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SCATMECH > Classes and Functions >
Polarization >
StokesVector
class StokesVector
The class StokesVector represents a Stokes vector in
the Stokes-Mueller representation of polarization states.
Arithmetic operations between Mueller matrices and Stokes
vectors, various properties of a Stokes vector, and
transformation operations are defined.
The elements of the Stokes vector are
(Is+Ip,
Is-Ip, Is+p-Is-p,
Ilcp-Ircp), where
Is is the intensity of the light
polarized in the s-direction, Ip is the
intensity of the light polarized in the p-direction,
Is+p is the intensity of the light
polarized in the s+p-direction, Is-p is
the intensity of the light polarized in the s-p-direction,
Ilcp is the left circularly polarized
intensity, Ircp is the right circularly
polarized intensity,
Include file:
#include "mueller.h"
Source code:
stokes.cpp
See also:
SCATMECH Home,
Conventions, MuellerMatrix, JonesMatrix, JonesVector
C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).
H.C. van de Hulst, Light Scattering by Small Particles, (Dover, New York, 1981).
R.A. Chipman, "Polarimetry." in Handbook of Optics, (McGraw-Hill, New York, 1995).
Definition of public
elements:
class StokesVector {
public:
StokesVector();
StokesVector(double I,double Q,double U,double V);
StokesVector(const StokesVector& x);
StokesVector(const JonesVector& j);
StokesVector& operator=(const StokesVector& x);
double& I();
double I() const;
double& Q();
double Q() const;
double& U();
double U() const;
double& V();
double V() const;
double& operator[](int i);
double operator[](int i) const;
StokesVector operator*(const MuellerMatrix& matrix) const;
double operator*(const StokesVector& a) const;
StokesVector operator+(const StokesVector& a) const;
StokesVector operator-(const StokesVector& a) const;
StokesVector operator-() const;
StokesVector operator*(double d) const;
friend StokesVector operator*(double d,const StokesVector& s);
StokesVector& operator*=(double d);
StokesVector operator/(double d) const;
StokesVector& operator/=(double d);
StokesVector rotate(double angle) const;
double eta() const;
double intensity() const;
double DOLP() const;
double DOP() const;
double DOCP() const;
double e() const;
double delta() const;
double psi() const;
double eccentricity() const;
bool valid() const;
StokesVector pol_part() const;
StokesVector unpol_part() const;
};
ostream& operator<<(ostream& os,const StokesVector& j);
istream& operator>>(istream& is, StokesVector& j);
StokesVector()
The default constructor leaves the elements unassigned.
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StokesVector(double I,double Q,double U,double V)
Constructor for a StokesVector that initializes
the vector with four real numbers.
Example:
StokesVector s(1,0,0,0); // Unpolarized light of unity intensity
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StokesVector(const StokesVector& x)
Copy constructor.
Example:
StokesVector a;
StokesVector b(a);
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StokesVector(const JonesVector& j)
Constructor that converts a JonesVector to a
StokesVector.
Example:
JonesVector j;
StokesVector s(j);
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StokesVector& operator=(const StokesVector& x)
Assignment operator.
Example:
StokesVector a,b
a=b;
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Operators that return references to each of the elements
of the StokesVector, using the notation (I,Q,U,V).
Example:
StokesVector s;
// Circularly polarized light:
s.I()=1.;
s.Q()=0.;
s.U()=0.;
s.V()=1.;
cout << s.I() << '/t' << s.Q() << '/t' << s.U() << '/t' << s.V() << '/t' << endl;
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Operators that returns a reference to a specific element
by number.
Example:
StokesVector s;
// Circularly polarized light...
s[0]=1.;
s[1]=0.;
s[2]=0.;
s[3]=1.;
cout << s[0] << '/t' << s[1] << '/t' << s[2] << '/t' << s[3] << '/t' << endl;
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StokesVector operator*(const MuellerMatrix& matrix) const
Right multiplication of a StokesVector by a
MuellerMatrix.
Example:
StokesVector vector;
MuellerMatrix matrix;
vector = vector*matrix;
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double operator*(const StokesVector& a) const
Scalar product between two StokesVector objects.
Example:
StokesVector vector1,vector2;
double scalar = vector1*vector2;
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StokesVector operator+(const StokesVector& a) const
StokesVector operator-(const StokesVector& a) const
Addition or subtraction of two StokesVector
objects.
Example:
StokesVector vector1,vector2,vector3;
vector3 = vector1+vector2;
vector3 = vector1-vector2;
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Negation of a StokesVector.
Example:
StokesVector vector;
vector = -vector;
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Multiplication and division of a StokesVector by a
scalar.
Example:
StokesVector vector;
double scalar;
vector = vector*scalar;
vector = scalar*vector; // Same thing.
vector *= scalar; // Also same thing.
vector = vector/scalar;
vector /= scalar; // Same thing.
vector = scalar/vector; // Not allowed.
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Function that returns a StokesVector rotated by
some angle. The vector is rotated in a clockwise
direction for positive angle.
Example:
StokesVector a,b;
a = b.rotate(45.*PI/180.); // rotate b by 45 degrees.
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Function that returns the principal angle of the
polarization. The angle is measured counterclockwise from
s-polarization.
Example:
StokesVector a;
cout << "Principal angle = " << a.eta()/PI*180. << " degrees" << endl;
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Function that returns the intensity associated with a
StokesVector. This function is equivalent to
I().
Example:
StokesVector a;
cout << "Intensity = " << a.intensity() << endl;
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Functions that return the degrees of linear polarization
(DOLP), full polarization (DOP), and
circular polarization (DOCP). The degree of
circular polarization is positive for left-circularly
polarized light.
Example:
StokesVector a;
cout << "Degrees of polarization: " << endl
<< "DOLP: " << a.DOLP() << endl
<< "DOP: " << a.DOP() << endl
<< "DOCP: " << a.DOCP() << endl;
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Function that returns the ellipticity of the field (ratio
of minor axis to major axis).
Example:
StokesVector a;
cout << "Ellipticity = " << a.e() << endl;
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Function that returns the phase difference between the
two components of the light.
Example:
StokesVector a;
cout << "delta = " << a.delta() << endl;
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Function that returns the arc tangent of the ratio
between the two components of the polarized part of the
light. The returned value is zero for p-polarized light.
Example:
StokesVector a;
cout << "delta = " << a.delta() << endl;
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Function that returns the eccentricity of the light.
Example:
StokesVector a;
cout << "eccentricity = " << a.eccentricity() << endl;
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Function that returns true if the Stokes vector is physically valid and false otherwise. It
checks that the first element is greater than or equal to the square rooot of the sum of squares of
the other elements.
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Functions that return the polarized and unpolarized parts
of a StokesVector.
Example:
StokesVector a,pol,unpol;
pol = a.pol();
unpol = a.unpol();
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Operator that prints a StokesVector to an output
stream. The output contains four floating point numbers, separated by commas, and surrounded by parentheses, e.g.,
(5.321,3.432,-2.332,1.034)
Example:
StokesVector a;
cout << "a = " << a << endl;
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Operator that reads a StokesVector from an input
stream. The input must contain four floating point numbers, separated by commas, and be surrounded by parentheses, e.g.,
(5.321,3.432,-2.332,1.034).
Example:
StokesVector a;
cin >> a;
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Current SCATMECH version: 7.22 (April 2021)
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