Accurate mechanical–optical theoretical model of cross-axis sensitivity of an interferometric micro-optomechanical accelerometer

Weidong Fang; Qixuan Zhu; Jian Bai; Jian Bai; Jiaxiao Chen; Xiang Xv; Chen Wang; Qianbo Lu

doi:10.1364/AO.447762

Applied Optics
Vol. 61,
Issue 11,
pp. 3201-3208
(2022)
•https://doi.org/10.1364/AO.447762

Accurate mechanical–optical theoretical model of cross-axis sensitivity of an interferometric micro-optomechanical accelerometer

Weidong Fang, Qixuan Zhu, Jian Bai, Jiaxiao Chen, Xiang Xv, Chen Wang, and Qianbo Lu

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Weidong Fang, Qixuan Zhu, Jian Bai, Jiaxiao Chen, Xiang Xv, Chen Wang, and Qianbo Lu, "Accurate mechanical–optical theoretical model of cross-axis sensitivity of an interferometric micro-optomechanical accelerometer," Appl. Opt. 61, 3201-3208 (2022)

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Table of Contents Category
- Optical Devices, Sensors, and Detectors
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About this Article
History
- Original Manuscript: November 19, 2021
- Revised Manuscript: March 15, 2022
- Manuscript Accepted: March 21, 2022
- Published: April 7, 2022

Abstract

An interferometric micro-optomechanical accelerometer usually has ultrahigh sensitivity and accuracy. However, cross-axis interference inevitably degrades the performance, including its detection accuracy and output signal contrast. To accurately clarify the influence of cross-axis interference, a modified mechanical–optical theoretical model is established. The rotation of the proof mass and the detected light intensity are quantitatively investigated with a load of cross-axis acceleration. A simulation and experiment are performed to verify the correctness of the theoretical model when the cross-axis acceleration is from 0 to 0.175 g. The results demonstrate that this model has a more than fivefold accuracy increase compared with conventional theoretical models when the cross-axis acceleration is from 0.06 to 0.175 g. In addition, we provide a suppression method to diminish the rotation of the proof mass based on squeeze film air damping, which significantly suppresses the contrast reduction caused by cross-axis interference.

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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 requests.

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Parameter Name	Value
Half-length of the proof mass $a$	$1.5 \times 1 0^{- 3} m$
Height of the proof mass $h$	$4.0 \times 1 0^{- 6} m$
Length of thigh part of crab-shaped cantilever $l_{1}$	$3.35 \times 1 0^{- 3} m - 10.35 \times 1 0^{- 3} m$
Length of shin part of crab-shaped cantilever $l_{2}$	$1.0 \times 1 0^{- 3} m$
Width of crab-shaped cantilever $w$	$3.0 \times 1 0^{- 4} m$
Thickness of crab-shaped cantilever $t$	$1.0 \times 1 0^{- 5} m$
Elastic modulus of silicon $E$	166 GPa
Shear modulus of silicon $G$	64 GPa
Cross-axis acceleration $a_{c}$	$1 m / s^{2}$

Parameter Name	Value
Radius of the laser beam $r$	$4.0 \times 1 0^{- 4} m$
Wavelength of the laser $λ$	632.8 nm
Pitch of the grating $d$	$1.6 \times 1 0^{- 6} m$
Thickness of the grating $t$	$5.0 \times 1 0^{- 4} m$
Initial distance between the lower surface of the grating and the upper surface of the proof mass $z$	$1 \times 1 0^{- 2} m$
Initial distance between the upper surface of the grating and the light source $L$	0.2 m
Cross-axis acceleration $a_{c}$	$g \sin α$

Parameter Name	Value
Half-length of the proof mass $a$	$1.5 \times 1 0^{- 3} m$
Height of the proof mass $h$	$4.0 \times 1 0^{- 6} m$
Length of thigh part of crab-shaped cantilever $l_{1}$	$3.35 \times 1 0^{- 3} m - 10.35 \times 1 0^{- 3} m$
Length of shin part of crab-shaped cantilever $l_{2}$	$1.0 \times 1 0^{- 3} m$
Width of crab-shaped cantilever $w$	$3.0 \times 1 0^{- 4} m$
Thickness of crab-shaped cantilever $t$	$1.0 \times 1 0^{- 5} m$
Elastic modulus of silicon $E$	166 GPa
Shear modulus of silicon $G$	64 GPa
Cross-axis acceleration $a_{c}$	$1 m / s^{2}$

Parameter Name	Value
Radius of the laser beam $r$	$4.0 \times 1 0^{- 4} m$
Wavelength of the laser $λ$	632.8 nm
Pitch of the grating $d$	$1.6 \times 1 0^{- 6} m$
Thickness of the grating $t$	$5.0 \times 1 0^{- 4} m$
Initial distance between the lower surface of the grating and the upper surface of the proof mass $z$	$1 \times 1 0^{- 2} m$
Initial distance between the upper surface of the grating and the light source $L$	0.2 m
Cross-axis acceleration $a_{c}$	$g \sin α$

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Equations (28)

Applied Optics