Abstract

A UV ozone differential-absorption lidar (DIAL) utilizing a Nd:YAG laser and a single Raman cell filled with carbon dioxide (CO2) is designed, developed, and evaluated. The generated wavelengths are 276, 287, and 299  nm, comprising the first to third Stokes lines of the stimulated Raman scattering technique. The correction terms originated from the aerosol extinction, the backscatter, and the absorption by other gases are estimated using a model atmosphere. The experimental results demonstrate that the emitted output energies were 13 mJ∕pulse at 276   nm and 287   nm and 5  mJ/pulse at 299  nm, with pump energy of 91 mJ∕pulse and a CO2 pressure of 0.7 MPa. The three Stokes lines account for 44.0% of the available energy. The use of argon or helium as a buffer gas in the Raman cell was also investigated, but this leads to a dramatic decrease in the third Stokes line, which makes this wavelength practically unusable. Our observations confirmed that 30 min of integration were sufficient to observe ozone concentration profiles up to 10  km. Aerosol extinction and backscatter correction are estimated and applied. The aerosol backscatter correction profile using 287 and 299   nm as reference wavelengths is compared with that using 355   nm. The estimated statistical error is less than 5% at 1 .5   km and 10% at 2 .6   km. Comparisons with the operational carbon–iodine type chemical ozonesondes demonstrate 20% overestimation of the ozone profiles by the DIAL technique.

© 2007 Optical Society of America

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2004 (1)

S. Tzortzakis, G. Tsaknakis, A. Papayannis, and A. A. Serafetinides, "Investigation of the spatial profile of stimulated Raman scattering beams in D2 and H2 gases using a pulsed Nd:YAG laser at 266 nm," Appl. Phys. B 79, 71-75 (2004).
[CrossRef]

2003 (1)

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

2002 (1)

M. Schroter, A. Obermeier, D. Bruggemann, and O. Klemm, "Application of ground-based lidar for studies of the dynamics of ozone in a mountainous basin," Envir. Sci. Pollut. Res. 9, 381-384 (2002).
[CrossRef]

2001 (1)

L. Fiorani and E. Durieux, "Comparison among error calculations in differential absorption lidar measurements," Opt. Laser Technol. 33, 371-377 (2001).
[CrossRef]

1999 (2)

1998 (5)

L. Schoulepnikoff, V. Mitev, V. Simeonov, B. Calpini, and H. van den Bergh, "Experimental investigation of high-power single-pass Raman shifters in the ultraviolet with Nd:YAG and KrF lasers," Appl. Opt. 36, 5026-5043 (1998).
[CrossRef]

G. Ancellet and F. Ravetta, "Compact airborne lidar for tropospheric ozone: description and field measurements," Appl. Opt. 37, 5509-5521 (1998).
[CrossRef]

V. Simeonov, V. Mitev, H. van den Bergh, and B. Calpini, "Raman frequency shifting in a CH4:H2:Ar mixture pumped by the fourth harmonic of a Nd:YAG laser," Appl. Opt. 37, 7112-7115 (1998).
[CrossRef]

A. O. Langford and S. J. Reid, "Dissipation and mixing of a small-scale stratospheric intrusion in the upper troposphere," J. Geophys. Res. 103, 31265-31276 (1998).
[CrossRef]

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (3)

J. A. Sunesson, A. Apiuley, and D. P. J. Swart, "Differential absorption lidar system for routine monitoring of tropospheric ozone," Appl. Opt. 33, 7045-7058 (1994).
[CrossRef] [PubMed]

T. Fujimoto and O. Uchino, "Estimation of the error caused by smoothing on DIAL measurements of stratospheric ozone," J. Meteorol. Soc. Jpn. 72, 605-611 (1994).

U. Kempfer, W. Carnuth, R. Lotz, and T. Trickl, "A wide-range ultraviolet lidar system for tropospheric ozone measurements: development and application," Rev. Sci. Instrum. 65, 3145-3164 (1994).
[CrossRef]

1991 (5)

M. Uchiumi, T. Shibata, and M. Maeda, "Measurement of changes in lower tropospheric ozone distribution through one day using a compact UV solar-blind lidar," J. Meteorol. Soc. Jpn. 69, 513-521 (1991).

G. Ancellet, J. Pelon, M. Beekmann, A. Papayannis, and G. Mégie, "Ground-based lidar studies of ozone exchanges between the stratosphere and the troposphere," J. Geophys. Res. 96, 22401-22421 (1991).
[CrossRef]

D. Diebel, M. Bristow, and R. Zimmermann, "Stokes shifted laser lines in KrF-pumped hydrogen: reduction of beam divergence by addition of helium," Appl. Opt. 30, 626-628 (1991).
[CrossRef] [PubMed]

O. Uchino and I. Tabata, "Mobile lidar for simultaneous measurements of ozone, aerosols, and temperature in the stratosphere," Appl. Opt. 30, 2005-2012 (1991).
[CrossRef] [PubMed]

W. B. Grant, E. V. Browell, N. S. Higdon, and S. Ismail, "Raman shifting of KrF laser radiation for tropospheric ozone measurements," Appl. Opt. 30, 2628-2633 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

G. Ancellet, A. Papayannis, J. Pelon, and G. Mégie, "DIAL tropospheric ozone measurement using a Nd:YAG laser and the Raman shifting technique," J. Atmos. Ocean. Technol. 6, 832-839 (1989).
[CrossRef]

1987 (4)

E. Browell, E. Danielsen, S. Ismail, G. L. Gregory, and S. M. Beck, "Tropopose fold structure determined from airborne lidar and in situ measurements," J. Geophys. Res. 92, 2112-2120 (1987).
[CrossRef]

T. Shibata, M. Maeda, A. Utsunomiya, and T. Mizoguchi, "Simultaneous measurements of ozone by UV lidar and chemical ozonesonde," J. Meteorol. Soc. Jpn. 65, 999-1003 (1987).

H. Edner, K. Fredriksson, A. Sunesson, S. Svanberg, L. Uneus, and W. Wendt, "Mobile remote sensing system for atmospheric monitoring," Appl. Opt. 26, 4330-4338 (1987).
[CrossRef] [PubMed]

A. Luches, V. Nassisi, and M. R. Perrone, "Stimulated Raman scattering in H2-Ar mixtures," Opt. Lett. 12, 33-35 (1987).
[CrossRef] [PubMed]

1986 (1)

L. T. Molina and M. J. Molina, "Absolute absorption cross sections of ozone in the 185- to 350-nm wavelength range," J. Geophys. Res. 91, 14501-14508 (1986).
[CrossRef]

1985 (1)

1984 (1)

1983 (1)

1980 (1)

1972 (1)

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, "Optical properties of the atmosphere (3rd ed.)," Air Force Systems Command, United States Air Force, AFCRL-72-0497 (1972).

1970 (1)

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, "Transient stimulated rotational and vibrational Raman scattering in gases," Appl. Phys. Lett. 16, 209-211 (1970).
[CrossRef]

1966 (1)

G. Eckhardt, "Selection of Raman laser materials," IEEE J. Quantum Electron. QE-2, 1-8 (1966).
[CrossRef]

Alvarez, R. J.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Ancellet, G.

G. Ancellet and F. Ravetta, "Compact airborne lidar for tropospheric ozone: description and field measurements," Appl. Opt. 37, 5509-5521 (1998).
[CrossRef]

G. Ancellet, J. Pelon, M. Beekmann, A. Papayannis, and G. Mégie, "Ground-based lidar studies of ozone exchanges between the stratosphere and the troposphere," J. Geophys. Res. 96, 22401-22421 (1991).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, and G. Mégie, "Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere," Appl. Opt. 29, 467-476 (1990).
[CrossRef] [PubMed]

G. Ancellet, A. Papayannis, J. Pelon, and G. Mégie, "DIAL tropospheric ozone measurement using a Nd:YAG laser and the Raman shifting technique," J. Atmos. Ocean. Technol. 6, 832-839 (1989).
[CrossRef]

G. Ancellet and J. Bosenberg, "Chapter 2 methodology," in Instrument Development for Atmospheric Research and Monitoring, J. Bosenberg, D. Brassington, and P. C. Simon, eds. (Springer, 1997), p. 19.

Apiuley, A.

Balin, J.

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

Banta, R. M.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Beck, S. M.

E. Browell, E. Danielsen, S. Ismail, G. L. Gregory, and S. M. Beck, "Tropopose fold structure determined from airborne lidar and in situ measurements," J. Geophys. Res. 92, 2112-2120 (1987).
[CrossRef]

Beekmann, M.

G. Ancellet, J. Pelon, M. Beekmann, A. Papayannis, and G. Mégie, "Ground-based lidar studies of ozone exchanges between the stratosphere and the troposphere," J. Geophys. Res. 96, 22401-22421 (1991).
[CrossRef]

Bergwerff, H. B.

Bisson, S. E.

Bloembergen, N.

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, "Transient stimulated rotational and vibrational Raman scattering in gases," Appl. Phys. Lett. 16, 209-211 (1970).
[CrossRef]

Bosenberg, J.

G. Ancellet and J. Bosenberg, "Chapter 2 methodology," in Instrument Development for Atmospheric Research and Monitoring, J. Bosenberg, D. Brassington, and P. C. Simon, eds. (Springer, 1997), p. 19.

Bristow, M.

Browell, E.

E. Browell, E. Danielsen, S. Ismail, G. L. Gregory, and S. M. Beck, "Tropopose fold structure determined from airborne lidar and in situ measurements," J. Geophys. Res. 92, 2112-2120 (1987).
[CrossRef]

Browell, E. V.

Bruggemann, D.

M. Schroter, A. Obermeier, D. Bruggemann, and O. Klemm, "Application of ground-based lidar for studies of the dynamics of ozone in a mountainous basin," Envir. Sci. Pollut. Res. 9, 381-384 (2002).
[CrossRef]

Calpini, B.

V. Simeonov, V. Mitev, H. van den Bergh, and B. Calpini, "Raman frequency shifting in a CH4:H2:Ar mixture pumped by the fourth harmonic of a Nd:YAG laser," Appl. Opt. 37, 7112-7115 (1998).
[CrossRef]

L. Schoulepnikoff, V. Mitev, V. Simeonov, B. Calpini, and H. van den Bergh, "Experimental investigation of high-power single-pass Raman shifters in the ultraviolet with Nd:YAG and KrF lasers," Appl. Opt. 36, 5026-5043 (1998).
[CrossRef]

V. Simeonov, B. Calpini, and H. van den Bergh, "New Raman-shifted sources for ozone DIAL applications," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L.Bissonnette, G.Roy, and G.Vallee, eds. (Defence R&D Canada, 2002), pp. 19-22.

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

V. Simeonov, B. Lazzarotto, P. Quaglia, H. van den Bergh, and B. Calpini, "Three-wavelength UV ozone DIAL based on a Raman cell filled with two Raman active gases," The 20th International Laser Radar Conference (Vichy, 2000).

Carman, R. L.

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, "Transient stimulated rotational and vibrational Raman scattering in gases," Appl. Phys. Lett. 16, 209-211 (1970).
[CrossRef]

Carnuth, W.

U. Kempfer, W. Carnuth, R. Lotz, and T. Trickl, "A wide-range ultraviolet lidar system for tropospheric ozone measurements: development and application," Rev. Sci. Instrum. 65, 3145-3164 (1994).
[CrossRef]

Carswell, A. I.

Clark, R. D.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Claude, H.

Collier, P. J.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Danielsen, E.

E. Browell, E. Danielsen, S. Ismail, G. L. Gregory, and S. M. Beck, "Tropopose fold structure determined from airborne lidar and in situ measurements," J. Geophys. Res. 92, 2112-2120 (1987).
[CrossRef]

Diebel, D.

Doddridge, B.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Donovan, D. P.

Durieux, E.

L. Fiorani and E. Durieux, "Comparison among error calculations in differential absorption lidar measurements," Opt. Laser Technol. 33, 371-377 (2001).
[CrossRef]

Eckhardt, G.

G. Eckhardt, "Selection of Raman laser materials," IEEE J. Quantum Electron. QE-2, 1-8 (1966).
[CrossRef]

Edner, H.

Eichinger, W. E.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004), pp. 333-337.

Eisele, H.

H. Eisele, H. E. Scheel, R. Sladovic, and T. Trickl, "High-resolution lidar measurements of stratosphere-troposphere exchange," J. Atmos. Sci. 56, 319-330 (1999).
[CrossRef]

Fehsenfeld, F. C.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, "Optical properties of the atmosphere (3rd ed.)," Air Force Systems Command, United States Air Force, AFCRL-72-0497 (1972).

Fernald, F. G.

Fiorani, L.

L. Fiorani and E. Durieux, "Comparison among error calculations in differential absorption lidar measurements," Opt. Laser Technol. 33, 371-377 (2001).
[CrossRef]

Fredriksson, K.

Fujimoto, T.

T. Fujimoto and O. Uchino, "Estimation of the error caused by smoothing on DIAL measurements of stratospheric ozone," J. Meteorol. Soc. Jpn. 72, 605-611 (1994).

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, "Optical properties of the atmosphere (3rd ed.)," Air Force Systems Command, United States Air Force, AFCRL-72-0497 (1972).

Godin, S.

Grant, W. B.

Gregory, G. L.

E. Browell, E. Danielsen, S. Ismail, G. L. Gregory, and S. M. Beck, "Tropopose fold structure determined from airborne lidar and in situ measurements," J. Geophys. Res. 92, 2112-2120 (1987).
[CrossRef]

Gross, M. R.

Hardesty, R. M.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Higdon, N. S.

Ismail, S.

Jimenez, R.

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

Kempfer, U.

U. Kempfer, W. Carnuth, R. Lotz, and T. Trickl, "A wide-range ultraviolet lidar system for tropospheric ozone measurements: development and application," Rev. Sci. Instrum. 65, 3145-3164 (1994).
[CrossRef]

Klemm, O.

M. Schroter, A. Obermeier, D. Bruggemann, and O. Klemm, "Application of ground-based lidar for studies of the dynamics of ozone in a mountainous basin," Envir. Sci. Pollut. Res. 9, 381-384 (2002).
[CrossRef]

Kovalev, V. A.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004), pp. 333-337.

Langford, A. O.

A. O. Langford and S. J. Reid, "Dissipation and mixing of a small-scale stratospheric intrusion in the upper troposphere," J. Geophys. Res. 103, 31265-31276 (1998).
[CrossRef]

M. H. Proffitt and A. O. Langford, "Ground-based differential absorption lidar system for day or night measurements of ozone throughout the free troposphere," Appl. Opt. 36, 2568-2585 (1997).
[CrossRef] [PubMed]

Lazzarotto, B.

V. Simeonov, B. Lazzarotto, P. Quaglia, H. van den Bergh, and B. Calpini, "Three-wavelength UV ozone DIAL based on a Raman cell filled with two Raman active gases," The 20th International Laser Radar Conference (Vichy, 2000).

Lotz, R.

U. Kempfer, W. Carnuth, R. Lotz, and T. Trickl, "A wide-range ultraviolet lidar system for tropospheric ozone measurements: development and application," Rev. Sci. Instrum. 65, 3145-3164 (1994).
[CrossRef]

Luches, A.

Mack, M. E.

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, "Transient stimulated rotational and vibrational Raman scattering in gases," Appl. Phys. Lett. 16, 209-211 (1970).
[CrossRef]

Maeda, M.

M. Uchiumi, T. Shibata, and M. Maeda, "Measurement of changes in lower tropospheric ozone distribution through one day using a compact UV solar-blind lidar," J. Meteorol. Soc. Jpn. 69, 513-521 (1991).

T. Shibata, M. Maeda, A. Utsunomiya, and T. Mizoguchi, "Simultaneous measurements of ozone by UV lidar and chemical ozonesonde," J. Meteorol. Soc. Jpn. 65, 999-1003 (1987).

O. Uchino, M. Tokunaga, M. Maeda, and Y. Miyazoe, "Differential-absorption-lidar measurement of tropospheric ozone with excimer-Raman hybrid laser," Opt. Lett. 8, 347-349 (1983).
[CrossRef] [PubMed]

Mayor, S. D.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, "Optical properties of the atmosphere (3rd ed.)," Air Force Systems Command, United States Air Force, AFCRL-72-0497 (1972).

McDermid, I. S.

McGee, T. J.

McNider, R. T.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Mégie, G.

G. Ancellet, J. Pelon, M. Beekmann, A. Papayannis, and G. Mégie, "Ground-based lidar studies of ozone exchanges between the stratosphere and the troposphere," J. Geophys. Res. 96, 22401-22421 (1991).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, and G. Mégie, "Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere," Appl. Opt. 29, 467-476 (1990).
[CrossRef] [PubMed]

G. Ancellet, A. Papayannis, J. Pelon, and G. Mégie, "DIAL tropospheric ozone measurement using a Nd:YAG laser and the Raman shifting technique," J. Atmos. Ocean. Technol. 6, 832-839 (1989).
[CrossRef]

G. Mégie and R. T. Menzies, "Complementarity of UV and IR differential absorption lidar for global measurements of atmospheric species," Appl. Opt. 19, 1173-1183 (1980).
[CrossRef] [PubMed]

Menzies, R. T.

Mitev, V.

Miyazoe, Y.

Mizoguchi, T.

T. Shibata, M. Maeda, A. Utsunomiya, and T. Mizoguchi, "Simultaneous measurements of ozone by UV lidar and chemical ozonesonde," J. Meteorol. Soc. Jpn. 65, 999-1003 (1987).

Molina, L. T.

L. T. Molina and M. J. Molina, "Absolute absorption cross sections of ozone in the 185- to 350-nm wavelength range," J. Geophys. Res. 91, 14501-14508 (1986).
[CrossRef]

Molina, M. J.

L. T. Molina and M. J. Molina, "Absolute absorption cross sections of ozone in the 185- to 350-nm wavelength range," J. Geophys. Res. 91, 14501-14508 (1986).
[CrossRef]

Nakane, H.

Nassisi, V.

Neuber, R.

Obermeier, A.

M. Schroter, A. Obermeier, D. Bruggemann, and O. Klemm, "Application of ground-based lidar for studies of the dynamics of ozone in a mountainous basin," Envir. Sci. Pollut. Res. 9, 381-384 (2002).
[CrossRef]

Papayannis, A.

S. Tzortzakis, G. Tsaknakis, A. Papayannis, and A. A. Serafetinides, "Investigation of the spatial profile of stimulated Raman scattering beams in D2 and H2 gases using a pulsed Nd:YAG laser at 266 nm," Appl. Phys. B 79, 71-75 (2004).
[CrossRef]

G. Ancellet, J. Pelon, M. Beekmann, A. Papayannis, and G. Mégie, "Ground-based lidar studies of ozone exchanges between the stratosphere and the troposphere," J. Geophys. Res. 96, 22401-22421 (1991).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, and G. Mégie, "Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere," Appl. Opt. 29, 467-476 (1990).
[CrossRef] [PubMed]

G. Ancellet, A. Papayannis, J. Pelon, and G. Mégie, "DIAL tropospheric ozone measurement using a Nd:YAG laser and the Raman shifting technique," J. Atmos. Ocean. Technol. 6, 832-839 (1989).
[CrossRef]

Parrish, D.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Pelon, J.

G. Ancellet, J. Pelon, M. Beekmann, A. Papayannis, and G. Mégie, "Ground-based lidar studies of ozone exchanges between the stratosphere and the troposphere," J. Geophys. Res. 96, 22401-22421 (1991).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, and G. Mégie, "Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere," Appl. Opt. 29, 467-476 (1990).
[CrossRef] [PubMed]

G. Ancellet, A. Papayannis, J. Pelon, and G. Mégie, "DIAL tropospheric ozone measurement using a Nd:YAG laser and the Raman shifting technique," J. Atmos. Ocean. Technol. 6, 832-839 (1989).
[CrossRef]

Perrone, M. R.

Philbrick, C. R.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Proffitt, M. H.

Quaglia, P.

V. Simeonov, B. Lazzarotto, P. Quaglia, H. van den Bergh, and B. Calpini, "Three-wavelength UV ozone DIAL based on a Raman cell filled with two Raman active gases," The 20th International Laser Radar Conference (Vichy, 2000).

Ravetta, F.

Reid, S. J.

A. O. Langford and S. J. Reid, "Dissipation and mixing of a small-scale stratospheric intrusion in the upper troposphere," J. Geophys. Res. 103, 31265-31276 (1998).
[CrossRef]

Reintjes, J.

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, "Transient stimulated rotational and vibrational Raman scattering in gases," Appl. Phys. Lett. 16, 209-211 (1970).
[CrossRef]

Ristori, P.

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

Sasaki, T.

T. Sasaki, Japan Meteorological Agency, 1-3-4 Ohtemachi, Chiyoda-ku, Tokyo 100-8122, Japan (personal communication, 2006).

Scheel, H. E.

H. Eisele, H. E. Scheel, R. Sladovic, and T. Trickl, "High-resolution lidar measurements of stratosphere-troposphere exchange," J. Atmos. Sci. 56, 319-330 (1999).
[CrossRef]

Schoulepnikoff, L.

Schroter, M.

M. Schroter, A. Obermeier, D. Bruggemann, and O. Klemm, "Application of ground-based lidar for studies of the dynamics of ozone in a mountainous basin," Envir. Sci. Pollut. Res. 9, 381-384 (2002).
[CrossRef]

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, "Optical properties of the atmosphere (3rd ed.)," Air Force Systems Command, United States Air Force, AFCRL-72-0497 (1972).

Senff, C. J.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Serafetinides, A. A.

S. Tzortzakis, G. Tsaknakis, A. Papayannis, and A. A. Serafetinides, "Investigation of the spatial profile of stimulated Raman scattering beams in D2 and H2 gases using a pulsed Nd:YAG laser at 266 nm," Appl. Phys. B 79, 71-75 (2004).
[CrossRef]

Shibata, T.

M. Uchiumi, T. Shibata, and M. Maeda, "Measurement of changes in lower tropospheric ozone distribution through one day using a compact UV solar-blind lidar," J. Meteorol. Soc. Jpn. 69, 513-521 (1991).

T. Shibata, M. Maeda, A. Utsunomiya, and T. Mizoguchi, "Simultaneous measurements of ozone by UV lidar and chemical ozonesonde," J. Meteorol. Soc. Jpn. 65, 999-1003 (1987).

Shipley, S. T.

Simeonov, V.

V. Simeonov, V. Mitev, H. van den Bergh, and B. Calpini, "Raman frequency shifting in a CH4:H2:Ar mixture pumped by the fourth harmonic of a Nd:YAG laser," Appl. Opt. 37, 7112-7115 (1998).
[CrossRef]

L. Schoulepnikoff, V. Mitev, V. Simeonov, B. Calpini, and H. van den Bergh, "Experimental investigation of high-power single-pass Raman shifters in the ultraviolet with Nd:YAG and KrF lasers," Appl. Opt. 36, 5026-5043 (1998).
[CrossRef]

V. Simeonov, B. Calpini, and H. van den Bergh, "New Raman-shifted sources for ozone DIAL applications," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L.Bissonnette, G.Roy, and G.Vallee, eds. (Defence R&D Canada, 2002), pp. 19-22.

V. Simeonov, B. Lazzarotto, P. Quaglia, H. van den Bergh, and B. Calpini, "Three-wavelength UV ozone DIAL based on a Raman cell filled with two Raman active gases," The 20th International Laser Radar Conference (Vichy, 2000).

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

Sladovic, R.

H. Eisele, H. E. Scheel, R. Sladovic, and T. Trickl, "High-resolution lidar measurements of stratosphere-troposphere exchange," J. Atmos. Sci. 56, 319-330 (1999).
[CrossRef]

Steinbrecht, W.

Sunesson, A.

Sunesson, J. A.

Svanberg, S.

Swart, D. P. J.

Tabata, I.

Tokunaga, M.

Trainer, M.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Trickl, T.

H. Eisele, H. E. Scheel, R. Sladovic, and T. Trickl, "High-resolution lidar measurements of stratosphere-troposphere exchange," J. Atmos. Sci. 56, 319-330 (1999).
[CrossRef]

U. Kempfer, W. Carnuth, R. Lotz, and T. Trickl, "A wide-range ultraviolet lidar system for tropospheric ozone measurements: development and application," Rev. Sci. Instrum. 65, 3145-3164 (1994).
[CrossRef]

Tsaknakis, G.

S. Tzortzakis, G. Tsaknakis, A. Papayannis, and A. A. Serafetinides, "Investigation of the spatial profile of stimulated Raman scattering beams in D2 and H2 gases using a pulsed Nd:YAG laser at 266 nm," Appl. Phys. B 79, 71-75 (2004).
[CrossRef]

Tzortzakis, S.

S. Tzortzakis, G. Tsaknakis, A. Papayannis, and A. A. Serafetinides, "Investigation of the spatial profile of stimulated Raman scattering beams in D2 and H2 gases using a pulsed Nd:YAG laser at 266 nm," Appl. Phys. B 79, 71-75 (2004).
[CrossRef]

Uchino, O.

Uchiumi, M.

M. Uchiumi, T. Shibata, and M. Maeda, "Measurement of changes in lower tropospheric ozone distribution through one day using a compact UV solar-blind lidar," J. Meteorol. Soc. Jpn. 69, 513-521 (1991).

Uneus, L.

Unni, S.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Utsunomiya, A.

T. Shibata, M. Maeda, A. Utsunomiya, and T. Mizoguchi, "Simultaneous measurements of ozone by UV lidar and chemical ozonesonde," J. Meteorol. Soc. Jpn. 65, 999-1003 (1987).

Valente, R. J.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

van den Bergh, H.

L. Schoulepnikoff, V. Mitev, V. Simeonov, B. Calpini, and H. van den Bergh, "Experimental investigation of high-power single-pass Raman shifters in the ultraviolet with Nd:YAG and KrF lasers," Appl. Opt. 36, 5026-5043 (1998).
[CrossRef]

V. Simeonov, V. Mitev, H. van den Bergh, and B. Calpini, "Raman frequency shifting in a CH4:H2:Ar mixture pumped by the fourth harmonic of a Nd:YAG laser," Appl. Opt. 37, 7112-7115 (1998).
[CrossRef]

V. Simeonov, B. Calpini, and H. van den Bergh, "New Raman-shifted sources for ozone DIAL applications," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L.Bissonnette, G.Roy, and G.Vallee, eds. (Defence R&D Canada, 2002), pp. 19-22.

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

V. Simeonov, B. Lazzarotto, P. Quaglia, H. van den Bergh, and B. Calpini, "Three-wavelength UV ozone DIAL based on a Raman cell filled with two Raman active gases," The 20th International Laser Radar Conference (Vichy, 2000).

Verghese, S. J.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, "Optical properties of the atmosphere (3rd ed.)," Air Force Systems Command, United States Air Force, AFCRL-72-0497 (1972).

von der Gathen, P.

Wendt, W.

White, A. B.

R. M. Banta, C. J. Senff, A. B. White, M. Trainer, R. T. McNider, R. J. Valente, S. D. Mayor, R. J. Alvarez, R. M. Hardesty, D. Parrish, and F. C. Fehsenfeld, "Daytime buildup and nighttime transport of urban ozone in the boundary layer during a stagnation episode," J. Geophys. Res. 103, 22519-22544 (1998).
[CrossRef]

Willitsford, A.

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

Zimmermann, R.

Appl. Opt. (15)

G. Mégie and R. T. Menzies, "Complementarity of UV and IR differential absorption lidar for global measurements of atmospheric species," Appl. Opt. 19, 1173-1183 (1980).
[CrossRef] [PubMed]

F. G. Fernald, "Analysis of atmospheric lidar observations: some comments," Appl. Opt. 23, 652-653 (1984).
[CrossRef] [PubMed]

E. V. Browell, S. Ismail, and S. T. Shipley, "Ultraviolet DIAL measurements of O3 profiles in regions of spatially inhomogeneous aerosols," Appl. Opt. 24, 2827-2836 (1985).
[CrossRef] [PubMed]

D. Diebel, M. Bristow, and R. Zimmermann, "Stokes shifted laser lines in KrF-pumped hydrogen: reduction of beam divergence by addition of helium," Appl. Opt. 30, 626-628 (1991).
[CrossRef] [PubMed]

O. Uchino and I. Tabata, "Mobile lidar for simultaneous measurements of ozone, aerosols, and temperature in the stratosphere," Appl. Opt. 30, 2005-2012 (1991).
[CrossRef] [PubMed]

W. B. Grant, E. V. Browell, N. S. Higdon, and S. Ismail, "Raman shifting of KrF laser radiation for tropospheric ozone measurements," Appl. Opt. 30, 2628-2633 (1991).
[CrossRef] [PubMed]

J. A. Sunesson, A. Apiuley, and D. P. J. Swart, "Differential absorption lidar system for routine monitoring of tropospheric ozone," Appl. Opt. 33, 7045-7058 (1994).
[CrossRef] [PubMed]

M. H. Proffitt and A. O. Langford, "Ground-based differential absorption lidar system for day or night measurements of ozone throughout the free troposphere," Appl. Opt. 36, 2568-2585 (1997).
[CrossRef] [PubMed]

L. Schoulepnikoff, V. Mitev, V. Simeonov, B. Calpini, and H. van den Bergh, "Experimental investigation of high-power single-pass Raman shifters in the ultraviolet with Nd:YAG and KrF lasers," Appl. Opt. 36, 5026-5043 (1998).
[CrossRef]

G. Ancellet and F. Ravetta, "Compact airborne lidar for tropospheric ozone: description and field measurements," Appl. Opt. 37, 5509-5521 (1998).
[CrossRef]

S. E. Bisson, "Parametric study of an excimer-pumped nitrogen Raman shifter for lidar applications," Appl. Opt. 34, 3406-3412 (1995).
[CrossRef] [PubMed]

V. Simeonov, V. Mitev, H. van den Bergh, and B. Calpini, "Raman frequency shifting in a CH4:H2:Ar mixture pumped by the fourth harmonic of a Nd:YAG laser," Appl. Opt. 37, 7112-7115 (1998).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, and G. Mégie, "Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere," Appl. Opt. 29, 467-476 (1990).
[CrossRef] [PubMed]

S. Godin, A. I. Carswell, D. P. Donovan, H. Claude, W. Steinbrecht, I. S. McDermid, T. J. McGee, M. R. Gross, H. Nakane, D. P. J. Swart, H. B. Bergwerff, O. Uchino, P. von der Gathen, and R. Neuber, "Ozone differential absorption lidar algorithm intercomparison," Appl. Opt. 38, 6225-6236 (1999).
[CrossRef]

H. Edner, K. Fredriksson, A. Sunesson, S. Svanberg, L. Uneus, and W. Wendt, "Mobile remote sensing system for atmospheric monitoring," Appl. Opt. 26, 4330-4338 (1987).
[CrossRef] [PubMed]

Appl. Phys. B (1)

S. Tzortzakis, G. Tsaknakis, A. Papayannis, and A. A. Serafetinides, "Investigation of the spatial profile of stimulated Raman scattering beams in D2 and H2 gases using a pulsed Nd:YAG laser at 266 nm," Appl. Phys. B 79, 71-75 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, "Transient stimulated rotational and vibrational Raman scattering in gases," Appl. Phys. Lett. 16, 209-211 (1970).
[CrossRef]

Envir. Sci. Pollut. Res. (1)

M. Schroter, A. Obermeier, D. Bruggemann, and O. Klemm, "Application of ground-based lidar for studies of the dynamics of ozone in a mountainous basin," Envir. Sci. Pollut. Res. 9, 381-384 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Eckhardt, "Selection of Raman laser materials," IEEE J. Quantum Electron. QE-2, 1-8 (1966).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

G. Ancellet, A. Papayannis, J. Pelon, and G. Mégie, "DIAL tropospheric ozone measurement using a Nd:YAG laser and the Raman shifting technique," J. Atmos. Ocean. Technol. 6, 832-839 (1989).
[CrossRef]

J. Atmos. Sci. (1)

H. Eisele, H. E. Scheel, R. Sladovic, and T. Trickl, "High-resolution lidar measurements of stratosphere-troposphere exchange," J. Atmos. Sci. 56, 319-330 (1999).
[CrossRef]

J. Geophys. Res. (5)

E. Browell, E. Danielsen, S. Ismail, G. L. Gregory, and S. M. Beck, "Tropopose fold structure determined from airborne lidar and in situ measurements," J. Geophys. Res. 92, 2112-2120 (1987).
[CrossRef]

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Other (10)

P. J. Collier, S. Unni, S. J. Verghese, A. Willitsford, C. R. Philbrick, R. D. Clark, and B. Doddridge, "Raman lidar measurements of tropospheric ozone," in Proceedings of the 5th Conference on Atmospheric Chemistry:Gases, Aerosols, and Clouds (American Meteorological Society, 2003), paper 6.3.

V. Simeonov, B. Lazzarotto, P. Quaglia, H. van den Bergh, and B. Calpini, "Three-wavelength UV ozone DIAL based on a Raman cell filled with two Raman active gases," The 20th International Laser Radar Conference (Vichy, 2000).

U.S. Standard Atmosphere (U.S. GPO, 1976).

V. Simeonov, B. Calpini, and H. van den Bergh, "New Raman-shifted sources for ozone DIAL applications," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L.Bissonnette, G.Roy, and G.Vallee, eds. (Defence R&D Canada, 2002), pp. 19-22.

V. Simeonov, B. Calpini, J. Balin, P. Ristori, R. Jimenez, and H. van den Bergh, "UV ozone DIAL based on a N2 Raman converter: Design and results during ESCOMPTE field campaign," in Lidar Remote Sensing in Atmospheric and Earth Sciences, Proceedings of the ILRC21, L. Bissonnette, G. Roy, and G. Vallee, eds. (Defence R&D Canada, 2002), pp. 403-406.

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Figures (10)

Fig. 1
Fig. 1

Relationship between the ozone absorption cross section in the Hartley band and the Stokes wavelengths generated from Nd:YAG fourth harmonics ( 266   nm ) in CO 2 . P, S1, S2, and S3 denote the pump and the Stokes lines of the corresponding order.

Fig. 2
Fig. 2

Spectrum factor for various wavelength pairs. The vertical axis denotes the difference between the on-line and off-line wavelengths, whereas the horizontal axis represents the on-line wavelength. The contours represent the magnitudes of the spectrum factor in m 2 defined in the text. Vertical lines in the figure indicate the scale of the estimated maximum observable height in meter. The U.S. standard atmosphere, integration of 20,000 laser shots, laser output energies of 10 mJ∕pulse for on-line and off-line wavelengths, and the receiving system constants for measurement in the free troposphere described in Section 3 are assumed. The stimulated Raman scattering of Nd:YAG fourth harmonics in CO 2 can produce the underlined wavelength pairs. This figure is cited from Ancellet and Bosenberg (Ref. [27]) and marked with the additional information above.

Fig. 3
Fig. 3

Simulated contribution of each term in Eq. (1) to the ozone profile for the 287 / 299   nm and the 276 / 287   nm pairs. The assumed measurement range is also illustrated as a nonshaded region depending on the wavelength pairs. The U.S. standard atmosphere is used as the model profile except for the aerosol extinction coefficient, which is after MacClatchey et al. (Ref. [34]) as plotted in the figure. Also plotted are the ratios defined by the same terms as those in the left panel except for normalized by the model ozone profile. Labels in the right panel (for Ratio) denote abbreviations of those in the left (for Ozone Number Density).

Fig. 4
Fig. 4

Schematic of the tropospheric ozone DIAL with CO 2 Raman cell developed at the Meteorological Research Institute.

Fig. 5
Fig. 5

Output energy for each wavelength as a function of CO 2 pressure. The pump energy was 91 mJ / pulse .

Fig. 6
Fig. 6

Output energy from the Raman cell as a function of Ar and He pressure. The pump energy was 91 mJ∕pulse. The CO 2 pressure was 0.7 MPa.

Fig. 7
Fig. 7

Comparison of a lidar-derived ozone profile with one obtained from the routine KC ozonesonde at approximately 0600 UTC (1500 JST) on 4 February 2005. The statistical error in the DIAL measurement, the correction terms computed using Eqs. (2) and (3), and the difference between the DIAL and KC96 ozonesonde measurements are also plotted.

Fig. 8
Fig. 8

Same as Fig. 7 except on 14 January 2005.

Fig. 9
Fig. 9

Backscatter correction profiles obtained from (a) 287   nm (below 2600 m) and 299   nm (above 2600 m) and (b) 355   nm as reference wavelengths on 19 April 2006. The difference of (a) and (b) and backscatter ratio at 355   nm are also plotted in (c) and (d).

Fig. 10
Fig. 10

Eighteen hour sequence of ozone profiles derived from lidar measurements on 4 February 2005, at Tsukuba, Japan.

Tables (2)

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Table 1 Stokes Wavelengths Obtained from the Stimulated Raman Scattering of Nd:YAG Fourth Harmonics in Various Gases a , b

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Table 2 Specifications for the Tropospheric Ozone DIAL with CO2 Raman Cell Developed at the Meteorological Research Institute

Equations (5)

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n ( r ) = 1 2 Δ σ { d d r [ ln P o n ( r ) P o f f ( r ) ] } + 1 2 Δ σ { d d r [ ln β o n ( r ) β o f f ( r ) ] } 1 Δ σ [ α o n ( r ) α o f f ( r ) ] ,
Δ n β ( r ) = ( 4 ξ ) B λ 2 Δ r [ Q off ( r ) 1 + Q off ( r ) Q off ( r + Δ r ) 1 + Q off ( r + Δ r ) ] ,
Δ n e ( r ) = B λ u α p , off ( r ) 4 α m , off ( r ) ,
B λ = 1 λ off [ Δ σ Δ λ ] ,
Q off ( r ) = Q ref ( r ) ( λ off λ ref ) 4 ξ ,

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