Micro-angle Measurement Method and Its Accuracy Evaluation Based on Fabry-Perot Etalon

Yuan LIU; Xiaoyan SHEN; Shinan ZHOU; Xubo GUO; Jing YU; Dongsheng LI; Xuhui LAN

doi:10.3788/gzxb20215007.0712004

Journals >Acta Photonica Sinica >Volume 50 >Issue 7 >Page 161 > Article

Acta Photonica Sinica
Vol. 50, Issue 7, 161 (2021)

Micro-angle Measurement Method and Its Accuracy Evaluation Based on Fabry-Perot Etalon

Yuan LIU¹, Xiaoyan SHEN¹, Shinan ZHOU¹, Xubo GUO²..., Jing YU¹, Dongsheng LI¹ and Xuhui LAN¹|Show fewer author(s)

Author Affiliations

¹College of Metrology & Measurement Engineering， China Jiliang University， Hangzhou3008， China

²Department of Physics， Tsinghua University， Beijing100084， China

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DOI: 10.3788/gzxb20215007.0712004 Cite this Article

Yuan LIU, Xiaoyan SHEN, Shinan ZHOU, Xubo GUO, Jing YU, Dongsheng LI, Xuhui LAN. Micro-angle Measurement Method and Its Accuracy Evaluation Based on Fabry-Perot Etalon[J]. Acta Photonica Sinica, 2021, 50(7): 161 Copy Citation Text

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Fig. 1. Micro-angle measurement optical path based on F-P etalon

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Fig. 2. Basic process of lens focal length and center micro-displacement measurement

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Fig. 3. Micro-angle measuring device

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Fig. 4. Concentric interference ring at 546 nm wavelength

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Fig. 5. Schematic diagram of circle data processing

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Position	$F W H M x +$	$F W H M x -$	$F W H M y +$	$F W H M y -$	$\bar{F W H M}$
0	10.225	8.843	11.422	18.467	12.239
1	8.945	7.625	11.026	11.681	9.819
2	7.687	7.538	10.428	11.729	9.345
3	6.495	6.451	8.129	13.581	8.664
4	5.607	6.080	6.625	8.668	6.745
5	5.268	6.257	5.823	5.493	5.710
6	5.356	6.001	6.052	5.316	5.681
7	6.816	6.553	8.530	7.064	7.241
8	7.682	6.866	11.664	11.038	9.313
9	9.788	7.517	13.704	13.164	11.043
10	8.785	8.459	20.348	12.068	12.415

Table 1. FWHM value under different focusing positions （）

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Serial number of the ring i	$s_{x' +}$	$s_{x' -}$	$s_{y' +}$	$s_{y' -}$	$\bar{s}$
1	0.080	0.088	0.081	0.090	0.085
2	0.056	0.064	0.056	0.064	0.060
3	0.043	0.061	0.052	0.056	0.053
4	0.034	0.052	0.043	0.047	0.044
5	0.033	0.046	0.041	0.038	0.039
6	0.024	0.044	0.038	0.035	0.035
7	0.019	0.046	0.031	0.027	0.031
8	0.016	0.039	0.026	0.024	0.026
9	0.017	0.030	0.023	0.019	0.022
10	0.015	0.033	0.015	0.013	0.019
11	0.015	0.029	0.013	0.012	0.017
12	0.015	0.025	0.012	0.010	0.015
13	0.018	0.021	0.012	0.011	0.016
14	0.019	0.023	0.015	0.011	0.017
15	0.019	0.019	0.014	0.014	0.017
16	0.021	0.016	0.014	0.014	0.016
17	0.025	0.017	0.017	0.014	0.018

Table 2. Calculated result of the standard deviationof the peak position coordinates in different directions and the average （）

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No.	$f$ /mm	$\frac{U'_{p} (f_{w})}{f_{w}}$	$δ$ /μm	$s_{δ}$ /μm	$α$ /（″）	$U_{p} {(α)}_{1}$ /（″）
0-1	78.18	0.014	0.157	0.012	0.207	0.041
0-2			0.269	0.012	0.354	0.041
0-3			0.263	0.012	0.348	0.041
1-1			76.991	0.014	101.567	0.056
1-2			77.169	0.013	101.802	0.056
1-3			77.237	0.012	101.891	0.056
2-1			153.655	0.014	202.701	0.071
2-2			153.699	0.013	202.759	0.071
2-3			153.806	0.013	202.900	0.071
3-1			230.224	0.012	303.710	0.087
3-2			230.291	0.012	303.800	0.087
3-3			230.434	0.013	303.988	0.087
4-1			306.901	0.012	404.863	0.102
4-2			306.958	0.012	404.937	0.102
4-3			307.099	0.011	405.123	0.102
5-1			383.563	0.012	505.993	0.117
5-2			383.611	0.012	506.057	0.117
5-3			383.819	0.012	506.330	0.117
6-1			460.229	0.012	607.128	0.132
6-2			460.323	0.012	607.252	0.132
6-3			460.297	0.012	607.217	0.132

Table 3. Experimental results of 600″ inner angle measurement

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Measurement uncertainty	Uncertainty component	Expression
$U_{p} (δ_{w})$ $(υ_{e f f 1} = 39, p = 0.95)$	${u_{1}}_{r e l}$	Take 15th $s_{δ_{w}}$ ， ${u_{1}}_{r e l} = {\bar{s}}_{δ_{w}} = 0.0030 w'$
	${u_{2}}_{r e l}$	$L \leq \pm 0.001 w'$ ， ${u_{2}}_{r e l} = \frac{L}{\sqrt[]{3}} = 5.8 \times 10^{- 4} w'$
	${u_{3}}_{r e l}$	d=2015522.7 nm， $Δ n = \pm 4.75 \times 10^{- 7}$ ， Cosine of the cone angle of the optimal ring $c o s θ = 0.9983$ ， ${u_{3}}_{r e l} = \frac{Δ c}{\sqrt[]{3}} = \frac{d Δ n / c o s θ}{\sqrt[]{3}} = 1.4 \times 10^{- 4} w'$
	${u_{4}}_{r e l}$	$β = 3.5 \times 10^{- 6} K^{- 1}$ ，Optimal ring diameter $l = 2328.978 w'$ ， $Δ t \leq \pm 0.5 ℃$ ， ${u_{4}}_{r e l} = \frac{Δ l}{\sqrt[]{3}} = \frac{β l Δ t}{\sqrt[]{3}} = 0.0024 w'$
$U_{p} (f_{w})$ $(υ_{e f f 2} = 21, p = 0.95)$	${u_{5}}_{r e l}$	$f_{w} = 19743.904 w'$ ， ${s_{f}}_{_{w}} = 0.13 w'$ ， ${u_{5}}_{r e l} = s_{f_{w}} = 0.13 w'$
$U_{p} (f_{w})$ $(υ_{e f f 2} = 21, p = 0.95)$	${u_{6}}_{r e l}$	$u_{f a d} = \pm 2.466 w'$ ， ${u_{6}}_{r e l} = \frac{u_{f a d}}{\sqrt[]{3}} = 1.4 w'$

Table 4. Calculation instructions of measurement uncertainty

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No.	$f$ /mm	$\frac{U'_{p} (f_{w})}{f_{w}}$	$δ$ /μm	$s_{δ}$ /μm	$α$ /（″）	$U_{p} {(α)}_{2}$ /（″）
0-1	78.157	0.014	0. 163	0.010	0.216	0.038
0-2			0. 162	0.011	0.214	0.038
0-3			0. 138	0.012	0.181	0.038
1-1			7.630	0.012	10.069	0.040
1-2			7.676	0.011	10.129	0.040
1-3			7.550	0.011	9.962	0.040
2-1			15.770	0.011	20.810	0.041
2-2			15.912	0.011	20.996	0.041
2-3			15.939	0.011	21.032	0.041
3-1			24.089	0.012	31.786	0.043
3-2			24.176	0.011	31.901	0.043
3-3			24.181	0.012	31.908	0.043
4-1			32.446	0.012	42.814	0.045
4-2			32.602	0.012	43.020	0.045
4-3			32.516	0.012	42.906	0.045