Abstract

We demonstrate a digital holographic setup for Terahertz imaging of surfaces in reflection. The set-up is based on a high-power continuous wave (CW) THz laser and a high-resolution (640 × 480 pixel) bolometer detector array. Wave propagation to non-parallel planes is used to reconstruct the object surface that is rotated relative to the detector plane. In addition we implement synthetic aperture methods for resolution enhancement and compare Fourier transform phase retrieval to phase stepping methods. A lateral resolution of 200 μm and a relative phase sensitivity of about 0.4 rad corresponding to a depth resolution of 6 μm are estimated from reconstructed images of two specially prepared test targets, respectively. We highlight the use of digital THz holography for surface profilometry as well as its potential for video-rate imaging.

© 2015 Optical Society of America

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References

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2014 (2)

2013 (2)

X. Xu, G. Lu, G. Han, F. Gao, Z. Jiao, and D. Li, “Phase stitching and error correction in aperture synthesis for generalized phase-shifting interferometry,” Appl. Opt. 52, 4864–4870 (2013).
[Crossref] [PubMed]

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE Int. Soc. Opt. Eng. 8846, 88460S (2013).

2012 (2)

G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photonics 4, 472–553 (2012).
[Crossref]

K. Xue, Q. Li, Y.-D. Li, and Q. Wang, “Continuous-wave terahertz in-line digital holography,” Opt. Lett. 37, 3228–3230 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

2008 (1)

2007 (3)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys 70, 1325–1379 (2007).
[Crossref]

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[Crossref]

2006 (2)

2005 (1)

2003 (1)

2002 (1)

1999 (1)

1998 (1)

Alfieri, D.

Banerjee, P. P.

G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photonics 4, 472–553 (2012).
[Crossref]

Bespalov, V. G.

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE Int. Soc. Opt. Eng. 8846, 88460S (2013).

Binet, R.

Boreman, J. W.

J. W. Boreman, Modulation Transfer Function in Optical and Electro-optical Systems (SPIE, 2001).
[Crossref]

Chan, W. L.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys 70, 1325–1379 (2007).
[Crossref]

Chen, Z.

Colineau, J.

Creath, K.

K. Creath and J. Wyant, “Moiré and fringe projection techniques,” in “Optical Shop Testing,”, D. Malacara, ed. (John Wiley & Sons, 1992), 2nd ed.

Cuche, E.

Deibel, J.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys 70, 1325–1379 (2007).
[Crossref]

Delen, N.

Deng, J.

Depeursinge, C.

Ding, S.-H.

Everitt, H. O.

Ferraro, P.

Finizio, A.

Gao, F.

García, J.

García-Martínez, P.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (MacGraw-Hill, 1996), chap. 3.10.

Gorodetsky, A. A.

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE Int. Soc. Opt. Eng. 8846, 88460S (2013).

Gregory, D. A.

Hack, E.

E. Hack and P. Zolliker, “Terahertz holography for imaging amplitude and phase objects,” Opt. Express 22, 16079–16086 (2014).
[Crossref] [PubMed]

P. Zolliker and E. Hack, “Resolution limits of terahertz holography using a QCL,” in “Proceedings of the 39th Int. Conf. on Infrared, Millimeter, and THz Waves,” (2014).

Han, G.

Heimbeck, M. S.

Hooker, B.

Huang, H.

Jiao, Z.

Kang, K.

Kim, M. K.

Kreis, T.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[Crossref]

Latychevskaia, T.

Lehureau, J.-C.

Li, D.

Li, Q.

Li, Y.-D.

Li, Z.

Liu, J.-P.

T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography with Matlab (Cambridge University Press, 2014), 1st ed.

Lu, G.

Marquet, P.

Matsushima, K.

Mico, V.

Mittleman, D. M.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys 70, 1325–1379 (2007).
[Crossref]

Nehmetallah, G.

G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photonics 4, 472–553 (2012).
[Crossref]

Nicola, S. D.

Petrov, N. V.

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE Int. Soc. Opt. Eng. 8846, 88460S (2013).

Pierattini, G.

Poon, T.-C.

T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography with Matlab (Cambridge University Press, 2014), 1st ed.

Rong, L.

Schimmel, H.

Schlüter, K.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[Crossref]

Szeliski, R.

R. Szeliski, “Image alignment and stitching: A tutorial,” Found. Trends. Comput. Graph. Vis. 2, 1–104 (2006).
[Crossref]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Wang, D.

Wang, Q.

Wang, Y.

Wyant, J.

K. Creath and J. Wyant, “Moiré and fringe projection techniques,” in “Optical Shop Testing,”, D. Malacara, ed. (John Wiley & Sons, 1992), 2nd ed.

Wyrowski, F.

Xu, X.

Xue, K.

Yao, R.

Zalevsky, Z.

Zhang, L.

Zhao, Z.

Zhou, X.

Zolliker, P.

E. Hack and P. Zolliker, “Terahertz holography for imaging amplitude and phase objects,” Opt. Express 22, 16079–16086 (2014).
[Crossref] [PubMed]

P. Zolliker and E. Hack, “Resolution limits of terahertz holography using a QCL,” in “Proceedings of the 39th Int. Conf. on Infrared, Millimeter, and THz Waves,” (2014).

Adv. Opt. Photonics (1)

G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photonics 4, 472–553 (2012).
[Crossref]

Appl. Opt. (6)

Found. Trends. Comput. Graph. Vis. (1)

R. Szeliski, “Image alignment and stitching: A tutorial,” Found. Trends. Comput. Graph. Vis. 2, 1–104 (2006).
[Crossref]

J. Opt. Soc. Am. A (3)

Nat. Photonics (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Opt. Eng. (1)

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE Int. Soc. Opt. Eng. (1)

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE Int. Soc. Opt. Eng. 8846, 88460S (2013).

Rep. Prog. Phys (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys 70, 1325–1379 (2007).
[Crossref]

Other (6)

T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography with Matlab (Cambridge University Press, 2014), 1st ed.

P. Zolliker and E. Hack, “Resolution limits of terahertz holography using a QCL,” in “Proceedings of the 39th Int. Conf. on Infrared, Millimeter, and THz Waves,” (2014).

P. Rastogi and E. Hack, eds., Phase Estimation in Optical Interferometry (CRC, 2014).

J. Goodman, Introduction to Fourier Optics (MacGraw-Hill, 1996), chap. 3.10.

K. Creath and J. Wyant, “Moiré and fringe projection techniques,” in “Optical Shop Testing,”, D. Malacara, ed. (John Wiley & Sons, 1992), 2nd ed.

J. W. Boreman, Modulation Transfer Function in Optical and Electro-optical Systems (SPIE, 2001).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) Tiling of frames for synthetic aperture. Frame centers are shown with red circles and the sequence of stitching is marked with arrows. (b) Two single frames from different camera positions with overlap area marked. (c) Stitched frames of (b), for a final stitched image see also Fig. 3, top left.
Fig. 2
Fig. 2 Experimental setup. The reference mirror is translated for phase stepping, and the camera can be moved in x and y direction for synthetic aperture.
Fig. 3
Fig. 3 Sample 1: Photo (far left). Hologram (top left) and phase at hologram plane (bottom left). Intensity and phase of reconstructed object: using the full synthetic aperture data and PSA (middle), using a single frame and FTM (right).
Fig. 4
Fig. 4 Lateral resolution as a function of the effective Numerical Aperture (NA) for simulations (0° and 45° geometry) and experimental data (PSA and FTM).
Fig. 5
Fig. 5 Sample 2: Comparison of THz and projection moiré topography. Photo (top left), moiré phase image (top middle), moiré profile (top right), THz intensity (bottom left), THz phase (bottom middle), THz profile (bottom right), scale for profile images (far right). The numbers on the photo identify the hollows for depth measurements.
Fig. 6
Fig. 6 Depth differences compared to optical microscopy for THz holography and projection moiré.
Fig. 7
Fig. 7 Sample 3: Photo (top left), moiré phase image (top middle), moiré profile (top right), THz intensity (bottom left), THz phase (bottom middle), THz profile (bottom right), scale for profile images (far right).

Tables (2)

Tables Icon

Table 1 Lateral resolution as a function of the effective Numerical Aperture (NA) for experimental data (PSA and FTM).

Tables Icon

Table 2 Depth determination of sample 2 compared with optical measurement. Numbers in parentheses are estimated standard deviation in units of the last digit. For hollow numbering see Fig. 5.

Equations (11)

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I = I ref + I obj + 2 I ref I obj cos ( ϕ ref ϕ obj + δ ϕ ) ,
f ( x , y , z 0 ) = 1 { F ( u , v ) e 2 π i w ( u , v ) z 0 }
w ( u , v ) = λ 2 u 2 v 2
R = [ a 1 a 4 a 7 a 2 a 5 a 8 a 3 a 6 a 9 ] , R 1 = R T = [ a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 ]
u = a 1 u ^ + a 2 v ^ + a 3 w ( u ^ , v ^ )
v = a 4 u ^ + a 5 v ^ + a 6 w ( u ^ , v ^ )
f ^ ( x ^ , y ^ , 0 ) = F ^ ( u ^ , v ^ ) e 2 π i ( u ^ x ^ + v ^ y ^ ) d u ^ d v ^ = 1 { F ^ ( u ^ , v ^ ) }
F ^ ( u ^ , v ^ ) + F ( a 1 u ^ + a 2 v ^ + a 3 w ^ ( u ^ , v ^ ) , a 4 u ^ + a 5 v ^ + a 6 w ^ ( u ^ , v ^ ) ) | J ( u ^ , v ^ ) | ,
J ( u ^ , v ^ ) = ( a 2 a 6 a 3 a 5 ) u ^ w ^ ( u ^ , v ^ ) + ( a 3 a 4 a 1 a 6 ) v ^ w ^ ( u ^ , v ^ ) + ( a 1 a 5 a 2 a 4 )
R y ( ψ ) = [ cos ψ 0 sin ψ 0 1 0 sin ψ 0 cos ψ ]
F ^ ( u ^ , v ^ ) = F ( cos ψ u ^ + sin ψ w ^ ( u ^ , v ^ ) , v ^ ) | cos ψ + sin ψ u ^ w ^ ( u ^ , v ^ ) |

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