In an apparatus and method for measuring parameters related to retardance and slow axis azimuth in sample specimens, a sample is illuminated by circularly polarized monochromatic light which is then analyzed by an elliptical analyzer at different settings. In another embodiment, light conditioned by an elliptical polarizer at various settings illuminates a specimen and the beam exiting the sample is analyzed by a circular analyzer. Background images obtained with selected settings of the elliptical analyzer/polarizer, but without the sample present. Algorithms are described which employ two specimen images with elliptical settings and three or two background images; or which employ three specimen images with elliptical settings; or which employ four specimen images with elliptical settings without an extinction setting; or which employ five specimen images with four elliptical settings and one extinction setting. These algorithms allow one to variously optimize measurements for speed, sensitivity, and accuracy.