Note: Richard Hill [rkhill@caci.com] provided the following info:
The definition of Stokes Vector components on (this) site is in error. Wolfram has it wrong also. The easiest way to see that it is wrong is to take horizontally polarized light (1, 1, 0, 0) and solve for the intensities. The total intensity I0 is ½ and the horizontal intensity I1 is 1. That obviously doesn't add. The Wikipedia explanation is consistent (Lord help us). S0 = I0 = I(horizontal) + I(vertical) S1 = I(horizontal) - I(vertical) = 2*I(horizontal) - I0 S2 = I(+45) - I(-45) Please correct as desired.
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Polarization | Stokes Vector |
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Unpolarized | ![]() |
Linear Horizontal | ![]() |
Linear Vertical | ![]() |
Linear +45° | ![]() |
Linear -45° | ![]() |
Circular, Right-Handed | ![]() |
Circular, Left-Handed | ![]() |
Optical elements can be applied to Stokes vectors using Mueller matrices. The Stokes vector describes the polarization of a plane wave, and the Mueller matrix describes how the polarization changes upon scattering at a change in electrical or magnetic properties.
The Mueller Matrix contains everything optically one can obtain from a system of scatterers in a turbid medium. It is a matrix that can be used to reproduce the effect of a given optical element when applied to a Stokes vector.
Optical Element | Mueller Matrix |
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Clear Filter | ![]() |
Linear Horizontal Polarizer | ![]() |
Linear Vertical Polarizer | ![]() |
Linear Polarizer at +45° | ![]() |
Linear Polarizer at -45° | ![]() |
Quarter-Wave Plate, Fast Axis Vertical | ![]() |
Quarter-Wave Plate, Fast Axis Horizontal | ![]() |
Circular Polarizer, Right-Handed | ![]() |
Circular Polarizer, Left-Handed | ![]() |
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