Laser confocal cylindrical radius measurement method and its system

Yang Xiao; Lirong Qiu; Weiqian Zhao

doi:10.1364/AO.56.006596

Applied Optics
Vol. 56,
Issue 23,
pp. 6596-6602
(2017)
•https://doi.org/10.1364/AO.56.006596

Laser confocal cylindrical radius measurement method and its system

Yang Xiao, Lirong Qiu, and Weiqian Zhao

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Yang Xiao, Lirong Qiu, and Weiqian Zhao, "Laser confocal cylindrical radius measurement method and its system," Appl. Opt. 56, 6596-6602 (2017)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: May 9, 2017
- Revised Manuscript: July 14, 2017
- Manuscript Accepted: July 19, 2017
- Published: August 9, 2017

Abstract

This paper proposes a laser confocal cylindrical radius of the curvature measurement (CCRM) method. The CCRM method precisely identifies the positions of the vertex and curvature center of the test cylindrical surface by using the property so that the maximum point of the laser confocal axial intensity curve precisely corresponds to the focus of the laser confocal measurement system, and the accurate distance of these two positions is obtained by the distance measuring instrument, thus achieving the precise measurement of the cylindrical radius. The quadratic fitting method is used to further improve the measurement accuracy. Compared with existing measurement methods, the CCRM method has high measurement precision, simple structure, and strong environmental interference capability, and it is more suitable for engineering applications. Based on the CCRM, the CCRM system is established, and theoretical analysis and preliminary experiments indicate that the relative uncertainty of cylindrical radius measurement is better than 0.045%. Therefore, the CCRM provides an effective approach for the high-precision measurement of cylindrical radius.

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Polynomial	Coefficient ( $λ$ )	Expression	Aberration Name
$Z_{4}$	0.069	$2 ρ^{2} - 1$	Defocus
$Z_{5}$	−0.099	$ρ^{2} \sin (2 θ)$	Primary astigmatism at 45°
$Z_{6}$	−0.202	$ρ^{2} \cos (2 θ)$	Primary astigmatism at 0°
$Z_{7}$	−0.001	$(3 ρ^{3} - 2 ρ) \sin θ$	Primary $y$ coma
$Z_{8}$	−0.124	$(3 ρ^{3} - 2 ρ) \cos θ$	Primary $x$ coma
$Z_{11}$	−0.001	$6 ρ^{4} - 6 ρ^{2} + 1$	Primary spherical

Polynomial	Coefficient ( $λ$ )	Expression	Aberration Name
$Z_{4}$	0.064	$2 ρ^{2} - 1$	Defocus
$Z_{5}$	−0.107	$ρ^{2} \sin (2 θ)$	Primary astigmatism at 45°
$Z_{6}$	−0.214	$ρ^{2} \cos (2 θ)$	Primary astigmatism at 0°
$Z_{7}$	−0.006	$(3 ρ^{3} - 2 ρ) \sin θ$	Primary $y$ coma
$Z_{8}$	−0.102	$(3 ρ^{3} - 2 ρ) \cos θ$	Primary $x$ coma
$Z_{11}$	−0.012	$6 ρ^{4} - 6 ρ^{2} + 1$	Primary spherical

Polynomial	Coefficient ( $λ$ )	Expression	Aberration Name
$Z_{4}$	0.069	$2 ρ^{2} - 1$	Defocus
$Z_{5}$	−0.099	$ρ^{2} \sin (2 θ)$	Primary astigmatism at 45°
$Z_{6}$	−0.202	$ρ^{2} \cos (2 θ)$	Primary astigmatism at 0°
$Z_{7}$	−0.001	$(3 ρ^{3} - 2 ρ) \sin θ$	Primary $y$ coma
$Z_{8}$	−0.124	$(3 ρ^{3} - 2 ρ) \cos θ$	Primary $x$ coma
$Z_{11}$	−0.001	$6 ρ^{4} - 6 ρ^{2} + 1$	Primary spherical

Polynomial	Coefficient ( $λ$ )	Expression	Aberration Name
$Z_{4}$	0.064	$2 ρ^{2} - 1$	Defocus
$Z_{5}$	−0.107	$ρ^{2} \sin (2 θ)$	Primary astigmatism at 45°
$Z_{6}$	−0.214	$ρ^{2} \cos (2 θ)$	Primary astigmatism at 0°
$Z_{7}$	−0.006	$(3 ρ^{3} - 2 ρ) \sin θ$	Primary $y$ coma
$Z_{8}$	−0.102	$(3 ρ^{3} - 2 ρ) \cos θ$	Primary $x$ coma
$Z_{11}$	−0.012	$6 ρ^{4} - 6 ρ^{2} + 1$	Primary spherical

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Applied Optics