## Terahertz digital holography using angular spectrum and dual wavelength reconstruction methods |

Optics Express, Vol. 19, Issue 10, pp. 9192-9200 (2011)

http://dx.doi.org/10.1364/OE.19.009192

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### Abstract

Terahertz digital off-axis holography is demonstrated using a Mach-Zehnder interferometer with a highly coherent, frequency tunable, continuous wave terahertz source emitting around 0.7 THz and a single, spatially-scanned Schottky diode detector. The reconstruction of amplitude and phase objects is performed digitally using the angular spectrum method in conjunction with Fourier space filtering to reduce noise from the twin image and DC term. Phase unwrapping is achieved using the dual wavelength method, which offers an automated approach to overcome the 2π phase ambiguity. Potential applications for nondestructive test and evaluation of visually opaque dielectric and composite objects are discussed.

© 2011 OSA

## 1. Introduction

1. G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. **43**(10), 1039–1055 (2005). [CrossRef]

2. M. K. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express **7**(9), 305–310 (2000). [CrossRef] [PubMed]

7. D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. **43**(36), 6536–6544 (2004). [CrossRef]

10. G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, S. Grilli, M. Iodice, C. Magro, and G. Pierattini, “Characterization of MEMS structures by microscopic digital holography,” Proc. SPIE **4945**, 71–78 (2003). [CrossRef]

13. P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. **44**(3), 337–343 (2005). [CrossRef] [PubMed]

14. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**(34), 6994–7001 (1999). [CrossRef]

15. G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, “Numerical reconstruction and twin-image suppression using an off-axis Fresnel digital hologram,” Appl. Phys. B **90**(3-4), 527–532 (2008). [CrossRef]

16. L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. **30**(16), 2092–2094 (2005). [CrossRef] [PubMed]

17. C. J. Mann, L. Yu, C.-M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express **13**(22), 8693–8698 (2005). [CrossRef] [PubMed]

20. K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microw. Theory Tech. **56**(12), 2771–2778 (2008). [CrossRef]

21. J. Pearce, H. Choi, D. M. Mittleman, J. White, and D. Zimdars, “Terahertz wide aperture reflection tomography,” Opt. Lett. **30**(13), 1653–1655 (2005). [CrossRef] [PubMed]

24. R. J. Mahon, J. A. Murphy, and W. Lanigan, “Digital holography at millimetre wavelengths,” Opt. Commun. **260**(2), 469–473 (2006). [CrossRef]

25. Y. Zhang, W. Zhou, X. Wang, Y. Cui, and W. Sun, “Terahertz Digital Holography,” Strain **44**(5), 380–385 (2008). [CrossRef]

16. L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. **30**(16), 2092–2094 (2005). [CrossRef] [PubMed]

27. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. **28**(13), 1141–1143 (2003). [CrossRef] [PubMed]

## 2. Experiment

*θ*between the object and reference beams. The beam splitters also allow the relative beam intensities to be adjusted since amplitude objects generally require a stronger object beam than phase objects. However, a strong reference beam is also desirable as it relaxes the minimum reference angle required to separate the real and virtual images containing the object wavefield information from the on-axis “DC” term [29].

*f*of the interference pattern formed by the object and reference was found to be 0.51 cycles/mm for a 0.712 THz beam (

_{c}*λ*= 0.4213 mm). Figure 1(b) shows a 100 x 100 mm interferogram from the interfering object and reference waves. The maximum off-axis angle

*θ*between the two beams is thereforewhich is 12.41 degrees in this experiment. Customized detector horns with optimized gain and antenna pattern characteristics may be able to resolve higher spatial frequencies and allow for larger off-axis angles, improving the separability of the real and imaginary images from the DC term. Other methods to increase image resolution, such as hologram magnification or super resolution techniques, may be necessary in the future as an intermediate step between THz hologram generation and recording [30

_{max}30. U. Schnars, T. M. Kreis, and W. P. O. Jüpner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. **35**(4), 977–982 (1996). [CrossRef]

34. C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. **81**(17), 3143 (2002). [CrossRef]

*F{I(x,y)}*results in the spatial frequency spectrum of

*I(x,y)*containing four Fourier spectra corresponding to the four terms in Eq. (2), which can be abbreviated as

*O*.

^{2}+ R^{2}+ O*R + OR**|F{O*represents the autocorrelation of

^{2}}|*O*, whose spectrum has twice the bandwidth (

*2B*) of

*O*and is located symmetrically around the origin

*f*= 0.

_{x},f_{y}*|F{R*is a delta function located at

^{2}}|*f*= 0, assuming

_{x},f_{y}*R*is a plane wave.

*|F{O*R}|*contains the spectrum of the real image of

*O*and is located symmetrically around

*f*= 0,

_{x}*f*=

_{y}*-η*. Similary,

*|F{OR*}|*contains the spectrum of the virtual image of

*O*and is located symmetrically around

*f*= 0,

_{x}*f*=

_{y}*η*. Figure 2(a) illustrates the locations of the four spectra for the case where the spectra can be fully separated. Figure 2(b) considers the approximation where the reference wave is much stronger in magnitude than the object wave, in which case

*F{O*becomes negligible.

^{2}}## 3. Sampling

35. B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, M. G. Vlasenko, M. A. Dem’yanenko, and D. G. Esaev, “Real-Time Imaging Using a High-Power Monochromatic Terahertz Source: Comparative Description of Imaging Techniques with Examples of Application: Journal of Infrared Millimeter Terahertz Waves (online-only) (2011).

36. W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. **33**(9), 974–976 (2008). [CrossRef] [PubMed]

37. C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. **49**(19), E67–E82 (2010). [CrossRef] [PubMed]

*f*of the detector occurs where the OTF has its first zero, which is

_{c}*f*= 1/

_{c}*w =*0.50 cycles/mm, producing an off-axis angle of

*θ*= 12.40 degrees. At this angle, the fringe amplitude is reduced to approximately 27% of its peak value due to the antenna horn pattern as shown in Fig. 3. Nyquist sampling requires the detector be scanned with ~0.5 mm steps, but to take advantage of sub-wavelength depth resolution using this interferometric technique, a scan step of 0.2 mm was rarely exceeded.

_{max}## 4. Reconstruction process

38. M. K. Kim, L. Yu, and C. J. Mann, “Interference techniques in digital holography,” J. Opt. A, Pure Appl. Opt. **8**(7), S518–S523 (2006). [CrossRef]

38. M. K. Kim, L. Yu, and C. J. Mann, “Interference techniques in digital holography,” J. Opt. A, Pure Appl. Opt. **8**(7), S518–S523 (2006). [CrossRef]

*z*is chosen to be the object – hologram plane distance, but any location of

*z*can be chosen. If the object – detector plane distance is unknown, it can be found by varying

*z*until the reconstructed object is in focus. The original object wavefield

*U(x,y,z)*is then computed with another FFT, this time of

*A(α/λ,β/λ,z)*.

*A(α/λ,β/λ,z)*can be multiplied by a filter that rejects the twin image and DC spectra. Here the filter is a rectangular or circular array of zeroes wherever the spectra is to be rejected and ones wherever the spectra of the real image is located. In optical holography, the hologram must be illuminated by the same reference wave in order to form a real or virtual image. The digital reconstruction process requires the same and can be approached digitally. The hologram is multiplied by the reference wave described bywhere the off axis angle

*θ*is assumed in the y-z plane. The filtered version of

*A(α/λ,β/λ,z = 0)*, which at this point should contain only the frequency content of the real wavefield, is then back-propagated using Eq. (4), after which another FFT reproduces the original object wavefield

*U(x,y,z)*. In summary, the cascaded steps to find

*U(x,y,z)*arewhere iFFT means inverse FFT.

27. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. **28**(13), 1141–1143 (2003). [CrossRef] [PubMed]

*λ*as long as the hologram can be recorded at two wavelengths

_{b}*λ*and

_{1}*λ*such that

_{2}*λ*and

_{1}*λ*range between -π and π. Following the procedure described in [27

_{2}27. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. **28**(13), 1141–1143 (2003). [CrossRef] [PubMed]

## 5. Results

*ω =*1.22

*λ/D*where

*D*is the diameter of the objective aperture. Here, for

*D*= 80 mm

*ω*= 0.0064, which is equivalent to a lateral object point separation of 0.64 mm at a object – detector distance of 200 mm. The upper row of holes on the object containing three holes of diameters from 1.5 mm to 2.0 mm are sufficiently separated from each other to satisfy this resolution limit and are therefore clearly visible in Fig. 4(d). The second row of holes contains a set of nine 0.9 mm diameter holes arranged horizontally. These holes are separated 0.9 mm from each other horizontally but only 0.4 mm vertically from the third row of holes. Therefore, the diffraction limit is satisfied horizontally but not vertically, which is evident in Fig. 4(d) showing that the nine holes are indicated in the horizontal direction but smear together with the third row of holes in the vertical direction. The subsequent rows of holes range in diameter from 0.8 – 0.4 mm from top to bottom. Although the four holes on the bottom row are only about the size of the wavelength, they are horizontally separated at about 1.0 mm from each other, which makes them distinguishable in the horizontal direction as their separation satisfies the diffraction limit. Clearly, the spatial resolution of the amplitude reconstruction is determined by diffraction, not by the maximum spatial frequency of 0.5 cycles/mm or the 2 x 2 mm detector aperture.

*h*= 2.0 ± 0.01 mm, which was measured with a caliper. Figures 6(b,c) show the recorded holograms at 680.0 and 725.0 GHz, corresponding to the wavelengths of

_{c}*λ*= 0.4418 mm and

_{1}*λ*= 0.4438 mm, respectively. The scanned field of view is 80 x 80 mm with 400 x 400 pixels. Each hologram is processed using the angular spectrum method (at reconstruction distance of 280 mm) to obtain the amplitude (Figs. 6(d,e)), and phase (Figs. 6(f,g)) images shown, where the gray scale of the phase images spans the range of -

_{2}*π*to +

*π*. The two phase profiles are combined, according to the procedure described above, to yield the unwrapped phase profile in Fig. 6(h), and rendered in pseudo-3D perspective view in Fig. 6(j). Figure 6(i) shows a side view through the middle of the unwrapped phase map, where the vertical scale is in radians. The optical path difference (OPD) between the edge and center of the lens resulted in a phase difference of 0.89 ± 0.10 radians according to the hologram reconstruction corresponding to an OPD of 2.92 ± 0.10 mm. Therefore, the refractive index

*n*= 1.46 ± 0.01 of the lens material could be ascertained from the OPD according to the hologram reconstruction and the physical thickness variation according to the caliper measurement. A refractive index of 1.46 is typical for PMP at THz frequencies while variations at the second decimal are a known quality issue for polymer lenses. Figure 6(i) also illustrates that a subwavelength thickness resolution of about 10 μm (

*λ*/40 at 725 GHz) was obtained. The lens’s edge thickness of 10.70 ± 0.01 mm according to the caliper measurement is larger than one beat wavelength but less than 2

*λ*. Therefore, the phase floor of approximately −1.30 radians outside the lens (Fig. 6(i)) corresponds to −1.50 x 2π = −9.40 radians considering the phase reversal at approximately −4.30 radians. Therefore, the lens thickness at the edge can be estimated as (8.8 – 4.3)/2

_{b}*π*x

*λ*/(

_{b}*n*-1) = 10.20 ± 1.00 mm, which is in excellent agreement with the measured value considering the previously mentioned variations in the refractive index. The cause for index variations in lens materials can be due to several factors including density variations in the material as well as birefringence effects. In fact, the reconstruction shows several interesting features in the lens that are not physically present on the surface of the lens. Beyond the obvious diffraction rings, the reconstruction (Fig. 6(j)) exhibits a cross-shaped area (yellow color) in the center of the lens typical of plates and lenses that exhibit birefringence. The remaining irregularities may be contributed by aliasing in the scanning mechanism, diffraction from other optics, and the spatial quality of the THz beam itself.

## 6. Conclusion

## References and links

1. | G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. |

2. | M. K. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express |

3. | B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. |

4. | W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” in |

5. | G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. |

6. | P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. |

7. | D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. |

8. | X. Song, Z. Tang, and H. Wang, “Simple and robust digital holography for phase imaging of microstructure,” |

9. | L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. |

10. | G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, S. Grilli, M. Iodice, C. Magro, and G. Pierattini, “Characterization of MEMS structures by microscopic digital holography,” Proc. SPIE |

11. | Z. Fan, H. Pang, W. Wang, C. Ning, and F. Guo, “Three dimensional deformation measurements with digital holography,” |

12. | G. Pedrini and H. J. Tiziani, “Quantitative evaluation of two-dimensional dynamic deformations using digital holography,” Opt. Laser Technol. |

13. | P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. |

14. | E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. |

15. | G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, “Numerical reconstruction and twin-image suppression using an off-axis Fresnel digital hologram,” Appl. Phys. B |

16. | L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. |

17. | C. J. Mann, L. Yu, C.-M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express |

18. | |

19. | |

20. | K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microw. Theory Tech. |

21. | J. Pearce, H. Choi, D. M. Mittleman, J. White, and D. Zimdars, “Terahertz wide aperture reflection tomography,” Opt. Lett. |

22. | A. Tamminen, J. Ala-Laurinaho, and A.V. Rӓisӓnen, “Indirect holographic imaging: evaluation of image quality at 310 GHz,” Proc. SPIE |

23. | A. A. Gorodetsky and V. G. Bespalov, “THz computational holography process & optimization,” Proc. SPIE |

24. | R. J. Mahon, J. A. Murphy, and W. Lanigan, “Digital holography at millimetre wavelengths,” Opt. Commun. |

25. | Y. Zhang, W. Zhou, X. Wang, Y. Cui, and W. Sun, “Terahertz Digital Holography,” Strain |

26. | A. A. Gorodetsky and V. G. Bespalov, “THz pulse time-domain holography,” Proc. SPIE |

27. | J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. |

28. | Attempts to collimate the beam using plastic lenses made of polytetrafluoroethylene (PTFE) and high-density polyethylene (HDPE) showed undesirable Fabry-Perot effects between the lens surfaces, causing significant phase noise in the hologram. |

29. | J. W. Goodman, |

30. | U. Schnars, T. M. Kreis, and W. P. O. Jüpner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. |

31. | J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. |

32. | S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. |

33. | V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Superresolved imaging in digital holography by superposition of tilted wavefronts,” Appl. Opt. |

34. | C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. |

35. | B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, M. G. Vlasenko, M. A. Dem’yanenko, and D. G. Esaev, “Real-Time Imaging Using a High-Power Monochromatic Terahertz Source: Comparative Description of Imaging Techniques with Examples of Application: Journal of Infrared Millimeter Terahertz Waves (online-only) (2011). |

36. | W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. |

37. | C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. |

38. | M. K. Kim, L. Yu, and C. J. Mann, “Interference techniques in digital holography,” J. Opt. A, Pure Appl. Opt. |

39. |

**OCIS Codes**

(090.1995) Holography : Digital holography

(110.6795) Imaging systems : Terahertz imaging

**ToC Category:**

Holography

**History**

Original Manuscript: March 10, 2011

Revised Manuscript: April 15, 2011

Manuscript Accepted: April 20, 2011

Published: April 26, 2011

**Citation**

Martin S. Heimbeck, Myung K. Kim, Don A. Gregory, and Henry O. Everitt, "Terahertz digital holography using angular spectrum and dual wavelength reconstruction methods," Opt. Express **19**, 9192-9200 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9192

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### References

- G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. 43(10), 1039–1055 (2005). [CrossRef]
- M. K. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express 7(9), 305–310 (2000). [CrossRef] [PubMed]
- B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008). [CrossRef] [PubMed]
- W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” in Proceedings of the National Academy of Science USA, (PNAS, 2001) pp. 11301–11305.
- G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004). [CrossRef] [PubMed]
- P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]
- D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43(36), 6536–6544 (2004). [CrossRef]
- X. Song, Z. Tang, and H. Wang, “Simple and robust digital holography for phase imaging of microstructure,” Proceedings of IEEE, Control and Decision Conference (IEEE, 2009), pp.4656–4658.
- L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40(28), 5046–5051 (2001). [CrossRef]
- G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, S. Grilli, M. Iodice, C. Magro, and G. Pierattini, “Characterization of MEMS structures by microscopic digital holography,” Proc. SPIE 4945, 71–78 (2003). [CrossRef]
- Z. Fan, H. Pang, W. Wang, C. Ning, and F. Guo, “Three dimensional deformation measurements with digital holography,” Proceedings of IEEE International Congress on Image and Signal Processing (IEEE, 2009), pp. 1–5.
- G. Pedrini and H. J. Tiziani, “Quantitative evaluation of two-dimensional dynamic deformations using digital holography,” Opt. Laser Technol. 29(5), 249–256 (1997). [CrossRef]
- P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. 44(3), 337–343 (2005). [CrossRef] [PubMed]
- E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). [CrossRef]
- G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, “Numerical reconstruction and twin-image suppression using an off-axis Fresnel digital hologram,” Appl. Phys. B 90(3-4), 527–532 (2008). [CrossRef]
- L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30(16), 2092–2094 (2005). [CrossRef] [PubMed]
- C. J. Mann, L. Yu, C.-M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13(22), 8693–8698 (2005). [CrossRef] [PubMed]
- www.virginiadiodes.com
- www.zomega-terahertz.com
- K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. H. Siegel, “Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar,” IEEE Trans. Microw. Theory Tech. 56(12), 2771–2778 (2008). [CrossRef]
- J. Pearce, H. Choi, D. M. Mittleman, J. White, and D. Zimdars, “Terahertz wide aperture reflection tomography,” Opt. Lett. 30(13), 1653–1655 (2005). [CrossRef] [PubMed]
- A. Tamminen, J. Ala-Laurinaho, and A.V. Rӓisӓnen, “Indirect holographic imaging: evaluation of image quality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).
- A. A. Gorodetsky and V. G. Bespalov, “THz computational holography process & optimization,” Proc. SPIE 6893, F1–F9 (2008).
- R. J. Mahon, J. A. Murphy, and W. Lanigan, “Digital holography at millimetre wavelengths,” Opt. Commun. 260(2), 469–473 (2006). [CrossRef]
- Y. Zhang, W. Zhou, X. Wang, Y. Cui, and W. Sun, “Terahertz Digital Holography,” Strain 44(5), 380–385 (2008). [CrossRef]
- A. A. Gorodetsky and V. G. Bespalov, “THz pulse time-domain holography,” Proc. SPIE 7601, 71–76 (2010).
- J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28(13), 1141–1143 (2003). [CrossRef] [PubMed]
- Attempts to collimate the beam using plastic lenses made of polytetrafluoroethylene (PTFE) and high-density polyethylene (HDPE) showed undesirable Fabry-Perot effects between the lens surfaces, causing significant phase noise in the hologram.
- J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Englewood, Greenwood Village, Colorado, 2005).
- U. Schnars, T. M. Kreis, and W. P. O. Jüpner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996). [CrossRef]
- J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27(24), 2179–2181 (2002). [CrossRef]
- S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006). [CrossRef] [PubMed]
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