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Recurrence-based calculations of the scattering angle-dependent coefficients πn and τn (see Mie theory: Overview) require no special algorithms to minimize the rounding error effects. Following Wiscombe (1996) or Wiscombe (1980), these coefficients can be efficiently calculated by the upward recurrence as follows:
| τn = nt - πn | (1) |
| πn+1 = s + t (n + 1) / n | (2) |
where s = cosθ πn and t = s - πn-1. The required initial values for πn are:
| π0 = 0 | (3a) |
| π1 = 1 | (3b) |
| CITATION: Jonasz M. 2006. Mie theory: Algorithms for functions π and τ (www.tpdsci.com/Tpc/MieCalcPiTau.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 10-Mar-2006 Modified: 18-Apr-2006 Peer-reviewed: PENDING |
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