Abstract class Polarized_Phase_Function


The abstract class Polarized_Phase_Function adds the polarization behavior and the coefficients for absorption and scattering to Phase_Function. This class is used to store information about the angular distribution of scattering in bulk material, needed for example, by First_Diffuse_BRDF_Model. While the code is configured to handle anisotropy, no models currently use that feature.

The following models are available:

Instantiable Models and Their Parameters:

Parameter Data Type Description Default
Unpolarized_Phase_Function:
This model is a completely depolarizing phase function.
phase_function Phase_Function_Ptr The scalar part of the phase function. Henyey_Greenstein_Phase_Function
log_absorption double The natural logarithm of the Naperian absorption coefficient [1/µm]. -20
log_scattering double The natural logarithm of the Naperian scattering coefficient [1/µm]. 0
CodeWhitney_Phase_Function:
The phase function defined by Code and Whitney [A.D. Code and B.A. Whitney, "ePolarization from scattering in blobs,"e; Astrophysical Journal 441, 400-407 (1995)], adapted to allow for any scalar phase function. That is, the polarized phase function is given by \begin{equation} {\bf P}(\theta)=p(\theta)\times\left( \begin{array}{cccc} 1 & - p_l \sin^2\theta-1)/(1+\cos^2\theta) & 0 & 0 \\ - p_l \sin^2\theta-1)/(1+\cos^2\theta) & 1 & 0 & 0 \\ 0 & 0 & 2 \cos\theta/(1+\cos^2\theta) & p_c \sin\theta_f/(1+\cos^2\theta_f) \\ 0 & 0 & - p_c \sin\theta_f/(1+\cos^2\theta_f) & 2 \cos\theta/(1+\cos^2\theta) \end{array}\right) \end{equation} where $p(\theta)$ is the scalar phase function, $\theta_f = \theta [1+3.13 s \exp(-7\theta/\pi)]$, and $p_l$, $p_c$, and $s$ are parameters.
phase_function Phase_Function_Ptr The scalar part of the phase function. Henyey_Greenstein_Phase_Function
log_absorption double The natural logarithm of the Naperian absorption coefficient [1/µm]. -20
log_scattering double The natural logarithm of the Naperian scattering coefficient [1/µm]. 0
plmax double The maximum degree of linear polarization, $p_l$. 1
pcmax double The maximum degree of circular polarization, $p_c$. 0
s double The circular polarization asymmetry parameter, $s$. 0
Constrained_Phase_Function:
The phase function defined by Germer [T.A. Germer, "e;Polarized single-scattering phase function determined for a common reflectance standard from bidirectional reflectance measurements,"e; Proc. SPIE 10655, 1065504 (2018)]. It defines values for the polarized part of the phase function at 0°, 60°, 120°, and 180°, imposing requirements in the forward and backward scattering direction, and performing a cubic spline for all other angles. The phase function is given by \begin{equation} {\bf P}(\theta)=p(\theta)\times\left( \begin{array}{cccc} 1 & m_{01} & 0 & 0 \\ m_{01} & m_{11} & 0 & 0 \\ 0 & 0 & m_{22} & m_{23} \\ 0 & 0 & -m_{23} & m_{33} \end{array}\right) \end{equation}
phase_function Phase_Function_Ptr The scalar part of the phase function. Henyey_Greenstein_Phase_Function
log_absorption double The natural logarithm of the Naperian absorption coefficient [1/µm]. -20
log_scattering double The natural logarithm of the Naperian scattering coefficient [1/µm]. 0
m11_0 double The value of $m_{11}$ and $m_{22}$ at $\theta = 0^\circ$. 1
m11_60 double The value of $m_{11}$ at $\theta = 60^\circ$. 0
m11_120 double The value of $m_{11}$ at $\theta = 120^\circ$. 0
m11_180 double The value of $m_{11}$ and $-m{22}$ at $\theta = 180^\circ$. 0
m22_60 double The value of $m_{22}$ at $\theta = 60^\circ$. 0
m22_120 double The value of $m_{22}$ at $\theta = 120^\circ$. 0
m33_0 double The value of $m_{33}$ at $\theta = 0^\circ$. 1
m33_60 double The value of $m_{33}$ at $\theta = 60^\circ$. 1
m33_120 double The value of $m_{33}$ at $\theta = 120^\circ$. 1
m33_180 double The value of $m_{33}$ at $\theta = 180^\circ$. 1
m10_60 double The value of $m_{10}$ at $\theta = 60^\circ$. 0
m10_120 double The value of $m_{10}$ at $\theta = 120^\circ$. 0
m23_60 double The value of $m_{23}$ at $\theta = 60^\circ$. 0
m23_120 double The value of $m_{23}$ at $\theta = 120^\circ$. 0
SphericalScatterer_Phase_Function:
This model uses a SphericalScatterer to determine the phase function.
scatterer SphericalScatterer_Ptr The model for a spherical scatterer. MieScatterer
volume_density double The volume number density of scatterers [&\micro;m-3]. 1E-4
Distributed_Mie_Phase_Function:
This model averages the Mie scattering function over a distribution of sphere sizes to determine the phase function.
lambda double The wavelength of the light in vacuum. 0.532
medium dielectric_function The optical constants of the medium surrounding the spheres, expressed as a complex number (n,k) or, optionally, as a function of wavelength. 0.532
sphere dielectric_function The optical constants of the spheres, expressed as a complex number (n,k) or, optionally, as a function of wavelength. 0.532
distribution VolumeParticleSizeDistribution_Ptr The diameter distribution and number of spheres. VolumeParticleSizeDistribution
integralStart double The starting diameter for the integral over diameter [µm]. 0.1
integralEnd double The ending diameter for the integral over diameter [µm]. 100
integralStep double The fractional step diameter for integration. (The integral is performed logarithmically.) 0.01

See also:

SCATMECH Home,   First_Diffuse_BRDF_Model,   Phase_Function  

Include file:

#include "phasefunction.h"

Source code:

phasefunction.cpp

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Current SCATMECH version: 7.22 (April 2021)