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The geometric approach presented in this paper concerns the degree ofpolarization (DoP) of a random 3D statistical electromagnetic field. We usethat a 3*3 coherency matrix can always be decomposed into an incoherentsuperposition of three specific coherency matrices, to construct the firstorthant of a spherical shell(0<x,y,z<1,sqrt(3)/3<r<1) . For a random 3Dstatistical electromagnetic field, the polarimetric result of the can beexpressed in terms of a point located in the first orthant of this sphericalshell physically. Furthermore, based on the intrinsic relationship between thedefined parameters (DoP3D_P,DoP3D_PP) and DoP, a spatially quadric surface isobtained to quantify the values of DoP the for all physically reachable pointscontained in the first orthant of this spherical shell. Within this geometricapproach, two examples are cited to demonstrate the applicability of 3Dpolarimetry to intuitively display the polarimetric result of a random 3Dstatistical electromagnetic field.

Geometric approach of degree of polarization in 3D polarimetry