Abstract

We propose and experimentally demonstrate a new reconstruction scheme for coherence holography using computer-generated phase-shift coherence holograms. A 3D object encoded into the spatial coherence function is reconstructed directly from a set of incoherently illuminated computer-generated holograms with numerically introduced phase shifts. Although a rotating ground glass is used to introduce spatially incoherent illumination, the phase-shifting portion of the system is simple and free from mechanically moving components.

© 2010 Optical Society of America

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References

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  3. W. Wang, H. Kozaki, J. Rosen, and M. Takeda, Appl. Opt. 41, 1962 (2002).
    [CrossRef] [PubMed]
  4. Z. Duan, Y. Miyamoto, and M. Takeda, Opt. Express 14, 12109 (2006).
    [CrossRef] [PubMed]
  5. J. Rosen and M. Takeda, Appl. Opt. 39, 4107 (2000).
    [CrossRef]
  6. W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. 10.
  8. J. W. Goodman, Statistical Optics, 1st ed. (Wiley, 1985), Chap. 5.
  9. Z. Liu, T. Gemma, J. Rosen, and M. Takeda, Proc. SPIE 5531, 220 (2004).
    [CrossRef]
  10. M. V. R. K. Murty, Appl. Opt. 3, 853 (1964).
    [CrossRef]
  11. P. Handel, IEEE Trans. Instrum. Meas. 49, 1189 (2000).
    [CrossRef]

2009 (1)

2006 (2)

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Z. Duan, Y. Miyamoto, and M. Takeda, Opt. Express 14, 12109 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, Proc. SPIE 5531, 220 (2004).
[CrossRef]

2002 (1)

2000 (2)

J. Rosen and M. Takeda, Appl. Opt. 39, 4107 (2000).
[CrossRef]

P. Handel, IEEE Trans. Instrum. Meas. 49, 1189 (2000).
[CrossRef]

1964 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. 10.

Duan, Z.

Ezawa, T.

Gemma, T.

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, Proc. SPIE 5531, 220 (2004).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley, 1985), Chap. 5.

Handel, P.

P. Handel, IEEE Trans. Instrum. Meas. 49, 1189 (2000).
[CrossRef]

Hanson, S. G.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Kozaki, H.

Liu, Z.

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, Proc. SPIE 5531, 220 (2004).
[CrossRef]

Miyamoto, Y.

Murty, M. V. R. K.

Naik, D. N.

Rosen, J.

Takeda, M.

Wang, W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. 10.

Appl. Opt. (3)

IEEE Trans. Instrum. Meas. (1)

P. Handel, IEEE Trans. Instrum. Meas. 49, 1189 (2000).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (1)

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Proc. SPIE (1)

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, Proc. SPIE 5531, 220 (2004).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. 10.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley, 1985), Chap. 5.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for reconstruction in coherence holography.

Fig. 2
Fig. 2

Phase-shifted coherence holograms.

Fig. 3
Fig. 3

Interference images corresponding to the phase-shifted holograms shown in Fig. 2.

Fig. 4
Fig. 4

Reconstructed images: (a) shows the fringe contrast and (b) shows the fringe phase jointly representing the complex coherence function.

Equations (8)

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G ( x ^ , y ^ ) = | G ( x ^ , y ^ ) | exp [ i Φ ( x ^ , y ^ ) ] = g ( x , y ) exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x d y .
G ( x ^ , y ^ ; m ) = G ( x ^ , y ^ ) exp ( i 2 π m / N ) ,
H ( x ^ , y ^ ; m ) | G ( x ^ , y ^ ) | + 1 2 G ( x ^ , y ^ ) exp ( i 2 m π N ) + 1 2 G * ( x ^ , y ^ ) exp ( i 2 m π N ) .
u ( x , y ; m ) = H ( x ^ , y ^ ; m ) exp [ i Φ R ( x ^ , y ^ ) ] exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x ^ d y ^ ,
I ( Δ x , Δ y ; m ) = | u ( x 1 , y 1 ; m ) + u ( x 2 , y 2 ; m ) | 2 = 2 Γ ( 0 , 0 ; m ) + 2 Re [ Γ ( Δ x , Δ y ; m ) ] ,
Γ ( Δ x , Δ y ; m ) = u * ( x 1 , y 1 ; m ) u ( x 2 , y 2 ; m ) = H ( x ^ , y ^ ; m ) exp [ i 2 π λ f ( x ^ Δ x + y ^ Δ y ) ] d x ^ d y ^ .
Γ ( Δ x , Δ y ; m ) = g ˜ ( Δ x , Δ y ) + 1 2 g ( Δ x , Δ y ) exp ( i 2 m π N ) + 1 2 g * ( Δ x , Δ y ) exp ( i 2 m π N ) ,
I ( Δ x , Δ y ; m ) = Re { 2 g ˜ ( 0 , 0 ) + g ( 0 , 0 ) exp ( i 2 m π N ) + g * ( 0 , 0 ) exp ( i 2 m π N ) + 2 g ˜ ( Δ x , Δ y ) + g ( Δ x , Δ y ) exp ( i 2 m π N ) + g * ( Δ x , Δ y ) exp ( i 2 m π N ) } .

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