Vacuum compatible vertical-laser alignment method based on an oil mirror and air-spaced doublets

Tao Zeng; Yang Bai; Zhengkun Li; Yue Wang

doi:10.1364/AO.480950

Applied Optics
Vol. 62,
Issue 3,
pp. 601-611
(2023)
•https://doi.org/10.1364/AO.480950

Vacuum compatible vertical-laser alignment method based on an oil mirror and air-spaced doublets

Tao Zeng, Yang Bai, Zhengkun Li, and Yue Wang

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Tao Zeng, Yang Bai, Zhengkun Li, and Yue Wang, "Vacuum compatible vertical-laser alignment method based on an oil mirror and air-spaced doublets," Appl. Opt. 62, 601-611 (2023)

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Abstract

In the field of precision measurement and metrology, a vertical laser is a valuable measurement tool. Its applications include, but are not limited to, the measurement of vertical displacement and attitude in the Kibble balance and joule balance for kilogram realization. A vacuum compatible, vertical-laser alignment method based on an oil mirror and air-spaced doublets is proposed to measure and compensate the vertical deviation angle of the laser beams. Dimethyl silicone oil was selected as the natural direction reference, and the air-spaced doublets were designed as the focusing elements to make the deviation angle correspond to a distance of spots. The corresponding alignment system is vacuum compatible, nonmagnetic, and can be miniaturized. In addition to the mass traceability in the realization of a kilogram, this system can also be applied to the gravity measurements of outer space planets in the field of aerospace science. The off-axis error, which is the highly influential systematic error of the alignment system, is suppressed by replacing the plano-convex lens with a combined optical element—“air-spaced doublets+aperture.” The performance of the alignment system has been investigated by experiments. The Type B uncertainty of the alignment system was evaluated to be 19.19 µrad.

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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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Matrix	$F$	$E$	$A$	$B$	$C$	$S$
row and column	$1 \times 2$	$2 \times 2$	$2 \times 1$	$2 \times 4$	$5 \times 1$	$1 \times 1$
in $x$	$[f f]$	$[\begin{matrix} \frac{1}{\cos θ_{3 x}} & 0 \\ 0 & \frac{1}{\cos θ_{3 x}} \end{matrix}]$	$[\begin{matrix} θ_{x} \\ θ_{x} \end{matrix}]$	$[\begin{matrix} - 2 & 1 & 2 & 2 \\ 2 & 1 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1 \\ θ_{0 x} \\ θ_{1 x} \\ \begin{array}{l} θ_{2 x} \\ θ_{3 x} \end{array} \end{matrix}]$	$S_{x}$
in $y$	$[f f]$	$[\begin{matrix} \frac{1}{\cos θ_{3 y}} & 0 \\ 0 & \frac{1}{\cos θ_{3 y}} \end{matrix}]$	$[\begin{matrix} θ_{y} \\ θ_{y} \end{matrix}]$	$[\begin{matrix} - 2 & 1 & 2 & 2 \\ 2 & 1 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1 \\ θ_{0 y} \\ θ_{1 y} \\ \begin{array}{l} θ_{2 y} \\ θ_{3 x} \end{array} \end{matrix}]$	$S_{y}$

Error Source	Standard Uncertainty
$θ_{0}$	100.72 µrad
$θ_{1}$	2.80 µrad
$θ_{2}$	4.21 µrad
$θ_{3}$	6.99 mrad
$θ_{4}$	2.52 mrad
$f$	289 µm
$S$	1.58 µm

Liquid Material	Water	Alcohol	Silicone Oil
Dynamic viscosity $(20^{\circ} C) / P a \cdot s$	0.001	0.002	0.35
Position variation of liquid reflection spot/µm	$\pm 55 µ m$	$\pm 8 µ m$	$\pm 0.8 µ m$

Error Source	Standard Uncertainty	Sensitivity Coefficient	$u_{θ - 1}$
$θ_{0}$	100.72 µrad	0	18.61 µrad
$θ_{1}$	2.80 µrad	$- 1$
$θ_{2}$	4.21 µrad	$- 1.5$
$θ_{3}$	6.99 mrad	$- 1$
$θ_{4}$	2.52 mrad	0
$f$	289 µm	$0.52 \times 10^{- 6} {m m}^{- 1}$
$S$	1.58 µm	$1 \times 10^{- 5} µ m^{- 1}$

Matrix	$F$	$E$	$A$	$B$	$C$	$S$
row and column	$1 \times 2$	$2 \times 2$	$2 \times 1$	$2 \times 4$	$5 \times 1$	$1 \times 1$
in $x$	$[f f]$	$[\begin{matrix} \frac{1}{\cos θ_{3 x}} & 0 \\ 0 & \frac{1}{\cos θ_{3 x}} \end{matrix}]$	$[\begin{matrix} θ_{x} \\ θ_{x} \end{matrix}]$	$[\begin{matrix} - 2 & 1 & 2 & 2 \\ 2 & 1 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1 \\ θ_{0 x} \\ θ_{1 x} \\ \begin{array}{l} θ_{2 x} \\ θ_{3 x} \end{array} \end{matrix}]$	$S_{x}$
in $y$	$[f f]$	$[\begin{matrix} \frac{1}{\cos θ_{3 y}} & 0 \\ 0 & \frac{1}{\cos θ_{3 y}} \end{matrix}]$	$[\begin{matrix} θ_{y} \\ θ_{y} \end{matrix}]$	$[\begin{matrix} - 2 & 1 & 2 & 2 \\ 2 & 1 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1 \\ θ_{0 y} \\ θ_{1 y} \\ \begin{array}{l} θ_{2 y} \\ θ_{3 x} \end{array} \end{matrix}]$	$S_{y}$

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Applied Optics