Abstract

A novel method has been developed to measure nanometric displacement under a conventional optical microscope. The magnified image of a pinhole was divided into two parts using a prism-shaped mirror. The difference of light intensity between the divided images was determined, which was proportional to displacement of the pinhole. Using a 5-μm diam pinhole, the accuracy to determine displacement was ∼1 nm. Instead of a pinhole, polystyrene microbeads were used in the new method. Displacement of the microbeads was also measured with nanometric accuracy. This technique could be used to probe nanometric phenomena using optical microscopes.

© 1987 Optical Society of America

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References

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  1. K. P. Roos, A. J. Brady, “Individual Sarcomere Length Determination from Isolated Cardiac Cells Using High-Resolution Optical Microscopy and Digital Image Processing,” Biophys. J. 40, 233 (1982).
    [CrossRef] [PubMed]
  2. W. Mirande, “Absolutmessungen von Strukturbreiten in Mikrometerbereich mit dem Lichtmiktoskop,” PTB Mitt. 94, 157 (1984).
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  4. N. A. Massie, “Real-Time Digital Heterodyne Interferometry: A System,” Appl. Opt. 19, 154 (1980).
    [CrossRef] [PubMed]
  5. M. Tanaka, K. Nakayama, “A New Optical Interferometer for Absolute Measurement of Linear Displacement in the Sub-nanometer Range,” Jpn. J. Appl. Phys. 22, L233 (1983).
    [CrossRef]
  6. T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
    [CrossRef]
  7. R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
    [CrossRef]
  8. A. Rembaum, W. J. Dreyer, “Immunomicrospheres: Reagents for Cell Labeling and Separation,” Science 208, 364 (1980).
    [CrossRef] [PubMed]
  9. M. C. Beckerle, “Microinjected Fluorescent Beads Exhibit Saltatory Motion in Tissue Culture Cells,” J. Cell Biol 98, 2126 (1984).
    [CrossRef] [PubMed]
  10. R. J. Adams, D. Bray, “Rapid Transport of Foreign Particles Microinjected into Crab Axons,” Nature London 303, 718 (1983).
    [CrossRef] [PubMed]
  11. M. P. Sheetz, J. A. Spudich, “Movement of Myosin-Coated Beads on Actin Cables in Vitro,” Nature London 303, 31 (1983).
    [CrossRef] [PubMed]
  12. R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
    [CrossRef] [PubMed]
  13. T. Shimmen, M. Yano, “Active Sliding Movement of Latex Beads Coated with Skeletal Myosin on Chara Actin Bundles,” Protoplasma 121, 132 (1984).
    [CrossRef]

1985 (1)

R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
[CrossRef] [PubMed]

1984 (4)

T. Shimmen, M. Yano, “Active Sliding Movement of Latex Beads Coated with Skeletal Myosin on Chara Actin Bundles,” Protoplasma 121, 132 (1984).
[CrossRef]

M. C. Beckerle, “Microinjected Fluorescent Beads Exhibit Saltatory Motion in Tissue Culture Cells,” J. Cell Biol 98, 2126 (1984).
[CrossRef] [PubMed]

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

W. Mirande, “Absolutmessungen von Strukturbreiten in Mikrometerbereich mit dem Lichtmiktoskop,” PTB Mitt. 94, 157 (1984).

1983 (3)

M. Tanaka, K. Nakayama, “A New Optical Interferometer for Absolute Measurement of Linear Displacement in the Sub-nanometer Range,” Jpn. J. Appl. Phys. 22, L233 (1983).
[CrossRef]

R. J. Adams, D. Bray, “Rapid Transport of Foreign Particles Microinjected into Crab Axons,” Nature London 303, 718 (1983).
[CrossRef] [PubMed]

M. P. Sheetz, J. A. Spudich, “Movement of Myosin-Coated Beads on Actin Cables in Vitro,” Nature London 303, 31 (1983).
[CrossRef] [PubMed]

1982 (1)

K. P. Roos, A. J. Brady, “Individual Sarcomere Length Determination from Isolated Cardiac Cells Using High-Resolution Optical Microscopy and Digital Image Processing,” Biophys. J. 40, 233 (1982).
[CrossRef] [PubMed]

1980 (2)

A. Rembaum, W. J. Dreyer, “Immunomicrospheres: Reagents for Cell Labeling and Separation,” Science 208, 364 (1980).
[CrossRef] [PubMed]

N. A. Massie, “Real-Time Digital Heterodyne Interferometry: A System,” Appl. Opt. 19, 154 (1980).
[CrossRef] [PubMed]

1975 (1)

R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
[CrossRef]

1974 (1)

Adams, R. J.

R. J. Adams, D. Bray, “Rapid Transport of Foreign Particles Microinjected into Crab Axons,” Nature London 303, 718 (1983).
[CrossRef] [PubMed]

Beckerle, M. C.

M. C. Beckerle, “Microinjected Fluorescent Beads Exhibit Saltatory Motion in Tissue Culture Cells,” J. Cell Biol 98, 2126 (1984).
[CrossRef] [PubMed]

Brady, A. J.

K. P. Roos, A. J. Brady, “Individual Sarcomere Length Determination from Isolated Cardiac Cells Using High-Resolution Optical Microscopy and Digital Image Processing,” Biophys. J. 40, 233 (1982).
[CrossRef] [PubMed]

Brangaccio, D. J.

Bray, D.

R. J. Adams, D. Bray, “Rapid Transport of Foreign Particles Microinjected into Crab Axons,” Nature London 303, 718 (1983).
[CrossRef] [PubMed]

Bruning, J. H.

Dreyer, W. J.

A. Rembaum, W. J. Dreyer, “Immunomicrospheres: Reagents for Cell Labeling and Separation,” Science 208, 364 (1980).
[CrossRef] [PubMed]

R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
[CrossRef]

Gallagher, J. E.

Herriott, D. R.

Kanou, T.

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

Massie, N. A.

Mirande, W.

W. Mirande, “Absolutmessungen von Strukturbreiten in Mikrometerbereich mit dem Lichtmiktoskop,” PTB Mitt. 94, 157 (1984).

Moday, R. S.

R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
[CrossRef]

Nakayama, K.

M. Tanaka, K. Nakayama, “A New Optical Interferometer for Absolute Measurement of Linear Displacement in the Sub-nanometer Range,” Jpn. J. Appl. Phys. 22, L233 (1983).
[CrossRef]

Reese, T. S.

R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
[CrossRef] [PubMed]

Rembaum, A.

A. Rembaum, W. J. Dreyer, “Immunomicrospheres: Reagents for Cell Labeling and Separation,” Science 208, 364 (1980).
[CrossRef] [PubMed]

R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
[CrossRef]

Roos, K. P.

K. P. Roos, A. J. Brady, “Individual Sarcomere Length Determination from Isolated Cardiac Cells Using High-Resolution Optical Microscopy and Digital Image Processing,” Biophys. J. 40, 233 (1982).
[CrossRef] [PubMed]

Rosenfeld, D. P.

Schnapp, B. J.

R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
[CrossRef] [PubMed]

Sheetz, M. P.

R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
[CrossRef] [PubMed]

M. P. Sheetz, J. A. Spudich, “Movement of Myosin-Coated Beads on Actin Cables in Vitro,” Nature London 303, 31 (1983).
[CrossRef] [PubMed]

Shimmen, T.

T. Shimmen, M. Yano, “Active Sliding Movement of Latex Beads Coated with Skeletal Myosin on Chara Actin Bundles,” Protoplasma 121, 132 (1984).
[CrossRef]

Spudich, J. A.

M. P. Sheetz, J. A. Spudich, “Movement of Myosin-Coated Beads on Actin Cables in Vitro,” Nature London 303, 31 (1983).
[CrossRef] [PubMed]

Tanaka, M.

M. Tanaka, K. Nakayama, “A New Optical Interferometer for Absolute Measurement of Linear Displacement in the Sub-nanometer Range,” Jpn. J. Appl. Phys. 22, L233 (1983).
[CrossRef]

Vale, R. D.

R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
[CrossRef] [PubMed]

White, A. D.

Yano, M.

T. Shimmen, M. Yano, “Active Sliding Movement of Latex Beads Coated with Skeletal Myosin on Chara Actin Bundles,” Protoplasma 121, 132 (1984).
[CrossRef]

Yatagai, T.

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

Yen, S. P. S.

R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
[CrossRef]

Appl. Opt. (2)

Biophys. J. (1)

K. P. Roos, A. J. Brady, “Individual Sarcomere Length Determination from Isolated Cardiac Cells Using High-Resolution Optical Microscopy and Digital Image Processing,” Biophys. J. 40, 233 (1982).
[CrossRef] [PubMed]

Cell (1)

R. D. Vale, B. J. Schnapp, T. S. Reese, M. P. Sheetz, “Organelle, Bead, and Microtubule Translocations Promoted by Soluble Factors from the Squid Giant Axon,” Cell 40, 559 (1985).
[CrossRef] [PubMed]

J. Cell Biol (2)

M. C. Beckerle, “Microinjected Fluorescent Beads Exhibit Saltatory Motion in Tissue Culture Cells,” J. Cell Biol 98, 2126 (1984).
[CrossRef] [PubMed]

R. S. Moday, W. J. Dreyer, A. Rembaum, S. P. S. Yen, “New Immunolatex Spheres: Visual Markers of Antigens on Lymphocytes for Scanning Electron Microscopy,” J. Cell Biol 64, 75 (1975).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Tanaka, K. Nakayama, “A New Optical Interferometer for Absolute Measurement of Linear Displacement in the Sub-nanometer Range,” Jpn. J. Appl. Phys. 22, L233 (1983).
[CrossRef]

Nature London (2)

R. J. Adams, D. Bray, “Rapid Transport of Foreign Particles Microinjected into Crab Axons,” Nature London 303, 718 (1983).
[CrossRef] [PubMed]

M. P. Sheetz, J. A. Spudich, “Movement of Myosin-Coated Beads on Actin Cables in Vitro,” Nature London 303, 31 (1983).
[CrossRef] [PubMed]

Opt. Eng. (1)

T. Yatagai, T. Kanou, “Aspherical Surface Testing with Shearing Interferometer Using Fringe Scanning Detection Method,” Opt. Eng. 23, 357 (1984).
[CrossRef]

Protoplasma (1)

T. Shimmen, M. Yano, “Active Sliding Movement of Latex Beads Coated with Skeletal Myosin on Chara Actin Bundles,” Protoplasma 121, 132 (1984).
[CrossRef]

PTB Mitt (1)

W. Mirande, “Absolutmessungen von Strukturbreiten in Mikrometerbereich mit dem Lichtmiktoskop,” PTB Mitt. 94, 157 (1984).

Science (1)

A. Rembaum, W. J. Dreyer, “Immunomicrospheres: Reagents for Cell Labeling and Separation,” Science 208, 364 (1980).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram illustrating the apparatus: M, prism-shaped mirror; P, photodiode; C, current–voltage converter; S, mechanical stage with a piezomechanical actuator.

Fig. 2
Fig. 2

(A) Calculated curve showing the relationship between linear displacement of the pinhole and expected output of the apparatus which is the areal difference between two divided portions of the pinhole image. R is the radius of the pinhole image. (B) Real curve showing the relationship between driving voltage given to the piezomechanical actuator and output of the sensing system. Scales are 1 and 20 V/division in vertical and horizontal axes, respectively. It is shown that the response of the sensor is proportional to the displacement when the pinhole image is divided into two almost equal parts (midpoint of each curve). Slight difference of curvatures is due to uneven distribution of light intensity in the real image of the pinhole.

Fig. 3
Fig. 3

Piezomechanical actuator was driven with 0.4-s square pulses and with various voltages as shown in Fig. 4. The relationship between output of the photosensing system and voltage of the driving pulses given to the piezomechanical actuator (abscissa) in the 0–0.8- and 0–100-V range is shown in (A) and (B), respectively. (C) Displacement of the pinhole determined directly using an ocular micrometer in the 0–120-V range of the driving pulses. The piezomechanical stage is driven by 30 nm/V in the micrometric range (1–3 μm) and 19 nm/V in the nanometric range (<16 nm).

Fig. 4
Fig. 4

(A) Results using a 5-μm diam pinhole. Outputs of the photosensing device are shown when 0.052-, 0.10-, 0.21-, 0.42-, and 0.82-V driving pulses were given to the piezomechanical actuator, which correspond to 1.0-, 2.0-, 4.0-, 8.0-, and 16-nm displacement of the pinhole under the optical microscope (numbers shown on the right-hand side). The sensitivity of the output was 25 mV per 1 nm of the displacement. The trace designated as m represents mechanical noise which was recorded without driving input to the piezomechanical actuator. Trace e shows record when light illumination given to the optical microscope was interrupted, indicating purely electric noise of the present system. Results using polystyrene microbeads attached to a glass slide in 0.1-M KCl are shown in (B). Output was 39 mV per 1 nm of displacement.

Equations (1)

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So = R 2 × ( π 2 θ + sin 2 θ ) ,

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