Abstract

The A_n of Mie scattering coefficients can be calculated by backward recurrence through a continued fraction technique,¹ but extra terms are needed to obtain a stabilized A_n value; thus forward recurrence is still preferred if the terms are needed before it becomes unstabilized. Using both forward and backward recurrence to study A_n, we are able to determine the term where the forward recurrence is still allowed. By relating it to the refractive index of the medium, we find in the nonabsorbing medium, the valid term is proportional to the product of the refractive index of the medium and its size parameter. As the imaginery refractive index increases the valid term decreases, but it reaches the minimum as the imaginary part equals the real part of the refractive index. Using the nonabsorbing medium as a reference, we determine the valid term as the imaginary refractive index is not zero. The relationship of the valid term vs the precision of the machine is under study. This research was done on a twelve-digit HP 9845.

© 1988 Optical Society of America