Abstract

This paper presents experimental results from a pulsed quantum cascade laser based cavity ringdown spectrometer used as a high-throughput detection system. The results were obtained from an optical cavity with 99.8% input and output coupling mirrors that was rapidly swept (0.2s to 7s sweep times) between 1582.25 cm−1 (6.3201μm) and 1697.00 cm−1 (5.8928μm). The spectrometer was able to monitor gas species over the pressure range 585 torr to 1μtorr, and the analysis involves a new digital data processing system that optimises the processing speed and minimises the data storage requirements. In this approach we show that is it not necessary to make direct measurements of the ringdown time of the cavity to obtain the system dynamics. Furthermore, we show that correct data processing is crucial for the ultimate implementation of a wideband IR spectrometer that covers a range similar to that of commercial Fourier transform infrared instruments.

© 2012 OSA

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    [CrossRef]

2011

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

B. J. Orr and Y. He, “Rapidly swept continuous-wave cavity-ringdown spectroscopy,” Chem. Phys. Lett.512, 1–20 (2011).
[CrossRef]

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, “Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity,” Opt. Express19, 6377–6386 (2011).
[CrossRef] [PubMed]

T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “A frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express19, 8092–8101 (2011).
[CrossRef] [PubMed]

2010

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

F. Capasso, “High-performance midinfrared quantum cascade lasers,” Opt. Eng.49, 111102 (2010).
[CrossRef]

2009

J. H. van Helden, R. Peverall, G. A. D. Ritchie, and R. J. Walker, “Rapid passage effects in nitrous oxide induced by a chirped external cavity quantum cascade laser,” Appl. Phys. Lett.94, 051116 (2009).
[CrossRef]

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

2008

G. Hancock, S. J. Horrocks, G. A. D. Ritchie, J. H. van Helden, and R. J. Walker, “Time-resolved detection of the CF3 photofragment using chirped QCL radiation,” J. Phys. Chem. A112, 9751–9757 (2008).
[CrossRef] [PubMed]

M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum.79, 023108 (2008).
[CrossRef] [PubMed]

2007

D. S. Moore, “Recent advances in trace explosives detection instrumentation,” Sens. Imaging8, 9–38 (2007).
[CrossRef]

2006

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

2005

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

R. W. Beal and T. B. Brill, “Vibrational behavior of the - NO2 group in energetic compounds,” Appl. Spect.59, 1194–1202 (2005).
[CrossRef]

2004

D. Moore, “Instrumentation for trace detection of high explosives,” Rev. Sci. Instrum.75, 2499–2512 (2004).
[CrossRef]

2002

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

2000

1999

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum.70, 1233–1257 (1999).
[CrossRef]

1998

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

1988

A. O’Keefe and D. A. G. Deacon, “Cavity ringdown optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum.59, 2544–2551 (1988).
[CrossRef]

1984

Allen, N. T.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Anderson, D. Z.

D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt.23, 1238–1245 (1984).
[CrossRef] [PubMed]

D. Z. Anderson, “Reflectometer based on optical cavity decay time,” U.S. patent 4,571,085 (February18, 1986).

Anderson, J. G.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Arnold, J. T.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Atkinson, D. B.

M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum.79, 023108 (2008).
[CrossRef] [PubMed]

Baillargeon, J. N.

Beal, R. W.

R. W. Beal and T. B. Brill, “Vibrational behavior of the - NO2 group in energetic compounds,” Appl. Spect.59, 1194–1202 (2005).
[CrossRef]

Beames, J. M.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

Berden, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ringdown spectroscopy: experimental schemes and application,” Int. Rev. Phys. Chem.19, 565–607 (2000).
[CrossRef]

Boyson, T. K.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, “Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity,” Opt. Express19, 6377–6386 (2011).
[CrossRef] [PubMed]

T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “A frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express19, 8092–8101 (2011).
[CrossRef] [PubMed]

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Robust nonlinear estimation for a Fabry-Perot optical cavity,” in 8th Asian Control Conference (Kaohsiung, Taiwan) (2011), pp. 1454–1459.

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Nonlinear Estimation of a Fabry-Perot Optical Cavity for Cavity Ring-Down Spectroscopy,” in IEEE Intern. Conf. on Cont. Applic. (CCA), (Yokohama, Japan) (2010), pp. 298–303.

Brill, T. B.

R. W. Beal and T. B. Brill, “Vibrational behavior of the - NO2 group in energetic compounds,” Appl. Spect.59, 1194–1202 (2005).
[CrossRef]

Busch, K. W.

K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy: An Ultratrace-Absorption Measurement Technique (ACS Symp. Ser. 720, American Chemical Society, Washington, DC, 1999).
[CrossRef]

Busch, M. A.

K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy: An Ultratrace-Absorption Measurement Technique (ACS Symp. Ser. 720, American Chemical Society, Washington, DC, 1999).
[CrossRef]

Butler, T. J. A.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

Calzada, M. E.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “A frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express19, 8092–8101 (2011).
[CrossRef] [PubMed]

Capasso, F.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

F. Capasso, “High-performance midinfrared quantum cascade lasers,” Opt. Eng.49, 111102 (2010).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, R. N. Zare, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Cavity ringdown spectroscopy using mid-infrared quantum-cascade lasers,” Opt. Lett.25, 666–668 (2000).
[CrossRef]

Cho, A. Y.

Clair, J. M. St.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Conroy, K. J.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

Coy, S. L.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Curl, R. F.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

De Haseth, J. A.

P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry, 2nd. ed. (Wiley-Interscience, Hoboken, NJ, USA, 2007).
[CrossRef]

Deacon, D. A. G.

A. O’Keefe and D. A. G. Deacon, “Cavity ringdown optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum.59, 2544–2551 (1988).
[CrossRef]

Demusz, J. N.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Dunayevskiy, I. G.

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

Engel, G. S.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Everest, M. A.

M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum.79, 023108 (2008).
[CrossRef] [PubMed]

Frisch, J. C.

Gmachl, C.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, R. N. Zare, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Cavity ringdown spectroscopy using mid-infrared quantum-cascade lasers,” Opt. Lett.25, 666–668 (2000).
[CrossRef]

Go, R.

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

Greenberg, M.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Griffiths, P. R.

P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry, 2nd. ed. (Wiley-Interscience, Hoboken, NJ, USA, 2007).
[CrossRef]

Hancock, G.

G. Hancock, S. J. Horrocks, G. A. D. Ritchie, J. H. van Helden, and R. J. Walker, “Time-resolved detection of the CF3 photofragment using chirped QCL radiation,” J. Phys. Chem. A112, 9751–9757 (2008).
[CrossRef] [PubMed]

Hanisco, T. F.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Harb, C. C.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, “Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity,” Opt. Express19, 6377–6386 (2011).
[CrossRef] [PubMed]

T. K. Boyson, T. G. Spence, M. E. Calzada, and C. C. Harb, “A frequency domain analysis method for cavity ring-down spectroscopy,” Opt. Express19, 8092–8101 (2011).
[CrossRef] [PubMed]

B. A. Paldus, C. C. Harb, T. G. Spence, R. N. Zare, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Cavity ringdown spectroscopy using mid-infrared quantum-cascade lasers,” Opt. Lett.25, 666–668 (2000).
[CrossRef]

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Nonlinear Estimation of a Fabry-Perot Optical Cavity for Cavity Ring-Down Spectroscopy,” in IEEE Intern. Conf. on Cont. Applic. (CCA), (Yokohama, Japan) (2010), pp. 298–303.

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Robust nonlinear estimation for a Fabry-Perot optical cavity,” in 8th Asian Control Conference (Kaohsiung, Taiwan) (2011), pp. 1454–1459.

Harris, J. S.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

He, Y.

B. J. Orr and Y. He, “Rapidly swept continuous-wave cavity-ringdown spectroscopy,” Chem. Phys. Lett.512, 1–20 (2011).
[CrossRef]

Horrocks, S. J.

G. Hancock, S. J. Horrocks, G. A. D. Ritchie, J. H. van Helden, and R. J. Walker, “Time-resolved detection of the CF3 photofragment using chirped QCL radiation,” J. Phys. Chem. A112, 9751–9757 (2008).
[CrossRef] [PubMed]

Hunter, M.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Hutchinson, A. L.

Istratov, A. A.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum.70, 1233–1257 (1999).
[CrossRef]

Kachanov, A.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Kallapur, A. G.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, “Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity,” Opt. Express19, 6377–6386 (2011).
[CrossRef] [PubMed]

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Nonlinear Estimation of a Fabry-Perot Optical Cavity for Cavity Ring-Down Spectroscopy,” in IEEE Intern. Conf. on Cont. Applic. (CCA), (Yokohama, Japan) (2010), pp. 298–303.

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Robust nonlinear estimation for a Fabry-Perot optical cavity,” in 8th Asian Control Conference (Kaohsiung, Taiwan) (2011), pp. 1454–1459.

Keutsch, F. N.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Kirkbride, K. P.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

Kosterev, A. A.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

Kroll, J. H.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Kruger, C. H.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Kuffner, P. C.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

Lapson, L.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Lewicki, R.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

Martin, J.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Martin, T.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Masser, C. S.

Mazurenka, M.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

McManus, B.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

Meijer, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ringdown spectroscopy: experimental schemes and application,” Int. Rev. Phys. Chem.19, 565–607 (2000).
[CrossRef]

Milford, G.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

Moore, D.

D. Moore, “Instrumentation for trace detection of high explosives,” Rev. Sci. Instrum.75, 2499–2512 (2004).
[CrossRef]

Moore, D. S.

D. S. Moore, “Recent advances in trace explosives detection instrumentation,” Sens. Imaging8, 9–38 (2007).
[CrossRef]

Moyer, E. J.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

O’Brien, A.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

O’Keefe, A.

A. O’Keefe and D. A. G. Deacon, “Cavity ringdown optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum.59, 2544–2551 (1988).
[CrossRef]

Orr, B. J.

B. J. Orr and Y. He, “Rapidly swept continuous-wave cavity-ringdown spectroscopy,” Chem. Phys. Lett.512, 1–20 (2011).
[CrossRef]

Orr-Ewing, A. J.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

Owano, T. G.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Paldus, B. A.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, R. N. Zare, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Cavity ringdown spectroscopy using mid-infrared quantum-cascade lasers,” Opt. Lett.25, 666–668 (2000).
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Patel, C. K. N.

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

Paul, J. B.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Peeters, R.

G. Berden, R. Peeters, and G. Meijer, “Cavity ringdown spectroscopy: experimental schemes and application,” Int. Rev. Phys. Chem.19, 565–607 (2000).
[CrossRef]

Petersen, I. R.

P. C. Kuffner, K. J. Conroy, T. K. Boyson, G. Milford, A. G. Kallapur, I. R. Petersen, M. E. Calzada, T. G. Spence, K. P. Kirkbride, and C. C. Harb, “Quantum cascade laser-based substance detection: approaching the quantum noise limited,” Proc. SPIE8032, 80320C-1–80320C-10 (2011).

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, “Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity,” Opt. Express19, 6377–6386 (2011).
[CrossRef] [PubMed]

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Robust nonlinear estimation for a Fabry-Perot optical cavity,” in 8th Asian Control Conference (Kaohsiung, Taiwan) (2011), pp. 1454–1459.

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Nonlinear Estimation of a Fabry-Perot Optical Cavity for Cavity Ring-Down Spectroscopy,” in IEEE Intern. Conf. on Cont. Applic. (CCA), (Yokohama, Japan) (2010), pp. 298–303.

Peverall, R.

J. H. van Helden, R. Peverall, G. A. D. Ritchie, and R. J. Walker, “Rapid passage effects in nitrous oxide induced by a chirped external cavity quantum cascade laser,” Appl. Phys. Lett.94, 051116 (2009).
[CrossRef]

Prasanna, M.

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

Provencal, R. A.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Pusharsky, M.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

Pushkarsky, M. B.

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

Ritchie, G. A. D.

J. H. van Helden, R. Peverall, G. A. D. Ritchie, and R. J. Walker, “Rapid passage effects in nitrous oxide induced by a chirped external cavity quantum cascade laser,” Appl. Phys. Lett.94, 051116 (2009).
[CrossRef]

G. Hancock, S. J. Horrocks, G. A. D. Ritchie, J. H. van Helden, and R. J. Walker, “Time-resolved detection of the CF3 photofragment using chirped QCL radiation,” J. Phys. Chem. A112, 9751–9757 (2008).
[CrossRef] [PubMed]

Rivero, M.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Sayres, D. S.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

Shillings, A. J. L.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

Sivco, D. L.

Spence, T. G.

Steinfeld, J. I.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Tittel, F. K.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

Todd, M. W.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Tsekoun, A. G.

M. B. Pushkarsky, I. G. Dunayevskiy, M. Prasanna, A. G. Tsekoun, R. Go, and C. K. N. Patel, “High-sensitivity detection of TNT,” Proc. Natl. Acad. Sci. U.S.A.103, 19630–19634 (2006).
[CrossRef] [PubMed]

Tuozzolo, C.

D. S. Sayres, E. J. Moyer, T. F. Hanisco, J. M. St. Clair, F. N. Keutsch, A. O’Brien, N. T. Allen, L. Lapson, J. N. Demusz, M. Rivero, T. Martin, M. Greenberg, C. Tuozzolo, G. S. Engel, J. H. Kroll, J. B. Paul, and J. G. Anderson, “A new cavity based absorption instrument for detection of water isotopologues in the upper troposphere and lower stratosphere,” Rev. Sci. Instrum.80, 044102 (2009).
[CrossRef] [PubMed]

van Helden, J. H.

J. H. van Helden, R. Peverall, G. A. D. Ritchie, and R. J. Walker, “Rapid passage effects in nitrous oxide induced by a chirped external cavity quantum cascade laser,” Appl. Phys. Lett.94, 051116 (2009).
[CrossRef]

G. Hancock, S. J. Horrocks, G. A. D. Ritchie, J. H. van Helden, and R. J. Walker, “Time-resolved detection of the CF3 photofragment using chirped QCL radiation,” J. Phys. Chem. A112, 9751–9757 (2008).
[CrossRef] [PubMed]

Vodopyanov, K. L.

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

Vyvenko, O. F.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum.70, 1233–1257 (1999).
[CrossRef]

Wada, R.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

Wahl, E. H.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Walker, R. J.

J. H. van Helden, R. Peverall, G. A. D. Ritchie, and R. J. Walker, “Rapid passage effects in nitrous oxide induced by a chirped external cavity quantum cascade laser,” Appl. Phys. Lett.94, 051116 (2009).
[CrossRef]

G. Hancock, S. J. Horrocks, G. A. D. Ritchie, J. H. van Helden, and R. J. Walker, “Time-resolved detection of the CF3 photofragment using chirped QCL radiation,” J. Phys. Chem. A112, 9751–9757 (2008).
[CrossRef] [PubMed]

Wysocki, G.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487, 1–18 (2010).
[CrossRef]

Xie, J.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Zare, R. N.

B. A. Paldus, C. C. Harb, T. G. Spence, R. N. Zare, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Cavity ringdown spectroscopy using mid-infrared quantum-cascade lasers,” Opt. Lett.25, 666–668 (2000).
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett.284, 387–395 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. B

M. W. Todd, R. A. Provencal, T. G. Owano, B. A. Paldus, A. Kachanov, K. L. Vodopyanov, M. Hunter, S. L. Coy, J. I. Steinfeld, and J. T. Arnold, “Application of mid-infrared cavity ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (68 μm) optical parametric,” Appl. Phys. B75, 367–376 (2002).
[CrossRef]

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B81, 135–141 (2005).
[CrossRef]

Appl. Phys. Lett.

J. H. van Helden, R. Peverall, G. A. D. Ritchie, and R. J. Walker, “Rapid passage effects in nitrous oxide induced by a chirped external cavity quantum cascade laser,” Appl. Phys. Lett.94, 051116 (2009).
[CrossRef]

Appl. Spect.

R. W. Beal and T. B. Brill, “Vibrational behavior of the - NO2 group in energetic compounds,” Appl. Spect.59, 1194–1202 (2005).
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Figures (11)

Fig. 1
Fig. 1

Components of a laser-based wideband spectrometer.

Fig. 2
Fig. 2

Diagram of (a) Single exponential decays, (b) 10 consecutive exponential decays and (c) relationship between τ and R as a function of the data collection window w.

Fig. 3
Fig. 3

LANL experimental setup for the pulsed laser measurements.

Fig. 4
Fig. 4

(a) Pulse train signal of the Daylight Solutions tunable mid-IR external cavity laser system; (b) Power spectral density of (a).

Fig. 5
Fig. 5

Measurement of ≈ 1m room air at 1 atmosphere (at 7500ft. elevation above sea level) using the QCL (blue) compared to the HITRAN data base (red). The QCL data has been normalised by the laser intensity at each wavelength.

Fig. 6
Fig. 6

Single pass measurements of nitromethane, CH3NO2 and acetone, C3H6O.

Fig. 7
Fig. 7

CRDS signals as measured by the MCT on a Tektronix DPO4104 oscilloscope. The PSD was determined using the pwelch command in MATLAB®.

Fig. 8
Fig. 8

Continuous wavelength spectrum measuring Nitromethane, CH3NO2, at various pressures.

Fig. 9
Fig. 9

Continuous wavelength spectrum measuring Acetone, C3H6O, at various pressures.

Fig. 10
Fig. 10

Continuous wavelength spectrum measuring CH3NO2 and C3H6O combined with room air, at various pressures.

Fig. 11
Fig. 11

Continuous wavelength spectrum measuring Trinitrotoluene, C7H5N3O6, at various equilibrium times.

Equations (7)

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

S ( t ) = k = 1 10 S k ( t ) , 0 t 10 w ,
S k ( t ) = { I 0 e ( t ( k 1 ) w ) / τ + O if ( k 1 ) w t k w 0 otherwise
A 1 = 0 10 w S ( t ) cos ( 2 π t w ) d t = 10 0 w ( I 0 e t / τ + O ) cos ( 2 π t w ) d t = 10 I 0 τ w 2 e w τ 1 w 2 + 4 π 2 τ 2
A 2 = 0 10 w S ( t ) cos ( 4 π t w ) d t = 10 0 w ( I 0 e t / τ + O ) cos ( 4 π t w ) d t = 10 I 0 τ w 2 e w τ 1 w 2 + 16 π 2 τ 2 .
R = A 2 A 1 = w 2 + 4 π 2 τ 2 w 2 + 16 π 2 τ 2 .
τ = w 2 π 1 R 4 R 1 .
A = log ( 𝒯 ) = log ( I 0 I ) = n × l 2.303 × c ( 1 τ 1 τ 0 ) .

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