Abstract

We demonstrate for the first time that the Hartmann wavefront sensor (HWS) principle can be applied for characterizing the wavefronts of terahertz (THz) electromagnetic radiation. The THz Hartmann wavefront sensor consists of a metallic plate with an array of holes and a two-dimensional scanable pyro-electric detector. The THz radiation with different wavefronts was generated by a far-infrared gas laser operated at 2.5 THz in combination with a number of objects that result in known wavefronts. To measure the wavefront, a beam passing through an array of holes generates intensity spots, for which the positions of the individual spot centroids are measured and compared with reference positions. The reconstructed wavefronts are in good agreement with the model expectations.

© 2012 OSA

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    [CrossRef]

2012

J. Zmuidzinas, “Superconducting microresonators: Physics and Applications,” Ann. Rev. Condens. Matter Phys. 3(1), 169–214 (2012).
[CrossRef]

2011

S. Hadjiloucas, G. C. Walker, and J. W. Bowen, “Extending murty interferometry to the Terahertz part of the spectrum,” J. Phys. Conf. Ser. 307, 012012 (2011).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

C. Kulesa, “Terahertz spectroscopy for astronomy: From comets to cosmology,” IEEE Trans. Terahertz Sci. Technol. 1(1), 232–240 (2011).
[CrossRef]

F. Castignoles, T. Lepine, P. Chavel, and G. Cohen, “Shack-Hartmann multiple spots with diffractive lenses,” Opt. Lett. 36(8), 1422–1424 (2011).
[CrossRef] [PubMed]

2010

J. Schwiegerling and E. DeHoog, “Problems testing diffractive intraocular lenses with Shack-Hartmann sensors,” Appl. Opt. 49(16), D62–D68 (2010).
[CrossRef] [PubMed]

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

2009

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

2008

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14(2), 476–481 (2008).
[CrossRef]

2007

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

2006

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state of the art,” Astronomy with High Contrast Imaging III 22, 165–185 (2006).

2005

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection: transition-edge sensors,” Top. Appl. Phys. 99, 64–149 (2005).

2004

P. F. Taday, “Applications of terahertz spectroscopy to pharmaceutical sciences,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1815), 351–364 (2004).
[CrossRef] [PubMed]

2002

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37(4), 331–340 (2002).
[CrossRef]

2001

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

1996

M. Schrader and S. W. Hell, “Wavefronts in the focus of a light microscope,” J. Microsc. 184, 143–148 (1996).

1994

1993

J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31(1), 13–62 (1993).
[CrossRef]

1992

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

1980

1975

1974

1965

Amanti, M. I.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Beck, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Beckers, J. M.

J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31(1), 13–62 (1993).
[CrossRef]

Bille, J. F.

Bitzer, A.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14(2), 476–481 (2008).
[CrossRef]

Bowen, J. W.

S. Hadjiloucas, G. C. Walker, and J. W. Bowen, “Extending murty interferometry to the Terahertz part of the spectrum,” J. Phys. Conf. Ser. 307, 012012 (2011).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Campbell, H. I.

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state of the art,” Astronomy with High Contrast Imaging III 22, 165–185 (2006).

Castignoles, F.

Chavel, P.

Chen, Z.

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

Cohen, G.

De Nicola, S.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37(4), 331–340 (2002).
[CrossRef]

DeHoog, E.

Deng, J.

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

Densing, R.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

Erstling, A.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

Faist, J.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Ferraro, P.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37(4), 331–340 (2002).
[CrossRef]

Finizio, A.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37(4), 331–340 (2002).
[CrossRef]

Fischer, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Gallagher, J. E.

Gatesman, A.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

Gemünd, H.-P.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

Gibson, A. P.

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

Goelz, S.

Gogolewski, M.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

Golden, L. J.

Greenaway, A. H.

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state of the art,” Astronomy with High Contrast Imaging III 22, 165–185 (2006).

Grimm, B.

Hadjiloucas, S.

S. Hadjiloucas, G. C. Walker, and J. W. Bowen, “Extending murty interferometry to the Terahertz part of the spectrum,” J. Phys. Conf. Ser. 307, 012012 (2011).
[CrossRef]

Haines, K. A.

Hebden, J. C.

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

Hell, S. W.

M. Schrader and S. W. Hell, “Wavefronts in the focus of a light microscope,” J. Microsc. 184, 143–148 (1996).

Helm, H.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14(2), 476–481 (2008).
[CrossRef]

Herriott, D. R.

Hilton, G. C.

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection: transition-edge sensors,” Top. Appl. Phys. 99, 64–149 (2005).

Hosako, I.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Irie, T.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Irwin, K. D.

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection: transition-edge sensors,” Top. Appl. Phys. 99, 64–149 (2005).

Kulesa, C.

C. Kulesa, “Terahertz spectroscopy for astronomy: From comets to cosmology,” IEEE Trans. Terahertz Sci. Technol. 1(1), 232–240 (2011).
[CrossRef]

Kurashina, S.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Laufer, J. G.

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

Leith, E. N.

Lepine, T.

Liang, J.

Lundershausen, G.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

Oda, N.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Pickwell-MacPherson, E.

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

Pierattini, G.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37(4), 331–340 (2002).
[CrossRef]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Reid, C. B.

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

Rosenfeld, D. P.

Sano, M.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Sasaki, T.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Scalari, G.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Schrader, M.

M. Schrader and S. W. Hell, “Wavefronts in the focus of a light microscope,” J. Microsc. 184, 143–148 (1996).

Schwiegerling, J.

Sekine, N.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Southwell, W. H.

Sudoh, T.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Taday, P. F.

P. F. Taday, “Applications of terahertz spectroscopy to pharmaceutical sciences,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1815), 351–364 (2004).
[CrossRef] [PubMed]

Upatnieks, J.

Walker, G. C.

S. Hadjiloucas, G. C. Walker, and J. W. Bowen, “Extending murty interferometry to the Terahertz part of the spectrum,” J. Phys. Conf. Ser. 307, 012012 (2011).
[CrossRef]

Wallace, V. P.

C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace, “Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55(16), 4825–4838 (2010).
[CrossRef] [PubMed]

Walther, M.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14(2), 476–481 (2008).
[CrossRef]

Wang, Y.

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

White, A. D.

Williams, B. S.

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

Yoneyama, H.

N. Oda, H. Yoneyama, T. Sasaki, M. Sano, S. Kurashina, I. Hosako, N. Sekine, T. Sudoh, and T. Irie, “Detection of terahertz radiation from quantum cascade laser using vanadium oxide microbolometer focal plane arrays,” Proc. SPIE 6940, 69402Y, 69402Y-12 (2008).
[CrossRef]

Zhang, L.

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

Zhao, Z.

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

Zmuidzinas, J.

J. Zmuidzinas, “Superconducting microresonators: Physics and Applications,” Ann. Rev. Condens. Matter Phys. 3(1), 169–214 (2012).
[CrossRef]

Ann. Rev. Condens. Matter Phys.

J. Zmuidzinas, “Superconducting microresonators: Physics and Applications,” Ann. Rev. Condens. Matter Phys. 3(1), 169–214 (2012).
[CrossRef]

Annu. Rev. Astron. Astrophys.

J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31(1), 13–62 (1993).
[CrossRef]

Appl. Opt.

Astronomy with High Contrast Imaging III

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state of the art,” Astronomy with High Contrast Imaging III 22, 165–185 (2006).

IEEE J. Sel. Top. Quantum Electron.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14(2), 476–481 (2008).
[CrossRef]

IEEE Trans. Terahertz Sci. Technol.

C. Kulesa, “Terahertz spectroscopy for astronomy: From comets to cosmology,” IEEE Trans. Terahertz Sci. Technol. 1(1), 232–240 (2011).
[CrossRef]

Infrared Phys.

R. Densing, A. Erstling, M. Gogolewski, H.-P. Gemünd, G. Lundershausen, and A. Gatesman, “Effective far infrared laser operation with mesh coupler,” Infrared Phys. 33(3), 219–226 (1992).
[CrossRef]

J. Microsc.

M. Schrader and S. W. Hell, “Wavefronts in the focus of a light microscope,” J. Microsc. 184, 143–148 (1996).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Conf. Ser.

S. Hadjiloucas, G. C. Walker, and J. W. Bowen, “Extending murty interferometry to the Terahertz part of the spectrum,” J. Phys. Conf. Ser. 307, 012012 (2011).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, L. Zhang, and J. Deng, “Surface profile measurement by terahertz interferometric phase imaging,” J. Phys. Conf. Ser. 276, 012222 (2011).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Simulations of spot patterns for a THz radiation beam passing through an array of holes by varying the diameter of holes (d) and the periodicity (p) in three masks shown in the first column. The simulated spot fields on the detection plane that is 5mm and 7mm behind the mask are shown in the first and second row, respectively.

Fig. 2
Fig. 2

Schematic of the measurement setup to demonstrate a THz Hartmann wavefront sensor (HWS). The beam generated from a FIR gas laser passes through a beam splitter. One part of the beam is monitored so that the change of the total power can been measured. Another part of the beam is reflected by two mirrors and shines onto the phase object. The HWS that contains a Hartmann mask and a pyro-electric detector on a 2D translation stage is used to measure the incident wavefront that is distorted by the phase object. The detector plane is located 7mm behind the Hartmann mask.

Fig. 3
Fig. 3

(a) Directly measured spot field of the incident THz planar wavefront in the detection plane for a given Hartmann mask position; (b) the HWS spot field that consists of the extracted centriods of the imaging spots in (a), but measured by shifting the Hartmann mask by 1 mm in either x- or y-direction and in total 9 times. (c) The reconstructed wavefront from the centriods data in (b).

Fig. 4
Fig. 4

In the first row: the HWS spot fields of spherical THz wavefronts generated by three lenses with different focal distance. The radii of curvature of the lenses are 20 mm (the first column), 30 mm (the second column) and 40 mm (the third column), respectively. In the second row: reconstructed wavefronts. In the third row: difference between measured wavefronts and perfect spherical wavefronts from a simulation.

Fig. 5
Fig. 5

(a) HDPE lens that combines a convex lens in the center with a concave lens on the edge functions as the first complex phase object. (b) The intensity distribution at the detection plane behind the phase object, measured without the Hartmann mask.

Fig. 6
Fig. 6

(a) HWS spot field of the THz wavefront generated by the first complex phase object described in Fig. 5. The black circle indicates the transition region from the inner lens to the outer lens. The spots coming from the inner lens are drawn in red and the spots from the outer lens are drawn in blue. (b) The reconstructed wavefront from (a).

Fig. 7
Fig. 7

(a) HDPE lens that combines a concave lens in the center with a convex lens on the edge acts as the 2nd complex phase object. (b) The intensity distribution at the detection plane behind the phase object, measured without the Hartmann mask.

Fig. 8
Fig. 8

(a) HWS spot field of the THz wavefront generated by the second complex phase object described in Fig. 7. The red spots originated from the inner lens and the blue ones from the outer lens. The two spots coming from the same hole are connected by a black line. (b) The reconstructed wavefront from (a). The weighted centers of each two spots connected through a black line are used to construct a continuous wavefront.

Tables (1)

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Table 1 The focal distances of the lenses used to generate spherical wavefronts. The measured radius refers to the radius of a reconstructed wavefront, and the expected radius refers to the calculated radius.

Equations (2)

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E( x,y,0 )=U( x,y )G( x,y )
E ^ ( k x , k y ,L )= E ^ ( k x , k y ,0 ) e i k z L k z = k 0 2 k x 2 k y 2

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