Abstract

We construct a full-field phase-shifting terahertz digital holography (PS-THz-DH) system by use of a THz quantum cascade laser and an uncooled, 2D micro-bolometer array. The PS-THz-DH enables us to separate the necessary diffraction-order image from unnecessary diffraction-order images without the need for spatial Fourier filtering, leading to suppress the decrease of spatial resolution. 3D shape of a visibly opaque object is visualized with a sub-millimeter lateral resolution and a sub-µm axial resolution. Also, the digital focusing of amplitude image enables the visualization of internal structure with the millimeter-order axial selectivity. Furthermore, the internal stress distribution of an externally compressed object is visualized from the phase image. The demonstrated results imply a possibility for non-destructive inspection of visibly opaque non-metal materials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

D. M. Mittleman, “Twenty years of terahertz imaging,” Opt. Express 26(8), 9417–9431 (2018).
[Crossref]

H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photonics 10(4), 843–938 (2018).
[Crossref]

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

2017 (2)

2016 (1)

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10(2), 68–71 (2016).
[Crossref]

2015 (3)

P. Zolliker and E. Hack, “THz holography in reflection using a high resolution microbolometer array,” Opt. Express 23(9), 10957–10967 (2015).
[Crossref]

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
[Crossref]

2014 (2)

2013 (2)

M. Jewariya, E. Abraham, T. Kitaguchi, Y. Ohgi, M. Minami, T. Araki, and T. Yasui, “Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse,” Opt. Express 21(2), 2423–2433 (2013).
[Crossref]

T. Yasui, M. Jewariya, T. Yasuda, M. Schirmer, T. Araki, and E. Abraham, “Real-time two-dimensional spatio-temporal terahertz imaging based on non-collinear free-space electro-optic sampling and application to functional terahertz imaging of moving object,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8600110 (2013).
[Crossref]

2012 (3)

2011 (2)

2010 (1)

N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010).
[Crossref]

2008 (1)

2007 (2)

2006 (3)

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]

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

K. L. Nguyen, M. L. Johns, L. F. Gladden, C. H. Worrall, P. Alexander, H. E. Beere, M. Pepper, D. A. Ritchie, J. Alton, S. Barbieri, and E. H. Linfield, “Three-dimensional imaging with a terahertz quantum cascade laser,” Opt. Express 14(6), 2123–2129 (2006).
[Crossref]

2005 (1)

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

2002 (1)

1998 (1)

1997 (2)

Abbot, D.

Abdelsalam, D. G.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

Abraham, E.

T. Yasui, M. Jewariya, T. Yasuda, M. Schirmer, T. Araki, and E. Abraham, “Real-time two-dimensional spatio-temporal terahertz imaging based on non-collinear free-space electro-optic sampling and application to functional terahertz imaging of moving object,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8600110 (2013).
[Crossref]

M. Jewariya, E. Abraham, T. Kitaguchi, Y. Ohgi, M. Minami, T. Araki, and T. Yasui, “Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse,” Opt. Express 21(2), 2423–2433 (2013).
[Crossref]

M. Bessou, B. Chassagne, J.-P. Caumes, C. Pradère, P. Maire, M. Tondusson, and E. Abraham, “Three-dimensional terahertz computed tomography of human bones,” Appl. Opt. 51(28), 6738–6744 (2012).
[Crossref]

E. Abraham, Y. Ohgi, M. Minami, M. Jewariya, M. Nagai, T. Araki, and T. Yasui, “Real-time line projection for fast terahertz spectral computed tomography,” Opt. Lett. 36(11), 2119–2121 (2011).
[Crossref]

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

Alexander, P.

Alton, J.

Araki, T.

M. Jewariya, E. Abraham, T. Kitaguchi, Y. Ohgi, M. Minami, T. Araki, and T. Yasui, “Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse,” Opt. Express 21(2), 2423–2433 (2013).
[Crossref]

T. Yasui, M. Jewariya, T. Yasuda, M. Schirmer, T. Araki, and E. Abraham, “Real-time two-dimensional spatio-temporal terahertz imaging based on non-collinear free-space electro-optic sampling and application to functional terahertz imaging of moving object,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8600110 (2013).
[Crossref]

E. Abraham, Y. Ohgi, M. Minami, M. Jewariya, M. Nagai, T. Araki, and T. Yasui, “Real-time line projection for fast terahertz spectral computed tomography,” Opt. Lett. 36(11), 2119–2121 (2011).
[Crossref]

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “A terahertz paintmeter for non-contact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44(32), 6849–6856 (2005).
[Crossref]

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Barbieri, S.

Bartalini, S.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

Beere, H. E.

Bessou, M.

Boivin, L.

Caumes, J.-P.

Chassagne, B.

Chen, C.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
[Crossref]

Cicchi, R.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

Consolino, L.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

De Natale, P.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

English, C.

Ferguson, B.

Földesy, P.

Gladden, L. F.

Gray, D.

Guerboukha, H.

H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photonics 10(4), 843–938 (2018).
[Crossref]

Hack, E.

Heintzmann, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10(2), 68–71 (2016).
[Crossref]

Horstmeyer, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10(2), 68–71 (2016).
[Crossref]

Huang, H.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
[Crossref]

L. Rong, T. Latychevskaia, D. Wang, X. Zhou, H. Huang, Z. Li, and Y. Wang, “Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation,” Opt. Express 22(14), 17236–17245 (2014).
[Crossref]

Hunsche, S.

Iwata, T.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

Jewariya, M.

T. Yasui, M. Jewariya, T. Yasuda, M. Schirmer, T. Araki, and E. Abraham, “Real-time two-dimensional spatio-temporal terahertz imaging based on non-collinear free-space electro-optic sampling and application to functional terahertz imaging of moving object,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8600110 (2013).
[Crossref]

M. Jewariya, E. Abraham, T. Kitaguchi, Y. Ohgi, M. Minami, T. Araki, and T. Yasui, “Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse,” Opt. Express 21(2), 2423–2433 (2013).
[Crossref]

E. Abraham, Y. Ohgi, M. Minami, M. Jewariya, M. Nagai, T. Araki, and T. Yasui, “Real-time line projection for fast terahertz spectral computed tomography,” Opt. Lett. 36(11), 2119–2121 (2011).
[Crossref]

Jia, P.

Johns, M. L.

Kim, M. K.

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]

Kitaguchi, T.

Kofman, J.

Kreis, T.

T. Kreis, Handbook of holographic interferometry: optical and digital methods (John Wiley & Sons, 2006).

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Kumar, S.

S. Kumar, “Recent progress in terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17(1), 38–47 (2011).
[Crossref]

Latychevskaia, T.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
[Crossref]

L. Rong, T. Latychevskaia, D. Wang, X. Zhou, H. Huang, Z. Li, and Y. Wang, “Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation,” Opt. Express 22(14), 17236–17245 (2014).
[Crossref]

Leval, J.

Li, Q.

Li, Y.

Li, Z.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
[Crossref]

L. Rong, T. Latychevskaia, D. Wang, X. Zhou, H. Huang, Z. Li, and Y. Wang, “Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation,” Opt. Express 22(14), 17236–17245 (2014).
[Crossref]

Linfield, E. H.

Locatelli, M.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

Maciejewski, J.

J. Maciejewski, “Visualizing residual stresses in plastic and glass,” J. Fail. Anal. and Preven. 17(1), 5–7 (2017).
[Crossref]

Maire, P.

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]

Minami, M.

Minamikawa, T.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

Mittleman, D. M.

Mizutani, Y.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

Nagai, M.

Nallappan, K.

H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photonics 10(4), 843–938 (2018).
[Crossref]

Nguyen, K. L.

Nuss, M. C.

Oda, N.

N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010).
[Crossref]

Ogawa, T.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

Ohgi, Y.

Okabe, K.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
[Crossref]

Pavone, F.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

Pepper, M.

Picart, P.

Popescu, G.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10(2), 68–71 (2016).
[Crossref]

Pradère, C.

Ravaro, M.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

Ritchie, D. A.

Rong, L.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
[Crossref]

L. Rong, T. Latychevskaia, D. Wang, X. Zhou, H. Huang, Z. Li, and Y. Wang, “Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation,” Opt. Express 22(14), 17236–17245 (2014).
[Crossref]

Sasada, M.

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Adv. Opt. Photonics (1)

H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photonics 10(4), 843–938 (2018).
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Appl. Opt. (3)

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared, Millimeter, Terahertz Waves 39(6), 561–572 (2018).
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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).
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J. Opt. Soc. Am. A (1)

Nat. Photonics (2)

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10(2), 68–71 (2016).
[Crossref]

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

Opt. Commun. (1)

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

Opt. Express (7)

Opt. Lett. (7)

Sci. Rep. (2)

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5(1), 13566 (2015).
[Crossref]

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5(1), 8445 (2015).
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Other (1)

T. Kreis, Handbook of holographic interferometry: optical and digital methods (John Wiley & Sons, 2006).

Supplementary Material (1)

NameDescription
» Visualization 1       Digital-focusing amplitude movie of a visibly opaque, foamed polystyrene block including two metal nails.

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Figures (10)

Fig. 1.
Fig. 1. Experimental setup. THz-QCL, THz quantum cascade laser; OA-PM, off-axis parabolic mirror; OC, optical chopper; M, mirror; BS, silicon beam splitter; RR, retro reflector.
Fig. 2.
Fig. 2. (a) Optical photograph of a visibly opaque, plastic sample with two impressed letters, “P” and “S”. THz digital holograms with a phase-shift of (b) 0 rad, (c) π/2 rad, (d) π rad, and (e) 3π/2 rad. Reconstructed images of (f) amplitude and (g) phase.
Fig. 3.
Fig. 3. (a) Intensity image of two orthogonally-placed plastic lines obtained by squaring the reconstructed amplitude image. Intensity profile across (b) vertical and (c) horizontal lines in Fig. 3(a).
Fig. 4.
Fig. 4. Spatial distribution of phase noise.
Fig. 5.
Fig. 5. (a) Optical photograph and schematic diagram of a visibly opaque, silicon sample with a checker pattern. Reconstructed images of (b) amplitude and (c) phase. (d) 3D image calculated by the phase image in Fig. 5(c).
Fig. 6.
Fig. 6. (a) Amplitude images and (b) phase images with respect to different THz power. (c) Mean amplitude and (d) spatial phase noise with respect to normalized THz power.
Fig. 7.
Fig. 7. (a) Optical photograph of a visibly opaque, foamed polystyrene block including two metal nails. Digital-focusing amplitude images at (b) z = 36 mm and (c) z = 49 mm. The corresponding movie is Visualization 1. (d) Change of diameter of two metal nails calculated with respect to reconstruction distance z.
Fig. 8.
Fig. 8. Differential phase images of the compressed sample when the external compression stress was set to (a) 0 MPa, (b) 2.45 MPa, (c) 4.9 MPa, and (d) 7.35 MPa, respectively. (e) Relation between external compression stress and the mean phase difference in the black square region of Figs. 8(a) to 8(d). (f) Spatial distribution of internal stress when the external compression stress of 7.35 MPa was applied to the sample.
Fig. 9.
Fig. 9. Schematic drawing of spatial-frequency spectrum in (a) visible PS-DH and (b) PS-THz-DH.
Fig. 10.
Fig. 10. Schematic drawing of spatial-frequency spectrum in PS-THz-DH when (a) 2NA ≥ sinθ, (b) 2NA < sinθ < 3NA, and (c) 3NA ≤ sinθ. Simulation results of spatial resolution in the amplitude image. (d) Sample, (e) amplitude image in the PS-THz-DH, and (f) amplitude image in the OA-THz-DH.

Equations (16)

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u o ( x , y ) = a o ( x , y ) exp [ i ϕ o ( x , y ) ] ,
u r ( x , y ) = a r ( x , y ) exp [ i ϕ r ( x , y ) ] ,
I ( x , y ; δ ) = | u o ( x , y ) + u r ( x , y ) exp ( i δ ) | 2 = | u o ( x , y ) | 2 + | u r ( x , y ) | 2 + u o ( x , y ) u r ( x , y ) exp ( i δ ) + u o ( x , y ) u r ( x , y ) exp ( i δ ) ,
I 0 ( x , y ) = | u o ( x , y ) | 2 + | u r ( x , y ) | 2 + u o ( x , y ) u r ( x , y ) + u o ( x , y ) u r ( x , y ) ,
I π / 2 ( x , y ) = | u o ( x , y ) | 2 + | u r ( x , y ) | 2 + i u o ( x , y ) u r ( x , y ) i u o ( x , y ) u r ( x , y ) ,
I π ( x , y ) = | u o ( x , y ) | 2 + | u r ( x , y ) | 2 u o ( x , y ) u r ( x , y ) u o ( x , y ) u r ( x , y ) ,
I 3 π / 2 ( x , y ) = | u o ( x , y ) | 2 + | u r ( x , y ) | 2 i u o ( x , y ) u r ( x , y ) + i u o ( x , y ) u r ( x , y ) .
u o ( x , y ) = 1 4 u r ( x , y ) { [ I 0 ( x , y ) I π ( x , y ) ] + i [ I π / 2 ( x , y ) I 3 π / 2 ( x , y ) ] } ,
u o ( x , y ) = 1 4 { [ I 0 ( x , y ) I π ( x , y ) ] + i [ I π / 2 ( x , y ) I 3 π / 2 ( x , y ) ] } .
U o ( f x , f y ; z ) = U o ( f x , f y ; 0 ) exp [ i 2 π λ z 1 ( λ f x ) 2 ( λ f y ) 2 ] ,
L R x = 0.61 λ sin [ tan 1 ( M Δ x 2 z ) ] = 0.61 × 100 × 10 6 sin [ tan 1 ( 320 × 23.5 × 10 6 2 × 41 × 10 3 ) ] = 668 μ m
L R y = 0.61 λ sin [ tan 1 ( N Δ y 2 z ) ] = 0.61 × 100 × 10 6 sin [ tan 1 ( 240 × 23.5 × 10 6 2 × 41 × 10 3 ) ] = 889 μ m
t ( x , y ) = λ 2 π ( n S i n a i r ) ϕ ( x , y ) ,
ε z ( x , y ) = Δ z ( x , y ) z = 1 z [ λ 2 π ( n w p n a i r ) Δ ϕ ( x , y ) ] = λ Δ ϕ ( x , y ) 2 π ( n w p n a i r ) z ,
ε y ( x , y ) = ε z ( x , y ) ν = λ Δ ϕ ( x , y ) 2 π ( n w p n a i r ) z ν ,
σ y ( x , y ) = E ε y ( x , y ) = E λ Δ ϕ ( x , y ) 2 π ( n w p n a i r ) z ν ,

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