Mathematically modeling of imperfect polarized laser beam in laser encoders for automotive applications

Abstract

Laser encoders can be used in robotic, control, and automation systems. In this paper, periodic nonlinear error of laser encoder resulting from imperfect polarized laser beam 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. In addition, with the aim of compensating the periodic nonlinear error, the effect of reducing grating period of scale grating is examined. Simulation results show that there is a direct relationship between the grating period and periodic nonlinear error. Results reveal that by changing the grating period from 1 pm to 0.4 pm, the periodic nonlinear error reduces from 14.8 nm to 5.8 nm.