Nanometer measurement with a dual Fabry–Perot interferometer

Benyong Chen; Ruogu Zhu; Zhaotong Wu; Dacheng Li; Songling Guo

doi:10.1364/AO.40.005632

Applied Optics
Vol. 40,
Issue 31,
pp. 5632-5637
(2001)
•https://doi.org/10.1364/AO.40.005632

Nanometer measurement with a dual Fabry–Perot interferometer

Benyong Chen, Ruogu Zhu, Zhaotong Wu, Dacheng Li, and Songling Guo

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Benyong Chen, Ruogu Zhu, Zhaotong Wu, Dacheng Li, and Songling Guo, "Nanometer measurement with a dual Fabry–Perot interferometer," Appl. Opt. 40, 5632-5637 (2001)

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Abstract

On the basis of analyzing sinusoidal phase-modulating Fabry–Perot interferometry, a method, believed to be novel, is proposed for achieving nanometer measurement accuracy by measuring the time interval between equal amplitudes of the two elementary frequency signals of the transmitted intensities of a dual Fabry–Perot interferometer. A nanometer measurement system based on the method was designed and tested. The experimental results show that the displacement resolution of the system is 0.32 nm at a 1-kHz modulating signal.

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V (V)	ΔV (V)	V′ (V)	Δt′ (µs)	Δt (µs)	Δd (nm)	d′ (nm)
7.3			42.6
7.8	0.5		45.4	2.8	0.89
8.2	0.4	0.9	47.7	2.3	0.73	1.62
8.7	0.5	1.4	51.4	3.7	1.17	2.79
9.1	0.4	1.8	53.2	1.8	0.57	3.36
9.5	0.4	2.2	55.5	2.3	0.73	4.09
9.8	0.3	2.5	57.3	1.8	0.57	4.66
10.2	0.4	2.9	59.8	2.5	0.79	5.45
10.7	0.5	3.4	63.6	3.8	1.20	6.65
11.8	1.1	4.5	69.3	5.7	1.81	8.46
12.5	0.7	5.2	74.7	5.4	1.71	10.17
13.0	0.5	5.7	78.0	3.3	1.04	11.21
13.4	0.4	6.1	80.5	2.5	0.79	12.00
14.2	0.8	6.9	85.0	4.5	1.42	13.42
14.9	0.7	7.6	89.1	4.1	1.30	14.72
15.3	0.4	8.0	92.0	2.9	0.92	15.64
15.7	0.4	8.4	95.3	3.3	1.04	16.68
16.2	0.5	8.9	99.1	3.8	1.20	17.88
16.6	0.4	9.3	101.2	2.1	0.66	18.54
17.1	0.5	9.8	105.1	3.9	1.23	19.77

V (V)	ΔV (V)	V′ (V)	Δt′ (µs)	Δt (µs)	Δd (nm)	d′ (nm)
6.9			263.7
7.4	0.5		266.6	2.9	0.92
7.8	0.4	0.9	270.1	3.5	1.11	2.03
8.4	0.6	1.5	274.3	4.2	1.33	3.36
8.9	0.5	2.0	277.4	3.1	0.98	4.34
9.6	0.7	2.7	283.7	6.3	1.99	6.33
10.1	0.4	3.1	286.5	2.8	0.89	7.22
10.8	0.7	3.8	291.0	4.5	1.42	8.64
11.6	0.8	4.6	295.7	4.7	1.49	10.13
12.0	0.4	5.0	299.1	3.4	1.07	11.20
12.3	0.3	5.3	302.1	3.0	0.95	12.15
12.9	0.6	5.9	306.4	4.3	1.36	13.51
13.6	0.7	6.6	311.1	4.7	1.49	15.00
14.3	0.7	7.3	316.6	5.5	1.74	16.74
15.2	0.9	8.2	323.7	7.1	2.25	18.99
16.5	0.3	8.5	325.6	1.9	0.60	19.59
17.2	0.7	9.2	331.9	6.3	1.99	21.58

Displacement Number	SEM (µs)
1	0.65
2	0.68
3	0.33
4	0.78
5	0.52
6	0.20
7	0.37
8	0.70
9	0.07
10	0.20
11	0.62
12	0.37
13	0.67
14	0.60
15	0.50
16	0.13
17	0.13
18	0.10
19	0.10
20	0.03
21	0.10

V (V)	ΔV (V)	V′ (V)	Δt′ (µs)	Δt (µs)	Δd (nm)	d′ (nm)
7.3			42.6
7.8	0.5		45.4	2.8	0.89
8.2	0.4	0.9	47.7	2.3	0.73	1.62
8.7	0.5	1.4	51.4	3.7	1.17	2.79
9.1	0.4	1.8	53.2	1.8	0.57	3.36
9.5	0.4	2.2	55.5	2.3	0.73	4.09
9.8	0.3	2.5	57.3	1.8	0.57	4.66
10.2	0.4	2.9	59.8	2.5	0.79	5.45
10.7	0.5	3.4	63.6	3.8	1.20	6.65
11.8	1.1	4.5	69.3	5.7	1.81	8.46
12.5	0.7	5.2	74.7	5.4	1.71	10.17
13.0	0.5	5.7	78.0	3.3	1.04	11.21
13.4	0.4	6.1	80.5	2.5	0.79	12.00
14.2	0.8	6.9	85.0	4.5	1.42	13.42
14.9	0.7	7.6	89.1	4.1	1.30	14.72
15.3	0.4	8.0	92.0	2.9	0.92	15.64
15.7	0.4	8.4	95.3	3.3	1.04	16.68
16.2	0.5	8.9	99.1	3.8	1.20	17.88
16.6	0.4	9.3	101.2	2.1	0.66	18.54
17.1	0.5	9.8	105.1	3.9	1.23	19.77

V (V)	ΔV (V)	V′ (V)	Δt′ (µs)	Δt (µs)	Δd (nm)	d′ (nm)
6.9			263.7
7.4	0.5		266.6	2.9	0.92
7.8	0.4	0.9	270.1	3.5	1.11	2.03
8.4	0.6	1.5	274.3	4.2	1.33	3.36
8.9	0.5	2.0	277.4	3.1	0.98	4.34
9.6	0.7	2.7	283.7	6.3	1.99	6.33
10.1	0.4	3.1	286.5	2.8	0.89	7.22
10.8	0.7	3.8	291.0	4.5	1.42	8.64
11.6	0.8	4.6	295.7	4.7	1.49	10.13
12.0	0.4	5.0	299.1	3.4	1.07	11.20
12.3	0.3	5.3	302.1	3.0	0.95	12.15
12.9	0.6	5.9	306.4	4.3	1.36	13.51
13.6	0.7	6.6	311.1	4.7	1.49	15.00
14.3	0.7	7.3	316.6	5.5	1.74	16.74
15.2	0.9	8.2	323.7	7.1	2.25	18.99
16.5	0.3	8.5	325.6	1.9	0.60	19.59
17.2	0.7	9.2	331.9	6.3	1.99	21.58

Abstract

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Equations (17)

Applied Optics