## On the extinction of radiation by a homogeneous but spatially correlated random medium

JOSA A, Vol. 18, Issue 8, pp. 1929-1933 (2001)

http://dx.doi.org/10.1364/JOSAA.18.001929

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### Abstract

Exponential extinction of incoherent radiation intensity in a random medium (sometimes referred to as the Beer–Lambert law) arises early in the development of several branches of science and underlies much of radiative transfer theory and propagation in turbid media with applications in astronomy, atmospheric science, and oceanography. We adopt a stochastic approach to exponential extinction and connect it to the underlying Poisson statistics of extinction events. We then show that when a dilute random medium is statistically homogeneous but spatially correlated, the attenuation of incoherent radiation with depth is often slower than exponential. This occurs because spatial correlations among obstacles of the medium spread out the probability distribution of photon extinction events. Therefore the probability of transmission (no extinction) is increased.

© 2001 Optical Society of America

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(030.5290) Coherence and statistical optics : Photon statistics

(030.5620) Coherence and statistical optics : Radiative transfer

(030.6600) Coherence and statistical optics : Statistical optics

**Citation**

Alexander B. Kostinski, "On the extinction of radiation by a homogeneous but spatially correlated random medium," J. Opt. Soc. Am. A **18**, 1929-1933 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-8-1929

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### References

- L. Romanova, “Radiative transfer in a horizontally inhomogeneous scattering medium,” Izv., Acad. Sci. USSR Atmos. Oceanic Phys. 11, 509–513 (1975).
- J. Weinman and Harshvardhan, “Solar reflection from a regular array of horizontally finite clouds,” Appl. Opt. 21, 2940–2944 (1982).
- G. L. Stephens, P. M. Gabriel, and S. C. Tsay, “Statistical radiative transport in one-dimensional media and its application to the terrestrial atmosphere,” Transp. Theory Stat. Phys. 20, 139–175 (1991).
- W. I. Newman, J. K. Lew, G. L. Siscoe, and R. G. Fovell, “Systematic effects of randomness in radiative transfer,” J. Atmos. Sci. 52, 427–435 (1995).
- A. Marshak, A. Davis, W. Wiscombe, and R. Cahalan, “Radiative effects of sub-mean free path liquid water variability observed in stratiform clouds,” J. Geophys. Res. 103, 19557–19567 (1998).
- A. Davis, “Radiation transport in scale-invariant optical media,” Ph.D. dissertation (McGill University, Montreal, 1992).
- A. Davis and A. Marshak, “Levy kinetics in slab geometry: scaling of transmission probability,” in Fractal Frontiers, M. Novak and T. Dewey, eds. (World Scientific, Singapore, 1997), pp. 63–72.
- Y. Knyazikhin, J. Kranigk, R. B. Myneni, O. Panfyorov, and G. Gravenhorsi, “Influence of small-scale structure on radiative transfer and photosynthesis in vegetation canopies,” J. Geophys. Res. 103, 6133–6144 (1998).
- G. C. Pomraning, Linear Kinetic Theory and Particle Transport in Stochastic Mixtures (World Scientific, Singapore, 1991).
- R. Goody and Y. Yung, Atmospheric Radiation (Oxford U. Press, Oxford, UK, 1989).
- L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Pergamon, New York, 1980).
- Sir James Jeans, The Dynamical Theory of Gases (Dover, New York, 1954).
- A. Burshtein, Introduction to Thermodynamics and Kinetic Theory of Matter (Wiley, New York, 1995).
- J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
- F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).
- W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968), Vol. 1.
- A. Davis, A. Marshak, H. Gerber, and W. Wiscombe, “Horizontal structure of marine boundary layers from centimeter to kilometer scales,” J. Geophys. Res. 104, 6123–6144 (1999).
- A. Kostinski and A. Jameson, “Fluctuation properties of precipitation. Part I: Deviations of single size drop counts from the Poisson distribution,” J. Atmos. Sci. 54, 2174–2186 (1997).
- A. Kostinski and A. Jameson, “On the spatial distribution of cloud particles,” J. Atmos. Sci. 57, 901–915 (2000).
- R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, UK, 1983).
- L. Mandel, E. C. D. Sudarshan, and E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, New York, 1995).
- A. Pumir, B. Shraiman, and E. D. Siggia, “Exponential tails and random advection,” Phys. Rev. Lett. 66, 2984 (1991).
- K. Pfeilsticker, “First geometrical pathlength distribution measurements of skylight using the oxygen a-band absorption technique. Part 2: Derivation of the Levy-index for skylight transmitted by mid-latitude clouds,” J. Geophys. Res. 104, 4101–4116 (1999).

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