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Canonical forms of depolarizing Mueller matrices.

Razvigor Ossikovski¹

¹LPICM, Ecole Polytechnique, CNRS, 91128 Palaiseau, France. razvigor.ossikovski@polytechnique.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|December 26, 2009

Summary

Depolarizing Mueller matrices can be simplified into two canonical forms, enabling their classification into diagonalizable and non-diagonalizable types based on Stokes properties.

Area of Science:

Polarization optics
Matrix algebra
Optical characterization

Background:

Mueller matrix formalism is crucial for describing polarization properties of optical elements.
Depolarization phenomena complicate the analysis of optical systems.
Canonical forms offer a simplified representation of complex matrices.

Purpose of the Study:

To introduce a product decomposition for any depolarizing Mueller matrix.
To establish two canonical forms for depolarizing Mueller matrices: diagonal and non-diagonal.
To classify Mueller matrices based on these canonical forms into Stokes diagonalizable and non-diagonalizable categories.

Main Methods:

Utilizing product decomposition of Mueller matrices.
Identifying and discussing characteristic properties of the canonical depolarizer forms.

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Analyzing the mathematical structure of depolarizing Mueller matrices.

Main Results:

Demonstrated that any depolarizing Mueller matrix can be reduced to one of two canonical forms.
Established a clear division of depolarizing Mueller matrices into Stokes diagonalizable and non-diagonalizable sets.
Characterized the unique properties of both diagonal and non-diagonal canonical depolarizers.

Conclusions:

The two canonical depolarizer forms provide a fundamental framework for understanding depolarization.
This classification simplifies the analysis and interpretation of experimental Mueller matrix data.
The findings are validated by experimental examples from existing literature.