Abstract class BRDF_Model
The abstract class BRDF_Model handles the generic operations associated with any bidirectional reflectance distribution function (BRDF) scattering model and acts as an interface by which programs can access different models. A pointer to a BRDF_Model (or a BRDF_Model_Ptr, which is a typedef to Model_Ptr<BRDF_Model>) can point to one of any number of specific models.
The convention of BRDF_Model is that the function
Mueller returns the Mueller matrix BRDF in
the desired geometry. The function Jones returns
a JonesMatrix that upon typecasting to
MuellerMatrix is the Mueller matrix BRDF.
Classes inheriting BRDF_Model are required to provide either a function
jones or mueller, returning these matrices. The class BRDF_Model provides
these functions with four variables of type double: thetai, thetas, phis, and rotation, specifying
the angles 
i,
s,
s, and β, respectively, defined in the figure
below.
The angle i (thetai) is defined as the angle that a vector
pointing to the source makes with respect to the surface
normal. The angle s (thetas) is the angle that a vector pointing in
the scattering direction makes with respect to the surface
normal. The angle s (phis) is the azimuthal angle of the scattered
light, measured in a right-handed fashion about the surface
normal from the plane defined by the incident direction and
the surface normal. Finally, the angle β (rotation) represents the rotation of the
sample in a counterclockwise fashion.
To write your own BRDF_Model class, see the outline given in "Writing your own BRDF model."
Parameters:
| Parameter | Data Type | Description | Default |
|---|---|---|---|
| lambda | double | Wavelength of the light in vacuum [µm]. | 0.532 |
| type | int |
Indicates whether the light is incident from above the
substrate or from within the substrate and whether the
scattering is evaluated in reflection or transmission.
The choices are: 0 : Light is incident from the above the substrate, and scattering is evaluated in reflection. 1 : Light is incident from the above the substrate, and scattering is evaluated in transmission. 2 : Light is incident from within the substrate, and scattering is evaluated in reflection. 3 : Light is incident from within the substrate, and scattering is evaluated in transmission. For 1, 2, and 3, the substrate must be non-absorbing. Not all modes are supported for all models inheriting BRDF_Model. |
0 |
| substrate | dielectric_function | The optical constants of the substrate, expressed as a complex number (n,k) or, optionally, as a function of wavelength. | (4.05,0.05) |
See also:
SCATMECH Home, Conventions, MuellerMatrix, JonesMatrix, List of child classes
J. C. Stover, Optical Scattering: Measurement and
Analysis, (SPIE Optical Engineering Press, Bellingham,
WA, 1995).
D. S. Flynn and C. Alexander,
"Polarized surface scattering expressed in terms of a
bidirectional reflectance distribution function matrix,"
Opt. Eng. 34(6), 1646-1650 (1995).
Include file:
#include "brdf.h"
Source code:
brdf.cpp reg_brdf.cpp
Definition of public and protected elements:
class BRDF_Model : public Model { public: enum Coordinate_System {psps = 0,xyxy = 1,plane = 2}; enum { Type_DOWNUP = 0, Type_DOWNDOWN = 1, Type_UPDOWN = 2, Type_UPUP = 3 }; JonesMatrix Jones(double thetai, double thetas, double phis, double rotation, Coordinate_System cs = psps); MuellerMatrix Mueller(double thetai, double thetas, double phis, double rotation, Coordinate_System cs = psps); JonesMatrix Jones(Vector& source, Vector& viewer, Vector& normal, Vector& xaxis, Coordinate_System cs = plane); MuellerMatrix Mueller(Vector& source, Vector& viewer, Vector& normal, Vector& xaxis, Coordinate_System cs = plane); Coordinate_System get_model_cs(); protected: virtual void setup(); Coordinate_System model_cs; virtual JonesMatrix jones(); virtual MuellerMatrix mueller(); double thetai; double thetas; double phii; double rotation; }; typedef Model_Ptr<BRDF_Model> BRDF_Model_Ptr;
double thetai
double thetas
double phis
double rotation
These variables represent the geometry for which the calculation is to be performed. They are set by the public functions Mueller() and Jones(). They are used by the functions mueller() or jones().
The variable thetai is the incident polar angle in radians.
The variable thetas is the scattering polar angle in radians.
The variable phis is the scattering azimuthal angle in radians.
The variable rotation is the rotation angle of the sample in radians about the surface normal.
enum Coordinate_System
Coordinate_System
model_cs
Coordinate_System
get_model_cs()
This variable stores the coordinate system for which the scattering is defined in the code. By default, it is set to BRDF_Model::psps. A scattering model which inherits the properties of BRDF_Model and which has its scattering defined with respect to another coordinate system should set this variable in its constructor. The value can be publicly queried using get_model_cs.
The different coordinate systems are:
BRDF_Model::psps - This coordinate system uses the standard {s,p,k} right-handed basis vectors appropriate for both the incident and scattered light. The k direction is the respective direction of propagation, the s direction is parallel to the plane defined by k and the surface normal, and the p direction is perpendicular to that plane. Most models are coded using this coordinate system.
BRDF_Model::xyxy - This coordinate system uses the same coordinates as BRDF_Model::psps for the incident light, but rotates the scattered light coordinates by the angle phis. Near the surface normal, this coordinate system is close to the directions x and y, where x is a vector in the plane of incidence and the plane of the sample, and y is a vector perpendicular to the plane of incidence. This coordinate system removes an apparent singularity which exists at the surface normal using the BRDF_Model::psps coordinate system.
BRDF_Model::plane - This coordinate system is defined by the plane which includes the incident and scattered directions. The basis vectors are parallel and perpendicular to this plane, respectively, for both the incident and the scattered light. This coordinate system may be more appropriate than the others for rendering applications.
JonesMatrix Jones(double thetai,
double thetas, double phis, double rotation,
Coordinate_System cs)
MuellerMatrix
Mueller(double thetai, double thetas,
double phis, double rotation,
Coordinate_System cs)
Example:These public functions return the Jones matrix or the Mueller matrix associated with the model, as a function of scattering geometry and polarization coordinate system. The value of cs defines the coordinate system for which the scattering matrix will be returned.
double ti,ts,ps;
JonesVector incidentlight;
BRDF_Model *model;
JonesVector jones = model->Jones(ti,ts,ps,0,
BRDF_Model::plane)*incidentlight;
JonesMatrix Jones(Vector& source,
Vector& viewer, Vector& normal,
Vector& xaxis,Coordinate_System cs)
MuellerMatrix
Mueller(Vector& source, Vector& viewer,
Vector& normal,
Vector& xaxis,Coordinate_System cs)
Example:These public functions return the Jones matrix or the Mueller matrix associated with the model, as a function of scattering geometry and polarization coordinate system. The value of cs defines the coordinate system for which the scattering matrix will be returned. source is a Vector pointing from the sample to the light source. viewer is a Vector pointing in the scattering direction. normal is a Vector pointing in the outward surface normal. xaxis is a Vector which must have a component along the substrate surface, and defines the x-axis of that surface.Neither source, viewer, normal, or xaxis need be normalized. If xaxis is the zero vector, the sample rotation will be set to zero degrees.
Note that the coordinate system defaults to BRDF_Model::plane, which is most natural for rendering applications.
The following is an example of how one might use the Vector-based Mueller function. The sample is assumed to be tilted in the y-direction by an angle tilt, while the light is incident at an angle thetai and the receiver is collecting light at a polar angle of thetas and azimuthal angle phis.
Vector source(-sin(thetai),0.,cos(thetai));
Vector receiver(sin(thetas)*cos(phis),sin(thetas)*sin(phis),cos(thetas));
Vector normal(0.,sin(tilt),cos(tilt));
StokesVector incidentlight;
Some_BRDF_Model model; // Assume that Some_BRDF_Model is a BRDF_Model...
StokesVector stokes = model.Mueller(source,
receiver,
normal,
Vector(0,0,0))*incidentlight;
virtual void setup()
All functions that modify model parameters set Model::recalc to a non-zero value. The function setup() performs any housekeeping that is necessary if parameters have been changed. All inherited classes should have such a setup() function if they require such operations. They should all begin by calling the parent's setup() function.
virtual JonesMatrix jones()
This function returns the Jones scattering matrix. It uses the variables thetai, thetas, phis, and rotation, defined above. If this function is not defined for an inherited class, it throws an exception if called. One of the functions, mueller or jones, must be defined by any inherited class.
virtual MuellerMatrix mueller()
This function returns the Mueller matrix BRDF. It uses the variables thetai, thetas, phis, and rotation, defined above. If this function is not defined for an inherited class, it defaults to a JonesMatrix to MuellerMatrix conversion. One of the functions, mueller or jones, must be defined by any inherited class.
typedef Model_Ptr<BRDF_Model> BRDF_Model_Ptr
The typedef BRDF_Model_Ptr behaves like a pointer to an instance of class BRDF_Model. The following statement will query the user for an instance of class BRDF_Model:
BRDF_Model_Ptr model = Get_Model_Ptr();
The next statement will also create an instance of class BRDF_Model:
BRDF_Model_Ptr model = "Microroughness_BRDF_Model";
See Model_Ptr<model>.
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Current SCATMECH version: 7.22 (April 2021)