pyrt.construct_henyey_greenstein#

pyrt.construct_henyey_greenstein(asymmetry_parameter, scattering_angles)[source]#

Construct a Henyey-Greenstein phase function.

Parameters:

asymmetry_parameter (float) – The Henyey-Greenstein asymmetry parameter. Must be between -1 and 1.
scattering_angles (ArrayLike) – 1-dimensional array of scattering angles [degrees].

Returns:

1-dimensiona phase function corresponding to each value in scattering_angles.

Return type:

np.ndarray

Notes

The Henyey-Greenstein phase function (per solid angle) is defined as

\[p(\theta) = \frac{1}{4\pi} \frac{1 - g^2} {[1 + g^2 - 2g \cos(\theta)]^\frac{3}{2}}\]

where \(p\) is the phase function, \(\theta\) is the scattering angle, and \(g\) is the asymemtry parameter.

Warning

The normalization for the Henyey-Greenstein phase function is not the same as for a regular phase function. For this phase function,

\[\int_{4\pi} p(\theta) = 1\]

not 4 \(\pi\)! To normalize it simply multiply the output by 4 \(\pi\).

Examples

Construct a Henyey-Greenstein phase function.

>>> import numpy as np
>>> import pyrt
>>> scattering_angles = np.arange(181)
>>> g = 0.5
>>> hg_pf = pyrt.construct_henyey_greenstein(g, scattering_angles)
>>> hg_pf.shape
(181,)