Abstract

Recently, we demonstrated an interferometric materials analysis scheme at terahertz frequencies based on the self-mixing effect in terahertz quantum cascade lasers. Here, we examine the impact of variations in laser operating parameters, target characteristics, laser–target system properties, and the quality calibration standards on our scheme. We show that our coherent scheme is intrinsically most sensitive to fluctuations in interferometric phase, arising primarily from variations in external cavity length. Moreover we demonstrate that the smallest experimental uncertainties in the determination of extinction coefficients are expected for lossy materials.

© 2014 Optical Society of America

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2014 (4)

2013 (5)

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
[CrossRef]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[CrossRef]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21, 22194–22205 (2013).
[CrossRef]

T. Bardon, R. K. May, P. F. Taday, and M. Strlič, “Systematic study of terahertz time-domain spectra of historically informed black inks,” Analyst 138, 4859–4869 (2013).
[CrossRef] [PubMed]

2012 (2)

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

G. C. Walker, J. W. Bowen, J. Labaune, J. B. Jackson, S. Hadjiloucas, J. Roberts, G. Mourou, and M. Menu, “Terahertz deconvolution,” Opt. Express 20, 27230 (2012).
[CrossRef] [PubMed]

2011 (4)

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36, 2587–2589 (2011).
[CrossRef] [PubMed]

J.-P. Caumes, A. Younus, S. Salort, B. Chassagne, B. Recur, A. Ziéglé, A. Dautant, and E. Abraham, “Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery,” Appl. Opt. 50, 3604–3608 (2011).
[CrossRef] [PubMed]

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]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[CrossRef]

2009 (1)

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y.-T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

2008 (4)

P. U. Jepsen, J. K. Jensen, and U. Møller, “Characterization of aqueous alcohol solutions in bottles with THz reflection spectroscopy,” Opt. Express 16, 9318–9331 (2008).
[CrossRef] [PubMed]

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “7 GHz resolution waveguide THz spectroscopy of explosives related solids showing new features,” Opt. Express 16, 4094–4105 (2008).
[CrossRef] [PubMed]

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11, 18–26 (2008).
[CrossRef]

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (1)

G. Plantier, C. Bès, and T. M. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

2002 (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

1998 (1)

1995 (2)

1992 (1)

S. Shinohara, H. Yoshida, H. Ikeda, K. Nishide, and M. Sumi, “Compact and high-precision range finder with wide dynamic range and its application,” IEEE Trans. Instrum. Meas. 41, 40–44 (1992).
[CrossRef]

1987 (1)

M. Osiński and J. Buus, “Linewidth broadening factor in semiconductor lasers — An overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[CrossRef]

1986 (1)

1984 (1)

G. A. Acket, D. Lenstra, A. J. den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163– 1169 (1984).
[CrossRef]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[CrossRef]

1978 (1)

S. Donati, “Laser interferometry by induced modulation of cavity field,” J. Appl. Phys. 49, 495–497 (1978).
[CrossRef]

Abraham, E.

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

J.-P. Caumes, A. Younus, S. Salort, B. Chassagne, B. Recur, A. Ziéglé, A. Dautant, and E. Abraham, “Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery,” Appl. Opt. 50, 3604–3608 (2011).
[CrossRef] [PubMed]

Acket, G. A.

G. A. Acket, D. Lenstra, A. J. den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163– 1169 (1984).
[CrossRef]

Ahuja, A. T.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y.-T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Ancona, A.

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
[CrossRef]

Bakar, A. A. A.

Bakunov, M. I.

Bardon, T.

T. Bardon, R. K. May, P. F. Taday, and M. Strlič, “Systematic study of terahertz time-domain spectra of historically informed black inks,” Analyst 138, 4859–4869 (2013).
[CrossRef] [PubMed]

Beere, H. E.

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
[CrossRef]

Beheim, G.

Beltram, F.

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
[CrossRef]

Bertling, K.

R. Kliese, T. Taimre, A. A. A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
[CrossRef] [PubMed]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[CrossRef]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21, 22194–22205 (2013).
[CrossRef]

Y. L. Lim, K. Bertling, P. Rio, J. Tucker, and A. D. Rakić, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE6038, 60381O-1 (2006).

Bès, C.

G. Plantier, C. Bès, and T. M. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

Bessou, M.

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

Borri, S.

Bosch, T.

Bosch, T. M.

G. Plantier, C. Bès, and T. M. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

Botev, Z. I.

D. P. Kroese, T. Taimre, and Z. I. Botev, Handbook of Monte Carlo Methods (Wiley, New York, 2011).
[CrossRef]

Bowen, J. W.

Brambilla, M.

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
[CrossRef]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
[CrossRef]

Burnett, A.

Burnett, A. D.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11, 18–26 (2008).
[CrossRef]

Buus, J.

M. Osiński and J. Buus, “Linewidth broadening factor in semiconductor lasers — An overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[CrossRef]

Caumes, J.-P.

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

J.-P. Caumes, A. Younus, S. Salort, B. Chassagne, B. Recur, A. Ziéglé, A. Dautant, and E. Abraham, “Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery,” Appl. Opt. 50, 3604–3608 (2011).
[CrossRef] [PubMed]

Chassagne, B.

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

J.-P. Caumes, A. Younus, S. Salort, B. Chassagne, B. Recur, A. Ziéglé, A. Dautant, and E. Abraham, “Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery,” Appl. Opt. 50, 3604–3608 (2011).
[CrossRef] [PubMed]

Columbo, L. L.

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
[CrossRef]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

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F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
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Fan, W.

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G. A. Acket, D. Lenstra, A. J. den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163– 1169 (1984).
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R. Kliese, T. Taimre, A. A. A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
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K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
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A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21, 22194–22205 (2013).
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P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36, 2587–2589 (2011).
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Y. L. Lim, K. Bertling, P. Rio, J. Tucker, and A. D. Rakić, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE6038, 60381O-1 (2006).

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Lugarà, P. M.

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
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R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
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Martos-Levif, D.

D. Giovannacci, D. Martos-Levif, G. C. Walker, M. Menu, and V. Detalle, “Terahertz applications in cultural heritage: case studies,” in Fundamentals of Laser-Assisted Micro- and Nanotechnologies 2013, Proc. SPIE9065, 906510 (2013).
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T. Bardon, R. K. May, P. F. Taday, and M. Strlič, “Systematic study of terahertz time-domain spectra of historically informed black inks,” Analyst 138, 4859–4869 (2013).
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Menu, M.

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F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
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F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
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G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
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K. Fukunaga and M. Picollo, “Characterisation of Works of Art,” in Terahertz Spectroscopy and Imaging, K.-E. Peiponen, A. Zeitler, and M. Kuwata-Gonokami, (eds.), pp. 521–538, (Springer, Berlin, 2013).

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P. Spencer, P. Rees, and I. Pierce, “Theoretical analysis,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor LasersD. M. Kane and K. A. Shore, eds. (John Wiley & Sons, 2005), pp. 23–54.
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[CrossRef]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21, 22194–22205 (2013).
[CrossRef]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36, 2587–2589 (2011).
[CrossRef] [PubMed]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
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Recur, B.

Rees, P.

P. Spencer, P. Rees, and I. Pierce, “Theoretical analysis,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor LasersD. M. Kane and K. A. Shore, eds. (John Wiley & Sons, 2005), pp. 23–54.
[CrossRef]

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Y. L. Lim, K. Bertling, P. Rio, J. Tucker, and A. D. Rakić, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE6038, 60381O-1 (2006).

Ritchie, D. A.

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
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Salort, S.

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

J.-P. Caumes, A. Younus, S. Salort, B. Chassagne, B. Recur, A. Ziéglé, A. Dautant, and E. Abraham, “Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery,” Appl. Opt. 50, 3604–3608 (2011).
[CrossRef] [PubMed]

Scamarcio, G.

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
[CrossRef]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
[CrossRef]

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Shinohara, S.

S. Shinohara, H. Yoshida, H. Ikeda, K. Nishide, and M. Sumi, “Compact and high-precision range finder with wide dynamic range and its application,” IEEE Trans. Instrum. Meas. 41, 40–44 (1992).
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Spagnolo, V.

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
[CrossRef]

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P. Spencer, P. Rees, and I. Pierce, “Theoretical analysis,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor LasersD. M. Kane and K. A. Shore, eds. (John Wiley & Sons, 2005), pp. 23–54.
[CrossRef]

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T. Bardon, R. K. May, P. F. Taday, and M. Strlič, “Systematic study of terahertz time-domain spectra of historically informed black inks,” Analyst 138, 4859–4869 (2013).
[CrossRef] [PubMed]

Sumi, M.

S. Shinohara, H. Yoshida, H. Ikeda, K. Nishide, and M. Sumi, “Compact and high-precision range finder with wide dynamic range and its application,” IEEE Trans. Instrum. Meas. 41, 40–44 (1992).
[CrossRef]

Taday, P. F.

T. Bardon, R. K. May, P. F. Taday, and M. Strlič, “Systematic study of terahertz time-domain spectra of historically informed black inks,” Analyst 138, 4859–4869 (2013).
[CrossRef] [PubMed]

Taimre, T.

Tredicucci, A.

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
[CrossRef]

Tucker, J.

Y. L. Lim, K. Bertling, P. Rio, J. Tucker, and A. D. Rakić, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE6038, 60381O-1 (2006).

Upadhya, P. C.

Valavanis, A.

Verbeek, B. H.

G. A. Acket, D. Lenstra, A. J. den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163– 1169 (1984).
[CrossRef]

Vitiello, M. S.

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
[CrossRef]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21, 13748–13757 (2013).
[CrossRef] [PubMed]

von Edlinger, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[CrossRef]

von Staden, J.

Walker, G. C.

G. C. Walker, J. W. Bowen, J. Labaune, J. B. Jackson, S. Hadjiloucas, J. Roberts, G. Mourou, and M. Menu, “Terahertz deconvolution,” Opt. Express 20, 27230 (2012).
[CrossRef] [PubMed]

D. Giovannacci, D. Martos-Levif, G. C. Walker, M. Menu, and V. Detalle, “Terahertz applications in cultural heritage: case studies,” in Fundamentals of Laser-Assisted Micro- and Nanotechnologies 2013, Proc. SPIE9065, 906510 (2013).
[CrossRef]

Wallace, V. P.

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

Wang, Y. X. J.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y.-T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Weih, R.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[CrossRef]

Wilson, S. J.

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21, 22194–22205 (2013).
[CrossRef]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[CrossRef]

Xu, J.-H.

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
[CrossRef]

Yeung, D. K. W.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y.-T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Yoshida, H.

S. Shinohara, H. Yoshida, H. Ikeda, K. Nishide, and M. Sumi, “Compact and high-precision range finder with wide dynamic range and its application,” IEEE Trans. Instrum. Meas. 41, 40–44 (1992).
[CrossRef]

Younus, A.

Zhang, Y.-T.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y.-T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Ziéglé, A.

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

J.-P. Caumes, A. Younus, S. Salort, B. Chassagne, B. Recur, A. Ziéglé, A. Dautant, and E. Abraham, “Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery,” Appl. Opt. 50, 3604–3608 (2011).
[CrossRef] [PubMed]

Analyst (1)

T. Bardon, R. K. May, P. F. Taday, and M. Strlič, “Systematic study of terahertz time-domain spectra of historically informed black inks,” Analyst 138, 4859–4869 (2013).
[CrossRef] [PubMed]

Appl. Opt. (7)

Appl. Phys. Lett. (4)

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[CrossRef]

R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 071106 (2008).
[CrossRef]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[CrossRef]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
[CrossRef]

Appl. Spectrosc. (1)

IEEE J. Quantum Electron. (5)

G. A. Acket, D. Lenstra, A. J. den Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163– 1169 (1984).
[CrossRef]

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

M. Osiński and J. Buus, “Linewidth broadening factor in semiconductor lasers — An overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[CrossRef]

G. Plantier, C. Bès, and T. M. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

S. Shinohara, H. Yoshida, H. Ikeda, K. Nishide, and M. Sumi, “Compact and high-precision range finder with wide dynamic range and its application,” IEEE Trans. Instrum. Meas. 41, 40–44 (1992).
[CrossRef]

J. Appl. Phys. (1)

S. Donati, “Laser interferometry by induced modulation of cavity field,” J. Appl. Phys. 49, 495–497 (1978).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

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

Laser Photon.Rev. (1)

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]

Mater. Today (1)

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11, 18–26 (2008).
[CrossRef]

Opt. Commun. (1)

M. Bessou, H. Duday, J.-P. Caumes, S. Salort, B. Chassagne, A. Dautant, A. Ziéglé, and E. Abraham, “Advantage of terahertz radiation versus X-ray to detect hidden organic materials in sealed vessels,” Opt. Commun. 285, 4175–4179 (2012).
[CrossRef]

Opt. Express (5)

Opt. Lett. (3)

Phys. Med. Biol. (1)

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y.-T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Phys. Procedia (1)

F. P. Mezzapesa, L. L. Columbo, A. Ancona, M. Dabbicco, V. Spagnolo, M. Brambilla, P. M. Lugarà, and G. Scamarcio, “On Line Sensing of Ultrafast Laser Microdrilling Processes by Optical Feedback Interferometry,” Phys. Procedia 41, 670–676 (2013).
[CrossRef]

Other (7)

K. Petermann, Laser Diode Modulation and Noise (Kluwer, Dordrecht, 1991).

P. Spencer, P. Rees, and I. Pierce, “Theoretical analysis,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor LasersD. M. Kane and K. A. Shore, eds. (John Wiley & Sons, 2005), pp. 23–54.
[CrossRef]

K. Fukunaga and M. Picollo, “Characterisation of Works of Art,” in Terahertz Spectroscopy and Imaging, K.-E. Peiponen, A. Zeitler, and M. Kuwata-Gonokami, (eds.), pp. 521–538, (Springer, Berlin, 2013).

D. Giovannacci, D. Martos-Levif, G. C. Walker, M. Menu, and V. Detalle, “Terahertz applications in cultural heritage: case studies,” in Fundamentals of Laser-Assisted Micro- and Nanotechnologies 2013, Proc. SPIE9065, 906510 (2013).
[CrossRef]

Y. L. Lim, K. Bertling, P. Rio, J. Tucker, and A. D. Rakić, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE6038, 60381O-1 (2006).

S. Donati, Electro-Optical Instrumentation: Sensing and Measuring with Lasers (Prentice Hall, Upper Saddle River, 2004).

D. P. Kroese, T. Taimre, and Z. I. Botev, Handbook of Monte Carlo Methods (Wiley, New York, 2011).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Three mirror model for a laser under feedback. Light recirculates in the laser cavity between mirrors M0 and Ms — solid arrows in laser cavity of length L. Light exits through Ms, is reflected from the external target Mext, and is reinjected into the laser cavity — solid arrows in external cavity of length Lext.

Fig. 2
Fig. 2

Systematic sensitivity of the system when η ≈ 0 and ηΓ 0, in terms of equivalent change in amplitude reflection coefficient Δ R A and phase-shift on reflection Δ θ R A, for a range of laser wavelengths (frequencies). Blue contours are lines of constant λ0γ. Red contours are lines of constant γ.

Fig. 3
Fig. 3

Sensitivity of the system to random variations in ( R A, θ R A) for a range of plastics. 95% confidence intervals are drawn for each plastic, with Var ( R A ) 0.00316 (Var( R A) = 10−5) and Var ( θ R A ) 0.00316 rad (Var( θ R A) = 10−5 rad2), at ν = 2.59 THz with Var ( ν ) = 10 kHz (Var(ν) = 108 Hz2), and an external cavity of Lext = 500 mm. Black contours are lines of constant n. Red contours are lines of constant k. Plastics at 2.59 THz are POM (dot), PA6 (circle), PVC (×), HDPE (cross), PTFE (star), PMMA (square), HDPE Black (diamond), and PC (triangle).

Fig. 4
Fig. 4

Sensitivity of swept-frequency self-mixing signals to systematic and random changes. (a) Systematic change in external cavity length (ΔL) of 0, 250, and 500 wavelengths on Lext = 500 mm, for fixed RA = 0.01 and θ R A= 0.05 rad. (b) Systematic change in RA from 0.001, 0.01, and 0.1, for fixed Lext = 500 mm and θ R A= 0.05 rad. (c) Systematic change in θ R Afrom 0.01 rad, 0.05 rad, and 0.1 rad, for fixed Lext = 500 mm and RA = 0.01. (d)–(f) As (a)–(c), with additive zero-mean Gaussian variation in Lext with standard deviation 10−4 λ 0 m; R Awith standard deviation 10−2; and θ R Awith standard deviation 10−2 rad.

Equations (39)

Equations on this page are rendered with MathJax. Learn more.

R = ( n 0 n ) 2 + k 2 ( n 0 + n ) 2 + k 2 , θ R = arctan ( 2 n 0 k n 0 2 n 2 k 2 ) ,
n = 1 R 1 + R 2 R cos ( θ R ) , k = 1 R sin ( θ R ) 1 + R 2 R cos ( θ R ) .
φ ( t ) = φ 0 + Φ Δ T t θ R ,
φ S φ FB = C sin ( φ FB + arctan α ) ,
V = V 0 + β cos ( φ FB ) ,
C C ( α ) = τ ext τ L κ ext 1 + α 2 ,
κ ext = ε R R s ( 1 R s ) .
R M = C 1 + α 2 = ε ( 1 R s ) n in L in R s L ext R A ,
θ R M = θ R A 4 π c ν 0 L ext ,
R M = a R + b R R A
θ R M = a θ + b θ θ R A ,
R 1 A = a R + b R R 1 M , R 2 A = a R + b R R 2 M , θ R , 1 A = a θ + b θ θ R , 1 M , θ R , 2 A = a θ + b θ θ R , 2 M .
a R = R 1 A R 2 M R 1 M R 2 A R 1 M R 2 M , b R = R 1 A R 2 M R 1 M R 2 M ,
a θ = θ R , 1 A θ R , 2 M θ R , 1 M θ R , 2 A θ R , 1 M θ R , 2 M , b θ = θ R , 1 A θ R , 2 A θ R , 1 M θ R , 2 M .
φ + Δ φ = 4 π c ( ν 0 + Δ ν ) ( L ext + Δ L ) ( θ R A + θ R A ) ,
C + Δ C = ε 1 + α 2 ( 1 R s ) n in L in R s ( L ext + Δ L ) ( R A + Δ R A ) .
θ R M = θ R A + Δ θ R A 4 π c ( ν 0 L ext + ν 0 Δ L + Δ ν L ext + Δ ν Δ L ) .
R M = ε ( 1 R s ) n in L in R s ( L ext + Δ L ) ( R A + Δ R A ) .
θ R M = θ R A + Δ θ R A 4 π { Γ + γ + η ( Γ + γ ) } .
Δ θ R A 4 π = 1 4 γ + η ( Γ + γ ) Δ θ R A 4 π + 1 4 .
R M = ε ( 1 R s ) n in L in R s ( Γ + γ ) λ 0 ( R A + Δ R A ) .
( R M θ R M ) ~ N ( μ , Σ ) ,
μ = ( 𝔼 R M 𝔼 θ R M ) , and Σ = ( Var ( R M ) Cov ( R M , θ R M ) Cov ( R M , θ R M ) Var ( θ R M ) ) .
𝔼 R M = ε ( 1 R s ) n in L in R s 𝔼 R A 𝔼 L ext , 𝔼 θ R M = 𝔼 θ R A 4 π c 𝔼 ν 𝔼 L ext .
Var ( R M ) = ( ε ( 1 R s ) n in L in R s ) 2 ( Var( L ext ) Var ( R A ) + ( 𝔼 L ext ) 2 Var ( R A ) + ( 𝔼 R A ) 2 Var ( L ext ) ) ,
Var ( θ R M ) = Var ( θ M A ) + ( 4 π c ) 2 ( Var ( L ext ) Var ( ν ) + ( 𝔼 L ext ) 2 Var ( ν ) + ( 𝔼 ν ) 2 Var ( L ext ) ) ,
Cov ( R M , θ R M ) = ε ( 1 R s ) n i n L i n R s 4 π c 𝔼 R A 𝔼 ν Var ( L e x t ) .
( R A θ R A ) = A ( R M θ R M ) + b ~ N ( A μ + b , A Σ A T )
( n k ) = g ( R M , θ R M ) ~ approx N ( g ( A μ + b ) , J g A Σ A T J g T ) ,
( n ^ k ^ ) = g ( R M ¯ , θ R M ¯ ) , R M ¯ = 1 N i = 1 N R M i , θ R M ¯ = 1 N i = 1 N θ R , i M ,
( R M ¯ θ R M ¯ ) ~ N ( μ , Σ / N ) .
R M i = β 0 + β x ( x i x 0 ) + β y ( y i y 0 ) ,
A = ( 1 x 1 x 0 y 1 y 0 1 x 2 x 0 y 2 y 0 1 x N x 0 y N y 0 ) , β = ( β 0 β x β y ) ,
( A T A ) β ^ = A T v .
v i ˜ = v i β x ^ ( x i x 0 ) β y ^ ( y i y 0 ) , i = 1 , , N .
J g = ( n R n θ R k R k θ R , )
n R = 2 ( 2 R + ( 1 + R ) cos ( θ R ) ) ( 1 + R 2 R cos ( θ R ) ) 2 , n θ R = 2 R ( 1 + R ) sin ( θ R ) ( 1 + R 2 R cos ( θ R ) ) 2 ,
k R = 2 ( 1 + R ) sin ( θ R ) ( 1 + R 2 R cos ( θ R ) ) 2 , k θ R = 2 R ( 2 R + ( 1 + R ) cos ( θ R ) ) ( 1 + R 2 R cos ( θ R ) ) 2 .
θ * argmin θ Θ S ( θ ) , with S ( θ ) = k = 1 n w k ( V k V ( t k ; θ ) ) 2 ,

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