Design of a precise subdivision system for gratings using a modified CORDIC algorithm

摘要

The authors have proposed a robust linearisation method for determining the angles of sinusoidal signals generated by gratings. This scheme solves the problem of non-linear subdivision by compensating sinusoidal signal. The conventional coordinate rotation digital computer (CORDIC) algorithm is optimised by double-rotation iteration, and the calculation accuracy of arcsine and arccosine functions is improved. A pipeline preprocessing circuit based on the CORDIC is designed for the signal compensation and digital subdivision. The two processes are implemented on a field-programmable gate array chip, which exhibits a wide input range and good dynamic response. A theoretical analysis using stable signals from a function generator verifies that the subdivision system achieves the ideal subdivision effect. The subdivision system is further applied to an angle-measuring device for a 16,384-line circular grating. The results of subdivision exhibit good linearity for the grating moire signal. Compared to the angular measurement by a laser interferometer within the three grating lines, the angle-measurement accuracy of +/- 0.000138 degrees (0.5 '') and the relative error is +/- 0.63% over a travel angle of three grating lines. Notably, the measurement error of the subdivision system is only half of that in a similar commercial product (MicroE system).