A polarimeter using selected Glan-Thompson polarizers, a spatially filtered probe laser beam, precision polarizer orientation, and spatially filtered output coupling into an optical fiber achieves a static extinction ratio between crossed and parallel polarizer and analyzer orientations of I(perpendicular)/I(parallel) approximately = 2 x 10(-10). This instrument allows the detection of retardance as small as 0.0015 nm to better than 1%, enabling the first detailed study of the in-plane birefringence of molecular monolayers. We demonstrate the performance of the polarimeter with measurements of the photoinduced birefringence of azobenzene-based monolayers self-assembled on glass.