Abstract

We present a new method to numerically reconstruct images on a tilted plane by digital holography in Fourier configuration. The proposed technique is based on a quadratic deformation of spatial coordinates of the digital hologram. By this approach we demonstrate that it is possible to recover the extended focus image (EFI) of a tilted object in a single reconstruction step from the deformed hologram.

© 2009 OSA

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  1. W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
    [CrossRef]
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    [CrossRef] [PubMed]
  3. Z. Zalevsky and S. Ben-Yaish, “Extended depth of focus imaging with birefringent plate,” Opt. Express 15(12), 7202–7210 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7202 .
    [CrossRef] [PubMed]
  4. G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express 15(15), 9184–9193 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-15-9184 .
    [CrossRef] [PubMed]
  5. H. Zhao, Q. Li, and H. Feng, “Improved logarithmic phase mask to extend the depth of field of an incoherent imaging system,” Opt. Lett. 33(11), 1171–1173 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ol-33-11-1171 .
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free View 3-D Visualization of Occluded Objects by using Computational Synthetic Aperture Integral Imaging,” J. Disp. Technol. 3(1), 64–70 (2007).
    [CrossRef]
  10. Y. Takaki and H. Ohzu, “Hybrid holographic microscopy: visualization of three-dimensional object information by use of viewing angles,” Appl. Opt. 39(29), 5302–5308 (2000).
    [CrossRef]
  11. E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15(4), 601–612 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. S. J. Jeong and C. K. Hong, “Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method,” Appl. Opt. 47(16), 3064–3071 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ao-47-16-3064 .
    [CrossRef] [PubMed]
  20. K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47(19), D110–D116 (2008).
    [CrossRef] [PubMed]
  21. C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008).
    [CrossRef] [PubMed]
  22. D. Leseberg, C. Frère,, and Detlef Leseberg and Christian Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-14-3020 .
    [CrossRef] [PubMed]
  23. P. Ferraro, M. Paturzo, P. Memmolo and A. Finizio, “Controlling depth-of-focus in 3D image reconstructions by flexible and adaptive deformation of digital holograms,” Opt. Lett. 34, 2787-2789 (2009).
    [CrossRef] [PubMed]

2009 (1)

2008 (7)

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(19), D12–D20 (2008).
[CrossRef] [PubMed]

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008).
[CrossRef] [PubMed]

S. Bagheri and B. Javidi, “Extension of depth of field using amplitude and phase modulation of the pupil function,” Opt. Lett. 33(7), 757–759 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ol-33-7-757 .
[CrossRef] [PubMed]

K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47(19), D110–D116 (2008).
[CrossRef] [PubMed]

H. Zhao, Q. Li, and H. Feng, “Improved logarithmic phase mask to extend the depth of field of an incoherent imaging system,” Opt. Lett. 33(11), 1171–1173 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ol-33-11-1171 .
[CrossRef] [PubMed]

S. J. Jeong and C. K. Hong, “Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method,” Appl. Opt. 47(16), 3064–3071 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ao-47-16-3064 .
[CrossRef] [PubMed]

M. Antkowiak, N. Callens, C. Yourassowsky, and F. Dubois, “Extended focused imaging of a microparticle field with digital holographic microscopy,” Opt. Lett. 33(14), 1626–1628 (2008).
[CrossRef] [PubMed]

2007 (4)

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free View 3-D Visualization of Occluded Objects by using Computational Synthetic Aperture Integral Imaging,” J. Disp. Technol. 3(1), 64–70 (2007).
[CrossRef]

Z. Zalevsky and S. Ben-Yaish, “Extended depth of focus imaging with birefringent plate,” Opt. Express 15(12), 7202–7210 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7202 .
[CrossRef] [PubMed]

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express 15(15), 9184–9193 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-15-9184 .
[CrossRef] [PubMed]

2006 (1)

2005 (2)

2004 (2)

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet sparsity criterion,” J. Opt. Soc. Am. A 21(12), 2424–2430 (2004).
[CrossRef]

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15(4), 601–612 (2004).
[CrossRef]

2003 (1)

2000 (1)

1995 (1)

1988 (1)

1983 (1)

Abras, J. N.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15(4), 601–612 (2004).
[CrossRef]

Alfieri, D.

Antkowiak, M.

Bagheri, S.

Basiji, D. A.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Ben-Yaish, S.

Callens, N.

Cathey, W. T.

Coppola, G.

De Nicola, S.

Dowski, E. R.

Dubois, F.

Feng, H.

Ferraro, P.

Finizio, A.

Frère,, C.

Frost, K.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Grilli, S.

Hall, B. E.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Hennelly, B. M.

Hong, C. K.

Hong, S.-H.

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free View 3-D Visualization of Occluded Objects by using Computational Synthetic Aperture Integral Imaging,” J. Disp. Technol. 3(1), 64–70 (2007).
[CrossRef]

Hwang, Y. S.

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free View 3-D Visualization of Occluded Objects by using Computational Synthetic Aperture Integral Imaging,” J. Disp. Technol. 3(1), 64–70 (2007).
[CrossRef]

Jaroszewicz, Z.

Javidi, B.

Jeong, S. J.

Kanka, M.

Katz, J.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15(4), 601–612 (2004).
[CrossRef]

Kolodziejczyk, A.

Korpel, A.

Kreuzer, H. J.

Leseberg, D.

Li, Q.

Liang, L.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Liebling, M.

Malkiel, E.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15(4), 601–612 (2004).
[CrossRef]

Matsushima, K.

McElhinney, C. P.

Mikula, G.

Naughton, T. J.

Ohzu, H.

Ortyn, W. E.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Osten, W.

Pedrini, G.

Perry, D. J.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Petelczyc, K.

Pieper, R. J.

Pierattini, G.

Riesenberg, R.

Schockaert, C.

Striano, V.

Sypek, M.

Takaki, Y.

Unser, M.

Venkatachalam, V.

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

Wang, D.

Yourassowsky, C.

Zalevsky, Z.

Zhang, F.

Zhao, H.

Zhao, J.

Appl. Opt. (8)

R. J. Pieper and A. Korpel, “Image processing for extended depth of field,” Appl. Opt. 22(10), 1449–1453 (1983).
[CrossRef] [PubMed]

E. R. Dowski and W. T. Cathey, “Extended depth of field through wavefront coding,” Appl. Opt. 34(11), 1859–1866 (1995).
[CrossRef] [PubMed]

D. Leseberg, C. Frère,, and Detlef Leseberg and Christian Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-14-3020 .
[CrossRef] [PubMed]

Y. Takaki and H. Ohzu, “Hybrid holographic microscopy: visualization of three-dimensional object information by use of viewing angles,” Appl. Opt. 39(29), 5302–5308 (2000).
[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(19), D12–D20 (2008).
[CrossRef] [PubMed]

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008).
[CrossRef] [PubMed]

K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47(19), D110–D116 (2008).
[CrossRef] [PubMed]

S. J. Jeong and C. K. Hong, “Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method,” Appl. Opt. 47(16), 3064–3071 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=ao-47-16-3064 .
[CrossRef] [PubMed]

Cytometry A (1)

W. E. Ortyn, D. J. Perry, V. Venkatachalam, L. Liang, B. E. Hall, K. Frost, and D. A. Basiji, “Extended depth of field imaging for high speed cell analysis,” Cytometry A 71A(4), 215–231 (2007), http://dx.doi.org/10.1002/cyto.a.20370 .
[CrossRef]

J. Disp. Technol. (1)

Y. S. Hwang, S.-H. Hong, and B. Javidi, “Free View 3-D Visualization of Occluded Objects by using Computational Synthetic Aperture Integral Imaging,” J. Disp. Technol. 3(1), 64–70 (2007).
[CrossRef]

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

Meas. Sci. Technol. (1)

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15(4), 601–612 (2004).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Other (1)

P. Ferraro, M. Paturzo, P. Memmolo and A. Finizio, “Controlling depth-of-focus in 3D image reconstructions by flexible and adaptive deformation of digital holograms,” Opt. Lett. 34, 2787-2789 (2009).
[CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: AVI (3084 KB)     

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Figures (4)

Fig. 1
Fig. 1

Experimental set-up: BS, beam splitter; MO, microscope objectives; PH, pinhole.

Fig. 2
Fig. 2

Numerical reconstruction of the holograms for an object tilted with an angle of 55 degrees as acquired by the CCD (Movie_1).

Fig. 3
Fig. 3

Numerical reconstruction of the holograms for an object tilted with an angle of 55 degrees after the quadratic deformation.

Fig. 4
Fig. 4

Numerical reconstruction of the holograms for an object tilted with an angle of 75 degrees as acquired by the CCD (a) and after the quadratic deformation (b).

Equations (8)

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

h(ξ,η)=f(aξ,aη)
h^(x,y)=1af^(xa,ya)
D=L(1+2αl')
h(x)=g(f(x))=G(l)ei2πlf(x)dl
h^(k)=ei2πkxG(l)ei2πlf(x)dldx
=G(l)P(k,l)dl
h^(k)=G(l)P(k,l)dl=eiπ4G(l)12αlei2π(kl)24αldl
[00100100α000]

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