Abstract
Depolarization has been found to be a useful contrast mechanism in biological and medical imaging. The Mueller matrix can be used to describe polarization effects of a depolarizing material. An historical review of relevant polarization algebra, measures of depolarization, and purity spaces is presented, and the connections with the eigenvalues of the coherency matrix are discussed. The advantages of a barycentric eigenvalue space are outlined. A new parameter, the diattenuation-corrected purity, is introduced. We propose the use of a combination of the eigenvalues of coherency matrices associated with both a Mueller matrix and its canonical Mueller matrix to specify the depolarization condition. The relationships between the optical and polarimetric radar formalisms are reviewed. We show that use of a beam splitter in a reflectance polarization imaging system gives a Mueller matrix similar to the Sinclair–Mueller matrix for exact backscattering. The effect of the reflectance is canceled by the action of the beam splitter, so that the remaining features represent polarization effects in addition to the reflection process. For exact backscattering, the Mueller matrix is at most Rank 3, so only three independent complex-valued measurements are obtained, and there is insufficient information to extract polarization properties in the general case. However, if some prior information is known, a reconstruction of the sample properties is possible. Some experimental Mueller matrices are considered as examples.
Highlights
There is growing interest in polarization imaging in optical systems such as microscopes, as polarization is a powerful contrast mechanism
We examine the effects of the beam splitter on the measured polarization
Kuntman et al showed that a deterministic Mueller matrix can be factored into a product M = ZZ∗ where Z is the polarization coupling matrix introduced by Chipman, which contains the elements of the coherency vector z [54,89]
Summary
There is growing interest in polarization imaging in optical systems such as microscopes, as polarization is a powerful contrast mechanism. A layer can be imaged in transmission by placing the sample on a mirror and observing in a reflection geometry [14,15] This approach has been used in confocal transmission microscopy to cancel out movement of the confocal spot, which is caused by refractive effects in the sample. A cascaded system is represented by successive matrix premultiplications This is a cause of one of the disadvantages of the Mueller matrix: even multiplication of two matrices results in a Mueller matrix, where, in general, each element depends on all of the elements of the original matrices. The Mueller matrix represents the overall polarization state of an optical system or medium, which could be generated by many alternative combinations of systems or media. We start with a review of relevant developments in polarization algebra, in order to review the theory and describe our notation
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