Degree of polarization surfaces and maps for analysis of depolarization

Abstract

The concept of degree of polarization surfaces is introduced as an aid to classifying the depolarization properties of Mueller matrices. Degree of polarization surfaces provide a visualization of the dependence of depolarization on incident polarization state. The surfaces result from a non-uniform contraction of the Poincaré sphere corresponding to the depolarization properties encoded in a Mueller matrix. For a given Mueller matrix, the degree of polarization surface is defined by moving each point on the unit Poincaré sphere radially inward until its distance from the origin equals the output state degree of polarization for the corresponding input state. Of the sixteen elements in a Mueller matrix, twelve contribute to the shape of the degree of polarization surface, yielding a complex family of surfaces. The surface shapes associated with the numerator and denominator of the degree of polarization function are analyzed separately. Protrusion of the numerator surface through the denominator surface at any point indicates non-physical Mueller matrices. Degree of polarization maps are plots of the degree of polarization on flat projections of the sphere. These maps reveal depolarization patterns in a manner well suited for quantifying the degree of polarization variations, making degree of polarization surfaces and maps valuable tools for categorizing and classifying the depolarization properties of Mueller matrices.

Depolarization properties of the normal human fovea

“…If θ is half the latitude on the Poincaré sphere and ε is the latitude, the variation of DoP in terms of incident polarization states can be easily shown on the DoP map. [23] ( ) ( ) 0,0 0,1 0,2 0,3 …”

Q(M) and the depolarization index scalar metrics

“…That means the metric is applied directly to the Mueller matrix. The degree of polarization, DoPðM; SÞ, has been defined by [5][6][7][8][9][10][11] …”

“…On the other hand, the entropy is a function of the Mueller matrix elements and needs no scanning over input polarizations, as has been defined by Cloude [4]. Chipman and coworkers [5][6][7][8][9] and Brosseau [10] have employed recently the degree of polarization [5,11] and have defined other derived metrics as the average and the weighted degree of polarization [6][7][8]. The degree of polarization has been studied for a broad kind of systems and links where the diattenuation and the polarizance vectors have been analyzed [9,10].…”

Polarization scatter measurements with a Mueller matrix imaging polarimeter

“…The DoP surface, then, is a specific contraction of the Poincaré sphere relating to how a Mueller matrix depolarizes, and may be useful for classifying properties of the matrix, as discussed in Ref. 20. Figure 10 gives an arbitrary Mueller matrix and its corresponding DoP surface in terms of Stokes input coordinates (S 1 , S 2 , S 3 ).…”