Open AccessDesign of a precise subdivision system for gratings using a modified CORDIC algorithm
Author(s) -
Zhu Weibin,
Ye Shengjin,
Huang Yao,
Xue Zi
Publication year - 2019
Publication title -
iet circuits, devices and systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.251
H-Index - 49
eISSN - 1751-8598
pISSN - 1751-858X
DOI - 10.1049/iet-cds.2019.0150
Subject(s) - subdivision , cordic , grating , algorithm , signal (programming language) , computer science , function generator , rotation (mathematics) , inverse trigonometric functions , optics , mathematics , chip , physics , field programmable gate array , engineering , computer vision , mathematical analysis , computer hardware , telecommunications , civil engineering , programming language
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).