Abstract

We present an improved method for recording a synthesized Fourier hologram under incoherent white-light illumination. The advantage of the method is that the number of real projections needed for generating the hologram is significantly reduced. The new method, designated as synthetic projection holography, is demonstrated experimentally. We show that the synthetic projection holography barely affects the reconstructed images. However, by increasing the number of observed projections one can improve the synthetic projection hologram quality.

©2007 Optical Society of America

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References

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  1. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1269 (1997).
    [Crossref] [PubMed]
  2. Y. Li, D. Abookasis, and J. Rosen, “Computer-generated holograms of three-dimensional realistic objects recorded without wave interference,” Appl. Opt. 40, 2864–2870 (2001).
    [Crossref]
  3. D. Abookasis and J. Rosen, “Computer-generated holograms of three-dimensional objects synthesized from their multiple angular viewpoints,” J. Opt. Soc. Am. A 20, 1537–1545 (2003).
    [Crossref]
  4. Y. Sando, M. Itoh, and T. Yatagai, “Holographic three-dimensional display synthesized from three-dimensional Fourier spectra of real existing objects,” Opt. Lett. 28, 2518–2520 (2003).
    [Crossref] [PubMed]
  5. Y. Sando, M. Itoh, and T. Yatagai, “Full-color computer-generated holograms using 3-D Fourier spectra,” Opt. Express,  12, 6246–6251 (2004).
    [Crossref] [PubMed]
  6. N. T. Shaked, J. Rosen, and A. Stern, “Integral holography: white-light single-shot hologram acquisition,” Opt. Express 15, 5754–5760 (2007).
    [Crossref] [PubMed]
  7. D. Scharstein, “View Synthesis using Stereo Vision” Lecture Notes in Computer Science (LNCS) (Springer-Verlag, 1999) 1583, Chap. 2.
  8. J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
    [Crossref]
  9. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5.

2007 (1)

2006 (1)

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
[Crossref]

2004 (1)

2003 (2)

2001 (1)

1997 (1)

Abookasis, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5.

Hwang, D.-C.

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
[Crossref]

Itoh, M.

Kim, E.-S.

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
[Crossref]

Li, Y.

Park, J.-S.

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
[Crossref]

Rosen, J.

Sando, Y.

Scharstein, D.

D. Scharstein, “View Synthesis using Stereo Vision” Lecture Notes in Computer Science (LNCS) (Springer-Verlag, 1999) 1583, Chap. 2.

Shaked, N. T.

Shin, D.-H.

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
[Crossref]

Stern, A.

Yamaguchi, I.

Yatagai, T.

Zhang, T.

Appl. Opt. (1)

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

Opt. Eng. (1)

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Enhanced-resolution computational integral imaging reconstruction using an intermediate-view reconstruction technique,” Opt. Eng. 45, 1170041–1170047 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5.

D. Scharstein, “View Synthesis using Stereo Vision” Lecture Notes in Computer Science (LNCS) (Springer-Verlag, 1999) 1583, Chap. 2.

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Figures (6)

Fig. 1.
Fig. 1. Illustration of the view synthesis algorithm.

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Fig. 2.
Fig. 2. Results of the different steps in the view synthesis algorithm. Two observed projections (a) and (b), their two images of vertical edges (c) and (d), the warped images (e) and (f) and the final middle synthesized projection (g).

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Fig. 3.
Fig. 3. Illustration of the proposed method.

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Fig.4.
Fig.4. Magnitude (a) and phase (b) of the complex amplitude of the object’s 1-D Fourier transform obtained from the set of the fully observed projections.

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Fig. 5.
Fig. 5. Best in-focus reconstructed planes (a, b and c) obtained from the fully-observed hologram; planes (d, e and f) obtained from SPH with 2 observed projections and planes (g, h and i) obtained from SPH with 55 observed projections.

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Fig. 6.
Fig. 6. MSE versus the number of observed projections.

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Equations (4)

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PW 1 ( x + ⌊ 1 2 + D N × C 1 x y ⌋ , y ) = ( 1 − D N ) × P 1 O x y
PW 2 ( x − ⌊ 1 2 + ( 1 − D N ) × C 2 x y ⌋ , y ) = D N × P 2 O x y ,
MSE = 1 M ∙ K ∑ i = 1 M ∑ j = 1 K [ P i j − β ∙ P ˜ i j ] 2 ,
β = [ ∑ i = 1 M ∑ j = 1 K P i j ∙ P ˜ i j ] ∑ i = 1 M ∑ j = 1 K P ˜ i j ∙ P ˜ i j

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