## Partition calculation for zero-order and conjugate image removal in digital in-line holography |

Optics Express, Vol. 20, Issue 2, pp. 1805-1815 (2012)

http://dx.doi.org/10.1364/OE.20.001805

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### Abstract

Conventional digital in-line holography requires at least two phase-shifting holograms to reconstruct an original object without zero-order and conjugate image noise. We present a novel approach in which only one in-line hologram and two intensity values (namely the object wave intensity and the reference wave intensity) are required. First, by subtracting the two intensity values the zero-order diffraction can be completely eliminated. Then, an algorithm, called partition calculation, is proposed to numerically remove the conjugate image. A preliminary experimental result is given to confirm the proposed method. The method can simplify the procedure of phase-shifting digital holography and improve the practical feasibility for digital in-line holography.

© 2012 OSA

## 1. Introduction

1. H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. **55**(18), 2989–3000 (2008). [CrossRef]

2. T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. **36**(8), 2357–2360 (1997). [CrossRef]

3. G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express **15**(14), 8851–8856 (2007). [CrossRef] [PubMed]

4. Y. C. Dong and J. Wu, “Space-shifting digital holography with dc term removal,” Opt. Lett. **35**(8), 1287–1289 (2010). [CrossRef] [PubMed]

5. E. Cuche, P. Marquet, and C. Deperursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. **39**(23), 4070–4075 (2000). [CrossRef] [PubMed]

6. L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. **56**(21), 2377–2383 (2009). [CrossRef]

7. J. W. Weng, J. G. Zhong, and C. Y. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express **16**(26), 21971–21981 (2008). [CrossRef] [PubMed]

8. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. **22**(16), 1268–1270 (1997). [CrossRef] [PubMed]

10. T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. **35**(13), 2281–2283 (2010). [CrossRef] [PubMed]

## 2. Theoretical derivation

*△ x*and

*△y*are the corresponding pixel sizes,

*rect()*is the rectangle function, λ is the wavelength of the laser used to record the hologram, A is the amplitude of the reference wave on the plane of the hologram,

*z*is the distance of the point reference light source from the hologram plane.

*x*,

*y*) denotes the object wave on the plane of hologram. An in-line hologram and two intensity distribution (object wave intensity and reference wave intensity) are recorded sequentially and expressed as

*I*still contains the conjugate image. In order to eliminate the conjugate image, we propose an algorithm of partition calculation. The complex hologram is divided equally to four regions, as shown in Fig. 2 . Coordinate of the centers of the four regions can be given as

_{C}(x, y)*F*

^{denotes}Fourier transform operation. By utilizing the property of the Fourier transform, the spatial frequency spectrums of

*z*of the point reference light source from the hologram plane is, the higher the object wave frequency which can be recorded will be. However, to satisfy Nyquist sampling rate, the distance

*z*has a minimum valueWhere max() is to take the larger value of these two values. By substituting Eq. (12) in Eq. (11) and assuming that

*sw*denotes the effective space-bandwidth product of CCD camera.

_{CCD}*x-z*plane, the highest frequency of the object wave in

*x*dimension must not exceed a maximum value

## 3. Algorithm illustration

## 4. Experimental results and analysis

## 5. Conclusion

## Acknowledgments

## References and links

1. | H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. |

2. | T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. |

3. | G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express |

4. | Y. C. Dong and J. Wu, “Space-shifting digital holography with dc term removal,” Opt. Lett. |

5. | E. Cuche, P. Marquet, and C. Deperursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. |

6. | L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. |

7. | J. W. Weng, J. G. Zhong, and C. Y. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express |

8. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

9. | Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. |

10. | T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. |

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(090.1995) Holography : Digital holography

**ToC Category:**

Holography

**History**

Original Manuscript: October 24, 2011

Revised Manuscript: December 8, 2011

Manuscript Accepted: January 4, 2012

Published: January 12, 2012

**Citation**

Lihong Ma, Hui Wang, Yong Li, and Hongzhen Jin, "Partition calculation for zero-order and conjugate image removal in digital in-line holography," Opt. Express **20**, 1805-1815 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1805

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### References

- H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt.55(18), 2989–3000 (2008). [CrossRef]
- T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng.36(8), 2357–2360 (1997). [CrossRef]
- G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express15(14), 8851–8856 (2007). [CrossRef] [PubMed]
- Y. C. Dong and J. Wu, “Space-shifting digital holography with dc term removal,” Opt. Lett.35(8), 1287–1289 (2010). [CrossRef] [PubMed]
- E. Cuche, P. Marquet, and C. Deperursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt.39(23), 4070–4075 (2000). [CrossRef] [PubMed]
- L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt.56(21), 2377–2383 (2009). [CrossRef]
- J. W. Weng, J. G. Zhong, and C. Y. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express16(26), 21971–21981 (2008). [CrossRef] [PubMed]
- I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22(16), 1268–1270 (1997). [CrossRef] [PubMed]
- Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt.47(19), D183–D189 (2008). [CrossRef] [PubMed]
- T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett.35(13), 2281–2283 (2010). [CrossRef] [PubMed]

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