Mathematically Modeling of Imperfect Polarizing-Beam Splitter in Laser Encoders for Automotive Applications

Laser encoders can be used in robotic, control, and automation systems. In this paper, periodic nonlinear error of laser encoder resulting from imperfection of polarizing-beam splitter is mathematically analyzed and modeled by using the Jones matrix analysis for a robotic system. The photocurrents of each photodetector are mathematically obtained and simulated and the nano-displacement of scale grating is calculated by arctangent method. We show that the maximum periodic nonlinear errors resulting from polarizing-beam splitter is 0.07164 rad which is equal to 11.48 nm in displacement, considering 1 µm pitch of gratings.