Abstract

Imaging at terahertz frequencies has recently received considerable attention because many materials are semitransparent to THz waves. The principal challenge that impedes a widespread use of THz imaging is the slow acquisition time of a conventional point-by-point raster scan. In this work, we present a theoretical formulation and an experimental demonstration of a novel technique for fast compressionless terahertz imaging based on broadband Fourier optics. The technique exploits k-vector/frequency duality in Fourier optics that allows the use of a single-pixel detector to perform angular scans along a circular path, while the broadband spectrum is used to scan along the radial dimension in Fourier domain. The proposed compressionless image reconstruction technique (hybrid inverse transform) requires only a small number of measurements that scales linearly with an image’s linear size, thus promising real-time acquisition of high-resolution THz images. Additionally, our imaging technique handles equally well and on an equal theoretical footing amplitude contrast and phase contrast images, which makes this technique useful for many practical applications. A detailed analysis of the technique’s advantages and limitations is presented, and its place among other existing THz imaging techniques is clearly identified.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (3)

2015 (1)

H. Guerboukha, A. Markov, H. Qu, and M. Skorobogatiy, “Time resolved dynamic measurements at THz frequencies using a rotary optical delay line,” IEEE Trans. Terahertz Sci. Technol. 5, 564–572 (2015).
[Crossref]

2014 (5)

2013 (1)

2012 (4)

2011 (2)

S. Preu, G. H. Döhler, S. Malzer, L. J. Wand, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 061301 (2011).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging–Modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

2010 (2)

E. Abraham, A. Younus, J. C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys. A 100, 585–590 (2010).
[Crossref]

K. Lee, K. H. Jin, J. C. Ye, and J. Ahn, “Coherent optical computing for T-ray imaging,” Opt. Lett. 35, 508–510 (2010).
[Crossref]

2009 (3)

F. Blanchard, G. Sharma, X. Ropagnol, L. Razzari, R. Morandotti, and T. Ozaki, “Improved terahertz two-color plasma sources pumped by high intensity laser beam,” Opt. Express 17, 6044–6052 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

Y. C. Chen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrot, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95, 231112 (2009).
[Crossref]

2008 (4)

B. Pradarutti, R. Müller, W. Freese, G. Mattahaüs, S. Riehemann, G. Notni, S. Nolte, and A. Tünnermann, “Terahertz line detection by a microlens array coupled photoconductive antenna array,” Opt. Express 16, 18443–18450 (2008).
[Crossref]

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

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

G.-J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “High speed scanning of terahertz pulse by a rotary optical delay line,” Rev. Sci. Instrum. 79, 106102 (2008).
[Crossref]

2007 (3)

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

G. G. Lamouche, M. Dufour, B. Gauthier, V. Bartulovic, M. Hewko, and J.-P. Monchalin, “Optical delay line using rotating rhombic prisms,” Proc. SPIE 6429, 64292G (2007).
[Crossref]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref]

2006 (2)

E. Pickwell and V. P. Wallave, “Biomedical applications of terahertz technology,” J. Phys. D 39, R301–R310 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

2005 (1)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications–explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
[Crossref]

2004 (1)

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Nondestructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2004).
[Crossref]

2001 (1)

K. McClatchey, M. T. Reiten, and R. A. Cheville, “Time resolved synthetic aperture terahertz impulse imaging,” Appl. Phys. Lett. 79, 4485–4487 (2001).
[Crossref]

2000 (1)

1999 (2)

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electrooptic effect,” IEEE Microw. Compon. Lett. 47, 2644–2650 (1999).
[Crossref]

S.-G. Park, M. R. Melloch, and A. M. Weiner, “Analysis of terahertz waveforms measured by photoconductive and electrooptic sampling,” IEEE J. Quantum Electron. 35, 810–819 (1999).
[Crossref]

1998 (1)

J. Szydlo, N. Delachenal, R. Gianotti, R. Walti, H. Bleuler, and P. R. Salathe, “Air-turbine driven optical low coherence reflectometry at 28.6-kHz scan repetition rate,” Opt. Commun. 154, 1–4 (1998).
[Crossref]

1997 (1)

1996 (1)

Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
[Crossref]

1995 (1)

1991 (2)

D. C. Edelstein, R. B. Romney, and M. Scheuermann, “Rapid programmable 300 ps optical delay scanner and signal averaging system for ultrafast measurements,” Rev. Sci. Instrum. 62, 579–583 (1991).
[Crossref]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Abraham, E.

E. Abraham, A. Younus, J. C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys. A 100, 585–590 (2010).
[Crossref]

Ahn, J.

Ballif, J.

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

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

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications–explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
[Crossref]

Barland, S.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Bartels, A.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

Bartulovic, V.

G. G. Lamouche, M. Dufour, B. Gauthier, V. Bartulovic, M. Hewko, and J.-P. Monchalin, “Optical delay line using rotating rhombic prisms,” Proc. SPIE 6429, 64292G (2007).
[Crossref]

Blanchard, F.

Bleuler, H.

J. Szydlo, N. Delachenal, R. Gianotti, R. Walti, H. Bleuler, and P. R. Salathe, “Air-turbine driven optical low coherence reflectometry at 28.6-kHz scan repetition rate,” Opt. Commun. 154, 1–4 (1998).
[Crossref]

Brady, D.

Brady, D. J.

Brahm, A.

Broderick, N.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Burnett, A.

Y. C. Chen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrot, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95, 231112 (2009).
[Crossref]

Busch, S.

Busch, S. F.

Cerna, R.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

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

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Chatterjee, S.

Chavanne, P.

Chen, Y. C.

Y. C. Chen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrot, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95, 231112 (2009).
[Crossref]

Cheville, R. A.

K. McClatchey, M. T. Reiten, and R. A. Cheville, “Time resolved synthetic aperture terahertz impulse imaging,” Appl. Phys. Lett. 79, 4485–4487 (2001).
[Crossref]

Churkin, D. V.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Cole, B. E.

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Nondestructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2004).
[Crossref]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging–Modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

Cunningham, J. E.

Y. C. Chen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrot, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95, 231112 (2009).
[Crossref]

Davies, A. G.

Y. C. Chen, L. Gan, M. Stringer, A. Burnett, K. Tych, H. Shen, J. E. Cunningham, E. P. J. Parrot, J. A. Zeitler, L. F. Gladden, E. H. Linfield, and A. G. Davies, “Terahertz pulsed spectroscopic imaging using optimized binary masks,” Appl. Phys. Lett. 95, 231112 (2009).
[Crossref]

Dekorsy, T.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

Delachenal, N.

J. Szydlo, N. Delachenal, R. Gianotti, R. Walti, H. Bleuler, and P. R. Salathe, “Air-turbine driven optical low coherence reflectometry at 28.6-kHz scan repetition rate,” Opt. Commun. 154, 1–4 (1998).
[Crossref]

Delagnes, J. C.

E. Abraham, A. Younus, J. C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys. A 100, 585–590 (2010).
[Crossref]

Diddams, S. A.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref]

Dietz, R. J. B.

Döhler, G. H.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wand, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 061301 (2011).
[Crossref]

Donc, Y.

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
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Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996).
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IEEE Microw. Compon. Lett. (1)

Z. Jiang and X.-C. Zhang, “Terahertz imaging via electrooptic effect,” IEEE Microw. Compon. Lett. 47, 2644–2650 (1999).
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D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
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IEEE Trans. Terahertz Sci. Technol. (1)

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J. Appl. Phys. (1)

S. Preu, G. H. Döhler, S. Malzer, L. J. Wand, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 061301 (2011).
[Crossref]

J. Pharm. Sci. (1)

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Nondestructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2004).
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E. Pickwell and V. P. Wallave, “Biomedical applications of terahertz technology,” J. Phys. D 39, R301–R310 (2006).
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[Crossref]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Nature (2)

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
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K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
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Opt. Commun. (1)

J. Szydlo, N. Delachenal, R. Gianotti, R. Walti, H. Bleuler, and P. R. Salathe, “Air-turbine driven optical low coherence reflectometry at 28.6-kHz scan repetition rate,” Opt. Commun. 154, 1–4 (1998).
[Crossref]

Opt. Express (8)

D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single-pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
[Crossref]

B. Pradarutti, R. Müller, W. Freese, G. Mattahaüs, S. Riehemann, G. Notni, S. Nolte, and A. Tünnermann, “Terahertz line detection by a microlens array coupled photoconductive antenna array,” Opt. Express 16, 18443–18450 (2008).
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Proc. SPIE (1)

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Science (1)

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J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications–explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
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Z. Jiang and X. C. Zhang, “Free-space electro-optic techniques,” in Sensing with Terahertz Radiation (Springer, 2013).

C.-L. Wang and C.-L. Pan, “Scanning optical delay device having a helicoid reflecting mirror,” U.S. patent5,907,423 A (May 25, 1999).

K. Nallappan, J. Li, H. Guerboukha, A. Markov, B. Petrov, D. Morris, and M. Skorobogatiy, “A dynamically reconfigurable terahertz array antenna for near-field imaging applications,” arXiv:1705.10624 (2017).

K. Nallappan, J. Li, H. Guerboukha, A. Markov, B. Petrov, D. Morris, and M. Skorobogatiy, “A dynamically reconfigurable array antenna for 2D-imaging applications,” in Photonics North, Ontario, Canada, 2017, paper 36.30.

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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Hybrid image reconstruction algorithm: (a) schematic of the object plane and the Fourier plane; (b) raster scanning on a 2D Cartesian grid in the Fourier plane; and (c) corresponding hyperspectral k-space cube. (d) Hybrid reconstruction algorithm with a 1D circular scan in the Fourier plane and (e) corresponding k-space inferred using spectral information.
Fig. 2.
Fig. 2. Reconstruction of a binary amplitude image in the form of a maple leaf cutout in the metallic plate. (a) Schematic of the maple leaf cutout. Standard raster scanning: (b) amplitude and (c) phase of the k-space at a single frequency of 0.57 THz (4624 pixels). (d) Image reconstruction using the standard inverse Fourier transform (2). Image reconstruction using the hybrid inverse transform (12): (e) inferred k-space amplitude and (f) phase distribution using spectra of the THz time traces acquired at 180 pixels positioned along a circle of radius ρ0=25  mm around the origin of the Fourier plane. (g) Image reconstructed using hybrid inverse transform (12) with 180 pixels, (h) 45 pixels, and (i) 20 pixels.
Fig. 3.
Fig. 3. Reconstruction of a phase contrast image in the form of the shallow engraving of the Greek letter π onto a slab of transparent plastic. (a)–(b) Schematic of the sample na=1, nm=1.654, and Lm=1  mm. Image reconstruction using the hybrid inverse transform (17): (c) inferred k-space amplitude and (d) phase distribution using spectra of the THz time traces acquired at 180 pixels positioned along a circle of radius ρ0=25  mm around the origin of the Fourier plane. (e) Reconstructed phase image of a substrate with engraving Im{S˜(r¯)} and (f) without the engraving Im{S˜0(r¯)}. (g) Improved phase image of the engraving Im{S˜(r¯)}Im{S˜0(r¯)}. (h) Reconstructed depth of the engraving from Eq. (18) and a supplementary beam amplitude measurement.
Fig. 4.
Fig. 4. Impact of the THz bandwidth and the radial position of the detector on phase image resolution. Schematics of (a) the k-space and (b) the object plane showing relations between resolutions and image sizes. (c) Photograph of the phase mask in the form of a snowflake cutout in very thin (100  μm) paper. Reconstructed phase images using Eq. (17) with ρ0=25  mm and (d) νmax=0.46  THz, (e) νmax=0.66  THz, and (f) νmax=0.86  THz. Reconstruction with ρ0=30  mm and (g) νmax=0.46  THz, (h) νmax=0.66  THz, and (i) νmax=0.86  THz.

Equations (18)

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U(ξ,η,ν)=νjcFdxdy·S(x,y,ν)exp[j2πνcF(xξ+yη)],
S(x,y,ν)=jνcFdξdη·U(ξ,η,ν)exp[+j2πνcF(xξ+yη)].
kξ=ξνcFkη=ηνcF.
kη=η0ξ0kξwithkξξ0cF[νmin,νmax].
U(ρ,ν)=νjcFdφrdr·S(r,ν)exp[j2πρcFr·ρ],
S(r,ν)=jνcFdθρdρ·U(ρ,ν)exp[+j2πρcFr·ρ]=dθ(jνρcF)d(jνρcF)·U(ρ,ν)jν/cFexp[+2π(jρcF)·r].
S˜(r)=dθνdν(jρ02cFνU(ρ0,ν,θ))exp[+j2πνcFr·ρ0].
S˜(r)=dθνdν(jρ02cFνU(ρ0,ν)Uref(ν))exp[+j2πνcFr·ρ0],
S(r,ν)=S(r)E(ν).
Uref(ν)=(jcF/ν)·U(0,ν).
Uref(ν)=jcFν·U(0,ν)=E(ν)drS(r).
S˜(r,φ)=dθdν[ν(ρ0cF)2U(ρ0,ν)U0(0,ν)]exp[+j2πρ0cFr·ρ0].
S˜(r,φ)=S(r,φ)S(r,φ)dφrdr.
Δ(r)=Δ0μ(r)=[Lana+Lmnm][(nmna)h(r)],
S(r,ν)=S(r)E(ν)exp[j2πν(Δ0μ(r))/c],
Uref(ν)=jcF·U(0,ν)=νE(ν)exp(j2πνΔ0/c)drS(r).
S˜(r,φ)=dθdν[(ρ0cF)2U(ρ0,ν)U0(0,ν)]exp[+j2πρ0cFr·ρ0].
Im{S˜(r)}=2πcS(r)drS(r)(nmna)h(r),

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