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By Yuan Long, Fiona Fui-Hoon Nah, Zhanbei Zhu

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Appl. Opt. 41, 7114–7134. M. I. Mishchenko (2003). Microphysical approach to polarized radiative transfer: extension to the case of an external observation point. Appl. Opt. 42, 4963– 4967. J. Clerk Maxwell (1891). A Treatise on Electricity and Magnetism (Clarendon Press, Oxford) (reprinted by Dover, New York, 1954). H. Poincaré (1892). Théorie Mathématique de la Lumière, Vol. 2 (Georges Carré, Paris). 44 M. I. MISHCHENKO AND L. D. TRAVIS 22. E. Whittaker (1987). A History of the Theories of Aether and Electricity, Vols.

I. MISHCHENKO AND L. D. 18) aϕ sin δ ϕ = a sin β cos δ sin ζ − a cos β sin δ cos ζ . 17) Squaring and adding Eqs. 17) and Eqs. 20) = a (sin β sin ζ + cos β cos ζ ). 21) aϕ2 2 2 2 2 2 Multiplying Eqs. 18) and Eqs. 19) and adding yields aθ aϕ cos ∆ = − 12 a 2 cos 2 β sin 2ζ . 22) Similarly, multiplying Eqs. 18) and Eqs. 19) and subtracting gives aθ aϕ sin ∆ = − 12 a 2 sin 2 β . 23) Comparing Eqs. 6) with Eqs. 24) Q = − I cos 2 β cos 2ζ , U = I cos 2 β sin 2ζ , V = − I sin 2 β . 27) I = 1 2 The parameters of the polarization ellipse are thus expressed in terms of the Stokes parameters as follows.

9) with P(0) = P. A retarder is an optical element that changes the phase of the beam by causing a phase shift of + ζ 2 along the θ - axis and a phase shift of − ζ 2 along the ϕ - axis (Fig. 3). 12) where é1 ê0 R (ζ ) = ê ê0 ê0 ë 0 0 1 0 0 cos ζ 0 − sin ζ 0 ù 0 ú ú sin ζ ú cos ζ úû is the Mueller matrix of the retarder. 13) MAXWELL EQUATIONS, EM WAVES, & STOKES PARAMETERS 37 Consider now the optical path shown in Fig. 4. The beam of light goes through a retarder and a rotated ideal perfect linear polarizer and then impinges on the surface of a polarization-insensitive detector.

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