SCATMECH > Classes and Functions > Property Models > Slope_Distribution_Function

Abstract class Slope_Distribution_Function

The abstract class Slope_Distribution_Function is used by Facet_BRDF_Model to store information about the distribution of facet slopes. As an abstract class, it contains no executable code. However, several specific classes inheriting its properties are provided. The user may provide other distribution functions for Facet_BRDF_Model by creating classes inheriting the properties of Slope_Distribution_Function.

Instantiable Models and Their Parameters:

Parameter Data Type Description Default
Unit_Slope_Distribution_Function:
A trivial slope distribution function which is uniform. It is not normalized, and so any model using it will not have absolute scaling. It is useful when one would like to evaluate the scattering per unit slope distribution function.
Unit_Slope_Distribution_Function has no parameters.
Exponential_Slope_Distribution_Function:
A slope distribution function that is exponentially distributed in slope.
s double The root-mean-square of the surface slope. 0.1
Gaussian_Slope_Distribution_Function:
A slope distribution function that is normally distributed in slope.
s double The root-mean-square of the surface slope. 0.1
Table_Slope_Distribution_Function:
A slope distribution function that is interpolated from a table of values.
T Table The table containing the distribution in slope. 1
Anisotropic_Exponential_Slope_Distribution_Function:
A slope distribution function that is exponential in each of the x and y directions, but can have a different decay constant for each of the two directions.
sx double The RMS slope in the x-direction. 0.1
sx double The RMS slope in the y-direction. 0.01
Ellipsoid_Slope_Distribution_Function:
A slope distribution function for a surface covered with ellipsoidal bumps or dips. The distribution can be anisotropic.
rx double Semiaxis of ellipsoids in x-direction [µm]. 10
ry double Semiaxis of ellipsoids in y-direction [µm]. 10
rz double Semiaxis of ellipsoids in z-direction (height or depth) [µm]. 1
density double Number density of ellipsoids on surface [µm-2]. 0.0001
Gaussian_Angle_Distribution_Function:
A slope distribution function which is Gaussian (normal) in the polar angle of the surface normal.
sigma double Standard deviation of the orientation angle [deg]. 5
Exponential_Angle_Distribution_Function:
A slope distribution function which is exponential in the polar angle of the surface normal.
sigma double Standard deviation of the orientation angle [deg]. 5
Table_Angle_Distribution_Function:
A slope distribution function which is given by a table specifying the distribution in the polar angle of the surface normal.
T Table The table containing the distribution in orientation angle. 1
Two_Slope_Distribution_Function:
A slope distribution function given by the sum of two other slope distribution functions.
s1 Slope_Distribution_Function The first slope distribution function.. Exponential_Slope_Distribution_Function
s2 Slope_Distribution_Function The second slope distribution function.. Exponential_Slope_Distribution_Function
fract double The relative amount of the second to the first slope distribution function. fract should be between 0 (all first slope distribution function) and 1 (all second slope distribution function). 0.5

See also:

SCATMECH Home,   Conventions,   Facet_BRDF_Model  

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Ant. and Prop. AP-16 (4), 449-454 (1968).

Include file:

#include "facet.h"

Source code:

facet.cpp

Definition of public elements:

class Slope_Distribution_Function : public Model {
    virtual double f(double slopex,double slopey);
};

typedef Model_Ptr<Slope_Distribution_Function> Slope_Distribution_Function_Ptr;

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double f(double slopex,double slopey)

This function evaluates the distribution function at the two-dimensional slope (slopex,slopey). If the local surface normal is (nx,ny,nz), the local surface slope in the x and y directions are
    \begin{eqnarray*}\zeta_x &=& n_x/n_z\\ \zeta_y &=& n_y/n_z\end{eqnarray*} .
The differential probability of a specific spot having a surface slope is
    $p(\zeta_x,\zeta_y)~{\rm d}\zeta_x \, {\rm d}\zeta_y$.

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Current SCATMECH version: 7.22 (April 2021)