Calculation of far-field scattering from nonspherical particles using a geometrical optics approach

Abstract

A numerical method was developed using geometrical optics to predict far-field optical scattering from particles that are symmetric about the optic axis. The diffractive component of scattering is calculated and combined with the reflective and refractive components to give the total scattering pattern. The phase terms of the scattered light are calculated as well. Verification of the method was achieved by assuming a spherical particle and comparing the results to Mie scattering theory. Agreement with the Mie theory was excellent in the forward-scattering direction. However, small-amplitude oscillations near the rainbow regions were not observed using the numerical method. Numerical data from spheroidal particles and hemispherical particles are also presented. The use of hemispherical particles as a calibration standard for intensity-type optical particle-sizing instruments is discussed.

The refractive angle of light propagation at absorbing media interface

“…s t ) =  t − t ,  t is the angle of refractive, t is the angle between z-axis and q t . And exist the following expressions k si sin  i = k st sin  t k qi sin i = k qt sin t (8) For the refracted wave require that Then we find…”

“…Studies on the geometrical optics approximation (GOA) of light scattering have been of interest to many researchers during the past several decades [4][5][6][7][8][9][10][11][12][13][14][15][16], it can avoiding calculate large particle scattering amplitude time-consuming difficulties in Mie theory. But the GOA calculations of light scattering are rare due to the difficulties in calculating the propagation of light in the absorbing medium and its Fresnel coefficients at the interface of the media.…”

Ray scattering by an arbitrarily oriented spheroid II Transmission and cross-polarization effects

“…[13][14][15][16][17][18][19] Ray-tracing programs for scattering by an arbitrarily shaped particle have also been developed for certain specialized applications. 20,21 The purpose of this paper, along with a companion paper 22 that is hereafter designated as part I, is to describe scattering in the forward hemisphere of an arbitrarily polarized plane wave by an arbitrarily oriented dielectric spheroid by the use of ray theory. In part I diffraction and specular reflection were considered.…”

“…We next considered the end-on spheroid case l 5 0.6328 µm, n 5 1.33, b@a 5 1.5, a 5 10.0 µm, x 5 90°, and u 5 0°and compared our results with those in figure 8 of Ref. 21, in which the ray-theory intensity was calculated with another method. Again the results matched exactly.…”

Ray scattering by an arbitrarily oriented spheroid I Diffraction and specular reflection

“…Ray theory has been applied to spheroid scattering when the plane wave is incident along the spheroid major axis. 28,29 In this case the trajectory of a given light ray is confined to a single plane, thus considerably simplifying the treatment and eliminating all cross-polarization effects. Ray theory has also been applied to spheroid scattering for the purpose of examining the role of one-internal-reflection rays and two-internal-reflection rays in rainbow formation when the plane wave is incident along one of the spheroid minor axes.…”