Abstract

Digital holography has some desirable properties for refractometry of microscopic objects since it gives phase and amplitude information of an object in all depths of focus from one set of exposures. We show that the amplitude part of the image can be used to observe how the Becke lines move between different depths of focus and hence determine whether an object has a higher or a lower index of refraction than its surrounding medium, i.e., the sign of the relief. It is also shown that one single-phase image provides an independent technique to determine the sign of relief between an object and the surrounding medium.

© 2004 Optical Society of America

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References

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  1. M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
    [CrossRef]
  2. F. Dubois, C. Minetti, O. Monnom, C. Yourassowsky, J. C. Legros, P. Kischel, “Pattern recognition with a digital holographic microscope working in partially coherent illumination,” Appl. Opt. 41, 4108–4119 (2002).
    [CrossRef] [PubMed]
  3. U. Schnars, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  4. S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
    [CrossRef]
  5. W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).
  6. M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
    [CrossRef]
  7. W. D. Nesse, Introduction to Optical Mineralogy, 2nd ed. (Oxford University Press, New York, 1991).
  8. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).
  9. D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

2004

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

2002

2001

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Baumbach, T.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Bengtsson, B.

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

Dubois, F.

Egelberg, P.

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

Gustafsson, M.

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Jacquot, M.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Jericho, M. H.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).

Jüptner, W.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Jüptner, W. P. O.

U. Schnars, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kischel, P.

Kreuzer, H. J.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).

Legros, J. C.

Lenart, T.

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).

Minetti, C.

Monnom, O.

Nesse, W. D.

W. D. Nesse, Introduction to Optical Mineralogy, 2nd ed. (Oxford University Press, New York, 1991).

Osten, W.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Pettersson, S.-G.

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

Sandoz, P.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Schnars, U.

U. Schnars, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Sebesta, M.

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Seebacher, S.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

Tribillon, G.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

Xu, W.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).

Yourassowsky, C.

Appl. Opt.

Cell Biol.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Cell Biol. 98, 11301–11305 (2001).

Meas. Sci. Technol.

U. Schnars, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Commun.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Opt. Lasers Eng.

S. Seebacher, W. Osten, T. Baumbach, W. Jüptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. 36, 103–126 (2001).
[CrossRef]

M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, T. Lenart, “High resolution digital transmission microscopy—a Fourier holography approach,” Opt. Lasers Eng. 41, 553–563 (2004).
[CrossRef]

Other

W. D. Nesse, Introduction to Optical Mineralogy, 2nd ed. (Oxford University Press, New York, 1991).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

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Figures (7)

Fig. 1
Fig. 1

Illustrations of the lens effect when a wave impinges on objects with lower and higher indices of refraction than the mounting medium. The horizontal lines show the lines of constant phase for the wave field. The phase of an object with low (high) refractive index is advanced (retarded) and if the object is convex it also acts as a divergent (convergent) lens as depicted to the left (right).

Fig. 2
Fig. 2

Amplitude and phase images of an oil, water, and air mixture. (a) The Becke lines are seen to move into the regions with a higher refractive index as the image plane shifts in the direction of the illuminated wave, i.e., toward the sensor from -50 to 50 μm. (b) Phase image of an air bubble with water droplets. The phase increases when going from an object with a lower refractive index to an object with a higher refractive index, i.e., the color changes from black over gray to white and back to black, modulus 2π.

Fig. 3
Fig. 3

Amplitude images of lactose crystals mounted in a liquid with n m = 1.570. The Becke lines move from the crystals into the liquid as the image plane shifts in the direction of the illuminated wave, i.e., toward the sensor from -100 to 100 μm.

Fig. 4
Fig. 4

Phase images of lactose crystals mounted in a liquid with n m = 1.570. The phase decreases when going from the liquid into the crystals: (a) the wrapped phase image where the color changes from white over gray to black and back to white, modulus 2π, in the crystals; (b) the unwrapped phase image; (c) the rewrapped phase image.

Fig. 5
Fig. 5

Amplitude images of lactose crystals mounted in a liquid with n m = 1.542. The Becke lines move into the regions with a higher refractive index as the image plane shifts in the direction of the illuminated wave, i.e., toward the sensor from -100 to 100 μm.

Fig. 6
Fig. 6

Phase images of lactose crystals mounted in a liquid with n m = 1.542. The phase increases (decreases) when going from an object with a higher (lower) refractive index to an object with a lower (higher) refractive index: (a) the unwrapped phase image and (b) the rewrapped phase image.

Fig. 7
Fig. 7

Digital Fourier holographic setup. A beam splitter reflects the reference point source that creates a virtual point source close to the object.

Equations (3)

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E˜o=|Eo+Er|2-|Eo|2-|Er|2/E˜r*,
minnlactosenmaxnlactose.
minnlactosenmmaxnlactose.

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