Stokes Parameters - Definitions

Definitions

The relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations below and the figure at right.

\begin{align} S_0 &= I \\ S_1 &= p I \cos 2\psi \cos 2\chi\\ S_2 &= p I \sin 2\psi \cos 2\chi\\ S_3 &= p I \sin 2\chi \end{align}

Here, and are the spherical coordinates of the three-dimensional vector of cartesian coordinates . is the total intensity of the beam, and is the degree of polarization. The factor of two before represents the fact that any polarization ellipse is indistinguishable from one rotated by 180°, while the factor of two before indicates that an ellipse is indistinguishable from one with the semi-axis lengths swapped accompanied by a 90° rotation. The four Stokes parameters are sometimes denoted I, Q, U and V, respectively.

If given the Stokes parameters one can solve for the spherical coordinates with the following equations:

\begin{align} I &= S_0 \\ p &= \frac{\sqrt{S_1^2 + S_2^2 + S_3^2}}{S_0} \\ 2\psi &= \mathrm{atan} \frac{S_2}{S_1}\\ 2\chi &= \mathrm{atan} \frac{S_3}{\sqrt{S_1^2+S_2^2}}\\ \end{align}

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