Abstract

The sensitivity of a microscope-based holographic system designed for mapping the motion of components of a living cell is calibrated by means of a simple procedure. Bubbles of air are allowed to drift with known velocity in a nearly horizontal, glycerine-filled capillary observed through the microscope. The ultrafine motion of the bubbles is captured interferometrically by subtractive superposition of a pair of holograms recorded a few milliseconds apart. Stationary portions of the field of view are rendered dimly in images reconstructed from the interferogram, while the brightness of moving portions varies monotonically with their displacement. Displacements as small as 1.1 nm were betrayed in the images. Analysis of the experimental conditions suggests that bubble displacements as small as 0.7 nm will become detectable once minor improvements are made in the apparatus.

© 1990 Optical Society of America

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References

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  1. S. Tolansky, Microstructure of Surfaces Using Interferometry (Elsevier, New York, 1978).
  2. D. Gabor, “Holography, 1948–1971,” Science 177, 299–313 (1972).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. S. Inoue, Video Microscopy (Plenum, New York, 1986).
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    [CrossRef] [PubMed]
  7. M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential Holography and the Polysarcomeric Unit of Activation of Skeletal Muscle,” Science 223, 822–825 (1984).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. K. A. Haines, B. P. Hildebrand, “Surface-Deformation Measurement Using the Wavefront Reconstruction Technique,” Appl. Opt. 5, 595–602 (1966).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. R. F. Van Ligten, H. Osterberg, “Holographic Microscope,” Nature London 211, 282–283 (1966).
  20. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
    [CrossRef]
  21. Type I 1002, Gaertner Instrument Co., Chicago, IL.

1985 (1)

1984 (1)

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential Holography and the Polysarcomeric Unit of Activation of Skeletal Muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

1978 (1)

K. A. Stetson, “The Use of an Image Derotator in Hologram Interferometry and Speckle Photography of Rotating Objects,” Exp. Mech. 18, 67–73 (1978).
[CrossRef]

1972 (1)

D. Gabor, “Holography, 1948–1971,” Science 177, 299–313 (1972).
[CrossRef] [PubMed]

1966 (4)

K. A. Haines, B. P. Hildebrand, “Surface-Deformation Measurement Using the Wavefront Reconstruction Technique,” Appl. Opt. 5, 595–602 (1966).
[CrossRef] [PubMed]

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic Interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

G. W. Ellis, “Holomicrography: Transformation of Image During Reconstruction a Posteriori,” Science 154, 1195–1196 (1966).
[CrossRef] [PubMed]

R. F. Van Ligten, H. Osterberg, “Holographic Microscope,” Nature London 211, 282–283 (1966).

1965 (2)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, “Interferometric Vibration Analysis by Wavefront Reconstruction,” J. Opt. Soc. Am. 55, 1593–1598 (1965).
[CrossRef]

1962 (1)

1957 (1)

A. I. Johnson, L. Braida, “The Velocity of Fall of Circulating and Oscillating Liquid Drops Through Quiescent Liquid Phases,” Can. J. Chem. Eng. 35, 165–172 (1957).

1955 (1)

S. Hu, R. C. Kintner, “The Fall of Single Liquid Drops Through Water,” AIChE J. 1, 42–48 (1955).
[CrossRef]

1943 (1)

R. Hubbard, G. Brown, “The Rolling Ball Viscometer,” Ind. Eng. Chem. 15, 212–218 (1943).

1905 (1)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann”. Phys. 17, 549–560 (1905).

Braida, L.

A. I. Johnson, L. Braida, “The Velocity of Fall of Circulating and Oscillating Liquid Drops Through Quiescent Liquid Phases,” Can. J. Chem. Eng. 35, 165–172 (1957).

Brehm, L. P.

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential Holography and the Polysarcomeric Unit of Activation of Skeletal Muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

Brooks, R. E.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic Interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Brown, G.

R. Hubbard, G. Brown, “The Rolling Ball Viscometer,” Ind. Eng. Chem. 15, 212–218 (1943).

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Einstein, A.

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann”. Phys. 17, 549–560 (1905).

Ellis, G. W.

G. W. Ellis, “Holomicrography: Transformation of Image During Reconstruction a Posteriori,” Science 154, 1195–1196 (1966).
[CrossRef] [PubMed]

Ennos, A. E.

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1984), pp. 203–253.

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Gabor, D.

D. Gabor, “Holography, 1948–1971,” Science 177, 299–313 (1972).
[CrossRef] [PubMed]

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Gardner, H.

H. Gardner, P. Holdt, Paint and Varnish Manufacturing Association of the U.S.A., Circular No. 128 (1921).

Haines, K. A.

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic Interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Hildebrand, B. P.

Holdt, P.

H. Gardner, P. Holdt, Paint and Varnish Manufacturing Association of the U.S.A., Circular No. 128 (1921).

Hu, S.

S. Hu, R. C. Kintner, “The Fall of Single Liquid Drops Through Water,” AIChE J. 1, 42–48 (1955).
[CrossRef]

Hubbard, R.

R. Hubbard, G. Brown, “The Rolling Ball Viscometer,” Ind. Eng. Chem. 15, 212–218 (1943).

Inoue, S.

S. Inoue, Video Microscopy (Plenum, New York, 1986).

Johnson, A. I.

A. I. Johnson, L. Braida, “The Velocity of Fall of Circulating and Oscillating Liquid Drops Through Quiescent Liquid Phases,” Can. J. Chem. Eng. 35, 165–172 (1957).

Karcher, T. H.

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential Holography and the Polysarcomeric Unit of Activation of Skeletal Muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

Kintner, R. C.

S. Hu, R. C. Kintner, “The Fall of Single Liquid Drops Through Water,” AIChE J. 1, 42–48 (1955).
[CrossRef]

Leith, E.

Osterberg, H.

R. F. Van Ligten, H. Osterberg, “Holographic Microscope,” Nature London 211, 282–283 (1966).

Powell, R. L.

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Sharnoff, M.

M. Sharnoff, “Microdifferential Holography,” J. Opt. Soc. Am. A 2, 1619–1628 (1985).
[CrossRef] [PubMed]

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential Holography and the Polysarcomeric Unit of Activation of Skeletal Muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

Stetson, K. A.

K. A. Stetson, “The Use of an Image Derotator in Hologram Interferometry and Speckle Photography of Rotating Objects,” Exp. Mech. 18, 67–73 (1978).
[CrossRef]

R. L. Powell, K. A. Stetson, “Interferometric Vibration Analysis by Wavefront Reconstruction,” J. Opt. Soc. Am. 55, 1593–1598 (1965).
[CrossRef]

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Tolansky, S.

S. Tolansky, Microstructure of Surfaces Using Interferometry (Elsevier, New York, 1978).

Upatnieks, J.

Van Ligten, R. F.

R. F. Van Ligten, H. Osterberg, “Holographic Microscope,” Nature London 211, 282–283 (1966).

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic Interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

AIChE J. (1)

S. Hu, R. C. Kintner, “The Fall of Single Liquid Drops Through Water,” AIChE J. 1, 42–48 (1955).
[CrossRef]

Ann”. Phys. (1)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann”. Phys. 17, 549–560 (1905).

Appl. Opt. (1)

Can. J. Chem. Eng. (1)

A. I. Johnson, L. Braida, “The Velocity of Fall of Circulating and Oscillating Liquid Drops Through Quiescent Liquid Phases,” Can. J. Chem. Eng. 35, 165–172 (1957).

Exp. Mech. (1)

K. A. Stetson, “The Use of an Image Derotator in Hologram Interferometry and Speckle Photography of Rotating Objects,” Exp. Mech. 18, 67–73 (1978).
[CrossRef]

Ind. Eng. Chem. (1)

R. Hubbard, G. Brown, “The Rolling Ball Viscometer,” Ind. Eng. Chem. 15, 212–218 (1943).

J. Appl. Phys. (1)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, “Holographic Interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Nature London (1)

R. F. Van Ligten, H. Osterberg, “Holographic Microscope,” Nature London 211, 282–283 (1966).

Phys. Lett. (1)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, “Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transformation,” Phys. Lett. 18, 116–118 (1965).
[CrossRef]

Science (3)

M. Sharnoff, T. H. Karcher, L. P. Brehm, “Microdifferential Holography and the Polysarcomeric Unit of Activation of Skeletal Muscle,” Science 223, 822–825 (1984).
[CrossRef] [PubMed]

D. Gabor, “Holography, 1948–1971,” Science 177, 299–313 (1972).
[CrossRef] [PubMed]

G. W. Ellis, “Holomicrography: Transformation of Image During Reconstruction a Posteriori,” Science 154, 1195–1196 (1966).
[CrossRef] [PubMed]

Other (6)

S. Tolansky, Microstructure of Surfaces Using Interferometry (Elsevier, New York, 1978).

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1984), pp. 203–253.

S. Inoue, Video Microscopy (Plenum, New York, 1986).

Bath wax, catalog no. 15-532, Fisher Scientific Co.

H. Gardner, P. Holdt, Paint and Varnish Manufacturing Association of the U.S.A., Circular No. 128 (1921).

Type I 1002, Gaertner Instrument Co., Chicago, IL.

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Figures (6)

Fig. 1
Fig. 1

Control interferogram made with zero reference path shift, showing three bubbles and the millimetric scale. The bubble at the left is stationary.

Fig. 2
Fig. 2

Montage of six consecutive control interferograms, made 5.0 ± 0.2 min apart, of the bubbles shown in Fig. 1. The images of the millimetric scale were snipped away from five of the negatives, and the montage was constructed by superposing these on the sixth. The limb of the stationary bubble, present in each of the six negatives, was used as the fiducial mark; the superposition has exaggerated its brightness in the print. The bubble speeds are easily determined from the montage. They are 3.1 and 1.6 mm/h, or 0.86 and 0.44 nm/ms.

Fig. 3
Fig. 3

Interferograms of the bubbles shown in Figs. 1 and 2, made some minutes apart, but exposed and printed by identical procedures. Interflash intervals were t = 2.5, 5.0, 10.0, 15.0, and 20.0 ms, increasing from bottom to top, with δ = 0 in all cases. In consequence of noise in the laser beam, the stationary bubble is weakly and irregularly visible at the left in four of the five interferograms. The more slowly moving bubble makes its definitive appearance at t = 10.0 ms, and the more rapidly moving one at t = 5.0 ms. Thereafter, the bubble brightness increases approximately quadratically in t. The figure shows that displacements as small as 4.3 nm can be reliably detected and mapped, point by point.

Fig. 4
Fig. 4

Interferograms of another set of bubbles. At the top is a control interferogram made with zero reference path shift; the bubble at the left is stationary, and the one at the right is known to be drifting toward it with a speed of 0.43 nm/ms. The interferogram immediately below was made with δ = 0. One of the two interferograms at the bottom was made with δ = +0.012, and the other with δ = −0.012. All three were printed by identical photographic protocol, and the interflash interval t was 2.5 ms. As expected from Eq. (3), the stationary bubble has the same brightness in the two lowermost interferograms. The moving bubble is imaged more brightly than the stationary bubble in one of these, and less brightly in the other. The figure confirms that displacements as small as 1.1 nm can be revealed by comparison of intensity between conjugate interferograms.

Fig. 5
Fig. 5

Same situation as in Fig. 4, but with t = 5.0 ms. The control interferogram has been omitted. Fluctuation in the laser beam has caused the stationary bubble at the left to appear weakly in the δ = 0 interferogram at the top and with slightly differing intensities in the |δ| = 0.012 interferograms beneath it. These two effects are typical of the brightness noise, and the figure shows them to be weak in comparison to the systematic incremental brightness of the moving bubble. Apart from their greater magnification, the interferograms in this figure and the one following were photographed and printed according to the same protocol as the lower three interferograms in Fig. 4.

Fig. 6
Fig. 6

Same situation as in Fig. 5, but with t = 10.0 ms. In the middle image the displacement of the moving bubble is such [Eq. (3)] as to make (πδ)2 ≈ − (2π2δ/λ)(qn sinθi). From this fact the displacement of the moving bubble can be estimated to be ≈0.0090λ, or 4.6 nm. This estimate is close to the value of 4.3 nm inferred from the known drift speed. The moving bubble’s brightness in the δ = 0 interferogram is also consistent with the inferred value. Taken together with Figs. 4 and 5, this figure shows that when δ ≠ 0, the brightness with which the moving bubble is imaged depends approximately linearly on its displacement.

Equations (7)

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x 2 = ( k T / 3 π η a ) t ,
I / I 0 = ( π / λ ) 2 ( q n sin θ i ) 2 .
I / I 0 - [ π δ ] 2 = ( π 2 δ / λ ) ( q n sin θ i ) 2 .
q m = λ d δ / ( n sin θ i ) = 0.0012 λ / ( n sin θ i ) .
q 0 = 0.003 λ / ( n sin θ i )
q δ = 0.0005 λ / ( n sin θ i )
q t h = 0.0013 λ / ( n sin θ i ) .

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