Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method

doi:10.1007/s40436-024-00509-w

Advances in Manufacturing ›› 2025, Vol. 13 ›› Issue (3): 493-510.doi: 10.1007/s40436-024-00509-w

• • 上一篇

Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method

Ting Chen¹, Pei-De Yang², Xiang-Chao Zhang², Wei Lang², Yu-Nuo Chen², Min Xu^1,2

1. Academy for Engineering and Technology, Fudan University, Shanghai, 200433, People's Republic of China;
2. Shanghai Engineering Research Center of Ultra-Precision Optical Manufacturing, School of Information Science and Technology, Fudan University, Shanghai, 200438, People's Republic of China

收稿日期:2023-08-02 修回日期:2023-12-26 发布日期:2025-09-19
通讯作者: Xiang-Chao Zhang,E-mail:zxchao@fudan.edu.cn E-mail:zxchao@fudan.edu.cn
作者简介:Ting Chen received the B.E. degree from Jiangsu Normal University in 2020. She is currently pursuing the Ph.D. degree in optical engineering major from Fudan University. Her research interests include optical measurement technology by def lectometry and optical imaging.
Pei-De Yang received the B.E. degree from Tianjin University in 2021. He is currently pursuing the M.E. degree in Electronic and Information Engineering at Fudan University. His research interests include 3D optical measurement technology, image processing and machine learning.
Xiang-Chao Zhang received the B.E degree in measurement technology from the University of Science and Technology of China in 2005 and the Ph.D. degree in precision measurement and instrumentation from the University of Huddersfield, UK in 2009. He is currently a professor with the Department of Optical Science and Engineering, Fudan University. He is a senior member of SPIE, and a member of IEEE and OSA. His research interests include optical measurement technology, micro/nano optics and image processing.
Wei Lang received the B.E. degree from Henan Normal University in 2017, and the M.E. degree from Sichuan University, in 2020. He is currently pursuing the Ph.D. degree in optical engineering major from Fudan University. His research interests include 3D optical measurement technology and machine vision.
Yu-Nuo Chen received his B.E. degree from Xiamen University in 2020. He is currently pursuing the Ph.D. degree in optical engineering major from Fudan University. His research interests include 3D optical measurement technology and machine learning.
Min Xu received his M.E. and Ph. D degrees in Precision Optical Measurement and Technology from Zhejiang University in 1990 and 1998. Since 2008, he has been with the Department of Optical Science and Engineering, Fudan University as a professor. He is the executive director of the Chinese Society of Optical Engineering. He was awarded the second prize of Science and Technology Progress Award of the Ministry of Education in 2015. His research interests include fabrication and measurement technology of optical aspherical surfaces, freeform surfaces and microstructure arrays of various materials.
基金资助:
This work is supported in part by the National Natural Science Foundation of China (Grant No. 51875107) and Jiangsu Provincial Key Research and Development Program (Grant No. BE2021035).

Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method

Ting Chen¹, Pei-De Yang², Xiang-Chao Zhang², Wei Lang², Yu-Nuo Chen², Min Xu^1,2

1. Academy for Engineering and Technology, Fudan University, Shanghai, 200433, People's Republic of China;
2. Shanghai Engineering Research Center of Ultra-Precision Optical Manufacturing, School of Information Science and Technology, Fudan University, Shanghai, 200438, People's Republic of China

Received:2023-08-02 Revised:2023-12-26 Published:2025-09-19
Supported by:
This work is supported in part by the National Natural Science Foundation of China (Grant No. 51875107) and Jiangsu Provincial Key Research and Development Program (Grant No. BE2021035).

摘要/Abstract

摘要： Transparent optical elements play a significant role in optical imaging and sensing, and the form qualities of these elements are critical to the functionalities of opto-electrical equipment. Therefore, rapid measurement of advanced transparent optical devices is urgently needed. Deflectometry, as a commonly used measurement method, has broad applications in form measurement. However, there are some challenges in the reflective deflectometric measurement of transparent elements, such as fringe superposition, low reflectivity, and non-uniform backgrounds, which severely affect the measurement accuracy. To address these issues, a single-frame fringe separation method is proposed for the deflectometric measurement of transparent elements. A fast iterative filtering method is utilized for coarse fringe separation and a convolutional neural network is adopted to solve the information leakage and incomplete fringe separation. The construction of the neural network involves improving and refining the filtering method to achieve precise separation of fringes. The proposed method achieves fringe separation and forms reconstruction of the upper and lower surfaces. Through simulations and experiments, the effectiveness and robustness of the proposed method are demonstrated, and the measurement accuracy can achieve 65 nm root-of-mean-squared-error (RMSE).

The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-024-00509-w

关键词: Transparent element, Deflectometry, Fringe separation, Fast iterative filtering, Deep learning

Abstract: Transparent optical elements play a significant role in optical imaging and sensing, and the form qualities of these elements are critical to the functionalities of opto-electrical equipment. Therefore, rapid measurement of advanced transparent optical devices is urgently needed. Deflectometry, as a commonly used measurement method, has broad applications in form measurement. However, there are some challenges in the reflective deflectometric measurement of transparent elements, such as fringe superposition, low reflectivity, and non-uniform backgrounds, which severely affect the measurement accuracy. To address these issues, a single-frame fringe separation method is proposed for the deflectometric measurement of transparent elements. A fast iterative filtering method is utilized for coarse fringe separation and a convolutional neural network is adopted to solve the information leakage and incomplete fringe separation. The construction of the neural network involves improving and refining the filtering method to achieve precise separation of fringes. The proposed method achieves fringe separation and forms reconstruction of the upper and lower surfaces. Through simulations and experiments, the effectiveness and robustness of the proposed method are demonstrated, and the measurement accuracy can achieve 65 nm root-of-mean-squared-error (RMSE).

The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-024-00509-w

Key words: Transparent element, Deflectometry, Fringe separation, Fast iterative filtering, Deep learning

Ting Chen, Pei-De Yang, Xiang-Chao Zhang, Wei Lang, Yu-Nuo Chen, Min Xu. Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method[J]. Advances in Manufacturing, 2025, 13(3): 493-510.

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Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method

Separation of fringe patterns in fast deflectometric measurement of transparent optical elements based on neural network-assisted fast iterative filtering method

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