Abstract

An optical laser differential interferometer, based on a modified differential interference contrast microscope, has been developed to measure the thermal motion of microscopic protrusions (stereocilia) that are the sites of mechanoelectrical transduction in auditory hair cells. The measurement sensitivity was limited at high frequencies mainly by shot noise, at intermediate frequencies by acoustic interference, and at low frequencies by thermal drift. The power spectral density of the instrumental noise was found to be as low as 1pm/Hz in the shot noise regime. We could, thus, measure the Brownian motion of hair bundles over the frequency range from 1 Hz–100 kHz. Experimental data that test and demonstrate the sensitivity and spatial discrimination of the instrument were found to be in agreement with theoretical estimates.

© 1990 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  4. J. J. Art, A. C. Crawford, R. Fettiplace, “A Method for Measuring Cellular Movements less than the Wavelength of Light,” J. Physiol. London 371, 18P (1986).
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    [CrossRef] [PubMed]
  6. J. Gelles, B. J. Schnapp, M. P. Scheetz, “Tracking Kinesin-Driven Movements with Nanometre Scale Precision,” Nature 331, 450–453 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. P. R. Dragsten, W. W. Webb, J. A. Paton, R. R. Capranica, “Auditory Membrane Vibrations: Measurements at Sub-Ångstrom Levels by Optical Heterodyne Spectrosocpy,” Science 185, 55–57 (1974).
    [CrossRef] [PubMed]
  9. J. Howard, A. J. Hudspeth, “Mechanical Relaxation of the Hair Bundle Mediates Adaptation in Mechanoelectrical Transduction by the Bullfrog’s Saccular Hair Cell,” Proc. Nat. Acad. Sci. USA 84, 3064–3068 (1987).
    [CrossRef] [PubMed]
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  11. J. Howard, J. F. Ashmore, “Stiffness of Sensory Hairbundles in the Sacculus of the Frog,” Hearing Res. 23, 93–104 (1986).
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    [CrossRef]
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    [CrossRef]
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  32. R. S. Bondurant, J. H. Shaprio, “Squeezed States in Phase-Sensing Interferometers,” Phys. Rev. A 30, 2548–2556 (1984).
  33. D. F. Walls, “Squeezed States of Light,” Nature 306, 141–146 (1983).
    [CrossRef]
  34. A. Boivin, E. Wolf, “Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam,” Phys. Rev. B 138, 1561–1565 (1965).
    [CrossRef]
  35. B. Richards, E. Wolf, “Electromagnetic Diffraction in Optical Systems II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
  36. T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  37. A. Ashkin, D. J. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectrical Particles, Opt. Lett. 11, 288–290 (1986).
    [CrossRef] [PubMed]
  38. A. Ashkin, J. M. Dziedzic, “Optical Trapping and Manipulation of Viruses and Bacteria,” Science 235, 1517–1520 (1987).
    [CrossRef] [PubMed]
  39. B. Drake et al., “Imaging Crystals, Polymers, and Processes in Water with the Atomic Force Microscope, Science 243, 1586–1589 (1989).
    [CrossRef] [PubMed]
  40. H. B. Callen, T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34–40 (1951).
    [CrossRef]
  41. L. E. Reichl, A Modern Course in Statistical Physics (U. Texas, Austin) 1980.
  42. D. L. Johnson, “Elastodynamics of Gels,” J. Chem. Phys. 77, 1531–1539 (1982).
    [CrossRef]

1989

W. Denk, W. W. Webb, A. J. Hudspeth, “The Mechanical Properties of Sensory Hair Bundles are Reflected in their Brownian Motion Measured with a Laser Differential Interferometer,” Proc. Nat. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Thermal Noise Limited Transduction Observed in Mechano-Sensory Receptors of the Inner Ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

B. Drake et al., “Imaging Crystals, Polymers, and Processes in Water with the Atomic Force Microscope, Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

1988

W. M. Roberts, J. Howard, A. J. Hudspeth, “Hair Cells: Transduction, Tuning, and Transmission in the Inner Ear,” Ann. Rev. Cell. Biol. 4, 63–92 (1988).
[CrossRef]

J. Gelles, B. J. Schnapp, M. P. Scheetz, “Tracking Kinesin-Driven Movements with Nanometre Scale Precision,” Nature 331, 450–453 (1988).
[CrossRef] [PubMed]

1987

J. Howard, A. J. Hudspeth, “Mechanical Relaxation of the Hair Bundle Mediates Adaptation in Mechanoelectrical Transduction by the Bullfrog’s Saccular Hair Cell,” Proc. Nat. Acad. Sci. USA 84, 3064–3068 (1987).
[CrossRef] [PubMed]

J. F. Ashmore, “A Fast Motile Response in the Guinea-Pig Outer Hair Cells: The Cellular Basis of the Cochlear Amplifier,” J. Physiol. London 388, 323–347 (1987).
[PubMed]

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical Trapping and Manipulation of Single Cells using Infrared Laser Beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical Trapping and Manipulation of Viruses and Bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

S. Kamimura, “Direct Measurement of Nanometric Displacement Under an Optical Microsocpe,” Appl. Opt. 26, 3425–3427 (1987).
[CrossRef] [PubMed]

1986

A. Ashkin, D. J. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectrical Particles, Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

J. J. Art, A. C. Crawford, R. Fettiplace, “A Method for Measuring Cellular Movements less than the Wavelength of Light,” J. Physiol. London 371, 18P (1986).

N. Bobroff, “Position Measurement with a Resolution- and Noise-Limited Instrument,” Rev. Sci. Instrum. 57, 1152–1157 (1986).
[CrossRef]

J. Howard, J. F. Ashmore, “Stiffness of Sensory Hairbundles in the Sacculus of the Frog,” Hearing Res. 23, 93–104 (1986).
[CrossRef]

W. Denk, A. J. Hudspeth, W. W. Webb, “Optical Measurement of the Brownian Motion Spectrum of Hair Bundles in the Transducing Hair Cells of the Frog Auditory System,” Biophys. J. 49, 21a (1986).

P. Muralt, D. W. Pohl, W. Denk, “Wide-Range, Low-Operating-Voltage, Bimorph STM: Application as Potentiometer,” IBM J. Res. Dev. 30, 443–450 (1986).
[CrossRef]

1985

A. C. Crawford, R. Fettiplace, “The Mechanical Properties of Ciliary Hair Bundles of Turtle Cochlea Hair Cells,” J. Physiol. London 364, 359–379 (1985).
[PubMed]

1984

A. Flock, D. Strelioff, “Graded and Nonlinear Mechanical Properties of Sensory Hairs in the Mammalian Hearing Organ,” Nature 310, 397–398 (1984).
[CrossRef]

R. S. Bondurant, J. H. Shaprio, “Squeezed States in Phase-Sensing Interferometers,” Phys. Rev. A 30, 2548–2556 (1984).

1983

D. F. Walls, “Squeezed States of Light,” Nature 306, 141–146 (1983).
[CrossRef]

1982

C. J. R. Sheppard, T. Wilson, “The Image of a Single Point in Microscopes of Large Numerical Aperture,” Proc. R. Soc. London Ser. A 379, 145–158 (1982).
[CrossRef]

D. L. Johnson, “Elastodynamics of Gels,” J. Chem. Phys. 77, 1531–1539 (1982).
[CrossRef]

1980

D. P. Corey, A. J. Hudspeth, “Mechanical Stimulation and Micromanipulation with Piezoelectrical Bimorph Elements, J. Neurosci. Methods 3, 183–202 (1980).
[CrossRef] [PubMed]

1974

P. R. Dragsten, W. W. Webb, J. A. Paton, R. R. Capranica, “Auditory Membrane Vibrations: Measurements at Sub-Ångstrom Levels by Optical Heterodyne Spectrosocpy,” Science 185, 55–57 (1974).
[CrossRef] [PubMed]

1971

H. Berg, “How to Track Bacteria,” Rev. Sci. Instrum. 42, 868–871 (1971).
[CrossRef] [PubMed]

1968

R. D. Allen, G. B. David, G. Nomarski, “The Zeiss-Nomarski Differential Interference Equipment for Transmitted-Light Microscopy, Z. wiss. Mikrosk. 69, 193–221 (1968).

1967

B. M. Johnstone, A. J. F. Boyle, “Basilar Membrane Vibration Examined with the Mossbauer Technique,” Science 158, 389–390 (1967).
[CrossRef] [PubMed]

1965

A. Boivin, E. Wolf, “Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam,” Phys. Rev. B 138, 1561–1565 (1965).
[CrossRef]

1959

B. Richards, E. Wolf, “Electromagnetic Diffraction in Optical Systems II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

1955

G. Nomarski, “Microinterféromtrè Différentiel à ondes Polarisées,” J. Phys. Radium 16, S9–S13 (1955).

1951

H. B. Callen, T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34–40 (1951).
[CrossRef]

1936

F. Zernike, “Das Phasenkontrastverfahren bei der Microscopischen Beobachtung,” Z. Tech. Phys. 16, 454–457 (1936).

1884

L. Boltzmann, “Ableitung des Stephan’schen Gesetzes betreffend der Abhängigkeit der Warmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie, Ann. Physik 22, 291 (1884).
[CrossRef]

Allen, R. D.

R. D. Allen, G. B. David, G. Nomarski, “The Zeiss-Nomarski Differential Interference Equipment for Transmitted-Light Microscopy, Z. wiss. Mikrosk. 69, 193–221 (1968).

Art, J. J.

J. J. Art, A. C. Crawford, R. Fettiplace, “A Method for Measuring Cellular Movements less than the Wavelength of Light,” J. Physiol. London 371, 18P (1986).

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Optical Trapping and Manipulation of Viruses and Bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical Trapping and Manipulation of Single Cells using Infrared Laser Beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, D. J. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectrical Particles, Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

Ashmore, J. F.

J. F. Ashmore, “A Fast Motile Response in the Guinea-Pig Outer Hair Cells: The Cellular Basis of the Cochlear Amplifier,” J. Physiol. London 388, 323–347 (1987).
[PubMed]

J. Howard, J. F. Ashmore, “Stiffness of Sensory Hairbundles in the Sacculus of the Frog,” Hearing Res. 23, 93–104 (1986).
[CrossRef]

Berg, H.

H. Berg, “How to Track Bacteria,” Rev. Sci. Instrum. 42, 868–871 (1971).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Bobroff, N.

N. Bobroff, “Position Measurement with a Resolution- and Noise-Limited Instrument,” Rev. Sci. Instrum. 57, 1152–1157 (1986).
[CrossRef]

Boivin, A.

A. Boivin, E. Wolf, “Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam,” Phys. Rev. B 138, 1561–1565 (1965).
[CrossRef]

Boltzmann, L.

L. Boltzmann, “Ableitung des Stephan’schen Gesetzes betreffend der Abhängigkeit der Warmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie, Ann. Physik 22, 291 (1884).
[CrossRef]

Bondurant, R. S.

R. S. Bondurant, J. H. Shaprio, “Squeezed States in Phase-Sensing Interferometers,” Phys. Rev. A 30, 2548–2556 (1984).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Boyle, A. J. F.

B. M. Johnstone, A. J. F. Boyle, “Basilar Membrane Vibration Examined with the Mossbauer Technique,” Science 158, 389–390 (1967).
[CrossRef] [PubMed]

Callen, H. B.

H. B. Callen, T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34–40 (1951).
[CrossRef]

Capranica, R. R.

P. R. Dragsten, W. W. Webb, J. A. Paton, R. R. Capranica, “Auditory Membrane Vibrations: Measurements at Sub-Ångstrom Levels by Optical Heterodyne Spectrosocpy,” Science 185, 55–57 (1974).
[CrossRef] [PubMed]

Chu, S.

Corey, D. P.

D. P. Corey, A. J. Hudspeth, “Mechanical Stimulation and Micromanipulation with Piezoelectrical Bimorph Elements, J. Neurosci. Methods 3, 183–202 (1980).
[CrossRef] [PubMed]

Crawford, A. C.

J. J. Art, A. C. Crawford, R. Fettiplace, “A Method for Measuring Cellular Movements less than the Wavelength of Light,” J. Physiol. London 371, 18P (1986).

A. C. Crawford, R. Fettiplace, “The Mechanical Properties of Ciliary Hair Bundles of Turtle Cochlea Hair Cells,” J. Physiol. London 364, 359–379 (1985).
[PubMed]

David, G. B.

R. D. Allen, G. B. David, G. Nomarski, “The Zeiss-Nomarski Differential Interference Equipment for Transmitted-Light Microscopy, Z. wiss. Mikrosk. 69, 193–221 (1968).

Denk, W.

W. Denk, W. W. Webb, A. J. Hudspeth, “The Mechanical Properties of Sensory Hair Bundles are Reflected in their Brownian Motion Measured with a Laser Differential Interferometer,” Proc. Nat. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Thermal Noise Limited Transduction Observed in Mechano-Sensory Receptors of the Inner Ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

W. Denk, A. J. Hudspeth, W. W. Webb, “Optical Measurement of the Brownian Motion Spectrum of Hair Bundles in the Transducing Hair Cells of the Frog Auditory System,” Biophys. J. 49, 21a (1986).

P. Muralt, D. W. Pohl, W. Denk, “Wide-Range, Low-Operating-Voltage, Bimorph STM: Application as Potentiometer,” IBM J. Res. Dev. 30, 443–450 (1986).
[CrossRef]

W. Denk, W. W. Webb, “Simultaneous Recording of Fluctuations of Hair-Bundle Deflection and Intracellular Voltage in Saccular Hair Cells.” In Cochlear Mechanics, Structure, Function and ModelsJ. P. Wilson, D. T. Kemp, Eds. (Plenum, New York1989), pp. 125–134.
[CrossRef]

Dicke, R. H.

R. H. Dicke, J. P. Wittke, Introduction to Quantum Mechanics (Addison-Wesley, Reading, MA, 1960), p. 130.

Dragsten, P. R.

P. R. Dragsten, W. W. Webb, J. A. Paton, R. R. Capranica, “Auditory Membrane Vibrations: Measurements at Sub-Ångstrom Levels by Optical Heterodyne Spectrosocpy,” Science 185, 55–57 (1974).
[CrossRef] [PubMed]

Drake, B.

B. Drake et al., “Imaging Crystals, Polymers, and Processes in Water with the Atomic Force Microscope, Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Dziedzic, D. J.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Optical Trapping and Manipulation of Viruses and Bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical Trapping and Manipulation of Single Cells using Infrared Laser Beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Fettiplace, R.

J. J. Art, A. C. Crawford, R. Fettiplace, “A Method for Measuring Cellular Movements less than the Wavelength of Light,” J. Physiol. London 371, 18P (1986).

A. C. Crawford, R. Fettiplace, “The Mechanical Properties of Ciliary Hair Bundles of Turtle Cochlea Hair Cells,” J. Physiol. London 364, 359–379 (1985).
[PubMed]

Flock, A.

A. Flock, D. Strelioff, “Graded and Nonlinear Mechanical Properties of Sensory Hairs in the Mammalian Hearing Organ,” Nature 310, 397–398 (1984).
[CrossRef]

Gelles, J.

J. Gelles, B. J. Schnapp, M. P. Scheetz, “Tracking Kinesin-Driven Movements with Nanometre Scale Precision,” Nature 331, 450–453 (1988).
[CrossRef] [PubMed]

Heisenberg, W.

W. Heisenberg, The Physical Principles of Quantum Mechanics (U. Chicago Press, Chicago, 1930), p. 21.

Howard, J.

W. M. Roberts, J. Howard, A. J. Hudspeth, “Hair Cells: Transduction, Tuning, and Transmission in the Inner Ear,” Ann. Rev. Cell. Biol. 4, 63–92 (1988).
[CrossRef]

J. Howard, A. J. Hudspeth, “Mechanical Relaxation of the Hair Bundle Mediates Adaptation in Mechanoelectrical Transduction by the Bullfrog’s Saccular Hair Cell,” Proc. Nat. Acad. Sci. USA 84, 3064–3068 (1987).
[CrossRef] [PubMed]

J. Howard, J. F. Ashmore, “Stiffness of Sensory Hairbundles in the Sacculus of the Frog,” Hearing Res. 23, 93–104 (1986).
[CrossRef]

Hudspeth, A. J.

W. Denk, W. W. Webb, A. J. Hudspeth, “The Mechanical Properties of Sensory Hair Bundles are Reflected in their Brownian Motion Measured with a Laser Differential Interferometer,” Proc. Nat. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

W. M. Roberts, J. Howard, A. J. Hudspeth, “Hair Cells: Transduction, Tuning, and Transmission in the Inner Ear,” Ann. Rev. Cell. Biol. 4, 63–92 (1988).
[CrossRef]

J. Howard, A. J. Hudspeth, “Mechanical Relaxation of the Hair Bundle Mediates Adaptation in Mechanoelectrical Transduction by the Bullfrog’s Saccular Hair Cell,” Proc. Nat. Acad. Sci. USA 84, 3064–3068 (1987).
[CrossRef] [PubMed]

W. Denk, A. J. Hudspeth, W. W. Webb, “Optical Measurement of the Brownian Motion Spectrum of Hair Bundles in the Transducing Hair Cells of the Frog Auditory System,” Biophys. J. 49, 21a (1986).

D. P. Corey, A. J. Hudspeth, “Mechanical Stimulation and Micromanipulation with Piezoelectrical Bimorph Elements, J. Neurosci. Methods 3, 183–202 (1980).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, (Wiley, New York, 1975).

Johnson, D. L.

D. L. Johnson, “Elastodynamics of Gels,” J. Chem. Phys. 77, 1531–1539 (1982).
[CrossRef]

Johnstone, B. M.

B. M. Johnstone, A. J. F. Boyle, “Basilar Membrane Vibration Examined with the Mossbauer Technique,” Science 158, 389–390 (1967).
[CrossRef] [PubMed]

Kamimura, S.

Kandel, Eric R.

Eric R. Kandel, James H. Schwartz, “Principles of Neural Science” (Elsevier, New York, 1985), p. 290.

Muralt, P.

P. Muralt, D. W. Pohl, W. Denk, “Wide-Range, Low-Operating-Voltage, Bimorph STM: Application as Potentiometer,” IBM J. Res. Dev. 30, 443–450 (1986).
[CrossRef]

Nomarski, G.

R. D. Allen, G. B. David, G. Nomarski, “The Zeiss-Nomarski Differential Interference Equipment for Transmitted-Light Microscopy, Z. wiss. Mikrosk. 69, 193–221 (1968).

G. Nomarski, “Microinterféromtrè Différentiel à ondes Polarisées,” J. Phys. Radium 16, S9–S13 (1955).

Paton, J. A.

P. R. Dragsten, W. W. Webb, J. A. Paton, R. R. Capranica, “Auditory Membrane Vibrations: Measurements at Sub-Ångstrom Levels by Optical Heterodyne Spectrosocpy,” Science 185, 55–57 (1974).
[CrossRef] [PubMed]

Pohl, D. W.

P. Muralt, D. W. Pohl, W. Denk, “Wide-Range, Low-Operating-Voltage, Bimorph STM: Application as Potentiometer,” IBM J. Res. Dev. 30, 443–450 (1986).
[CrossRef]

Reichl, L. E.

L. E. Reichl, A Modern Course in Statistical Physics (U. Texas, Austin) 1980.

Richards, B.

B. Richards, E. Wolf, “Electromagnetic Diffraction in Optical Systems II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Roberts, W. M.

W. M. Roberts, J. Howard, A. J. Hudspeth, “Hair Cells: Transduction, Tuning, and Transmission in the Inner Ear,” Ann. Rev. Cell. Biol. 4, 63–92 (1988).
[CrossRef]

Scheetz, M. P.

J. Gelles, B. J. Schnapp, M. P. Scheetz, “Tracking Kinesin-Driven Movements with Nanometre Scale Precision,” Nature 331, 450–453 (1988).
[CrossRef] [PubMed]

Schnapp, B. J.

J. Gelles, B. J. Schnapp, M. P. Scheetz, “Tracking Kinesin-Driven Movements with Nanometre Scale Precision,” Nature 331, 450–453 (1988).
[CrossRef] [PubMed]

Schwartz, James H.

Eric R. Kandel, James H. Schwartz, “Principles of Neural Science” (Elsevier, New York, 1985), p. 290.

Shaprio, J. H.

R. S. Bondurant, J. H. Shaprio, “Squeezed States in Phase-Sensing Interferometers,” Phys. Rev. A 30, 2548–2556 (1984).

Sheppard, C.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Sheppard, C. J. R.

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D. F. Walls, “Squeezed States of Light,” Nature 306, 141–146 (1983).
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W. Denk, W. W. Webb, A. J. Hudspeth, “The Mechanical Properties of Sensory Hair Bundles are Reflected in their Brownian Motion Measured with a Laser Differential Interferometer,” Proc. Nat. Acad. Sci. USA 86, 5371–5375 (1989).
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W. Denk, W. W. Webb, “Thermal Noise Limited Transduction Observed in Mechano-Sensory Receptors of the Inner Ear,” Phys. Rev. Lett. 63, 207–210 (1989).
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W. Denk, A. J. Hudspeth, W. W. Webb, “Optical Measurement of the Brownian Motion Spectrum of Hair Bundles in the Transducing Hair Cells of the Frog Auditory System,” Biophys. J. 49, 21a (1986).

P. R. Dragsten, W. W. Webb, J. A. Paton, R. R. Capranica, “Auditory Membrane Vibrations: Measurements at Sub-Ångstrom Levels by Optical Heterodyne Spectrosocpy,” Science 185, 55–57 (1974).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, “Simultaneous Recording of Fluctuations of Hair-Bundle Deflection and Intracellular Voltage in Saccular Hair Cells.” In Cochlear Mechanics, Structure, Function and ModelsJ. P. Wilson, D. T. Kemp, Eds. (Plenum, New York1989), pp. 125–134.
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C. J. R. Sheppard, T. Wilson, “The Image of a Single Point in Microscopes of Large Numerical Aperture,” Proc. R. Soc. London Ser. A 379, 145–158 (1982).
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T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

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R. H. Dicke, J. P. Wittke, Introduction to Quantum Mechanics (Addison-Wesley, Reading, MA, 1960), p. 130.

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A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical Trapping and Manipulation of Single Cells using Infrared Laser Beams,” Nature 330, 769–771 (1987).
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Ann. Physik

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Appl. Opt.

Biophys. J.

W. Denk, A. J. Hudspeth, W. W. Webb, “Optical Measurement of the Brownian Motion Spectrum of Hair Bundles in the Transducing Hair Cells of the Frog Auditory System,” Biophys. J. 49, 21a (1986).

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J. Howard, J. F. Ashmore, “Stiffness of Sensory Hairbundles in the Sacculus of the Frog,” Hearing Res. 23, 93–104 (1986).
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P. Muralt, D. W. Pohl, W. Denk, “Wide-Range, Low-Operating-Voltage, Bimorph STM: Application as Potentiometer,” IBM J. Res. Dev. 30, 443–450 (1986).
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J. F. Ashmore, “A Fast Motile Response in the Guinea-Pig Outer Hair Cells: The Cellular Basis of the Cochlear Amplifier,” J. Physiol. London 388, 323–347 (1987).
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A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical Trapping and Manipulation of Single Cells using Infrared Laser Beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

D. F. Walls, “Squeezed States of Light,” Nature 306, 141–146 (1983).
[CrossRef]

J. Gelles, B. J. Schnapp, M. P. Scheetz, “Tracking Kinesin-Driven Movements with Nanometre Scale Precision,” Nature 331, 450–453 (1988).
[CrossRef] [PubMed]

A. Flock, D. Strelioff, “Graded and Nonlinear Mechanical Properties of Sensory Hairs in the Mammalian Hearing Organ,” Nature 310, 397–398 (1984).
[CrossRef]

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A. Boivin, E. Wolf, “Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam,” Phys. Rev. B 138, 1561–1565 (1965).
[CrossRef]

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W. Denk, W. W. Webb, “Thermal Noise Limited Transduction Observed in Mechano-Sensory Receptors of the Inner Ear,” Phys. Rev. Lett. 63, 207–210 (1989).
[CrossRef] [PubMed]

Proc. Nat. Acad. Sci. USA

J. Howard, A. J. Hudspeth, “Mechanical Relaxation of the Hair Bundle Mediates Adaptation in Mechanoelectrical Transduction by the Bullfrog’s Saccular Hair Cell,” Proc. Nat. Acad. Sci. USA 84, 3064–3068 (1987).
[CrossRef] [PubMed]

W. Denk, W. W. Webb, A. J. Hudspeth, “The Mechanical Properties of Sensory Hair Bundles are Reflected in their Brownian Motion Measured with a Laser Differential Interferometer,” Proc. Nat. Acad. Sci. USA 86, 5371–5375 (1989).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A

B. Richards, E. Wolf, “Electromagnetic Diffraction in Optical Systems II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

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W. Denk, W. W. Webb, “Simultaneous Recording of Fluctuations of Hair-Bundle Deflection and Intracellular Voltage in Saccular Hair Cells.” In Cochlear Mechanics, Structure, Function and ModelsJ. P. Wilson, D. T. Kemp, Eds. (Plenum, New York1989), pp. 125–134.
[CrossRef]

F. J. Sigworth, “Electronic Design of the Patch Clamp,” in Single-Channel RecordingB. Sackmann, E. Neher, Eds. (Plenum, New York, 1983), pp. 3–35.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

The optical setup was built around an inverted microscope (Zeiss, ICM 405). Only the essential optical components are shown. Light from the He–Ne laser passes through an acoustooptical modulator (not shown), a gradient index (GRIN) lens (G1) an single-mode optical fiber (OF), and another GRIN lens (G2), which can be translated (not shown) along three axis to steer and focus the beam. The laser light then enters the microscope proper through a 25× Eyepiece (E1), passes a polarizer (P1) and a quarter wave plate (λ/4), and is combined by a partially reflecting mirror (PM) with the light that comes from a tungsten filament (TF) and is polarized by P2. Incandescent and laser light then pass the first DIC-slider (W1), the lower objective (O1, 40×, N.A. = 0.75, water immersion), the sample in its dish (SD), the upper objective lens (O2, identical to the lower) and a second DIC-Slider (W2). Part of the light is then diverted for visual observation by the beam splitter (BS) inside a triocular phototube. The remaining light encounters next a interference bandpass filter (IF) centered at 633nm wavelength. Most of the laser light passes this filter and is distributed by a polarizing beamsplitter cube (BSC) to the photodetectors at its exit faces. Most of the incandescent light and some of the laser light is reflected off IF and reaches via a front surface mirror (FM) and a green filter (GF, 2× BG19, Melles Griot) a CCD-TV camera (CCD). Note that the BSC is oriented parallel to the original polarization direction while the shear direction of W1 and W2 is rotated by 45°.

Fig. 2
Fig. 2

Schematic diagram of the signal detection and amplification circuitry. After being split into its polarization components by a polarizing beam-splitter cube (BSC) the laser light is detected by silicon photodiodes integrated with preamplifiers (u1 and u2; HAD 1100; EG&G Electro Optics). A difference signal (amplified 10×) is calculated by a instrumentation amplifier (u3; AD 524, Analog Devices) and the sum signal is calculated with a summing, inverting amplifier (u4; LF 346; National Semiconductor). The difference signal is then divided by the sum signal with an analog divider (u5; MPY 534 Burr Brown). The gain of the summing amplifier is adjustable to allow setting of the optimal denominator level. The output of the divider goes to a lock-in amplifier (LI; 124 A; EG&G Princeton Applied Research) and to a spectrum analyzer (DSA; 3562; A Hewlett Packard), which measured power- and cross-spectral densities of position and external signals. The calibration motion of the bimorph stage (stage) is driven by sine- and cosine-waves of the same frequencies and amplitudes, which are generated by a quadrature oscillator (u10; 4423; Burr Brown) and amplified by high voltage operational amplifiers (u6u9; LM 143; National Semiconductor).

Fig. 3
Fig. 3

Measured and calculated spatial discrimination. Measurements (solid line) were performed by translating a latex microsphere through the focal region with the piezoelectric bimorph stage. Theoretical calculations (see text) were made in the parfocal limit for a weakly scattering point object and also for an extended object, approximating the micro sphere. The experimental and theoretical difference signals (Δ, see text) are plotted as a function of the position of the object along the three spatial axes: (a) x-displacement; (b) y-displacement; and (c) z-displacement. All curves were normalized to their maxima. Note the different scale on the abszissa of the z-scan.

Fig. 4
Fig. 4

The power spectral density of the apparent motion of a latex microsphere, embedded in agarose (top trace), is compared in this figure with the power spectral densities of the output signal when no object was located in the focal region (bright) and when no light reached the detectors (dark). All data shown are referred to displacements in the focal plane. The straight horizontal line indicates the level of photoelectron shot noise (shot) expected from the measured amount of DC photocurrent (1.17 μA). Note that the noise level approaches, for high frequencies, the expected shot noise level. The increase of the smooth background towards lower frequencies could be caused by residual Brownian motion.42 The amplitude was calibrated by normalizing the power under the peak at 50 Hz (cal. peak) to 12.5 × 10−18 m2. This peak is due to the 10 nm peak-to-peak calibration motion.

Fig. 5
Fig. 5

The Brownian motion spectral density of a sensory hair bundle from a bullfrog sacculus shows some similarity to that expected from an overdamped harmonic oscillator.16 To obtain the high frequency portion of this spectrum, spectra where taken with the laser focus at, 10 μm above and 10 μm blow the tip of the horizontally-oriented hair bundle. The average of the power spectral densities from above and below the tip was then subtracted density measured at the tip itself. The spikes a t 20 kHz and its harmonics coincided with the switching frequency of the laser power supply.

Equations (26)

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δ x 2 2 4 δ p 2 ,
δ p 2 = δ k 2 2 N ph .
N ph = p o t m ω × σ π A l 2 λ 2 × 1 - 1 - ( A r / n ) 2 2 ,
δ k 2 = 2 π 2 A l A r / λ 2 ,
δ x = λ 3 c n 2 π 2 σ p 0 t m A 6 .
d = s T 4 A 2 ,
p t = s T 1 λ l 2 / π .
S = 1 / 2 ( O + + O - ) ( O + + O - ) ,
D = 1 / 2 ( O + - O - ) ( O + + O - ) .
O + = I T ( x + / 2 , y , z ) = I T + ,
O - = exp ( i π / 2 ) I T ( x - / 2 , y , z ) = i I T - ,
Δ = i I T + T - * - T - T + * I = 2 × Im ( I T + T - * I .
T ( x , y , z ) = 1 + E ( x , y , z ) ,
Δ = 2 × Im I E + - E - I .
I E ( x , y , z ) I = L ( x , y , z ) δ n V 2 π / λ .
δ x = [ ( S + D ) t m ω ] 1 / 2 ( Δ / x ) - 1 ,
Δ x = 2 [ L x ( x + / 2 , y , z ) - L x ( x - / 2 , y , z ) ] δ n V 2 π / λ .
L ( x , y , z ) = p 0 2 π A 2 λ 2 | 0 1 J 0 ( 2 π A x 2 + y 2 η / λ ) × exp ( - i η 2 π A 2 z / λ ) η d η 2 ,
S = [ 1 + cos ( ϕ + ξ ) ] I I ,
D = [ 1 - cos ( ϕ + ξ ) ] I I .
D / ξ = - sin ( ϕ + ξ ) I I ,
S / ξ = sin ( ϕ + ξ ) I I .
N S = 2 ω S = 2 ω [ 1 + cos ( ϕ + ξ ) ] I I ,
N D = 2 ω D = 2 ω [ 1 - cos ( ϕ + ξ ) ] I I .
ξ ^ = [ D - D ω D - S - S ω S ] ω D S S D / ξ - D S / ξ .
N ξ = ( ξ ^ D ) 2 N D + ( ξ ^ S ) N S = ω S + D = ω p 0 ,

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