SCATMECH > Classes and Functions > Property Models > PSD_Function

Abstract class PSD_Function

The abstract class PSD_Function is used by Roughness_BRDF_Model to store information about the power spectral density (PSD) function of the surface height function. The user may provide other PSD functions for Roughness_BRDF_Model by creating classes inheriting the properties of PSD_Function. There are several classes inheriting the properties of Slope_Distribution_Function.

Instantiable Models and Their Parameters:

Parameter Data Type Description Default
Unit_PSD_Function:
A trivial power spectral density function that is uniform with unit value. 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 of power spectral density.
Unit_PSD_Function has no parameters.
ABC_PSD_Function:
A power spectrum that is given by $S_2(f)=A/(1+B^2f^2)^{C/2}$.
A double Parameter A [µm4] 0.01
B double Parameter B [µm] 362
C double Parameter C 2.5
Table_PSD_Function:
A power spectrum that is interpolated from a table of values.
T Table The table containing the PSD. 1
Fractal_PSD_Function:
A power spectrum that is given by $S_2(f)=A/f^\gamma$.
A double Power spectrum amplitude factor [µm4] 0.01
exponent double The fractal exponent $\gamma$. 2.5
Gaussian_PSD_Function:
A power spectrum appropriate for a Gaussian rough surface.
sigma double The standard deviation of the surface height [µm] 0.05
length double The lateral correlation length [µm] 5
Elliptical_Mesa_PSD_Function:
A power spectrum appropriate for elliptical mesas. That is, the surface is assumed to be zero everywhere outside of the ellipse, and a given height inside of it. The surface is assumed to be covered with a given density of these features.
axisx double The length of the axis of the ellipse along the x-direction [µm] 1.5
axisy double The length of the axis of the ellipse along the y-direction [µm] 1.5
height double The height or depth of the mesas [µm] 0.01
density double The surface number density of the ellipses [µm-2] 0.01
Rectangular_Mesa_PSD_Function:
A power spectrum appropriate for rectangular mesas. That is, the surface is assumed to be zero everywhere outside of the rectangle, and a given height inside of it. The surface is assumed to be covered with a given density of these features.
lengthx double The length of the rectangle along the x-direction [µm] 1.5
lengthy double The length of the rectangle along the y-direction [µm] 1.5
height double The height or depth of the mesas [µm] 0.01
density double The surface number density of the rectangles [µm-2] 0.01
Triangular_Mesa_PSD_Function:
A power spectrum appropriate for equilateral triangular mesas. That is, the surface is assumed to be zero everywhere outside of the equilateral triangle, and a given height inside of it. The surface is assumed to be covered with a given density of these features.
side double The length of the sides of the triangle [µm] 1.5
height double The height or depth of the mesas [µm] 0.01
density double The surface number density of triangles [µm-2] 0.01
Rectangular_Pyramid_PSD_Function:
A power spectrum appropriate for rectangular pyramids. The surface is assumed to be covered with a given density of these features.
lengthx double The length of the rectangular base along the x-direction [µm] 1.5
lengthy double The length of the rectangular base along the y-direction [µm] 1.5
height double The height or depth of the pyramids [µm] 0.01
density double The surface number density of the pyramids [µm-2] 0.01
Triangular_Pyramid_PSD_Function:
A power spectrum appropriate for pyramids with triangular base. The surface is assumed to be covered with a given density of these features.
side double The length of the sides of the triangular base [µm] 1.5
height double The height or depth of the pyramids [µm] 0.01
density double The surface number density of pyramids [µm-2] 0.01
Parabolic_Dimple_PSD_Function:
A power spectrum appropriate for elliptical features, whose profile is parabolic in nature. That is, the surface is assumed to be zero everywhere outside of the ellipse, has a maximum height or depth at its center, and decays parabolically to the edge of the ellipse. For small heights, this surface approximates ellipsoidal dimples or mounds. The surface is assumed to be covered with a given density of these features.
axisx double The length of the axis of the ellipse along the x-direction [µm] 1.5
axisy double The length of the axis of the ellipse along the y-direction [µm] 1.5
height double The height or depth of the dimple or mound [µm] 0.01
density double The surface number density of the features. [µm-2] 0.01
Double_PSD_Function:
A power spectrum given by the sum of any two other power spectra.
psd1 PSD_Function_Ptr The first power spectrum. ABC_PSD_Function
psd2 PSD_Function_Ptr The second power spectrum. ABC_PSD_Function

See also:

SCATMECH Home,   Conventions,   Roughness_BRDF_Model  

Include file:

#include "rough.h"

Source code:

rough.cpp

Definition of public elements:

class PSD_Function : public Model {
    virtual double PSD(double freqx, double freqy) = 0;
};

typedef Model_Ptr<PSD_Function> PSD_Function_Ptr;

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double PSD(double freqx,double freqy)

This function evaluates the PSD function at the two-dimensional spatial frequency (freqx,freqy). This function is defined as the two-dimensional PSD function, evaluated along the (x,y) direction.

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Current SCATMECH version: 7.22 (April 2021)