Optimal alignment of mirror-based pentaprisms for scanning deflectometric devices

Abstract

Replacement of a bulk pentaprism with a mirror-based pentaprism (MBPP) in slope-measuring instruments, such as long trace profilers and autocollimator-based deflectometers, is a well-established way to significantly improve the reliability of surface slope measurements. This is due to the elimination of systematic errors introduced by inhomogeneity of the optical material and fabrication imperfections of bulk pentaprisms. Proper use of an MBPP requires precision mutual alignment of its mirrors. In a recent work we have reported on an original experimental procedure for optimal alignment of MBPP mirrors. The procedure has been verified with numerical ray tracing simulations and via test experiments with the developmental long trace profiler, a slope measuring profiler available at the Advanced Light Source Optical Metrology Laboratory. In the present article, we provide an analytical derivation and verification of easily executed optimal alignment algorithms for two different designs of mirror-based pentaprisms. We also provide an analytical description for a mechanism for reduction of the systematic errors introduced by a typical high quality bulk pentaprism. It is also shown that residual misalignments of an MBPP introduce entirely negligible systematic errors in surface slope measurements with scanning deflectometric devices.