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Martinelli M, Gardner A, Cuccia D, Hayakawa C, Spanier J, Venugopalan V. Analysis of single Monte Carlo methods for prediction of reflectance from turbid media. OPTICS EXPRESS 2011; 19:19627-42. [PMID: 21996904 PMCID: PMC3347703 DOI: 10.1364/oe.19.019627] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Starting from the radiative transport equation we derive the scaling relationships that enable a single Monte Carlo (MC) simulation to predict the spatially- and temporally-resolved reflectance from homogeneous semi-infinite media with arbitrary scattering and absorption coefficients. This derivation shows that a rigorous application of this single Monte Carlo (sMC) approach requires the rescaling to be done individually for each photon biography. We examine the accuracy of the sMC method when processing simulations on an individual photon basis and also demonstrate the use of adaptive binning and interpolation using non-uniform rational B-splines (NURBS) to achieve order of magnitude reductions in the relative error as compared to the use of uniform binning and linear interpolation. This improved implementation for sMC simulation serves as a fast and accurate solver to address both forward and inverse problems and is available for use at http://www.virtualphotonics.org/.
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Affiliation(s)
- Michele Martinelli
- Dipartimento di Fisica, Politecnico di Milano, Milan, 20133,
Italy
- Department of Chemical Engineering and Materials Science, University of California, Irvine, Irvine, CA 92697-2575,
USA
- Laser Microbeam and Medical Program, Beckman Laser Institute, University of California, Irvine, Irvine, CA 92697-3010,
USA
| | - Adam Gardner
- Department of Chemical Engineering and Materials Science, University of California, Irvine, Irvine, CA 92697-2575,
USA
- Laser Microbeam and Medical Program, Beckman Laser Institute, University of California, Irvine, Irvine, CA 92697-3010,
USA
| | - David Cuccia
- Modulated Imaging, Inc., 1002 Health Sciences Road, Irvine, CA 92612,
USA
| | - Carole Hayakawa
- Department of Chemical Engineering and Materials Science, University of California, Irvine, Irvine, CA 92697-2575,
USA
- Laser Microbeam and Medical Program, Beckman Laser Institute, University of California, Irvine, Irvine, CA 92697-3010,
USA
| | - Jerome Spanier
- Laser Microbeam and Medical Program, Beckman Laser Institute, University of California, Irvine, Irvine, CA 92697-3010,
USA
| | - Vasan Venugopalan
- Department of Chemical Engineering and Materials Science, University of California, Irvine, Irvine, CA 92697-2575,
USA
- Laser Microbeam and Medical Program, Beckman Laser Institute, University of California, Irvine, Irvine, CA 92697-3010,
USA
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