When a particle dimension is comparable to the laser light wavelength, scattering calculations require the use of Mie or similar infinite series. The terms in the series may be an infinite set of complex determinants. Despite the power of modern computers these equations are difficult to compute with, because of the lack of analytical criteria for terminating the computations. Commonly, the series computations are stopped when the value of the series is changed by an amount less than a predetermined factor as a result of the addition of the computed term. This procedure has led to large errors. These series are easily transformed into the continued fraction form of the Fsad6 approximates. Complex continued fractions are more stable, computationally, than infinite series and frequently converge more rapidly. Further, an anlytical test exists for determining the circular domain within which the value of the continued fraction must lie. This permits an accurate and precise delineation of the maximum residual error. There is a disadvantage in the use of continued fractions. If the order of the creates convergent is not great enough for the desired accuracy, the computation must be repeated. This is not a serious handicap in actual use.
Thomas Y. Palmer,
"MIE Scattering From Continued Fractions", Proc. SPIE 0125, Advances in Laser Technology for the Atmospheric Sciences, (18 November 1977); doi: 10.1117/12.955878; https://doi.org/10.1117/12.955878