Mueller scattering matrix

The relation between the incident and the scattered Stokes parameters is given by the Mueller scattering matrix (or simply the scattering matrix) defined as follows... 

In an absorptive medium, the elements of the Mueller scattering matrix (Eq. 43) depend on the radial distance from the particle and can not be directly related to the scattering cross-section as given above (Eq. 44). In this case the different elements of the matrix are used individually in the analysis of scattering phenomena. In practice, their values are normalized by the total scattered rate aroimd the particle at the radiation zone, which can be derived from the integral of Pn for all scattering angles. 

We may represent a beam of arbitrary polarization, including partially polarized light, by a column vector, the Stokes vector, the four elements of which are the Stokes parameters. In general, the state of polarization of a beam is changed on interaction with an optical element (e.g., polarizer, retarder, reflector, scatterer). Thus, it is possible to represent such optical elements by a 4 X 4 matrix (Mueller, 1948). The Mueller matrix describes the relation between incident and transmitted Stokes vectors by incident is meant before interaction with the optical element, and by transmitted is meant after interaction. As an example, consider the Mueller matrix for an ideal linear polarizer. Such a polarizer transmits, without change of amplitude, only electric field components parallel to a particular axis called the transmission axis. Electric field components in other directions are completely removed from the transmitted beam by some means which we need not explicitly consider. The relation between incident field components (E, E i) and field components ( l, E () transmitted by the polarizer is... 

A variety of choices are available for the PSG section of this experiment. As before, the selection is based on the Mueller matrix components of the sample that are sought. A convenient arrangement that has been used for samples subject to uniaxial deformation is described in detail in reference 22 and collects the Raman scattered light in the forward direction. The PSG section of the instrument consists of a polarizer oriented at zero degrees, and a photoelastic modulator at 45°. Following the sample, the PSA section consists of a polarizer oriented at 45°. The signal measured at the photomultiplier tube was shown to have the form ... 

G. Videen, W.L. Wolfe, and W.S. Bickel, Light scattering Mueller matrix for a furface contaminated by a single particle in the Rayleith limit, Opt. Eng. 31, 341-349 (1992). 

Experimentally, we obtained the following form of the Mueller matrix for transmitted and back scattered light for English oak leaves [4] ... 

These matrices correspond stmcturally with the Mueller matrix of so-called macroscopically isotropic and mirror-symmetric scattering media composed of randomly oriented particles with plane of symmetry and/or equal numbers of randomly oriented particles and their mirror-symmetric counterparts [46] ... 

Another way to identify the dominant contributions of the order parameter for a particular line, is to experimentally determine the reflecting Mueller matrix of the Bragg-reflecting blue phase. The polarizations of light incident and scattered from a surface can be described by four-component Stokes vectors. The matrix which transforms one to the other (and describes the blue phase) is a 4 x 4 Mueller matrix. By analyzing the reflected Stokes vectors for a range of incident Stokes vectors, the complete Mueller matrix can be determined. The result of such measurements [61], [62] was that the e 2 coefficient completely dominates the other coefficients, which rules out certain space groups. 

The P matrix elements contain the full information about the scattering event. In non absorptive media the elements of the Mueller matrix (Eq. 43) ean be used to define the scattering cross-section and anisotropy. The scattering eross-seetion <7 is defined... 

---