Abstract

An optical photorefractive frequency-domain method is described for measuring displacement amplitude and phase of vibrating surfaces. The method is applicable to diffusely scattering surfaces and usable in either a point-detection or imaging configuration. The method utilizes an optical lock-in approach to measure phase modulation of light scattered from continuously vibrating surfaces. Picometer displacement sensitivities have been demonstrated over a frequency range of 100 Hz to greater than 100 kHz. The response of the spectral method is independent of the vibration frequency above the photorefractive cutoff frequency. Two methods are described that produce a readout beam intensity that is a direct function of the vibration amplitude suitable for imaging.

© 1997 Optical Society of America

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References

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  1. J. W. Wagner, Optical Detection of Ultrasound, Vol. 19 of Physical Acoustics, R. N. Thurston, A. D. Pierce, eds. (Academic, New York, 1990), Chap. 5.
  2. S. Ellingsrud, G. O. Rosvold, “Analysis of a data-based TV-holography system used to measure small vibration amplitudes,” J. Opt. Soc. Am. A 9, 237–251 (1992).
    [CrossRef]
  3. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  4. S. I. Stepanov, International Trends in Optics (Academic, New York, 1991), Chap. 9.
  5. J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
    [CrossRef]
  6. H. R. Hofmeister, A. Yariv, “Vibration detection using dynamic photorefractive gratings in KTN/KLTN crystals,” Appl. Phys. Lett. 61, 2395–2397 (1992).
    [CrossRef]
  7. H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76, 81–84 (1994).
    [CrossRef]
  8. T. C. Chatters, K. L. Telschow, Optical Lock-in Vibration Detection Using Photorefractive Four-Wave Mixing, in Vol. 15B of Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson, D. E. Chimenti, eds. (Plenum, New York, 1996), pp. 2165–2171.
  9. T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
    [CrossRef]
  10. T. C. Hale, K. L. Telschow, “Vibration modal analysis using all-optical photorefractive processing,” in Proceedings of the Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications II, F. T. Yu, S. Yin, eds., Proc. SPIE2849, 300–307 (1996).
  11. J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, “Photorefractive optical lock-in detector,” Opt. Lett. 16, 1442–1444 (1991).
    [CrossRef] [PubMed]
  12. C. C. Aleksoff, “Temporally modulated holography,” Appl. Opt. 10, 1329–1341 (1971).
    [CrossRef] [PubMed]
  13. R. C. Troth, J. C. Dainty, “Holographic interferometry using anisotropic self-diffraction in Bi12SiO20,” Opt. Lett. 16, 53–55 (1991).
    [CrossRef] [PubMed]
  14. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]

1996 (1)

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

1994 (1)

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76, 81–84 (1994).
[CrossRef]

1992 (2)

H. R. Hofmeister, A. Yariv, “Vibration detection using dynamic photorefractive gratings in KTN/KLTN crystals,” Appl. Phys. Lett. 61, 2395–2397 (1992).
[CrossRef]

S. Ellingsrud, G. O. Rosvold, “Analysis of a data-based TV-holography system used to measure small vibration amplitudes,” J. Opt. Soc. Am. A 9, 237–251 (1992).
[CrossRef]

1991 (2)

1981 (1)

1971 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Aleksoff, C. C.

Chatters, T. C.

T. C. Chatters, K. L. Telschow, Optical Lock-in Vibration Detection Using Photorefractive Four-Wave Mixing, in Vol. 15B of Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson, D. E. Chimenti, eds. (Plenum, New York, 1996), pp. 2165–2171.

Cronin-Golomb, M.

Dainty, J. C.

Ellingsrud, S.

Hale, T. C.

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

T. C. Hale, K. L. Telschow, “Vibration modal analysis using all-optical photorefractive processing,” in Proceedings of the Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications II, F. T. Yu, S. Yin, eds., Proc. SPIE2849, 300–307 (1996).

Hofmeister, H. R.

H. R. Hofmeister, A. Yariv, “Vibration detection using dynamic photorefractive gratings in KTN/KLTN crystals,” Appl. Phys. Lett. 61, 2395–2397 (1992).
[CrossRef]

Huignard, J. P.

Khoury, J.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Marrakchi, A.

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76, 81–84 (1994).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef]

Petersen, P. M.

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76, 81–84 (1994).
[CrossRef]

Rohleder, H.

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76, 81–84 (1994).
[CrossRef]

Rosvold, G. O.

Ryan, V.

Stepanov, S. I.

S. I. Stepanov, International Trends in Optics (Academic, New York, 1991), Chap. 9.

Telschow, K.

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

Telschow, K. L.

T. C. Hale, K. L. Telschow, “Vibration modal analysis using all-optical photorefractive processing,” in Proceedings of the Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications II, F. T. Yu, S. Yin, eds., Proc. SPIE2849, 300–307 (1996).

T. C. Chatters, K. L. Telschow, Optical Lock-in Vibration Detection Using Photorefractive Four-Wave Mixing, in Vol. 15B of Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson, D. E. Chimenti, eds. (Plenum, New York, 1996), pp. 2165–2171.

Troth, R. C.

Wagner, J. W.

J. W. Wagner, Optical Detection of Ultrasound, Vol. 19 of Physical Acoustics, R. N. Thurston, A. D. Pierce, eds. (Academic, New York, 1990), Chap. 5.

Woods, C.

Yariv, A.

H. R. Hofmeister, A. Yariv, “Vibration detection using dynamic photorefractive gratings in KTN/KLTN crystals,” Appl. Phys. Lett. 61, 2395–2397 (1992).
[CrossRef]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. R. Hofmeister, A. Yariv, “Vibration detection using dynamic photorefractive gratings in KTN/KLTN crystals,” Appl. Phys. Lett. 61, 2395–2397 (1992).
[CrossRef]

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Appl. Phys. (1)

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76, 81–84 (1994).
[CrossRef]

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

Opt. Lett. (3)

Other (5)

J. W. Wagner, Optical Detection of Ultrasound, Vol. 19 of Physical Acoustics, R. N. Thurston, A. D. Pierce, eds. (Academic, New York, 1990), Chap. 5.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

S. I. Stepanov, International Trends in Optics (Academic, New York, 1991), Chap. 9.

T. C. Chatters, K. L. Telschow, Optical Lock-in Vibration Detection Using Photorefractive Four-Wave Mixing, in Vol. 15B of Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson, D. E. Chimenti, eds. (Plenum, New York, 1996), pp. 2165–2171.

T. C. Hale, K. L. Telschow, “Vibration modal analysis using all-optical photorefractive processing,” in Proceedings of the Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications II, F. T. Yu, S. Yin, eds., Proc. SPIE2849, 300–307 (1996).

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Figures (12)

Fig. 1
Fig. 1

Experimental setup for optical lock-in, point vibration detection by use of photorefractive four-wave mixing. PRC: photorefractive crystal; EOM: electro-optic modulator; BS: beam splitter; M: mirror, δ1 and δ2: phase-modulated signal and reference beams.

Fig. 2
Fig. 2

Power spectrum mode: measurement of a surface vibrating at a fixed frequency while the reference frequency is swept asynchronously.

Fig. 3
Fig. 3

Swept network mode: amplitude spectrum (top) of a vibrating mirror specimen (solid curve) along with the noise level (dotted curve) and corresponding phase shift (bottom).

Fig. 4
Fig. 4

Swept network mode: effect of reference EOM amplitude δ2 on the photodetector output signal magnitude. Specimen displacement was fixed at ζ = 0.15 nm rms.

Fig. 5
Fig. 5

Swept network mode: linear response of calibrated vibrating mirror specimen. Reference modulation was fixed at δ2 = 1.1 rad.

Fig. 6
Fig. 6

Diagrammatic representations of the first (top left) through sixth (bottom right) vibrational mode shapes for a rigidly clamped disc. Plus (+) and minus signs (-) denote regions of positive phase relative to regions of negative phase. Resonant frequencies are given for each mode shape; values determined experimentally are shown in parentheses.

Fig. 7
Fig. 7

Comparison of theoretical resonant frequencies (circles) with the vibration spectra determined experimentally. Curves are swept spectra taken with the probing beam positioned at the center (solid) and just off center of the specimen (dashed).

Fig. 8
Fig. 8

Four-wave vibration-imaging measurements showing the first through the third vibrational mode shapes of the specularly reflecting, rigidly clamped, 19.1-mm diameter, and 0.79-mm-thick disc.

Fig. 9
Fig. 9

Four-wave vibration-imaging measurements showing the fourth through the sixth vibrational mode shapes of the specularly reflecting, rigidly clamped, 19.1-mm diameter, and 0.79-mm-thick disc.

Fig. 10
Fig. 10

Experimental setup for optical lock-in vibration imaging with photorefractive two-wave mixing: PRC, photorefractive crystal; EOM, electro-optic modulator; BS, beam splitter; δ1 and δ2, phase-modulated object and reference beams, respectively.

Fig. 11
Fig. 11

Two-wave mixing vibration-imaging measurements showing the first through the sixth vibrational mode shapes of the diffuse reflecting clamped circular plate.

Fig. 12
Fig. 12

Intensity profile (bottom) through the center of the second mode shape image (top), demonstrating direct displacement amplitude and phase detection.

Equations (15)

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δSIG=4πξλ=δ1 sinω1t+φ1,  δ1=4πξ0λ.
A1r, t=I1 expik1·R1-2πνt+δSIG=I1 expik1·R1-2πνt×n=-Jnδ1expinω1t+ϕ1,
A2r, t=I2 expik2·R2-2πνt+δREF=I2 expik2·R2-2πνt×n=-Jnδ2expinω2t+ϕ2,
I=I01+M cosK·r+Σ+δSIG-δREF,  I0=I1+I2,  M=2I1I21/2I0,
Esct+Escτ=iEqτ2A1A2*I0,
Escr, t=EqMn=-Jnδ1Jnδ2×sinnΩt+Φ+ψn+K·r+Σ1+n2Ω2τ21/2=EqMftsinK·r+Σ,
ζπn1Lλ cos θ=πn03r41EqL2λ cos θMft=ζqMft,
I4=I3 exp-αL/cos θsin ζ2,
I4=I3 exp-αL cos θζq2M2J02δ2+4δ1J0δ2J1δ2×cosΩt+Φ+Ψ1+Ω2τ21/2,
Pdc=P4J02δ2,
in2R=2qηqPdchνBR,
Pac=P44δ1J0δ2J1δ2cosΩt+Φ+ψ1+Ω2τ21/2.
is2R=ηqPachν2R2.
SNR=is2in2=δ12ηP4hνB4J12δ21+Ω2τ2.
ξmin=λ4πhνBηP41/21+Ω2τ21/22J1δ2.

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