The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array

Zekui Lv,Zhiming Yang,Zhikun Su,Xinghua Li,Fengzhou Fang,Dong Zhang,Lingyu Gao,Haitao Zhang

doi:10.3390/app9173485

Zekui Lv, Zhiming Yang + Show 6 more

Open Access

https://doi.org/10.3390/app9173485

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Abstract

The elliptical paraboloid array plays an important role in precision measurement, astronomical telescopes, and communication systems. The calibration of the vertex distance of elliptical paraboloids is of great significance to precise 2D displacement measurement. However, there are some difficulties in determining the vertex position with contact measurement. In this study, an elliptical paraboloid array and an optical slope sensor for displacement measurement were designed and analyzed. Meanwhile, considering the geometrical relationship and relative angle between elliptical paraboloids, a non-contact self-calibration method for the vertex distance of the elliptical paraboloid array was proposed. The proposed self-calibration method was verified by a series of experiments with a high repeatability, within 3 μ m in the X direction and within 1 μ m in the Y direction. Through calibration, the displacement measurement system error was reduced from 100 μ m to 3 μ m . The self-calibration method of the elliptical paraboloid array has great potential in the displacement measurement field, with a simple principle and high precision.

Highlights

Sensor arrays are widely used in modern scientific research and industrial production [1,2,3].Depending on the application requirements, sensor arrays can be designed with different geometries, including those that are linear [4], circular [5], planar [6], L-shaped [7], and so on
The displacement measurement system error was reduced from 100 μm to 3 μm, which satisfies the measuring requirement
The elliptical paraboloid array was placed along the X direction of the coordinate measuring machine (CMM), and the optical slope sensor was mounted on the quill of the CMM to perform multi-point measurement on each of the rings

Summary

Introduction

Sensor arrays are widely used in modern scientific research and industrial production [1,2,3].Depending on the application requirements, sensor arrays can be designed with different geometries, including those that are linear [4], circular [5], planar [6], L-shaped [7], and so on. Sensor arrays are widely used in modern scientific research and industrial production [1,2,3]. Rui et al [8] proposed a capacitance-sensor-array-based imaging system to detect water leakage inside insulating slabs with porous cells. Tan et al [9] developed a giant magneto resistance sensor array which included various types of small gaps, curling wires, wide fractures, and abrasion to detect defects in various types of wire rope. Wu et al [11] presented a novel instrumentation system, including an infrared laser source and a photodiode sensor array, to provide an accurate measurement of the gas void fraction of two-phase CO2 flow. Dario [12] demonstrated a novel sensor array based on SnO2 , CuO, and WO2 nanowires, which is able to discriminate four typical compounds added to food products. Forough et al [14] developed a fluorometric sensor array for the detection of TNT

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