The Mueller Matrix


Both Jones calculus and Mueller calculus use matrix algebra to determine theoretical results of polarization transformations of light. However, Mueller matrices and vectors are much more complete in their description of light beams and polarization optics. Mueller calculus includes intensity values and can therefore represent partially polarized light. Jones calculus cannot represent circularly or elliptically polarized light in this same, direct manner without the use of, i [7]. Thus, Mueller calculus is the better choice when dealing with the partial depolarization of light, which occurs during backscattering.

In the Mueller calculus, a beam of light can be represented by a 4x1 vector. All four elements of the vector can be tangibly acquired by measuring the intensities of the light after passing through varying optics.

I0 is the intensity after passing through an isotropic polarizer (optic which admits all polarization states equally)

I1 is the intensity after passing through a horizontal linear polarizer

I2 is the intensity after passing through a linear polarizer turned at 45 degrees

I3 is the intensity after passing through a right-handed circular polarizer (quarter-wave plate)

These values can be physically found with experimentation. Each polarization optic is assumed to transmit half of the initial intensity if the incident light is unpolarized. These intensity values are represented by the elements of the Stokes vector as follows [8]:

Diagram Under Construction


[I] is the intensity of the beam

[Q] - reflects tendency of beam to be either horizontally (Q > 0) or vertically (Q < 0) polarized

[U] - reflects tendency of beam to be either polarized at +45\degree (U > 0) or -45\degree (U < 0)

[V] - reflects tendency of beam to be either right handed (V > 0) or left handed (V < 0) circularly polarized

In this manner, any beam of light can be fully represented for use in the Mueller calculus. For example:

Diagram Under Construction


These Stokes vectors are then multiplied by a Mueller matrix to create a new vector which will describe the polarization of the resulting light. The Mueller matrix is made up of 16 elements, which are labelled as follows:

Diagram Under Construction







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