OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 946–967

Markov chain formalism for polarized light transfer in plane-parallel atmospheres, with numerical comparison to the Monte Carlo method

Feng Xu, Anthony B. Davis, Robert A. West, and Larry W. Esposito  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 946-967 (2011)
http://dx.doi.org/10.1364/OE.19.000946


View Full Text Article

Enhanced HTML    Acrobat PDF (1606 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03.

© 2011 OSA

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(290.5855) Scattering : Scattering, polarization

ToC Category:
Scattering

History
Original Manuscript: October 14, 2010
Revised Manuscript: December 1, 2010
Manuscript Accepted: December 20, 2010
Published: January 7, 2011

Virtual Issues
Vol. 6, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Feng Xu, Anthony B. Davis, Robert A. West, and Larry W. Esposito, "Markov chain formalism for polarized light transfer in plane-parallel atmospheres, with numerical comparison to the Monte Carlo method," Opt. Express 19, 946-967 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-946


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. W. Esposito and L. L. House, “Radiative transfer calculated by a Markov chain formalism,” Astrophys. J. 219, 1058–1067 (1978). [CrossRef]
  2. L. W. Esposito, “An ‘adding’ algorithm for the Markov chain formalism for radiation transfer,” Astrophys. J. 233, 661–663 (1979). [CrossRef]
  3. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16(4), 527–610 (1974). [CrossRef]
  4. K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991). [CrossRef]
  5. Q. L. Min and M. Duan, “A successive order of scattering model for solving vector radiative transfer in the atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 87(3-4), 243–259 (2004). [CrossRef]
  6. S. Y. Kotchenova, E. F. Vermote, R. Matarrese, and F. J. Klemm., “Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: path radiance,” Appl. Opt. 45(26), 6762–6774 (2006). [CrossRef] [PubMed]
  7. P. W. Zhai, Y. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17(4), 2057–2079 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-4-2057 . [CrossRef] [PubMed]
  8. J. H. Hannay, “Radiative transfer: exact Rayleigh scattering series and a daylight formula,” J. Opt. Soc. Am. A 26(3), 669–675 (2009). [CrossRef]
  9. F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere–I. Theory,” J. Quant. Spectrosc. Radiat. Transf. 47(1), 19–33 (1992). [CrossRef]
  10. R. J. D. Spurr, “VLIDORT: A linearized pseudo-spherical vector discrete ordinate radiative transfer code for forward model and retrieval studies in multilayer multiple scattering media,” J. Quant. Spectrosc. Radiat. Transf. 102(2), 316–342 (2006). [CrossRef]
  11. F. M. Schulz, K. Stamnes, and F. Weng, “VDISORT, an improved and generalized discrete ordinate method for polarized (vector) radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 61(1), 105–122 (1999). [CrossRef]
  12. J. V. Dave, “Intensity and polarization of the radiation emerging from a plane-parallel atmosphere containing monodispersed aerosols,” Appl. Opt. 9(12), 2673–2684 (1970). [CrossRef] [PubMed]
  13. J. W. Hovenier, “Symmetry relations for scattering of polarized light in a slab of randomly oriented particles,” J. Atmos. Sci. 26(3), 488–499 (1969). [CrossRef]
  14. C. E. Siewert, “On the phase matrix basic to the scattering of polarized light,” Astron. Astrophys. 109, 195–200 (1982).
  15. J. W. Hovenier, and C. V. M. van der Mee, “Basic Relationships for Matrices Describing Scattering by Small Particles”, in Light Scattering by Nonspherical Particles, pp. 61–85, M. Mishchenko, J. W. Hovenier and L. Travis, (eds.), Academic Press, San Diego, 2000.
  16. A. B. Davis and F. Xu, “Monte Carlo modeling of polarized light transfer in vertically varying plane-parallel atmospheres, with application to lofted aerosol layer detection using O2 spectroscopy,” J. Quant. Spectrosc. Radiat. Transf.
  17. A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010). [CrossRef]
  18. G. Marchuk, G. Mikhailov, N. Nazaraliev, R. Darbinjan, B. Kargin, and B. Elepov, The Monte Carlo Methods in Atmospheric Optics, Springer-Verlag, New-York, NY (1980).
  19. K. F. Evans, and A. Marshak, “Numerical Methods,” in 3D Radiative Transfer in Cloudy Atmospheres, pp. 243–281, A. Marshak and A. B. Davis (eds.), Springer, Heidelberg, Germany (2005).
  20. A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010). [CrossRef]
  21. D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998). [CrossRef]
  22. P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994). [CrossRef]
  23. M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007). [CrossRef]
  24. D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004). [CrossRef]
  25. V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007). [CrossRef]
  26. V. Natraj and R. J. D. Spurr, “A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 107(2), 263–293 (2007). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited