Abstract

We present a method for submicrometer tomographic imaging using multiple wavelengths in digital holographic microscopy. This method is based on the recording, at different wavelengths equally separated in the k domain, in off-axis geometry, of the interference between a reference wave and an object wave reflected by a microscopic specimen and magnified by a microscope objective. A CCD camera records the holograms consecutively, which are then numerically reconstructed following the convolution formulation to obtain each corresponding complex object wavefront. Their relative phases are adjusted to be equal in a given plane of interest and the resulting complex wavefronts are summed. The result of this operation is a constructive addition of complex waves in the selected plane and destructive addition in the others. Tomography is thus obtained by the attenuation of the amplitude out of the plane of interest. Numerical variation of the plane of interest enables one to scan the object in depth. For the presented simulations and experiments, 20 wavelengths are used in the 480700  nm range. The result is a sectioning of the object in slices 725  nm thick.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Wolf, "Three-dimensional structure determination of semi-transparent object from holographic data," Opt. Commun. 1, 153-156 (1969).
    [CrossRef]
  2. W. H. Carter, "Computational reconstruction of scattering objects from holograms," J. Opt. Soc. Am. 60, 306-314 (1970).
    [CrossRef]
  3. R. Dändliker and D. Weiss, "Reconstruction of three-dimensional refractive index from scattered waves," Opt. Commun. 1, 323-328 (1970).
    [CrossRef]
  4. A. F. Fercher, H. Bartelt, H. Becker, and E. Wiltschko, "Image formation by inversion of scattered field data: experiments and computational simulation," Appl. Opt. 18, 2427-2439 (1979).
    [CrossRef] [PubMed]
  5. V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
    [CrossRef] [PubMed]
  6. A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000).
    [CrossRef]
  7. F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
    [CrossRef] [PubMed]
  8. J. C. Marron and K. S. Schroeder, "Holographic laser radar," Opt. Lett. 18, 385-387 (1993).
    [CrossRef] [PubMed]
  9. J. C. Marron and K. W. Gleichman, "Three-dimensional imaging using a tunable laser source," Opt. Eng. 39, 47-51 (2000).
    [CrossRef]
  10. E. Arons and D. Dilworth, "Analysis of Fourier synthesis holography for imaging through scattering materials," Appl. Opt. 34, 1841-1847 (1995).
    [CrossRef] [PubMed]
  11. M. K. Kim, "Wavelength-scanning digital interference holography for optical section imaging," Opt. Lett. 24, 1693-1695 (1999).
    [CrossRef]
  12. M. K. Kim, "Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography," Opt. Express 7, 305-310 (2000).
    [CrossRef] [PubMed]
  13. L. Yu and M. K. Kim, "Wavelength scanning digital interference holography for variable tomographic scanning," Opt. Express. 13, 5621-5627 (2005).
    [CrossRef] [PubMed]
  14. L. Yu and M. K. Kim, "Variable tomographic scanning with wavelength scanning digital interference holography," Opt. Commun. 260, 462-468 (2006).
    [CrossRef]
  15. A. Dakoff, J. Gass, and M. K. Kim, "Microscopic three-dimensional imaging by digital interference holography," J. Electron. Imaging 12, 643-647 (2003).
    [CrossRef]
  16. E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999).
    [CrossRef]
  17. E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999).
    [CrossRef]
  18. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
    [CrossRef] [PubMed]
  19. T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, "Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram," Opt. Express 14, 4300-4306 (2006).
    [CrossRef] [PubMed]
  20. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
    [CrossRef]
  21. P. Ferraro, S. D. Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, "Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms," Opt. Lett. 29, 854-856 (2004).
    [CrossRef] [PubMed]
  22. E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
    [CrossRef]
  23. F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Purely numerical correction of the microscope objective induced curvature in digital holographic microscopy," J. Opt. Soc. Am. A 23, 2944-2953 (2006).
    [CrossRef]
  24. M. K. Kim, L. Yu, and C. J. Mann, "Interference techniques in digital holography," J. Opt. A , Pure Appl. Opt. 8, S518-S523 (2006).
    [CrossRef]

2006 (7)

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

L. Yu and M. K. Kim, "Variable tomographic scanning with wavelength scanning digital interference holography," Opt. Commun. 260, 462-468 (2006).
[CrossRef]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
[CrossRef] [PubMed]

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, "Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram," Opt. Express 14, 4300-4306 (2006).
[CrossRef] [PubMed]

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Purely numerical correction of the microscope objective induced curvature in digital holographic microscopy," J. Opt. Soc. Am. A 23, 2944-2953 (2006).
[CrossRef]

M. K. Kim, L. Yu, and C. J. Mann, "Interference techniques in digital holography," J. Opt. A , Pure Appl. Opt. 8, S518-S523 (2006).
[CrossRef]

2005 (1)

L. Yu and M. K. Kim, "Wavelength scanning digital interference holography for variable tomographic scanning," Opt. Express. 13, 5621-5627 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

A. Dakoff, J. Gass, and M. K. Kim, "Microscopic three-dimensional imaging by digital interference holography," J. Electron. Imaging 12, 643-647 (2003).
[CrossRef]

2002 (1)

V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

2000 (4)

1999 (3)

1995 (1)

1993 (1)

1979 (1)

1970 (2)

W. H. Carter, "Computational reconstruction of scattering objects from holograms," J. Opt. Soc. Am. 60, 306-314 (1970).
[CrossRef]

R. Dändliker and D. Weiss, "Reconstruction of three-dimensional refractive index from scattered waves," Opt. Commun. 1, 323-328 (1970).
[CrossRef]

1969 (1)

E. Wolf, "Three-dimensional structure determination of semi-transparent object from holographic data," Opt. Commun. 1, 153-156 (1969).
[CrossRef]

Alfieri, D.

Arons, E.

Aspert, N.

Bartelt, H.

Barty, A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Becker, H.

Bevilacqua, F.

Bourquin, S.

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

Carter, W. H.

Charrière, F.

Colomb, T.

Coppola, G.

Cuche, E.

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
[CrossRef] [PubMed]

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Purely numerical correction of the microscope objective induced curvature in digital holographic microscopy," J. Opt. Soc. Am. A 23, 2944-2953 (2006).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

Dakoff, A.

A. Dakoff, J. Gass, and M. K. Kim, "Microscopic three-dimensional imaging by digital interference holography," J. Electron. Imaging 12, 643-647 (2003).
[CrossRef]

Dändliker, R.

R. Dändliker and D. Weiss, "Reconstruction of three-dimensional refractive index from scattered waves," Opt. Commun. 1, 323-328 (1970).
[CrossRef]

Depeursinge, C.

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
[CrossRef] [PubMed]

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, "Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram," Opt. Express 14, 4300-4306 (2006).
[CrossRef] [PubMed]

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Purely numerical correction of the microscope objective induced curvature in digital holographic microscopy," J. Opt. Soc. Am. A 23, 2944-2953 (2006).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999).
[CrossRef]

Dilworth, D.

Fercher, A. F.

Ferraro, P.

Finizio, A.

Gass, J.

A. Dakoff, J. Gass, and M. K. Kim, "Microscopic three-dimensional imaging by digital interference holography," J. Electron. Imaging 12, 643-647 (2003).
[CrossRef]

Gleichman, K. W.

J. C. Marron and K. W. Gleichman, "Three-dimensional imaging using a tunable laser source," Opt. Eng. 39, 47-51 (2000).
[CrossRef]

Kim, M. K.

L. Yu and M. K. Kim, "Variable tomographic scanning with wavelength scanning digital interference holography," Opt. Commun. 260, 462-468 (2006).
[CrossRef]

M. K. Kim, L. Yu, and C. J. Mann, "Interference techniques in digital holography," J. Opt. A , Pure Appl. Opt. 8, S518-S523 (2006).
[CrossRef]

L. Yu and M. K. Kim, "Wavelength scanning digital interference holography for variable tomographic scanning," Opt. Express. 13, 5621-5627 (2005).
[CrossRef] [PubMed]

A. Dakoff, J. Gass, and M. K. Kim, "Microscopic three-dimensional imaging by digital interference holography," J. Electron. Imaging 12, 643-647 (2003).
[CrossRef]

M. K. Kim, "Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography," Opt. Express 7, 305-310 (2000).
[CrossRef] [PubMed]

M. K. Kim, "Wavelength-scanning digital interference holography for optical section imaging," Opt. Lett. 24, 1693-1695 (1999).
[CrossRef]

Kühn, J.

Lauer, V.

V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

Mann, C. J.

M. K. Kim, L. Yu, and C. J. Mann, "Interference techniques in digital holography," J. Opt. A , Pure Appl. Opt. 8, S518-S523 (2006).
[CrossRef]

Marian, A.

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

Marquet, P.

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
[CrossRef] [PubMed]

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, "Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram," Opt. Express 14, 4300-4306 (2006).
[CrossRef] [PubMed]

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Purely numerical correction of the microscope objective induced curvature in digital holographic microscopy," J. Opt. Soc. Am. A 23, 2944-2953 (2006).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999).
[CrossRef]

Marron, J. C.

J. C. Marron and K. W. Gleichman, "Three-dimensional imaging using a tunable laser source," Opt. Eng. 39, 47-51 (2000).
[CrossRef]

J. C. Marron and K. S. Schroeder, "Holographic laser radar," Opt. Lett. 18, 385-387 (1993).
[CrossRef] [PubMed]

Montfort, F.

Nicola, S. D.

Nugent, K. A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Paganin, D.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Pierattini, G.

Roberts, A.

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Schroeder, K. S.

Weiss, D.

R. Dändliker and D. Weiss, "Reconstruction of three-dimensional refractive index from scattered waves," Opt. Commun. 1, 323-328 (1970).
[CrossRef]

Wiltschko, E.

Wolf, E.

E. Wolf, "Three-dimensional structure determination of semi-transparent object from holographic data," Opt. Commun. 1, 153-156 (1969).
[CrossRef]

Yu, L.

L. Yu and M. K. Kim, "Variable tomographic scanning with wavelength scanning digital interference holography," Opt. Commun. 260, 462-468 (2006).
[CrossRef]

M. K. Kim, L. Yu, and C. J. Mann, "Interference techniques in digital holography," J. Opt. A , Pure Appl. Opt. 8, S518-S523 (2006).
[CrossRef]

L. Yu and M. K. Kim, "Wavelength scanning digital interference holography for variable tomographic scanning," Opt. Express. 13, 5621-5627 (2005).
[CrossRef] [PubMed]

Appl. Opt. (5)

J. Electron. Imaging (1)

A. Dakoff, J. Gass, and M. K. Kim, "Microscopic three-dimensional imaging by digital interference holography," J. Electron. Imaging 12, 643-647 (2003).
[CrossRef]

J. Microsc. (1)

V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

J. Opt. A (1)

M. K. Kim, L. Yu, and C. J. Mann, "Interference techniques in digital holography," J. Opt. A , Pure Appl. Opt. 8, S518-S523 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Purely numerical correction of the microscope objective induced curvature in digital holographic microscopy," J. Opt. Soc. Am. A 23, 2944-2953 (2006).
[CrossRef]

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23 (2006).
[CrossRef]

Opt. Commun. (4)

L. Yu and M. K. Kim, "Variable tomographic scanning with wavelength scanning digital interference holography," Opt. Commun. 260, 462-468 (2006).
[CrossRef]

R. Dändliker and D. Weiss, "Reconstruction of three-dimensional refractive index from scattered waves," Opt. Commun. 1, 323-328 (1970).
[CrossRef]

E. Wolf, "Three-dimensional structure determination of semi-transparent object from holographic data," Opt. Commun. 1, 153-156 (1969).
[CrossRef]

A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000).
[CrossRef]

Opt. Eng. (1)

J. C. Marron and K. W. Gleichman, "Three-dimensional imaging using a tunable laser source," Opt. Eng. 39, 47-51 (2000).
[CrossRef]

Opt. Express (2)

Opt. Express. (1)

L. Yu and M. K. Kim, "Wavelength scanning digital interference holography for variable tomographic scanning," Opt. Express. 13, 5621-5627 (2005).
[CrossRef] [PubMed]

Opt. Lett. (5)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Experimental setup. O, object arm; R, reference arm; OPA, adjustable wavelength laser; NF, neutral filter; BS, beam splitters; BE, beam expander; MO, microscope objective; OC, object beam condenser; RL, reference lens; CCD, charged-coupled device camera; DS, delay system.

Fig. 2
Fig. 2

Chromatic aberration compensation. The amplitude and the phase reconstructions are presented, respectively, on the left and on the right (the phase values between −180° and 180° are linearly distributed on the gray scaling). The wavelength and the reconstruction distances are (a), (b) λ = 480   nm , d = 2.7   cm and (c)–(f) λ = 700   nm , d = 0.30   cm . The white rectangles and lines define, respectively, the specimen size and position, (solid lines) for the reference defined at 480   nm and (dashed lines) for the reconstruction before the application of the numerical magnification and shift at 700   nm . (e), (f) Reconstructions by applying a magnification M = 1.0038 and a numerical shifting to achieve a perfect superposition of the reconstructed specimen for all the wavelengths.

Fig. 3
Fig. 3

Reconstructed mean amplitude from the 20 holograms recorded at different wavelengths (a) before and (b) after compensation of the chromatic aberrations.

Fig. 4
Fig. 4

Schematic of the scattering by a point P located at ( x 0 , y 0 , z 0 ) and measured at an arbitrary point Q = ( x , y , z ) within an object with refractive index distribution n ( x , y , z ) : IW is the illuminating wave, s ^ 0 is the incident wave direction, s ^ p is the collection direction between P and Q.

Fig. 5
Fig. 5

Filter obtained by the sum of 20 k regularly separated wavelengths taken between 480 and 700   nm . Axial extent of Λ = 14.5 μ m , axial resolution of δ = 725   nm .

Fig. 6
Fig. 6

Application of a phase shift to obtain the same phase on the selected reference zone defined by the dashed rectangle. The mean phase values computed in the same area defined in Figs. 2(b) and 2(f) are subtracted from the entire phase images of Figs. 2(b) and 2(f) and give, respectively, (a) and (b).

Fig. 7
Fig. 7

Simulated target with steps of 375, 525, 975, 1200, and 1275   nm .

Fig. 8
Fig. 8

Simulated (lower-case letters) and experimental (upper-case letters) results of six reconstructed sections at 0, 375, 525, 975, 1200, 1275   nm [(a), (b), (c), (d), (e), (f), respectively] as well as the specimen average amplitudes of the (a) simulated and (A) experimental targets.

Fig. 9
Fig. 9

Normalized intensity profiles T ( r P Q ) for the 0, 375, 525, 975, 1200, 1275   nm planes of interest [(a), (b), (c), (d), (e), (f), respectively]. S denotes the results for the simulated specimen and E is for the experimental data.

Fig. 10
Fig. 10

Filter function curve T ( r P Q ) with theoretical, simulated, and experimental points.

Equations (8)

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

Ψ j ( Q ) V A ( P ) exp ( i k r P Q ) d 3 r P Q .
k min = 2 π λ max , k max = 2 π λ min , Δ k = k max k min N 1 .
Ψ ( Q ) = j = 0 N 1 Ψ j ( Q ) j = 0 N 1 V A ( P ) exp ( i k j r P Q ) d 3 r P Q V A ( P ) j = 0 N 1 exp ( i k j r P Q ) d 3 r P Q .
Ψ ( Q ) V A ( P ) exp ( i k ¯ r P Q ) T ( r P Q ) d 3 r P Q ,
T ( r P Q ) = sin ( Δ k r P Q N 2 ) sin ( Δ k r P Q 1 2 )  has   { maxima for r P Q = p 2 π N Δ k ,     p = q N minima for r PQ = p 2 π N Δ k ,     p q N ,
lim N Ψ ( Q ) V A ( P ) exp ( i k ¯ r P Q ) δ ( r P Q ) d 3 r P Q A ( Q ) .
Ψ ( Q ) = j = 0 N 1 Ψ j ( Q ) exp ( i φ j ) .
Δ φ j = 2 π λ j ϵ .

Metrics