Polarized optical microscopy of anisotropic media: Imaging theory and simulation

Abstract

A polarized microscope image is the intensity distribution of the projection, onto the image plane, of a certain component of the local electric susceptibility tensor within the object. The tensor component is that with respect to the polarizer direction and the analyzer direction. From a single scattering approximation, a theory and formulas are derived for computing a polarized microscope image from the dielectric permittivity distribution of a given object. Effects of microscope aberrations are accounted for. Predicted images are displayed for spherulites, fused spheres, oblate and prolate spheroids, ellipsoids, toroids, and Dupin cyclides, in which the principal directions of the susceptibility tensor bear a known relation to the local distinguished directions of the generating surfaces or axes of the object. Lamellar structures are sufficient but not necessary to yield the predicted images: any similar anisotropy of susceptibility suffices. The images that can be generated range from the well known Maltese crosses seen in polymer spherulites to more intricate patterns from structures possible in nematic, smectic, and cholesteric liquid crystals. The predictions include the effects of object orientation on the image, a valuable tool for image interpretation. The results reveal that geometrically different objects may appear very similar in polarizing microscopy if they are viewed in too few orientations. A tangent construction is presented that bypasses computations yet successfully predicts the simulated images.