The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1851, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system. They can be determined from directly observable phenomena. The original Stokes paper was discovered independently by Francis Perrin in 1942 and by Subrahamanyan Chandrasekhar in 1947, who named it as the Stokes parameters.
Definitions
The relationship of the Stokes parameters S0, S1, S2, S3 to intensity and polarization ellipse parameters is shown in the equations below and the figure on the right.
S 0 = I S 1 = I p cos 2 ψ cos 2 χ S 2 = I p sin 2 ψ cos 2 χ S 3 = I p sin 2 χ {\displaystyle {\begin{aligned}S_{0}&=I\\S_{1}&=Ip\cos 2\psi \cos 2\chi \\S_{2}&=Ip\sin 2\psi \cos 2\chi \\S_{3}&=Ip\sin 2\chi \end{aligned}}}
Here I p {\displaystyle Ip} , 2 ψ {\displaystyle 2\psi } and 2 χ {\displaystyle 2\chi } are the spherical coordinates of the three-dimensional vector of cartesian coordinates ( S 1 , S 2 , S 3 ) {\displaystyle (S_{1},S_{2},S_{3})} . I {\displaystyle I} is the total intensity of the beam, and p {\displaystyle p} is the degree of polarization, constrained by 0 ≤ p ≤ 1 {\displaystyle 0\leq p\leq 1} . The factor of two before ψ {\displaystyle \psi } represents the fact that any polarization ellipse is indistinguishable from one rotated by 180°, while the factor of two before χ {\displaystyle \chi } indicates that an ellipse is indistinguishable from one with the semi-axis lengths swapped accompanied by a 90° rotation. The phase information of the polarized light is not recorded in the Stokes parameters. The four Stokes parameters are sometimes denoted I, Q, U and V, respectively. Given the Stokes parameters, one can solve for the spherical coordinates with the following equations:
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