Two-dimensional displacement measurement based on two parallel gratings

Abstract

In this paper, a two-dimensional (2-D) planar encoder based on two parallel gratings, which includes a scanning grating and scale grating, is presented. The scanning grating is a combined transmission rectangular grating comprised of a 2-D grating located at the center and two one-dimensional (1-D) gratings located at the sides. The grating lines of the two 1-D gratings are perpendicular to each other and parallel with the 2-D grating lines. The scale grating is a 2-D reflective-type rectangular grating placed in parallel with the scanning grating, and there is an angular difference of 45° between the grating lines of the two 2-D gratings. With the special structural design of the scanning grating, the encoder can measure the 2-D displacement in the grating plane simultaneously, and the measured interference signals in the two directions are uncoupled. Moreover, by utilizing the scanning grating to modulate the phase of the interference signals instead of the prisms, the structure of the encoder is compact. Experiments were implemented, and the results demonstrate the validity of the 2-D planar grating encoder.

An Inductive Sensor for Two-Dimensional Displacement Measurement

“…Meanwhile, a0 and b0 are assigned with A2 and A3, and then β is acquired. As shown as Equation (12), the displacements x and y are calculated by solving the system of linear equations. The detailed description of the resolving process is described in Section 3.…”

“…In [11], the authors developed a fiber optic sensor, and the linear sensitivity was equal to 11.20 ± 0.12 mV/µm within a range of 13.03 mm. A 2D planar grating encoder based on the double diffraction grating principle was reported in [12]. The encoder included a combined transmission rectangular grating and 2D reflective type rectangular grating.…”

Optical Sensors for Multi-Axis Angle and Displacement Measurement Using Grating Reflectors

“…In responding to the above requirements, two-axis optical angle sensors [46,47,48,49,50,51] based on the laser autocollimation [51], as well as the three-axis autocollimator [52], have been developed. The applications of planar encoders or surface encoders [53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79], which can carry out simultaneous detection of the position in a plane or in 3D space with the enhancement of a planar scale grating, is another possible solution. The planar encoders/surface encoders are expected to achieve multi-axis angle and/or displacement measurement, while complying with the Abbe principle and avoiding the increase of measurement uncertainty due to the increase of the degrees of freedom.…”