## THz phase-contrast computed tomography based on Mach-Zehnder interferometer using continuous wave source: proof of the concept |

Optics Express, Vol. 21, Issue 21, pp. 25389-25402 (2013)

http://dx.doi.org/10.1364/OE.21.025389

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### Abstract

In this study, we propose a THz computed tomography (CT) method based on phase contrast, which retrieves the phase shift information at each data point through a phase modulation technique using a Mach-Zehnder interferometer with a continuous wave (CW) source. The THz CT is based on first-generation CT, which acquires a set of projections by translational and rotational scans using a thin beam. From the phase-shift projections, we reconstruct a spatial distribution of refractive indices in a cross section of interest. We constructed a preliminary system using a highly coherent CW THz source with a frequency of 0.54 THz to prove the concept and performed an imaging experiment using phantoms to investigate its imaging features such as artifact-immune imaging, quantitative measurement, and selective detection.

© 2013 Optical Society of America

## 1. Introduction

1. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. **20**(16), 1716–1718 (1995). [CrossRef] [PubMed]

8. Y. Kawada, T. Yasuda, H. Takahashi, and S. Aoshima, “Real-time measurement of temporal waveforms of a terahertz pulse using a probe pulse with a tilted pulse front,” Opt. Lett. **33**(2), 180–182 (2008). [CrossRef] [PubMed]

10. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. **22**(12), 904–906 (1997). [CrossRef] [PubMed]

11. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. **27**(15), 1312–1314 (2002). [CrossRef] [PubMed]

13. E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. **283**(10), 2050–2055 (2010). [CrossRef]

17. N. Sunaguchi, Y. Sasaki, N. Maikusa, M. Kawai, T. Yuasa, and C. Otani, “Depth-resolving THz imaging with tomosynthesis,” Opt. Express **17**(12), 9558–9570 (2009). [CrossRef] [PubMed]

## 2. Phase shift retrieval

*n*is unity in air,

*n*– 1 is zero in the region outside the sample. Thus, from Eq. (8),This means that the estimated phase shift is equal to the line integral of

*n*– 1 along the direction of the signal beam propagation, that is, the projection data of

*n*– 1. Therefore, by conducting the measurements while translating and rotating the sample according to the data-acquisition scheme in first-generation CT, we can prepare a set of projections. Using the filtered back projection (FBP) method, we can reconstruct the cross-section from the projections. Finally, noting that the reconstructed image is a spatial distribution of

*n*– 1, we can easily determine the refractive-index distribution from the reconstructed image.

*κ*is zero in the region outside the sample, we obtainThis is the line integral of the absorption coefficient. Therefore, we can simultaneously obtain the projections of the absorption coefficient from the measured data as well. However, we cannot obtain a high-quality reconstructed image, since the absorption projections are contaminated with unintended reflection, refraction, and scattering at the boundaries with the mismatch of the refractive index.

## 3. Experimental setup

*n*– 1.

## 4. Imaging experiment

*λ*/8 using the translational stage. We finally obtained four sets of projection data in a similar manner.

*λ*/4,

*λ*/2, and 3

*λ*/4 are shown in Figs. 5(a)–5(d), respectively, where each image was 400 × 360 pixels in size. The brightness varies with the difference in path length. Figure 6(a) shows the sinogram image of the phase-shift estimated by Eq. (13) from the four sets of raw sinogram images shown in Fig. 5. Figure 6(b) shows a line profile of the first row of the sinogram, which is indicated by a red line in Fig. 6(a). We observe that a jump of 2π occurs at the boundaries between air and the sample. This is owing to the fact that the phase-shift is wrapped between –π and π because of the arctangent in Eq. (13). Therefore, the wrapped sinogram presents discontinuities at the boundaries. It is necessary to unwrap the sinogram to obtain projections from which the cross-sectional images are reconstructed. We applied the phase-unwrap algorithm devised by Cusack et al [21

21. R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. **34**(5), 781–789 (1995). [CrossRef] [PubMed]

22. G. Zhao, M. Mors, T. Wenckebach, and P. C. M. Planken, “Terahertz dielectric properties of polystyrene foam,” J. Opt. Soc. Am. B **19**(6), 1476–1479 (2002). [CrossRef]

## 5. Selective detection from scattered wave

^{2}with a center corresponding with the cross point between the optical axis and the scanning plane, and both the horizontal and vertical scanning steps were of 0.5 mm.

*I*= 0.352 mV and

_{D}*I*= 0.053 mV from Eqs. (6) and (7), respectively. On the other hand, from Fig. 11, the maximum (

_{A}*M*) and minimum (

*m*) of signal at P2 are 0.392 mV and 0.306 mV, respectively. Assuming that the signal is a sinusoidal function while it is distorted because the sample has inhomogeneous regions in refractive index, the center of oscillation and amplitude are obtained as 0.349 mV and 0.0043 mV from (

*M*+

*m*) / 2 and (

*M*–

*m*) / 2, which are regarded as the estimated values of

*I*and

_{D}*I*, respectively. In spite of the rough assumption that the signal is a sinusoidal function, these values are close to the above values obtained from Eqs. (6) and (7) using experimental data from Fig. 10. Also for signals at P3 and P4, similar results are derived as shown in Table 1. From the results, we can see that interference is observed in the region where the intensity of mixed beam is not zero. It addition, the amplitude of mixed signal depends on the intensity of signal beam, and the center of oscillation of mixed signal depends on the intensity of reference beam. Therefore, we can conclude that the interferometer selectively detects only the forward-scattered component, propagating in the same direction as that of the local oscillator beam and preserving the phase information, from among multiply and divergently scattered signal waves emerging from the sample when the signal beam is mixed with the local oscillator beam. This is because the imaging system could quantitatively reproduce the cross section with no remarkable artifacts in spite of the mismatch in the refractive index, as described in Section 4.

_{A}## 6. Conclusion

## References and links

1. | B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. |

2. | R. M. Woodward, V. P. Wallace, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulsed imaging of skin cancer in the time and frequency domain,” J. Biol. Phys. |

3. | R. Wilk, F. Breitfeld, M. Mikulics, and M. Koch, “Continuous wave terahertz spectrometer as a noncontact thickness measuring device,” Appl. Opt. |

4. | T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paint meters by multiple-regression analysis,” Appl. Opt. |

5. | T. Kiwa, J. Kondo, S. Oka, I. Kawayama, H. Yamada, M. Tonouchi, and K. Tsukada, “Chemical sensing plate with a laser-terahertz monitoring system,” Appl. Opt. |

6. | S. R. Murrill, E. L. Jacobs, S. K. Moyer, C. E. Halford, S. T. Griffin, F. C. De Lucia, D. T. Petkie, and C. C. Franck, “Terahertz imaging system performance model for concealed-weapon identification,” Appl. Opt. |

7. | Y. Kawada, T. Yasuda, H. Takahashi, and S.-i. Aoshima, “Real-time measurement of temporal waveforms of a terahertz pulse using a probe pulse with a tilted pulse front,” Opt. Lett. |

8. | Y. Kawada, T. Yasuda, H. Takahashi, and S. Aoshima, “Real-time measurement of temporal waveforms of a terahertz pulse using a probe pulse with a tilted pulse front,” Opt. Lett. |

9. | C. Kak and M. Slanery, “Principles of Computerized Tomographic Imaging,” New York: IEEE Press (1987). |

10. | D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. |

11. | B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. |

12. | S. Wang, B. Ferguson, and X.-C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. |

13. | E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. |

14. | D. Porterfield, J. Hesler, T. Crowe, W. Bishop, and D. Woolard, “Integrated terahertz transmit / receive modules,” Proc. of 33rd European Microwave Conference, 1319–1322 (2003). |

15. | A. Dobroiu, M. Yamashita, Y. N. Ohshima, Y. Morita, C. Otani, and K. Kawase, “Terahertz imaging system based on a backward-wave oscillator,” Appl. Opt. |

16. | B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express |

17. | N. Sunaguchi, Y. Sasaki, N. Maikusa, M. Kawai, T. Yuasa, and C. Otani, “Depth-resolving THz imaging with tomosynthesis,” Opt. Express |

18. | J. Hsieh, |

19. | S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. |

20. | A. Rosenfeld and C. Kak, |

21. | R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. |

22. | G. Zhao, M. Mors, T. Wenckebach, and P. C. M. Planken, “Terahertz dielectric properties of polystyrene foam,” J. Opt. Soc. Am. B |

**OCIS Codes**

(110.6960) Imaging systems : Tomography

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(110.6795) Imaging systems : Terahertz imaging

(110.6955) Imaging systems : Tomographic imaging

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: June 6, 2013

Revised Manuscript: September 7, 2013

Manuscript Accepted: October 4, 2013

Published: October 17, 2013

**Citation**

Masayuki Suga, Yoshiaki Sasaki, Takeshi Sasahara, Tetsuya Yuasa, and Chiko Otani, "THz phase-contrast computed tomography based on Mach-Zehnder interferometer using continuous wave source: proof of the concept," Opt. Express **21**, 25389-25402 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25389

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### References

- B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett.20(16), 1716–1718 (1995). [CrossRef] [PubMed]
- R. M. Woodward, V. P. Wallace, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulsed imaging of skin cancer in the time and frequency domain,” J. Biol. Phys.29(2/3), 257–259 (2003). [CrossRef] [PubMed]
- R. Wilk, F. Breitfeld, M. Mikulics, and M. Koch, “Continuous wave terahertz spectrometer as a noncontact thickness measuring device,” Appl. Opt.47(16), 3023–3026 (2008). [CrossRef] [PubMed]
- T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paint meters by multiple-regression analysis,” Appl. Opt.46(30), 7518–7526 (2007). [CrossRef] [PubMed]
- T. Kiwa, J. Kondo, S. Oka, I. Kawayama, H. Yamada, M. Tonouchi, and K. Tsukada, “Chemical sensing plate with a laser-terahertz monitoring system,” Appl. Opt.47(18), 3324–3327 (2008). [CrossRef] [PubMed]
- S. R. Murrill, E. L. Jacobs, S. K. Moyer, C. E. Halford, S. T. Griffin, F. C. De Lucia, D. T. Petkie, and C. C. Franck, “Terahertz imaging system performance model for concealed-weapon identification,” Appl. Opt.47(9), 1286–1297 (2008). [CrossRef] [PubMed]
- Y. Kawada, T. Yasuda, H. Takahashi, and S.-i. Aoshima, “Real-time measurement of temporal waveforms of a terahertz pulse using a probe pulse with a tilted pulse front,” Opt. Lett.33(2), 180–182 (2008). [CrossRef] [PubMed]
- Y. Kawada, T. Yasuda, H. Takahashi, and S. Aoshima, “Real-time measurement of temporal waveforms of a terahertz pulse using a probe pulse with a tilted pulse front,” Opt. Lett.33(2), 180–182 (2008). [CrossRef] [PubMed]
- C. Kak and M. Slanery, “Principles of Computerized Tomographic Imaging,” New York: IEEE Press (1987).
- D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett.22(12), 904–906 (1997). [CrossRef] [PubMed]
- B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett.27(15), 1312–1314 (2002). [CrossRef] [PubMed]
- S. Wang, B. Ferguson, and X.-C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys.37(4), R1–R36 (2004). [CrossRef]
- E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun.283(10), 2050–2055 (2010). [CrossRef]
- D. Porterfield, J. Hesler, T. Crowe, W. Bishop, and D. Woolard, “Integrated terahertz transmit / receive modules,” Proc. of 33rd European Microwave Conference, 1319–1322 (2003).
- A. Dobroiu, M. Yamashita, Y. N. Ohshima, Y. Morita, C. Otani, and K. Kawase, “Terahertz imaging system based on a backward-wave oscillator,” Appl. Opt.43(30), 5637–5646 (2004). [CrossRef] [PubMed]
- B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express19(6), 5105–5117 (2011). [CrossRef] [PubMed]
- N. Sunaguchi, Y. Sasaki, N. Maikusa, M. Kawai, T. Yuasa, and C. Otani, “Depth-resolving THz imaging with tomosynthesis,” Opt. Express17(12), 9558–9570 (2009). [CrossRef] [PubMed]
- J. Hsieh, Computed Tomography Principles, Design, Artifacts, and Recent Advances, Second Edition (John Wiley & Sons, Inc. & SPIE, 2009).
- S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26(8), 485–487 (2001). [CrossRef] [PubMed]
- A. Rosenfeld and C. Kak, Digital Picture Processing, 2nd Ed., Vol. I (Academic Press, 1982).
- R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt.34(5), 781–789 (1995). [CrossRef] [PubMed]
- G. Zhao, M. Mors, T. Wenckebach, and P. C. M. Planken, “Terahertz dielectric properties of polystyrene foam,” J. Opt. Soc. Am. B19(6), 1476–1479 (2002). [CrossRef]

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