<title>Comparative analysis of different solutions of light scattering problem for nonspherical particles</title>

Abstract

The model of homogeneous spheroids were chosen to provide the detailed comparison of two popular solutions of the light scattering problem: T-Matrix Method and Discrete Dipole Approximation. The exact solution by the Separation of Variables Method were used as a standard giving the most accurate results. We have computed the scattering cross-sections of prolate and oblate spheroids with the refractive index m equals 1.3 and 2.5 at fixed orientation in a wide range of the aspect ratios and sizes. We found that: (1) the coincidence of the T- Matrix Method and the Separation of Variables Method is very good (> 6 - 10 digits) up to some boundary particle size; for larger particles the precision of T-Matrix results sharply drops; (2) the Discrete Dipole Approximation code gives the satisfactory results (the deviations from other methods less 5 - 10%) for large values of size and aspect ratio even if the number of dipoles is 1,000 - 1,500; the accuracy less than 1% may be obtained if the number of dipoles exceed 10,000 - 50,000; (3) the accuracy of the methods decrease with the growth of the parameter (tau) equals m (DOT) (2(pi) r_v/(lambda) ) (DOT) (a/b), where r_v is the radius of equivolume sphere, (lambda) the wavelength of incident radiation, a/b the aspect ratio. If a/b <EQ 4, the coincidence of the results with those of the Separation of Variables Method is within 1 - 3% for r approximately equals 8 - 16 (Discrete Dipole Approximation) and r approximately equals 50 - 65 (T-Matrix Method). For the particles with a/b >= 10, the Separation of Variables Method is preferable, if 2(pi) r_v/(lambda) >= 2 - 3.