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| '''Mueller calculus''' is a matrix method for manipulating [[Stokes vectors]], which represent the [[Polarization (waves)|polarization]] of light. It was developed in 1943 by [[Hans Mueller (physicist)|Hans Mueller]], a professor of physics at the [[Massachusetts Institute of Technology]]. In this technique, the effect of a particular optical element is represented by a Mueller matrix—a 4×4 matrix that is a generalization of the [[Jones calculus|Jones matrix]].
| | The name of the author is Numbers but it's not the most masucline name out there. California is our birth location. My working day job is a meter reader. Doing ceramics is what adore doing.<br><br>Feel free to surf to my blog ... std home test ([http://www.streaming.iwarrior.net/blog/258268 please click the up coming post]) |
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| 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 [[coherence_(physics)|coherent]] light (such as from a [[laser]]) must be treated with Jones calculus, because it works with [[amplitude]] rather than [[intensity (physics)|intensity]] of light, and retains information about the [[phase (waves)|phase]] of the waves.
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| Any fully polarized, partially polarized, or unpolarized state of light can be represented by a [[Stokes vector]] {{nowrap|(<math>\vec S</math>)}}. Any optical element can be represented by a Mueller matrix (M).
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| If a beam of light is initially in the state <math>\vec S_i</math> and then passes through an optical element M and comes out in a state <math>\vec S_o</math>, then it is written
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| :<math> \vec S_o = \mathrm M \vec S_i \ .</math>
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| If a beam of light passes through optical element M<sub>1</sub> followed by M<sub>2</sub> then M<sub>3</sub> it is written
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| :<math> \vec S_o = \mathrm M_3 \big(\mathrm M_2 (\mathrm M_1 \vec S_i) \big) \ </math>
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| given that [[matrix multiplication]] is [[associative]] it can be written
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| :<math> \vec S_o = \mathrm M_3 \mathrm M_2 \mathrm M_1 \vec S_i \ .</math>
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| Matrix multiplication is not commutative, so in general
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| :<math> \mathrm M_3 \mathrm M_2 \mathrm M_1 \vec S_i \ne \mathrm M_1 \mathrm M_2 \mathrm M_3 \vec S_i \ .</math>
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| Below are listed the Mueller matrices for some ideal common optical elements:
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| :<math>
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| {1 \over 2}
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| \begin{pmatrix}
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| 1 & 1 & 0 & 0 \\
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| 1 & 1 & 0 & 0 \\
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| 0 & 0 & 0 & 0 \\
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| 0 & 0 & 0 & 0
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| \end{pmatrix}
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| \quad
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| </math> Linear polarizer (Horizontal Transmission)
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| :<math>
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| {1 \over 2}
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| \begin{pmatrix}
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| 1 & -1 & 0 & 0 \\
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| -1 & 1 & 0 & 0 \\
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| 0 & 0 & 0 & 0 \\
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| 0 & 0 & 0 & 0
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| \end{pmatrix}
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| \quad
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| </math> Linear polarizer (Vertical Transmission)
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| :<math>
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| {1 \over 2}
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| \begin{pmatrix}
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| 1 & 0 & 1 & 0 \\
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| 0 & 0 & 0 & 0 \\
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| 1 & 0 & 1 & 0 \\
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| 0 & 0 & 0 & 0
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| \end{pmatrix}
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| \quad
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| </math> Linear polarizer (+45° Transmission)
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| :<math>
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| {1 \over 2}
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| \begin{pmatrix}
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| 1 & 0 & -1 & 0 \\
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| 0 & 0 & 0 & 0 \\
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| -1 & 0 & 1 & 0 \\
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| 0 & 0 & 0 & 0
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| \end{pmatrix}
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| \quad
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| </math> Linear polarizer (-45° Transmission)
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| :<math>
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| \begin{pmatrix}
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| 1 & 0 & 0 & 0 \\
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| 0 & 1 & 0 & 0 \\
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| 0 & 0 & 0 & -1 \\
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| 0 & 0 & 1 & 0
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| \end{pmatrix}
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| \quad
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| </math> Quarter [[wave plate]] (fast-axis vertical)
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| :<math>
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| \begin{pmatrix}
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| 1 & 0 & 0 & 0 \\
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| 0 & 1 & 0 & 0 \\
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| 0 & 0 & 0 & 1 \\
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| 0 & 0 & -1 & 0
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| \end{pmatrix}
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| \quad
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| </math> Quarter [[wave plate]] (fast-axis horizontal)
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| :<math>
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| \begin{pmatrix}
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| 1 & 0 & 0 & 0 \\
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| 0 & 1 & 0 & 0 \\
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| 0 & 0 & -1 & 0 \\
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| 0 & 0 & 0 & -1
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| \end{pmatrix}
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| \quad
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| </math> Half [[wave plate]] (fast-axis vertical)
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| :<math>
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| {1 \over 4}
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| \begin{pmatrix}
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| 1 & 0 & 0 & 0 \\
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| 0 & 1 & 0 & 0 \\
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| 0 & 0 & 1 & 0 \\
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| 0 & 0 & 0 & 1
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| \end{pmatrix}
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| \quad
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| </math> Attenuating filter (25% Transmission)
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| == See also ==
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| * [[Stokes parameters]]
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| * [[Jones calculus]]
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| * [[Polarization (waves)]]
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| ==References==
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| *E. Collett, ''Field Guide to Polarization'', SPIE Field Guides vol. '''FG05''', SPIE (2005). ISBN 0-8194-5868-6.
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| *E. Hecht, ''Optics'', 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X.
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| *{{Cite book
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| | last = del Toro Iniesta
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| | first = Jose Carlos
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| | authorlink =
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| | coauthors =
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| | title = Introduction to Spectropolarimetry
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| | publisher = Cambridge University Press
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| | date = 2003
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| | location = Cambridge, UK
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| | pages = 227
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| | url = http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521818273
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| | doi =
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| | id =
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| | isbn = 978-0-521-81827-8 }}
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| [[Category:Polarization (waves)]]
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| [[Category:Matrices]]
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The name of the author is Numbers but it's not the most masucline name out there. California is our birth location. My working day job is a meter reader. Doing ceramics is what adore doing.
Feel free to surf to my blog ... std home test (please click the up coming post)