Abstract
In this work, an alternative route to analyze a set of coherency matrices associated to a medium is addressed by means of the Independent Component Analysis (ICA) technique. We highlight the possibility of extracting an underlying structure of the medium in relation to a model of constituent components. The medium is considered as a mixture of unknown constituent components weighted by unknown but statistically independent random coefficients of thickness. The ICA technique can determine the number of components necessary to characterize a set of sample of the medium. An estimate of the value of these components and their respective weights is also determined. Analysis of random matrices generated by multiplying random diattenuators and depolarizers is presented to illustrate the proposed approach and demonstrate its capabilities.
Highlights
Mueller matrix as linear mapping between the input and output Stokes vectors of light interacting with media, is a very powerful tool for polarimetric characterization of linear media
If we consider the medium to be described by the coherency matrix H at any point in the space, we wish to be able to identify the presence of a set of constituent components Di
An alternative route to analyze a set of coherency matrices associated to a medium is addressed by means of the Independent Component Analysis technique
Summary
Mueller matrix as linear mapping between the input and output Stokes vectors of light interacting with media, is a very powerful tool for polarimetric characterization of linear media. Constituent components are not localised into the medium but may be regarded as distributed contributions along the light path This approach can be extended when defining the logarithmic scalar multiplication of a HPD matrix H by a scalar α∈R in the same way as Arsigny proposed for symmetric matrix [14]. If the mixing matrix is assumed to be unknown too, this problem can be solved but assuming that the random components αj are statistically independent variables This is the starting point for ICA method. Considering a Mueller matrix as a mixing of independent physical quantities (birefringence or dichroïsm for instance) is one example Since these quantities can have different values from one moment to another or from one location to another, a set of matrices with independent latent variables can be measured and analyzed according to the proposed approach. Illustrating this issue is exactly what we will do with the example below
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