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.

The polarization properties of light scattered or diffusely reflected from seven different man-made samples are studied. For each diffusely reflecting sample an in-plane Mueller matrix bidirectional reflectance distribution function is measured at a fixed bistatic angle using a Mueller matrix imaging polarimeter. The measured profile of depolarization index with changing scattering geometry for most samples is well approximated by an inverted Gaussian function. Depolarization is minimum for specular reflection and increases asymptotically in a Gaussian fashion as the angles of incidence and scatter increase. Parameters of the Gaussian profiles fitted to the depolarization data are used to compare samples. The dependence of depolarization on the incident polarization state is compared for each Stokes basis vector: horizontal, vertical, 45 degrees, 135 degrees, and right- and left-circular polarized light. Linear states exhibit similar depolarization profiles that typically differ in value by less than 0.06 (where 1.0 indicates complete depolarization). Circular polarization states are depolarized more than linear states for all samples tested, with the output degree of polarization reduced from that of linear states by as much as 0.15. The depolarization difference between linear and circular states varies significantly between samples.

A new technique for precise focal-length measurement with a hologram is presented. This technique is widely applicable and is particularly useful for measuring large, slow lenses. In diffraction, the Fresnel-zone plate hologram emulates the reflective properties of a convex spherical mirror for use during transmission null tests of an optic by use of a phase-shifting interferometer. The hologram is written lithographically and therefore offers a higher degree of precision at a lower cost than its spherical mirror counterpart. A hologram offers the additional benefit of easy characterization by use of the same interferometer employed in examining the test optic. Better than +/-0.01% precision is achieved during measurement of a 9-m focal-length lens by use of a 150-mm aperture interferometer.