Abstract

By applying the methods of obtaining sum rules in particle physics to the dispersion relations for optical scattering amplitudes, we obtain a number of sum rules. The most useful show that the total volume fraction of arbitrarily shaped scatterers is proportional to the integral of the attenuation coefficient over wavelength. For spheres, we show that the volume-weighted mean-square radius is related to the second moment of the attenuation coefficient.

© 1982 Optical Society of America

Sum rules and optical moments for a coarse scattering medium

R. Lai and A. J. Sievers
J. Opt. Soc. Am. A 13(5) 1036-1045 (1996)

Sum rules for optical scattering amplitudes: erratum

Bruce H. J. McKellar, Michael A. Box, and Craig F. Bohren
J. Opt. Soc. Am. A 1(12) 1206-1206 (1984)

Sum rules for Mie scattering

Michael A. Box, Phil Attard, Gary Bryant, and Bruce H. J. McKellar
J. Opt. Soc. Am. A 4(5) 795-799 (1987)

Superconvergence relations and sum rules for reflection spectroscopy

D. Y. Smith and Corinne A. Manogue
J. Opt. Soc. Am. 71(8) 935-947 (1981)

Dispersion relations and sum rules for magnetoreflectivity*

David Y. Smith
J. Opt. Soc. Am. 66(6) 547-554 (1976)