Analog Electronic Method for Solving Nonlinear Errors of Sinusoidal Waves in Interferometry

Nonlinear errors, including direct current (dc) offset, lack of quadrature, and unstable amplitude, are inevitable in the sinusoidal waves of interferometry due to an unsatisfactory detector system. Precision and possible measuring range of interferometry are limited by the errors. An analog electronic method to solve the nonlinear errors is proposed in this article. Preamplifier circuits, dc offset compensation circuits based on low-pass filters, orthogonalized circuits based on vector operations, and regularized circuits based on automatic gain control (AGC) technology are analyzed, designed, and verified, respectively. Using the designed circuits, a polarizing Michelson interferometer (PMI) system has been developed and used to measure a high-precision stage with a stroke of 15 mm and a maximum angular error of 35 arc-sec. Experimental results show that the errors of the sinusoidal waves between 20 Hz and 2 kHz in frequency and between 200 mV and 5 V in amplitude can be reduced effectively by the developed circuits. The expanded uncertainty of the developed PMI system is 47 nm. Further experiments have been carried out on a common guide rail with a length of 600 mm. Experimental results reveal that the tolerable angular error motion of the reflecting mirror of the PMI system is improved from ±68.5 to ±274 arc-sec in a measuring distance of 500 mm. The proposed method can be used to reduce the nonlinear errors in sinusoidal wave signal processing fields.