.. _phase-tabphase_polarized:

Lookup table (polarized) phase function (:monosp:`tabphase_polarized`)
------------------------------------------------

.. pluginparameters::

 * - m11
   - |string|
   - A comma-separated list of phase matrix coefficient 1,1 of the
     phase function, parametrized by the cosine of the scattering angle.
   - |exposed|

 * - m12
   - |string|
   - A comma-separated list of phase matrix coefficient 1,2 of the
     phase function, parametrized by the cosine of the scattering angle.
   - |exposed|

 * - m22
   - |string|
   - A comma-separated list of phase matrix coefficient 2,2 of the
     phase function, parametrized by the cosine of the scattering angle.
   - |exposed|

 * - m33
   - |string|
   - A comma-separated list of phase matrix coefficient 3,3 of the
     phase function, parametrized by the cosine of the scattering angle.
   - |exposed|

 * - m34
   - |string|
   - A comma-separated list of phase matrix coefficient 3,4 of the
     phase function, parametrized by the cosine of the scattering angle.
   - |exposed|

 * - m44
   - |string|
   - A comma-separated list of phase matrix coefficient 4,4 of the
     phase function, parametrized by the cosine of the scattering angle.
   - |exposed|

 * - nodes
   - |string|
   - A comma-separated list of :math:`\cos \theta` specifying the grid on which
     `values` are defined. Bounds must be [-1, 1] and values must be strictly
     increasing. Must have the same length as `values`.
   - |exposed|

This plugin implements a generic phase function model for isotropic media
parametrized by a lookup table giving values of the phase function as a
function of the cosine of the scattering angle.

.. admonition:: Notes

   * The scattering angle cosine is here defined as the dot product of the
     incoming and outgoing directions, where the incoming, resp. outgoing
     direction points *toward*, resp. *outward* the interaction point.
   * From this follows that :math:`\cos \theta = 1` corresponds to forward
     scattering.
   * Lookup table points are regularly spaced between -1 and 1.
   * Phase function values are automatically normalized.
   * For polarized phase functions, this assumes (for the time being) the
     structure of a phase function with spherically symmetric particles,
     i.e. there are only four unique elements of the Mueller matrix:
     `M_{11}`, `M_{12}`, `M_{33}`, and `M_{34}`