## Sensitivity of multiple-scattering inverse transport methods to measurement errors

JOSA A, Vol. 2, Issue 11, pp. 1972-1978 (1985)

http://dx.doi.org/10.1364/JOSAA.2.001972

Enhanced HTML Acrobat PDF (816 KB)

### Abstract

Inverse multiple-scattering transport methods, derived from the linear Boltzmann equation, are potentially suitable for remote-sensing studies because they do not require measurements within the scattering medium. The methods investigated yield the single-frequency angular redistribution function for a homogeneous one-dimensional slab medium that is uniformly illuminated. Illustrative numerical results for a monodirectional incident beam show that the methods are ill conditioned with respect to simulated measurement errors, with the severity depending strongly on the direction of the incident beam.

© 1985 Optical Society of America

**History**

Original Manuscript: January 7, 1985

Manuscript Accepted: April 2, 1985

Published: November 1, 1985

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-11-1972

Sort: Year | Journal | Reset

### References

- C. E. Siewert, “The inverse problem for a finite slab,” Nucl. Sci. Eng. 67, 259–260 (1978).
- C. E. Siewert, “On establishing a two-term scattering law in the theory of radiative transfer,” Z. Angew. Math. Phys. 30, 522–525 (1979). [CrossRef]
- C. E. Siewert, “On the inverse problem for a three-term phase function,” J. Quant. Spectrosc. Radiat. Transfer 22, 441–446 (1979). [CrossRef]
- N. J. McCormick, “Transport scattering coefficients from reflection and transmission measurements,” J. Math. Phys. 20, 1504–1507 (1979). [CrossRef]
- C. E. Siewert, W. L. Dunn, “On inverse problems for plane-parallel media with non-uniform surface illumination,” J. Math. Phys. 23, 1376–1378 (1982). [CrossRef]
- E. W. Larsen, “Solution of multidimensional inverse transport problems,” J. Math. Phys. 25, 131–135 (1984). [CrossRef]
- R. Sanchez, N. J. McCormick, “General solutions to inverse transport problems,” J. Math. Phys. 22, 847–855 (1981). [CrossRef]
- C. E. Siewert, “Solutions to an inverse problem in radiative transfer with polarization—I,” J. Quant. Spectrosc. Radiat. Transfer 30, 523–526 (1983). [CrossRef]
- N. J. McCormick, R. Sanchez, “Solutions to an inverse problem in radiative transfer with polarization—II,” J. Quant. Spectrosc. Radiat. Transfer 30, 527–535 (1983). [CrossRef]
- N. J. McCormick, R. Sanchez, “Inverse problem transport calculations for anisotropic scattering coefficients,” J. Math. Phys. 22, 199–208 (1981). [CrossRef]
- R. Sanchez, N. J. McCormick, “Numerical evaluation of optical single-scattering properties using multiple-scattering inverse transport methods,” J. Quant. Spectrosc. Radiat. Transfer 28, 169–184 (1982). [CrossRef]
- C. E. Siewert, “The FN-method for solving radiative transfer problems in plane geometry,” Astrophys. Space Sci. 58, 131–137 (1978). [CrossRef]
- R. D. M. Garcia, C. E. Siewert, “Radiative transfer in finite homogeneous plane-parallel atmospheres,” J. Quant. Spectrosc Radiat. Transfer 27, 141–148 (1982). [CrossRef]
- C. Devaux, C. E. Siewert, Y. L. Yuan, “The complete solution for radiative transfer problems with reflecting boundaries and internal sources,” Astrophys. J. 253, 773–784 (1982). [CrossRef]
- W. L. Dunn, J. R. Maiorino, “On the numerical characteristics of an inverse solution for three-term radiative transfer,” J. Quant. Spectrosc. Rad. Transfer 24, 203–209 (1980). [CrossRef]
- N. J. McCormick, “Inverse methods for remote determination of properties of optically thick atmospheres,” Appl. Opt. 22, 2556–2558 (1983). [CrossRef] [PubMed]
- L. W. Johnson, R. D. Riess, Numerical Analysis (Addison-Wesley, Reading, Mass., 1982).
- A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).
- S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

## 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.