  Emerging microstructural characterization methods have received increased
attention owing to their promise of relatively inexpensive and rapid
measurement of polycrystalline surface morphology and crystallographic
orientations. Among these nascent methods, polarized light microscopy (PLM) is
attractive for characterizing alloys comprised of hexagonal crystals, but is
hindered by its inability to measure complete crystal orientations. In this
study, we explore the potential to reconstruct quasi-deterministic orientations
for titanium microstructures characterized via PLM by considering the Burgers
orientation relationship between the room temperature $\alpha$ (HCP) phase
fibers measured via PLM, and the $\beta$ (BCC) phase orientations of the parent
grains present above the transus temperature. We describe this method -- which
is capable of narrowing down the orientations to one of four possibilities --
and demonstrate its abilities on idealized computational samples in which the
parent $\beta$ microstructure is fully, unambiguously known. We further utilize
this method to inform the instantiation of samples for crystal plasticity
simulations, and demonstrate the significant improvement in deformation field
predictions when utilizing this reconstruction method compared to using results
from traditional PLM.
