Dynamic displacement measurement beyond half-wavelength in phase-modulated optical interferometer

Osamu Furukawa; Shinya Takemae; Yosuke Tanaka

doi:10.1364/JOSAA.393422

Journal of the Optical Society of America A
Vol. 37,
Issue 9,
pp. B78-B86
(2020)
•https://doi.org/10.1364/JOSAA.393422

Dynamic displacement measurement beyond half-wavelength in phase-modulated optical interferometer

Osamu Furukawa, Shinya Takemae, and Yosuke Tanaka

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Osamu Furukawa, Shinya Takemae, and Yosuke Tanaka, "Dynamic displacement measurement beyond half-wavelength in phase-modulated optical interferometer," J. Opt. Soc. Am. A 37, B78-B86 (2020)

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About this Article
History
- Original Manuscript: March 24, 2020
- Revised Manuscript: June 26, 2020
- Manuscript Accepted: July 14, 2020
- Published: August 11, 2020
Virtual Issues
JOSA A Feature Issue: Advances in Optical Metrology and Instrumentation (2020)

Abstract

We demonstrate an interference signal-processing method that extends the measurement range of dynamic displacement beyond half the wavelength of light without deteriorating the measurement accuracy in a phase-modulated optical interferometer. The measurement range extension is realized by the algorithm focusing on peak direction of the interference signal waveform. Deterioration of measurement accuracy is avoided by the data processing that removes noisy data sets. Performance of the proposed system is evaluated by the experiments using a pseudo-vibrator composed of a phase modulator. In the experiments using a lead zirconate titanate (PZT) device as a sample, we successfully measure the dynamic displacement of up to 3127 nm, which is larger than the light source wavelength of 1537 nm. Proof-of-principle simulations, including the evaluation of the measurement error, are also conducted, the results of which show that the measurement error of the proposed method is small in principle.

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		Second Interference Signal Peak
		Maximum		Minimum
First interference signal peak	maximum	$Z_{0} = z_{0} + 1$	$Z_{1} = z_{0}$	$Z_{0} = z_{0} + 1$	$Z_{1} = z_{0} - 1$
First interference signal peak	minimum	$Z_{0} = z_{0} - 1$	$Z_{1} = z_{0} + 1$	$Z_{0} = z_{0} - 1$	$Z_{1} = z_{0}$

		Peak Directions of $p_{b e f o r e}$ and $p_{a f t e r}$
		Same		Different
$Z_{2 (k + q + r) - 1} - Z_{2 k}$	$- 2, + 1$	$Z_{2 (k + q + r)} = Z_{2 k}$	$Z_{2 (k + q + r) + 1} = Z_{2 k + 1}$	$Z_{2 (k + q + r)} = Z_{2 k} - 1$	$Z_{2 (k + q + r) + 1} = Z_{2 k + 1} - 1$
$Z_{2 (k + q + r) - 1} - Z_{2 k}$	$- 1, + 2$	$Z_{2 (k + q + r)} = Z_{2 k}$	$Z_{2 (k + q + r) + 1} = Z_{2 k + 1}$	$Z_{2 (k + q + r)} = Z_{2 k} + 1$	$Z_{2 (k + q + r) + 1} = Z_{2 k + 1} + 1$

Term	RE of Amplitude (%)	RSD of Amplitude (%)
Linear chirp vibration	$- 0.2$	0.3
Dumped vibration	$- 0.2$	0.2

Term	RE of Amplitude (%)	RSD of Amplitude (%)
Linear chirp vibration	7.1	0.4
Dumped vibration	3.6	0.6

Parameter	Symbol	Value
Optical input power to PD	$P_{I N}$	$9.2 \times 1 0^{- 4} W$
PD dark current	$I_{D}$	$2.4 \times 1 0^{- 10} A$
PD response susceptibility	$S$	0.95 A/W
PD bandwidth	$B_{P D}$	1.2 GHz
PD output impedance	$R_{P D}$	50 Ω
ADC input impedance	$R_{A D}$	50 Ω
ADC bandwidth	$B_{A D}$	4 GHz
ADC offset accuracy	$V_{e o}$	$\pm 3.4 m V$
ADC gain accuracy	$V_{e g}$	$\pm 3.2 m V$
ADC timing jitter (rms)	$T_{j}$	2.2 ps
ADC quantization bits	$Q$	16 bit
Electrical input voltage to ADC	$V_{A D}$	34 mV
Ambient temperature	$T$	297.15 K

Parameter	Symbol	Value
Power of PD dark current	$P_{N 1}$	–145.6
Power of PD shot noise	$P_{N 2}$	–77.7
Power of PD thermal noise	$P_{N 3}$	–77.1
Power of ADC thermal noise	$P_{N 4}$	–71.8
Power of ADC equivalent input noise	$P_{N 5}$	–38.0
Power of ADC quantization noise	$P_{N 6}$	–112.8

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Journal of the Optical Society of America A