Abstract
This paper reviews scattering theory required for analysis of light reflected by planetary atmospheres. Section 1 defines the radiative quantities which are observed. Section 2 demonstrates the dependence of single-scattered radiation on the physical properties of the scatterers. Section 3 describes several methods to compute the effects of multiple scattering on the reflected light.
Similar content being viewed by others
References
Abhyankar, K. D. and Fymat, A. L.: 1971, Astrophys. J. Suppl. 23, 35.
Allen, C. W.: 1963, Astrophysical Quantities, Athlone Press, London, 291 pp.
Ambartsumian, V. A.: 1942, Astr. Zh. (Russ.) 19, 30.
Ambartsumian, V. A.: 1958, Theoretical Astrophysics, Pergamon Press, New York, 645 pp.
Appleby, J. F. and van Blerkom, D. J.: 1974, submitted to Icarus.
Bellman, R., Kagiwada, H., Kalaba, R., and Ueno, S.: 1967, Icarus 7, 365.
Bellman, R. E., Kagiwada, H. H., Kalaba, R. E., and Ueno, S.: 1969, Icarus 11, 417.
Bellman, R. E., Kalaba, R. E., and Prestrud, M. C.: 1963, Invariant Imbedding and Radiative Transfer in Slabs of Finite Thickness, American Elsevier, New York, 346 pp.
Bellman, R., Kalaba, R., and Ueno, S.: 1963a, Icarus 1, 297.
Bellman, R., Kalaba, R., and Ueno, S.: 1963b, J. Math. Anal. Appl. 7, 310.
Bellman, R., Kalaba, R., and Wing, G. M.: 1960, J. Math. Phys. 1, 280.
Belton, M. J. S., Hunten, D. M., and Goody, R. M.: 1968, in J. C. Brandt and M. B. McElroy (eds.), The Atmospheres of Venus and Mars, Gordon and Breach, New York, 288 pp.
Bond, G. R. and Siewert, C. E.: 1971, Astrophys. J. 164, 97.
Born, M. and Wolf, E.: 1959, Principles of Optics, Pergamon Press, New York, 803 pp.
Bryant, H. C. and Cox, A. J.: 1966, J. Opt. Soc. Amer. 56, 1529.
Bryant, H. C. and Jarmie, N.: 1974, Sci. Amer. 231, 60.
Busbridge, I. W.: 1960, The Mathematics of Radiative Transfer, Cambridge Univ. Press, Cambridge, 143 pp.
Busbridge, I. W.: 1967, Astrophys. J. 149, 195.
Cabannes, J.: 1929, La Diffusion Moléculaire de la Lumière, Les Presses Universitaires de France, Paris, 326 pp.
Carlstedt, J. L. and Mullikin, T. W.: 1966, Astrophys. J. Suppl. 12, 449.
Case, K. M.: 1960, Ann. Phys. 9, 1.
Case, K. M.: 1967, in E. Inönü and P. F. Zweifel (eds.), Developments in Transport Theory, Academic Press, New York, 381 pp.
Case, K. M. and Zweifel, P. F.: 1967, Linear Transport Theory, Addison-Wesley, Reading, Mass., 342 pp.
Cashwell, E. D. and Everett, C. J.: 1959, Monte Carlo Method, Pergamon Press, New York, 153 pp.
Chandrasekhar, S.: 1944, Astrophys. J. 100, 76.
Chandrasekhar, S.: 1950, Radiative Transfer, Oxford Univ. Press, 393 pp.
Coffeen, D. L. and Gehrels, T.: 1969, Astron. J. 74, 433.
Coffeen, D. L. and Hansen, J. E.: 1974, in T. Gehrels (ed.), Planets, Stars and Nebulae Studied With Photopolarimetry, Univ. Arizona Press, Tucson, p. 518.
Collins, D. G. and Wells, M. B.: 1965, REP. RRA-T54 (Radiation Research Associates, Inc., Ft. Worth, Texas), Vols. 1 and 2.
Collins, D. G., Blattner, W. G., Wells, M. B., and Horak, H. G.: 1972, Appl. Opt. 11, 2684.
Coulson, K. L., Dave, J. V., and Sekera, Z.: 1960, Tables Related to Radiation Emerging From a Planetary Atmosphere with Rayleigh Scattering, Univ. of Calif. Press, Berkeley, 584 pp.
Danielson, R. E., Moore, D. R., and van de Hulst, H. C.: 1969, J. Atmospheric Sci. 26, 1078.
Dave, J. V.: 1964, Astrophys. J. 140, 1292.
Dave, J. V.: 1969, Appl. Opt. 8, 155.
Dave, J. V.: 1970, Appl. Opt. 9, 2673.
Dave, J. V. and Armstrong, B. H.: 1974, submitted to J. Atmospheric Sci.
Dave, J. V. and Canosa, J.: 1974, J. Atmospheric Sci. 31, 1089.
Dave, J. V. and Gazdag, J.: 1970, Appl. Opt. 9, 1457.
Davison, B.: 1958, Neutron Transport Theory, Oxford Univ. Press, London, 450 pp.
Deirmendjian, D.: 1964, Appl. Opt. 3, 187.
Deirmendjian, D.: 1969, Electromagnetic Scattering on Spherical Polydispersions, American Elsevier, New York, 290 pp.
Deuze, J. L., Devaux, C., and Herman, M.: 1973, Nouv. Rev. Optique 4, 307.
de Vaucouleurs, G.: 1951, Ann. Phys. 6, 211.
Diem, M.: 1948, Meteor. Rund. 1, 261.
Dollfus, A. and Coffeen, D. L.: 1970, Astron. Astrophys. 8, 251.
Feinstein, D. L., Butler, F. E., Piech, K. R., and Leonard, A.: 1972, Phys. Fluids 15, 1641.
Friend, J. P.: 1966, Tellus 18, 465.
Grant, I. P. and Hunt, G. E.: 1969, Proc. Roy. Soc. London A 313, 183.
Hammersley, J. M. and Handscomb, D. C.: 1964, Monte Carlo Methods, John Wiley, New York, 178 pp.
Hamming, R. W.: 1973, Numerical Methods For Scientists and Engineers, McGraw-Hill, New York, 721 pp.
Hansen, J. E.: 1969, J. Atmospheric Sci. 26, 478.
Hansen, J. E.: 1971a, J. Atmospheric Sci. 28, 120.
Hansen, J. E.: 1971b, J. Atmospheric Sci. 28, 1400.
Hansen, J. E.: 1971c, J. Atmospheric Sci. 28, 1515.
Hansen, J. E. and Hovenier, J. W.: 1971, J. Quant. Spectr. Radiat. Transfer 11, 809.
Hansen, J. E. and Hovenier, J. W.: 1974, J. Atmospheric Sci. 31, 1137.
Hansen, J. E. and Pollack, J. B.: 1970, J. Atmospheric Sci. 27, 265.
Herman, B. M. and Browning, S. R.: 1965, J. Atmospheric Sci. 22, 559.
Horak, H. G.: 1950, Astrophys. J. 112, 445.
Horak, H. G. and Chandrasekhar, S.: 1961, Astrophys. J. 134, 45.
House, L. L. and Avery, L. W.: 1969, J. Quant. Spectr. Radiat. Transfer 9, 1579.
Hovenier, J. W.: 1969, J. Atmospheric Sci. 26, 488.
Hovenier, J. W.: 1971, Astron. Astrophys. 13, 7.
Irvine, W. M.: 1963, Bull. Astron. Inst. Neth. 17, 176.
Irvine, W. M.: 1965, Astrophys. J. 142, 1563.
Junge, C. E.: 1963, Air Chemistry and Radiochemistry, Academic Press, New York, 382 pp.
Kaper, H. G., Shultis, J. K., and Veninga, J. G.: 1970, J. Comp. Phys. 6, 288.
Kastner, S. O.: 1964, Goddard Space Flight Center rept. TMX-55062, 12 pp.
Kattawar, G. W. and Adams, C. N.: 1971, Astrophys. J. 167, 183.
Kattawar, G. W. and Plass, G. N.: 1967, Appl. Opt. 6, 1377.
Kattawar, G. W., Plass, G. N., and Guinn, J. A.: 1973, J. Phys. Ocean. 3, 353.
Kemp, J. C.: 1974, in T. Gehrels (ed.), Planets, Stars and Nebulae Studied with Photopolarimetry, Univ. Arizona Press, Tucson, p. 607.
Kemp, J. C., Swedlund, J. B., Murphy, R. E., and Wolstencroft, R. D.: 1971a, Nature 231, 169.
Kemp, J. C., Wolstencroft, R. D., and Swedland, J. B.: 1971b, Nature 232 165.
Kendall, M. G. and Stuart, A.: 1963, The Advanced Theory of Statistics, Vol. 1, Distribution Theory, Hafner Publ. Com., New York, 433 pp.
Kerker, M.: 1969, The Scattering of Light, Academic Press, New York, 666 pp.
Khrgian, A. Kh.: 1961, Cloud Physics, Israel Prog. Scien. Trans., Jerusalem, 392 pp.
Kofink, W.: 1967, in E. Inönü and P. F. Zweifel (eds.), Developments in Transport Theory, Academic Press, New York, 381 pp.
Kolesov, A. K. and Smotkii, O. I.: 1972, Soviet Astron. A. J. 15, 802.
Kuščer, I.: 1955, J. Math. Phys. 34, 256.
Kuščer, I. and McCormick, N. J.: 1974, UCLA International Conference on Radiation and Remote Probing of the Atmosphere, Western Periodicals, North Hollywood, 506 pp.
Lacis, A. A. and Hansen, J. E.: 1974, J. Atmospheric Sci. 31, 118.
Lenoble, J.: 1956, Rev. Opt. 35, 1.
Lenoble, J.: 1961, Compt. Rend. Acta. Sci. 252, 2087.
Lenoble, J.: 1970, J. Quant. Spectr. Radiat. Transfer 10, 533.
Liou, K. N.: 1973, J. Atmospheric Sci. 30, 1303.
Liou, K. N.: 1974, J. Atmospheric Sci., 31, 1473.
Liou, K. N. and Hansen, J. E.: 1971, J. Atmospheric Sci. 28, 995.
Lorenz, L.: 1898, Oeuvres Scientifiques, Vol. 1, Lehman and Stage, Copenhagen, p. 405.
Lyot, B.: 1929, Ann. Obs. Paris (Meudon) 8, 161.
Marchuk, G. I. and Mikhailov, G. A.: 1967a, Izv. Atmospheric Ocean. Phys. 3, 258.
Marchuk, G. I. and Mikhailov, G. A.: 1967b, Izv. Atmospheric Ocean. Phys. 3, 394.
Mark, J. C.: 1944, Nat. Res. Coun. Canada, Atomic Energy Project report MT 92.
Marshak, R. E.: 1947, Phys. Rev. 71, 443.
Mathews, D. R., Hansen, K. F., and Mason, E. A.: 1967, Nucl. Sci. Eng. 27, 263.
McCormick, N. J. and Kuščer, I.: 1966, J. Math. Phys. 7, 2036.
McCormick, N. J. and Kuščer, I.: 1973, in E. J. Henley and J. Lewins (eds.), Advances in Nuclear Science and Technology 7, pp. 181, Academic Press, New York, 379 pp.
McKee, T. B. and Cox, S. K.: 1974, submitted to J. Atmospheric Sci.
Mie, G.: 1908, Ann. Phys. 25, 377.
Mika, J. R.: 1961, Nucl. Sci. Eng. 11, 415.
Mingle, J. D.: 1973, The Invariant Imbedding Theory of Nuclear Transport, American Elsevier, New York, 131 pp.
Mossop, S. C.: 1965, Geochim. Cosmochim. Acta 29, 201.
Pahor, S.: 1966, Nucl. Sci. Eng. 26, 192.
Pahor, S.: 1967, Nucl. Sci. Eng. 29, 248.
Pahor, S. and Kuščer, I.: 1966, Astrophys. J. 143, 888.
Peebles, G. H. and Plesset, M. S.: 1951, Phys. Rev. 81, 430.
Penndorf, R.: 1957, J. Opt. Soc. Amer. 47, 176.
Plass, G. N. and Kattawar, G. W.: 1968, Appl. Opt. 7, 415.
Plass, G. N. and Kattawar, G. W.: 1971, J. Atmospheric Sci. 28, 1187..
Plass, G. N., Kattawar, G. W., and Catchings, F. E.: 1973, Appl. Opt. 12, 314.
Pollack, J. B.: 1967, Icarus 7, 42.
Porch, W. M., Ensor, D. S., Charlson, R. J., and Heintzenberg, J.: 1973, Appl. Opt. 12, 34.
Potter, J. F.: 1970, J. Atmospheric Sci. 27, 943.
Rayleigh, Lord (J. W. Strutt): 1871, Phil. Mag. 41, 107, 274 and 477.
Rayleigh, Lord (J. W. Strutt): 1918, Phil. Mag. 35, 373.
Samuelson, R. E.: 1969, Icarus 10, 258.
Schuster, A.: 1905, Astrophys. J. 21, 1.
Schwarzschild, K.: 1906, Göttinger Nachrichten, 41.
Sekera, Z.: 1966, Memorandums RM-4951-PR and RM-5056-PR, Rand Corporation, Santa Monica.
Sekera, Z. and Kahle, A. B.: 1966, Memorandum R-452-PR, Rand Corporation, Santa Monica.
Shreider, Y. A.: 1966, The Monte Carlo Method, Pergamon Press, New York, 381 pp.
Shurcliff, W. A.: 1962, Polarized Light, Harvard Univ. Press, Cambridge, 207 pp.
Sobolev, V. V.: 1974, Light Scattering in Planetary Atmospheres, Pergamon Press, New York (in press).
Spanier, J. and Gelbard, E. M.: 1969, Monte Carlo Principles and Neutron Transport Problems, Addison-Wesley, Reading, Mass., 234 pp.
Stibbs, D. W. N. and Weir, R. E.: 1959, Monthly Notices Roy. Astron. Soc. 119, 512.
Stokes, G. G.: 1862, Proc. Roy. Soc. (London) 11, 545.
Sweigart, A. V.: 1970, Astrophys. J. Suppl. 22, 1.
Travis, L. D.: 1974, in preparation.
Twomey, S., Jacobowitz, H., and Howell, H. B.: 1966, J. Atmospheric Sci. 23, 289.
Uesugi, A. and Irvine, W. M.: 1970, Astrophys. J. 159, 127.
van Blerkom, D. J.: 1971, Astrophys. J. 166, 235.
van de Hulst, H. C.: 1948, Astrophys. J. 107, 220.
van de Hulst, H. C.: 1957, Light Scattering by Small Particles, Wiley, New York, 470 pp.
van de Hulst, H. C.: 1963, Tech. Rept., Inst. Space Studies, NASA, New York, 81 pp.
van de Hulst, H. C.: 1970, Astron. Astrophys. 9, 359.
van de Hulst, H. C. and Irvine, W. M.: 1962, La Physique des planètes (11th Liège International Astrophysical Symposium), p. 78.
Weickmann, H. K. and aufm Kampe, H. J.: 1953, J. Meteor. 10, 204.
Weinman, J. A. and Guetter, P. J.: 1972, J. Appl. Meteor. 11, 136.
Wick, G. C.: 1943, Z. Phys. 120, 702.
Wing, G. M.: 1962, An Introduction to Transport Theory, John Wiley, New York, 169 pp.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hansen, J.E., Travis, L.D. Light scattering in planetary atmospheres. Space Sci Rev 16, 527–610 (1974). https://doi.org/10.1007/BF00168069
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00168069