Abstract

Holographic rendering of off-axis intensity digital holograms is discussed. A review of some of the main numerical processing methods, based either on the Fourier transform interpretation of the propagation integral or on its linear system counterpart, is reported. Less common methods such as adjustable magnification reconstruction schemes and Fresnelet decomposition are presented and applied to the digital treatment of off-axis holograms. The influence of experimental parameters on the classical hologram reconstruction methods is assessed, offering guidelines for optimal image rendering regarding the hologram recording conditions.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
    [CrossRef] [PubMed]
  2. D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A 197, 454–487 (1949).
    [CrossRef]
  3. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
    [CrossRef]
  4. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [CrossRef]
  5. M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).
  6. L. P. Yaroslvsky and N. S. Merzlyakov, Methods of Digital Holography (Springer, 1980).
  7. L. Onural and P. D. Scott, “Digital recording of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
  8. 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]
  9. J. R. Fienup, “Phase retrieval algorithms, a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  10. L. Onural and M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992).
    [CrossRef]
  11. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  12. A. Lozano, J. Kostas, and J. Soria, “Use of holography in particle image velocimetry measurements of a swirling flow,” Exp. Fluids 27, 251–261 (1999).
    [CrossRef]
  13. H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
    [CrossRef]
  14. Y. Pu and H. Meng, “Four-dimensional dynamic flow measurement by holographic particle image velocimetry,” Appl. Opt. 44, 7697–7708 (2005).
    [CrossRef] [PubMed]
  15. F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. 45, 864–871 (2006).
    [CrossRef] [PubMed]
  16. M. Atlan and M. Gross, “Laser Doppler imaging, revisited,” Rev. Sci. Instrum. 77, 116103 (2006).
    [CrossRef]
  17. J-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471–5480 (2008).
    [CrossRef] [PubMed]
  18. N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
    [CrossRef] [PubMed]
  19. N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Determination of 3D-region of interest using digital in-line holography with astigmatic Gaussian beams,” J. Europ. Opt. Soc. Rapid Publ. 4, 09038 (2009).
    [CrossRef]
  20. N. Verrier, C. Remacha, M. Brunel, D. Lebrun, and S. Coëtmellec, “Micropipe flow visualization using digital in-line holographic microscopy,” Opt. Express 18, 7807–7819(2010).
    [CrossRef] [PubMed]
  21. S. Schedin, G. Pedrini, and H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000).
    [CrossRef]
  22. 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]
  23. F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express 14, 7005–7013(2006).
    [CrossRef] [PubMed]
  24. 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]
  25. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
    [CrossRef] [PubMed]
  26. M. Simonutti, M. Paques, J. A. Sahel, M. Gross, B. Samson, C. Magnain, and M. Atlan, “Holographic laser Doppler ophthalmoscopy,” Opt. Lett. 35, 1941–1943 (2010).
    [CrossRef] [PubMed]
  27. R. L. Powell and K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593–1597 (1965).
    [CrossRef]
  28. C. C. Aleksoff, “Temporally modulated holography,” Appl. Opt. 10, 1329–1341 (1971).
    [CrossRef] [PubMed]
  29. F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
    [CrossRef]
  30. U. Iemma, L. Morino, and M. Diez, “Digital holography and Karhunen-Loève decomposition for the modal analysis of two-dimensional vibrating structures,” J. Sound Vib. 291, 107–131 (2006).
    [CrossRef]
  31. P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. 44, 337–343 (2005).
    [CrossRef] [PubMed]
  32. J. Leval, P. Picart, J-P. Boileau, and J-C. Pascal, “Full-field vibrometry with digital Fresnel holography,” Appl. Opt. 44, 5763–5772 (2005).
    [CrossRef] [PubMed]
  33. D. Borza, “Mechanical vibration measurement by high-resolution time-averaged digital holography,” Meas. Sci. Technol. 16, 1853–1864 (2005).
    [CrossRef]
  34. A. Asundi and V. R. Singh, “Time-averaged in-line digital holographic interferometry for vibration analysis,” Appl. Opt. 45, 2391–2395 (2006).
    [CrossRef] [PubMed]
  35. F. Joud, F. Lanoë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by sideband digital holography,” Opt. Express 17, 2774–2779 (2009).
    [CrossRef] [PubMed]
  36. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting holography,” Appl. Opt. 45, 975–983 (2006).
    [CrossRef] [PubMed]
  37. K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18, 18453–18463(2010).
    [CrossRef] [PubMed]
  38. D. Lebrun, A. Benkouider, S. Coëtmellec, and M. Malek, “Particle field digital holographic reconstruction in arbitrary tilted planes,” Opt. Express 11, 224–229 (2003).
    [CrossRef] [PubMed]
  39. S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, and D. Alfieri, “Angular spectrum method with correction of anamorphism for numerical reconstruction on tilted planes,” Opt. Express 13, 9935–9940 (2005).
    [CrossRef] [PubMed]
  40. N. Verrier, S. Coëtmellec, M. Brunel, D. Lebrun, and A. J. E. M. Janssen, “Digital in-line holography with an elliptical, astigmatic, Gaussian beam: wide angle reconstruction,” J. Opt. Soc. Am. A 25, 1459–1466 (2008).
    [CrossRef]
  41. F. Soulez, L. Denis, C. Fournier, E. Thiébaut, and C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007).
    [CrossRef]
  42. F. Soulez, L. Denis, E. Thiébaut, C. Fournier, and C. Goepfert, “Inverse-problem approach in particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (2007).
    [CrossRef]
  43. L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
    [CrossRef] [PubMed]
  44. M. Marim, E. Angelini, J-C. Olivo-Marin, and M. Atlan, “Off-axis compressed holographic microscopy in low-light conditions,” Opt. Lett. 36, 79–81 (2011).
    [CrossRef] [PubMed]
  45. T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776–11781(2008).
    [CrossRef] [PubMed]
  46. L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
    [CrossRef]
  47. T. Shimobaba, N. Masuda, Y. Ichihashi, and T. Ito, “Real-time digital holographic microscopy observable in multi-view and multi-resolution,” J. Opt. 12, 065402 (2010).
    [CrossRef]
  48. B. Samson, F. Verpillat, M. Gross, and M. Atlan, “Video-rate wide-field laser vibrometry by heterodyne holography,” Opt. Lett. 36, 1449–1451 (2011).
    [CrossRef] [PubMed]
  49. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  50. M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. 32, 1456–1458 (2007).
    [CrossRef] [PubMed]
  51. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  52. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. 53, 1377–1381 (1963).
    [CrossRef]
  53. 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]
  54. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
    [CrossRef]
  55. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  56. J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
    [CrossRef]
  57. U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  58. L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005).
    [CrossRef] [PubMed]
  59. J. Li, P. Tankam, Z. Peng, and P. Picart, “Digital holographic reconstruction of large object using a convolution approach and adjustable magnification,” Opt. Lett. 34, 572–574 (2009).
    [CrossRef] [PubMed]
  60. P. Picart, P. Tankam, D. Mounier, Z-j. Peng, and J. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express 17, 9145–9156 (2009).
    [CrossRef] [PubMed]
  61. P. Ferraro, S. De 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]
  62. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
    [CrossRef] [PubMed]
  63. D. Wang, J. Zhao, F. Zhang, G. Pedrini, and W. Osten, “High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms,” Appl. Opt. 47, D12–D20 (2008).
    [CrossRef] [PubMed]
  64. 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, 3177–3190(2006).
    [CrossRef]
  65. J. Li, Z. Peng, P. Tankam, Q. Song, and P. Picart, “Digital holographic reconstruction of a local object field using an adjustable magnification,” J. Opt. Soc. Am. A 28, 1291–1296(2011).
    [CrossRef]
  66. J. F. Restrepo and J. Garcia-Sucerquia, “Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform,” Appl. Opt. 49, 6430–6435 (2010).
    [CrossRef] [PubMed]
  67. L. Bleustein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
    [CrossRef]
  68. B. Hennelly, D. Kelly, N. Pandey, and D. Monaghan, “Zooming algorithms for digital holography,” J. Phys. Conf. Ser. 206, 012027 (2010).
    [CrossRef]
  69. M. Liebling, T. Blu, and M. Unser, “Fresnelet: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
    [CrossRef]
  70. E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shift digital hologram compression,” IEEE Trans. Image Process. 15, 3804–3811 (2006).
    [CrossRef] [PubMed]
  71. E. Darakis, T. J. Naughton, and J. J. Soraghan, “Compression defect in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586(2007).
    [CrossRef] [PubMed]
  72. M. Liebling, T. Blu, and M. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–559 (2003).
    [CrossRef]
  73. M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
    [CrossRef]
  74. M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004).
    [CrossRef]
  75. M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Process. 30, 141–162 (1993).
    [CrossRef]
  76. L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000).
    [CrossRef]

2011

2010

2009

2008

2007

2006

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, 3177–3190(2006).
[CrossRef]

A. Asundi and V. R. Singh, “Time-averaged in-line digital holographic interferometry for vibration analysis,” Appl. Opt. 45, 2391–2395 (2006).
[CrossRef] [PubMed]

F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. 45, 864–871 (2006).
[CrossRef] [PubMed]

M. Atlan and M. Gross, “Laser Doppler imaging, revisited,” Rev. Sci. Instrum. 77, 116103 (2006).
[CrossRef]

F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express 14, 7005–7013(2006).
[CrossRef] [PubMed]

I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting holography,” Appl. Opt. 45, 975–983 (2006).
[CrossRef] [PubMed]

U. Iemma, L. Morino, and M. Diez, “Digital holography and Karhunen-Loève decomposition for the modal analysis of two-dimensional vibrating structures,” J. Sound Vib. 291, 107–131 (2006).
[CrossRef]

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shift digital hologram compression,” IEEE Trans. Image Process. 15, 3804–3811 (2006).
[CrossRef] [PubMed]

2005

2004

2003

M. Liebling, T. Blu, and M. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–559 (2003).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Fresnelet: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

D. Lebrun, A. Benkouider, S. Coëtmellec, and M. Malek, “Particle field digital holographic reconstruction in arbitrary tilted planes,” Opt. Express 11, 224–229 (2003).
[CrossRef] [PubMed]

2002

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

2001

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
[CrossRef]

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]

2000

1999

A. Lozano, J. Kostas, and J. Soria, “Use of holography in particle image velocimetry measurements of a swirling flow,” Exp. Fluids 27, 251–261 (1999).
[CrossRef]

1997

1994

1993

M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Process. 30, 141–162 (1993).
[CrossRef]

1992

1987

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

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]

1982

1972

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).

1971

1970

L. Bleustein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
[CrossRef]

1967

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

1965

R. L. Powell and K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593–1597 (1965).
[CrossRef]

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

1963

1962

1949

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A 197, 454–487 (1949).
[CrossRef]

1948

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

Absil, E.

Ahrenberg, L.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
[CrossRef]

Aldroubi, A.

M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Process. 30, 141–162 (1993).
[CrossRef]

Aleksoff, C. C.

Alfieri, D.

Angelini, E.

Aspert, N.

Asundi, A.

Atlan, M.

Benkouider, A.

Bleustein, L.

L. Bleustein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
[CrossRef]

Blu, T.

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–559 (2003).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Fresnelet: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Boileau, J-P.

Born, M.

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

Borza, D.

D. Borza, “Mechanical vibration measurement by high-resolution time-averaged digital holography,” Meas. Sci. Technol. 16, 1853–1864 (2005).
[CrossRef]

Bourquin, S.

Brunel, M.

Callens, N.

Charrière, F.

Coëtmellec, S.

Colomb, T.

Cooley, J. W.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Coppola, G.

Cuche, E.

Darakis, E.

E. Darakis, T. J. Naughton, and J. J. Soraghan, “Compression defect in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586(2007).
[CrossRef] [PubMed]

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shift digital hologram compression,” IEEE Trans. Image Process. 15, 3804–3811 (2006).
[CrossRef] [PubMed]

De Nicola, S.

Denis, L.

Depeursinge, C.

Desse, J-M.

Diez, M.

U. Iemma, L. Morino, and M. Diez, “Digital holography and Karhunen-Loève decomposition for the modal analysis of two-dimensional vibrating structures,” J. Sound Vib. 291, 107–131 (2006).
[CrossRef]

Dubois, F.

Eden, M.

M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Process. 30, 141–162 (1993).
[CrossRef]

Ferraro, P.

Fienup, J. R.

Finizio, A.

Fournier, C.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A 197, 454–487 (1949).
[CrossRef]

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

Garcia-Sucerquia, J.

Goepfert, C.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Gougeon, S.

Gross, M.

Hare, J.

Heger, T. J.

Hennelly, B.

B. Hennelly, D. Kelly, N. Pandey, and D. Monaghan, “Zooming algorithms for digital holography,” J. Phys. Conf. Ser. 206, 012027 (2010).
[CrossRef]

Hennelly, B. M.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
[CrossRef]

Hoyos, M.

Ichihashi, Y.

T. Shimobaba, N. Masuda, Y. Ichihashi, and T. Ito, “Real-time digital holographic microscopy observable in multi-view and multi-resolution,” J. Opt. 12, 065402 (2010).
[CrossRef]

Iemma, U.

U. Iemma, L. Morino, and M. Diez, “Digital holography and Karhunen-Loève decomposition for the modal analysis of two-dimensional vibrating structures,” J. Sound Vib. 291, 107–131 (2006).
[CrossRef]

Ito, T.

T. Shimobaba, N. Masuda, Y. Ichihashi, and T. Ito, “Real-time digital holographic microscopy observable in multi-view and multi-resolution,” J. Opt. 12, 065402 (2010).
[CrossRef]

T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776–11781(2008).
[CrossRef] [PubMed]

Janssen, A. J. E. M.

Jericho, M. H.

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]

Joud, F.

Jüptner, W.

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

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

Kato, J.

Kelly, D.

B. Hennelly, D. Kelly, N. Pandey, and D. Monaghan, “Zooming algorithms for digital holography,” J. Phys. Conf. Ser. 206, 012027 (2010).
[CrossRef]

Kemper, B.

Kim, M. K.

Kostas, J.

A. Lozano, J. Kostas, and J. Soria, “Use of holography in particle image velocimetry measurements of a swirling flow,” Exp. Fluids 27, 251–261 (1999).
[CrossRef]

Kreuzer, H. J.

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]

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).

Kühn, J.

Kurowski, P.

Lanoë, F.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Lebrun, D.

Leith, E. N.

Leval, J.

Li, J.

Liebling, M.

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[CrossRef]

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–559 (2003).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Fresnelet: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

Liu, G.

Lorenz, D.

Lozano, A.

A. Lozano, J. Kostas, and J. Soria, “Use of holography in particle image velocimetry measurements of a swirling flow,” Exp. Fluids 27, 251–261 (1999).
[CrossRef]

Magnain, C.

Malek, M.

Marian, A.

Marim, M.

Marquet, P.

Masuda, N.

T. Shimobaba, N. Masuda, Y. Ichihashi, and T. Ito, “Real-time digital holographic microscopy observable in multi-view and multi-resolution,” J. Opt. 12, 065402 (2010).
[CrossRef]

Matsushima, K.

McDonald, J. B.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
[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. USA 98, 11301–11305 (2001).
[CrossRef] [PubMed]

Meng, H.

Y. Pu and H. Meng, “Four-dimensional dynamic flow measurement by holographic particle image velocimetry,” Appl. Opt. 44, 7697–7708 (2005).
[CrossRef] [PubMed]

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[CrossRef]

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).

L. P. Yaroslvsky and N. S. Merzlyakov, Methods of Digital Holography (Springer, 1980).

Mills, G.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Mills, G. A.

Mitchell, E. A. D.

Miura, J.

Mizuno, J.

Monaghan, D.

B. Hennelly, D. Kelly, N. Pandey, and D. Monaghan, “Zooming algorithms for digital holography,” J. Phys. Conf. Ser. 206, 012027 (2010).
[CrossRef]

Monnom, O.

Montfort, F.

Morino, L.

U. Iemma, L. Morino, and M. Diez, “Digital holography and Karhunen-Loève decomposition for the modal analysis of two-dimensional vibrating structures,” J. Sound Vib. 291, 107–131 (2006).
[CrossRef]

Mounier, D.

Naughton, T. J.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
[CrossRef]

E. Darakis, T. J. Naughton, and J. J. Soraghan, “Compression defect in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586(2007).
[CrossRef] [PubMed]

Ohta, S.

Olivo-Marin, J-C.

Onural, L.

Osten, W.

Ozgen, M. T.

Page, A. J.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
[CrossRef]

Pan, G.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[CrossRef]

Pandey, N.

B. Hennelly, D. Kelly, N. Pandey, and D. Monaghan, “Zooming algorithms for digital holography,” J. Phys. Conf. Ser. 206, 012027 (2010).
[CrossRef]

Paques, M.

Pascal, J-C.

Pavillon, N.

Pedrini, G.

Peng, Z.

Peng, Z-j.

Picart, P.

Pierattini, G.

Powell, R. L.

Pu, Y.

Y. Pu and H. Meng, “Four-dimensional dynamic flow measurement by holographic particle image velocimetry,” Appl. Opt. 44, 7697–7708 (2005).
[CrossRef] [PubMed]

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[CrossRef]

Rappaz, B.

Remacha, C.

Restrepo, J. F.

Sahel, J. A.

Samson, B.

Sato, Y.

Schedin, S.

Schnars, U.

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

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

Scott, P. D.

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

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]

Shimobaba, T.

T. Shimobaba, N. Masuda, Y. Ichihashi, and T. Ito, “Real-time digital holographic microscopy observable in multi-view and multi-resolution,” J. Opt. 12, 065402 (2010).
[CrossRef]

T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776–11781(2008).
[CrossRef] [PubMed]

Simonutti, M.

Singh, V. R.

Song, Q.

Soraghan, J. J.

E. Darakis, T. J. Naughton, and J. J. Soraghan, “Compression defect in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586(2007).
[CrossRef] [PubMed]

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shift digital hologram compression,” IEEE Trans. Image Process. 15, 3804–3811 (2006).
[CrossRef] [PubMed]

Soria, J.

A. Lozano, J. Kostas, and J. Soria, “Use of holography in particle image velocimetry measurements of a swirling flow,” Exp. Fluids 27, 251–261 (1999).
[CrossRef]

Soulez, F.

Stetson, K. A.

Takenouchi, M.

Tankam, P.

Thiébaut, E.

Tiziani, H. J.

Trede, D.

Tukey, J. W.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Unser, M.

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[CrossRef]

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–559 (2003).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Fresnelet: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Process. 30, 141–162 (1993).
[CrossRef]

Upatnieks, J.

Valera, J. D. R.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Verpillat, F.

Verrier, N.

von Bally, G.

Wang, D.

Wolf, E.

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

Woodward, S. H.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[CrossRef]

Xu, W.

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]

Yamaguchi, I.

Yamamoto, K.

Yaroslavsky, L. P.

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
[CrossRef] [PubMed]

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).

Yaroslvsky, L. P.

L. P. Yaroslvsky and N. S. Merzlyakov, Methods of Digital Holography (Springer, 1980).

Yokota, M.

I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting holography,” Appl. Opt. 45, 975–983 (2006).
[CrossRef] [PubMed]

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Yourassowsky, C.

Yu, L.

Zhang, F.

Zhang, T.

Zhao, J.

Appl. Opt.

J. R. Fienup, “Phase retrieval algorithms, a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

Y. Pu and H. Meng, “Four-dimensional dynamic flow measurement by holographic particle image velocimetry,” Appl. Opt. 44, 7697–7708 (2005).
[CrossRef] [PubMed]

F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. 45, 864–871 (2006).
[CrossRef] [PubMed]

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef] [PubMed]

S. Schedin, G. Pedrini, and H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000).
[CrossRef]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
[CrossRef] [PubMed]

C. C. Aleksoff, “Temporally modulated holography,” Appl. Opt. 10, 1329–1341 (1971).
[CrossRef] [PubMed]

P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. 44, 337–343 (2005).
[CrossRef] [PubMed]

J. Leval, P. Picart, J-P. Boileau, and J-C. Pascal, “Full-field vibrometry with digital Fresnel holography,” Appl. Opt. 44, 5763–5772 (2005).
[CrossRef] [PubMed]

I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting holography,” Appl. Opt. 45, 975–983 (2006).
[CrossRef] [PubMed]

A. Asundi and V. R. Singh, “Time-averaged in-line digital holographic interferometry for vibration analysis,” Appl. Opt. 45, 2391–2395 (2006).
[CrossRef] [PubMed]

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]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
[CrossRef]

D. Wang, J. Zhao, F. Zhang, G. Pedrini, and W. Osten, “High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms,” Appl. Opt. 47, D12–D20 (2008).
[CrossRef] [PubMed]

J. F. Restrepo and J. Garcia-Sucerquia, “Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform,” Appl. Opt. 49, 6430–6435 (2010).
[CrossRef] [PubMed]

E. Darakis, T. J. Naughton, and J. J. Soraghan, “Compression defect in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586(2007).
[CrossRef] [PubMed]

L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000).
[CrossRef]

Appl. Phys. Lett.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Exp. Fluids

A. Lozano, J. Kostas, and J. Soria, “Use of holography in particle image velocimetry measurements of a swirling flow,” Exp. Fluids 27, 251–261 (1999).
[CrossRef]

IEEE J. Display Technol.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” IEEE J. Display Technol. 5, 111–119 (2009).
[CrossRef]

IEEE Trans. Audio Electroacoust.

L. Bleustein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
[CrossRef]

IEEE Trans. Image Process.

M. Liebling, T. Blu, and M. Unser, “Fresnelet: new multiresolution wavelet bases for digital holography,” IEEE Trans. Image Process. 12, 29–43 (2003).
[CrossRef]

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shift digital hologram compression,” IEEE Trans. Image Process. 15, 3804–3811 (2006).
[CrossRef] [PubMed]

J. Europ. Opt. Soc. Rapid Publ.

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Determination of 3D-region of interest using digital in-line holography with astigmatic Gaussian beams,” J. Europ. Opt. Soc. Rapid Publ. 4, 09038 (2009).
[CrossRef]

J. Opt.

T. Shimobaba, N. Masuda, Y. Ichihashi, and T. Ito, “Real-time digital holographic microscopy observable in multi-view and multi-resolution,” J. Opt. 12, 065402 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

L. Onural and M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992).
[CrossRef]

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]

N. Verrier, S. Coëtmellec, M. Brunel, D. Lebrun, and A. J. E. M. Janssen, “Digital in-line holography with an elliptical, astigmatic, Gaussian beam: wide angle reconstruction,” J. Opt. Soc. Am. A 25, 1459–1466 (2008).
[CrossRef]

F. Soulez, L. Denis, C. Fournier, E. Thiébaut, and C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007).
[CrossRef]

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, and C. Goepfert, “Inverse-problem approach in particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (2007).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[CrossRef]

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004).
[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, 3177–3190(2006).
[CrossRef]

J. Li, Z. Peng, P. Tankam, Q. Song, and P. Picart, “Digital holographic reconstruction of a local object field using an adjustable magnification,” J. Opt. Soc. Am. A 28, 1291–1296(2011).
[CrossRef]

J. Phys. Conf. Ser.

B. Hennelly, D. Kelly, N. Pandey, and D. Monaghan, “Zooming algorithms for digital holography,” J. Phys. Conf. Ser. 206, 012027 (2010).
[CrossRef]

J. Sound Vib.

U. Iemma, L. Morino, and M. Diez, “Digital holography and Karhunen-Loève decomposition for the modal analysis of two-dimensional vibrating structures,” J. Sound Vib. 291, 107–131 (2006).
[CrossRef]

Math. Comput.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Meas. Sci. Technol.

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

D. Borza, “Mechanical vibration measurement by high-resolution time-averaged digital holography,” Meas. Sci. Technol. 16, 1853–1864 (2005).
[CrossRef]

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[CrossRef]

Nature

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

Opt. Eng.

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

Opt. Express

J-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471–5480 (2008).
[CrossRef] [PubMed]

N. Verrier, C. Remacha, M. Brunel, D. Lebrun, and S. Coëtmellec, “Micropipe flow visualization using digital in-line holographic microscopy,” Opt. Express 18, 7807–7819(2010).
[CrossRef] [PubMed]

K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18, 18453–18463(2010).
[CrossRef] [PubMed]

D. Lebrun, A. Benkouider, S. Coëtmellec, and M. Malek, “Particle field digital holographic reconstruction in arbitrary tilted planes,” Opt. Express 11, 224–229 (2003).
[CrossRef] [PubMed]

S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, and D. Alfieri, “Angular spectrum method with correction of anamorphism for numerical reconstruction on tilted planes,” Opt. Express 13, 9935–9940 (2005).
[CrossRef] [PubMed]

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]

F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express 14, 7005–7013(2006).
[CrossRef] [PubMed]

T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776–11781(2008).
[CrossRef] [PubMed]

F. Joud, F. Lanoë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by sideband digital holography,” Opt. Express 17, 2774–2779 (2009).
[CrossRef] [PubMed]

P. Picart, P. Tankam, D. Mounier, Z-j. Peng, and J. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express 17, 9145–9156 (2009).
[CrossRef] [PubMed]

Opt. Lett.

P. Ferraro, S. De 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]

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
[CrossRef] [PubMed]

L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005).
[CrossRef] [PubMed]

J. Li, P. Tankam, Z. Peng, and P. Picart, “Digital holographic reconstruction of large object using a convolution approach and adjustable magnification,” Opt. Lett. 34, 572–574 (2009).
[CrossRef] [PubMed]

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
[CrossRef] [PubMed]

M. Marim, E. Angelini, J-C. Olivo-Marin, and M. Atlan, “Off-axis compressed holographic microscopy in low-light conditions,” Opt. Lett. 36, 79–81 (2011).
[CrossRef] [PubMed]

B. Samson, F. Verpillat, M. Gross, and M. Atlan, “Video-rate wide-field laser vibrometry by heterodyne holography,” Opt. Lett. 36, 1449–1451 (2011).
[CrossRef] [PubMed]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. 32, 1456–1458 (2007).
[CrossRef] [PubMed]

M. Simonutti, M. Paques, J. A. Sahel, M. Gross, B. Samson, C. Magnain, and M. Atlan, “Holographic laser Doppler ophthalmoscopy,” Opt. Lett. 35, 1941–1943 (2010).
[CrossRef] [PubMed]

Opt. Rev.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Proc. Natl. Acad. Sci. USA

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. R. Soc. Lond. A

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A 197, 454–487 (1949).
[CrossRef]

Proc. SPIE

M. Liebling, T. Blu, and M. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–559 (2003).
[CrossRef]

Rev. Sci. Instrum.

M. Atlan and M. Gross, “Laser Doppler imaging, revisited,” Rev. Sci. Instrum. 77, 116103 (2006).
[CrossRef]

Signal Process.

M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Process. 30, 141–162 (1993).
[CrossRef]

Sov. Phys. Tech. Phys.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 419–420 (1972).

Other

L. P. Yaroslvsky and N. S. Merzlyakov, Methods of Digital Holography (Springer, 1980).

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

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

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 (8)

Fig. 1
Fig. 1

(a) Hologram recording in off-axis configuration, (b) spatial frequency representation of off-axis holograms.

Fig. 2
Fig. 2

Angular acceptance of digital holographic reconstruction process. Solid lines are associated with the single-FFT reconstruction, and dashed lines correspond to the convolution approaches.

Fig. 3
Fig. 3

Reconstruction of a hologram for γ = 0.8 , 1 , 2.5 × γ 0 . (a), (c), (e) Quadratic lens method, (b), (d), (f) Fresnel–Bluestein method.

Fig. 4
Fig. 4

Illustrations of alias and replica phenomena. (a) Reconstruction with γ = 0.5 × γ 0 , (c) reconstruction with γ = 4 × γ 0 , (d) same as (a) with replica removal, (f) same as (c) with alias filtering, (b), (e) reconstruction with γ = γ 0 .

Fig. 5
Fig. 5

(a) Synoptics of the antialias procedure, (b) replica removal scheme.

Fig. 6
Fig. 6

Experimental procedure for the holographic reconstruction benchmarking.

Fig. 7
Fig. 7

Holographic reconstructions of the USAF target located at different distances.

Fig. 8
Fig. 8

Fresnelet decomposition of the hologram recorded for Δ ξ > Δ x . (a) Fresnelet coefficients computed within the single-FFT scheme, (b) Fresnelet coefficients computed within the three-FFT scheme, (c) hologram reconstruction from (a), (d) hologram reconstruction from (b).

Equations (34)

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

E ( x , y ) = | R ( x , y ) | 2 + | O ( x , y ) | 2 + O * ( x , y ) R ( x , y ) + O ( x , y ) R * ( x , y ) ,
α max λ 2 Δ x ,
E rec ( ξ , η ) = i z λ R 2 E ( x , y ) exp ( i k r ) r d x d y .
r = z 2 + ( x ξ ) 2 + ( y η ) 2 ,
r = z [ 1 + 1 2 ( x ξ z ) 2 + 1 2 ( y η z ) 2 ] ,
E rec ( ξ , η ) = exp ( i 2 π λ z ) i λ z R 2 E ( x , y ) exp { i π λ z [ ( x ξ ) 2 + ( y η ) 2 ] } d x d y .
E rec ( p ) = exp ( i 2 π λ z ) i λ z exp ( i π λ z p 2 Δ ξ 2 ) n = 0 N 1 E ( n ) exp ( i π λ z n 2 Δ x 2 ) exp ( i 2 π λ z n p Δ x Δ ξ ) ,
Δ ξ = λ z N Δ x .
E rec ( p ) = exp ( i 2 π λ z ) i λ z exp ( i π λ z p 2 N 2 Δ x 2 ) n = 0 N 1 E ( n ) exp ( i π λ z n 2 Δ x 2 ) exp ( i 2 π n p N ) .
E rec ( ξ ) = exp ( i 2 π λ z ) i λ z exp ( i π λ z p 2 N 2 Δ x 2 ) F { E ( x ) exp ( i π λ z x 2 ) } .
h z ( x ) = exp ( i π λ z x 2 ) .
E rec ( ξ ) = exp ( i 2 π λ z ) i λ z F 1 [ F { E ( x ) } × F { h z ( x ) } ] ,
H ( u ) exp [ 2 i π z λ ( 1 1 2 λ 2 u 2 ) ] ,
E rec ( ξ ) = 1 i λ z F 1 [ F { E ( x ) } × H ( u ) ] .
L ( x ) = exp ( i π λ R c x 2 ) ,
R c = γ z γ 1 .
E rec ( ξ ) = exp ( i 2 π λ z ) i λ z F 1 [ F { E ( x ) L ( x ) } × F { h z ( x ) } ] ,
E rec ( ξ ) = exp ( i 2 π λ z ) i λ z F 1 [ F { E ( x ) L ( x ) } × H ( u ) ] ,
E rec ( p ) = exp ( i 2 π λ z ) i λ z exp [ i π λ z Δ ξ ( Δ x Δ ξ ) p 2 ] n = 0 N E ( n ) exp [ i π λ z Δ x ( Δ x Δ ξ ) n 2 ] × exp [ i π λ z Δ x Δ ξ ( p n ) 2 ] .
E rec ( p ) = exp ( i 2 π λ z ) i λ z exp [ i π λ z γ ( 1 γ ) Δ x 2 p 2 ] n = 0 N E ( n ) exp [ i π λ z ( 1 γ ) n 2 Δ x 2 ] × exp [ i π λ z γ ( p n ) 2 Δ x 2 ] .
f ( n ) = E ( n ) exp [ i π λ z ( 1 γ ) n 2 Δ x 2 ]
g ( n ) = exp ( i π λ z γ n 2 Δ x 2 ) .
E rec ( ξ ) = exp ( i 2 π λ z ) i λ z exp [ i π λ z γ ( 1 γ ) Δ x 2 p 2 ] F 1 [ F { f ( x ) } × F { g ( x ) } ] .
γ < γ 0
γ > γ 0
C ( x ) = exp ( i π λ z x 2 ) .
β n ( x ) = β 0 * * β 0 n + 1 ( x ) ,
β 0 ( x ) = { 1 , 0 < x < 1 1 2 , x = 0     or     x = 1 0 , otherwise ,
β n ( x 2 ) = k Z h ( k ) β n ( x k ) .
{ ψ j , k n = 2 j 2 ψ n ( 2 j x k ) } j , k Z ,
ψ n ( x 2 ) = k Z g ( k ) β n ( x k ) .
{ ψ ˜ j , k n = 2 j 2 ψ ˜ n ( 2 j x k ) } j , k Z ,
ψ ˜ n ( x 2 ) = k Z g ( k ) β ˜ n ( x k ) ,
β ˜ n ( x 2 ) = k Z h ( k ) β ˜ n ( x k ) .

Metrics