Surface characterization using Zernike polynomials

Liang Jingyuan; Li Xiwen; Ke Chenghu; Ke Xizheng

doi:10.12086/oee.2024.240163

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Liang J Y, Li X W, Ke C H, et al. Surface characterization using Zernike polynomials[J]. Opto-Electron Eng, 2024, 51(11): 240163. doi: 10.12086/oee.2024.240163

Citation:

Liang J Y, Li X W, Ke C H, et al. Surface characterization using Zernike polynomials[J]. Opto-Electron Eng, 2024, 51(11): 240163. doi: 10.12086/oee.2024.240163

Surface characterization using Zernike polynomials

1.
School of Automation and Information Engineering, Xi'an University of Technology, Xi’an, Shaanxi 710048, China
2.
School of Information Engineering, Xi’an University, Xi’an, Shaanxi 710048, China
3.
Shaanxi Civil-Military Integration Key Laboratory of Intelligence Collaborative Networks, Xi’an, Shaanxi 710048, China

Fund Project: Project supported by Key Industrial Innovation Project of Shaanxi Province (2017ZDCXL-GY-06-01), and National Natural Science Foundation of China (61377080)

More Information

^*Corresponding author: xzke@263.net
CSTR: 32245.14.oee.2024.240163

Received Date 12 July 2024

Revised Date 26 October 2024

Accepted Date 26 October 2024

Published Date 25 November 2024

Abstract

Abstract

Zernike polynomials, due to their orthogonality and rotational invariance, are widely used in the characterization and optimization of optical surfaces. They can effectively reduce fitting errors and provide high-precision descriptions of complex surfaces with only a few coefficients, contributing to improved imaging quality and simplified performance analysis in optical systems. This paper provides an overview of freeform surface description methods, including both global and local approaches. It discusses the research progress on Zernike polynomials in surface characterization, both domestically and internationally, explores their practical applications in this field, and finally anticipates the future prospects of Zernike polynomials in surface characterization.
- Zernike polynomials /
- freeform surface /
- surface characterization /
- optical design

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References

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Overview

Overview

This manuscript offers a detailed review of the advancements in the application of Zernike polynomials for surface characterization in optics. Zernike polynomials, known for their orthogonality and rotational invariance, have been extensively utilized in the characterization and optimization of optical surfaces. This paper first provides an overview of freeform surface description methods and discusses significant progress in the research of Zernike polynomials both domestically and internationally, exploring their practical applications in surface characterization. Finally, it anticipates the future prospects of Zernike polynomials in the field of surface characterization. Freeform surfaces, due to their non-rotational symmetric properties, present significant challenges for traditional optical design. Zernike polynomials offer a precise method to describe these complex surfaces, significantly improving the imaging quality and overall performance of optical systems. The paper highlights the application of Zernike polynomials in optical wavefront analysis and wavefront distortion, emphasizing their ability to decompose complex surfaces into independent components, reducing redundancy, and simplifying error analysis and characterization processes. International research has expanded the application range of Zernike polynomials beyond circular apertures, addressing limitations in traditional methods. These studies have explored applications, such as wavefront reconstruction and optical surface characterization. By developing orthogonal polynomials for elliptical, rectangular, and square apertures, researchers have significantly broadened the applicability of Zernike polynomials. Domestically, Chinese researchers have made significant contributions by generating orthogonal polynomials for non-circular apertures and studying the impact of sampling points on fitting accuracy. This research has enhanced the precision of Zernike polynomials in surface characterization, with applications including wavefront reconstruction and wavefront analysis, demonstrating the versatility and accuracy of Zernike polynomials in various optical design tasks. Compared with other characterization methods such as Q-type polynomials and XY polynomials, Zernike polynomials stand out for their high precision and flexibility, though combining these methods can further enhance the accuracy and efficiency of surface characterization. The manuscript suggests future research should focus on continued theoretical advancements, improved computational efficiency, and integration with other polynomial methods. These improvements will expand the application range and precision of Zernike polynomials in optical system design and optimization, driving progress in optical technology. Continued research and innovation in this field will further enhance the accuracy and efficiency of surface characterization, making Zernike polynomials an increasingly important tool in the advancement of optical systems.