Abstract

Measuring transmission and optical thickness of an object with a single intensity recording is desired in many fields of imaging research. One possibility to achieve this is to employ phase retrieval algorithms. We propose a method to significantly improve the performance of such algorithms in optical imaging. The method relies on introducing a specially designed phase object into the specimen plane during the image recording, which serves as a constraint in the subsequent phase retrieval algorithm. This leads to faster algorithm convergence and improved final accuracy. Quantitative imaging can be performed by a single recording of the resulting diffraction pattern in the camera plane, without using lenses or other optical elements. The method allows effective suppression of the “twin-image”, an artefact that appears when holograms are read out. Results from numerical simulations and experiments confirm a high accuracy which can be comparable to that of phase-stepping interferometry.

© 2012 OSA

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  1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
    [CrossRef] [PubMed]
  2. I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification with computational 3-D holographic microscopy,” Opt. Photonics News 22, 18–23 (2011).
    [CrossRef]
  3. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98, 11301–11305 (2001).
    [CrossRef] [PubMed]
  4. Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18, 8213–8219 (2010).
    [CrossRef] [PubMed]
  5. P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
    [CrossRef] [PubMed]
  6. M. Kanka, R. Riesenberg, P. Petruck, and C. Graulig, “High resolution (NA=0.8) in lensless in-line holographic microscopy with glass sample carriers,” Opt. Lett. 36, 3651–3653 (2011).
    [CrossRef] [PubMed]
  7. W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190–191 (1951).
    [CrossRef] [PubMed]
  8. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. 53, 1377–1381 (1963).
    [CrossRef]
  9. O. Bryngdahl and A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58, 620–624 (1968).
    [CrossRef]
  10. L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
  11. K. A. Nugent, “Twin-image elimination in Gabor holography,” Opt. Commun. 78, 293–299 (1990).
    [CrossRef]
  12. G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4, 159–165 (1987).
    [CrossRef]
  13. G. Koren, F. Polack, and D. Joyeux, “Iterative algorithms for twin-image elimination in in-line holography using finite-support constraints,” J. Opt. Soc. Am. A 10, 423–433 (1993).
    [CrossRef]
  14. F. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Image reconstruction for in-line holography with the Yang-Gu algorithm,” Appl. Opt. 42, 6452–6457 (2003).
    [CrossRef] [PubMed]
  15. T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
    [CrossRef] [PubMed]
  16. C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Twin-image reduction in inline digital holography using an object segmentation heuristic,” J. Phys.: Conf. Ser. 139, 012014 (2008).
    [CrossRef]
  17. S. M. Raupach, “Cascaded adaptive-mask algorithm for twin-image removal and its application to digital holograms of ice crystals,” Appl. Opt. 48, 287–301 (2009).
    [CrossRef] [PubMed]
  18. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).
  19. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003).
    [CrossRef]
  20. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
    [CrossRef]
  21. J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508 (2006).
    [CrossRef] [PubMed]
  22. G. Koren, D. Joyeux, and F. Polack, “Twin-image elimination in in-line holography of finite-support complex objects,” Opt. Lett. 16, 1979–1981 (1991).
    [CrossRef] [PubMed]
  23. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  24. 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] [PubMed]
  25. S. Bernet, W. Harm, A. Jesacher, and M. Ritsch-Marte, “Lensless digital holography with diffuse illumination through a pseudo-random phase mask,’ Opt. Express 19, 25113–25124 (2011).
    [CrossRef]

2011 (3)

2010 (1)

2009 (1)

2008 (1)

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Twin-image reduction in inline digital holography using an object segmentation heuristic,” J. Phys.: Conf. Ser. 139, 012014 (2008).
[CrossRef]

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[CrossRef] [PubMed]

2006 (2)

2003 (2)

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. U.S.A. 98, 11301–11305 (2001).
[CrossRef] [PubMed]

1999 (1)

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

1990 (1)

K. A. Nugent, “Twin-image elimination in Gabor holography,” Opt. Commun. 78, 293–299 (1990).
[CrossRef]

1987 (3)

1982 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

1968 (1)

1963 (1)

1951 (1)

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190–191 (1951).
[CrossRef] [PubMed]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Anand, A.

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification with computational 3-D holographic microscopy,” Opt. Photonics News 22, 18–23 (2011).
[CrossRef]

Bernet, S.

Brady, D.

Bragg, W. L.

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190–191 (1951).
[CrossRef] [PubMed]

Bryngdahl, O.

Choi, K.

Daneshpanah, M.

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification with computational 3-D holographic microscopy,” Opt. Photonics News 22, 18–23 (2011).
[CrossRef]

Elser, V.

Fienup, J. R.

Fink, H.-W.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Garcia-Sucerquia, J.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

Graulig, C.

Harm, W.

Hennelly, B. M.

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Twin-image reduction in inline digital holography using an object segmentation heuristic,” J. Phys.: Conf. Ser. 139, 012014 (2008).
[CrossRef]

Horisaki, R.

Javidi, B.

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification with computational 3-D holographic microscopy,” Opt. Photonics News 22, 18–23 (2011).
[CrossRef]

Jericho, M. H.

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] [PubMed]

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

Jericho, S. K.

Jesacher, A.

Joyeux, D.

Kanka, M.

Klages, P.

Koren, G.

Kreuzer, H. J.

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] [PubMed]

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

Latychevskaia, T.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[CrossRef] [PubMed]

Leith, E. N.

Li, H.

Liu, G.

Liu, Z.

Lohmann, A.

McElhinney, C. P.

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Twin-image reduction in inline digital holography using an object segmentation heuristic,” J. Phys.: Conf. Ser. 139, 012014 (2008).
[CrossRef]

Meinertzhagen, I. A.

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

Moon, I.

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification with computational 3-D holographic microscopy,” Opt. Photonics News 22, 18–23 (2011).
[CrossRef]

Naughton, T. J.

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Twin-image reduction in inline digital holography using an object segmentation heuristic,” J. Phys.: Conf. Ser. 139, 012014 (2008).
[CrossRef]

Nugent, K. A.

K. A. Nugent, “Twin-image elimination in Gabor holography,” Opt. Commun. 78, 293–299 (1990).
[CrossRef]

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Osten, W.

Pedrini, G.

Petruck, P.

Polack, F.

Psaltis, D.

Raupach, S. M.

Raven, C.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[CrossRef] [PubMed]

Riesenberg, R.

Ritsch-Marte, M.

Rogers, G. L.

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190–191 (1951).
[CrossRef] [PubMed]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

Scott, P. D.

G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4, 159–165 (1987).
[CrossRef]

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Shi, K.

Snigirev, A.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[CrossRef] [PubMed]

Snigireva, I.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[CrossRef] [PubMed]

Spanne, P.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[CrossRef] [PubMed]

Tiziani, H. J.

Upatnieks, J.

Xu, Q.

Xu, W.

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] [PubMed]

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

Zhang, F.

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

J. Phys.: Conf. Ser. (1)

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Twin-image reduction in inline digital holography using an object segmentation heuristic,” J. Phys.: Conf. Ser. 139, 012014 (2008).
[CrossRef]

Nature (2)

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190–191 (1951).
[CrossRef] [PubMed]

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

K. A. Nugent, “Twin-image elimination in Gabor holography,” Opt. Commun. 78, 293–299 (1990).
[CrossRef]

Opt. Eng. (1)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Opt. Express (3)

Opt. Lett. (2)

Opt. Photonics News (1)

I. Moon, M. Daneshpanah, A. Anand, and B. Javidi, “Cell identification with computational 3-D holographic microscopy,” Opt. Photonics News 22, 18–23 (2011).
[CrossRef]

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Jena) 35, 237–246 (1972).

Phys. Med. Biol. (1)

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

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

Supplementary Material (1)

» Media 1: AVI (3223 KB)     

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Figures (7)

Fig. 1
Fig. 1

Left: for plane wave illumination, the fields passing by and going through the object show only little overlap at the recording plane. Right: a designed periphery can maximise this overlap.

Fig. 2
Fig. 2

(a) Experimental set-up; (b) typical image recorded by the CMOS sensor; (c) amplitude and phase of the wing, reconstructed from the image shown in (b).

Fig. 3
Fig. 3

Once the complex field has been obtained, it is possible to perform numerical refocussing. The images contain field amplitudes that have been obtained via phase retrieval. Left: Focussed onto the wing. Right: Focussed onto the scattering disc, located seven millimetres in front of the wing. A movie is provided ( Media 1) that shows how the amplitude develops in the volume between these planes.

Fig. 4
Fig. 4

Automated object segmentation: The algorithm initially assumes a sufficiently large object support Sini that is automatically refined after a few iterations.

Fig. 5
Fig. 5

Experimental comparison of different methods for complex field reconstruction. The object under investigation is an insect wing. 1st image column: interferometry; 2nd column: phase retrieval using random phase periphery; 3rd column: phase retrieval using plane wave periphery; 4th column: inline holography. The first two rows contain the reconstructed amplitude and phase images, the third row the difference of the reconstructed complex field to the interferometric measurement. The graphs in the lower half compare the reconstructed phase along different sections through the insect wing. The locations of the sections are indicated in the interferometry phase image.

Fig. 6
Fig. 6

(a) Four different phase objects were chosen for the numerical simulations. Black curves: the residual errors after three iterations of the error-reduction algorithm as functions of the angular width w of the spot created by the designed peripheries; red curves: the corresponding values of M; (b) error convergence behaviour for one of the four objects (see inset), calculated for different peripheries: cyan: “plane wave” periphery; blue: 1° random scatterer; red: designed periphery. The corresponding values for M are stated above the curves.

Fig. 7
Fig. 7

Left: residual error after 30 iterations for different sizes of the scattering periphery. For the designed periphery, reasonable results are obtained if it is larger than the object by a factor of about 2. Right: phase of the reconstructed department logo after 30 iterations, framed by the designed scattering periphery which covers an area 1.6× larger than that of the logo. The areas of the scattering periphery Ascat and object support S are coloured in yellow and red, respectively.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

M = 2 | E ref | | E tot | | E ref | 2 + | E tot | 2 .
E ( r , z rec ) = | E tot ( r , z rec ) | E ref ( r , z rec ) / | E ref ( r , z rec ) | .
E ( r , z obj ) = F { E ( r , z rec ) } .
E ( r , z obj ) = { E ( r , z obj ) if r S ini E ref ( r , z obj ) if r S ini .
E ( r , z rec ) = F 1 { E ( r , z obj ) } .
E ( r , z rec ) = | E tot ( r , z rec ) | E ( r , z rec ) / | E ( r , z rec ) | .
σ = | E orig E recon | 2 .

Metrics