Absolute measurement method for a spherical surface by random off-axis rotation based on Zernike polynomials

Pengfeng Sheng; Pengfeng Sheng; Weicheng Gu; Weicheng Gu; Jun Yu; Jun Yu

doi:10.1364/AO.437978

Applied Optics
Vol. 60,
Issue 30,
pp. 9333-9341
(2021)
•https://doi.org/10.1364/AO.437978

Absolute measurement method for a spherical surface by random off-axis rotation based on Zernike polynomials

Pengfeng Sheng, Weicheng Gu, and Jun Yu

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Pengfeng Sheng, Weicheng Gu, and Jun Yu, "Absolute measurement method for a spherical surface by random off-axis rotation based on Zernike polynomials," Appl. Opt. 60, 9333-9341 (2021)

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Abstract

An off-axis rotation absolute measurement method by regarding random shift-rotation movement as off-axis rotation is proposed. The off-axis rotation center is calculated by matching feature points on the measured surface. Then the surface profile is calculated relying on Zernike polynomial fitting. Multiple rotations are carried out to reduce symmetrical and environment errors. $N(N - {1}){/2}$ results can be collected after $ N $ times rotation. Compared to traditional methods, this method can obtain accurate results with high efficiency and does not need high precision positioning.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (19)

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	$T_{1}$ and $T_{2}$	$T_{1}$ and $T_{3}$	$T_{1}$ and $T_{4}$	$T_{2}$ and $T_{3}$	$T_{2}$ and $T_{4}$	$T_{3}$ and $T_{4}$
$X$ coordinate of center	36.323	27.155	−48.557	6.264	0.611	7.100
$Y$ coordinate of center	19.500	5.993	16.863	−42.653	14.111	3.857
Rotation angle (°)	13.603	27.610	−9.966	14.018	−23.568	−37.576

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Applied Optics