Abstract

A simple technique for visualizing two-dimensional traveling surface acoustic wave (SAW) phenomena in real time was developed. The technique requires illumination of a SAW carrying substrate with a collimated, sinusoidally amplitude-modulated laser beam. Though at first the technique may appear to be stroboscopic in nature, it in fact has its foundations in spatiotemporal correlation theory. It is shown that if the modulation frequency of the illumination beam is equal to, or an integer fraction of, the SAW frequency (i.e., if they are temporally correlated) then, after simple spatial filtering, high-visibility stationary fringes can be produced. In fact, it is shown that a maximum fringe visibility of nearly 60% can be achieved. It is believed that this is the highest visibility yet reported for similar SAW visualization techniques.

© 2000 Optical Society of America

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References

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  1. R. Adler, A. Korpel, P. Desmares, “An instrument for making surface waves visible,” IEEE Trans. Sonics Ultrason. SU-15, 157–161 (1968).
    [CrossRef]
  2. H. F. Pollard, Sound Waves in Solids (Pion, London, 1977).
  3. A. Korpel, L. J. Laub, H. C. Sievering, “Measurement of acoustic surface wave propagation characteristics by reflected light,” Appl. Phys. Lett. 10, 295 (1967).
    [CrossRef]
  4. G. I. Stegeman, “Optical probing of surface waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
    [CrossRef]
  5. J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 485–499 (1986).
    [CrossRef]
  6. Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).
  7. I. A. Viktorov, Rayleigh and Lamb Waves: Physical Theory and Applications (Plenum, New York, 1967).
    [CrossRef]
  8. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).
  9. P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Aksen Associates, Boston, 1991), Chap. 6.
  10. K. D. Möller, Optics (University Science Books, Mill Valley, Calif., 1988), Chap. 7, pp. 292–294.
  11. G. W. Farnell, “Properties of elastic surface waves,” in Physical Acoustics, Principles and Methods, Vol. VI, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), pp. 109–166.
  12. G. W. Farnell, E. L. Adler, “Elastic wave propagation in thin layers,” in Physical Acoustics, Principles and Methods, Vol. IX, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1972), pp. 35–127.
  13. D. A. Larson, T. D. Black, M. Green, R. G. Torti, Y. Wang, “Optical modulation by a traveling surface acoustic wave and a holographic reference grating,” J. Opt. Soc. Am. A 7, 1745–1750 (1990).
    [CrossRef]
  14. X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
    [CrossRef]
  15. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 9, p. 363.
  16. L. W. Couch, Digital and Analog Communication Systems, 3rd ed. (MacMillan, New York, 1990), Chap. 4, pp. 304–307.
  17. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

1990

1988

Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).

1986

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 485–499 (1986).
[CrossRef]

1976

G. I. Stegeman, “Optical probing of surface waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

1968

R. Adler, A. Korpel, P. Desmares, “An instrument for making surface waves visible,” IEEE Trans. Sonics Ultrason. SU-15, 157–161 (1968).
[CrossRef]

1967

A. Korpel, L. J. Laub, H. C. Sievering, “Measurement of acoustic surface wave propagation characteristics by reflected light,” Appl. Phys. Lett. 10, 295 (1967).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 9, p. 363.

Adler, E. L.

G. W. Farnell, E. L. Adler, “Elastic wave propagation in thin layers,” in Physical Acoustics, Principles and Methods, Vol. IX, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1972), pp. 35–127.

Adler, R.

R. Adler, A. Korpel, P. Desmares, “An instrument for making surface waves visible,” IEEE Trans. Sonics Ultrason. SU-15, 157–161 (1968).
[CrossRef]

Banerjee, P. P.

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Aksen Associates, Boston, 1991), Chap. 6.

Black, T. D.

Couch, L. W.

L. W. Couch, Digital and Analog Communication Systems, 3rd ed. (MacMillan, New York, 1990), Chap. 4, pp. 304–307.

Desmares, P.

R. Adler, A. Korpel, P. Desmares, “An instrument for making surface waves visible,” IEEE Trans. Sonics Ultrason. SU-15, 157–161 (1968).
[CrossRef]

Farnell, G. W.

G. W. Farnell, “Properties of elastic surface waves,” in Physical Acoustics, Principles and Methods, Vol. VI, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), pp. 109–166.

G. W. Farnell, E. L. Adler, “Elastic wave propagation in thin layers,” in Physical Acoustics, Principles and Methods, Vol. IX, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1972), pp. 35–127.

Gan, J.-F.

X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Green, M.

Hui, P.

Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).

Korpel, A.

R. Adler, A. Korpel, P. Desmares, “An instrument for making surface waves visible,” IEEE Trans. Sonics Ultrason. SU-15, 157–161 (1968).
[CrossRef]

A. Korpel, L. J. Laub, H. C. Sievering, “Measurement of acoustic surface wave propagation characteristics by reflected light,” Appl. Phys. Lett. 10, 295 (1967).
[CrossRef]

Larson, D. A.

Laub, L. J.

A. Korpel, L. J. Laub, H. C. Sievering, “Measurement of acoustic surface wave propagation characteristics by reflected light,” Appl. Phys. Lett. 10, 295 (1967).
[CrossRef]

Ming, Y.

Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).

Möller, K. D.

K. D. Möller, Optics (University Science Books, Mill Valley, Calif., 1988), Chap. 7, pp. 292–294.

Monchalin, J.-P.

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 485–499 (1986).
[CrossRef]

Pollard, H. F.

H. F. Pollard, Sound Waves in Solids (Pion, London, 1977).

Poon, T.-C.

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Aksen Associates, Boston, 1991), Chap. 6.

Sievering, H. C.

A. Korpel, L. J. Laub, H. C. Sievering, “Measurement of acoustic surface wave propagation characteristics by reflected light,” Appl. Phys. Lett. 10, 295 (1967).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, “Optical probing of surface waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 9, p. 363.

Torti, R. G.

Viktorov, I. A.

I. A. Viktorov, Rayleigh and Lamb Waves: Physical Theory and Applications (Plenum, New York, 1967).
[CrossRef]

Wang, Y.

Xuanmin, Y.

Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).

Yang, G. X.

X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
[CrossRef]

Yang, X.-M.

X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).

Yi, M.

X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
[CrossRef]

Yin, L.-L.

X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
[CrossRef]

Zonghua, H.

Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).

Appl. Phys. Lett.

A. Korpel, L. J. Laub, H. C. Sievering, “Measurement of acoustic surface wave propagation characteristics by reflected light,” Appl. Phys. Lett. 10, 295 (1967).
[CrossRef]

Chin. J. Acoust.

Y. Ming, Y. Xuanmin, P. Hui, H. Zonghua, “Visualization of UHF acoustic traveling wavefront by cw laser: theory and experiment of spatial and temporal correlation,” Chin. J. Acoust. 7, 64–73 (1988).

IEEE Trans. Sonics Ultrason.

G. I. Stegeman, “Optical probing of surface waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

R. Adler, A. Korpel, P. Desmares, “An instrument for making surface waves visible,” IEEE Trans. Sonics Ultrason. SU-15, 157–161 (1968).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 485–499 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Other

X.-M. Yang, M. Yi, J.-F. Gan, G. X. Yang, L.-L. Yin, “Imaging the 2-D surface ultrasonic traveling wavefront and the applications for NDE,” in Acoustical Imaging, Vol. 20, Y. Wei, B. Gu, eds. (Plenum, New York, 1993), pp. 309–314.
[CrossRef]

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 9, p. 363.

L. W. Couch, Digital and Analog Communication Systems, 3rd ed. (MacMillan, New York, 1990), Chap. 4, pp. 304–307.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

H. F. Pollard, Sound Waves in Solids (Pion, London, 1977).

I. A. Viktorov, Rayleigh and Lamb Waves: Physical Theory and Applications (Plenum, New York, 1967).
[CrossRef]

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Aksen Associates, Boston, 1991), Chap. 6.

K. D. Möller, Optics (University Science Books, Mill Valley, Calif., 1988), Chap. 7, pp. 292–294.

G. W. Farnell, “Properties of elastic surface waves,” in Physical Acoustics, Principles and Methods, Vol. VI, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), pp. 109–166.

G. W. Farnell, E. L. Adler, “Elastic wave propagation in thin layers,” in Physical Acoustics, Principles and Methods, Vol. IX, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1972), pp. 35–127.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the traveling SAW visualization system.

Fig. 2
Fig. 2

Idealized representation of the spatial filter (SF) shown in Fig. 1.

Fig. 3
Fig. 3

SAW geometry.

Fig. 4
Fig. 4

Optimum SAW fringe visibility curves for the first three N = odd orders. Note that a fringe contrast reversal occurs when the visibility passes through zero.

Fig. 5
Fig. 5

Optimum SAW fringe visibility curves for the first three N = even orders. As with Fig. 4, a fringe contrast reversal occurs when the visibility passes through zero.

Tables (1)

Tables Icon

Table 1 Absolute Maximum Fringe Visibilities for the First Ten Ordersa

Equations (34)

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fϕx, y=expj 2πλ2h cos θsinΩt-K·r,
β=4πh/λcos θ,
expjβ sinΨ=n=- JnβexpjnΨ,
fϕx, y=n JnβexpjnΩt-K·r.
fϕx, yJ0β+J1βexpjΩt-K·r-exp-jΩt-K·r=f0x, y+f+1x, y+f-1x, y,
Iout=Iin sin2Φ/2,
Φ=ϕ0+πVt/Vπ,
ϕ0L=0,  VπL=λ/2no3r63,
ϕ0T=2πλ Lno-ne,  VπT=λdno3r63L,
Eout=E0 sinΦ/2sinω0t,
Vt=Vdc+V0 sinΩ/Nt,
Eout=E0 sinψ02+πV02Vπ sinΩN tsinω0t,
βr=πV0/2Vπ
Eout=E0 sinψ02+βr sinΩN tsinω0t=E0 Imexpj ψ02expjβr sinΩN tsinω0t=E0 Imexpj ψ02n Jnβrexpjn ΩN tsinω0t=E0n Jnβrsinψ02+n ΩN tsinω0t,
Es=E0n Jnβrsinψ02+n ΩN tf0+f+1+f-1.
DDLS=2.44λfDillum.
R0=λfΛ,
I=|Es01|2=E02nm JnβrJmβrsinψ02+n ΩN t×sinψ02+m ΩN t|Cf0+f+1|2,
|Cf0+f+1|2=C2J02β+J12β+2CJ0βJ1βcosΩt-K·r.
I=I0nm JnβrJmβrC2J02β+J12β×cosn-mN Ωt-cosψ0+n+mN Ωt+CJ0βJ1βcos1+n-mNΩt-K·r+cos1-n-mNΩt-K·r-cos1+n+mNΩt+ψ0-K·r-cos1-n+mNΩt-ψ0-K·r,
I=I0C2J02β+J12βn Jn2βr-cosψ0n-1nJn2βr+CJ0βJ1βcosK·rn JnβrJn+Nβr+cosK·rn JnβrJn-Nβr-cosψ0-K·rn JnβrJ-n+Nβr-cosψ0+K·rn JnβrJ-n-Nβr.
I=I0C2J02β+J12β1-cosψ0J02βr-CJ0βJ1βJN2βrcosψ0-K·r+-1N cosψ0+K·r.
I|N=odd=I0C2J02β+J12β1-cosψ0J02βr-2CJ0βJ1βJN2βrsinψ0sinK·r,
V|N=odd=A2A1=2CJ0βJ1βJN2βrsinψ0C2J02β+J12β1-cosψ0J02βr.
Vopt|N=odd=JN2βr|=|JNπV0/Vπ.
I|N=even=I0C2J02β+J12β1-cosψ0J02βr-2CJ0βJ1βJN2βrcosψ0cosK·r,
V|N=even=B2B1=2CJ0βJ1βJN2βrcosψ0C2J02β+J12β1-cosψ0J02βr.
Vopt|N=even=JN2βr1-J02βr=JNπV0/Vπ1-J0πV0/Vπ.
OD=-log10Iout/Iin=-2 log10|J1β/J0β|,
JN0=n=- JnxJn±Nx=0  for N0,
J00=n=- Jn2x=1,
JN2x=n=- JnxJ-n-Nx,
JN2x=-1Nn=- JnxJ-n+Nx,
J02x=n=--1nJn2x

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