Abstract

Acousto-optic interaction between a narrow laser beam and acoustic waves in air is analyzed theoretically. The photoelastic relation in air is used to derive the phase modulation of laser light in air-coupled reflection vibrometry induced by angular spatial spectral components comprising the acoustic beam. Maximum interaction was found for the zero spatial acoustic component propagating normal to the laser beam. The angular dependence of the imaging efficiency is determined for the axial and nonaxial acoustic components with the regard for the laser beam steering in the scanning mode. The sensitivity of air-coupled vibrometry is compared with conventional “Doppler” reflection vibrometry. Applications of the methodology for visualization of linear and nonlinear air-coupled fields are demonstrated.

© 2008 Optical Society of America

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References

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  1. P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer, 1979).
  2. A. Yarif, Optical Electronics (Saunders, 1971).
  3. A. Korpel, Acousto-Optics (Marcel Decker, 1988).
  4. C. C. Williams, “High resolution optical probe,” in Proc.-IEEE Ultrason. Sympos. 1, 951-955(1983).
  5. W. Dürr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537-1558(1986).
    [CrossRef]
  6. L. Zipser, “Refraktovibrometrie zur Messung und Visualisierung akustischer, fluidischer und spannungsmechanischer Phänomene,” http://www.polytec.com/ger/_files/07_Zipser_Refraktovibrometrie.pdf
  7. Polytec Inc., “Vibrometry Basics,” http://www.polytec.com/usa/158_942.asp
  8. L. Zipser and H. Franke, “Laser-scanning vibrometry for ultrasonic transducer development,” Sens. Actuators, A 110, 264-268 (2004).
    [CrossRef]
  9. I. Solodov and G. Busse, “Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials,” Appl. Phys. Lett. A 91, 251910 (2007).
    [CrossRef]

2007

I. Solodov and G. Busse, “Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials,” Appl. Phys. Lett. A 91, 251910 (2007).
[CrossRef]

2004

L. Zipser and H. Franke, “Laser-scanning vibrometry for ultrasonic transducer development,” Sens. Actuators, A 110, 264-268 (2004).
[CrossRef]

1986

W. Dürr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537-1558(1986).
[CrossRef]

1983

C. C. Williams, “High resolution optical probe,” in Proc.-IEEE Ultrason. Sympos. 1, 951-955(1983).

Busse, G.

I. Solodov and G. Busse, “Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials,” Appl. Phys. Lett. A 91, 251910 (2007).
[CrossRef]

Dürr, W.

W. Dürr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537-1558(1986).
[CrossRef]

Franke, H.

L. Zipser and H. Franke, “Laser-scanning vibrometry for ultrasonic transducer development,” Sens. Actuators, A 110, 264-268 (2004).
[CrossRef]

Gdoutos, E. E.

P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer, 1979).

Korpel, A.

A. Korpel, Acousto-Optics (Marcel Decker, 1988).

Solodov, I.

I. Solodov and G. Busse, “Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials,” Appl. Phys. Lett. A 91, 251910 (2007).
[CrossRef]

Theocaris, P. S.

P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer, 1979).

Williams, C. C.

C. C. Williams, “High resolution optical probe,” in Proc.-IEEE Ultrason. Sympos. 1, 951-955(1983).

Yarif, A.

A. Yarif, Optical Electronics (Saunders, 1971).

Zipser, L.

L. Zipser and H. Franke, “Laser-scanning vibrometry for ultrasonic transducer development,” Sens. Actuators, A 110, 264-268 (2004).
[CrossRef]

L. Zipser, “Refraktovibrometrie zur Messung und Visualisierung akustischer, fluidischer und spannungsmechanischer Phänomene,” http://www.polytec.com/ger/_files/07_Zipser_Refraktovibrometrie.pdf

Appl. Phys. Lett. A

I. Solodov and G. Busse, “Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials,” Appl. Phys. Lett. A 91, 251910 (2007).
[CrossRef]

Int. J. Infrared Millim. Waves

W. Dürr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537-1558(1986).
[CrossRef]

Sens. Actuators, A

L. Zipser and H. Franke, “Laser-scanning vibrometry for ultrasonic transducer development,” Sens. Actuators, A 110, 264-268 (2004).
[CrossRef]

Other

L. Zipser, “Refraktovibrometrie zur Messung und Visualisierung akustischer, fluidischer und spannungsmechanischer Phänomene,” http://www.polytec.com/ger/_files/07_Zipser_Refraktovibrometrie.pdf

Polytec Inc., “Vibrometry Basics,” http://www.polytec.com/usa/158_942.asp

P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer, 1979).

A. Yarif, Optical Electronics (Saunders, 1971).

A. Korpel, Acousto-Optics (Marcel Decker, 1988).

C. C. Williams, “High resolution optical probe,” in Proc.-IEEE Ultrason. Sympos. 1, 951-955(1983).

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Figures (5)

Fig. 1
Fig. 1

Setup for air-coupled vibrometry.

Fig. 2
Fig. 2

Phase modulation factor as a function of steering angle α.

Fig. 3
Fig. 3

Measured phase modulation factor: symbols refer to measurements in the center (cirles) and at the periphery (diamonds) of the acoustic beam. Calculations are made for K L = 12.5 (solid line) and KL = 19 (dashed line).

Fig. 4
Fig. 4

Airborne wave field radiated by plate waves.

Fig. 5
Fig. 5

Airborne fields radiated by flexural waves in cracked carbon composite. Left, fundamental frequency ( 40 kHz ); right, nonlinear emission ( 80 kHz ).

Equations (18)

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2 n Δ n = ( n 2 1 ) Δ ϱ ϱ .
Δ n = ( n o 1 ) Δ ϱ ϱ .
p ϱ γ = const ,
Δ p = ϱ o V 2 Δ ϱ ϱ o .
Δ n = ( n o 1 ) Δ p ϱ o V 2 .
n = n o + Δ n = n o ( 1 + Δ n n o ) = n o ( 1 + Δ c air c air ) .
Δ c air c air = ( n o 1 ) Δ p n o ϱ o V 2 .
Δ n = n o 1 ϱ o V 2 Δ p cos Ω t .
φ = ω t k ˜ air d x = ω t 2 k ˜ air L = ω t 2 k air ( 1 + Δ c air c air ) L ,
φ = 2 π f t 2 k air L ( 1 + n o 1 n o ϱ o V 2 Δ p cos Ω t ) .
f i = 1 2 π φ t = f ( 1 + 2 ( n o 1 ) L Ω c air n o ϱ o V 2 Δ p sin Ω t ) .
Δ c air ( x , t ) = Δ c air cos [ K x sin α ] cos Ω t .
φ = ω t 2 0 L k ˜ air ( x , t ) d x .
φ = ω t 2 k air L [ 1 + n o 1 n o ϱ o V 2 sin ( K L sin α ) K L sin α Δ p cos Ω t ] ,
φ D = ω t 2 k air L o ( 1 + L L o cos Ω t ) .
f i = 1 2 π φ t = f ( 1 + 2 v c air sin Ω t ) ,
v = n o 1 n o Ω L ϱ o V 2 Δ p .
v = n o 1 n o KL Δ v .

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