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.

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Abstract. We present a sensitivity analysis and performance evaluation of a six-degree-of-freedom measurement system that uses a diffraction grating as a cooperative target. To design the measurement system, we require a theoretical analysis of performance, such as sensitivity of each sensing direction. The intensity distributions of the diffracted beams are calculated with the scalar diffraction theory and sensitivity of the measurement system is analyzed against the variations of design parameter values. Using the results of sensitivity analysis, we design the measurement system and evaluate its performance with resolution, measurement error, and crosstalk. The resolution is less than 0.2 m in translation and 0.5 arcsec in rotation. In experiments, measurement error and crosstalk between sensing channels are within Ϯ0.5 m in translation and Ϯ2 arcsec in rotation.

A new multi-degree-of-freedom measurement system for milli-structures is presented. This methodology is based on optical beam deflection method and triangulation. It employs a diffraction grating as a reflective object, which reflects an incident laser beam into several directions. To obtain the pose information of a measured object, the detecting positions of zeroth- and first-order diffracted rays are measured using three two-dimensional detectors. From these values, we can calculate six-degree-of-freedom displacement through a kinematic analysis. The performance was evaluated with resolution, measurement errors and crosstalk. The results show that measurement errors and maximum crosstalk are within ±0.5 µm in translation and ±2'' in rotation. As an application, we measured the multi-DOF motion of a bimorph type PZT actuator and obtained its frequency response function.

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