Submicron Displacement Measurement Method Based on Fabry-Perot Etalon

Fig. 6. Concentric interference ring images. (a) Original concentric interference ring image; (b) concentric interference ring image with high brightness

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Fig. 7. Experimental device diagram for linearity comparison of micro-displacement measuring system based on F-P etalon

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Fig. 8. Fitting straight line of center displacements at different positions and interferometer indication values

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Table 1. Standard deviation of coordinate at peak position of each ring (No. 7-16)

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Table 1. Standard deviation of coordinate at peak position of each ring (No. 7-16)

RingNo.	$\begin{matrix} \bar{S} \end{matrix}$ y_+ij/w″	$\begin{matrix} \bar{S} \end{matrix}$ y'_-ij/w″	$\begin{matrix} \bar{S} \end{matrix}$ x_+ij/w″	$\begin{matrix} \bar{S} \end{matrix}$ x_-ij/w″	Averagevalue /w″
7	0.026	0.031	0.023	0.038	0.030
8	0.027	0.025	0.034	0.038	0.031
9	0.023	0.024	0.032	0.034	0.028
10	0.024	0.025	0.031	0.036	0.029
11	0.025	0.026	0.037	0.032	0.030
12	0.026	0.030	0.037	0.032	0.031
13	0.031	0.037	0.021	0.033	0.031
14	0.027	0.058	0.033	0.026	0.036
15	0.027	0.066	0.042	0.030	0.041
16	0.027	0.071	0.035	0.036	0.042

Table 2. Standard deviation of center coordinates at different positions within 3 mm

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Table 2. Standard deviation of center coordinates at different positions within 3 mm

Numbern	Axis	Initialposition /w″	Moving1 mm /w″	Moving2 mm /w″	Moving3 mm /w″
1	x'	0.0017	0.0020	0.0019	0.0026
	y'	0.0022	0.0022	0.0021	0.0019
2	x'	0.0016	0.0022	0.0027	0.0024
	y'	0.0020	0.0020	0.0018	0.0021
3	x'	0.0022	0.0021	0.0023	0.0031
	y'	0.0023	0.0022	0.0018	0.0020
4	x'	0.0019	0.0023	0.0019	0.0026
	y'	0.0024	0.0021	0.0020	0.0019
5	x'	0.0019	0.0022	0.0021	0.0026
	y'	0.0021	0.0024	0.0021	0.0021

Table 3. Center coordinates of the 14th ring of eight pictures and their standard deviation

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Table 3. Center coordinates of the 14th ring of eight pictures and their standard deviation

n	1	2	3	4	5	6	7	8
$\begin{matrix} {\bar{y}}_{0} \end{matrix}$ '	12.899w″	11.485w″	9.893w″	8.401w″	6.674w″	5.124w″	3.566w″	2.058w″
$\begin{matrix} \bar{y} \end{matrix}$ '^*₀_i	12.896w″	11.494w″	9.899w″	8.405w″	6.677w″	5.128w″	3.567w″	2.054w″
$\begin{matrix} S_{\bar{y}' 0 i} \end{matrix}$	0.0017w″	0.002w″	0.0013w″	0.0016w″	0.0012w″	0.0015w″	0.0014w″	0.0011w″
S_int	0.0038w″	0.0042w″	0.0031w″	0.0044w″	0.0036w″	0.0042w″	0.0041w″	0.0030w″
S_ext	0.0028w″	0.0033w″	0.0032w″	0.0031w″	0.0030w″	0.0028w″	0.0030w″	0.0032w″
S_y'₀_i	0.0038w″	0.0042w″	0.0032w″	0.0044w″	0.0036w″	0.0042w″	0.0041w″	0.0030w″
$\begin{matrix} \bar{x} \end{matrix}$ '₀	14.597w″	16.267w″	17.673w″	19.252w″	20.597w″	22.107w″	23.580w″	25.138w″
$\begin{matrix} \bar{x} \end{matrix}$ '^*₀_i	14.597w″	16.267w″	17.674w″	19.252w″	20.596w″	22.107w″	23.579w″	25.138w″
$\begin{matrix} S_{\bar{x}' 0 i} \end{matrix}$	0.0004w″	0.0006w″	0.0005w″	0.0005w″	0.0005w″	0.0004w″	0.0003w″	0.0003w″
S_ext	0.0012w″	0.0016w″	0.0014w″	0.0013w″	0.0014w″	0.0011w″	0.0007w″	0.0009w″
S_int	0.0029w″	0.004w″	0.0031w″	0.0039w″	0.0036w″	0.0035w″	0.0029w″	0.0036w″
S_x'₀_i	0.0029w″	0.004w″	0.0031w″	0.0039w″	0.0036w″	0.0035w″	0.0029w″	0.0036w″

Table 4. Center coordinate information, center shifts, and interferometer indication values at different positions

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Table 4. Center coordinate information, center shifts, and interferometer indication values at different positions

n	(x₀,y₀)/w″	δ/w″	S_δ/w″	Interferometerindication /nm
1	(14.597,12.897)	0	0	4794.20
2	(16.267,11.490)	2.184	0.0052	9782.72
3	(17.673,9.896)	4.298	0.0046	14772.23
4	(19.252,8.403)	6.471	0.0053	19756.09
5	(20.596,6.676)	8.643	0.0049	24727.58
6	(22.107,5.126)	10.807	0.0052	29717.13
7	(23.579,3.566)	12.952	0.0049	34709.35
8	(25.138,2.056)	15.121	0.0048	39701.36

Table 5. Calculation results of evaluation parameters of fitting straight line
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Table 5. Calculation results of evaluation parameters of fitting straight line
Parameter S_b₁/(w″·nm^-1) S_b₀/w″ $\begin{matrix} \frac{S_{b 0 / b 1}}{(b_{0} / b_{1})} \end{matrix}$ r² S_y/w″ U″_y'/w″ U_Lr /%
Value 4.8×10^-7 0.012 6.9×10^-3 1 0.016 0.041 0.27

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Xiaoyan Shen, Xuhui Lan, Henian Zhu, Zhipeng Sun, Jing Yu. Submicron Displacement Measurement Method Based on Fabry-Perot Etalon[J]. Chinese Journal of Lasers, 2019, 46(12): 1204002

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Paper Information

Category: measurement and metrology

Received: Jul. 4, 2019

Accepted: Aug. 19, 2019

Published Online: Dec. 2, 2019

The Author Email: Shen Xiaoyan (xyshen@cjlu.edu.cn)

DOI:10.3788/CJL201946.1204002

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Standard deviation of coordinate at peak position of each ring (No. 7-16)

Table 1. Standard deviation of coordinate at peak position of each ring (No. 7-16)

Table 2. Standard deviation of center coordinates at different positions within 3 mm

Table 2. Standard deviation of center coordinates at different positions within 3 mm

Table 3. Center coordinates of the 14th ring of eight pictures and their standard deviation

Table 3. Center coordinates of the 14th ring of eight pictures and their standard deviation

Table 4. Center coordinate information, center shifts, and interferometer indication values at different positions

Table 4. Center coordinate information, center shifts, and interferometer indication values at different positions

Table 5. Calculation results of evaluation parameters of fitting straight line

Table 5. Calculation results of evaluation parameters of fitting straight line