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

• Published in: IET circuits, devices & systems Vol. 13; no. 8; pp. 1284 - 1291
• Main Authors: Zhu, Weibin, Ye, Shengjin, Huang, Yao, Xue, Zi
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.11.2019; John Wiley & Sons, Inc
• Subjects: Accuracy; Algorithms; amplitude deviation; angle-measurement accuracy; angle-measuring device; angular measurement; arccosine functions; circular grating; digital arithmetic; Digital computers; digital subdivision; direct current offset deviation; double-rotation iteration; Dynamic response; Error analysis; error compensation; Field programmable gate arrays; field-programmable gate array chip; function generator; Function generators; Gate arrays; grating lines; grating moiré signal; ideal subdivision effect; light interferometers; Linearity; measurement error; measurement errors; Measuring instruments; MicroE system; modified CORDIC algorithm; moiré signals; nonlinear subdivision; precise subdivision system design; Research Article; robust linearisation method; Rotation; rotation digital computer algorithm; Sensors; Sine waves; sinusoidal signal; stable signals; field programmable gate arrays; function generators; angle-measuring device; moiré signals; stable signals; function generator; precise subdivision system design; digital arithmetic; grating lines; digital subdivision; angle-measurement accuracy; nonlinear subdivision; error compensation; MicroE system; measurement errors; angular measurement; double-rotation iteration; direct current offset deviation; modified CORDIC algorithm; field-programmable gate array chip; rotation digital computer algorithm; circular grating; grating moiré signal; light interferometers; measurement error; robust linearisation method; sinusoidal signal; arccosine functions; ideal subdivision effect; amplitude deviation; dynamic response
• ISSN: 1751-858X; 1751-8598; 1751-8598
• DOI: 10.1049/iet-cds.2019.0150

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 moiré signal. Compared to the angular measurement by a laser interferometer within the three grating lines, the angle-measurement accuracy of ±0.000138° (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).