## Real-time coherence holography

Optics Express, Vol. 18, Issue 13, pp. 13782-13787 (2010)

http://dx.doi.org/10.1364/OE.18.013782

Acrobat PDF (747 KB)

### 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.

© 2010 OSA

## 1. Introduction

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

11. V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. **30**(3), 224–226 (2005). [CrossRef] [PubMed]

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

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

7. 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]

8. 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]

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

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

2. 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]

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

13. M. V. R. K. Murty, “A compact radial shearing interferometer based on the law of refraction,” Appl. Opt. **3**(7), 853–857 (1964). [CrossRef]

14. G. Cochran, “New method of making Fresnel transforms,” J. Opt. Soc. Am. **56**(11), 1513–1517 (1966). [CrossRef]

2. 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]

16. 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]

## 2. Principles

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

*λ*is the wavelength of light, and

*f*is the distance between z = 0 and the hologram plane, which is made equal to the focal length of the Fourier transform lens L used in the reconstruction process. The innermost integral inside the curly brace represents the angular spectra of the object field distribution across the plane

*z*with

15. G. W. Stroke, D. Brumm, and A. Funkhouser, ““Three-Dimensional Holography with “Lensless” Fourier-Transform Holograms and Coarse P/N Polaroid Film,” J. Opt. Soc. Am. **55**(10), 1327–1328 (1965). [CrossRef]

*α*such that

## 3. Experiments

2. 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]

*α*= 1.1, the magnification for reconstruction becomes

## 4. Result

## 5. Conclusions

## Acknowledgement

## References and links

1. | M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express |

2. | 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 |

3. | D. N. Naik, T. Ezawa, Y. Miyamoto, and M. Takeda, “Phase-shift coherence holography,” Opt. Lett. |

4. | 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. |

5. | J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. |

6. | 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. |

7. | 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 |

8. | M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. |

9. | E. Baleine and A. Dogariu, “Variable coherence tomography,” Opt. Lett. |

10. | V. Ryabukho, D. Lyakin, and M. Lobachev, “Influence of longitudinal spatial coherence on the signal of a scanning interferometer,” Opt. Lett. |

11. | V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. |

12. | P. Pavliček, M. Halouzka, Z. Duan, and M. Takeda, “Spatial coherence profilometry on tilted surfaces,” Appl. Opt. |

13. | M. V. R. K. Murty, “A compact radial shearing interferometer based on the law of refraction,” Appl. Opt. |

14. | G. Cochran, “New method of making Fresnel transforms,” J. Opt. Soc. Am. |

15. | G. W. Stroke, D. Brumm, and A. Funkhouser, ““Three-Dimensional Holography with “Lensless” Fourier-Transform Holograms and Coarse P/N Polaroid Film,” J. Opt. Soc. Am. |

16. | M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. |

17. | M. Born, and E. Wolf, |

18. | J. W. Goodman, |

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(090.0090) Holography : Holography

(100.3010) Image processing : Image reconstruction techniques

**ToC Category:**

Holography

**History**

Original Manuscript: March 25, 2010

Revised Manuscript: May 19, 2010

Manuscript Accepted: June 4, 2010

Published: June 11, 2010

**Citation**

Dinesh N. Naik, Takahiro Ezawa, Yoko Miyamoto, and Mitsuo Takeda, "Real-time coherence holography," Opt. Express **18**, 13782-13787 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13782

Sort: Year | Journal | Reset

### References

- M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13(23), 9629–9635 (2005). [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]
- D. N. Naik, T. Ezawa, Y. Miyamoto, and M. Takeda, “Phase-shift coherence holography,” Opt. Lett. 35(10), 1728–1730 (2010). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- E. Baleine and A. Dogariu, “Variable coherence tomography,” Opt. Lett. 29(11), 1233–1235 (2004). [CrossRef] [PubMed]
- V. Ryabukho, D. Lyakin, and M. Lobachev, “Influence of longitudinal spatial coherence on the signal of a scanning interferometer,” Opt. Lett. 29(7), 667–669 (2004). [CrossRef] [PubMed]
- V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30(3), 224–226 (2005). [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]
- M. V. R. K. Murty, “A compact radial shearing interferometer based on the law of refraction,” Appl. Opt. 3(7), 853–857 (1964). [CrossRef]
- G. Cochran, “New method of making Fresnel transforms,” J. Opt. Soc. Am. 56(11), 1513–1517 (1966). [CrossRef]
- G. W. Stroke, D. Brumm, and A. Funkhouser, ““Three-Dimensional Holography with “Lensless” Fourier-Transform Holograms and Coarse P/N Polaroid Film,” J. Opt. Soc. Am. 55(10), 1327–1328 (1965). [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]
- 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.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.