Abstract

A heterodyne interferometer has been built in order to characterize vibrations on micro- and nanostructures. The interferometer offers the possibility of both absolute phase and high resolution absolute amplitude vibrational measurements. By using two acousto-optic modulators (AOMs) in one of the interferometer arms and varying the frequency inputs of both, the setup is designed to measure vibrations in the entire frequency range 0 - 1.2GHz. The system is here demonstrated on Capacitor Micromachined Ultrasonic Transducers (CMUTs) and a PZT transducer to show measurements from 5kHz up to 35MHz. We have measured absolute amplitudes with picometer resolution.

© 2007 Optical Society of America

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References

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  1. K. Midtbø, A. Rønnekleiv, and D. T. Wang, "Fabrication and characterization of CMUTs realized by wafer bonding," in Proceedings of IEEE Ultrasonics Symp. (IEEE, 2006), pp. 934-937.
  2. K. Kokkonen, J. V. Knuuttila, V. P. Plessky, and MarttiM.  Salomaa, "Phase-sensitive absolute-amplitude measurements of surface waves using heterodyne interferometry," in Proceedings of IEEE Ultrasonics Symp. (IEEE, 2003), pp. 1145-1148.
  3. J. Lawall and E. Kessler, "Michelson interferometry with 10 pm accuracy," Review of Scientific Instruments 71, 2669-2676 (2000).
    [CrossRef]
  4. T. Chiba, "Amplitude and phase measurement of surface acoustic waves within a SAW filter having fan-shaped transducers and numerical simulations," in Proceedings of IEEE Ultrasonics Symp. (IEEE, 2005), pp. 1584-1587.
  5. C. Gorecki, "Sub-micrometric displacement measurements by an all-fiber laser heterodyne interferometer using digital phase demodulation," J. Opt.  26, 29-34 (1995).
    [CrossRef]
  6. J. E. Graebner, B. P. Barber, P. L. Gammel, and D. S. Greywall, "Dynamic visualization of sub°angstrom highfrequency surface vibration," Appl. Phys. Lett. 78, 159-161 (2001).
    [CrossRef]
  7. H. Martinussen, A. Aksnes, and H. E. Engan, "Heterodyne Interferometry for high sensitivity absolute amplitude vibrational measurements," Proc. SPIE 6292, 0Z1-0Z11 (2006).
  8. A. Aksnes, H. Martinussen, and H. E. Engan, "Characterization of acoustic vibrations on micro- and nanostructures with picometer sensitivity," Proc. SPIE 6293, 0A1-0A12 (2006).
  9. P. Hariharan, Basics of Interferometry (Academic Press, Inc., USA, 1992).

2001

J. E. Graebner, B. P. Barber, P. L. Gammel, and D. S. Greywall, "Dynamic visualization of sub°angstrom highfrequency surface vibration," Appl. Phys. Lett. 78, 159-161 (2001).
[CrossRef]

2000

J. Lawall and E. Kessler, "Michelson interferometry with 10 pm accuracy," Review of Scientific Instruments 71, 2669-2676 (2000).
[CrossRef]

1995

C. Gorecki, "Sub-micrometric displacement measurements by an all-fiber laser heterodyne interferometer using digital phase demodulation," J. Opt.  26, 29-34 (1995).
[CrossRef]

Appl. Phys. Lett.

J. E. Graebner, B. P. Barber, P. L. Gammel, and D. S. Greywall, "Dynamic visualization of sub°angstrom highfrequency surface vibration," Appl. Phys. Lett. 78, 159-161 (2001).
[CrossRef]

J. Opt.

C. Gorecki, "Sub-micrometric displacement measurements by an all-fiber laser heterodyne interferometer using digital phase demodulation," J. Opt.  26, 29-34 (1995).
[CrossRef]

Review of Scientific Instruments

J. Lawall and E. Kessler, "Michelson interferometry with 10 pm accuracy," Review of Scientific Instruments 71, 2669-2676 (2000).
[CrossRef]

Other

T. Chiba, "Amplitude and phase measurement of surface acoustic waves within a SAW filter having fan-shaped transducers and numerical simulations," in Proceedings of IEEE Ultrasonics Symp. (IEEE, 2005), pp. 1584-1587.

K. Midtbø, A. Rønnekleiv, and D. T. Wang, "Fabrication and characterization of CMUTs realized by wafer bonding," in Proceedings of IEEE Ultrasonics Symp. (IEEE, 2006), pp. 934-937.

K. Kokkonen, J. V. Knuuttila, V. P. Plessky, and MarttiM.  Salomaa, "Phase-sensitive absolute-amplitude measurements of surface waves using heterodyne interferometry," in Proceedings of IEEE Ultrasonics Symp. (IEEE, 2003), pp. 1145-1148.

H. Martinussen, A. Aksnes, and H. E. Engan, "Heterodyne Interferometry for high sensitivity absolute amplitude vibrational measurements," Proc. SPIE 6292, 0Z1-0Z11 (2006).

A. Aksnes, H. Martinussen, and H. E. Engan, "Characterization of acoustic vibrations on micro- and nanostructures with picometer sensitivity," Proc. SPIE 6293, 0A1-0A12 (2006).

P. Hariharan, Basics of Interferometry (Academic Press, Inc., USA, 1992).

Supplementary Material (2)

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Figures (17)

Fig. 1.
Fig. 1.

The heterodyne interferometer.

Fig. 2.
Fig. 2.

The electrical system.

Fig. 3.
Fig. 3.

Fourier Transform of the detector signal.

Fig. 4.
Fig. 4.

Frequency diagram of signal components in the interferometer.

Fig. 5.
Fig. 5.

Microscope images of the CMUT structure.

Fig. 6.
Fig. 6.

Sketch of a 5.7µm radius CMUT.

Fig. 7.
Fig. 7.

Investigation of linear response of the CMUT.

Fig. 8.
Fig. 8.

Phase measurements before any corrections.

Fig. 9.
Fig. 9.

Tilted sample. When the sample is tilted the optical path length changes as the sample is moved by the translation table. In this sketch the maximum optical path difference is Δ between the two edges of the sample.

Fig. 10.
Fig. 10.

Phase measurements as a function of time.

Fig. 11.
Fig. 11.

Phase measurements as a function of AC RMS excitation performed at 31MHz and -20VDC.

Fig. 12.
Fig. 12.

Movies reconstructed from the amplitude and phase measurements. They demonstrate the vibration patterns of 6CMUTs excited at frequency 13.9MHz and 14.0MHz with 177mV RMS amplitude. [Media 1] [Media 2]

Fig. 13.
Fig. 13.

Sketch of the PZT device.

Fig. 14.
Fig. 14.

Measurements and simulations on PZT device.

Fig. 15.
Fig. 15.

Line scan across CMUT(21,3).

Fig. 16.
Fig. 16.

The detector circuit before modifications.

Fig. 17.
Fig. 17.

The detector circuit after modifications.

Equations (17)

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E 1 ( t ) = A 1 cos [ ω 0 t + ϕ 1 ] ,
E 2 ( t ) = A 2 cos [ ( ω 0 + Ω mod ) t + ϕ 2 ] .
I ( t ) ( E 1 ( t ) + E 2 ( t ) ) 2
= A 1 2 2 + A 2 2 2
+ 1 2 { A 1 2 cos [ 2 ω 0 t + 2 ϕ 1 ] + A 2 2 cos [ 2 ( ω 0 + Ω mod ) t + 2 ϕ 2 ] }
+ A 1 A 2 cos [ ( 2 ω 0 + Ω mod ) t + ϕ 1 + ϕ 2 ]
+ A 1 A 2 cos [ ( Ω mod ) t ϕ 1 + ϕ 2 ] .
Δ ϕ 1 ( t ) = 4 π a λ cos ( Ω a t + ϕ ) ,
I ( t ) = A 1 A 2 cos [ ( Ω mod ) t ϕ 1 + ϕ 2 ]
+ A 1 A 2 2 π a λ sin [ ( Ω a Ω mod ) t + ϕ 1 ϕ 2 + ϕ ]
+ A 1 A 2 2 π a λ sin [ ( Ω a + Ω mod ) t ϕ 1 + ϕ 2 + ϕ ] .
a = λ 2 π R I R N .
Ω mod = Ω a 2 Δ Ω ,
Ω a ( max ) = 2 · Ω mod ( max ) + 2 · Δ Ω = 1200.002 MHz .
ϕ I = ϕ 2 ϕ 1 ϕ + θ mix ( I ) + θ ref ( I ) ,
ϕ N = ϕ 2 ϕ 1 + θ mix ( N ) + θ ref ( N ) .
ϕ est = ϕ I ϕ N = ϕ + θ mix ( I ) θ mix ( N ) + θ ref ( I ) θ ref ( N ) .

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