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Register a new userCoherency vector formalism for polarimetric transformations
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Despite the virtues of Jones and Mueller formalisms for the representation of the polarimetric properties, for some purposes in both Optics and SAR Polarimetry, the concept of coherency vector associated with a nondepolarizing medium has proven to be an useful mathematical structure that inherits certain symmetries underlying the nature of linear polarimetric transformations of the states of polarization of light caused by its interaction with material media. While the Jones and Mueller matrices of a serial combination of devices are given by the respective conventional matrix products, the composition of coherency vectors of such serial combinations requires a specific and unconventional mathematical rule. In this work, a vector product of coherency vectors is presented that satisfies, in a meaningful and consistent manner, the indicated requirements. As a result, a new algebraic formalism is built where the representation of polarization states of electromagnetic waves through Stokes vectors is preserved, while nondepolarizing media are represented by coherency vectors and general media are represented by coherency matrices generated by partially coherent compositions of the coherency vectors of the components.
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An analysis of the matrix models representing the polarimetric properties of light and material media is carried out by using the concept of the coherency matrix, which leads to the identification and definition of their corresponding physical quantities. For light, cases of homogeneous and inhomogeneous wavefront are analyzed, and a model for 3D polarimetric purity is formulated. For linear passive material media, a general model is developed on the basis that any physically realizable linear transformation of Stokes vectors is equivalent to an ensemble average of passive, deterministic, nondepolarizing transformations. Through this framework, the relevant physical quantities, including the indices of polarimetric purity, are identified and decoupled. Some decompositions of the whole system into a set of well-defined components are considered, as well as techniques for isolating the unknown components by means of new procedures for subtracting coherency matrices. These results and methods constitute a powerful tool for analyzing and exploiting experimental and industrial polarimetry. Some particular application examples are indicated.
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