High-resolution electronic interferometry for the measurement of in-plane vibration

Ching-Yuan Chang; Shih-Hao Lin; Chien-Ching Ma

doi:10.1364/AO.51.005773

Applied Optics
Vol. 51,
Issue 24,
pp. 5773-5779
(2012)
•https://doi.org/10.1364/AO.51.005773

High-resolution electronic interferometry for the measurement of in-plane vibration

Ching-Yuan Chang, Shih-Hao Lin, and Chien-Ching Ma

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Ching-Yuan Chang, Shih-Hao Lin, and Chien-Ching Ma, "High-resolution electronic interferometry for the measurement of in-plane vibration," Appl. Opt. 51, 5773-5779 (2012)

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Abstract

This study proposes an algorithm based on the standard deviation in the temporal domain to remove influences from background noise and ambient disturbance and enhance the quality of images obtained using interferometric technology. From measurements of the first ten in-plane resonant frequencies and mode shapes of vibrating zirconate titanate (PZT) laminates, we investigated the resonant characteristics in both the $U$ and $V$ directions. The resulting interference fringes were used to quantify the vibration amplitude of PZT plates on a submicron scale. The resonant frequencies obtained using the proposed method are in excellent agreement with those obtained using the finite element method and an impedance analyzer.

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Properties	APC-855
Mechanical
density ( $kg / m^{3}$ )	$ρ$	7400
Elastic coefficients ( $N / m^{2}$ )	$c_{11}^{E}$	$1.218 \times 10^{11}$
	$c_{12}^{E}$	$8.021 \times 10^{10}$
	$c_{13}^{E}$	$8.527 \times 10^{10}$
	$c_{33}^{E}$	$1.164 \times 10^{11}$
	$c_{44}^{E}$	$2.299 \times 10^{10}$
Dielectric
Relative dielectric constants (at 1 kHz)	$ε_{11}^{S} / ε_{0}$	2720
	$ε_{33}^{S} / ε_{0}$	2600
Dielectric constant in vacuum ( $F / m$ )	$ε_{0}$	$8.85 \times 10^{- 12}$
Piezoelectric
Piezoelectric coefficients ( $C / m^{2}$ )	$e_{15}$	14.26
	$e_{31}$	$- 10.489$
	$e_{33}$	16.60

		$U$ Direction			$V$ Direction
	Mode	ESPI	FEM	IA	ESPI	FEM	IA
Frequency (Hz)	1	22,800	22,249	22,868	22,700	22,249	22,868
Error	1	(10 V)	$- 2.42 %$	0.30%	(40 V)	$- 1.99 %$	0.74%
Frequency (Hz)	2	39,750	39,106	39,952	39,600	39,106	39,952
Error	2	(30 V)	$- 1.62 %$	0.51%	(30 V)	$- 1.25 %$	0.89%
Frequency (Hz)	3	47,200	46,179	47,494	47,000	46,179	47,494
Error	3	(30 V)	$- 2.16 %$	0.62%	(10 V)	$- 1.75 %$	1.05%
Frequency (Hz)	4	50,550	49,540	51,210	50,500	49,540	51,210
Error	4	(40 V)	$- 2.00 %$	1.31%	(10 V)	$- 1.90 %$	1.41%
Frequency (Hz)	5	65,950	65,116	66,225	65,900	65,116	66,225
Error	5	(40 V)	$- 1.26 %$	0.42%	(15 V)	$- 1.19 %$	0.49%
Frequency (Hz)	6	73,000	70,582	73,788	73,100	70,582	73,788
Error	6	(30 V)	$- 3.31 %$	1.08%	(40 V)	$- 3.44 %$	0.94%
Frequency (Hz)	7	77,450	76,079	77,851	77,300	76,079	77,851
Error	7	(30 V)	$- 1.77 %$	0.52%	(30 V)	$- 1.58 %$	0.71%
Frequency (Hz)	8	88,300	88,139	90,250	87,700	88,139	90,250
Error	8	(50 V)	$- 0.18 %$	2.21%	(60 V)	$- 0.50 %$	2.91%
Frequency (Hz)	9	96,200	94,923	97,072	96,100	94,923	97,072
Error	9	(50 V)	$- 1.33 %$	0.91%	(50 V)	$- 1.22 %$	1.01%
Frequency (Hz)	10	107,550	106,966	108,328	107,450	106,966	108,328
Error	10	(50 V)	$- 0.54 %$	0.72%	(50 V)	$- 0.45 %$	0.82%
Avg. Abs. Error			1.66%	0.86%		1.53%	1.10%

Mode	Resonant Frequency	Anti-resonant Frequency	EMCC
1	22,868	23,689	0.261
2	39,952	40,333	0.137
3	47,494	48,652	0.217
4	51,210	55,858	0.399
5	66,225	66,966	0.148
6	73,788	75,136	0.189
7	77,851	78,479	0.126
8	90,250	91,195	0.144
9	97,072	97,451	0.088
10	108,328	109,216	0.127

Properties	APC-855
Mechanical
density ( $kg / m^{3}$ )	$ρ$	7400
Elastic coefficients ( $N / m^{2}$ )	$c_{11}^{E}$	$1.218 \times 10^{11}$
	$c_{12}^{E}$	$8.021 \times 10^{10}$
	$c_{13}^{E}$	$8.527 \times 10^{10}$
	$c_{33}^{E}$	$1.164 \times 10^{11}$
	$c_{44}^{E}$	$2.299 \times 10^{10}$
Dielectric
Relative dielectric constants (at 1 kHz)	$ε_{11}^{S} / ε_{0}$	2720
	$ε_{33}^{S} / ε_{0}$	2600
Dielectric constant in vacuum ( $F / m$ )	$ε_{0}$	$8.85 \times 10^{- 12}$
Piezoelectric
Piezoelectric coefficients ( $C / m^{2}$ )	$e_{15}$	14.26
	$e_{31}$	$- 10.489$
	$e_{33}$	16.60

		$U$ Direction			$V$ Direction
	Mode	ESPI	FEM	IA	ESPI	FEM	IA
Frequency (Hz)	1	22,800	22,249	22,868	22,700	22,249	22,868
Error	1	(10 V)	$- 2.42 %$	0.30%	(40 V)	$- 1.99 %$	0.74%
Frequency (Hz)	2	39,750	39,106	39,952	39,600	39,106	39,952
Error	2	(30 V)	$- 1.62 %$	0.51%	(30 V)	$- 1.25 %$	0.89%
Frequency (Hz)	3	47,200	46,179	47,494	47,000	46,179	47,494
Error	3	(30 V)	$- 2.16 %$	0.62%	(10 V)	$- 1.75 %$	1.05%
Frequency (Hz)	4	50,550	49,540	51,210	50,500	49,540	51,210
Error	4	(40 V)	$- 2.00 %$	1.31%	(10 V)	$- 1.90 %$	1.41%
Frequency (Hz)	5	65,950	65,116	66,225	65,900	65,116	66,225
Error	5	(40 V)	$- 1.26 %$	0.42%	(15 V)	$- 1.19 %$	0.49%
Frequency (Hz)	6	73,000	70,582	73,788	73,100	70,582	73,788
Error	6	(30 V)	$- 3.31 %$	1.08%	(40 V)	$- 3.44 %$	0.94%
Frequency (Hz)	7	77,450	76,079	77,851	77,300	76,079	77,851
Error	7	(30 V)	$- 1.77 %$	0.52%	(30 V)	$- 1.58 %$	0.71%
Frequency (Hz)	8	88,300	88,139	90,250	87,700	88,139	90,250
Error	8	(50 V)	$- 0.18 %$	2.21%	(60 V)	$- 0.50 %$	2.91%
Frequency (Hz)	9	96,200	94,923	97,072	96,100	94,923	97,072
Error	9	(50 V)	$- 1.33 %$	0.91%	(50 V)	$- 1.22 %$	1.01%
Frequency (Hz)	10	107,550	106,966	108,328	107,450	106,966	108,328
Error	10	(50 V)	$- 0.54 %$	0.72%	(50 V)	$- 0.45 %$	0.82%
Avg. Abs. Error			1.66%	0.86%		1.53%	1.10%

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Equations (7)

Applied Optics