Abstract

A new image reconstruction scheme for coherence holography using a modified Sagnac-type radial shearing interferometer with geometric phase shift is proposed, and the first experimental demonstration of generic Leith-type coherence holography, which reconstructs off-axis 3-D objects with depth information, is presented. The reconstructed image, represented by a coherence function, can be visualized with a controllable magnification, which opens up a new possibility for a coherence imaging microscope

© 2009 Optical Society of America

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References

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  1. M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, "Coherence Holography," Opt. Express 23, 9629-9635 (2005).
    [CrossRef]
  2. W. Wang, H. Kozaki, J. Rosen, and M. Takeda, "Synthesis of longitudinal coherence function by spatial modulation of an exteded light source: a new interpretation and experimental verifications," Appl. Opt. 41, 1962-1971 (2002).
    [CrossRef] [PubMed]
  3. J. Rosen and M. Takeda, "Longitudinal spatial coherence applied for surface profilometry," Appl. Opt. 39, 4107-4111 (2000).
    [CrossRef]
  4. 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, 073902 (2006).
    [CrossRef] [PubMed]
  5. 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, 12109-12121 (2006).
    [CrossRef] [PubMed]
  6. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), Chap. 10.
  7. J. W. Goodman, Statistical Optics, 1st ed. (Wiley, New York, 1985), Chap. 5.
  8. G. Cochran, "New method of making Fresnel transforms," J. Opt. Soc. Am. 56, 1513-1517 (1966).
    [CrossRef]
  9. M. V. R. K. Murty, "A compact radial shearing interferometer based on the law of refraction," Appl. Opt. 3, 853-857 (1964).
    [CrossRef]
  10. Z. Liu, T. Gemma, J. Rosen, and M. Takeda, "An improved illumination system for spatial coherence control," Proc. SPIE 5531, 220-227 (2004).
    [CrossRef]
  11. P. Hariharan and M. Roy, "A geometric-phase interferometer," J. Mod. Opt. 39, 1811-1815 (1992).
    [CrossRef]
  12. P. Handel, "Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm," IEEE Trans. Instrum. Meas. 49, 1189-1193(2000).
    [CrossRef]

2006 (2)

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, 073902 (2006).
[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, 12109-12121 (2006).
[CrossRef] [PubMed]

2005 (1)

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, "Coherence Holography," Opt. Express 23, 9629-9635 (2005).
[CrossRef]

2004 (1)

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, "An improved illumination system for spatial coherence control," Proc. SPIE 5531, 220-227 (2004).
[CrossRef]

2002 (1)

2000 (2)

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

P. Handel, "Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm," IEEE Trans. Instrum. Meas. 49, 1189-1193(2000).
[CrossRef]

1992 (1)

P. Hariharan and M. Roy, "A geometric-phase interferometer," J. Mod. Opt. 39, 1811-1815 (1992).
[CrossRef]

1966 (1)

1964 (1)

Cochran, G.

Duan, Z.

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, 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, 073902 (2006).
[CrossRef] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, "Coherence Holography," Opt. Express 23, 9629-9635 (2005).
[CrossRef]

Gemma, T.

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, "An improved illumination system for spatial coherence control," Proc. SPIE 5531, 220-227 (2004).
[CrossRef]

Handel, P.

P. Handel, "Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm," IEEE Trans. Instrum. Meas. 49, 1189-1193(2000).
[CrossRef]

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, 073902 (2006).
[CrossRef] [PubMed]

Hariharan, P.

P. Hariharan and M. Roy, "A geometric-phase interferometer," J. Mod. Opt. 39, 1811-1815 (1992).
[CrossRef]

Kozaki, H.

Liu, Z.

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, "An improved illumination system for spatial coherence control," Proc. SPIE 5531, 220-227 (2004).
[CrossRef]

Miyamoto, Y.

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, 073902 (2006).
[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, 12109-12121 (2006).
[CrossRef] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, "Coherence Holography," Opt. Express 23, 9629-9635 (2005).
[CrossRef]

Murty, M. V. R. K.

Rosen, J.

Roy, M.

P. Hariharan and M. Roy, "A geometric-phase interferometer," J. Mod. Opt. 39, 1811-1815 (1992).
[CrossRef]

Takeda, M.

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, 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, 073902 (2006).
[CrossRef] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, "Coherence Holography," Opt. Express 23, 9629-9635 (2005).
[CrossRef]

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, "An improved illumination system for spatial coherence control," Proc. SPIE 5531, 220-227 (2004).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, "Synthesis of longitudinal coherence function by spatial modulation of an exteded light source: a new interpretation and experimental verifications," Appl. Opt. 41, 1962-1971 (2002).
[CrossRef] [PubMed]

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

Wang, W.

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, 073902 (2006).
[CrossRef] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, "Coherence Holography," Opt. Express 23, 9629-9635 (2005).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, "Synthesis of longitudinal coherence function by spatial modulation of an exteded light source: a new interpretation and experimental verifications," Appl. Opt. 41, 1962-1971 (2002).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Trans. Instrum. Meas. (1)

P. Handel, "Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm," IEEE Trans. Instrum. Meas. 49, 1189-1193(2000).
[CrossRef]

J. Mod. Opt. (1)

P. Hariharan and M. Roy, "A geometric-phase interferometer," J. Mod. Opt. 39, 1811-1815 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (2)

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, 073902 (2006).
[CrossRef] [PubMed]

Proc. SPIE (1)

Z. Liu, T. Gemma, J. Rosen, and M. Takeda, "An improved illumination system for spatial coherence control," Proc. SPIE 5531, 220-227 (2004).
[CrossRef]

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 (7)

Fig. 1.
Fig. 1.

Recording and reconstruction of a coherence hologram

Fig. 2.
Fig. 2.

Experimental set up for reconstruction in 2D coherence holography

Fig. 3.
Fig. 3.

Conceptual diagram of generation of coherence hologram

Fig. 4.
Fig. 4.

(a) Coherence hologram of 2D letter Ψ ; (b) Coherence hologram of 3D letters U, E and C

Fig. 5.
Fig. 5.

Experimental set up for reconstruction in 3D coherence holography

Fig. 6.
Fig. 6.

Reconstructed images in 2D coherence holography. (a) Raw intensity image resulted from shearing interference; (b) phase image and (c) contrast image jointly representing the complex coherence function.

Fig. 7.
Fig. 7.

Reconstructed images in 3D coherency holography: (a), (b) and (c) show raw intensity image resulted from shearing interference at depths Δz=-8mm, Δz=0 and Δz=+8mm, respectively; (d), (e) and (f) show the corresponding phase images, and (g), (h) and (i) show their corresponding contrast images.

Equations (1)

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H (x,y)=Re [G(x,y)exp[iΦ(x,y)]] + C

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