Abstract

We present a new technique for enhancing the sensitivity of double-exposure stroboscopic television holography (TVH) to detect and measure vibrations of small amplitude. The technique is based in the modulation of the phase of the reference beam in synchronism with the vibration of the measurand and derives from a former technique that we originally contrived for phase evaluation. We propose two variants, characterized by the demodulation process used to generate the secondary correlograms, with different behaviors in terms of the sensitivity to the sign of the measurand and of the ease in detecting the presence and shape of the vibration. We have implemented this new technique in an electronic speckle-pattern interferometer and compared its performance with standard TVH techniques; vibrations with amplitudes as small as 8 nm have been observed with this setup.

© 2000 Optical Society of America

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References

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  1. O. J. Løkberg, K. Høgmoen, “Use of a modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
    [Crossref]
  2. O. J. Løkberg, K. Høgmoen, “Holographic methods madeuseful by phase modulated ESPI,” in First European Conference on Optics Applied to Metrology, M. H. Grosmann, ed., Proc. SPIE136, 222–225 (1978).
    [Crossref]
  3. A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
    [Crossref]
  4. A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
    [Crossref]
  5. A. F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000).
    [Crossref]
  6. R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949–972 (1981).
    [Crossref]

2000 (1)

A. F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000).
[Crossref]

1996 (1)

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

1981 (1)

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949–972 (1981).
[Crossref]

1976 (1)

O. J. Løkberg, K. Høgmoen, “Use of a modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[Crossref]

Doval, A. F.

A. F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000).
[Crossref]

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
[Crossref]

Fernández, J. L.

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
[Crossref]

Høgmoen, K.

O. J. Løkberg, K. Høgmoen, “Use of a modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[Crossref]

O. J. Løkberg, K. Høgmoen, “Holographic methods madeuseful by phase modulated ESPI,” in First European Conference on Optics Applied to Metrology, M. H. Grosmann, ed., Proc. SPIE136, 222–225 (1978).
[Crossref]

Jones, J. D. C.

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
[Crossref]

Jones, R.

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949–972 (1981).
[Crossref]

Løkberg, O. J.

O. J. Løkberg, K. Høgmoen, “Use of a modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[Crossref]

O. J. Løkberg, K. Høgmoen, “Holographic methods madeuseful by phase modulated ESPI,” in First European Conference on Optics Applied to Metrology, M. H. Grosmann, ed., Proc. SPIE136, 222–225 (1978).
[Crossref]

Pérez-Amor, M.

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
[Crossref]

Valera, J. D.

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
[Crossref]

Valera, J. D. R.

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

Wykes, C.

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949–972 (1981).
[Crossref]

J. Phys. E (1)

O. J. Løkberg, K. Høgmoen, “Use of a modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[Crossref]

Meas. Sci. Technol. (1)

A. F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000).
[Crossref]

Opt. Acta (1)

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949–972 (1981).
[Crossref]

Opt. Lasers Eng. (1)

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. R. Valera, J. D. C. Jones, “Contrast enhanced and phase controlled stroboscopic additive fiber optic TV holography for whole field out-of-plane vibration analysis,” Opt. Lasers Eng. 25, 323–342 (1996).
[Crossref]

Other (2)

O. J. Løkberg, K. Høgmoen, “Holographic methods madeuseful by phase modulated ESPI,” in First European Conference on Optics Applied to Metrology, M. H. Grosmann, ed., Proc. SPIE136, 222–225 (1978).
[Crossref]

A. F. Doval, J. L. Fernández, M. Pérez-Amor, J. D. Valera, J. D. C. Jones, “Phase-stepped additive stroboscopic fiber optic TV holography for vibration analysis,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 229–240 (1994).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Effect of ϕ rS on the normalized sensitivity to small phase changes Ŝ 0 = S 0/(sup{|S 0|}) of the secondary correlograms produced by (a) square-law detection and (b) full-wave rectification.

Fig. 2
Fig. 2

Reference phase-difference modulation scheme to maximize the sensitivity to small changes in the object phase difference (a) for square-law demodulation and (b) for full-wave rectification: ϕ o , vibration of the measurand in terms of optical phase; s n , illumination pulses; ϕ rA , asynchronous phase modulation between video frames (increments of π); ϕ rS , synchronous phase modulation between illumination pulses; ϕ r , resulting phase modulation; T F , frame period of the video camera.

Fig. 3
Fig. 3

Experimental prototype used to test the proposed sensitivity-enhancement techniques: AOM, acousto-optic modulator; GL, GRIN lens; DC, directional coupler; PD, photodiode; PM, phase modulator; PLC, polarization controller; VAD, variable attenuator; BS, beam splitter; ZL, zoom lens; CCD, charge-coupled-device video camera.

Fig. 4
Fig. 4

Sample secondary correlograms obtained with standard time averaging, with standard stroboscopic illumination, and with the two variants of our stroboscopic sensitivity-enhanced technique at diverse amplitudes of vibration.

Fig. 5
Fig. 5

Sample secondary correlograms of a circular plate vibrating with a maximum amplitude: w 0 max ≈ 22 nm, obtained with the two variants of our sensitivity-enhancement technique. Square-law demodulation is sensitive to the sign of the phase change whereas full-wave rectification is not.

Fig. 6
Fig. 6

Sample secondary correlograms of a circular plate vibrating with a maximum amplitude: w 0 max ≈ 8 nm, just above the sensitivity limit of our technique.

Fig. 7
Fig. 7

Normalized fringe profiles for the mean local brightness of sensitivity-enhanced secondary correlograms.

Tables (1)

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Table 1 Correspondence between the Notations used in this Paper and in our Previous Research

Equations (27)

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Ĩsl=g20V21+cosΔϕo-2ϕrS×1+cos2ψp+ϕ¯o
Ĩfw=2g0VcosΔϕo2-ϕrScosψp+ϕ¯o
Bsl=g20V21+cosΔϕo-2ϕrS
Bfw=4π g0VcosΔϕo2-ϕrS
S=BΔϕo.
Ssl=BslΔϕo=-g20V2sinΔϕo-2ϕrS,
Ssl0=limΔϕo0 Ssl=g20V2sin2ϕrS.
ϕrS=π4  sin2ϕrS=1,
Ĩsl=g20V21+sin Δϕo1+cos2ψp+ϕ¯o,
Bsl=g20V21+sin Δϕo.
Sfw=BfwΔϕo=-2π g0V cosΔϕo2-ϕrScosΔϕo2-ϕrS sinΔϕo2-ϕrS,
Sfw0=limΔϕo0 Sfw=2π g0V |cos ϕrS|cos ϕrS sin ϕrS.
ϕrS=π2  sin ϕrS=1.
Ĩfw=2g0V sinΔϕo2cosψp+ϕ¯o,
Bfw=4π g0V sinΔϕo2.
BˆΔϕo=BΔϕosup|BΔϕo|,
Bˆsl=Bsl2g20V2=121+sin Δϕo
Bˆfw=Bfw4π g0V=sinΔϕo2
Sˆsl=12 cos Δϕo,
Sˆfw=12sinΔϕo2sinΔϕo2 cosΔϕo2,
Iαβ0-Iαβπ=4I0V cosΔφoα-Δφoβ2-ΔφrS×cos Ψαβ,
Ψαβ=ψ+Δφoα+Δφoβ2.
Δϕo=Δφoα-Δφoβ=ϕo1-ϕo2,
ϕ¯o=Δφoα+Δφoβ2=ϕo1+ϕo22,
Iαβ0-Iαβπ=2g0V cosΔϕo2-ϕrScosψp+ϕ¯o.
Ĩsl=Iαβ0-Iαβπ2=g20V21+cosΔϕo-2ϕrS×1+cos2ψp+ϕ¯o,
Ĩfw=|Iαβ0-Iαβπ|=2g0VcosΔϕo2-ϕrScosψp+ϕ¯o,

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