[1] Wang W J, Zhang Y X, Sa Y et al. Quantitative simulation and experimental study of polarized diffraction characteristics of yeast cells[J]. Chinese Journal of Lasers, 50, 2107110(2023).

[2] Newman M E, Barkema G T[M]. Monte Carlo methods in statistical physics(1999).

[3] Wilson B C, Adam G. A Monte Carlo model for the absorption and flux distributions of light in tissue[J]. Medical Physics, 10, 824-830(1983).

[4] Wang L H, Jacques S L, Zheng L Q. MCML: Monte Carlo modeling of light transport in multi-layered tissues[J]. Computer Methods and Programs in Biomedicine, 47, 131-146(1995).

[5] Flock S T, Patterson M S, Wilson B C. Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory[J]. IEEE Transactions on Bio-Medical Engineering, 36, 1162-1168(1989).

[6] Farrell T J, Patterson M S, Wilson B. A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo[J]. Medical Physics, 19, 879-888(1992).

[7] Song Q, Sun X B, Liu X et al. Study on vector radiative transmission characteristics of polarization optics in underwater bubble environment[J]. Acta Optica Sinica, 42, 1210001(2022).

[8] Yong Z, Bin C, Dong L. A three-dimensional geometric Monte Carlo method for simulation of light propagation in biological tissues[J]. Chinese Journal of Lasers, 42, 0104003(2015).

[9] Li Y F, Shen F Z, Hu L T et al. A stare-down video-rate high-throughput hyperspectral imaging system and its applications in biological sample sensing[J]. IEEE Sensors Journal, 23, 23629-23637(2023).

[10] Yang S Q, Guo J H, Li T. Noninvasive optical monitoring of lung based on Monte Carlo analysis of visual Chinese human[J]. Chinese Journal of Lasers, 50, 1507205(2023).

[11] Flock S T, Wilson B C, Patterson M S. Monte Carlo modeling of light propagation in highly scattering tissues: comparison with measurements in phantoms[J]. IEEE Transactions on Bio-Medical Engineering, 36, 1169-1173(1989).

[12] Zhu C G, Liu Q. Review of Monte Carlo modeling of light transport in tissues[J]. Journal of Biomedical Optics, 18, 050902(2013).

[13] Maarek J M, Jarry G, de Cosnac B et al. A simulation method for the study of laser transillumination of biological tissues[J]. Annals of Biomedical Engineering, 12, 281-304(1984).

[14] Liu Q, Zhu C F, Ramanujam N. Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum[J]. Journal of Biomedical Optics, 8, 223-236(2003).

[15] Swartling J, Pifferi A, Enejder A M K et al. Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues[J]. Journal of the Optical Society of America A, 20, 714-727(2003).

[16] Van der Zee P, Delpy D T. Simulation of the point spread function for light in tissue by a Monte Carlo method[J]. Advances in Experimental Medicine and Biology, 215, 179-191(1987).

[17] Avrillier S, Tinet E, Delettre E. Monte Carlo simulation of collimated beam transmission through turbid media[J]. Journal De Physique, 51, 2521-2542(1990).

[18] Hasegawa Y, Yamada Y, Tamura M et al. Monte Carlo simulation of light transmission through living tissues[J]. Applied Optics, 30, 4515-4520(1991).

[19] Zaccanti G. Monte Carlo study of light propagation in optically thick media: point source case[J]. Applied Optics, 30, 2031-2041(1991).

[20] Key H, Davies E R, Jackson P C et al. Monte Carlo modelling of light propagation in breast tissue[J]. Physics in Medicine and Biology, 36, 591-602(1991).

[21] Yalavarthy P K, Karlekar K, Patel H S et al. Experimental investigation of perturbation Monte-Carlo based derivative estimation for imaging low-scattering tissue[J]. Optics Express, 13, 985(2005).

[22] Pfefer T J, Schomacker K T, Ediger M N et al. Light propagation in tissue during fluorescence spectroscopy with single-fiber probes[J]. IEEE Journal of Selected Topics in Quantum Electronics, 7, 1004-1012(2001).

[23] Pfefer T J, Barton J K, Chan E K et al. A three-dimensional modular adaptable grid numerical model for light propagation during laser irradiation of skin tissue[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2, 934-942(1996).

[24] Boas D A, Culver J P, Stott J J et al. Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head[J]. Optics Express, 10, 159-170(2002).

[25] Patwardhan S V, Dhawan A P, Relue P A. Monte Carlo simulation of light-tissue interaction: three-dimensional simulation for trans-illumination-based imaging of skin lesions[J]. IEEE Transactions on Biomedical Engineering, 52, 1227-1236(2005).

[26] Li H, Tian J, Zhu F P et al. A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method1[J]. Academic Radiology, 11, 1029-1038(2004).

[27] Margallo-Balbás E, French P J. Shape based Monte Carlo code for light transport in complex heterogeneous tissues[J]. Optics Express, 15, 14086-14098(2007).

[28] Ren N N, Liang J M, Qu X C et al. GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues[J]. Optics Express, 18, 6811-6823(2010).

[29] Shen H, Wang G. A tetrahedron-based inhomogeneous Monte Carlo optical simulator[J]. Physics in Medicine and Biology, 55, 947-962(2010).

[30] Fang Q Q. Mesh-based Monte Carlo method using fast ray-tracing in Plücker coordinates[J]. Biomedical Optics Express, 1, 165-175(2010).

[31] Luo B, He S L. An improved Monte Carlo diffusion hybrid model for light reflectance by turbid media[J]. Optics Express, 15, 5905-5918(2007).

[32] Cai F, Lu W. A dynamic accuracy estimation for GPU-based Monte Carlo simulation in tissue optics[J]. Current Optics and Photonics, 1, 551-555(2017).

[33] Flock S T, Wilson B C, Patterson M S. Hybrid Monte Carlo-diffusion theory modelling of light distributions in tissue[J]. Proceedings of SPIE, 908, 20-28(1988).

[34] Wang L, Jacques S L. Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media[J]. Journal of the Optical Society of America A, 10, 1746-1752(1993).

[35] Yan S J, Yao R Y, Intes X et al. Accelerating Monte Carlo modeling of structured-light-based diffuse optical imaging via “photon sharing”[J]. Optics Letters, 45, 2842-2845(2020).

[36] Mirzapour M, Hadad K, Faghihi R et al. Fast Monte-Carlo photon transport employing GPU-based parallel computation[J]. IEEE Transactions on Radiation and Plasma Medical Sciences, 4, 450-460(2020).

[37] Liao Y P, Shangguan M J, Yang Z F et al. GPU-accelerated Monte Carlo simulation for a single-photon underwater lidar[J]. Remote Sensing, 15, 5245(2023).

[38] Shi M Y, Myronakis M, Jacobson M et al. GPU-accelerated Monte Carlo simulation of MV-CBCT[J]. Physics in Medicine and Biology, 65, 235042(2020).

[39] Ma B, Gaens M, Caldeira L et al. Scatter correction based on GPU-accelerated full Monte Carlo simulation for brain PET/MRI[J]. IEEE Transactions on Medical Imaging, 39, 140-151(2020).

[40] LaRochelle E P M, Arce P, Pogue B W. Monte Carlo modeling photon-tissue interaction using on-demand cloud infrastructure[EB/OL]. http:∥arxiv.org/abs/2005.01108v1

[41] Brantley P S, Gentile N A, Lambert M A et al. A new implicit Monte Carlo thermal photon transport capability developed using shared Monte Carlo infrastructure[R](2019).

[42] Lai Y F, Zhong Y C, Chalise A et al. gPET: a GPU-based, accurate and efficient Monte Carlo simulation tool for PET[J]. Physics in Medicine and Biology, 64, 245002(2019).

[43] Afsharnejad Y. Accelerating 3D Monte Carlo photonic simulations on tightly coupled CPU-FPGA systems[D](2019).

[44] Preston M, Marciniewski P, Tegnér P E. FPGA-based algorithms for feature extraction in the PANDA shashlyk calorimeter[J]. Journal of Instrumentation, 15, C08011(2020).

[45] Abhyankar Y S, Dev S, Sarun O S et al. Monte Carlo processing on a chip (MCoaC)-preliminary experiments toward the realization of optimal-hardware for TOPAS/Geant4 to drive discovery[J]. Physica Medica, 64, 166-173(2019).

[46] Graaff R, Koelink M H, de Mul F F et al. Condensed Monte Carlo simulations for the description of light transport[J]. Applied Optics, 32, 426-434(1993).

[47] Kienle A, Patterson M S. Determination of the optical properties of turbid media from a single Monte Carlo simulation[J]. Physics in Medicine and Biology, 41, 2221-2227(1996).

[48] Pifferi A, Taroni P, Valentini G et al. Real-time method for fitting time-resolved reflectance and transmittance measurements with a Monte Carlo model[J]. Applied Optics, 37, 2774-2780(1998).

[49] Ostermeyer M R, Jacques S L. Perturbation theory for diffuse light transport in complex biological tissues[J]. Journal of the Optical Society of America A, 14, 255-261(1997).

[50] Sassaroli A, Martelli F. Convergence features of four Monte Carlo methods in the time domain[J]. Proceedings of SPIE, 8578, 857818(2013).

[51] Sassaroli A, Blumetti C, Martelli F et al. Monte Carlo procedure for investigating light propagation and imaging of highly scattering media[J]. Applied Optics, 37, 7392-7400(1998).

[52] Hayakawa C K, Spanier J, Bevilacqua F et al. Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues[J]. Optics Letters, 26, 1335-1337(2001).

[53] Sassaroli A. Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media[J]. Optics Letters, 36, 2095-2097(2011).

[54] Zhu C G, Liu Q. Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities[J]. Journal of Biomedical Optics, 17, 010501(2012).

[55] Hendricks J S, Booth T E. MCNP variance reduction overview[EB/OL]. https:∥link.springer.com/content/pdf/10.1007/bfb0049037.pdf

[56] Liu Q, Ramanujam N. Sequential estimation of optical properties of a two-layered epithelial tissue model from depth-resolved ultraviolet-visible diffuse reflectance spectra[J]. Applied Optics, 45, 4776-4790(2006).

[57] Li T, Gong H, Luo Q M. MCVM: Monte Carlo modeling of photon migration in voxelized media[J]. Journal of Innovative Optical Health Sciences, 3, 91-102(2010).

[58] Lima I T, Kalra A, Sherif S S. Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography[J]. Biomedical Optics Express, 2, 1069-1081(2011).

[59] Lima I T, Kalra A, Hernández-Figueroa H E et al. Fast calculation of multipath diffusive reflectance in optical coherence tomography[J]. Biomedical Optics Express, 3, 692-700(2012).

[60] Kumar Y P, Vasu R M. Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method[J]. Journal of Biomedical Optics, 9, 1002-1012(2004).

[61] Yao R Y, Intes X, Fang Q Q. Direct approach to compute Jacobians for diffuse optical tomography using perturbation Monte Carlo-based photon “replay”[J]. Biomedical Optics Express, 9, 4588-4603(2018).

[62] Wang L V. Rapid modeling of diffuse reflectance of light in turbid slabs[J]. Journal of the Optical Society of America A, 15, 936-944(1998).

[63] Alexandrakis G, Farrell T J, Patterson M S. Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain[J]. Applied Optics, 39, 2235-2244(2000).

[64] Hayashi T, Kashio Y, Okada E. Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region[J]. Applied Optics, 42, 2888-2896(2003).

[65] Donner C, Jensen H W. Rapid simulation of steady-state spatially resolved reflectance and transmittance profiles of multilayered turbid materials[J]. Journal of the Optical Society of America A, 23, 1382-1390(2006).

[66] Tinet E, Avrillier S, Tualle J M. Fast semianalytical Monte Carlo simulation for time-resolved light propagation in turbid media[J]. Journal of the Optical Society of America A, 13, 1903-1915(1996).

[67] Chatigny S, Morin M, Asselin D et al. Hybrid Monte Carlo for photon transport through optically thick scattering media[J]. Applied Optics, 38, 6075-6086(1999).

[68] Wu D F, Xu X F, Zhang L et al. A hybrid Monte Carlo model for the energy response functions of X-ray photon counting detectors[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 830, 397-406(2016).

[69] Yan S J, Fang Q Q. Hybrid mesh and voxel based Monte Carlo algorithm for accurate and efficient photon transport modeling in complex bio-tissues[J]. Biomedical Optics Express, 11, 6262-6270(2020).

[70] Chen N G, Bai J. Estimation of quasi-straightforward propagating light in tissues[J]. Physics in Medicine and Biology, 44, 1669-1676(1999).

[71] Chen N G. Controlled Monte Carlo method for light propagation in tissue of semi-infinite geometry[J]. Applied Optics, 46, 1597-1603(2007).

[72] Behin-Ain S, van Doorn T, Patterson J R. An indeterministic Monte Carlo technique for fast time of flight photon transport through optically thick turbid media[J]. Medical Physics, 29, 125-131(2002).

[73] Golosio B, Schoonjans T, Brunetti A et al. Monte Carlo simulation of X-ray imaging and spectroscopy experiments using quadric geometry and variance reduction techniques[J]. Computer Physics Communications, 185, 1044-1052(2014).

[74] Williamson J F. Monte Carlo simulation of photon transport phenomena: sampling techniques[M]. Monte Carlo simulation in the radiological sciences, 53-102(2019).

[75] Colasanti A, Guida G, Kisslinger A et al. Multiple processor version of a Monte Carlo code for photon transport in turbid media[J]. Computer Physics Communications, 132, 84-93(2000).

[76] Alerstam E, Svensson T, Andersson-Engels S. Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration[J]. Journal of Biomedical Optics, 13, 060504(2008).

[77] Alerstam E, Lo W C Y, Han T D et al. Next-generation acceleration and code optimization for light transport in turbid media using GPUs[J]. Biomedical Optics Express, 1, 658-675(2010).

[78] Kirkby D R, Delpy D T. Parallel operation of Monte Carlo simulations on a diverse network of computers[J]. Physics in Medicine and Biology, 42, 1203-1208(1997).

[79] Pratx G, Xing L. Monte Carlo simulation of photon migration in a cloud computing environment with MapReduce[J]. Journal of Biomedical Optics, 16, 125003(2011).

[80] Martinsen P, Blaschke J, Künnemeyer R et al. Accelerating Monte Carlo simulations with an NVIDIA® graphics processor[J]. Computer Physics Communications, 180, 1983-1989(2009).

[81] Fang Q Q, Boas D A. Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units[J]. Optics Express, 17, 20178-20190(2009).

[82] Leung T S, Powell S. Fast Monte Carlo simulations of ultrasound-modulated light using a graphics processing unit[J]. Journal of Biomedical Optics, 15, 055007(2010).

[83] Cai F H, He S L. Using graphics processing units to accelerate perturbation Monte Carlo simulation in a turbid medium[J]. Journal of Biomedical Optics, 17, 040502(2012).

[84] Cassidy J, Lilge L, Betz V. FullMonte: a framework for high-performance Monte Carlo simulation of light through turbid media with complex geometry[J]. Proceedings of SPIE, 8592, 85920H(2013).

[85] Young-Schultz T, Brown S, Lilge L et al. FullMonteCUDA: a fast, flexible, and accurate GPU-accelerated Monte Carlo simulator for light propagation in turbid media[J]. Biomedical Optics Express, 10, 4711-4726(2019).

[86] Franciosini G, Battistoni G, Cerqua A et al. GPU-accelerated Monte Carlo simulation of electron and photon interactions for radiotherapy applications[J]. Physics in Medicine & Biology, 68, 044001(2023).

[87] Fang Q Q, Yan S J. Graphics processing unit-accelerated mesh-based Monte Carlo photon transport simulations[J]. Journal of Biomedical Optics, 24, 115002(2019).

[88] Doronin A, Meglinski I. Peer-to-peer Monte Carlo simulation of photon migration in topical applications of biomedical optics[J]. Journal of Biomedical Optics, 17, 090504(2012).

[89] Lo W C Y, Redmond K, Luu J et al. Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning[J]. Journal of Biomedical Optics, 14, 014019(2009).

[90] Young-Schultz T, Lilge L, Brown S et al. Using OpenCL to enable software-like development of an FPGA-accelerated biophotonic cancer treatment simulator[C], 86-96(2020).

[91] Liu Q, Ramanujam N. Scaling method for fast Monte Carlo simulation of diffuse reflectance spectra from multilayered turbid media[J]. Journal of the Optical Society of America A, 24, 1011-1025(2007).