## Numerical twin image suppression by nonlinear segmentation mask in digital holography |

Optics Express, Vol. 20, Issue 20, pp. 22454-22464 (2012)

http://dx.doi.org/10.1364/OE.20.022454

Acrobat PDF (4566 KB)

### Abstract

The in-line holography has obvious advantages especially in wider spatial bandwidth over the off-axis holography. However, a direct current(DC)-noise and an unwanted twin image should be separated or eliminated in the in-line holography for a high quality reconstruction. An approach for suppressing the twin image is proposed by separating the real and twin image regions in the digital holography. Specifically, the initial region of real and twin images is obtained by a blind separation matrix, and the segmentation mask to suppress the twin image is calculated by nonlinear quantization from the segmented image. For the performance evaluation, the proposed method is compared with the existing approaches including the overlapping block variance and manual-based schemes. Experimental results showed that the proposed method has a better performance at the overlapped region of the real and twin images. Additionally, the proposed method causes less loss of real image than the overlapping block variance-based scheme. Therefore, we believe that the proposed scheme can be a useful tool for high quality reconstruction in the in-line holography.

© 2012 OSA

## 1. Introduction

1. Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express **19**, 7567–7579 (2011). [CrossRef] [PubMed]

2. C. S. Seelamantula, N. Pavillon, C. Depeursinge, and M. Unser, “Exact complex-wave reconstruction in digital holography,” J. Opt. Soc. Am. A **28**, 983–992 (2011). [CrossRef]

3. U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. **13**, 85–101 (2002). [CrossRef]

4. C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett. **32**, 1229–1231 (2007). [CrossRef] [PubMed]

4. C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett. **32**, 1229–1231 (2007). [CrossRef] [PubMed]

6. D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting **2010**, 1–14 (2010). [CrossRef]

4. C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett. **32**, 1229–1231 (2007). [CrossRef] [PubMed]

7. G. Koren, F. Polack, and D. Joyeux, “Iterative algorithms for twin-image elimination in in-line holography using finite-support constraints,” J. Opt. Soc. Am. A **10**, 423–433 (1993). [CrossRef]

8. L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. **19**, 1–10 (2008). [CrossRef]

9. B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. **34**, 3610–3612 (2009). [CrossRef] [PubMed]

11. J. Schwider, “Phase shifting interferometry: reference phase error reduction,” Appl. Opt. **28**, 3889–3892 (1989). [CrossRef] [PubMed]

13. T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. **8**, 225–232 (2012). [CrossRef]

## 2. Proposed approach: segmentation mask generation for suppressing twin image

*E*is an object wave with amplitude

_{O}*a*and phase

_{O}*φ*, and

_{O}*E*is a reference wave with amplitude

_{R}*a*and phase

_{R}*φ*. Therefore, a holographic fringe pattern, which is the interference pattern between the object and reference waves, is obtained as where a symbol * denotes the complex conjugate, and the first two terms, which are the intensity of the object and reference waves respectively, contribute to a DC-noise.

_{R}14. V. L. Tuft, HoloVision 2.2 User’s manual (http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf, 2001). [PubMed]

3. U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. **13**, 85–101 (2002). [CrossRef]

3. U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. **13**, 85–101 (2002). [CrossRef]

15. H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. **41**, 741–725 (2009). [CrossRef] [PubMed]

16. J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A **24**, 1617–1622 (2007). [CrossRef]

### 2.1. preprocessing to reduce the noise effect

*i*

_{R}_{1}after DC-noise reduction contains the focused real and unfocused twin images as illustrated in Fig. 1(a), while the in-focus twin image

*i*

_{T}_{1}after reducing the noise contains the focused twin and unfocused real images as shown in Fig. 1(b). Speckle noise occurs both in two images due to the diffusion of coherent light by an optical rough surface [3

**13**, 85–101 (2002). [CrossRef]

6. D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting **2010**, 1–14 (2010). [CrossRef]

16. J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A **24**, 1617–1622 (2007). [CrossRef]

18. J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. **3**, 289–294 (1971). [CrossRef]

*H*consists of a set of spatial and range filters as where

_{b}*ξ*and

*x*respectively denote the neighborhood center and a nearby point.

*d*(

*ξ*,

*x*) and

*δ*(

*ξ*,

*x*) indicate the Euclidean distance and the intensity difference, respectively, between

*ξ*and

*x*points.

*σ*and

_{s}*σ*represent the spatial and range parameters, respectively. The performance of bilateral filter is controlled by the spatial and range parameters. The spatial and range parameters,

_{r}*σ*= 2.0 and

_{s}*σ*= 0.5, are set, and the size of spatial filter is 3 × 3 in the proposed scheme. By applying it to two images,

_{r}*i*

_{R1}and

*i*

_{T}_{1}, two resultant images,

*i*

_{R}_{2}and

*i*

_{T}_{2}, in which the speckle noise has been suppressed, are obtained as illustrated in Fig. 3.

### 2.2. Real and twin image separation by a blind separation matrix

*A*as where

*I*is an observed vector that consists of the in-focus real

*i*

_{R}_{2}and twin

*i*

_{T}_{2}images, and

*S*indicates the source vector which is composed of the real

*s*and twin

_{R}*s*images. The matrix

_{T}*A*defines the mixing ratio of the real and twin images, in other words, models the relationship between the observed vector

*I*and the source vector

*S*.

*A*, is required, and the separated real and twin images can be rewritten by Therefore, the performance and complexity of the separation depend on the calculation of the blind separation matrix. Independent component analysis(ICA) based on neural network is one of the possible methods to obtain the matrix. However, it requires several iterations and operates under the independence or non-Gaussianity of sources [20–22]. Hence, to obtain the matrix without an iteration and restrictions of the source, the blind and weighted separation matrix is computed from the canceling coefficients [21

21. F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing **85**, 1389–1403 (2005). [CrossRef]

*c*represent Hadamard product and canceling coefficients, respectively.

_{η}*S*(

_{R}*w*) is zero, then the first coefficient is calculated by

*c*

_{1}=

*a*

_{11}/

*a*

_{21}, and if

*S*(

_{T}*w*) is zero, then the second coefficient is obtained from

*c*

_{2}=

*a*

_{12}/

*a*

_{22}. The blind separation matrix is calculated from the canceling coefficients in Eq. 6, and the in-focus real and twin images are separated into the regions of real and twin images as shown in Fig. 4, respectively. In practice, 3×3 block variance in ℱ(

*i*

_{R}_{2})/ℱ(

*i*

_{T}_{2}) is calculated. Then, the first and the second smallest variances are used for the first and second canceling coefficients [21

21. F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing **85**, 1389–1403 (2005). [CrossRef]

### 2.3. Segmentation mask generation by nonlinear quantization and compensation

*N*and

*M*are the row and column dimensions, respectively.

*x*,

*w*, and

*D*represent an input sequence, the slope of the quantization function, and the bit depth of

_{b}*s*, respectively.

_{R}*D*is assigned to 255 for 8 bit images in the paper.

_{b}**32**, 1229–1231 (2007). [CrossRef] [PubMed]

*i*is delivered to the hologram plane by numerical propagation [4

_{Ts}**32**, 1229–1231 (2007). [CrossRef] [PubMed]

**13**, 85–101 (2002). [CrossRef]

## 3. Experiment

14. V. L. Tuft, HoloVision 2.2 User’s manual (http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf, 2001). [PubMed]

*λ*=632.8

*nm*and a pixel pitch Δ=6.8

*μm*[14

14. V. L. Tuft, HoloVision 2.2 User’s manual (http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf, 2001). [PubMed]

**32**, 1229–1231 (2007). [CrossRef] [PubMed]

**13**, 85–101 (2002). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express |

2. | C. S. Seelamantula, N. Pavillon, C. Depeursinge, and M. Unser, “Exact complex-wave reconstruction in digital holography,” J. Opt. Soc. Am. A |

3. | U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol. |

4. | C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett. |

5. | C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information , Proc. SPIE |

6. | D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting |

7. | G. Koren, F. Polack, and D. Joyeux, “Iterative algorithms for twin-image elimination in in-line holography using finite-support constraints,” J. Opt. Soc. Am. A |

8. | L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol. |

9. | B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. |

10. | D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In |

11. | J. Schwider, “Phase shifting interferometry: reference phase error reduction,” Appl. Opt. |

12. | J. Hahn, H. Kim, S. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. |

13. | T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. |

14. | V. L. Tuft, HoloVision 2.2 User’s manual (http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf, 2001). [PubMed] |

15. | H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech. |

16. | J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A |

17. | C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in |

18. | J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. |

19. | R. C. Gonzalez and R. E. Woods, |

20. | J. V. Stone, |

21. | F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing |

22. | T. K. Moon, |

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(090.1995) Holography : Digital holography

**ToC Category:**

Image Processing

**History**

Original Manuscript: July 17, 2012

Revised Manuscript: August 16, 2012

Manuscript Accepted: September 11, 2012

Published: September 17, 2012

**Citation**

ChoongSang Cho, ByeongHo Choi, Hoonjong Kang, and Sangkeun Lee, "Numerical twin image suppression by nonlinear segmentation mask in digital holography," Opt. Express **20**, 22454-22464 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22454

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### References

- Y. Takaki and M. Yokouchi, “Speckle-free and grayscale hologram reconstruction using time-multiplexing technique,” Opt. Express19, 7567–7579 (2011). [CrossRef] [PubMed]
- C. S. Seelamantula, N. Pavillon, C. Depeursinge, and M. Unser, “Exact complex-wave reconstruction in digital holography,” J. Opt. Soc. Am. A28, 983–992 (2011). [CrossRef]
- U. Schnars and W.P. Jüptner, “Digital recording and numerical reconstruction of hologram,” Meas. Sci. Technol.13, 85–101 (2002). [CrossRef]
- C. P. McElhinney, J. B. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. J. Naughton, “Depth-independent segmentation of macroscopic three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett.32, 1229–1231 (2007). [CrossRef] [PubMed]
- C. McElhinney, B. M. Hennelly, L. Ahrenberg, and T. J. Naughton, “Removing the twin image in digital holography by segmented filtering of in-focus twin image,” in Optics and Photonics for Information, Proc. SPIE 7072, 707208 (2008).
- D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michalkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcasting2010, 1–14 (2010). [CrossRef]
- G. Koren, F. Polack, and D. Joyeux, “Iterative algorithms for twin-image elimination in in-line holography using finite-support constraints,” J. Opt. Soc. Am. A10, 423–433 (1993). [CrossRef]
- L Denis, C Fournier, T Fournel, and C Ducotter, “Numerical suppression of the twin image in in-line holography of a volume of micro-objects,” Meas. Sci. Technol.19, 1–10 (2008). [CrossRef]
- B. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett.34, 3610–3612 (2009). [CrossRef] [PubMed]
- D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin suppression in digital holography by mean of speckle reduction,” In Proceedings China-Ireland International Conference on Information and Communications Technologies, (Kildare, Ireland, 2009), 237–240.
- J. Schwider, “Phase shifting interferometry: reference phase error reduction,” Appl. Opt.28, 3889–3892 (1989). [CrossRef] [PubMed]
- J. Hahn, H. Kim, S. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt.47, 4068–4076 (2008). [CrossRef] [PubMed]
- T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol.8, 225–232 (2012). [CrossRef]
- V. L. Tuft, HoloVision 2.2 User’s manual ( http://www2.edge.no/projects/holovision/doc/holovision221manual.pdf , 2001). [PubMed]
- H. Cho, J.K. Woo, D. Kim, S. Shin, and Y. Yu, “DC suppression in-line digital holographic microscopes on the basis of an intensity-averaging method using variable pixel numbers,” Opt. & Laser Tech.41, 741–725 (2009). [CrossRef] [PubMed]
- J. Maycock, B. M. Hennelly, J. B. McDonald, Y. Frauel, A. Castro, B. Javidi, and T. J. Naughton, “Reduction of speckle in digital holography by discrete Fourier filtering,” J. Opt. Soc. Am. A24, 1617–1622 (2007). [CrossRef]
- C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of 6th IEEE International Conference on Computer Vision (IEEE, 1998), 839–846.
- J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun.3, 289–294 (1971). [CrossRef]
- R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2010).
- J. V. Stone, Independent Component Analysis (MIT Press, 2004).
- F. Abrard and Y. Deville, “A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources,” Signal Processing85, 1389–1403 (2005). [CrossRef]
- T. K. Moon, Mathematical Methods and Algorithms for Signal Processing (Prentice hall, 2009).

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