Pi¶

pyvsim.MieUtils.Pi(nmax, costheta)[source]¶

Returns a generator for the recursive calculation of the Pi function as defined in “Hahn, D. W. Light scattering theory Department of Mechanical and Aeorospace Engineering, University of Florida, 2009”, which is:

\[\Pi_n(cos \theta) = {P_n^{(1)} (cos \theta) \over sin(\theta)}\]

Where:

\[P_n^{(1)} \]

is a Legendre polynomial

Or, in the recursive form, as shown in Maetzler (Maetzler, C. Matlab functions for Mie scattering and absorption Institute of Applied Physics, University of Bern, 2002):

\[\Pi_n = {{2n-1} \over {n-1}} cos(\theta) P_{n-1} - {n \over {n-1}} \Pi_{n-2}\]

With:

\[\Pi_{0} = 0\]\[\Pi_{1} = 1 \]

Parameters :	nmax : int The number of coefficients to be calculated costheta: np.array (N) : The angles (in radians) to be used as input to the Pi function
Returns :	Pi : generator A generator capable of creating an \((N+1)\)-sized array with the values of the \(\Pi\) function