NY, USA},
  articleno = {2},
  author = {Shlomi Steinberg and Ling-Qi Yan},
  doi = {10.1145/3472293},
  issn = {0730-0301},
  issue_date = {February 2022},
  journal = {ACM Transactions on Graphics},
  keywords = {wave, speckle, coherent, partially-coherent, rendering, scattering, statistical surfaces, appearance reproduction, monte carlo, BSDF},
  number = {1},
  numpages = {23},
  publisher = {Association for Computing Machinery},
  title = {{Rendering of Subjective Speckle Formed by Rough Statistical Surfaces}},
  url = {https://ssteinberg.xyz/2022/01/26/rendering_subjective_speckle/},
  volume = {41},
  year = {2022},
}