Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller. In this technique, the effect of a particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix.
With disregard for coherence, light which is unpolarized or partially polarized must be treated using Mueller calculus, while fully polarized light can be treated with either Mueller calculus or the simpler Jones calculus. Many problems involving coherent light (such as from a laser) must be treated with Jones calculus, however, because it works with the electric field of the light rather than its intensity or power, and retains information about the phase of the waves.
Again with disregard for coherence, any fully polarized, partially polarized, or unpolarized state of light can be represented by a Stokes vector (); and any optical element can be represented by a Mueller matrix (M).
If a beam of light is initially in the state and then passes through an optical element M and comes out in a state , then it is written
If a beam of light passes through optical element M1 followed by M2 then M3 it is written
Matrix multiplication is not commutative, so in general
Below are listed the Mueller matrices for some ideal common optical elements:
- Linear polarizer (Horizontal Transmission)
- Linear polarizer (Vertical Transmission)
- Linear polarizer (+45° Transmission)
- Linear polarizer (-45° Transmission)
- Quarter wave plate (fast-axis vertical)
- Quarter wave plate (fast-axis horizontal)
- Half wave plate (fast-axis vertical)
- Attenuating filter (25% Transmission)
||This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (July 2014)|
- E. Collett, Field Guide to Polarization, SPIE Field Guides vol. FG05, SPIE (2005). ISBN 0-8194-5868-6.
- E. Hecht, Optics, 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X.
- del Toro Iniesta, Jose Carlos (2003). Introduction to Spectropolarimetry. Cambridge, UK: Cambridge University Press. p. 227. ISBN 978-0-521-81827-8.