Optimal alignment of mirror based pentaprisms for scanning deflectometric devices

In the recent work [Proc. of SPIE 7801, 7801-2/1-12 (2010), Opt. Eng. 50(5) (2011), in press], we have reported on improvement of the Developmental Long Trace Profiler (DLTP), a slope measuring profiler available at the Advanced Light Source Optical Metrology Laboratory, achieved by replacing the bulk pentaprism with a mirror based pentaprism (MBPP). An original experimental procedure for optimal mutual alignment of the MBPP mirrors has been suggested and verified with numerical ray tracing simulations. It has been experimentally shown that the optimally aligned MBPP allows the elimination of systematic errors introduced by inhomogeneity of the optical material and fabrication imperfections of the bulk pentaprism. In the present article, we provide the 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 the 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.