Abstract

We report the observation of the Talbot self-imaging effect in high resolution digital in-line holographic microscopy (DIHM) and its application to structural characterization of periodic samples. Holograms of self-assembled monolayers of micron-sized polystyrene spheres are reconstructed at different image planes. The point-source method of DIHM and the consequent high lateral resolution allows the true image (object) plane to be identified. The Talbot effect is then exploited to improve the evaluation of the pitch of the assembly and to examine defects in its periodicity.

© 2008 Optical Society of America

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  1. F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401-407 (1836).
  2. Lord Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. 11, 196-205(1881).
  3. J. M. Cowley and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486-496 (1956).
    [CrossRef]
  4. J. M. Cowley and A. F. Moodie, “Fourier images. II. The out-focus patterns,” Proc. Phys. Soc. B 70, 497-504 (1956).
    [CrossRef]
  5. J. M. Cowley and A. F. Moodie, “Fourier images. III. Finite sources,” Proc. Phys. Soc. B 70, 505-513 (1956).
    [CrossRef]
  6. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772-778 (1967).
    [CrossRef]
  7. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 3-101 (1989).
  8. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  9. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.
  10. R. Maripov and Y. Smanov, “The Talbot effect (a self-imaging phenomenon) in holography,” J. Opt. 25, 3-8 (1994).
    [CrossRef]
  11. S. De Nicola, P. Ferraro, G. Coppola, A. Finizio, G. Pierattini, and S. Grilli, “Talbot self-image effect in digital holography and its application to spectrometry,” Opt. Lett. 29, 104-106 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. G. S. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A 4, S376-S380 (2002).
    [CrossRef]
  15. D. S. Mehta, S. K. Dubey, C. Shakher, and M. Takeda, “Two-wavelength Talbot effect and its application for three-dimensional step-height measurement,” Appl. Opt. 45, 7602-7609 (2006).
    [CrossRef]
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  17. H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U.S. patent 6,411,406 B1 (25 June, 2002).
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    [CrossRef] [PubMed]
  19. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 98, 11301-11305 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836-850 (2006).
    [CrossRef]
  22. S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
    [CrossRef] [PubMed]
  23. J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. 31, 1211-1213 (2006).
    [CrossRef] [PubMed]
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2006 (4)

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

2004 (1)

2003 (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, H. J. Kreuzer, and I. A. Meinertzhagen, “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett. 28, 164-166 (2003).
[CrossRef] [PubMed]

2002 (1)

G. S. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A 4, S376-S380 (2002).
[CrossRef]

2001 (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 98, 11301-11305 (2001).
[CrossRef] [PubMed]

1994 (1)

R. Maripov and Y. Smanov, “The Talbot effect (a self-imaging phenomenon) in holography,” J. Opt. 25, 3-8 (1994).
[CrossRef]

1992 (1)

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

1989 (1)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 3-101 (1989).

1984 (2)

1983 (1)

1982 (1)

1967 (1)

1956 (3)

J. M. Cowley and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486-496 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. II. The out-focus patterns,” Proc. Phys. Soc. B 70, 497-504 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. III. Finite sources,” Proc. Phys. Soc. B 70, 505-513 (1956).
[CrossRef]

1881 (1)

Lord Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. 11, 196-205(1881).

1836 (1)

F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401-407 (1836).

Ambrosini, D.

G. S. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A 4, S376-S380 (2002).
[CrossRef]

Chavel, P.

Christodoulides, D. N.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Cohen-Sabban, Y.

Coppola, G.

Cowley, J. M.

J. M. Cowley and A. F. Moodie, “Fourier images. II. The out-focus patterns,” Proc. Phys. Soc. B 70, 497-504 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. III. Finite sources,” Proc. Phys. Soc. B 70, 505-513 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486-496 (1956).
[CrossRef]

De Nicola, S.

Dubey, S. K.

Ferraro, P.

Finizio,

Fink, H.-W.

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

Garcia-Sucerquia, J.

Grilli,

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

Jericho, M. H.

Jericho, S. K.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836-850 (2006).
[CrossRef]

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef] [PubMed]

Joyeux, D.

Klages, P.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836-850 (2006).
[CrossRef]

H. J. Kreuzer and P. Klages, “DIHM--a software package for the reconstruction of digital in-line and other holograms” (Helix Science Applications, 2006).
[CrossRef] [PubMed]

Kobayashi, S.

Kreuzer, H. J.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836-850 (2006).
[CrossRef]

J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. 31, 1211-1213 (2006).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, H. J. Kreuzer, and I. A. Meinertzhagen, “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett. 28, 164-166 (2003).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 98, 11301-11305 (2001).
[CrossRef] [PubMed]

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

H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U.S. patent 6,411,406 B1 (25 June, 2002).

H. J. Kreuzer and P. Klages, “DIHM--a software package for the reconstruction of digital in-line and other holograms” (Helix Science Applications, 2006).
[CrossRef] [PubMed]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Maripov, R.

R. Maripov and Y. Smanov, “The Talbot effect (a self-imaging phenomenon) in holography,” J. Opt. 25, 3-8 (1994).
[CrossRef]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

Mehta, D. S.

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, H. J. Kreuzer, and I. A. Meinertzhagen, “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett. 28, 164-166 (2003).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 98, 11301-11305 (2001).
[CrossRef] [PubMed]

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

Montgomery, W. D.

Moodie, A. F.

J. M. Cowley and A. F. Moodie, “Fourier images. II. The out-focus patterns,” Proc. Phys. Soc. B 70, 497-504 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. III. Finite sources,” Proc. Phys. Soc. B 70, 505-513 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486-496 (1956).
[CrossRef]

Nakamura, K.

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

Paoletti, D.

G. S. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A 4, S376-S380 (2002).
[CrossRef]

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 3-101 (1989).

Pierattini,

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. 11, 196-205(1881).

Schmid, H.

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

Shakher, C.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Smanov, Y.

R. Maripov and Y. Smanov, “The Talbot effect (a self-imaging phenomenon) in holography,” J. Opt. 25, 3-8 (1994).
[CrossRef]

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

Spagnolo, G. S.

G. S. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A 4, S376-S380 (2002).
[CrossRef]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

Strand, T. C.

Takeda, M.

Talbot, F.

F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401-407 (1836).

Wierzbicki, A.

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

Xu, W.

Appl. Opt. (5)

J. Opt. (1)

R. Maripov and Y. Smanov, “The Talbot effect (a self-imaging phenomenon) in holography,” J. Opt. 25, 3-8 (1994).
[CrossRef]

J. Opt. A (1)

G. S. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A 4, S376-S380 (2002).
[CrossRef]

J. Opt. Soc. Am. (2)

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Opt. Lett. (3)

Philos. Mag. (2)

F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401-407 (1836).

Lord Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. 11, 196-205(1881).

PRLC Newsletter (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” PRLC Newsletter 95, 053902 (2005) and references therein.

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

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. USA 98, 11301-11305 (2001).
[CrossRef] [PubMed]

Proc. Phys. Soc. B (3)

J. M. Cowley and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486-496 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. II. The out-focus patterns,” Proc. Phys. Soc. B 70, 497-504 (1956).
[CrossRef]

J. M. Cowley and A. F. Moodie, “Fourier images. III. Finite sources,” Proc. Phys. Soc. B 70, 505-513 (1956).
[CrossRef]

Prog. Opt. (1)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 3-101 (1989).

Rev. Sci. Instrum. (1)

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef] [PubMed]

Ultramicroscopy (1)

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

Other (2)

H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U.S. patent 6,411,406 B1 (25 June, 2002).

H. J. Kreuzer and P. Klages, “DIHM--a software package for the reconstruction of digital in-line and other holograms” (Helix Science Applications, 2006).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic setup of the digital in-line holographic microscope.

Fig. 2
Fig. 2

Hologram recorded by DIHM of a self-assembled monolayer of polystyrene spheres of diameter 1.09 μm . The hologram was acquired with a numerical aperture ( NA ) 0.46 and violet laser light ( λ = 405 nm )

Fig. 3
Fig. 3

Reconstruction from the hologram shown in Fig. 2 at the best focal plane; full reconstruction area 81.92 μ m × 81.92 μ m . The inset shows the intensity along the white line. The hexagonal packing is highlighted. The isolated spheres (arrowed) are well focused.

Fig. 4
Fig. 4

Self-images reconstructed from the hologram in Fig. 2. The arrow shows a single bead, well focused only at the plane where the real object is located.

Fig. 5
Fig. 5

Position of self-images along the optical axis relative to the point source. Points are the experimental data (Fig. 4), and the solid line is a fit with z r = R 2 λ / ( R λ a 2 ν ) for optimized value of a = 1.06 ± 0.02 μm .

Fig. 6
Fig. 6

Detection of defects with Talbot’s imaging in DIHM. The first and second columns are images for odd and even orders of self-images, respectively; the third column is the difference image between the pictures along the corresponding row. Arrows point to defects in the self-assembled monolayer. Both experiments were done with NA = 0.46 and λ = 405 nm .

Equations (2)

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K ( r ) = screen d 2 ξ I ˜ ( ξ ) exp [ i k r · ξ / | ξ | ] ,
1 z r R + 1 R = λ ν a 2 .

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