Abstract

A calibration method for interferometric systems is shown to produce a minimum wave amplitude to which these systems may be calibrated in the measurement of harmonic surface acoustic waves. The calibration limit is ~3 orders of magnitude larger than the theoretical detection limit. The method proposed allows experimental determination of the detection limit of these systems. The calibration of a fiber-optic heterodyne interferometer is demonstrated, and the experimentally derived detection limit for the interferometer is shown to be 5.5 × 10−5 m for unity detection bandwidth. This limit is obtained for a mirrored specimen with 0.14 mW of laser power incident on the optical detector.

© 1988 Optical Society of America

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References

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  1. J. W. Wagner, J. B. Spicer, “Theoretical Noise-Limited Sensitivity of Classical Interferometry,” J. Opt. Soc. Am. B 4, 1316 (1987).
    [CrossRef]
  2. D. A. Jackson, A. Dandridge, S. K. Sheem, “Measurement of Small Phase Shifts Using a Single-Mode Optical-Fiber Interferometer,” Opt. Lett. 5, 139 (1980).
    [CrossRef] [PubMed]
  3. H. C. Kim, H. K. Park, “Laser Interferometry for Measuring Displacement Amplitude of Acoustic Emission Signals,” J. Phys. D 17, 673 (1984).
    [CrossRef]
  4. J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
    [CrossRef]
  5. J. P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543 (1985).
    [CrossRef]
  6. J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Frequency Control UFFC-33, 485 (1986).
    [CrossRef]
  7. R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).
  8. R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-Induced Birefringence in Single-Mode Fibers,” Opt. Lett. 5, 273 (1980).
    [CrossRef] [PubMed]
  9. H. C. Lefevre, “Single-Mode Fibre Fractional Wave Devices and Polarisation Controllers,” Electronics Lett. 16, 778 (1980).
    [CrossRef]

1987 (1)

1986 (1)

J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Frequency Control UFFC-33, 485 (1986).
[CrossRef]

1985 (1)

J. P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543 (1985).
[CrossRef]

1984 (1)

H. C. Kim, H. K. Park, “Laser Interferometry for Measuring Displacement Amplitude of Acoustic Emission Signals,” J. Phys. D 17, 673 (1984).
[CrossRef]

1983 (1)

J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
[CrossRef]

1980 (3)

1972 (1)

R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).

Ash, E.

R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).

Bowers, J. E.

J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
[CrossRef]

Dandridge, A.

De La Rue, R.

R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).

Eickhoff, W.

Humphryes, R.

R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).

Jackson, D. A.

Jungerman, R. L.

J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
[CrossRef]

Khuri-Yakub, B. T.

J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
[CrossRef]

Kim, H. C.

H. C. Kim, H. K. Park, “Laser Interferometry for Measuring Displacement Amplitude of Acoustic Emission Signals,” J. Phys. D 17, 673 (1984).
[CrossRef]

Kino, G. S.

J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
[CrossRef]

Lefevre, H. C.

H. C. Lefevre, “Single-Mode Fibre Fractional Wave Devices and Polarisation Controllers,” Electronics Lett. 16, 778 (1980).
[CrossRef]

Mason, I.

R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).

Monchalin, J. P.

J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Frequency Control UFFC-33, 485 (1986).
[CrossRef]

J. P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543 (1985).
[CrossRef]

Park, H. K.

H. C. Kim, H. K. Park, “Laser Interferometry for Measuring Displacement Amplitude of Acoustic Emission Signals,” J. Phys. D 17, 673 (1984).
[CrossRef]

Rashleigh, S. C.

Sheem, S. K.

Spicer, J. B.

Ulrich, R.

Wagner, J. W.

Electronics Lett. (1)

H. C. Lefevre, “Single-Mode Fibre Fractional Wave Devices and Polarisation Controllers,” Electronics Lett. 16, 778 (1980).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Frequency Control (1)

J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Frequency Control UFFC-33, 485 (1986).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (1)

J. E. Bowers, R. L. Jungerman, B. T. Khuri-Yakub, G. S. Kino, “An All Fiber-Optic Sensor for Surface Acoustic Wave Measurement,” IEEE/OSA J. Lightwave Technol. LT-1, 429 (1983).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. D (1)

H. C. Kim, H. K. Park, “Laser Interferometry for Measuring Displacement Amplitude of Acoustic Emission Signals,” J. Phys. D 17, 673 (1984).
[CrossRef]

Opt. Lett. (2)

Proc. IEE (1)

R. De La Rue, R. Humphryes, I. Mason, E. Ash, “Acoustic-Surface-Wave Amplitude and Phase Measurements Using Laser Probes,” Proc. IEE 119 (1972).

Rev. Sci. Instrum. (1)

J. P. Monchalin, “Heterodyne Interferometric Laser Probe to Measure Continuous Ultrasonic Displacements,” Rev. Sci. Instrum. 56, 543 (1985).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Heterodyne fiber-optic interferometer for detection of surface waves.

Fig. 2
Fig. 2

First harmonic signal amplitude vs piezoelectric driver voltage amplitude.

Fig. 3
Fig. 3

Second harmonic signal amplitude vs piezoelectric driver voltage amplitude.

Fig. 4
Fig. 4

Voltage signal ratio (V2f/Vf) vs piezoelectric driver voltage amplitude.

Fig. 5
Fig. 5

Amplitude of voltage signal vs reference beam power.

Fig. 6
Fig. 6

Amplitude of noise voltage signal squared vs reference beam power.

Fig. 7
Fig. 7

Signal-to-noise ratio vs field contrast.

Equations (23)

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V 2 ω V ω = SNR 2 ω + 1 SNR ω + 1 ,
SNR ω = [ P 0 η 6 h ν Δ ν ] 1 / 2 k 0 δ ( 1 + N ) 1 / 2 ,
SNR 2 ω = [ P 0 η 6 h ν Δ ν ] 1 / 2 k 0 2 δ 2 2 ( 1 + N ) 1 / 2 ,
N = 6 k B T R h ν q 2 η P 0 .
0 = δ 2 - 2 V 2 ω k 0 V ω δ + ( 1 - V 2 ω V ω ) ( 6 h ν Δ ν P 0 η ) 1 / 2 2 ( 1 + N ) 1 / 2 k 0 2 .
δ = 1 k 0 { V 2 ω V ω + [ ( V 2 ω V ω ) 2 - 2 ( 6 h ν Δ ν P 0 η ) 1 / 2 ( 1 + N ) 1 / 2 ] 1 / 2 } .
δ = 2 k 0 V 2 ω V ω ,
δ min = 2 1 / 2 k 0 ( 1 + N ) 1 / 4 ( 6 h ν Δ ν P 0 η ) 1 / 4 .
SNR = V ω V N - 1 ,
V ω V N = δ δ lim + 1.
δ lim = 2 k 0 V 2 ω V N V ω 2 .
V 2 ω V ω = δ 2 + S 2 δ k 0 + S ,
S = ( 6 h ν Δ ν P 0 η ) 1 / 2 2 ( 1 + N ) 1 / 2 k 0 2 .
y = ( x 2 + A ) ( B x + A ) ,
δ = 2 x k 0 B ,
δ lim = k 0 2 S ,
δ lim = 2 k 0 A B 2 .
δ = ( 1.70 × 10 - 9 m / V ) x
δ lim = 5.50 × 10 - 15 m .
δ lim = 5.4 × 10 - 15 m .
V s = α P R 1 / 2 ;
V N 2 = γ P R + ϕ ,
SNR = β K ( 1 + K 2 ) 1 / 2 ,

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