Abstract

We have used digital in-line holography (DIH) with numerical reconstruction to image micrometer-sized latex spheres as well as ferrimagnetic beads suspended in gelatin. We have examined in detail theoretically and experimentally the conditions necessary to achieve submicrometer resolution of holographic reconstructions. We found that both transparent and opaque particles could be imaged with a resolution that was limited only by the wavelength of the light used. Simple inspection of intensity profiles through a particle allowed an estimate to be made of the particle’s three position coordinates within an accuracy of a few hundred nanometers. When the derivative of a second-order polynomial fitted to the intensity profiles was taken, the X, Y, Z position coordinates of particles could be determined within ±50 nm. More-accurate positional resolution should be possible with the help of more-advanced computer averaging techniques. Because a single hologram can give information about a large collection of distributed particles, DIH offers the prospect of a powerful new tool for three-dimensional tracking of particles.

© 2002 Optical Society of America

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References

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  1. H. J. Kreuzer, “Low energy electron point source microscopy,” Micron 26, 503–509 (1995).
    [CrossRef]
  2. H. Schmid, H.-W. Fink, H. J. Kreuzer, “In-line holography using low-energy electrons and photons: applications for manipulation on a nanometer scale,” J. Vac. Sci. Technol. B 13, 2428–2431 (1995).
    [CrossRef]
  3. H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
    [CrossRef]
  4. H. J. Kreuzer, R. A. Pawlitzek, “Fast implementation of in-line holography for high resolution shape measurement,” in Simulation and Experiment in Laser Metrology, Proceedings of the International Symposium on Laser Applications in Precision Measurements, Z. Füzessy, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1996).
  5. H. J. Kreuzer, R. A. Pawlitzek, “Numerical reconstruction for in-line holography under glancing incidence,” in Fringe ’97: Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1997).
  6. H. J. Kreuzer, N. Pomerleau, K. Blagrave, M. H. Jericho, “Digital in-line holography with numerical reconstruction,” in Interferometry ’99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 65–74 (1999).
    [CrossRef]
  7. W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
    [CrossRef]
  8. H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
    [CrossRef]
  9. R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
    [CrossRef]
  10. H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
    [CrossRef]
  11. H. J. Kreuzer, R. A. Pawlitzek, leeps, Version 1.2, software package for the simulation and reconstruction of low-energy electron point source images and other holograms (1993–1998).
  12. D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
    [CrossRef]
  13. J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
    [CrossRef] [PubMed]
  14. K. Heinz, U. Starke, J. Bernardt, “Surface holography with LEED electrons,” Prog. Surf. Sci. 64, 163–178 (2000).
    [CrossRef]
  15. H.-W. Fink, H. Schmid, H. J. Kreuzer, “State of the art of low-energy electron holography,” in Electron Holography, A. Tonomura, L. F. Allard, D. C. Pozzi, D. C. Joy, Y. A. Ono, eds. (Elsevier, Amsterdam, The Netherlands, 1995).
  16. A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  18. J. B. DeVelis, G. Parrent, B. J. Thompson, “Image reconstruction with Fraunhofer holograms,” J. Opt. Soc. Am. 56, 423–427 (1966).
    [CrossRef]
  19. B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
    [CrossRef] [PubMed]

2001 (3)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
[CrossRef]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
[CrossRef]

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

2000 (2)

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

K. Heinz, U. Starke, J. Bernardt, “Surface holography with LEED electrons,” Prog. Surf. Sci. 64, 163–178 (2000).
[CrossRef]

1998 (1)

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

1995 (3)

H. J. Kreuzer, “Low energy electron point source microscopy,” Micron 26, 503–509 (1995).
[CrossRef]

H. Schmid, H.-W. Fink, H. J. Kreuzer, “In-line holography using low-energy electrons and photons: applications for manipulation on a nanometer scale,” J. Vac. Sci. Technol. B 13, 2428–2431 (1995).
[CrossRef]

H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
[CrossRef]

1992 (1)

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

1991 (1)

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67, 3106–3109 (1991).
[CrossRef] [PubMed]

1988 (1)

J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
[CrossRef] [PubMed]

1966 (1)

1949 (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Barton, J. J.

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67, 3106–3109 (1991).
[CrossRef] [PubMed]

J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
[CrossRef] [PubMed]

Bernardt, J.

K. Heinz, U. Starke, J. Bernardt, “Surface holography with LEED electrons,” Prog. Surf. Sci. 64, 163–178 (2000).
[CrossRef]

Blagrave, K.

H. J. Kreuzer, N. Pomerleau, K. Blagrave, M. H. Jericho, “Digital in-line holography with numerical reconstruction,” in Interferometry ’99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 65–74 (1999).
[CrossRef]

Bonev, S.

H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
[CrossRef]

Butler, J. P.

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

DeVelis, J. B.

Fabry, B.

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

Fink, H.-W.

H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
[CrossRef]

H. Schmid, H.-W. Fink, H. J. Kreuzer, “In-line holography using low-energy electrons and photons: applications for manipulation on a nanometer scale,” J. Vac. Sci. Technol. B 13, 2428–2431 (1995).
[CrossRef]

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

H.-W. Fink, H. Schmid, H. J. Kreuzer, “State of the art of low-energy electron holography,” in Electron Holography, A. Tonomura, L. F. Allard, D. C. Pozzi, D. C. Joy, Y. A. Ono, eds. (Elsevier, Amsterdam, The Netherlands, 1995).

Friedberg, J. J.

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Gloganev, M.

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

Gölzhäuser, A.

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

Grunze, M.

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

Heinz, K.

K. Heinz, U. Starke, J. Bernardt, “Surface holography with LEED electrons,” Prog. Surf. Sci. 64, 163–178 (2000).
[CrossRef]

Jäger, B.

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

Jericho, M. H.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
[CrossRef]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
[CrossRef]

H. J. Kreuzer, N. Pomerleau, K. Blagrave, M. H. Jericho, “Digital in-line holography with numerical reconstruction,” in Interferometry ’99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 65–74 (1999).
[CrossRef]

Kreuzer, H. J.

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
[CrossRef]

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

H. J. Kreuzer, “Low energy electron point source microscopy,” Micron 26, 503–509 (1995).
[CrossRef]

H. Schmid, H.-W. Fink, H. J. Kreuzer, “In-line holography using low-energy electrons and photons: applications for manipulation on a nanometer scale,” J. Vac. Sci. Technol. B 13, 2428–2431 (1995).
[CrossRef]

H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
[CrossRef]

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

H. J. Kreuzer, N. Pomerleau, K. Blagrave, M. H. Jericho, “Digital in-line holography with numerical reconstruction,” in Interferometry ’99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 65–74 (1999).
[CrossRef]

H. J. Kreuzer, R. A. Pawlitzek, “Fast implementation of in-line holography for high resolution shape measurement,” in Simulation and Experiment in Laser Metrology, Proceedings of the International Symposium on Laser Applications in Precision Measurements, Z. Füzessy, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1996).

H.-W. Fink, H. Schmid, H. J. Kreuzer, “State of the art of low-energy electron holography,” in Electron Holography, A. Tonomura, L. F. Allard, D. C. Pozzi, D. C. Joy, Y. A. Ono, eds. (Elsevier, Amsterdam, The Netherlands, 1995).

H. J. Kreuzer, R. A. Pawlitzek, “Numerical reconstruction for in-line holography under glancing incidence,” in Fringe ’97: Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1997).

H. J. Kreuzer, R. A. Pawlitzek, leeps, Version 1.2, software package for the simulation and reconstruction of low-energy electron point source images and other holograms (1993–1998).

Maksym, G. N.

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
[CrossRef]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
[CrossRef]

Nakamura, K.

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

Navajas, D.

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

Owen, R. B.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Parrent, G.

Pawlitzek, R. A.

H. J. Kreuzer, R. A. Pawlitzek, “Fast implementation of in-line holography for high resolution shape measurement,” in Simulation and Experiment in Laser Metrology, Proceedings of the International Symposium on Laser Applications in Precision Measurements, Z. Füzessy, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1996).

H. J. Kreuzer, R. A. Pawlitzek, leeps, Version 1.2, software package for the simulation and reconstruction of low-energy electron point source images and other holograms (1993–1998).

H. J. Kreuzer, R. A. Pawlitzek, “Numerical reconstruction for in-line holography under glancing incidence,” in Fringe ’97: Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1997).

Pomerleau, N.

H. J. Kreuzer, N. Pomerleau, K. Blagrave, M. H. Jericho, “Digital in-line holography with numerical reconstruction,” in Interferometry ’99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 65–74 (1999).
[CrossRef]

Schmid, H.

H. Schmid, H.-W. Fink, H. J. Kreuzer, “In-line holography using low-energy electrons and photons: applications for manipulation on a nanometer scale,” J. Vac. Sci. Technol. B 13, 2428–2431 (1995).
[CrossRef]

H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
[CrossRef]

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

H.-W. Fink, H. Schmid, H. J. Kreuzer, “State of the art of low-energy electron holography,” in Electron Holography, A. Tonomura, L. F. Allard, D. C. Pozzi, D. C. Joy, Y. A. Ono, eds. (Elsevier, Amsterdam, The Netherlands, 1995).

Starke, U.

K. Heinz, U. Starke, J. Bernardt, “Surface holography with LEED electrons,” Prog. Surf. Sci. 64, 163–178 (2000).
[CrossRef]

Thompson, B. J.

Völkel, B.

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

Wierzbicki, A.

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

Xu, W.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
[CrossRef]

Xu, W.-B.

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
[CrossRef]

Zharnikov, M.

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

Zozulya, A. A.

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

J. Microsc. (1)

H. J. Kreuzer, H.-W. Fink, H. Schmid, S. Bonev, “Holography of holes, with electrons and photons,” J. Microsc. 178, 191–197 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Condens. Matter (1)

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, W.-B. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10,729–10,741 (2001).
[CrossRef]

J. Vac. Sci. Technol. A (1)

A. Gölzhäuser, B. Völkel, B. Jäger, M. Zharnikov, H. J. Kreuzer, M. Grunze, “Holographic imaging of macromolecules,” J. Vac. Sci. Technol. A 16, 3025–3028 (1998).
[CrossRef]

J. Vac. Sci. Technol. B (1)

H. Schmid, H.-W. Fink, H. J. Kreuzer, “In-line holography using low-energy electrons and photons: applications for manipulation on a nanometer scale,” J. Vac. Sci. Technol. B 13, 2428–2431 (1995).
[CrossRef]

Micron (1)

H. J. Kreuzer, “Low energy electron point source microscopy,” Micron 26, 503–509 (1995).
[CrossRef]

Opt. Eng. (1)

R. B. Owen, A. A. Zozulya, “In-line digital holographic sensor for monitoring and characterizing marine particulates,” Opt. Eng. 39, 2187–2197 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67, 3106–3109 (1991).
[CrossRef] [PubMed]

B. Fabry, G. N. Maksym, J. P. Butler, M. Gloganev, D. Navajas, J. J. Friedberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett. 87, 148102 (2001).
[CrossRef] [PubMed]

J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
[CrossRef] [PubMed]

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

W. Xu, M. H. Jericho, I. A. Meinertzhagen, H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 25, 11,301–11,305 (2001).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Prog. Surf. Sci. (1)

K. Heinz, U. Starke, J. Bernardt, “Surface holography with LEED electrons,” Prog. Surf. Sci. 64, 163–178 (2000).
[CrossRef]

Ultramicroscopy (1)

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, H. Schmid, “Theory of the point source electron microscope,” Ultramicroscopy 45, 381–403 (1992).
[CrossRef]

Other (5)

H. J. Kreuzer, R. A. Pawlitzek, leeps, Version 1.2, software package for the simulation and reconstruction of low-energy electron point source images and other holograms (1993–1998).

H. J. Kreuzer, R. A. Pawlitzek, “Fast implementation of in-line holography for high resolution shape measurement,” in Simulation and Experiment in Laser Metrology, Proceedings of the International Symposium on Laser Applications in Precision Measurements, Z. Füzessy, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1996).

H. J. Kreuzer, R. A. Pawlitzek, “Numerical reconstruction for in-line holography under glancing incidence,” in Fringe ’97: Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie-Verlag, Berlin, 1997).

H. J. Kreuzer, N. Pomerleau, K. Blagrave, M. H. Jericho, “Digital in-line holography with numerical reconstruction,” in Interferometry ’99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 65–74 (1999).
[CrossRef]

H.-W. Fink, H. Schmid, H. J. Kreuzer, “State of the art of low-energy electron holography,” in Electron Holography, A. Tonomura, L. F. Allard, D. C. Pozzi, D. C. Joy, Y. A. Ono, eds. (Elsevier, Amsterdam, The Netherlands, 1995).

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Figures (8)

Fig. 1
Fig. 1

Schematic of in-line holography: A coherent wave of radiation emanating from the point source (P) partially scatters off an object (O), creating a highly magnified hologram on a screen (C). In practice the point source is a pinhole illuminated by a laser (L).

Fig. 2
Fig. 2

Holograms and reconstructions of 5.13-µm spheres embedded in gelatin: (a) Raw hologram. (b) Single reconstructed section from (a). (c) Hologram with numerical background subtraction. (d) Single reconstructed section from (c). (e) Hologram from (a) minus the background hologram obtained with the sample removed. (f) Single reconstructed section from (e). (g) Hologram in (e) with bispline correction. (h) Single reconstructed section from (g). Blue laser; 1-µm pinhole; distance from source to sample, d SS = 0.55 mm; distance source to CCD camera, d SC = 1.75 cm.

Fig. 3
Fig. 3

Holograms and reconstructions of 5.13-µm spheres embedded in gelatin: (a) Compound-light microscope bright-field image (Zeiss, Ph2 Plan-Neofluar 40×/0.75 objective). (b) Hologram with 1024 × 1024 pixels over an area of 0.92 cm × 0.92 cm. (c) Single reconstructed section from (b). (d) Central section of (b) containing 512 × 512 pixels over an area of 0.46 cm × 0.46 cm. (e) Single reconstructed section from (d). (f) Hologram from (d) further truncated to an area of 0.23 cm × 0.23 cm. (g) One reconstructed section from hologram (f). Blue laser; 1-µm pinhole; d SS = 0.55 mm; d SC = 1.75 cm.

Fig. 4
Fig. 4

Bright-field images, hologram, and reconstructions of 5.13-µm latex spheres embedded in a gelatin slab: (a) Schematic of particle arrangement in the sample. (b) Contrast hologram of the sample structure. (c) Bright-field image of spheres attached to the upper coverslip. (d) Image of the particles on the upper glass plate from reconstruction of the hologram in (b). (e) Bright-field image of the particles attached to the lower glass slide. (f) Image of the particles attached to the lower surface from reconstruction of the hologram in (b). Arrows point to the particle groups that were used to define the image planes. (DIH: d SS = 1 mm, d SC = 2.7 cm.)

Fig. 5
Fig. 5

Bright-field and corresponding DIH reconstructions from a single hologram of 5.13-µm latex spheres suspended in gelatin: (a) Bright-field image; spheres close to the focal plane are marked by arrows. (b) Reconstructed image corresponding to (a); arrows point to spheres that were closest to the reconstruction plane. (c) Bright-field image in a plane that is 12 µm below the plane of (a). (d) Reconstruction in a plane that is 10 µm below (b). (e) Bright-field image in a plane 43 µm below the plane of (a). (f) Reconstruction in a plane that is 40 µm below (b). Corresponding spheres in the bright field and reconstructed images are marked by arrows. (DIH: d SS = 1.2 mm, d SC = 2.7 cm.)

Fig. 6
Fig. 6

Contrast holograms and reconstructed images of a 5.13-µm latex sphere and a 4.5-µm ferromagnetic bead embedded in gelatin: (a) 5.13-µm spheres contrast hologram. (b) Reconstructed image; also shown is the intensity variation along a horizontal line through the sphere. (c) Ferrimagnetic bead contrast hologram. (d) Reconstructed image with intensity profile as in (b). (DIH: d SS = 0.8 mm, d SC = 2.7 cm.)

Fig. 7
Fig. 7

Bright-field and DIH reconstructed images of latex and ferrimagnetic particles suspended in gelatin: (a) Bright-field image of 5.13-µm latex spheres (Zeiss, Ph2 Plan-Neofluar 40×/0.75 objective). (b) Reconstruction from a hologram of the region in (a); arrows point to the ferrimagnetic beads. (Blue laser; λ = 0.473 µm; 1-µm pinhole; d SS = 0.38mm; d SC = 1.75 cm.) (c) Bright-field image of 1.09-µm microspheres embedded in gelatin. (d) Corresponding reconstruction from a hologram (d SS = 0.23 mm). (e) Intensity profile in the reconstruction plane of the particle circled in (d); the plot indicates how well a particle can be localized in X and Y. (f) Plot of the maximum intensity of the circled particle as a function of the position of the reconstruction plane. Planes were separated in 1-µm steps, and the plot indicates how well a particle can be localized in the Z direction.

Fig. 8
Fig. 8

Example of the Z position resolution obtainable with DIH: (a) The intensity maxima of the spheres labeled a and b in Fig. 5(f) are plotted as a function of the position of the reconstruction plane in 0.5-µm intervals. A second-order polynomial fit to these plots and subsequent differentiation gave the Z position of a particle. Analysis of the intensity plots in this way showed that the centers of the two spheres were separated in Z by 4.45 ± 0.05 µm. (b) Maximum intensity as function of the position of the reconstruction plane in 0.25-µm intervals for spheres c and d shown in Fig. 5(d). Particle separation, 3.56 ± 0.05 µm.

Equations (4)

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Ĩr=Arefr+Ascatr2- Arefr2
=Aref*rAscatr+ArefrAscat*r+Ascatr2.
Kr=SdSĨξexp2πiξ · r/λξ,
Ĩnm=Inm-Inm0/ Inm0.

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