Six-degree-of-freedom displacement measurement system using a diffraction grating

Abstract

Articles you may be interested inMeasurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer Rev. Sci. Instrum. 85, 045110 (2014); 10.1063/1.4870904 A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques Rev. Sci. Instrum. 78, 095105 (2007); Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage Rev. Sci. Instrum. 78, 066103 (2007);Six-degree-of-freedom displacement measurement systems are applicable in many fields: precision machine control, precision assembly, vibration analysis, and so on. This article presents a new six-degree-of-freedom displacement measurement system utilizing typical features of a diffraction grating. It is composed of a laser source, three position sensitive detectors, a diffraction grating target, and several optical components. Six-degree-of-freedom displacement is calculated from the coordinates of diffracted rays on the detectors. A forward and an inverse problem were solved to compute the full pose of an object through kinematic analysis. The experimental results show that the measurement system had a maximum error of Ϯ10 m for translation and Ϯ0.012°for rotation. The repeatability is about 10 m for translation and 0.01°for rotation.

Determination of the position and orientation of a flat piezoelectric micro-stage by moving the optical axis

“…Kim et al proposed a six-DOF displacement measurement system in 2002 that used three position measuring sensors and optics collocated with reflective gratings to make their measurements. [6][7][8] Linear and angular repeatability of the proposed system was 10 μm and 0.01 • . In 2004, Gao et al used a two-dimensional a) Author to whom correspondence should be addressed.…”

Development of a simple system for the simultaneous measurement of pitch, yaw and roll angular errors of a linear stage

“…Also, an artifact standard part, such as a ball plate, ball array, cubic box, tetrahedron, quadrant detectors and position sensitive detectors, etc. was used to measure the geometric errors [20][21][22][23].…”

Application of sensitivity analysis for the design of six-degree-of-freedom measurement system

“…The variations of detector outputs according to the unit input displacement can be found with the kinematic analysis 5 and the intensity distributions of the diffracted beams. Each of these values is defined as sensitivity and composes the Jacobian matrix as where ␦d is an infinitesimal change of the detector output, and ␦p is an infinitesimal input displacement.…”

“…The detailed mathematical equations were explained in the reference paper. 5 In this measurement system, a quadrant photodiode ͑Q-PD͒ detects the 2-D movement of the diffracted beam. Two axial outputs of the Q-PD are the difference signals calculated from the voltage outputs proportional to the intensity of an incident beam on each photodiode cell, and so affected by the intensity distribution and power of the incident beam.…”

“…4 A new six-DOF measurement system using a diffraction grating target was proposed to overcome these problems. 5 Since this system uses several diffracted beams generated from a diffraction grating, it requires only one laser source and one cooperative target, which can simplify the structure of the measurement system. In addition, a diffraction grating can be produced through a microfabrication process or replication, and therefore this system can measure the displacement of a miniaturized object without any complicated devices.…”