Abstract

We introduce a new modality for dynamic phase imaging in confocal microscopy based on synthetic optical holography. By temporal demultiplexing of the detector signal into a series of holograms, we record time-resolved phase images directly in the time domain at a bandwidth as determined by the photo detector and digitizer. We demonstrate our method by optical imaging of transient vibrations in an atomic force microscope cantilever with 100 ns time resolution, and observe the dynamic deformation of the cantilever surface after excitation with broadband mechanical pulses. Temporal Fourier transform of a single data set acquired in 4.2 minutes yields frequency and mode profile of all excited out-of-plane vibration modes with sub-picometer vertical sensitivity and sub-micrometer lateral resolution. Our method has the potential for transient and spectroscopic vibration imaging of micromechanical systems at nano-and picosecond scale time resolution.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2017 (2)

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Z. Shen, X. Han, C.-L. Zou, and H. X. Tang, “Phase sensitive imaging of 10 ghz vibrations in an aln microdisk resonator,” Rev. Sci. Instruments 88, 123709 (2017).
[Crossref]

2016 (1)

2014 (2)

2013 (2)

2007 (4)

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for mems performance measurement,” J. Microelectromechanical Syst. 16, 668–674 (2007).
[Crossref]

Y. Fu, G. Pedrini, and W. Osten, “Vibration measurement by temporal fourier analyses of a digital hologram sequence,”Appl. Opt. 46, 5719–5727 (2007).
[Crossref] [PubMed]

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

2006 (5)

C. Rembe and A. Dräbenstedt, “Laser-scanning confocal vibrometer microscope: Theory and experiments,” Rev. Sci. Instruments 77, 083702 (2006).
[Crossref]

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser doppler vibrometry: Development of advanced solutions answering to technology’s needs,”Mech. Syst. Signal Process. 20, 1265–1285 (2006).
[Crossref]

G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456–3462 (2006).
[Crossref] [PubMed]

C. Perez-Lopez, M. H. D. l. Torre-Ibarra, and F. M. Santoyo, “Very high speed cw digital holographic interferometry,” Opt. Express 14, 9709–9715 (2006).
[Crossref] [PubMed]

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

2005 (1)

C. Chao, Z. Wang, W. Zhu, and O. Tan, “Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices,” Rev. Sci. Instruments 76, 063906 (2005).
[Crossref]

2004 (1)

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

2003 (1)

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of m(o)ems by optical techniques: status and trends,” J. Micromechanics Microengineering 13, S23 (2003).
[Crossref]

2002 (1)

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

2001 (2)

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

G. G. Fattinger and P. T. Tikka, “Modified mach–zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett. 79, 290–292 (2001).
[Crossref]

2000 (3)

M. R. Hart, R. A. Conant, K. Y. Lau, and R. S. Muller, “Stroboscopic interferometer system for dynamic mems characterization,”J. Microelectromechanical Syst. 9, 409–418 (2000).
[Crossref]

J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, “Scanning michelson interferometer for imaging surface acoustic wave fields,” Opt. Lett. 25, 613–615 (2000).
[Crossref]

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

1999 (1)

1986 (1)

D. Royer and E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[Crossref]

1985 (1)

J. Monchalin, “Heterodyne interferometric laser probe to measure continuous ultrasonic displacements,” Rev. Sci. Instruments 56, 543–546 (1985).
[Crossref]

Aksnes, A.

Allen, M. S.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Asundi, A.

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

Barton, J. S.

Benchabane, S.

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

Boedecker, S.

C. Rembe, S. Boedecker, A. Dräbenstedt, F. Pudewills, and G. Siegmund, “Heterodyne laser-doppler vibrometer with a slow-shear-mode bragg cell for vibration measurements up to 1.2 ghz,” in Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, vol. 7098 (SPIE, 2008), p. 12.

Bosseboeuf, A.

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of m(o)ems by optical techniques: status and trends,” J. Micromechanics Microengineering 13, S23 (2003).
[Crossref]

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Bucaro, J. A.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Carney, P. S.

Castellini, P.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser doppler vibrometry: Development of advanced solutions answering to technology’s needs,”Mech. Syst. Signal Process. 20, 1265–1285 (2006).
[Crossref]

Chabrier, A.

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Chao, C.

C. Chao, Z. Wang, W. Zhu, and O. Tan, “Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices,” Rev. Sci. Instruments 76, 063906 (2005).
[Crossref]

Chin, C. S.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

Conant, R. A.

M. R. Hart, R. A. Conant, K. Y. Lau, and R. S. Muller, “Stroboscopic interferometer system for dynamic mems characterization,”J. Microelectromechanical Syst. 9, 409–418 (2000).
[Crossref]

Conway, J. A.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for mems performance measurement,” J. Microelectromechanical Syst. 16, 668–674 (2007).
[Crossref]

Coste, P.

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Craighead, H. G.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

Danaie, K.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Dean, T.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Di Maio, D.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Diaspro, A.

Dieulesaint, E.

D. Royer and E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[Crossref]

Dirckx, J. J. J.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Dräbenstedt, A.

C. Rembe and A. Dräbenstedt, “Laser-scanning confocal vibrometer microscope: Theory and experiments,” Rev. Sci. Instruments 77, 083702 (2006).
[Crossref]

C. Rembe, S. Boedecker, A. Dräbenstedt, F. Pudewills, and G. Siegmund, “Heterodyne laser-doppler vibrometer with a slow-shear-mode bragg cell for vibration measurements up to 1.2 ghz,” in Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, vol. 7098 (SPIE, 2008), p. 12.

Dupeux, M.

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Engan, H. E.

Ewins, D. J.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Fattinger, G. G.

G. G. Fattinger and P. T. Tikka, “Modified mach–zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett. 79, 290–292 (2001).
[Crossref]

Fort, F.

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Fowler, J. D.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for mems performance measurement,” J. Microelectromechanical Syst. 16, 668–674 (2007).
[Crossref]

Fu, Y.

Gilles, J. P.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Gimzewski, J. K.

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

Gorecki, C.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Graebner, J. E.

J. E. Graebner, “Optical scanning interferometer for dynamic imaging of high-frequency surface motion,” in Ultrasonics Symposium, 2000 IEEE, vol. 1 (2000), pp. 733–736.

Griffiths, P. R.

P. R. Griffiths, J. A. D. Haseth, and J. D. Winefordner, Fourier Transform Infrared Spectrometry, 2nd Edition (John Wiley And Sons, Inc., 2007).
[Crossref]

Gusev, M. E.

Halkon, B. J.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Han, X.

Z. Shen, X. Han, C.-L. Zou, and H. X. Tang, “Phase sensitive imaging of 10 ghz vibrations in an aln microdisk resonator,” Rev. Sci. Instruments 88, 123709 (2017).
[Crossref]

Hand, D. P.

Hart, M. R.

M. R. Hart, R. A. Conant, K. Y. Lau, and R. S. Muller, “Stroboscopic interferometer system for dynamic mems characterization,”J. Microelectromechanical Syst. 9, 409–418 (2000).
[Crossref]

Haseth, J. A. D.

P. R. Griffiths, J. A. D. Haseth, and J. D. Winefordner, Fourier Transform Infrared Spectrometry, 2nd Edition (John Wiley And Sons, Inc., 2007).
[Crossref]

Hegde, G.

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

Hillenbrand, R.

Hosseini, P.

Houston, B. H.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Ilic, B.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

Jacobelli, A.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Jason, R.

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

Joanna, S.

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

Jones, J. D. C.

Jozwik, M.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Kacperski, J. M.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Kaivola, M.

I. Shavrin, L. Lipiäinen, K. Kokkonen, S. Novotny, M. Kaivola, and H. Ludvigsen, “Stroboscopic white-light interferometry of vibrating microstructures,” Opt. Express 21, 16901–16907 (2013).
[Crossref] [PubMed]

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

Khelif, A.

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

Kim, M. K.

M. K. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications (Springer-Verlag, 2011).
[Crossref]

Kim, Y.-H.

Knuuttila, J. V.

Kokkonen, K.

I. Shavrin, L. Lipiäinen, K. Kokkonen, S. Novotny, M. Kaivola, and H. Ludvigsen, “Stroboscopic white-light interferometry of vibrating microstructures,” Opt. Express 21, 16901–16907 (2013).
[Crossref] [PubMed]

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

Krylov, S.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

Kuang, C.

Lau, K. Y.

M. R. Hart, R. A. Conant, K. Y. Lau, and R. S. Muller, “Stroboscopic interferometer system for dynamic mems characterization,”J. Microelectromechanical Syst. 9, 409–418 (2000).
[Crossref]

Laude, V.

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

Leirset, E.

Lipiäinen, L.

Liu, X.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Ludvigsen, H.

Marcus, M. H.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Martarelli, M.

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser doppler vibrometry: Development of advanced solutions answering to technology’s needs,”Mech. Syst. Signal Process. 20, 1265–1285 (2006).
[Crossref]

Miao, J.

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

Monchalin, J.

J. Monchalin, “Heterodyne interferometric laser probe to measure continuous ultrasonic displacements,” Rev. Sci. Instruments 56, 543–546 (1985).
[Crossref]

Moore, A. J.

Morse, S. F.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Muller, R. S.

M. R. Hart, R. A. Conant, K. Y. Lau, and R. S. Muller, “Stroboscopic interferometer system for dynamic mems characterization,”J. Microelectromechanical Syst. 9, 409–418 (2000).
[Crossref]

Muyshondt, P.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Neuzil, P.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

Ngoi, B. K. A.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

Noël, N.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

Novotny, S.

Ober, C.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

Osborn, J. V.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for mems performance measurement,” J. Microelectromechanical Syst. 16, 668–674 (2007).
[Crossref]

Osten, W.

Paone, N.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Patorski, K.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Paul, W.

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

Pedrini, G.

Peres, C.

Perez-Lopez, C.

Perez-Roldan, M. J.

Petitgrand, S.

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of m(o)ems by optical techniques: status and trends,” J. Micromechanics Microengineering 13, S23 (2003).
[Crossref]

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

Photiadis, D. M.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Pudewills, F.

C. Rembe, S. Boedecker, A. Dräbenstedt, F. Pudewills, and G. Siegmund, “Heterodyne laser-doppler vibrometer with a slow-shear-mode bragg cell for vibration measurements up to 1.2 ghz,” in Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, vol. 7098 (SPIE, 2008), p. 12.

Puissant, J. P.

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Rembe, C.

C. Rembe and A. Dräbenstedt, “Laser-scanning confocal vibrometer microscope: Theory and experiments,” Rev. Sci. Instruments 77, 083702 (2006).
[Crossref]

C. Rembe, S. Boedecker, A. Dräbenstedt, F. Pudewills, and G. Siegmund, “Heterodyne laser-doppler vibrometer with a slow-shear-mode bragg cell for vibration measurements up to 1.2 ghz,” in Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, vol. 7098 (SPIE, 2008), p. 12.

Rothberg, S. J.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Royer, D.

D. Royer and E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[Crossref]

Ryan, T.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Salbut, L. A.

L. A. Salbut, K. Patorski, M. Jozwik, J. M. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques,” in Optical Metrology, vol. 5145 (SPIE, 2003), p. 10.

Salomaa, M. M.

Santoyo, F. M.

Schnell, M.

Sekaric, L.

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Senaratne, W.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

Shavrin, I.

Shen, Z.

Z. Shen, X. Han, C.-L. Zou, and H. X. Tang, “Phase sensitive imaging of 10 ghz vibrations in an aln microdisk resonator,” Rev. Sci. Instruments 88, 123709 (2017).
[Crossref]

Shen, Z. W.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

Siegmund, G.

C. Rembe, S. Boedecker, A. Dräbenstedt, F. Pudewills, and G. Siegmund, “Heterodyne laser-doppler vibrometer with a slow-shear-mode bragg cell for vibration measurements up to 1.2 ghz,” in Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, vol. 7098 (SPIE, 2008), p. 12.

Singh, V. R.

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

So, P. T. C.

Steger, H.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Tan, B.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

Tan, O.

C. Chao, Z. Wang, W. Zhu, and O. Tan, “Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices,” Rev. Sci. Instruments 76, 063906 (2005).
[Crossref]

Tang, H. X.

Z. Shen, X. Han, C.-L. Zou, and H. X. Tang, “Phase sensitive imaging of 10 ghz vibrations in an aln microdisk resonator,” Rev. Sci. Instruments 88, 123709 (2017).
[Crossref]

Tikka, P. T.

G. G. Fattinger and P. T. Tikka, “Modified mach–zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett. 79, 290–292 (2001).
[Crossref]

J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, “Scanning michelson interferometer for imaging surface acoustic wave fields,” Opt. Lett. 25, 613–615 (2000).
[Crossref]

Tomasini, E. P.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser doppler vibrometry: Development of advanced solutions answering to technology’s needs,”Mech. Syst. Signal Process. 20, 1265–1285 (2006).
[Crossref]

Torre-Ibarra, M. H. D. l.

Vanlanduit, S.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

Venkatakrishnan, K.

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

Vignola, J. F.

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

Wang, Z.

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

C. Chao, Z. Wang, W. Zhu, and O. Tan, “Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices,” Rev. Sci. Instruments 76, 063906 (2005).
[Crossref]

William, K.

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

Winefordner, J. D.

P. R. Griffiths, J. A. D. Haseth, and J. D. Winefordner, Fourier Transform Infrared Spectrometry, 2nd Edition (John Wiley And Sons, Inc., 2007).
[Crossref]

Yahiaoui, R.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

A. Bosseboeuf, J. P. Gilles, K. Danaie, R. Yahiaoui, M. Dupeux, J. P. Puissant, A. Chabrier, F. Fort, and P. Coste, “Versatile microscopic profilometer-vibrometer for static and dynamic characterization of micromechanical devices,” in Industrial Lasers and Inspection (EUROPTO Series), vol. 3825 (SPIE, 1999), p. 11.

Yaqoob, Z.

Zhou, R.

Zhu, W.

C. Chao, Z. Wang, W. Zhu, and O. Tan, “Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices,” Rev. Sci. Instruments 76, 063906 (2005).
[Crossref]

Zou, C.-L.

Z. Shen, X. Han, C.-L. Zou, and H. X. Tang, “Phase sensitive imaging of 10 ghz vibrations in an aln microdisk resonator,” Rev. Sci. Instruments 88, 123709 (2017).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (3)

G. G. Fattinger and P. T. Tikka, “Modified mach–zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett. 79, 290–292 (2001).
[Crossref]

D. Royer and E. Dieulesaint, “Optical probing of the mechanical impulse response of a transducer,” Appl. Phys. Lett. 49, 1056–1058 (1986).
[Crossref]

K. Kokkonen, M. Kaivola, S. Benchabane, A. Khelif, and V. Laude, “Scattering of surface acoustic waves by a phononic crystal revealed by heterodyne interferometry,” Appl. Phys. Lett. 91, 083517 (2007).
[Crossref]

J. Appl. Phys. (1)

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectrome-chanical oscillators,” J. Appl. Phys. 95, 3694–3703 (2004).
[Crossref]

J. Microelectromechanical Syst. (2)

M. R. Hart, R. A. Conant, K. Y. Lau, and R. S. Muller, “Stroboscopic interferometer system for dynamic mems characterization,”J. Microelectromechanical Syst. 9, 409–418 (2000).
[Crossref]

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for mems performance measurement,” J. Microelectromechanical Syst. 16, 668–674 (2007).
[Crossref]

J. Micromechanics Microengineering (1)

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of m(o)ems by optical techniques: status and trends,” J. Micromechanics Microengineering 13, S23 (2003).
[Crossref]

Mech. Syst. Signal Process. (1)

P. Castellini, M. Martarelli, and E. P. Tomasini, “Laser doppler vibrometry: Development of advanced solutions answering to technology’s needs,”Mech. Syst. Signal Process. 20, 1265–1285 (2006).
[Crossref]

Nanotechnology (1)

R. Jason, W. Paul, S. Joanna, K. William, and J. K. Gimzewski, “Observation of nanoscale dynamics in cantilever sensor arrays,” Nanotechnology 17, 3873 (2006).
[Crossref]

Nat. Commun. (1)

M. Schnell, P. S. Carney, and R. Hillenbrand, “Synthetic optical holography for rapid nanoimaging,” Nat. Commun. 5, 3499 (2014).
[Crossref] [PubMed]

Opt. Commun. (2)

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, N. Noël, Z. W. Shen, and C. S. Chin, “Two-axis-scanning laser doppler vibrometer for microstructure,” Opt. Commun. 182, 175–185 (2000).
[Crossref]

V. R. Singh, J. Miao, Z. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of mems diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (2)

S. J. Rothberg, M. S. Allen, P. Castellini, D. Di Maio, J. J. J. Dirckx, D. J. Ewins, B. J. Halkon, P. Muyshondt, N. Paone, T. Ryan, H. Steger, E. P. Tomasini, S. Vanlanduit, and J. F. Vignola, “An international review of laser doppler vibrometry: Making light work of vibration measurement,” Opt. Lasers Eng. 99, 11–22 (2017).
[Crossref]

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, “3d measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Lasers Eng. 36, 77–101 (2001).
[Crossref]

Opt. Lett. (2)

Rev. Sci. Instruments (5)

Z. Shen, X. Han, C.-L. Zou, and H. X. Tang, “Phase sensitive imaging of 10 ghz vibrations in an aln microdisk resonator,” Rev. Sci. Instruments 88, 123709 (2017).
[Crossref]

J. Monchalin, “Heterodyne interferometric laser probe to measure continuous ultrasonic displacements,” Rev. Sci. Instruments 56, 543–546 (1985).
[Crossref]

C. Chao, Z. Wang, W. Zhu, and O. Tan, “Scanning homodyne interferometer for characterization of piezoelectric films and microelectromechanical systems devices,” Rev. Sci. Instruments 76, 063906 (2005).
[Crossref]

J. F. Vignola, X. Liu, S. F. Morse, B. H. Houston, J. A. Bucaro, M. H. Marcus, D. M. Photiadis, and L. Sekaric, “Characterization of silicon micro-oscillators by scanning laser vibrometry,” Rev. Sci. Instruments 73, 3584–3588 (2002).
[Crossref]

C. Rembe and A. Dräbenstedt, “Laser-scanning confocal vibrometer microscope: Theory and experiments,” Rev. Sci. Instruments 77, 083702 (2006).
[Crossref]

Other (7)

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Supplementary Material (2)

NameDescription
» Visualization 1       Visualization 1 shows a movie of transient vibrations in an AFM cantilever excited with a sinc pulse (0 to 1 MHz bandwidth) with 100 ns time resolution.
» Visualization 2       Visualization 2 shows a movie of transient vibrations in an AFM cantilever excited with a linear chirped pulse (20 kHz to 1 MHz in 1ms) with 100 ns time resolution.

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Figures (7)

Fig. 1
Fig. 1 Time-resolved phase imaging in confocal microscopy with synthetic holographic confocal microscopy. (a) Setup. CW Laser: consisting of a stabilized 2mW HeNe laser, Faraday isolator and beam expander, BS: beam-splitter (50:50 nonpolarizing), MO: microscope objective (20x, 0.4 NA Nikon E Plan), TL: Lens (f = 25.4mm), PH: pin hole (100 µm diameter), PZM: Piezo-actuated mirror (Physikinstrumente, P-611.3S), DET: photo detector (Thorlabs, PDA36A), DAQ: Data acquisition card (GaGe CS8244). (b) Timing diagram showing the synchronization of the excitation signal Uex with the recording of the detector signal Udet at each pixel r = (x, y). Time t marks the time-delay from the beginning of the excitation pulse. (c) 3D Hologram stack Udet(r, t) as obtained by demultiplexing the data from (b) after image acquisition, yielding a time series of 20,000 individual holograms.
Fig. 2
Fig. 2 Imaging of transient vibrations in an AFM cantilever excited with a mechanical broadband pulse with 100 ns time resolution. (a) Time trace of the vertical position h(t) extracted at a pixel near the cantilever tip. Zooms show the time trace immediately after mechanical excitation (b), peak oscillation amplitude (c) and after ring down (d). (b–d) Evolution of the surface profile h (r, t) of the cantilever (see also Visualization 1).
Fig. 3
Fig. 3 Frequency and mode profiles of the cantilever vibrations obtained by Fourier analysis. (a) Spatially integrated spectrum Hint (b) Experimental mode profiles at the vibration frequencies identified in (a) L1-3 longitudinal modes, T1-2 torsional modes, P1-2 modes attributed to resonances in the piezoactuator (c) Calculated mode profiles of a model cantilever of 100 µm length × 37 µm width × 0.6 µm height; the material was Si3N4 with Young’s modulus adjusted to match the fundamental resonance.
Fig. 4
Fig. 4 Vertical sensitivity provided by the presented implementation of time-resolved phase imaging. (a) Momentary surface profile h(r, t) of the resting cantilever revealing 0.6 nm RMS spatial noise at 100 ns time resolution. (b–d) Vibration spectra taken at a single pixel near the cantilever tip, showing average vibration amplitude H. Note the logarithmic scale. (b) Resting cantilever without excitation signal applied, revealing a noise floor of 5.1pm RMS, corresponding to 230 fm / H z vertical sensitivity for the detection of vibration modes. Inset: residual L1 mode observed at 46.5 kHz. (c) Sinusoidal excitation signal tuned to the frequency of the L1 mode and at 100 mVpp amplitude (d) Chirped excitation signal, 20 kHz to 1 MHz in 1 ms, at 500 mVpp amplitude.
Fig. 5
Fig. 5 Comparison between sinc and chirped excitation waveforms. (a) Spatially integrated spectrum Hint (b) Experimental mode profiles at the vibration frequencies identified in (a).
Fig. 6
Fig. 6 Monitoring vibration excitation and decay with periodic chirped excitation. Chirped excitation waveform Uex linearly sweeping from 20 kHz to 1 MHz in 1 ms was applied. (a) Time trace of the vertical position h(t) extracted at a pixel near the cantilever tip. (b) Spatially integrated spectrogram Xint(τ, ω) of vibrations excited in the cantilever as obtained by Short-Fourier Transforms. (c) Decay time τ and quality factor Q of the vibration modes extracted from (b). Visualization 2 shows a movie of the cantilever vibrations.
Fig. 7
Fig. 7 Investigation of vibration modes P1 and P2. (a) Spatially integrated spectrum Hint over the cantilever base and the cantilever (areas marked in the respective color in the optical image). Data was scaled to fit. (b) Experimentally observed mode profiles P1 and P2. (c) COMSOL simulation of cantilever on support chip, showing a flexural mode of the support chip at 462 kHz (left panel shows zoom on cantilever).

Equations (2)

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U ˜ det ( q , t ) = C ( q , t ) + A R E ˜ S * ( k | | q , t ) + A R * E ˜ S ( k | | + q , t ) ,
h ( r , t ) = ( φ S ( r , t ) φ DC ( r ) ) λ / 4 π ,

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