Modal Reconstruction Based on Arbitrary High-Order Zernike Polynomials for Deflectometry

Duy-Thai Nguyen, Kim Cuc Thi Nguyen, Binh X. Cao, Tran Van-Thuc, Tiendung Vu () and Ngoc-Tam Bui
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Duy-Thai Nguyen: School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam
Kim Cuc Thi Nguyen: School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam
Binh X. Cao: School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam
Tran Van-Thuc: School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam
Tiendung Vu: School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam
Ngoc-Tam Bui: Innovative Global Program, Shibaura Institute of Technology, Tokyo 135-8548, Japan

Mathematics, 2023, vol. 11, issue 18, 1-12

Abstract: Deflectometry is a non-destructive, full-field phase measuring method, which is usually used for inspecting optical specimens with special characteristics, such as highly reflective or specular surfaces, as well as free-form surfaces. One of the important steps in the Deflectometry method is to retrieve the surface from slope data of points on the sample map or surface reconstruction. This paper proposes a modal reconstruction method using an adjustable number of Zernike polynomials. In addition, the proposed method enables the analyses on practical surfaces that require an infinite number of Zernike terms to be represented. Experiments on simulated surfaces indicated that the algorithm is able to reveal the number of major-contributing Zernike terms, as well as reconstruct the surface with a micrometer-scale from slope data with a signal-to-noise ratio of 10.

Keywords: deflectometry; modal reconstruction; zernike polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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