OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 6 — Jun. 1, 2004
  • pp: 1009–1017

Analytic inverse radiative transfer equations for atmospheric and hydrologic optics

Norman J. McCormick  »View Author Affiliations


JOSA A, Vol. 21, Issue 6, pp. 1009-1017 (2004)
http://dx.doi.org/10.1364/JOSAA.21.001009


View Full Text Article

Acrobat PDF (197 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Two new sets of analytical equations are derived with which the albedo of single scattering and the coefficients of a Legendre polynomial expansion of the scattering phase function can be determined for a source-free, homogeneous plane-parallel medium uniformly illuminated over the surfaces. The equations, essentially linear in the unknowns, require measurements of the radiance in the interior of the medium, but no iterative forward-problem calculations are needed. Sets of equations for both unpolarized and polarized radiation applications are given, as well as a side-by-side comparison with previously known sets of analytic inversion equations. Applications of the equations are suggested.

© 2004 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(030.5620) Coherence and statistical optics : Radiative transfer
(260.5430) Physical optics : Polarization
(290.3200) Scattering : Inverse scattering
(290.4210) Scattering : Multiple scattering

Citation
Norman J. McCormick, "Analytic inverse radiative transfer equations for atmospheric and hydrologic optics," J. Opt. Soc. Am. A 21, 1009-1017 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-6-1009


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. H. R. Gordon, “Inverse methods in hydrologic optics,” Oceanologia 44, 9–58 (2002).
  2. S. Stephany, H. F. de Campos Velho, F. M. Ramos, and C. D. Mobley, “Identification of inherent optical properties and bioluminescence source term in a hydrologic optics problem,” J. Quant. Spectrosc. Radiat. Transf. 67, 113–123 (2000).
  3. E. S. Chalhoub and H. F. Campos Velho, “Estimation of the optical properties of seawater from measurements of exit radiance,” J. Quant. Spectrosc. Radiat. Transf. 72, 551–565 (2002).
  4. K. M. Case, “Inverse problem in transport theory,” Phys. Fluids 16, 1607–1611 (1973).
  5. N. J. McCormick and I. Kuščer, “On the inverse problem in radiative transfer,” J. Math. Phys. 15, 926–927 (1974).
  6. C. E. Siewert, “On a possible experiment to evaluate the validity of the one-speed or constant cross section model of the neutron-transport equation,” J. Math. Phys. 19, 1587–1588 (1978).
  7. C. E. Siewert, “On the inverse problem for a three-term phase function,” J. Quant. Spectrosc. Radiat. Transf. 22, 441–446 (1979).
  8. N. J. McCormick, “Transport scattering coefficients from reflection and transmission measurements,” J. Math. Phys. 20, 1504–1507 (1979).
  9. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), pp. 149–154.
  10. R. Sanchez and N. J. McCormick, “General solutions to inverse transport problems,” J. Math. Phys. 22, 847–855 (1981).
  11. N. J. McCormick and R. Sanchez, “Inverse problem transport calculations for anisotropic scattering coefficients,” J. Math. Phys. 22, 199–208 (1981).
  12. R. Sanchez and N. J. McCormick, “Numerical evaluation of optical single-scattering properties using multiple-scattering inverse transport methods,” J. Quant. Spectrosc. Radiat. Transf. 28, 169–184 (1982).
  13. J. C. Oelund and N. J. McCormick, “Sensitivity of multiple-scattering inverse transport methods to measurement errors,” J. Opt. Soc. Am. A 2, 1972–1978 (1985).
  14. L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
  15. C. E. Siewert, “Inverse solutions to radiative-transfer problems based on the binomial or the Henyey–Greenstein scattering law,” J. Quant. Spectrosc. Radiat. Transf. 72, 827–835 (2002).
  16. A. H. Hakim and N. J. McCormick, “Ocean optics estimation for absorption, backscattering, and phase function parameters,” Appl. Opt. 42, 931–938 (2003).
  17. N. J. McCormick and R. Sanchez, “Solutions to an inverse problem in radiative transfer with polarization—II,” J. Quant. Spectrosc. Radiat. Transf. 30, 527–535 (1983).
  18. T. Viik and N. J. McCormick, “Numerical test of an inverse polarized radiative transfer algorithm,” J. Quant. Spectrosc. Radiat. Transf. 78, 235–241 (2003).
  19. K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34, 1614–1622 (1989).
  20. M. D. King, L. F. Radke, and P. V. Hobbs, “Determination of the spectral absorption of solar radiation by marine stratocumulus clouds from airborne measurements within clouds,” J. Atmos. Sci. 47, 894–907 (1990).
  21. K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), pp. 87–91.
  22. E. W. Larsen, “Solution of the inverse problem in multigroup transport theory,” J. Math. Phys. 22, 158–160 (1981).
  23. G. B. Rybicki, “Integrals of the transfer equation. I. Quadratic integrals for monochromatic, isotropic scattering,” Astrophys. J. 213, 165–176 (1977).
  24. N. J. McCormick, “Methods for solving inverse problems for radiation transport—an update,” Transp. Theory Stat. Phys. 15, 759–772 (1986).
  25. C. E. Siewert, “On the equation of transfer relevant to the scattering of polarized light,” Astrophys. J. 245, 1080–1086 (1981).
  26. C. E. Siewert, “On the phase matrix basic to the scattering of polarized light,” Astron. Astrophys. 109, 195–200 (1982).
  27. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
  28. J. W. Hovenier and C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).
  29. The definition of U in Ref. 17 should have been stated in this way.
  30. C. E. Siewert, “Solutions to an inverse problem in radiative transfer with polarization—I,” J. Quant. Spectrosc. Radiat. Transf. 30, 523–528 (1983).
  31. K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fish-eye’ camera radiance distribution system,” J. Atmos. Ocean. Phys. 6, 652–662 (1989).
  32. E. Aas and N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
  33. A. H. Hakim, B. D. Piening, and N. J. McCormick, “Near-asymptotic angle dependence of ocean optical radiance,” manuscript available from N. J. McCormick, mccor@u.washington.edu.
  34. C. D. Mobley, Light and Water Radiative Transfer in Natural Waters (Academic, New York, 1994), pp. 437–439.
  35. C. E. Siewert, “Inverse solutions to radiative-transfer problems with partially transparent boundaries and diffuse reflection,” J. Quant. Spectrosc. Radiat. Transf. 72, 299–313 (2002).
  36. N. J. McCormick, “Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient,” Limnol. Oceanogr. 40, 1013–1018 (1995).
  37. N. J. McCormick, “Analytical transport theory applications in optical oceanography,” Ann. Nucl. Energy 23, 381–395 (1995).

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