Citation: Cheng, F.; Zhou, D.; Yu, Q.;
Tjahjowidodo, T. A New Image
Grating Sensor for Linear
Displacement Measurement and Its
Error Analysis. Sensors 2022, 22, 4361.
https://doi.org/10.3390/s22124361
Academic Editor: Carlos Marques
Received: 15 April 2022
Accepted: 5 June 2022
Published: 9 June 2022
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Article
A New Image Grating Sensor for Linear Displacement
Measurement and Its Error Analysis
Fang Cheng
1,
*, Dongfang Zhou
1
, Qing Yu
1
and Tegoeh Tjahjowidodo
2
1
College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China;
zhoudf@stu.hqu.edu.cn (D.Z.); yuqing@hqu.edu.cn (Q.Y.)
2
Department of Mechanical Engineering, De Nayer Campus, KU Leuven, Jan Pieter de Nayerlaan 5,
2860 Sint-Katelijne-Waver, Belgium; tegoeh.tjahjowidodo@kuleuven.be
* Correspondence: chengfang@hqu.edu.cn
Abstract:
To improve the accuracy of the current vision-based linear displacement measurement in a
large range, a new type of linear displacement sensing system, namely, image grating, is proposed
in this paper. The proposed system included a patterned glass plate attached to the moving object
and an ultra-low distortion lens for high-accuracy image matching. A DFT local up-sampling phase
correlation method was adopted to obtain the sub-pixel translation of the patterns onto the target
plate. Multiple sets of stripe patterns with different designs were located on the glass plate to
expand the measurement range, based on the principle of phase correlation. In order to improve the
measurement accuracy, the main errors of the image grating system were analyzed, and the nonlinear
error compensation was completed based on the dynamic calibration of the pixel equivalent. The
measurement results, after the error compensation, showed that the total error of the proposed system
was less than 2.5
µ
m in the range of 60 mm, and the repeatability was within 0.16
µ
m, as quantified
by standard deviation.
Keywords:
displacement measurement; image grating; vision-based; phase correlation; range expan-
sion; error analysis
1. Introduction
Displacement measurement plays a very important role in various industries. Com-
mon displacement sensors include Hall sensors [
1
], fiber sensors [
2
,
3
], interferometric
sensors, grating-based sensors, etc. With the rapid development of advanced manufactur-
ing, high-precision displacement sensing techniques over a long range are in high demand.
Typical applications include the processing and measurement of large-size wafers [
4
],
positioning and process control of CNC machine tools [
5
], development of coordinate
measuring machines [
6
], etc. At present, most high-precision, large-range displacement
measurement systems are developed by using laser interferometry or traditional grating
sensing. Laser interferometers have the highest accuracy, but they require precise align-
ment installation and very strict environmental control, which limits their application in
industry [
7
,
8
]. Traditional grating displacement sensors include optical encoders, magnetic
encoders, capacitive encoders and the inductosyn. The resolution of these sensors depends
on the grating pitch, and there are obvious cumulative errors. In addition, they all adopt
a structure where the scale and the reading head are close to each other, and the short
stand-off distance limits their installation flexibility, which creates certain difficulties in
the optimization of the instrument structure [
9
]. For brownfield applications, where the
available manufacturing process does not allow disruptive updates or the replacement of
existing processes due to the constraints of time, cost or footprint, visual sensors with fast
and flexible installation are needed.
Therefore, visual measurement technology has been progressing rapidly in recent
years. With the advantages of modular design, low cost, non-contact, long stand-off,
Sensors 2022, 22, 4361. https://doi.org/10.3390/s22124361 https://www.mdpi.com/journal/sensors
