opcsim.mie.coef_ab¶

opcsim.mie.coef_ab(refr, x)¶

Compute the external field coefficients using the logarithmic derivative.

Bohren and Huffman (1983) equations 4.88 and 4.89 show how to compute \(a_n\) and \(b_n\) using the logarithmic derivative (Aden, 1951).

\[a_n=\frac{[D_n(mx)/m + n/x]\psi_n(x) - \psi_{n-1}(x)}{[D_n(mx)/m + n/x]\xi_n(x) - \xi_{n-1}(x)},\]

\[b_n=\frac{[mD_n(mx) + n/x]\psi_n(x) - \psi_{n-1}(x)}{[mD_n(mx) + n/x]\xi_n(x) - \xi_{n-1}(x)}\]

where the logarithmic derivative is computed as:

\[D_{n-1}=\frac{n}{\rho}-\frac{1}{D_n + n/\rho}\]

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