Abstract

Coherence holography capable of real-time recording and reconstruction is proposed and experimentally demonstrated with a generic Leith-type coherence hologram. The coherence hologram is optically generated in real-time using a Mach-Zehnder interferometer and reconstructed using a Sagnac radial shearing interferometer. With this method one can create an optical field distribution with a desired spatial coherence function, and visualize the coherence function in real-time as the contrast and phase variations in an interference fringe pattern. The reconstructed image of the complex coherence function has been quantified with the Fourier transform method of fringe-pattern analysis.

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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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] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

2009 (2)

2006 (2)

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free optical coherence depth sensing with a spatial frequency comb generated by an angular spectrum modulator,” Opt. Express 14(25), 12109–12121 (2006).
[CrossRef] [PubMed]

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96(7), 073902 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (2)

2003 (1)

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42(3), 830–836 (2003).
[CrossRef]

2002 (1)

2000 (1)

1982 (1)

1966 (1)

1965 (1)

1964 (1)

Baleine, E.

Brumm, D.

Cochran, G.

Dogariu, A.

Duan, Z.

P. Pavliček, M. Halouzka, Z. Duan, and M. Takeda, “Spatial coherence profilometry on tilted surfaces,” Appl. Opt. 48(34), H40–H47 (2009).
[CrossRef] [PubMed]

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free optical coherence depth sensing with a spatial frequency comb generated by an angular spectrum modulator,” Opt. Express 14(25), 12109–12121 (2006).
[CrossRef] [PubMed]

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96(7), 073902 (2006).
[CrossRef] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13(23), 9629–9635 (2005).
[CrossRef] [PubMed]

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42(3), 830–836 (2003).
[CrossRef]

Ezawa, T.

Funkhouser, A.

Gokhler, M.

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42(3), 830–836 (2003).
[CrossRef]

Halouzka, M.

Hanson, S. G.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96(7), 073902 (2006).
[CrossRef] [PubMed]

Ina, H.

Kobayashi, S.

Kozaki, H.

Lobachev, M.

Lyakin, D.

Miyamoto, Y.

Murty, M. V. R. K.

Naik, D. N.

Pavlicek, P.

Rosen, J.

Ryabukho, V.

Stroke, G. W.

Takeda, M.

D. N. Naik, T. Ezawa, Y. Miyamoto, and M. Takeda, “Phase-shift coherence holography,” Opt. Lett. 35(10), 1728–1730 (2010).
[CrossRef] [PubMed]

D. N. Naik, T. Ezawa, Y. Miyamoto, and M. Takeda, “3-D coherence holography using a modified Sagnac radial shearing interferometer with geometric phase shift,” Opt. Express 17(13), 10633–10641 (2009).
[CrossRef] [PubMed]

P. Pavliček, M. Halouzka, Z. Duan, and M. Takeda, “Spatial coherence profilometry on tilted surfaces,” Appl. Opt. 48(34), H40–H47 (2009).
[CrossRef] [PubMed]

Z. Duan, Y. Miyamoto, and M. Takeda, “Dispersion-free optical coherence depth sensing with a spatial frequency comb generated by an angular spectrum modulator,” Opt. Express 14(25), 12109–12121 (2006).
[CrossRef] [PubMed]

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96(7), 073902 (2006).
[CrossRef] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13(23), 9629–9635 (2005).
[CrossRef] [PubMed]

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42(3), 830–836 (2003).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications,” Appl. Opt. 41(10), 1962–1971 (2002).
[CrossRef] [PubMed]

J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39(23), 4107–4111 (2000).
[CrossRef]

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(1), 156–160 (1982).
[CrossRef]

Wang, W.

Appl. Opt. (4)

J. Opt. Soc. Am. (3)

Opt. Eng. (1)

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42(3), 830–836 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96(7), 073902 (2006).
[CrossRef] [PubMed]

Other (2)

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

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

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Figures (3)

Fig. 1
Fig. 1

Geometry for real-time coherence holography.

Fig. 2
Fig. 2

The experimental set up for real-time coherence holography.

Fig. 3
Fig. 3

Reconstructed images: (a) Raw intensity image resulted from shearing interference in real time described by Eq. (7); (b) Fourier spectrum of the interference image and (c) Contrast image representing the coherence function described by Eq. (8).

Equations (8)

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U ( x ^ , y ^ ) g ˜ ( x , y ) exp [ i 2 π λ f ( x x ^ + y y ^ ) ] exp [ i π λ f ( x ^ 2 + y ^ 2 ) ] d x d y ,
where g ˜ ( x , y ) = [ { g o ( x ˜ , y ˜ ; z ) exp [ i 2 π λ f ( x ^ x ˜ + y ^ y ˜ ) ] d x ˜ d y ˜ } exp [ i k z ( x ^ , y ^ ) z ] d z ] × exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x ^ d y ^
| H ( x ^ , y ^ ) | 2 1 + | U ( x ^ , y ^ ) | 2 g ˜ ( x , y ) exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x d y g ˜ * ( x , y ) exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x d y ,
g ' ( x , y ; z ) = | H ( x ^ , y ^ ) | 2 exp [ i k z ( x ^ , y ^ ) z ] exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x ^ d y ^ .
g ( x , y ; z ) = H ( x ^ , y ^ ) exp [ i Φ R ( x ^ , y ^ ) ] exp [ i k z ( x ^ , y ^ ) z ] exp [ i 2 π λ f ( x x ^ + y y ^ ) ] d x ^ d y ^ .
Γ ( Δ x , Δ y ; Δ z ) = g * ( x 1 , y 1 ; z 1 ) g ( x 2 , y 2 ; z 2 ) = H * ( x ^ 1 , y ^ 1 ) H ( x ^ 2 , y ^ 2 ) exp [ i Φ R ( x ^ 1 , y ^ 1 ) ] exp [ i Φ R ( x ^ 2 , y ^ 2 ) ] × exp [ i k z ( x ^ 1 , y ^ 1 ) z 1 ] exp [ i k z ( x ^ 2 , y ^ 2 ) z 2 ] × exp [ i 2 π λ f ( x 1 x ^ 1 + y 1 y ^ 1 ) ] exp [ i 2 π λ f ( x 2 x ^ 2 + y 2 y ^ 2 ) ] d x ^ 1 d y ^ 1 d x ^ 2 d y ^ 2 = | H ( x ^ 1 , y ^ 1 ) | 2 exp [ i k z ( x ^ 1 , y ^ 1 ) Δ z ] exp [ i 2 π λ f ( x ^ 1 Δ x + y ^ 1 Δ y ) ] d x ^ 1 d y ^ 1 ,
I ( x , y ; z ) = | g ( x 1 , y 1 ; z 1 ) + g ( x 2 , y 2 ; z 2 ) | 2 = 2 Γ ( 0 , 0 , 0 ) + 2 Re { Γ ( Δ x , Δ y ; Δ z ) } ,
Γ ( 0 , 0 , 0 ) = g * ( x 1 , y 1 ; z 1 ) g ( x 1 , y 1 ; z 1 ) = g * ( x 2 , y 2 ; z 2 ) g ( x 2 , y 2 ; z 2 ) Γ ( Δ x , Δ y , Δ z ) = g * ( x 1 , y 1 ; z 1 ) g ( x 2 , y 2 ; z 2 ) .

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