Abstract

A method for determining the spatial distribution of the emission coefficient in the limit of small self-absorption is based on solving the transfer equation for the flux which is observed at the detector when a mirror is present. From this solution and that corresponding to an interchange of the detector and mirror, integral equations for the absorption and emission coefficients are obtained. In the limit of small self-absorption, when the optical density over the entire path is much less than one, the integral equation for emission coefficient is approximated by an integral equation which is mathematically identical to that for the absorption coefficient. The method which was recently presented by Maldonado <i>et al.</i> for inverting such integral equations is then used to obtain series representations of the absorption and emission coefficients. The numerical procedure of Maldonado <i>et al.</i> for summing these series representations is applied to two hypothetical examples. The numerical results obtained for the absorption and emission coefficients are within 1% of exact theoretical results.

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  1. C. D. Maldonado, A. P. Caron, and H. N. Olsen, J. Opt. Soc. Am. 55, 1247 (1965).
  2. C. D. Maldonado and H. N. Olsen, J. Opt. Soc. Am. 56, 1305 (1966).
  3. M. P. Freeman and S. Katz, J. Opt. Soc. Am. 50, 826 (1960).
  4. R. W. Porter, S. I. A. M. Rev. 6, 228 (1964).
  5. S. Chandrasekbar, Radiativte Transfer (Dover Publications, Inc., New York, 1960).
  6. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1963), Vols. I and II.
  7. C. D. Maldonado, J. Math. Phys. 6, 1935 (1965).
  8. W. Gröbner and N. Hofreiter, Integraltafel erster Teil Unbestimmte Integrals (Springer-Verlag, Vienna, 1961).

Caron, A. P.

C. D. Maldonado, A. P. Caron, and H. N. Olsen, J. Opt. Soc. Am. 55, 1247 (1965).

Chandrasekbar, S.

S. Chandrasekbar, Radiativte Transfer (Dover Publications, Inc., New York, 1960).

Erdelyi, A.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1963), Vols. I and II.

Freeman, M. P.

M. P. Freeman and S. Katz, J. Opt. Soc. Am. 50, 826 (1960).

Gröbner, W.

W. Gröbner and N. Hofreiter, Integraltafel erster Teil Unbestimmte Integrals (Springer-Verlag, Vienna, 1961).

Hofreiter, N.

W. Gröbner and N. Hofreiter, Integraltafel erster Teil Unbestimmte Integrals (Springer-Verlag, Vienna, 1961).

Katz, S.

M. P. Freeman and S. Katz, J. Opt. Soc. Am. 50, 826 (1960).

Magnus, W.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1963), Vols. I and II.

Maldonado, C. D.

C. D. Maldonado, A. P. Caron, and H. N. Olsen, J. Opt. Soc. Am. 55, 1247 (1965).

C. D. Maldonado, J. Math. Phys. 6, 1935 (1965).

C. D. Maldonado and H. N. Olsen, J. Opt. Soc. Am. 56, 1305 (1966).

Oberhettinger, F.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1963), Vols. I and II.

Olsen, H. N.

C. D. Maldonado, A. P. Caron, and H. N. Olsen, J. Opt. Soc. Am. 55, 1247 (1965).

C. D. Maldonado and H. N. Olsen, J. Opt. Soc. Am. 56, 1305 (1966).

Porter, R. W.

R. W. Porter, S. I. A. M. Rev. 6, 228 (1964).

Tricomi, F. G.

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1963), Vols. I and II.

Other

C. D. Maldonado, A. P. Caron, and H. N. Olsen, J. Opt. Soc. Am. 55, 1247 (1965).

C. D. Maldonado and H. N. Olsen, J. Opt. Soc. Am. 56, 1305 (1966).

M. P. Freeman and S. Katz, J. Opt. Soc. Am. 50, 826 (1960).

R. W. Porter, S. I. A. M. Rev. 6, 228 (1964).

S. Chandrasekbar, Radiativte Transfer (Dover Publications, Inc., New York, 1960).

A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1963), Vols. I and II.

C. D. Maldonado, J. Math. Phys. 6, 1935 (1965).

W. Gröbner and N. Hofreiter, Integraltafel erster Teil Unbestimmte Integrals (Springer-Verlag, Vienna, 1961).

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