“A Monte Carlo framework for rendering speckle statistics in scattering media” by Bar, Alterman, Gkioulekas and Levin

  • ©Chen Bar, Marina Alterman, Ioannis Gkioulekas, and Anat Levin



Session Title:

    Light Science


    A Monte Carlo framework for rendering speckle statistics in scattering media



    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. These properties are at the core of imaging techniques for applications as diverse as tissue imaging, motion tracking, and non-line-of-sight imaging. Our rendering framework can replicate these properties 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.


    1. Eric Akkermans and Gilles Montambaux. 2007. Mesoscopic Physics of Electrons and Photons. Cambridge University Press.Google Scholar
    2. M. Batarseh, S. Sukhov, Z. Shen, H. Gemar, R. Rezvani, and A. Dogariu. 2018. Passive sensing around the corner using spatial coherence. Nature Communications.Google Scholar
    3. Ibrahim Baydoun, Diego Baresch, Romain Pierrat, and Arnaud Derode. 2016. Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation. Physical Review E.Google Scholar
    4. Stephan Bergmann, Mahsa Mohammadikaji, Stephan Irgenfried, Heinz Worn, Jürgen Beyerer, and Carsten Dachsbacher. 2016. A Phenomenological Approach to Integrating Gaussian Beam Properties and Speckle into a Physically-Based Renderer. In Vision, Modeling & Visualization. Google ScholarDigital Library
    5. Richard Berkovits and Shechao Feng. 1994. Correlations in coherent multiple scattering. Physics Reports (1994).Google Scholar
    6. Bruce J Berne and Robert Pecora. 2000. Dynamic light scattering: with applications to chemistry, biology, and physics. Courier Corporation.Google Scholar
    7. Jacopo Bertolotti, Elbert G. van Putten, Christian Blum, Ad Lagendijk, Willem L. Vos, and Allard P. Mosk. 2012. Non-invasive imaging through opaque scattering layers. Nature 491(7423), 232.Google ScholarCross Ref
    8. Benedikt Bitterli, Srinath Ravichandran, Thomas Müller, Magnus Wrenninge, Jan Novák, Steve Marschner, and Wojciech Jarosz. 2018. A radiative transfer framework for non-exponential media. In SIGGRAPH Asia. ACM, 225. Google ScholarDigital Library
    9. David A Boas and Arjun G. Yodh. 1997. Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation. J. Opt. Soc. Am. A.Google ScholarCross Ref
    10. Craig F. Bohren and Donald R. Huffman. 1983. Absorption and scattering of light by small particle. John Wiley & Sons.Google Scholar
    11. Tom Cuypers, Tom Haber, Philippe Bekaert, Se Baek Oh, and Ramesh Raskar. 2012. Reflectance Model for Diffraction. ACM Trans. Graph. 31, 5, Article 122, 11 pages. Google ScholarDigital Library
    12. Eugene d’Eon. 2018a. A Reciprocal Formulation of Non-Exponential Radiative Transfer. 2: Monte Carlo Estimation and Diffusion Approximation. arXiv preprint arXiv:1809.05881.Google Scholar
    13. Eugene d’Eon. 2018b. A reciprocal formulation of non-exponential radiative transfer with uncorrelated sources, detectors and boundaries. 1: Sketch and motivation. arXiv preprint arXiv:1803.03259.Google Scholar
    14. Ronald L. Dougherty, Bruce J. Ackerson, N.M. Reguigui, F. Dorri-Nowkoorani, and Ulf Nobbmann. 1994. Correlation transfer: Development and application. J. of Quantitative Spectroscopy and Radiative Transfer.Google Scholar
    15. Donald D. Duncan and Sean J. Kirkpatrick. 2008. Can laser speckle flowmetry be made a quantitative tool? J. Opt. Soc. Am. A 25, 8, 2088–2094.Google ScholarCross Ref
    16. Turgut Durduran, Regine Choe, Wesley B. Baker, and Arjun G. Yodh. 2010. Diffuse optics for tissue monitoring and tomography. Reports on Progress in Physics.Google Scholar
    17. Philip Dutré, Kavita Bala, and Philippe Bekaert. 2006. Advanced global illumination. AK Peters, Ltd. Google ScholarDigital Library
    18. Robert Erf. 1978. Speckle Metrology. Elsevier.Google Scholar
    19. Shechao Feng, Charles Kane, Patrick A Lee, and A Douglas Stone. 1988. Correlations and fluctuations of coherent wave transmission through disordered media. Physical review letters 61, 7, 834.Google Scholar
    20. James R. Fienup. 1982. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 15, 2758–2769.Google ScholarCross Ref
    21. Isaac Freund. 1990. Looking through walls and around corners. Physica: Statistical Mechanics and its App.Google Scholar
    22. Isaac Freund and Danny Eliyahu. 1992. Surface correlations in multiple-scattering media. Phys Rev A (1992).Google Scholar
    23. Isaac Freund, Michael Rosenbluh, and Shechao. Feng. 1988. Memory Effects in Propagation of Optical Waves through Disordered Media. Phys. Rev. Lett. 61, 2328–2331. Issue 20.Google ScholarCross Ref
    24. David L. Fried. 1982. Anisoplanatism in adaptive optics. J. Opt. Soc. Am. 72, 1, 52–61.Google ScholarCross Ref
    25. Jeppe Revall Frisvad, Niels Jørgen Christensen, and Henrik Wann Jensen. 2007. Computing the scattering properties of participating media using Lorenz-Mie theory. SIGGRAPH.Google Scholar
    26. Ioannis Gkioulekas, Anat Levin, and Todd Zickler. 2016. An Evaluation of Computational Imaging Techniques for Heterogeneous Inverse Scattering.Google Scholar
    27. I. Gkioulekas, S. Zhao, K. Bala, T. Zickler, and A. Levin. 2013. Inverse Volume Rendering with Material Dictionaries. ACM Transactions on Graphics (Proc. ACM SIGGRAPH Asia) (2013). Google ScholarDigital Library
    28. W. I. Goldburg. 1999. Dynamic light scattering. American Journal of Physics (1999).Google Scholar
    29. Goodman. 2007. Speckle Phenomena in Optics: Theory and Applications. Roberts and Company Pub.Google Scholar
    30. Vadim Holodovski, Yoav Y. Schechner, Anat Levin, Aviad Levis, and Amit Aides. 2016. In-situ multi-view multi-scattering stochastic tomography. In ICCP.Google Scholar
    31. Y.A. Ilyushin. 2012. Coherent backscattering enhancement in highly anisotropically scattering media: Numerical solution. Journal of Quantitative Spectroscopy and Radiative Transfer (2012).Google Scholar
    32. Akira Ishimaru. 1999. Wave propagation and scattering in random media. Vol. 12. John Wiley & Sons.Google Scholar
    33. P. Jacquot and J. M. Fournier. 2000. Interferometry in Speckle Light. Springer.Google Scholar
    34. Pierre Jacquot and Pramod K. Rastogi. 1979. Speckle motions induced by rigid-body movements in free-space geometry: an explicit investigation and extension to new cases. Appl. Opt. (1979).Google Scholar
    35. Wenzel Jakob. 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
    36. Wenzel Jakob, Adam Arbree, Jonathan T Moon, Kavita Bala, and Steve Marschner. 2010. A radiative transfer framework for rendering materials with anisotropic structure. In ACM Transactions on Graphics (TOG), Vol. 29. ACM, 53. Google ScholarDigital Library
    37. M. L. Jakobsen, H. T. Yura, and S. G. Hanson. 2012. Spatial filtering velocimetry of objective speckles for measuring out-of-plane motion. Appl. Opt. (2012).Google Scholar
    38. Adrian Jarabo, Carlos Aliaga, and Diego Gutierrez. 2018. A Radiative Transfer Framework for Spatially-Correlated Materials. ACM Transactions on Graphics 37, 4 (2018). Google ScholarDigital Library
    39. Adrian Jarabo and Victor Arellano. 2018. Bidirectional rendering of vector light transport. In Computer Graphics Forum, Vol. 37. Wiley Online Library, 96–105. Google ScholarDigital Library
    40. O. Katz, P. Heidmann, M. Fink, and S. Gigan. 2014. Non-invasive single-shot imaging through scattering layers and around corners via speckle correlation. Nat. Photonics (2014).Google Scholar
    41. O. Katz, E. Small, and Y. Silberberg. 2012. Looking around corners and through thin turbid layers in real time with scattered incoherent light. Nature (2012).Google Scholar
    42. Guillermo H. Kaufmann. 2011. Advances in Speckle Metrology and Related Techniques. Wiley.Google Scholar
    43. Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Novak. 2017. Spectral and decomposition tracking for rendering heterogeneous volumes. ACM Transactions on Graphics (TOG) 36, 4 (2017), 111. Google ScholarDigital Library
    44. Aviad Levis, Yoav Y. Schechner, Amit Aides, and Anthony B. Davis. 2015. Airborne three-dimensional cloud tomography. In ICCV. Google ScholarDigital Library
    45. J. H. Li and A. Z. Genack. 1994. Correlation in laser speckle. Phys. Rev. E 49 (May 1994), 4530–4533. Issue 5.Google Scholar
    46. Qiang Lu, Xiaosong Gan, Min Gu, and Qingming Luo. 2004. Monte Carlo modeling of optical coherence tomography imaging through turbid media. Applied optics 43, 8 (2004), 1628–1637.Google Scholar
    47. Johannes Meng, Marios Papas, Ralf Habel, Carsten Dachsbacher, Steve Marschner, Markus H Gross, and Wojciech Jarosz. 2015. Multi-scale modeling and rendering of granular materials. ACM Trans. Graph. 34, 4 (2015), 49–1. Google ScholarDigital Library
    48. M. Mesradi, A. Genoux, V. Cuplov, D. Abi Haidar, S. Jan, I. Buvat, and F. Pain. 2013. Experimental and analytical comparative study of optical coefficient of fresh and frozen rat tissues. Journal of Biomedical Optics (Nov. 2013).Google ScholarCross Ref
    49. M.I. Mishchenko, L.D. Travis, and A.A. Lacis. 2006. Multiple scattering of light by particles: radiative transfer and coherent backscattering. Cambridge Univ Pr.Google Scholar
    50. Jonathan T Moon, Bruce Walter, and Stephen R Marschner. 2007. Rendering discrete random media using precomputed scattering solutions. In Proceedings of the 18th Eurographics conference on Rendering Techniques. Eurographics Association, 231–242. Google ScholarDigital Library
    51. Allard P. Mosk, Ad Lagendijk, Geoffroy Lerosey, and Mathias Fink. 2013. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photonics (2013).Google Scholar
    52. Thomas Müller, Marios Papas, Markus H Gross, Wojciech Jarosz, and Jan Novák. 2016. Efficient rendering of heterogeneous polydisperse granular media. ACM Trans. Graph. 35, 6 (2016), 168–1. Google ScholarDigital Library
    53. S.G. Narasimhan, M. Gupta, C. Donner, R. Ramamoorthi, S.K. Nayar, and H.W.Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans. Graph. 25, 3 (2006). Google ScholarDigital Library
    54. Micha Nixon, Ori Katz, Eran Small, Yaron Bromberg, Asher A. Friesem, Yaron Silberberg, and Nir Davidson. 2013. Real-time wavefront shaping through scattering media by all-optical feedback. Nat. Photonics (2013).Google Scholar
    55. Jan Novak, Iliyan Georgiev, Johannes Hanika, and Wojciech Jarosz. 2018. Monte Carlo Methods for Volumetric Light Transport Simulation. Computer Graphics Forum (2018).Google Scholar
    56. Gerwin Osnabrugge, Roarke Horstmeyer, Ioannis N Papadopoulos, Benjamin Judkewitz, and Ivo M Vellekoop. 2017. Generalized optical memory effect. Optica 4, 8 (2017), 886–892.Google ScholarCross Ref
    57. Yingtian Pan, Reginald Birngruber, Jürgen Rosperich, and Ralf Engelhardt. 1995. Low-coherence optical tomography in turbid tissue: theoretical analysis. Applied optics 34, 28 (1995), 6564–6574.Google Scholar
    58. Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically based rendering: From theory to implementation. Morgan Kaufmann. Google ScholarDigital Library
    59. Romain Pierrat, Jean-Jacques Greffet, Rémi Carminati, and Rachid Elaloufi. 2005. Spatial coherence in strongly scattering media. J. Opt. Soc. Am. A 22, 11 (Nov 2005), 2329–2337.Google ScholarCross Ref
    60. DJ Pine, DA Weitz, PM Chaikin, and E Herbolzheimer. 1988. Diffusing wave spectroscopy. Physical review letters 60, 12 (1988), 1134.Google Scholar
    61. John Sawicki, Nikolas Kastor, and Min Xu. 2008. Electric field Monte Carlo simulation of coherent backscattering of polarized light by a turbid medium containing Mie scatterers. Opt. Express 16, 8 (Apr 2008), 5728–5738.Google ScholarCross Ref
    62. Joseph M Schmitt and A Knüttel. 1997. Model of optical coherence tomography of heterogeneous tissue. JOSA A 14, 6 (1997), 1231–1242.Google ScholarCross Ref
    63. Schott, Bertolotti, Léger, Bourdieu, and Gigan. 2015. Characterization of the angular memory effect of scattered light in biological tissues. Opt. Express (2015).Google Scholar
    64. Zhean Shen, Sergey Sukhov, and Aristide Dogariu. 2017. Monte Carlo method to model optical coherence propagation in random media. J. Opt. Soc. Am. A 34, 12 (Dec 2017), 2189–2193.Google ScholarCross Ref
    65. Brandon M. Smith, Pratham Desai, Vishal Agarwal, and Mohit Gupta. 2017. CoLux: Multi-object 3D Micro-motion Analysis Using Speckle Imaging. ACM Trans. Graph. (2017). Google ScholarDigital Library
    66. J. Stam. 1999. Diffraction shaders. In SIGGRAPH. Google ScholarDigital Library
    67. Bo Sun, Ravi Ramamoorthi, Srinivasa G Narasimhan, and Shree K Nayar. 2005. A practical analytic single scattering model for real time rendering. In ACM Transactions on Graphics (TOG), Vol. 24. ACM, 1040–1049. Google ScholarDigital Library
    68. F. Sur, B. Blaysat, and M. Grediac. 2018. Rendering deformed speckle images with a Boolean model. Journal of Mathematical Imaging and Vision (2018). Google ScholarDigital Library
    69. B. Thierry, X. Antoine, C. Chniti, and H. Alzubaidi. 2015. μ-diff: An open-source Matlab toolbox for computing multiple scattering problems by disks. Computer Physics Communications 192 (2015), 348 — 362.Google ScholarCross Ref
    70. B. E. Treeby and B. T. Cox. 2010. k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave-fields,. J. Biomed. Opt. (2010).Google Scholar
    71. V. Twersky. 1964. On propagation in random media of discrete scatterers. Am. Math. Sot. Symp. Stochastic Processes in Mathematical Physics and Engineering, Vol. 16, p. 84 (1964).Google ScholarCross Ref
    72. E. Veach. 1997. Robust Monte Carlo methods for light transport simulation. Ph.D. Dissertation. PhD thesis, Stanford University. Google ScholarDigital Library
    73. Eric Veach and Leonidas Guibas. 1995a. Bidirectional estimators for light transport. In Photorealistic Rendering Techniques. Springer, 145–167.Google Scholar
    74. Eric Veach and Leonidas J Guibas. 1995b. Optimally combining sampling techniques for Monte Carlo rendering. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM, 419–428. Google ScholarDigital Library
    75. Eric Veach and Leonidas J Guibas. 1997. Metropolis light transport. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 65–76. Google ScholarDigital Library
    76. Ivo M. Vellekoop and Christof M. Aegerter. 2010. Scattered light fluorescence microscopy: imaging through turbid layers. Opt. Lett. 35, 8 (Apr 2010), 1245–1247.Google ScholarCross Ref
    77. Bruce Walter, Shuang Zhao, Nicolas Holzschuch, and Kavita Bala. 2009. Single scattering in refractive media with triangle mesh boundaries. In ACM Transactions on Graphics (TOG), Vol. 28. ACM, 92. Google ScholarDigital Library
    78. Sebastian Werner, Zdravko Velinov, Wenzel Jakob, and Matthias B. Hullin. 2017. Scratch Iridescence: Wave-Optical Rendering of Diffractive Surface Structure. ACM SIGGRAPH Asia (2017). Google ScholarDigital Library
    79. Douglas R Wyman, Michael S Patterson, and Brian C Wilson. 1989. Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles. J. Comput. Phys. 81, 1 (1989), 137–150. Google ScholarDigital Library
    80. Min Xu. 2004. Electric field Monte Carlo simulation of polarized light propagation in turbid media. Opt. Express 12, 26 (Dec 2004), 6530–6539.Google ScholarCross Ref
    81. Ling-Qi Yan, Miloš Hašan, Bruce Walter, Steve Marschner, and Ravi Ramamoorthi. 2018. Rendering specular microgeometry with wave optics. ACM Transactions on Graphics (TOG) 37, 4 (2018), 75. Google ScholarDigital Library
    82. Xin Yang, Ye Pu, and Demetri Psaltis. 2014. Imaging blood cells through scattering biological tissue using speckle scanning microscopy. Opt. Express 22, 3 (Feb 2014), 3405–3413.Google Scholar
    83. K. Yee. 1966. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. EEE Trans. on Antennas and Propagation (1966).Google Scholar
    84. Hengchin Yeh, Ravish Mehra, Zhimin Ren, Lakulish Antani, Dinesh Manocha, and Ming Lin. 2013. Wave-ray Coupling for Interactive Sound Propagation in Large Complex Scenes. ACM Trans. Graph. (2013). Google ScholarDigital Library
    85. Shuang Zhao, Ravi Ramamoorthi, and Kavita Bala. 2014. High-order similarity relations in radiative transfer. ACM Transactions on Graphics (TOG) 33, 4 (2014), 104. Google ScholarDigital Library

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