Abstract

A cascaded Fresnel algorithm for the flexible reconstruction of digital holograms is proposed. Since the fast-Fourier-transform-based numerical realization of the Fresnel integral shows a dependency of its pixel resolution and its computation window size on the propagation distance different from that of the corresponding physical system, the computation window can be smaller than the actual physical diffraction field in the intermediate plane. Consequently, distortions in the final reconstruction may occur. A method is proposed to eliminate such distortion. The validity of this method is shown by both numerical simulations and experimental results.

© 2008 Optical Society of America

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2007 (2)

2006 (8)

F. Zhang, G. Pedrini, and W. Osten, "Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution," Opt. Lett. 31, 1633-11635 (2006).
[CrossRef] [PubMed]

F. Shen and A. Wang, "Fast-Fourier-transform-based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45, 1102-1110 (2006).
[CrossRef] [PubMed]

L. Yu and M. K. Kim, "Pixel resolution control in numerical reconstruction of digital holography," Opt. Lett. 31, 897-899 (2006).
[CrossRef] [PubMed]

A. Sten and B. Javidi, "Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields," J. Opt. Soc. Am. A 23, 1227-1235 (2006).
[CrossRef]

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]

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. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

T. Baumbach, W. Osten, C. von Kopylow, and W. Jüptner, "Remote metrology by comparative digital holography," Appl. Opt. 45, 925-934 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (5)

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]

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

Y. M. Engelberg and S. Ruschin, "Fast method for physical optics propagation of high-numerical-aperture beams," J. Opt. Soc. Am. A 21, 2135-2145 (2004).
[CrossRef]

2003 (2)

N. Demoli, D. Vukicevic, and M. Torzynski, "Dynamic digital holographic interferometry with three wavelengths," Opt. Express 11, 767-774 (2003).
[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]

2002 (1)

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

2000 (2)

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

T.-C. Poon, T. Kim, G. Indebetouw, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, "Twin-image elimination experiments for three-dimensional images in optical scanning holography," Opt. Lett. 25, 215-217 (2000).
[CrossRef]

1999 (3)

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, "Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology," Appl. Opt. 38, 4812-4820 (1999).
[CrossRef]

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

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

1997 (3)

T. M. Kreis, M. Adams, and W. P. O. Jüptner, "Methods of digital holography: a comparison," Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

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

D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

1994 (1)

1967 (1)

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

Adams, M.

T. M. Kreis, M. Adams, and W. P. O. Jüptner, "Methods of digital holography: a comparison," Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Alfieri, D.

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

Asundi, A.

Baumbach, T.

T. Baumbach, W. Osten, C. von Kopylow, and W. Jüptner, "Remote metrology by comparative digital holography," Appl. Opt. 45, 925-934 (2006).
[CrossRef] [PubMed]

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

Bevilacqua, F.

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

Charrière, F.

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (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]

Colomb, T.

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. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

Coppola, G.

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Cuche, E.

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. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

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

De Nicola, S.

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Demoli, N.

N. Demoli, D. Vukicevic, and M. Torzynski, "Dynamic digital holographic interferometry with three wavelengths," Opt. Express 11, 767-774 (2003).
[CrossRef] [PubMed]

DeNicola, S.

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

Depeursinge, C.

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (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]

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

Emery, Y.

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

Engelberg, Y. M.

Y. M. Engelberg and S. Ruschin, "Fast method for physical optics propagation of high-numerical-aperture beams," J. Opt. Soc. Am. A 21, 2135-2145 (2004).
[CrossRef]

Ferraro, P.

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

Finizio, A.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

Garcia-Sucerquia, 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]

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]

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 (McGraw-Hill, 1996), pp. 45-67.

Grilli, S.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Guo, Z.

Indebetouw, G.

Iodice, M.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Javidi, B.

A. Sten and B. Javidi, "Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. A 24, 163-168 (2007).
[CrossRef]

A. Sten and B. Javidi, "Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields," J. Opt. Soc. Am. A 23, 1227-1235 (2006).
[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]

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] [PubMed]

Jüptner, W.

Jüptner, W. P. O.

T. M. Kreis, M. Adams, and W. P. O. Jüptner, "Methods of digital holography: a comparison," Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Kato, J.

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

Kim, M. K.

L. Yu and M. K. Kim, "Pixel resolution control in numerical reconstruction of digital holography," Opt. Lett. 31, 897-899 (2006).
[CrossRef] [PubMed]

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

C. J. Mann, L. Yu, C.-M. Lo, and M. K. Kim, "High-resolution quantitative phase-contrast microscopy by digital holography," Opt. Express 13, 8693-8698 (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]

Kim, T.

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] [PubMed]

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P. O. Jüptner, "Methods of digital holography: a comparison," Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

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]

Kühn, J.

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (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]

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]

Lo, C.-M.

Mann, C. J.

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]

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

Marquet, P.

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. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

Matsumura, T.

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Merzlyakov, N. S.

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Plenum, 1980).

Miao, J.

Monfort, F.

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

Montfort, F.

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]

Muffoletto, R. P.

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, "Shifted Fresnel diffraction for computational holography," Opt. Express 15, 5631-5640 (2007).
[CrossRef] [PubMed]

Osten, W.

T. Baumbach, W. Osten, C. von Kopylow, and W. Jüptner, "Remote metrology by comparative digital holography," Appl. Opt. 45, 925-934 (2006).
[CrossRef] [PubMed]

F. Zhang, G. Pedrini, and W. Osten, "Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution," Opt. Lett. 31, 1633-11635 (2006).
[CrossRef] [PubMed]

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, "Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology," Appl. Opt. 38, 4812-4820 (1999).
[CrossRef]

Pedrini, G.

Peng, X.

Pierattini, G.

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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]

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

Poon, T.-C.

Ruschin, S.

Y. M. Engelberg and S. Ruschin, "Fast method for physical optics propagation of high-numerical-aperture beams," J. Opt. Soc. Am. A 21, 2135-2145 (2004).
[CrossRef]

Schilling, B. W.

Schnars, U.

Seebacher, S.

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, "Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology," Appl. Opt. 38, 4812-4820 (1999).
[CrossRef]

Shen, F.

F. Shen and A. Wang, "Fast-Fourier-transform-based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45, 1102-1110 (2006).
[CrossRef] [PubMed]

Shinoda, K.

Sten, A.

A. Sten and B. Javidi, "Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. A 24, 163-168 (2007).
[CrossRef]

A. Sten and B. Javidi, "Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields," J. Opt. Soc. Am. A 23, 1227-1235 (2006).
[CrossRef]

Suzuki, Y.

Tohline, J. E.

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, "Shifted Fresnel diffraction for computational holography," Opt. Express 15, 5631-5640 (2007).
[CrossRef] [PubMed]

Torzynski, M.

N. Demoli, D. Vukicevic, and M. Torzynski, "Dynamic digital holographic interferometry with three wavelengths," Opt. Express 11, 767-774 (2003).
[CrossRef] [PubMed]

Tyler, J. M.

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, "Shifted Fresnel diffraction for computational holography," Opt. Express 15, 5631-5640 (2007).
[CrossRef] [PubMed]

von Kopylow, C.

T. Baumbach, W. Osten, C. von Kopylow, and W. Jüptner, "Remote metrology by comparative digital holography," Appl. Opt. 45, 925-934 (2006).
[CrossRef] [PubMed]

Vukicevic, D.

N. Demoli, D. Vukicevic, and M. Torzynski, "Dynamic digital holographic interferometry with three wavelengths," Opt. Express 11, 767-774 (2003).
[CrossRef] [PubMed]

Wagner, C.

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, "Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology," Appl. Opt. 38, 4812-4820 (1999).
[CrossRef]

Wang, A.

F. Shen and A. Wang, "Fast-Fourier-transform-based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45, 1102-1110 (2006).
[CrossRef] [PubMed]

Weible, K.

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

Wu, M. H.

Xu, L.

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]

Yamaguchi, I.

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]

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

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

Yaroslavskii, L. P.

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Plenum, 1980).

Yaroslavsky, L. P.

Yu, L.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Zhang, F.

Zhang, T.

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

Appl. Opt. (4)

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]

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

T. Baumbach, W. Osten, C. von Kopylow, and W. Jüptner, "Remote metrology by comparative digital holography," Appl. Opt. 45, 925-934 (2006).
[CrossRef] [PubMed]

F. Shen and A. Wang, "Fast-Fourier-transform-based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45, 1102-1110 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

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

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

P. Ferraro, G. Coppola, D. Alfieri, S. De Nicola, A. Finizio, and G. Pierattini, "Controlling image parameters in the reconstruction process of digital holograms," IEEE J. Sel. Top. Quantum Electron. 10, 829-839 (2004).
[CrossRef]

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

A. Sten and B. Javidi, "Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields," J. Opt. Soc. Am. A 23, 1227-1235 (2006).
[CrossRef]

Y. M. Engelberg and S. Ruschin, "Fast method for physical optics propagation of high-numerical-aperture beams," J. Opt. Soc. Am. A 21, 2135-2145 (2004).
[CrossRef]

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. Mod. Opt. (1)

D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Opt. Commun. (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, "Fast algorithms for free-space diffraction pattern calculation," Opt. Commun. 164, 233-245 (1999).
[CrossRef]

Opt. Express (2)

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, "Shifted Fresnel diffraction for computational holography," Opt. Express 15, 5631-5640 (2007).
[CrossRef] [PubMed]

N. Demoli, D. Vukicevic, and M. Torzynski, "Dynamic digital holographic interferometry with three wavelengths," Opt. Express 11, 767-774 (2003).
[CrossRef] [PubMed]

Opt. Lett. (6)

L. Yu and M. K. Kim, "Pixel resolution control in numerical reconstruction of digital holography," Opt. Lett. 31, 897-899 (2006).
[CrossRef] [PubMed]

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

P. Ferraro, G. Coppola, S. DeNicola, A. Finizio, G. Pierattini, and D. Alfieri, "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. 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]

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

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

Opt. Eng. (1)

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Proc. SPIE (1)

T. M. Kreis, M. Adams, and W. P. O. Jüptner, "Methods of digital holography: a comparison," Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Other (2)

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Plenum, 1980).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 45-67.

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Figures (10)

Fig. 1
Fig. 1

Schematic of the diffraction field and the multiple-step Fresnel propagation.

Fig. 2
Fig. 2

Size of computation window and the diffraction field in the plane P 2 at the distance z 2 versus the distance ratio z 2 / z 1 .

Fig. 3
Fig. 3

Size of computation window in the plane P 0 , reconstructed through the intermediate plane at the distance z 2 versus the distance ratio z 2 / z 1 .

Fig. 4
Fig. 4

Pixel resolutions in the plane P 0 reconstructed from the computation window in the intermediate plane at the distance z 2 without and with the compensation versus the distance ratio z 2 / z 1 .

Fig. 5
Fig. 5

Original cosine amplitude grating and its optical diffraction field at the distance z 1 = 100 m m . (a) Original amplitude grating, (b) diffraction field.

Fig. 6
Fig. 6

Original computation window in the intermediate plane at the distance z 2 = 60 m m and its reconstruction by the SFFT-FR algorithm. (a) Original computation window, (b) central part of the reconstructed field.

Fig. 7
Fig. 7

Compensated computation window close to the optical diffraction field in the intermediate plane at the distance z 2 = 60 m m and its reconstruction by the SFFT-FR algorithm. (a) Compensated computation window, (b) central part of the reconstructed field.

Fig. 8
Fig. 8

Experimental setup for off-axis digital holography: NF, neutral density filter; λ / 2 , half-wave plate; PBS, polarizing beam splitter; BE1, BE2, beam expanders; M1, M2, mirrors; MO, microscope objective; BS, beam splitter.

Fig. 9
Fig. 9

Spectrum of the hologram and its enlarged image of one order.

Fig. 10
Fig. 10

Enlarged images of the central part in the final reconstructed field from the intermediate plane at the distance z 2 = 60 m m by the cascaded SFFT-FR algorithm. (a) Without compensation in the intermediate plane, (b) padding zeros to the computation window in the intermediate plane, (c) computation window in the intermediate plane is compensated to be close to the optical diffraction field.

Equations (13)

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U ( x ) = e j k z j λ z exp ( j π λ z x 2 ) U ( x 0 ) exp ( j π λ z x 0 2 ) × exp ( j 2 π λ z x x 0 ) d x 0 = e j k z j λ z exp ( j π λ z x 2 ) FT [ U ( x 0 ) exp ( j π λ z x 0 2 ) ] ,
U ( m ) = e j k z j λ z exp ( j π λ z m 2 Δ x 2 ) p = 0 M 1 U ( p Δ x 0 ) × exp ( j π λ z p 2 Δ x 0 2 ) exp ( j 2 π λ z p m Δ x Δ x 0 ) ,
U ( m ) = e j k z j λ z exp ( j π λ z m 2 Δ x 2 ) FFT [ U ( p Δ x 0 ) × exp ( j π λ z p 2 Δ x 0 2 ) ] .
L out = λ z Δ x 0 ,
Δ x = λ z M Δ x 0 = λ z L in ,
L z 1 = λ z 1 2 f 0 + L O ,
λ z 1 / Δ x N = λ z 1 2 f 0 .
L z 2 Fr = λ | z 2 | Δ x z 1 ,
Δ x z 2 = λ | z 2 | L H = λ | z 2 | M Δ x z 1 ,
L obj = | z 1 z 2 + 1 | M Δ x z 1 ,
Δ x obj = L obj M = | z 1 z 2 + 1 | Δ x z 1 ,
Δ x Obj _ New = λ | z 1 + z 2 | L z 2 OPT = λ | z 1 + z 2 | L H + λ z 2 2 f 0 .
2 f 0 = 2 sin θ λ L H L O λ z 1 .

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