pyrt.henyey_greenstein_legendre_coefficients#

pyrt.henyey_greenstein_legendre_coefficients(asymmetry_parameter, n_coefficients)[source]#

Get the Legendre coefficients of a Henyey-Greenstein phase function.

Parameters:

asymmetry_parameter (float) – The Henyey-Greenstein asymmetry parameter. Must be between -1 and 1.
n_coefficients (int) – The number of coefficients to keep.

Returns:

1-dimensional arrray of Legendre coefficients up to the specificed number of coefficients.

Return type:

np.ndarray

Notes

The Henyey-Greenstein phase function can be decomposed as follows:

\[p(\mu) = \sum_{n=0}^{\infty} (2n + 1)g^n P_n(\mu)\]

where \(p\) is the phase function, \(\mu\) is the cosine of the scattering angle, \(n\) is the moment number, \(g\) is the asymmetry parameter, and \(P_n(\mu)\) is the \(n\)^th Legendre polynomial.

Examples

Get the first 129 coefficients of the Henyey-Greenstein phase function for a given asymmetry parameter.

>>> import numpy as np
>>> import pyrt
>>> g = 0.5
>>> coeff = pyrt.henyey_greenstein_legendre_coefficients(g, 129)
>>> coeff.shape
(129,)

Construct a Henyey-Greenstein phase function, decompose it, and see how this result compares to the analytic decomposition performed above.

>>> ang = np.linspace(0, 180, num=181)
>>> pf = pyrt.construct_henyey_greenstein(g, ang) * 4 * np.pi  # normalize it
>>> lc = pyrt.decompose(pf, ang, 129)
>>> print(np.amax(np.abs(lc - coeff)) < 1e-10)
True