Electrodynamic solution for polarized reflectivity and wide-field orientation imaging of uniaxial metals

The polarized reflectivity of an ideally smooth metal with a uniaxial anisotropic complex refractive index, for instance, metals with hexagonally close-packed (HCP) symmetry, is derived from the electromagnetic wave equation for normal incidence and arbitrary crystal orientation. The resulting orientation-dependent Mueller matrices of the surface are applicable to c axis orientation imaging of metals including beryllium, magnesium, titanium, cobalt, zinc, zirconium, tin, and most of their alloys, as well as other uniaxial compounds. Comparing orientation images recorded with a generalized polarized-light microscope (PLM), in this case an original coherent laser PLM, with orientation images obtained by electron backscatter diffraction (EBSD) enables imaging ellipsometry (IE) at near-normal incidence and increases confidence in ellipsometric refractive-index measurements. In this initial study, without modeling oxides, the resulting c axis orientation images of several titanium alloys are still verified to better than 11% against EBSD maps of the same samples over instantaneous fields of view (FOVs) exceeding 1cm2 and FOVs approaching 1in2 obtained by stitching several such images together.