Abstract

There is growing interest in using the exquisite phase sensitivity of optical coherence tomography (OCT) to measure the vibratory response in organ systems such as the middle and inner ear. Using frequency domain analysis, it is possible to achieve picometer sensitivity to vibration over a wide frequency band. Here we explore the limits of the frequency domain vibratory sensitivity due to additive noise and consider the implication of phase noise statistics on the estimation of vibratory amplitude and phase. Noise statistics are derived in both the Rayleigh (s/n = 0) and Normal distribution (s/n > 3) limits. These theoretical findings are explored using simulation and verified with experiments using a swept-laser system and a piezo electric element. A metric for sensitivity is proposed based on the 98% confidence interval for the Rayleigh distribution.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]

2019 (1)

2018 (1)

2016 (3)

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

2015 (1)

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

2013 (1)

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

2012 (2)

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref]

2011 (1)

T. Y. Ren, W. X. He, and P. G. Gillespie, “Measurement of cochlear power gain in the sensitive gerbil ear,” Nat. Commun. 2(1), 216 (2011).
[Crossref]

2008 (2)

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint Spectral and Time Domain Optical Coherence Tomography,” Opt. Express 16(9), 6008–6025 (2008).
[Crossref]

2006 (1)

Y. C. Lin, H. Hocheng, W. L. Fang, and R. Chen, “Fabrication and fatigue testing of an electrostatically driven microcantilever beam,” Mater. Manuf. Processes 21(1), 75–80 (2006).
[Crossref]

2005 (2)

2004 (1)

L. Mallet, B. C. Lee, W. J. Staszewski, and F. Scarpa, “Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection,” Smart Mater. Struct. 13(2), 261–269 (2004).
[Crossref]

2003 (3)

2000 (1)

1998 (1)

S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, “Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae,” Science 282(5395), 1882–1884 (1998).
[Crossref]

1995 (1)

H. Gudbjartsson and S. Patz, “The Rician Distribution of Noisy Mri Data,” Magn. Reson. Med. 34(6), 910–914 (1995).
[Crossref]

1992 (1)

W. V. Sorin and D. M. Baney, “A Simple Intensity Noise-Reduction Technique for Optical Low-Coherence Reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

1990 (1)

P. R. Morkel, R. I. Laming, and D. N. Payne, “Noise Characteristics of High-Power Doped-Fiber Superluminescent Sources,” Electron. Lett. 26(2), 96–98 (1990).
[Crossref]

Akkin, T.

Anh, N. H.

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

Applegate, B. E.

W. Kim, S. Kim, S. Huang, J. S. Oghalai, and B. E. Applegate, “Picometer scale vibrometry in the human middle ear using a surgical microscope based Optical Coherence Tomography and Vibrometry system,” Biomed. Opt. Express 10(9), 4395–4410 (2019).
[Crossref]

W. Kim, S. Kim, J. S. Oghalai, and B. E. Applegate, “Endoscopic optical coherence tomography enables morphological and subnanometer vibratory imaging of the porcine cochlea through the round window,” Opt. Lett. 43(9), 1966–1969 (2018).
[Crossref]

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

Bajraszewski, T.

Baney, D. M.

W. V. Sorin and D. M. Baney, “A Simple Intensity Noise-Reduction Technique for Optical Low-Coherence Reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

Bouma, B. E.

Bowden, A. K. E.

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

Cense, B.

Chang, E. W.

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref]

Chen, R.

Y. C. Lin, H. Hocheng, W. L. Fang, and R. Chen, “Fabrication and fatigue testing of an electrostatically driven microcantilever beam,” Mater. Manuf. Processes 21(1), 75–80 (2006).
[Crossref]

Cheng, J. T.

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

Choma, M. A.

Choudhury, N.

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

Ciganovic, N.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Creazzo, T. L.

de Boer, J. E.

de Boer, J. F.

Ellerbee, A. K.

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

M. A. Choma, A. K. Ellerbee, C. H. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. 30(10), 1162–1164 (2005).
[Crossref]

Fang, W. L.

Y. C. Lin, H. Hocheng, W. L. Fang, and R. Chen, “Fabrication and fatigue testing of an electrostatically driven microcantilever beam,” Mater. Manuf. Processes 21(1), 75–80 (2006).
[Crossref]

Fercher, A. F.

Fernandez, A. D.

Fraser, S. E.

Fridberger, A.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

Gillespie, P. G.

T. Y. Ren, W. X. He, and P. G. Gillespie, “Measurement of cochlear power gain in the sensitive gerbil ear,” Nat. Commun. 2(1), 216 (2011).
[Crossref]

Grillet, N.

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

Grosh, K.

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

Gudbjartsson, H.

H. Gudbjartsson and S. Patz, “The Rician Distribution of Noisy Mri Data,” Magn. Reson. Med. 34(6), 910–914 (1995).
[Crossref]

Haskell, R. C.

He, W. X.

T. Y. Ren, W. X. He, and P. G. Gillespie, “Measurement of cochlear power gain in the sensitive gerbil ear,” Nat. Commun. 2(1), 216 (2011).
[Crossref]

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

Hitzenberger, C. K.

Hocheng, H.

Y. C. Lin, H. Hocheng, W. L. Fang, and R. Chen, “Fabrication and fatigue testing of an electrostatically driven microcantilever beam,” Mater. Manuf. Processes 21(1), 75–80 (2006).
[Crossref]

Hoeling, B. M.

Huang, E.

Huang, S.

Inman, D. J.

D. J. Inman, Vibration with control (Wiley, 2006).

Izatt, J. A.

Jacques, S. L.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

Joo, C.

Kim, J.

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

Kim, S.

Kim, W.

Kobler, J. B.

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref]

Kowalczyk, A.

Laming, R. I.

P. R. Morkel, R. I. Laming, and D. N. Payne, “Noise Characteristics of High-Power Doped-Fiber Superluminescent Sources,” Electron. Lett. 26(2), 96–98 (1990).
[Crossref]

Lee, B. C.

L. Mallet, B. C. Lee, W. J. Staszewski, and F. Scarpa, “Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection,” Smart Mater. Struct. 13(2), 261–269 (2004).
[Crossref]

Lee, H. Y.

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

Leitgeb, R.

Lin, Y. C.

Y. C. Lin, H. Hocheng, W. L. Fang, and R. Chen, “Fabrication and fatigue testing of an electrostatically driven microcantilever beam,” Mater. Manuf. Processes 21(1), 75–80 (2006).
[Crossref]

Liu, X. F.

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

Mallet, L.

L. Mallet, B. C. Lee, W. J. Staszewski, and F. Scarpa, “Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection,” Smart Mater. Struct. 13(2), 261–269 (2004).
[Crossref]

Morkel, P. R.

P. R. Morkel, R. I. Laming, and D. N. Payne, “Noise Characteristics of High-Power Doped-Fiber Superluminescent Sources,” Electron. Lett. 26(2), 96–98 (1990).
[Crossref]

Myers, W. R.

Narayan, S. S.

S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, “Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae,” Science 282(5395), 1882–1884 (1998).
[Crossref]

Nuttall, A. L.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

Oghalai, J. S.

W. Kim, S. Kim, S. Huang, J. S. Oghalai, and B. E. Applegate, “Picometer scale vibrometry in the human middle ear using a surgical microscope based Optical Coherence Tomography and Vibrometry system,” Biomed. Opt. Express 10(9), 4395–4410 (2019).
[Crossref]

W. Kim, S. Kim, J. S. Oghalai, and B. E. Applegate, “Endoscopic optical coherence tomography enables morphological and subnanometer vibratory imaging of the porcine cochlea through the round window,” Opt. Lett. 43(9), 1966–1969 (2018).
[Crossref]

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

Papoulis, A.

A. Papoulis and S. U. Pillai, Probability, random variables, and stochastic processes (Tata McGraw-Hill Education, 2002).

Park, B. H.

Park, J.

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

Patz, S.

H. Gudbjartsson and S. Patz, “The Rician Distribution of Noisy Mri Data,” Magn. Reson. Med. 34(6), 910–914 (1995).
[Crossref]

Payne, D. N.

P. R. Morkel, R. I. Laming, and D. N. Payne, “Noise Characteristics of High-Power Doped-Fiber Superluminescent Sources,” Electron. Lett. 26(2), 96–98 (1990).
[Crossref]

Petersen, D. C.

Petrie, T.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Pierce, M. C.

Pillai, S. U.

A. Papoulis and S. U. Pillai, Probability, random variables, and stochastic processes (Tata McGraw-Hill Education, 2002).

Porsov, E.

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

Ramamoorthy, S.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Raphael, P. D.

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

Recio, A.

S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, “Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae,” Science 282(5395), 1882–1884 (1998).
[Crossref]

Reichenbach, T.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Ren, T. Y.

T. Y. Ren, W. X. He, and P. G. Gillespie, “Measurement of cochlear power gain in the sensitive gerbil ear,” Nat. Commun. 2(1), 216 (2011).
[Crossref]

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

Richards, M. A.

M. A. Richards, “The discrete-time Fourier transform and discrete Fourier transform of windowed stationary white noise,” Georgia Institute of Technology, Tech. Rep (2013).

Roosli, C.

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

Rosowski, J. J.

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

Ruggero, M. A.

S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, “Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae,” Science 282(5395), 1882–1884 (1998).
[Crossref]

Sarunic, M. V.

Scarpa, F.

L. Mallet, B. C. Lee, W. J. Staszewski, and F. Scarpa, “Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection,” Smart Mater. Struct. 13(2), 261–269 (2004).
[Crossref]

Sorin, W. V.

W. V. Sorin and D. M. Baney, “A Simple Intensity Noise-Reduction Technique for Optical Low-Coherence Reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

Staszewski, W. J.

L. Mallet, B. C. Lee, W. J. Staszewski, and F. Scarpa, “Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection,” Smart Mater. Struct. 13(2), 261–269 (2004).
[Crossref]

Subhash, H. M.

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

Szkulmowska, A.

Szkulmowski, M.

Tearney, G. J.

Temchin, A. N.

S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, “Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae,” Science 282(5395), 1882–1884 (1998).
[Crossref]

Ungersma, S. E.

Wang, R. K. K.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

Wang, R. Y.

Warren, R. L.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Williams, M. E.

Wilson, T. M.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Wojtkowski, M.

Xia, A. P.

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

Yang, C. H.

Yun, S. H.

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

E. W. Chang, J. B. Kobler, and S. H. Yun, “Subnanometer optical coherence tomographic vibrography,” Opt. Lett. 37(17), 3678–3680 (2012).
[Crossref]

Zhang, Y.

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Biomed. Opt. Express (1)

Electron. Lett. (1)

P. R. Morkel, R. I. Laming, and D. N. Payne, “Noise Characteristics of High-Power Doped-Fiber Superluminescent Sources,” Electron. Lett. 26(2), 96–98 (1990).
[Crossref]

Hear. Res. (1)

E. W. Chang, J. T. Cheng, C. Roosli, J. B. Kobler, J. J. Rosowski, and S. H. Yun, “Simultaneous 3D imaging of sound-induced motions of the tympanic membrane and middle ear ossicles,” Hear. Res. 304, 49–56 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

W. V. Sorin and D. M. Baney, “A Simple Intensity Noise-Reduction Technique for Optical Low-Coherence Reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

J. Biomed. Opt. (1)

H. M. Subhash, N. H. Anh, R. K. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref]

J. Neurosci. (1)

H. Y. Lee, P. D. Raphael, A. P. Xia, J. Kim, N. Grillet, B. E. Applegate, A. K. E. Bowden, and J. S. Oghalai, “Two-Dimensional Cochlear Micromechanics Measured In Vivo Demonstrate Radial Tuning within the Mouse Organ of Corti,” J. Neurosci. 36(31), 8160–8173 (2016).
[Crossref]

Magn. Reson. Med. (1)

H. Gudbjartsson and S. Patz, “The Rician Distribution of Noisy Mri Data,” Magn. Reson. Med. 34(6), 910–914 (1995).
[Crossref]

Mater. Manuf. Processes (1)

Y. C. Lin, H. Hocheng, W. L. Fang, and R. Chen, “Fabrication and fatigue testing of an electrostatically driven microcantilever beam,” Mater. Manuf. Processes 21(1), 75–80 (2006).
[Crossref]

Nat. Commun. (2)

T. Y. Ren, W. X. He, and P. G. Gillespie, “Measurement of cochlear power gain in the sensitive gerbil ear,” Nat. Commun. 2(1), 216 (2011).
[Crossref]

A. P. Xia, X. F. Liu, P. D. Raphael, B. E. Applegate, and J. S. Oghalai, “Hair cell force generation does not amplify or tune vibrations within the chicken basilar papilla,” Nat. Commun. 7(1), 13133 (2016).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

P. Natl. Acad. Sci. USA (1)

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” P. Natl. Acad. Sci. USA 112, 3128–3133 (2015).
[Crossref]

Proc. Natl. Acad. Sci. U. S. A. (2)

W. X. He, A. Fridberger, E. Porsov, K. Grosh, and T. Y. Ren, “Reverse wave propagation in the cochlea,” Proc. Natl. Acad. Sci. U. S. A. 105(7), 2729–2733 (2008).
[Crossref]

R. L. Warren, S. Ramamoorthy, N. Ciganovic, Y. Zhang, T. M. Wilson, T. Petrie, R. K. K. Wang, S. L. Jacques, T. Reichenbach, A. L. Nuttall, and A. Fridberger, “Minimal basilar membrane motion in low-frequency hearing,” Proc. Natl. Acad. Sci. U. S. A. 113(30), E4304–E4310 (2016).
[Crossref]

Science (1)

S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, “Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae,” Science 282(5395), 1882–1884 (1998).
[Crossref]

Smart Mater. Struct. (1)

L. Mallet, B. C. Lee, W. J. Staszewski, and F. Scarpa, “Structural health monitoring using scanning laser vibrometry: II. Lamb waves for damage detection,” Smart Mater. Struct. 13(2), 261–269 (2004).
[Crossref]

Other (3)

M. A. Richards, “The discrete-time Fourier transform and discrete Fourier transform of windowed stationary white noise,” Georgia Institute of Technology, Tech. Rep (2013).

A. Papoulis and S. U. Pillai, Probability, random variables, and stochastic processes (Tata McGraw-Hill Education, 2002).

D. J. Inman, Vibration with control (Wiley, 2006).

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Figures (10)

Fig. 1.
Fig. 1. A flow chart showing the processing steps along with the statistical results such as distribution, mean (µ) and standard deviation (σ). Symbols: k, wavenumber; t, time; z, optical pathlength difference, related to the tissue depth (Δz) by z = 2nΔz, where n is refractive index; f, frequency; H(k, t), a time series of spectral interferogram; i${\mathfrak{F}}$k(·), inverse Fourier transform along the k dimension; ${\mathfrak{F}}$t(·), Fourier transform along the time dimension; |·|, magnitude; ∠, angle;. i(z, t), h(z, t) without noise; N, the number of spectral channels; M is the number of time samples; fN, subscript indicating frequency domain with normal distribution; fR, subscript indicating frequency domain with Rayleigh distribution; θvib, subscript indicating vibrational phase.
Fig. 2.
Fig. 2. Graphical phase noise analysis in the complex domain. |i(z)| and ϕi(z) are the magnitude and the phase of the ideal A-scan without noise. |nz(z)| and ϕn(z) are the magnitude and the phase of the noise, nz(z). ϕn-i(z) is the phase difference between the noise and ideal A-scan.
Fig. 3.
Fig. 3. (a) Example of modeled interferograms with additive noise. (b) A-scan of (a). (c) Time domain vibrational signal extracted from a set of A-scans. (d) Frequency domain vibrational signal transformed from (c).
Fig. 4.
Fig. 4. Simulation results for Anoise when Avib = 0. Top row is for 300 simulated M-scans and bottom row for 3000 M-scans. (a, c) are the measured and theoretical second moment as a function of the STD of the noise in the spectral interferogram, σk. (b, d) are histograms (blue) with Rayleigh distribution fits (red line) of frequency domain noise from the data of σk = 0.02.
Fig. 5.
Fig. 5. Simulation results for noise in the measure of Avib. Top row is for 300 simulated M-scans and bottom row for 3000 M-scans. (a, d) are the measured and theoretical mean (µfR) as a function of the STD of the noise in the spectral interferogram, σk. (b, e) are the measured and theoretical STD (σθfR) as a function of the STD of the noise in the spectral interferogram, σk. (c, f) are histograms (blue) with normal distribution fits (red line) of Anoise from the data of σk = 0.02.
Fig. 6.
Fig. 6. Simulation results for noise in the measure of θvib. Top row is for 300 simulated M-scans and bottom row for 3000 M-scans. (a, d) are the measured and theoretical mean (µθvib) as a function of the STD of the noise in the spectral interferogram, σk. (b, e) are the measured and theoretical STD (σθvib) as a function of the STD of the noise in the spectral interferogram, σk. (c, f) are histograms (blue) with normal distribution fits (red line) of θnoise from the data of σk = 0.02
Fig. 7.
Fig. 7. Averaged A-scans and frequency domain vibrational responses measured from 100 M-scan with a piezo electric element driven by 4 kHz. (a, d) are A-scan and 100 frequency domain vibrational responses, respectively when no ND filter is used while (b, e) and (c, f) are from the use of 1 ND and 2 ND filters, respectively. In (d, e, f), thick black line shows the RMS value of the frequency domain noise.
Fig. 8.
Fig. 8. Second moments and histograms of amplitude detection noise extracted in the frequency region where Avib = 0. (a, b) show theoretical and experimental second moments of Anoise and their percentage errors, respectively, where the second moments were measured in three frequency regions, 6∼10 kHz, 22∼32 kHz, and 50∼60 kHz. (c, d, e) display histograms (blue) with Rayleigh distribution fits (red line) of the data with a SNR of 56.33 dB acquired from 6∼10 kHz, 22∼32 kHz, and 50∼60 kHz, respectively.
Fig. 9.
Fig. 9. Mean and standard deviation of amplitude and phase detection noises in accordance with Ascan SNR. (a, b) show in picometer scale mean and standard deviation of amplitude detection noise while (d, e) display in degree those of phase detection noise. Blue lines and red circles represent theoretical results calculated using Eqs. (12) and (13), and experimentally measured ones, respectively. (c, f) show histograms (blue box) with normal distribution fits (red line) of measured amplitude and phase detection noises from the data with a SNR of 56.33 dB.
Fig. 10.
Fig. 10. RMS errors of amplitude and phase detection noises as function of A-scan SNR. (a) and (b) show percentage errors of amplitude detection noise and phase detection noise, respectively. RMS error was calculated by |Theoretical RMS – Experimental RMS|/Theoretical RMS × 100 where RMS was computed by the square root of mean squared plus standard deviation squared.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

H ( k , t ) = ρ b S ( k ) R R R S cos ( 2 k n Δ z + 2 k 0 n δ z ( t ) ) + n k ( k , t )
h ( z = 2 n Δ z , t ) = ρ s ( 0 ) R R R S 2 b e j 2 k 0 n δ z ( t ) + n z ( z = 2 n Δ z , t ) = i ( z = 2 n Δ z , t ) + n z ( z = 2 n Δ z , t )
ϕ n o i s e ( z ) = tan 1 ( | n z ( z ) | sin ( ϕ n i ( z ) ) | i ( z ) | + | n z ( z ) | cos ( ϕ n i ( z ) ) )
ϕ n o i s e ( z ) | n z ( z ) | sin ( ϕ n i ( z ) ) | i ( z ) |
E [ ϕ n o i s e ( z , t ) ] E [ | n z ( z , t ) | sin ( ϕ n i ( z , t ) ) | i ( z , t ) | ] = E [ | n z ( z , t ) | ( sin ( ϕ n ( z , t ) ) cos ( ϕ i ( z , t ) ) cos ( ϕ n ( z , t ) ) sin ( ϕ i ( z , t ) ) ) ] | i ( z ) | = E [ | n z ( z ) | ] E [ sin ( ϕ n ( z ) ) ] cos ( ϕ i ( z , t ) ) | i ( z ) | E [ | n z ( z ) | ] E [ cos ( ϕ n ( z ) ) ] sin ( ϕ i ( z , t ) ) | i ( z ) | = 0
E [ ϕ n o i s e 2 ( z , t ) ] E [ | n z 2 ( z , t ) | sin 2 ( ϕ n i ( z , t ) ) ] | i ( z ) | 2 = E [ | n z 2 ( z , t ) | ] E [ | n z 2 ( z , t ) | ] E [ cos ( 2 ϕ n ( z , t ) 2 ϕ i ( z , t ) ) ] 2 | i ( z ) | 2 = E [ | n z 2 ( z ) | ] 2 | i ( z ) | 2 = N σ k 2 2 | i ( z ) | 2 = 1 2 S N R z
ϕ ( t ) = 2 k 0 n δ z ( t ) + n t ( t ) = 2 k 0 n A v i b cos ( 2 π f v i b t + θ v i b ) + n t ( t )
ϕ ( f ) = 2 k 0 n δ z ( f ) + n f ( f ) = M k 0 n A v i b δ ( f ± f v i b ) e j θ v i b + n f ( f )
ϕ ( f v i b ) M k 0 n = A v i b e j θ v i b + n f ( f v i b ) M k 0 n = ( A v i b cos ( θ v i b ) + Re [ n f ( f v i b ) ] M k 0 n ) + j ( A v i b sin ( θ v i b ) + Im [ n f ( f v i b ) ] M k 0 n )
A n o i s e = A m e a A v i b
E [ A n o i s e 2 ] = μ f R 2 + σ f R 2 = σ t k 0 n 2 M π 2 + 4 π 2 = σ t k 0 n M
μ f N = E [ A n o i s e ] = E [ A m e a A v i b ] = E [ A m e a ] A v i b = A v i b 2 + σ t 2 2 M k 0 2 n 2 A v i b σ f N = E [ ( A n o i s e E [ A n o i s e ] ) 2 ] = E [ ( A m e a μ f N ) 2 ] = σ t k 0 n 2 M
μ θ v i b = E [ θ n o i s e ] = 0 σ θ v i b = E [ θ n o i s e 2 ] = 1 2 S N R f = M σ t 2 2 ( M k 0 n A v i b ) 2 = σ t 2 2 M k 0 2 n 2 A v i b 2 = σ t A v i b k 0 n 2 M
S N R = ρ S R s 2 b 2 D f s w e e p = ρ S R s 2 b 2 Δ t
s e n s = μ f R + 3 σ f R = ( π + 3 4 π 2 2 k 0 n ) ( M S N R ) 1 / 2
s e n s = ( π + 3 4 π 2 2 k 0 n ) 2 b 2 ρ S R s Δ t M
μ f R 2 + σ f R 2 = E [ A n o i s e 2 ] = E w σ t 2 k 0 2 n 2 W 2 ( 0 ) = σ t E w k 0 n W ( 0 )
= 1.225 σ t k 0 n M for Hann window

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