The math of Mie scattering

ECE532 Biomedical Optics
Steven L. Jacques, Scott A. Prahl
Oregon Graduate Institute

Consider a source, a spherical scattering particle, and an observer whose three positions define a plane called the scattering plane. Incident light and scattered light can be reduced to their components which are parallel or perpendicular to the scattering plane. As shown in the following figure, the parallel and perpendicular components can be experimentally selected by a linear polarization filter oriented parallel or perpendicular to the scattering plane.

The Scattering matrix describes the relationship between incident and scattered electric field components perpendicular and parallel to the scattering plane as observed in the "far-field" (ref: Bohren and Huffman):

The above expression simplifies in practical experiments:

Hence for practical scattering measurements, the above equation simplifies to the following:

Mie theory yields two sets of descriptors of scattering:

ANGULAR SCATTERING PATTERN OF POLARIZED LIGHT Mie theory calculates the angular dependence of the two elements, S1() and S2(), of the Scattering matrix, from which the scattered intensities of polarized light are computed (see example). The scattering pattern is also used to calculate the anisotropy, g, of scattering by the particle.

Example of angular scattering calculation

Example of anistoropy calculation

EFFICIENCIES OF SCATTERING AND ABSORPTION Mie theory calculates the efficiencies Qs and Qa of scattering and absorption, respectively, such that µa = QaA and µs = QsA, where A is the geometrical cross-sectional area a2 for a sphere of radius a.

Example of Qs and µs calculation

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