Abstract

We discuss a method to record and reconstruct color holograms by using a stack of photodiode sensors associated to a one-way reference beam. The reconstruction algorithm follows a convolution strategy in which a transverse magnification leads to the full reconstruction of the object in the reconstructed horizon. The transverse magnification of the object depends on the curvature of the reference wave. Analysis of the spatial resolution indicates that it is linked to the transversal magnification but that no extra information is gained or lost in the process. Experimental results confirm the validity of the proposed approach for two-color digital holography. The error due to spectral mixing is investigated and found to be quite irrelevant compared to the range of the phase measurement.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  2. 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).
  3. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994).
    [CrossRef] [PubMed]
  4. I. Yamaguchi, T. Matsumura, and J. Kato, “Phase shifting color digital holography,” Opt. Lett. 27, 1108-1110(2002).
    [CrossRef]
  5. D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113-116 (2006).
    [CrossRef]
  6. J. Zhao, H. Jiang, and J. Di, “Recording and reconstruction of a color holographic image by using digital lensless Fourier transform holography,” Opt. Express 16, 2514-2519(2008).
    [CrossRef] [PubMed]
  7. N. Demoli, D. Vukicevic, and M. Torzynski, “Dynamic digital holographic interferometry with three wavelengths,” Opt. Express 11, 767-774 (2003).
    [CrossRef] [PubMed]
  8. J. M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471-5480 (2008).
    [CrossRef] [PubMed]
  9. B. Javidi, P. Ferraro, S. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144-146 (2005).
    [CrossRef] [PubMed]
  10. J. Kuhn, T. Colomb, F. Montfort, F. Charriere, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231-7242 (2007).
    [CrossRef] [PubMed]
  11. P. Picart, D. Mounier, and J. M. Desse, “High resolution digital two-color holographic metrology,” Opt. Lett. 33, 276-278(2008).
    [CrossRef] [PubMed]
  12. P. Picart, P. Tankam, D. Mounier, Z. Peng, and J. C. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express 17, 9145-9156 (2009).
    [CrossRef] [PubMed]
  13. 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]
  14. C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16, 9753-9764 (2008).
    [CrossRef] [PubMed]
  15. A. Khmaladze, M. Kim, and C.-M. Lo, “Phase imaging of cells by simultaneous dual-wavelength reflection digital holography,” Opt. Express 16, 10900-10911 (2008).
    [CrossRef] [PubMed]
  16. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  17. J. C. Li, P. Tankam, Z. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. 34, 572-574(2009).
    [CrossRef] [PubMed]
  18. J. C. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280, 243-248 (2007).
    [CrossRef]
  19. 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]
  20. L. Yu and M. K. Kim, “Pixel resolution control in numerical reconstruction of digital holography,” Opt. Lett. 31, 897-899(2006).
    [CrossRef] [PubMed]
  21. 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]
  22. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and application to microscopy,” Appl. Opt. 40, 6177-6186 (2001).
    [CrossRef]
  23. P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, “Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms,” Opt. Eng. 43, 1169-1176 (2004).
    [CrossRef]
  24. T. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224-233(1997).
    [CrossRef]

2009

2008

2007

2006

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113-116 (2006).
[CrossRef]

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

2005

2004

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]

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, “Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms,” Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

2003

2002

2001

1997

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

1994

1972

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

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

Alfieri, D.

Berthelot, J.-M.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, “Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms,” Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Bingham, P. R.

Charriere, F.

Colomb, T.

Coppola, G.

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113-116 (2006).
[CrossRef]

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]

Cuche, E.

De Nicola, S.

Demoli, N.

Depeursinge, C.

Desse, J. M.

Di, J.

Diouf, B.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, “Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms,” Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Emery, Y.

Ferraro, P.

Finizio, A.

Fu, Y.

J. C. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280, 243-248 (2007).
[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, 2nd ed. (McGraw-Hill, 1996).

Hong, S.

Javidi, B.

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113-116 (2006).
[CrossRef]

B. Javidi, P. Ferraro, S. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144-146 (2005).
[CrossRef] [PubMed]

Jiang, H.

Jüptner, W.

T. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224-233(1997).
[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.

Khmaladze, A.

Kim, M.

Kim, M. K.

Kreis, T.

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

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).

Kuhn, J.

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]

Leval, J.

Li, J. C.

Lo, C.-M.

Lolive, E.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, “Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms,” Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Mann, C. J.

Marquet, P.

Matsumura, T.

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).

Mizuno, J.

Montfort, F.

Mounier, D.

Ohta, S.

Paquit, V. C.

Peng, Z.

Picart, P.

Pierattini, G.

Schnars, U.

Tankam, P.

Tobin, K. W.

Torzynski, M.

Vukicevic, D.

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).

Yu, L.

Zhao, J.

Appl. Opt.

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]

J. Opt. Soc. Am. A

Opt. Commun.

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113-116 (2006).
[CrossRef]

J. C. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280, 243-248 (2007).
[CrossRef]

Opt. Eng.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, “Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms,” Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

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

Sov. Phys. Tech. Phys.

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).

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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 (15)

Fig. 1
Fig. 1

Methods for simultaneous recording of color holograms.

Fig. 2
Fig. 2

Profile of resolution function with γ = 1.5 and ( K , L ) = ( 1024 , 1024 ) .

Fig. 3
Fig. 3

Profile of resolution function with γ = 1.5 and ( K , L ) = ( 2048 , 2048 ) .

Fig. 4
Fig. 4

Profile of resolution function with γ = 0.5 and ( K , L ) = ( 1024 , 1024 ) .

Fig. 5
Fig. 5

Two-color experimental setup with one-way reference beam (SF, spatial filter).

Fig. 6
Fig. 6

Spatial frequency spectrum of the red hologram (within circle, limits of the spatial bandwidth of the Fresnel transfer function).

Fig. 7
Fig. 7

Spatial frequency spectrum of the green hologram (within circle, limits of the spatial bandwidth of the Fresnel transfer function).

Fig. 8
Fig. 8

Green (left) and red (right) objects re constructed with the proposed method, with the resulting color hologram.

Fig. 9
Fig. 9

Red wrapped phase change computed from two reconstructed red objects.

Fig. 10
Fig. 10

Green wrapped phase change computed from two reconstructed green objects.

Fig. 11
Fig. 11

In-plane displacement field computed from the two unwrapped phase maps.

Fig. 12
Fig. 12

Out-of-plane displacement field computed from the two unwrapped phase maps.

Fig. 13
Fig. 13

R and G phase map errors computed from the unwrapped phase maps.

Fig. 14
Fig. 14

Probability density function of the red error (solid curve, measured; dashed curve, Gaussian fit).

Fig. 15
Fig. 15

Probability density function of the green error (solid curve, measured; dashed curve, Gaussian fit).

Equations (15)

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

H λ ( x , y ) = O 0 ( x , y ) + r ( x , y ) O * ( x , y ) + r * ( x , y ) O ( x , y ) ,
O ( x , y , d 0 ) = i exp ( i 2 π d 0 / λ ) λ d 0 exp [ i π λ d 0 ( x 2 + y 2 ) ] + + A ( x , y ) exp [ i π λ d 0 ( x 2 + y 2 ) ] exp [ 2 i π λ d 0 ( x x + y y ) ] d x d y ,
r ( x , y ) = a r exp [ 2 i π ( u 0 λ x + v 0 λ y ) + i π λ d s ( x 2 + y 2 ) ] ,
w ( x , y , λ c , R c ) = exp [ i π λ c R c ( x 2 + y 2 ) ] .
A + 1 R ( X , Y , d r ) = i exp ( 2 i π d r / λ c ) λ c d r exp [ i π λ c d r ( X 2 + Y 2 ) ] k = 0 k = K 1 l = 0 l = L 1 w ( l p x , k p y , λ c , R c ) r * ( l p x , k p y ) O ( l p x , k p y ) exp [ i π λ c d r ( l 2 p x 2 + k 2 p y 2 ) ] exp [ 2 i π λ c d r ( l X p x + k Y p y ) ] .
1 d r = λ c λ d s λ c λ d 0 + 1 R c .
γ = λ c λ d r d 0 .
H ˜ ( u , v , λ c , d r ) = { exp [ i π λ c d r ( ( u u 0 λ ) 2 + ( v v 0 λ ) 2 ) ] if    ( u u 0 λ ) 2 + ( v v 0 λ ) 2 γ Δ A / 2 λ c d r 0     elsewhere .
H ˜ ( u , v , λ c , d r ) = { exp [ i π λ c d r ( ( u u 0 λ ) 2 + ( v v 0 λ ) 2 ) ] if    | u u 0 λ | γ Δ A x / 2 λ c d r and | v v 0 λ | γ Δ A y / 2 λ c d r 0     elsewhere .
{ N p x 2 λ | d s | + γ Δ A x 2 λ c | d r | < | u 0 λ | M p y 2 λ | d s | + γ Δ A y 2 λ c | d r | < | v 0 λ | .
{ N p x 2 λ | d s | + Δ A x 2 λ d 0 < | u 0 λ | M p y 2 λ | d s | + Δ A y 2 λ d 0 < | v 0 λ | ,
| d s | sup { N p x d 0 2 λ d 0 | u 0 λ | Δ A x , M p y d 0 2 λ d 0 | v 0 λ | Δ A y } .
ρ x = λ c d r N p x = γ λ d 0 N p x = γ ρ x ,
ρ y = λ c d r M p y = γ λ d 0 M p y = γ ρ y ,
{ u x = + ( λ R Δ φ R λ G Δ φ G ) / 2 π sin ( θ ) u z = ( λ R Δ φ R + λ G Δ φ G ) / 2 π ( 1 + cos ( θ ) ) .

Metrics