Abstract

This paper proposes an all-numerical robust method to compensate for the chromatic aberrations induced by the optical elements in digital color holographic imaging. It combines a zero-padding algorithm and a convolution approach with adjustable magnification, using a single recording of a reference rectangular grid. Experimental results confirm and validate the proposed approach.

© 2013 Optical Society of America

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References

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  1. S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express15(15), 9394–9402 (2007).
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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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett.29(14), 1668–1670 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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  25. 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(8), 854–856 (2004).
    [CrossRef] [PubMed]
  26. P. Tankam and P. Picart, “Use of digital color holography for crack investigation in electronic components,” Opt. Lasers Eng.49(11), 1335–1342 (2011).
    [CrossRef]
  27. P. V. C. Hough, Method and means for recognizing complex patterns, US Patent 3069654 (1960).

2013 (3)

2012 (2)

J. Garcia-Sucerquia, “Color lensless digital holographic microscopy with micrometer resolution,” Opt. Lett.37(10), 1724–1726 (2012).
[CrossRef] [PubMed]

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

2011 (2)

2010 (3)

2009 (2)

2008 (3)

2007 (1)

2006 (1)

2005 (1)

2004 (2)

2002 (1)

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002).
[CrossRef]

2001 (1)

S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001).
[CrossRef]

2000 (1)

1996 (1)

U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng.35(4), 977–982 (1996).
[CrossRef]

Alfieri, D.

Aspert, N.

Awatsuji, Y.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Baumbach, T.

S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001).
[CrossRef]

Bieda, M.

Bingham, P. R.

Bourquin, S.

Charrière, F.

Colomb, T.

Coppola, G.

Cuche, E.

De Nicola, S.

Denicola, S.

Depeursinge, C.

Desse, J.-M.

Ferraro, P.

Finizio, A.

Garcia-Sucerquia, J.

Grilli, S.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol.4(1), 97–100 (2008).
[CrossRef]

S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett.30(20), 2706–2708 (2005).
[CrossRef] [PubMed]

Ito, Y.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Javidi, B.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol.4(1), 97–100 (2008).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express15(15), 9394–9402 (2007).
[CrossRef] [PubMed]

Juptner, W.

S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001).
[CrossRef]

Jüptner, W. O.

U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng.35(4), 977–982 (1996).
[CrossRef]

Kakue, T.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Karray, M.

Kim, M. K.

Kolodziejczyk, A.

Kowalczyk, A.

Kreis, T.

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng.49(12), 125801 (2010).
[CrossRef]

Kreis, T. M.

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002).
[CrossRef]

U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng.35(4), 977–982 (1996).
[CrossRef]

Kubota, T.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Kühn, J.

Leval, J.

Li, J. C.

Makowski, M.

Mann, C. J.

Marian, A.

Marquet, P.

Massig, J. H.

Matoba, O.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Miccio, L.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol.4(1), 97–100 (2008).
[CrossRef]

Montfort, F.

Mounier, D.

Mundt, J.

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng.49(12), 125801 (2010).
[CrossRef]

Nishio, K.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Osten, W.

S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001).
[CrossRef]

Paquit, V. C.

Peng, Z. J.

Picart, P.

Pierattini, G.

Restrepo, J. F.

Sansone, L.

Schnars, U.

U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng.35(4), 977–982 (1996).
[CrossRef]

Seebacher, S.

S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001).
[CrossRef]

Shimozato, Y.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Song, Q.

Stadelmaier, A.

Sypek, M.

Tahara, T.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Tankam, P.

Tobin, K. W.

Ura, S.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Xia, P.

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011).
[CrossRef] [PubMed]

Yamaguchi, I.

Yaroslavsky, L. P.

Yeom, S.

Zhang, F.

Appl. Opt. (4)

J. Disp. Technol. (2)

Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012).
[CrossRef]

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol.4(1), 97–100 (2008).
[CrossRef]

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

Opt. Eng. (3)

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002).
[CrossRef]

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng.49(12), 125801 (2010).
[CrossRef]

U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng.35(4), 977–982 (1996).
[CrossRef]

Opt. Express (4)

Opt. Lasers Eng. (2)

P. Tankam and P. Picart, “Use of digital color holography for crack investigation in electronic components,” Opt. Lasers Eng.49(11), 1335–1342 (2011).
[CrossRef]

S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001).
[CrossRef]

Opt. Lett. (7)

A. Stadelmaier and J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett.25(22), 1630–1632 (2000).
[CrossRef] [PubMed]

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(8), 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(14), 1668–1670 (2004).
[CrossRef] [PubMed]

S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett.30(20), 2706–2708 (2005).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, “Color lensless digital holographic microscopy with micrometer resolution,” Opt. Lett.37(10), 1724–1726 (2012).
[CrossRef] [PubMed]

P. Tankam, Q. Song, M. Karray, J. C. Li, J.-M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett.35(12), 2055–2057 (2010).
[CrossRef] [PubMed]

J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett.34(5), 572–574 (2009).
[CrossRef] [PubMed]

Other (3)

P. V. C. Hough, Method and means for recognizing complex patterns, US Patent 3069654 (1960).

R. Kingslake, Lens Design Fundamentals, (Academic Pr, 1978).

F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed., (McGraw-Hill, Inc., 1981).

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Figures (9)

Fig. 1
Fig. 1

Basic scheme for digital color holography using 3 wavelengths

Fig. 2
Fig. 2

Origins of chromatism in a digital color holographic set-up, (a) the negative lens in front of the sensor brings a shift in the positions and sizes of the virtual images, (b) a small misalignment of the three color-beams in the reference wave brings a spatial shift in the reconstruction of the images

Fig. 3
Fig. 3

Three reconstructed images, from left to right: λ = 457, 532 and 660nm respectively

Fig. 4
Fig. 4

Three reconstructed images superposed without any correction

Fig. 5
Fig. 5

Three reconstructed images superposed using the convolution algorithm with correction of the lateral shift only

Fig. 6
Fig. 6

Hough Transform of the reconstructed green image of the grid in the polar coordinates; the white squares circle the intersection points, indicating all the real lines

Fig. 7
Fig. 7

Three images superposed after the adjustable magnification and the lateral shift corrections

Fig. 8
Fig. 8

From left to right: color photography, the superposition of the non-corrected reconstructed images, and the superposition of the corrected reconstructed images of a yellow and pink mask

Fig. 9
Fig. 9

From left to right: color photography, the superposition of the non-corrected reconstructed images, and the superposition of the corrected reconstructed images of a green and purple mask

Tables (2)

Tables Icon

Table 1 Experimental results for the parameters used in the modified zero-padding algorithm

Tables Icon

Table 2 Size and magnification parameters estimated using the Hough transform

Equations (16)

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

A r ( x,y,d )= id λ c + + H( X,Y )w( X,Y, λ c , R c ) × exp[ 2iπ/ λ c d 2 + ( Xx ) 2 + ( Yy ) 2 ] d 2 + ( Xx ) 2 + ( Yy ) 2 dXdY
A r ( x,y,d )= iexp( 2iπd/λ ) λd exp[ iπ λd ( x 2 + y 2 ) ]× k=K/2 k=K/21 l=L/2 l=L/21 H(l p x, k p y )exp[ iπ λd ( l 2 p x 2 + k 2 p y 2 ) ]× exp[ 2iπ λd ( l p x x+k p y y ) ]
A r =F T 1 [ FT[ H×w ]×G ]
G( u,v,d )={ exp[ 2iπd/λ 1λ 2 ( u u 0 λ ) 2 λ 2 ( v v 0 λ ) 2 ] if| u u 0 λ |L p x /2λdand| v v 0 λ |K p y /2λd 0elsewhere
γ= d r d 0
Δd= p ' R 2 ν×f'
Δy'=y ' R Δ γ opt γ opt Δd p ' R
{ u 0 λ = sin θ x λ λ v 0 λ = sin θ y λ λ
Δη( λ )= λ d r λ K λ p x =constant
K λ 1 = λ 1 d r λ 1 λ 2 d r λ 2 K λ 2 , K λ Ν
{ d r λ 1 d r λ 2 = d 0 λ 1 d 0 λ 2 d r λ 1 + d r λ 2 = d 0 λ 1 + d 0 λ 2
K λ 1 = λ 1 d 0 λ 1 λ 2 d 0 λ 2 K λ 2 , K λ Ν
{ d r λ 1 = d 0 λ 1 + d 0 λ 2 1+ K λ 2 * λ 1 K λ1 * λ 2 d r λ 2 = d 0 λ 1 + d 0 λ 2 d r λ 1
{ K λ 3 * = λ 3 d 0 λ 3 λ 2 d 0 λ 2 K λ 2 * d r λ 3 = λ 2 K λ 3 * λ 3 K λ 2 * d r λ 2
d r 'λ =Γ(λ) d 0 λ
{ u 0 'λ = u 0 λ + Δ X λ λ d 0 λ v 0 'λ = v 0 λ + Δ Y λ λ d 0 λ

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