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Article

Accurate Lens-Distortion Measurement Through Detector Nyquist Sampling

by
Yongqiang Yang
1,2,
Zhiyi Wang
1,
Junlin Li
1,
Zhongming Li
1,
Jianlin Lv
1,
Min Zhao
1,
Yanfu Tang
1 and
Jianli Wang
1,2,*
1
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2
University of Chinese Academy of Sciences, Beijing 100049, China
*
Author to whom correspondence should be addressed.
Sensors 2026, 26(5), 1550; https://doi.org/10.3390/s26051550
Submission received: 22 January 2026 / Revised: 26 February 2026 / Accepted: 27 February 2026 / Published: 1 March 2026
(This article belongs to the Special Issue Measurement Sensors and Machine Learning Applications in Modern Manufacturing)
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Abstract

Distortion is a key parameter affecting the imaging performance of lenses. In this study, we propose a testing method based on detector Nyquist sampling of image data to achieve high-precision measurements of the distortion distribution of lenses. The distribution patterns of distortions in horizontal and vertical directions can be obtained by analyzing the distribution patterns of Moiré fringes in images under Nyquist sampling conditions and using phase-shift algorithms. The distortion-distribution characteristics of the lens are then calculated using distortion formulas. This method is characterized by high testing accuracy and sampling resolution. The image-plane distortion distribution exhibited a consistent linear trend when the object-plane position varied within a limited spatial range. Furthermore, the proposed method achieved a magnification deviation factor repeatability accuracy of approximately ±108 nm/cm and third-order distortion-measurement accuracy of approximately ±108 nm/cm3. This method enables a high-precision distortion evaluation of conventional industrial imaging lenses.
Keywords: fringe pattern; Nyquist sampling; phase shift; distortion fringe pattern; Nyquist sampling; phase shift; distortion

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MDPI and ACS Style

Yang, Y.; Wang, Z.; Li, J.; Li, Z.; Lv, J.; Zhao, M.; Tang, Y.; Wang, J. Accurate Lens-Distortion Measurement Through Detector Nyquist Sampling. Sensors 2026, 26, 1550. https://doi.org/10.3390/s26051550

AMA Style

Yang Y, Wang Z, Li J, Li Z, Lv J, Zhao M, Tang Y, Wang J. Accurate Lens-Distortion Measurement Through Detector Nyquist Sampling. Sensors. 2026; 26(5):1550. https://doi.org/10.3390/s26051550

Chicago/Turabian Style

Yang, Yongqiang, Zhiyi Wang, Junlin Li, Zhongming Li, Jianlin Lv, Min Zhao, Yanfu Tang, and Jianli Wang. 2026. "Accurate Lens-Distortion Measurement Through Detector Nyquist Sampling" Sensors 26, no. 5: 1550. https://doi.org/10.3390/s26051550

APA Style

Yang, Y., Wang, Z., Li, J., Li, Z., Lv, J., Zhao, M., Tang, Y., & Wang, J. (2026). Accurate Lens-Distortion Measurement Through Detector Nyquist Sampling. Sensors, 26(5), 1550. https://doi.org/10.3390/s26051550

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