Abstract

Digital holography is a modern imaging technique whereby a propagated object wave interferes with a known (spherical or plane) reference wave at a plane where a digital sensor is situated. The resulting intensity distribution is recorded by a CCD or CMOS sensor array to produce a digital hologram. This digital hologram can be processed in several ways to isolate the real image term. Using a propagation algorithm, the object wave can be numerically reconstructed from this real image term. Several factors limit the performance of such imaging systems, such as the finite extent of the sensor array and the finite size of the equally spaced sensor pixels, which average the light intensity incident upon them. Theoretical results indicate that in a Fresnel-based system the role of these finite-size pixels is to attenuate higher spatial frequencies by convolving the reconstructed signal with a rectangular function of equal size to the light-sensitive area of the pixel. However, when a spherical reference wave is used, as is the case with “lensless” Fourier-based systems, spatial frequencies will not be attenuated; rather it is the complex amplitude of the reconstructed signal that will be attenuated. In this manuscript we explore this question in more detail, providing new theoretical and experimental results. By assuming a fully developed speckle field for the object wave, we examine the first-order statistical distributions for the integrated intensity of the object wave, and the interference term, using numerical simulations. We show that the statistical distribution of the interference term can be changed, by varying the sphericity of the reference wave. Experimental results are provided where we compare the performance of a Fresnel and Fourier holographic system as a function of pixel size.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2012 (2)

2011 (6)

2009 (2)

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[CrossRef]

S. G. Hanson and H. T. Yura, “Statistics of spatially integrated speckle intensity difference,” J. Opt. Soc. Am. A 26, 371–375 (2009).
[CrossRef]

2008 (2)

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744–1761 (2008).
[CrossRef]

2007 (2)

2006 (4)

2005 (1)

2004 (3)

Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004).
[CrossRef]

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations,” Opt. Eng. 43, 2557–2563 (2004).
[CrossRef]

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250 (2004).
[CrossRef]

2003 (2)

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

C.-S. Guo, L. Zhang, Z.-Y. Rong, and H.-T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers “frequency analysis of digital holography” and “frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 42, 2768–2771 (2003).
[CrossRef]

2002 (1)

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

2000 (1)

1999 (1)

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

1997 (1)

1996 (1)

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

1994 (2)

1992 (1)

1990 (1)

1981 (1)

F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
[CrossRef]

1972 (1)

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

1967 (1)

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

Asundi, A.

Bernardo, L. M.

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

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill Science/Engineering/Math, 1999).

Bryanston-Cross, P.

Chang, N.-A.

Chi, W.

Chiang, F. P.

Claus, D.

Dainty, J. C.

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, Vol. XIV (North-Holland, 1976).

Ferreira, C.

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

Garcia, J.

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

George, N.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed.(McGraw-Hill, 1966).

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, Speckle Phenomena in Optics (Roberts and Company, 2007).

Gopinathan, U.

Gori, F.

F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
[CrossRef]

Gougeon, S.

Guo, C.-S.

C.-S. Guo, L. Zhang, Z.-Y. Rong, and H.-T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers “frequency analysis of digital holography” and “frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 42, 2768–2771 (2003).
[CrossRef]

Han, B.

Han, G.-S.

Hanson, S. G.

Hao, Y.

Healy, J. J.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5d imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

Hennelly, B. M.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5d imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[CrossRef]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O’Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861–2870 (2006).
[CrossRef]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Hernández, C.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

Iliescu, D.

Illueca, C.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

Javidi, B.

Jin, H.

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Juptner, W. P. O.

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

Jüptner, W.

Kelly, D. P.

D. Li, D. P. Kelly, R. Kirner, and J. T. Sheridan, “Speckle orientation in paraxial optical systems,” Appl. Opt. 51, A1–A10 (2012).
[CrossRef]

D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. part i. theory and numerical investigation,” J. Opt. Soc. Am. A 28, 1896–1903 (2011).
[CrossRef]

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5d imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. part ii. experimental investigation,” J. Opt. Soc. Am. A 28, 1904–1908 (2011).
[CrossRef]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[CrossRef]

D. P. Kelly, J. E. Ward, U. Gopinathan, and J. T. Sheridan, “Controlling speckle using lenses and free space,” Opt. Lett. 32, 3394–3396 (2007).
[CrossRef]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O’Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861–2870 (2006).
[CrossRef]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

J. Sheridan and D. P. Kelly, “Opto-numeric systems: lenses and pixels,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), p. DTu3C.2.

Kim, S.-W.

Kirchner, M.

Kirner, R.

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

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]

Leclercq, M.

Lehmann, M.

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

Leushacke, L.

Leval, J.

Li, D.

Li, Q. B.

Li, Y.

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Marinho, F.

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

Mas, D.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

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

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

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

Miret, J. J.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

Mounier, D.

Naughton, T. J.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[CrossRef]

O’Neill, F. T.

Onural, L.

L. Onural, “Exact analysis of the effects of sampling of the scalar diffraction field,” J. Opt. Soc. Am. A 24, 359–367(2007).
[CrossRef]

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations,” Opt. Eng. 43, 2557–2563 (2004).
[CrossRef]

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

Pandey, N.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[CrossRef]

Pérez, J.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

Picart, P.

Qiu, P.

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Rong, Z.-Y.

C.-S. Guo, L. Zhang, Z.-Y. Rong, and H.-T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers “frequency analysis of digital holography” and “frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 42, 2768–2771 (2003).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Juptner, “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]

Sheridan, J.

J. Sheridan and D. P. Kelly, “Opto-numeric systems: lenses and pixels,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), p. DTu3C.2.

Sheridan, J. T.

Stern, A.

A. Stern, “Sampling of linear canonical transformed signals,” Signal Process. 86, 1421–1425 (2006).
[CrossRef]

A. Stern 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]

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250 (2004).
[CrossRef]

Vázquez, C.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, “Fast numerical calculation of Fresnel patterns in convergent systems,” Opt. Commun. 227, 245–258(2003).
[CrossRef]

Wan, H.

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Wang, H.-T.

C.-S. Guo, L. Zhang, Z.-Y. Rong, and H.-T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers “frequency analysis of digital holography” and “frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 42, 2768–2771 (2003).
[CrossRef]

Wang, Z.

Ward, J. E.

Yamaguchi, I.

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

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

Yura, H. T.

Zhang, L.

C.-S. Guo, L. Zhang, Z.-Y. Rong, and H.-T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the papers “frequency analysis of digital holography” and “frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 42, 2768–2771 (2003).
[CrossRef]

Zhang, T.

Zhang, Y.

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Appl. Opt. (8)

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]

J. Eur. Opt. Soc. Rapid Pub. (1)

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5d imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

J. Mod. Opt. (1)

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, “The influence of structural parameters of ccd on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

J. Opt. Soc. Am. A (9)

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O’Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861–2870 (2006).
[CrossRef]

D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. part i. theory and numerical investigation,” J. Opt. Soc. Am. A 28, 1896–1903 (2011).
[CrossRef]

D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. part ii. experimental investigation,” J. Opt. Soc. Am. A 28, 1904–1908 (2011).
[CrossRef]

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