A closed-form method for calculating the angular distribution of multiply scattered photons through isotropic turbid slabs |
Optics Express, Vol. 19, Issue 24, pp. 23932-23937 (2011)
http://dx.doi.org/10.1364/OE.19.023932
Acrobat PDF (1036 KB)
Abstract
This paper develops a method for calculating the angular distribution (AD) of multiply scattered photons through isotropic turbid slabs. Extension to anisotropic scattering is also discussed. Previous studies have recognized that the AD of multiply scattered photons is critical for many applications, such as the design of imaging optics and estimation of image quality. This paper therefore develops a closed-from method that can accurately calculate the AD over a wide range of conditions. Other virtues of the method include its simplicity in implementation and its prospective for extension to anisotropic scattering.
© 2011 OSA
1. Introduction
1. J. C. Hebden, D. J. Hall, M. Firbank, and D. T. Delpy, “Time-Resolved Optical Imaging of a Solid Tissue-Equivalent Phantom,” Appl. Opt. 34(34), 8038–8047 (1995). [CrossRef] [PubMed]
3. M. A. Linne, M. Paciaroni, J. R. Gord, and T. R. Meyer, “Ballistic Imaging of The Liquid Core for a Steady Jet in Crossflow,” Appl. Opt. 44(31), 6627–6634 (2005). [CrossRef] [PubMed]
4. J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, and J. Reintjes, “Achievable Spatial Resolution of Time-Resolved Transillumination Imaging Systems Which Utilize Multiply Scattered Light,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1142–1155 (1996). [CrossRef] [PubMed]
5. J. A. Moon and J. Reintjes, “Image Resolution by Use of Multiply Scattered Light,” Opt. Lett. 19(8), 521–523 (1994). [CrossRef] [PubMed]
6. J. A. Moon, R. Mahon, M. D. Duncan, and J. Reintjes, “Resolution Limits for Imaging through Turbid Media with Diffuse Light,” Opt. Lett. 18(19), 1591–1593 (1993). [CrossRef] [PubMed]
7. M. Paciaroni and M. Linne, “Single-Shot, Two-Dimensional Ballistic Imaging Through Scattering Media,” Appl. Opt. 43(26), 5100–5109 (2004). [CrossRef] [PubMed]
8. A. A. Kokhanovsky, “Analytical Solutions of Multiple Light Scattering Problems: A Review,” Meas. Sci. Technol. 13(3), 233–240 (2002). [CrossRef]
4. J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, and J. Reintjes, “Achievable Spatial Resolution of Time-Resolved Transillumination Imaging Systems Which Utilize Multiply Scattered Light,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1142–1155 (1996). [CrossRef] [PubMed]
8. A. A. Kokhanovsky, “Analytical Solutions of Multiple Light Scattering Problems: A Review,” Meas. Sci. Technol. 13(3), 233–240 (2002). [CrossRef]
10. D. Contini, F. Martelli, and G. Zaccanti, “Photon Migration Through a Turbid Slab Described by a Model Based on Diffusion Approximation. 2. Theory,” Appl. Opt. 36(19), 4587–4599 (1997). [CrossRef] [PubMed]
12. E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part I: Experimental and Simulated Results for The Spatial Intensity Distribution,” Opt. Express 15(17), 10649–10665 (2007). [CrossRef] [PubMed]
13. M. D. King and Harshvardhan, “Comparative Accuracy of Selected Multiple Scattering Approximations,” J. Atmos. Sci. 43(8), 784–801 (1986). [CrossRef]
4. J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, and J. Reintjes, “Achievable Spatial Resolution of Time-Resolved Transillumination Imaging Systems Which Utilize Multiply Scattered Light,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1142–1155 (1996). [CrossRef] [PubMed]
10. D. Contini, F. Martelli, and G. Zaccanti, “Photon Migration Through a Turbid Slab Described by a Model Based on Diffusion Approximation. 2. Theory,” Appl. Opt. 36(19), 4587–4599 (1997). [CrossRef] [PubMed]
11. A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, “Photon Path-Length Distributions for Transmission through Optically Turbid Slabs,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(2), 810–818 (1993). [CrossRef] [PubMed]
14. R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, “Model for Photon Migration in Turbid Biological Media,” J. Opt. Soc. Am. A 4(3), 423–432 (1987). [CrossRef] [PubMed]
10. D. Contini, F. Martelli, and G. Zaccanti, “Photon Migration Through a Turbid Slab Described by a Model Based on Diffusion Approximation. 2. Theory,” Appl. Opt. 36(19), 4587–4599 (1997). [CrossRef] [PubMed]
11. A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, “Photon Path-Length Distributions for Transmission through Optically Turbid Slabs,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(2), 810–818 (1993). [CrossRef] [PubMed]
12. E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part I: Experimental and Simulated Results for The Spatial Intensity Distribution,” Opt. Express 15(17), 10649–10665 (2007). [CrossRef] [PubMed]
18. E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part II: Spatial and Temporal Analysis of Individual Scattering Orders via Monte Carlo Simulation,” Opt. Express 17(16), 13792–13809 (2009). [CrossRef] [PubMed]
2. Description of the method
12. E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part I: Experimental and Simulated Results for The Spatial Intensity Distribution,” Opt. Express 15(17), 10649–10665 (2007). [CrossRef] [PubMed]
11. A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, “Photon Path-Length Distributions for Transmission through Optically Turbid Slabs,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(2), 810–818 (1993). [CrossRef] [PubMed]
14. R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, “Model for Photon Migration in Turbid Biological Media,” J. Opt. Soc. Am. A 4(3), 423–432 (1987). [CrossRef] [PubMed]
11. A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, “Photon Path-Length Distributions for Transmission through Optically Turbid Slabs,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(2), 810–818 (1993). [CrossRef] [PubMed]
3. Results and discussions
4. Summary
References and links
1. | J. C. Hebden, D. J. Hall, M. Firbank, and D. T. Delpy, “Time-Resolved Optical Imaging of a Solid Tissue-Equivalent Phantom,” Appl. Opt. 34(34), 8038–8047 (1995). [CrossRef] [PubMed] |
2. | R. M. Measures, Laser Remote Sensing: Fundamentals and applications (Krieger Publishing Company, 1992). |
3. | M. A. Linne, M. Paciaroni, J. R. Gord, and T. R. Meyer, “Ballistic Imaging of The Liquid Core for a Steady Jet in Crossflow,” Appl. Opt. 44(31), 6627–6634 (2005). [CrossRef] [PubMed] |
4. | J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, and J. Reintjes, “Achievable Spatial Resolution of Time-Resolved Transillumination Imaging Systems Which Utilize Multiply Scattered Light,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1142–1155 (1996). [CrossRef] [PubMed] |
5. | J. A. Moon and J. Reintjes, “Image Resolution by Use of Multiply Scattered Light,” Opt. Lett. 19(8), 521–523 (1994). [CrossRef] [PubMed] |
6. | J. A. Moon, R. Mahon, M. D. Duncan, and J. Reintjes, “Resolution Limits for Imaging through Turbid Media with Diffuse Light,” Opt. Lett. 18(19), 1591–1593 (1993). [CrossRef] [PubMed] |
7. | M. Paciaroni and M. Linne, “Single-Shot, Two-Dimensional Ballistic Imaging Through Scattering Media,” Appl. Opt. 43(26), 5100–5109 (2004). [CrossRef] [PubMed] |
8. | A. A. Kokhanovsky, “Analytical Solutions of Multiple Light Scattering Problems: A Review,” Meas. Sci. Technol. 13(3), 233–240 (2002). [CrossRef] |
9. | A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, Englewood Cliffs, New Jersey, 1991). |
10. | D. Contini, F. Martelli, and G. Zaccanti, “Photon Migration Through a Turbid Slab Described by a Model Based on Diffusion Approximation. 2. Theory,” Appl. Opt. 36(19), 4587–4599 (1997). [CrossRef] [PubMed] |
11. | A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, “Photon Path-Length Distributions for Transmission through Optically Turbid Slabs,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(2), 810–818 (1993). [CrossRef] [PubMed] |
12. | E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part I: Experimental and Simulated Results for The Spatial Intensity Distribution,” Opt. Express 15(17), 10649–10665 (2007). [CrossRef] [PubMed] |
13. | M. D. King and Harshvardhan, “Comparative Accuracy of Selected Multiple Scattering Approximations,” J. Atmos. Sci. 43(8), 784–801 (1986). [CrossRef] |
14. | R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, “Model for Photon Migration in Turbid Biological Media,” J. Opt. Soc. Am. A 4(3), 423–432 (1987). [CrossRef] [PubMed] |
15. | K.-N. Liou, An Introduction to Atmospheric Radiation (Academic Press Ltd., 2002). |
16. | I. M. Sobol, The Monte Carlo Method (The University of Chicago Press, 1967). |
17. | J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo Programs of Polarized Light Transport into Scattering Media: Part I,” Opt. Express 13(12), 4420–4438 (2005). [CrossRef] [PubMed] |
18. | E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part II: Spatial and Temporal Analysis of Individual Scattering Orders via Monte Carlo Simulation,” Opt. Express 17(16), 13792–13809 (2009). [CrossRef] [PubMed] |
19. | Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables(Dover, 1965). |
OCIS Codes
(290.4020) Scattering : Mie theory
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media
ToC Category:
Scattering
History
Original Manuscript: July 22, 2011
Revised Manuscript: October 12, 2011
Manuscript Accepted: November 1, 2011
Published: November 10, 2011
Virtual Issues
Vol. 7, Iss. 1 Virtual Journal for Biomedical Optics
Citation
Xueqiang Sun, Xuesong Li, and Lin Ma, "A closed-form method for calculating the angular distribution of multiply scattered photons through isotropic turbid slabs," Opt. Express 19, 23932-23937 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-24-23932
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References
- J. C. Hebden, D. J. Hall, M. Firbank, and D. T. Delpy, “Time-Resolved Optical Imaging of a Solid Tissue-Equivalent Phantom,” Appl. Opt.34(34), 8038–8047 (1995). [CrossRef] [PubMed]
- R. M. Measures, Laser Remote Sensing: Fundamentals and applications (Krieger Publishing Company, 1992).
- M. A. Linne, M. Paciaroni, J. R. Gord, and T. R. Meyer, “Ballistic Imaging of The Liquid Core for a Steady Jet in Crossflow,” Appl. Opt.44(31), 6627–6634 (2005). [CrossRef] [PubMed]
- J. A. Moon, P. R. Battle, M. Bashkansky, R. Mahon, M. D. Duncan, and J. Reintjes, “Achievable Spatial Resolution of Time-Resolved Transillumination Imaging Systems Which Utilize Multiply Scattered Light,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics53(1), 1142–1155 (1996). [CrossRef] [PubMed]
- J. A. Moon and J. Reintjes, “Image Resolution by Use of Multiply Scattered Light,” Opt. Lett.19(8), 521–523 (1994). [CrossRef] [PubMed]
- J. A. Moon, R. Mahon, M. D. Duncan, and J. Reintjes, “Resolution Limits for Imaging through Turbid Media with Diffuse Light,” Opt. Lett.18(19), 1591–1593 (1993). [CrossRef] [PubMed]
- M. Paciaroni and M. Linne, “Single-Shot, Two-Dimensional Ballistic Imaging Through Scattering Media,” Appl. Opt.43(26), 5100–5109 (2004). [CrossRef] [PubMed]
- A. A. Kokhanovsky, “Analytical Solutions of Multiple Light Scattering Problems: A Review,” Meas. Sci. Technol.13(3), 233–240 (2002). [CrossRef]
- A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, Englewood Cliffs, New Jersey, 1991).
- D. Contini, F. Martelli, and G. Zaccanti, “Photon Migration Through a Turbid Slab Described by a Model Based on Diffusion Approximation. 2. Theory,” Appl. Opt.36(19), 4587–4599 (1997). [CrossRef] [PubMed]
- A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, “Photon Path-Length Distributions for Transmission through Optically Turbid Slabs,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(2), 810–818 (1993). [CrossRef] [PubMed]
- E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part I: Experimental and Simulated Results for The Spatial Intensity Distribution,” Opt. Express15(17), 10649–10665 (2007). [CrossRef] [PubMed]
- M. D. King and Harshvardhan, “Comparative Accuracy of Selected Multiple Scattering Approximations,” J. Atmos. Sci.43(8), 784–801 (1986). [CrossRef]
- R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, “Model for Photon Migration in Turbid Biological Media,” J. Opt. Soc. Am. A4(3), 423–432 (1987). [CrossRef] [PubMed]
- K.-N. Liou, An Introduction to Atmospheric Radiation (Academic Press Ltd., 2002).
- I. M. Sobol, The Monte Carlo Method (The University of Chicago Press, 1967).
- J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo Programs of Polarized Light Transport into Scattering Media: Part I,” Opt. Express13(12), 4420–4438 (2005). [CrossRef] [PubMed]
- E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser Light Scattering in Turbid Media Part II: Spatial and Temporal Analysis of Individual Scattering Orders via Monte Carlo Simulation,” Opt. Express17(16), 13792–13809 (2009). [CrossRef] [PubMed]
- Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables(Dover, 1965).
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