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

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2010 (3)

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 pulse time-domain holography,” Proc. SPIE 7601, 71–76 (2010).

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]

2008 (6)

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. 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]

A. A. Gorodetsky and V. G. Bespalov, “THz computational holography process & optimization,” Proc. SPIE 6893, F1–F9 (2008).

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]

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]

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

2006 (4)

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]

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]

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

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Superresolved imaging in digital holography by superposition of tilted wavefronts,” Appl. Opt. 45(5), 822–828 (2006).
[CrossRef] [PubMed]

2005 (6)

2004 (2)

2003 (2)

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]

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]

2002 (2)

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]

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27(24), 2179–2181 (2002).
[CrossRef]

2001 (1)

2000 (1)

1999 (1)

1997 (1)

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]

1996 (1)

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]

Ala-Laurinaho, J.

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).

Alexandrov, S. A.

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]

Asundi, A. K.

Badizadegan, K.

Baraniuk, R. G.

Bespalov, V. G.

A. A. Gorodetsky and V. G. Bespalov, “THz pulse time-domain holography,” Proc. SPIE 7601, 71–76 (2010).

A. A. Gorodetsky and V. G. Bespalov, “THz computational holography process & optimization,” Proc. SPIE 6893, F1–F9 (2008).

Bo, F.

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]

Brady, D. J.

Bryllert, T.

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]

Carl, D.

Chan, W. L.

Chang, C. C.

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]

Chattopadhyay, G.

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]

Chen, G. L.

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]

Choi, H.

Colomb, T.

Cooper, K. B.

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]

Coppola, G.

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]

Cuche, E.

Cui, Y.

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

Cull, C. F.

Dakoff, A.

Dasari, R. R.

De Nicola, S.

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]

Deflores, L. P.

Dengler, R. J.

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]

Depeursinge, C.

Emery, Y.

Feld, M. S.

Ferraro, P.

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]

Finizio, A.

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]

García, J.

García-Martínez, P.

Gass, J.

Gill, J.

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]

Gorodetsky, A. A.

A. A. Gorodetsky and V. G. Bespalov, “THz pulse time-domain holography,” Proc. SPIE 7601, 71–76 (2010).

A. A. Gorodetsky and V. G. Bespalov, “THz computational holography process & optimization,” Proc. SPIE 6893, F1–F9 (2008).

Gougeon, S.

Grilli, S.

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]

Gutzler, T.

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]

Hillman, T. R.

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]

Iodice, M.

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]

Iwai, H.

Jüpner, W. P. O.

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]

Kemper, B.

Kim, M. K.

Kreis, T. M.

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]

Kuo, M. K.

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]

Lanigan, W.

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

Lee, C.

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]

Leval, J.

Lin, C. Y.

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]

Liu, C.

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]

Liu, Z.

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]

Llombart, N.

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]

Lo, C.-M.

Magistretti, P. J.

Magro, C.

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]

Mahon, R. J.

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

Mait, J. N.

Mann, C. J.

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]

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]

Marquet, P.

Massig, J. H.

Mattheiss, M.

Mehdi, I.

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]

Miao, J.

Mico, V.

Mittleman, D. M.

Moravec, M. L.

Mounier, D.

Murphy, J. A.

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

Pearce, J.

Pedrini, G.

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]

Peng, X.

Picart, P.

Pierattini, G.

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]

Popescu, G.

R?is?nen, A.V.

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).

Rappaz, B.

Sampson, D. D.

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]

Schlecht, E.

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]

Schnars, U.

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]

Shen, G.

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]

Siegel, P. H.

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]

Skalare, A.

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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).

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Appl. Opt. (7)

Appl. Phys. B (1)

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[CrossRef]

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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]

IEEE Trans. Microw. Theory Tech. (1)

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).
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[CrossRef]

Opt. Lasers Eng. (1)

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Figures (6)

Fig. 1
Fig. 1

THz digital holography experimental configuration (a) and a typical interferogram at detector/hologram recording plane (b).

Fig. 2
Fig. 2

Illustration of separable Fourier spectra using off-axis holography for small (a) and large (b) reference signals.

Fig. 3
Fig. 3

THz detector horn pattern as a function of spatial frequency fx, fy ; the THz signal captured by the horn antenna at the off-axis angle θmax corresponding to a spatial frequency 0.5 cycles/mm is reduced to 27% of its peak value.

Fig. 4
Fig. 4

Steps in the reconstruction of the amplitude object at 0.712 THz: photograph (a), 80 x 80 mm hologram (b), filtered spectrum of real image (c), and amplitude reconstruction (d).

Fig. 5
Fig. 5

Digital object focusing to find the object-detector distance z. The best focus is near z = 200 mm.

Fig. 6
Fig. 6

Steps in the reconstruction of the phase object using dual wavelength reconstruction: photograph (a), holograms at 680 and 725 GHz (b-c), amplitude reconstructions (d-e), phase reconstructions (f-g), unwrapped reconstruction (h), cross-section through center of unwrappred reconstruction (i), pseudo 3D perspective of the unwrapped reconstruction (j).

Equations (7)

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θ max =sin -1 ( f c λ ) ,
I ( x , y ) = | O ( x , y ) | 2 + | R ( x , y ) | 2 + O ( x , y ) * R ( x , y ) exp ( j η 2 π y ) + O ( x , y ) R ( x , y ) * exp ( j η 2 π y ) .
OTF | F { rect ( y w ) } | 2 sinc 2 ( w f y ) .
Α ( α λ , β λ , z ) = A ( α λ , β λ , 0 ) exp ( j 2 π λ 1 α 2 β 2 z ) .
R ( θ ) = exp ( j 2 π λ y sin θ ) ,
U ( x,y,z ) = iFFT { backpropagation ( filtering ( FFT { U ( x,y,0 ) } ) ) } ,
λ b = λ 1 λ 2 | λ 2 λ 1 | .

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