The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array
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...
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| Format: | Article |
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MDPI AG
2019-08-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/9/17/3485 |
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| author | Zekui Lv Zhikun Su Dong Zhang Lingyu Gao Zhiming Yang Fengzhou Fang Haitao Zhang Xinghua Li |
| author_facet | Zekui Lv Zhikun Su Dong Zhang Lingyu Gao Zhiming Yang Fengzhou Fang Haitao Zhang Xinghua Li |
| author_sort | Zekui Lv |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula> in the X direction and within <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula> in the Y direction. Through calibration, the displacement measurement system error was reduced from <inline-formula> <math display="inline"> <semantics> <mrow> <mn>100</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula>. The self-calibration method of the elliptical paraboloid array has great potential in the displacement measurement field, with a simple principle and high precision. |
| first_indexed | 2024-12-10T15:23:09Z |
| format | Article |
| id | doaj.art-141a78f0ec834b4bbd6cf87019795aeb |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-10T15:23:09Z |
| publishDate | 2019-08-01 |
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| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-141a78f0ec834b4bbd6cf87019795aeb2022-12-22T01:43:36ZengMDPI AGApplied Sciences2076-34172019-08-01917348510.3390/app9173485app9173485The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid ArrayZekui Lv0Zhikun Su1Dong Zhang2Lingyu Gao3Zhiming Yang4Fengzhou Fang5Haitao Zhang6Xinghua Li7State Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, ChinaState Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, ChinaState Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, ChinaState Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, ChinaState Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, ChinaCentre of Micro/Nano Manufacturing Technology, University College Dublin, D04 V1W8 Dublin, IrelandKey Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, ChinaState Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072, ChinaThe 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula> in the X direction and within <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula> in the Y direction. Through calibration, the displacement measurement system error was reduced from <inline-formula> <math display="inline"> <semantics> <mrow> <mn>100</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula> to <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics> </math> </inline-formula>. The self-calibration method of the elliptical paraboloid array has great potential in the displacement measurement field, with a simple principle and high precision.https://www.mdpi.com/2076-3417/9/17/3485elliptical paraboloid arrayself-calibration methodvertex distanceoptical slope sensorgeometric relationshiprelative angle |
| spellingShingle | Zekui Lv Zhikun Su Dong Zhang Lingyu Gao Zhiming Yang Fengzhou Fang Haitao Zhang Xinghua Li The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array Applied Sciences elliptical paraboloid array self-calibration method vertex distance optical slope sensor geometric relationship relative angle |
| title | The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array |
| title_full | The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array |
| title_fullStr | The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array |
| title_full_unstemmed | The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array |
| title_short | The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array |
| title_sort | self calibration method for the vertex distance of the elliptical paraboloid array |
| topic | elliptical paraboloid array self-calibration method vertex distance optical slope sensor geometric relationship relative angle |
| url | https://www.mdpi.com/2076-3417/9/17/3485 |
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