StokesVector Class Reference

#include <StokesVector.hpp>

Inheritance diagram for StokesVector:

Public Member Functions
	StokesVector ()
	StokesVector (double I, double Q, double U, double V, Direction n)
void	applyMueller (double S11, double S12, double S22, double S33, double S34, double S44)
void	applyMueller (double S11, double S12, double S33, double S34)
bool	isPolarized () const
double	linearPolarizationDegree () const
Direction	normal () const
double	polarizationAngle () const
double	rotateIntoPlane (Direction k, Direction knew)
void	rotateStokes (double phi, Direction k)
void	setPolarized (const StokesVector &polarization)
void	setPolarized (double I, double Q, double U, double V)
void	setPolarized (double I, double Q, double U, double V, Direction n)
void	setUnpolarized ()
void	stokes (double &I, double &Q, double &U, double &V)
double	stokesI () const
double	stokesQ () const
double	stokesU () const
double	stokesV () const
double	totalPolarizationDegree () const

Private Attributes
Direction	_normal
bool	_polarized
double	_Q
double	_U
double	_V

Detailed Description

An object of the StokesVector class describes the polarization state of a photon packet, and offers functions to apply certain transformations to it. Specifically, a Stokes vector contains the four Stokes parameters \(I\), \(Q\), \(U\), and \(V\) that are defined with respect to a reference direction. For efficiency reasons we store the normal to the propagation direction of the photon and the Stokes vector reference direction instead of the reference direction itself. The first parameter ( \(I\)) indicates the total intensity, and the remaining parameters ( \(Q\), \(U\), and \(V\)) represent various degrees of linear and circular polarization. Stokes parameters have a dimension of intensity. However, in our implementation, the parameters are normalized to dimensionless values through division by \(I\). Consequently \(I=1\) at all times, so that this parameter does not need to be stored. As the StokesVector does not store the propagation direction, it has to be provided for most transformations. The StokesVector is initialized in an unpolarized state. While unpolarized, the stored normal is the zero vector.

Constructor & Destructor Documentation

StokesVector() [1/2]

StokesVector::StokesVector ( )

inline

The default constructor initializes the Stokes vector to an unpolarized state.

StokesVector() [2/2]

StokesVector::StokesVector	(	double	I,
		double	Q,
		double	U,
		double	V,
		Direction	n
	)

This constructor initializes the Stokes vector to the specified parameter values, after normalizing them through division by \(I\). If \(I=0\), the Stokes vector is set to an unpolarized state.

Member Function Documentation

applyMueller() [1/2]

void StokesVector::applyMueller	(	double	S11,
		double	S12,
		double	S22,
		double	S33,
		double	S34,
		double	S44
	)

This function transforms the polarization state described by this Stokes vector by applying to its existing state a Mueller matrix of the form

\[ {\bf{M}} \propto \begin{pmatrix} {\rm S}_{11} & {\rm S}_{12} & 0 & 0 \\ {\rm S}_{12} & {\rm S}_{22} & 0 & 0 \\ 0 & 0 & {\rm S}_{33} & {\rm S}_{34} \\ 0 & 0 & -{\rm S}_{34} & {\rm S}_{44} \end{pmatrix}, \]

assuming that \({\rm S}_{21} = {\rm S}_{12}\) and \({\rm S}_{43} = -{\rm S}_{34}\).

applyMueller() [2/2]

void StokesVector::applyMueller	(	double	S11,
		double	S12,
		double	S33,
		double	S34
	)

This function transforms the polarization state described by this Stokes vector by applying to its existing state a Mueller matrix of the form

\[ {\bf{M}} \propto \begin{pmatrix} {\rm S}_{11} & {\rm S}_{12} & 0 & 0 \\ {\rm S}_{12} & {\rm S}_{11} & 0 & 0 \\ 0 & 0 & {\rm S}_{33} & {\rm S}_{34} \\ 0 & 0 & -{\rm S}_{34} & {\rm S}_{33} \end{pmatrix}, \]

assuming that \({\rm S}_{21} = {\rm S}_{12}\), \({\rm S}_{43} = -{\rm S}_{34}\), \({\rm S}_{22} = {\rm S}_{11}\) and \({\rm S}_{44} = {\rm S}_{44}\).

isPolarized()

bool StokesVector::isPolarized ( ) const

inline

This function returns true if the Stokes vector represents polarised radiation, and false if it represents unpolarised radiation.

linearPolarizationDegree()

double StokesVector::linearPolarizationDegree

(

)

const

This function returns the linear polarization degree for the Stokes vector.

normal()

Direction StokesVector::normal ( ) const

inline

This function returns the normal to the propagation direction of the photon and the reference direction in which the Stokes vector is defined. If the Stokes vector is in an unpolarized state, the zero vector is returned.

polarizationAngle()

double StokesVector::polarizationAngle

(

)

const

This function returns the polarization position angle in radians for the Stokes vector.

rotateIntoPlane()

double StokesVector::rotateIntoPlane	(	Direction	k,
		Direction	knew
	)

This function adjusts the stokes vector reference axis so it is in the plane of the given propagation direction \(\bf{k}\) and any direction \(\bf{knew}\). The stored Stokes parameters are updated and the reference direction created if necessary. The function returns the angle by which the reference axis was rotated.

rotateStokes()

void StokesVector::rotateStokes	(	double	phi,
		Direction	k
	)

This function adjusts the Stokes vector for a rotation of the reference axis about the given flight direction \(\bf{k}\) over the specified angle \(\phi\), clockwise when looking along \(\bf{k}\). Such rotation is described by the transformation matrix

\[ {\bf{R}} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos 2\phi & \sin 2\phi & 0 \\ 0 & -\sin 2\phi & \cos 2\phi & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}. \]

setPolarized() [1/3]

void StokesVector::setPolarized

(

const StokesVector &

polarization

)

This function copies the specified Stokes vector into the receiver.

setPolarized() [2/3]

void StokesVector::setPolarized	(	double	I,
		double	Q,
		double	U,
		double	V
	)

This function sets the Stokes vector to the specified vector components leaving the normal to the reference direction unchanged. This function can be used when the reference direction should not be updated, or in case it is determined by an external convention and no further transformations will be performed on the Stokes vector. The \(Q, U, V\) components are normalized through division by \(I\). If \(I=0\), the Stokes vector is set to an unpolarized state.

setPolarized() [3/3]

void StokesVector::setPolarized	(	double	I,
		double	Q,
		double	U,
		double	V,
		Direction	n
	)

This function sets the Stokes vector to the specified vector components and the specified normal to the reference direction. The \(Q, U, V\) components are normalized through division by \(I\). If \(I=0\) or \(n\) is the null vector, the Stokes vector is set to an unpolarized state.

setUnpolarized()

void StokesVector::setUnpolarized ( )

inline

This function sets the Stokes vector to an unpolarized state.

stokes()

void StokesVector::stokes ( double &  I, double &  Q, double &  U, double &  V  )

inline

This function returns the Stokes parameters in the provided arguments.

stokesI()

double StokesVector::stokesI ( ) const

inline

This function returns the Stokes parameter \(I\), which is always equal to one.

stokesQ()

double StokesVector::stokesQ ( ) const

inline

This function returns the Stokes parameter \(Q\).

stokesU()

double StokesVector::stokesU ( ) const

inline

This function returns the Stokes parameter \(U\).

stokesV()

double StokesVector::stokesV ( ) const

inline

This function returns the Stokes parameter \(V\).

totalPolarizationDegree()

double StokesVector::totalPolarizationDegree

(

)

const

This function returns the total polarization degree for the Stokes vector.

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The documentation for this class was generated from the following file:

• StokesVector.hpp