Abstract

We propose a numerical method to obtain complex amplitude distribution of a three-dimensional (3D) object from a digital hologram. The method consists of two processes. The first process is to measure simultaneously a hologram of the 3D object and an object intensity distribution by two image sensors. These intensity distributions give us the amplitude and absolute value of phase of the 3D object at the image sensor plane. The second process is the determination of phase distribution by a proposed iterative process based on the criterion that the reconstructed 3D object is in focus and its conjugate reconstruction is out of focus. Numerical and experimental results show the effectiveness of the proposed method.

© 2007 Optical Society of America

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References

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  1. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  2. T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).
  3. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
    [CrossRef]
  4. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]
  5. Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
    [CrossRef]
  6. M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.
  7. Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, "Parallel three-step phase-shifting digital holography," Appl. Opt. 45, 2995-3002 (2006).
    [CrossRef] [PubMed]
  8. T. Nomura, S. Murata, E. Nitanai, and T. Numata, "Phase-shifting digital holography with a phase difference between orthogonal polarizations," Appl. Opt. 45, 4873-4877 (2006).
    [CrossRef] [PubMed]
  9. D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
    [CrossRef]

2006

2005

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).

2004

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

1997

1995

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

1982

Awatsuji, Y.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, "Parallel three-step phase-shifting digital holography," Appl. Opt. 45, 2995-3002 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Bernardo, L. B.

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

Fereira, C.

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

Fujii, A.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, "Parallel three-step phase-shifting digital holography," Appl. Opt. 45, 2995-3002 (2006).
[CrossRef] [PubMed]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Garcia, J.

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

Ina, H.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Kobayashi, S.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).

Kubota, T.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, "Parallel three-step phase-shifting digital holography," Appl. Opt. 45, 2995-3002 (2006).
[CrossRef] [PubMed]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

Marinho, F.

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

Mas, D.

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

Matoba, O.

Murata, S.

Nitanai, E.

Nomura, T.

Numata, T.

Sasada, M.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Takeda, M.

Yamaguchi, I.

Zhang, T.

Appl. Opt.

Appl. Phys. Lett.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

D. Mas, J. Garcia, C. Fereira, L. B. Bernardo, and F. Marinho, "Fast algorithms for free-space calculation," Opt. Commun. 164, 233-245 (1995).
[CrossRef]

Opt. Lett.

Other

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by simple optical setup and effective use of image-sensor pixels," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).

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Figures (8)

Fig. 1
Fig. 1

(Color online) Schematic of the proposed optical setup for recording simultaneously two intensity distributions: BE, beam expander; BS, beam splitter; HWP, half-wave plate; PBS, polarized beam splitter; P, polarizer.

Fig. 2
Fig. 2

Block diagram of the proposed iterative algorithm.

Fig. 3
Fig. 3

Numerical results. (a) Object used in the simulation, (b) a part of the enlarged object, and (c) and (d) the reconstructed images before and after the iterative algorithm, respectively.

Fig. 4
Fig. 4

(Color online) Error of estimated phase sign as a function of number of iterations.

Fig. 5
Fig. 5

(Color online) Minimum error of estimated phase sign as a function of threshold value.

Fig. 6
Fig. 6

(Color online) Relationship between the error and the position error in the reconstruction.

Fig. 7
Fig. 7

(Color online) Experimental setup: BE, beam expander; BS, beam splitter; M, mirror; S, shutter; P, polarizer; LC-SLM, liquid crystal-spatial light modulator.

Fig. 8
Fig. 8

Experimental results. (a) Object used in the experiment, and (b) and (c) the reconstructed images before and after the iterative algorithm, respectively.

Equations (36)

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

I 1
I 2
U ( x , y ) = A ( x , y ) exp { i Φ ( x , y ) }
U r = A r exp ( i Φ r )
I 1
I 2
I 1 ( x , y ) = A ( x , y ) 2 + A r 2 + 2 A ( x , y ) A r cos { Φ ( x , y ) Φ r } ,
I 2 ( x , y ) = A ( x , y ) 2 .
A r
Φ r
U 0 = A 0 exp ( i Φ 0 )
A 0 ( x , y ) = I 2 ( x , y ) ,
Φ 0 ( x , y ) = cos 1 ( I 1 ( x , y ) I 2 ( x , y ) A r 2 2 I 2 A r ) .
U k
U 0
u k
U k
u k
u k
U k
u k
U k
U k
U k + 1
1024 × 1024   pixels
λ = 0.532   μm
N = 1024 × 1024
16.4   μm × 16 .4   μm
300   mm
Error = k N | sgn ( Φ k ) sgn ( Φ ) | 2 N ,
Φ k
U k
λ = 532   nm
512 × 512
16   μm × 16   μm
386   mm

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