Abstract

This paper presents a method to compute the overlap function of a lidar system in which a step-index optical fiber (or a bundle of such fibers) is used to carry the light collected by the telescope to the photoreceiver and a field lens is placed between the telescope and the optical fiber to increase the receiver field of view (FOV). The use of field lenses is a classical way to increase the FOV of radiometric systems (such as the receiving part of a lidar) when there is no numerical aperture (NA) limitation after the lens. However, when such a limitation exists, as in the case studied here, it will place a limit on the maximum attainable FOV. In the case of lidars, which have range-resolution capabilities, the limited FOV has an effect on the fraction of power coming from scattering volumes at different ranges that actually reaches the photodetector. This fraction is a function (the so-called overlap function) of the range of the scattering volume and its behavior has an impact on the accuracy of the retrievals. The application of the method developed in this paper shows that, in spite of the fiber NA limit, in practical situations the goal is attained of making the overlap function steeper and reaching higher values by using a field lens.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.
  2. J. Riegl and M. Bernhard, “Empfangsleistung in Abhängigkeit von der Zielentfernung bei optischen Kurzstrecken-Radargeräten,” Appl. Opt. 13, 931–936 (1974).
    [CrossRef] [PubMed]
  3. T. Halldórsson and J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
    [CrossRef] [PubMed]
  4. J. Harms, W. Lahmann, and C. Weitkamp, “Geometrical compression of lidar return signals,” Appl. Opt. 17, 1131–1135(1978).
    [CrossRef] [PubMed]
  5. J. Harms, “Lidar return signals for coaxial and noncoaxial systems with central obstruction,” Appl. Opt. 18, 1559–1566(1979).
    [CrossRef] [PubMed]
  6. J. R. Jenness, Jr., D. B. Lysak, Jr., and C. R. Philbrick, “Design of a lidar receiver with fiber-optic output,” Appl. Opt. 36, 4278–4284 (1997).
    [CrossRef] [PubMed]
  7. G. Chourdakis, A. Papayannis, and J. Porteneuve, “Analysis of the receiver response for a noncoaxial lidar system with fiber-optic output,” Appl. Opt. 41, 2715–2723 (2002).
    [CrossRef] [PubMed]
  8. J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
    [CrossRef]
  9. U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
    [CrossRef] [PubMed]
  10. A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131(1992).
    [CrossRef] [PubMed]
  11. P. T. Brunozzi and F. Marenco, “A lidar for water vapour measurements in daytime at Lampedusa, Italy,” Ann. Geophys. 46, 459–465 (2003).
  12. A. I. Abramochkin and A. A. Tikhomirov, “Optimization of a lidar receiving system. 2. Spatial filters,” Atmos. Oceanic Opt. 12, 331–342 (1999).
  13. R. R. Agishev and A. Comeron, “Spatial filtering efficiency of monostatic biaxial lidar: analysis and applications,” Appl. Opt. 41, 7516–7521 (2002).
    [CrossRef]
  14. V. Freudenthaler, “Optimized background suppression in near field lidar telescopes,” in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP 2003), U.Wandinger, R.Engelmann, and K.Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 243–245.
  15. K. Sassen and G. Dodd, “Lidar crossover function and misalignment effects,” Appl. Opt. 21, 3162–3165 (1982).
    [CrossRef] [PubMed]
  16. Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979).
    [CrossRef] [PubMed]
  17. S. Hu, X. Wang, Y. Wu, C. Li, and H. Hu, “Geometrical form factor determination with Raman backscattering signals,” Opt. Lett. 30, 1879–1881 (2005).
    [CrossRef] [PubMed]
  18. V. Freudenthaler, “The Telecover Test: a quality assurance tool for the optical part of a lidar system,” in Reviewed and Revised Papers Presented at 23th International Laser Radar Conference, C.Nagasawa and N.Sugimoto, eds. (Organizing Committee of the 23th International Laser Radar Conference, 2006), pp. 145–146.
  19. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2008).
  20. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).
  21. H. W. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
    [CrossRef]

2005 (1)

2003 (1)

P. T. Brunozzi and F. Marenco, “A lidar for water vapour measurements in daytime at Lampedusa, Italy,” Ann. Geophys. 46, 459–465 (2003).

2002 (4)

1999 (1)

A. I. Abramochkin and A. A. Tikhomirov, “Optimization of a lidar receiving system. 2. Spatial filters,” Atmos. Oceanic Opt. 12, 331–342 (1999).

1997 (1)

1992 (1)

1982 (1)

1979 (2)

1978 (2)

1974 (1)

1966 (1)

H. W. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Abramochkin, A. I.

A. I. Abramochkin and A. A. Tikhomirov, “Optimization of a lidar receiving system. 2. Spatial filters,” Atmos. Oceanic Opt. 12, 331–342 (1999).

Agishev, R. R.

Amodeo, A.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Ansmann, A.

U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
[CrossRef] [PubMed]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131(1992).
[CrossRef] [PubMed]

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Apituley, A.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Arboledas, L. A.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Balis, D.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Bernhard, M.

Böckmann, C.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Bösenberg, J.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Brunozzi, P. T.

P. T. Brunozzi and F. Marenco, “A lidar for water vapour measurements in daytime at Lampedusa, Italy,” Ann. Geophys. 46, 459–465 (2003).

Campbell, J. R.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Chaikovsky, A.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Chourdakis, G.

Comeron, A.

R. R. Agishev and A. Comeron, “Spatial filtering efficiency of monostatic biaxial lidar: analysis and applications,” Appl. Opt. 41, 7516–7521 (2002).
[CrossRef]

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

D’Amico, G.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Dodd, G.

Flynn, C. J.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Freudenthaler, V.

V. Freudenthaler, “Optimized background suppression in near field lidar telescopes,” in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP 2003), U.Wandinger, R.Engelmann, and K.Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 243–245.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

V. Freudenthaler, “The Telecover Test: a quality assurance tool for the optical part of a lidar system,” in Reviewed and Revised Papers Presented at 23th International Laser Radar Conference, C.Nagasawa and N.Sugimoto, eds. (Organizing Committee of the 23th International Laser Radar Conference, 2006), pp. 145–146.

Gigorov, I.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Halldórsson, T.

Hanson, G.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Harms, J.

Hu, H.

Hu, S.

Hvlaka, D. L.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Jenness, J. R.

Kogelnik, H. W.

H. W. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Lahmann, W.

Langerholc, J.

Li, C.

Li, T.

H. W. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Linné, H.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Lysak, D. B.

Marenco, F.

P. T. Brunozzi and F. Marenco, “A lidar for water vapour measurements in daytime at Lampedusa, Italy,” Ann. Geophys. 46, 459–465 (2003).

Mattis, I.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Measures, R. M.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).

Michaelis, W.

Mitev, V.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Mona, L.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Mueller, D.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Nicolae, D.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Okuda, M.

Papayannis, A.

G. Chourdakis, A. Papayannis, and J. Porteneuve, “Analysis of the receiver response for a noncoaxial lidar system with fiber-optic output,” Appl. Opt. 41, 2715–2723 (2002).
[CrossRef] [PubMed]

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Pappalardo, G.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Perrone, M. R.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Philbrick, C. R.

Pietruczuk, A.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Porteneuve, J.

Pujadas, M.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Putaud, J.-P.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Ravetta, F.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Riebesell, M.

Riegl, J.

Rizi, V.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Sasano, Y.

Sassen, K.

Scott, V. S.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Shimizu, H.

Simeonov, V.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2008).

Spinelli, N.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Spinhirne, J. D.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Takeuchi, N.

Tikhomirov, A. A.

A. I. Abramochkin and A. A. Tikhomirov, “Optimization of a lidar receiving system. 2. Spatial filters,” Atmos. Oceanic Opt. 12, 331–342 (1999).

Trickl, T.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Turner, D. D.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Wandinger, U.

U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
[CrossRef] [PubMed]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131(1992).
[CrossRef] [PubMed]

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Wang, I. H.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Wang, X.

Weitkamp, C.

Welton, E. J.

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Wiegner, M.

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

Wu, Y.

Ann. Geophys. (1)

P. T. Brunozzi and F. Marenco, “A lidar for water vapour measurements in daytime at Lampedusa, Italy,” Ann. Geophys. 46, 459–465 (2003).

Appl. Opt. (11)

J. Riegl and M. Bernhard, “Empfangsleistung in Abhängigkeit von der Zielentfernung bei optischen Kurzstrecken-Radargeräten,” Appl. Opt. 13, 931–936 (1974).
[CrossRef] [PubMed]

T. Halldórsson and J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
[CrossRef] [PubMed]

J. Harms, W. Lahmann, and C. Weitkamp, “Geometrical compression of lidar return signals,” Appl. Opt. 17, 1131–1135(1978).
[CrossRef] [PubMed]

J. Harms, “Lidar return signals for coaxial and noncoaxial systems with central obstruction,” Appl. Opt. 18, 1559–1566(1979).
[CrossRef] [PubMed]

Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979).
[CrossRef] [PubMed]

K. Sassen and G. Dodd, “Lidar crossover function and misalignment effects,” Appl. Opt. 21, 3162–3165 (1982).
[CrossRef] [PubMed]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131(1992).
[CrossRef] [PubMed]

J. R. Jenness, Jr., D. B. Lysak, Jr., and C. R. Philbrick, “Design of a lidar receiver with fiber-optic output,” Appl. Opt. 36, 4278–4284 (1997).
[CrossRef] [PubMed]

U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
[CrossRef] [PubMed]

G. Chourdakis, A. Papayannis, and J. Porteneuve, “Analysis of the receiver response for a noncoaxial lidar system with fiber-optic output,” Appl. Opt. 41, 2715–2723 (2002).
[CrossRef] [PubMed]

R. R. Agishev and A. Comeron, “Spatial filtering efficiency of monostatic biaxial lidar: analysis and applications,” Appl. Opt. 41, 7516–7521 (2002).
[CrossRef]

Atmos. Oceanic Opt. (1)

A. I. Abramochkin and A. A. Tikhomirov, “Optimization of a lidar receiving system. 2. Spatial filters,” Atmos. Oceanic Opt. 12, 331–342 (1999).

J. Atmos. Ocean. Technol. (1)

J. R. Campbell, D. L. Hvlaka, E. J. Welton, C. J. Flynn, D. D. Turner, J. D. Spinhirne, V. S. Scott III, and I. H. Wang, “Full-time, eye-safe cloud and aerosol lidar observation at atmospheric radiation measurement program sites: instruments and data processing,” J. Atmos. Ocean. Technol. 19, 431–442(2002).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

H. W. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Other (5)

G. Pappalardo, J. Bösenberg, A. Amodeo, A. Ansmann, A. Apituley, L. A. Arboledas, D. Balis, C. Böckmann, A. Chaikovsky, A. Comeron, G. D’Amico, V. Freudenthaler, I. Gigorov, G. Hanson, H. Linné, I. Mattis, L. Mona, D. Mueller, V. Mitev, D. Nicolae, A. Papayannis, M. R. Perrone, A. Pietruczuk, M. Pujadas, J.-P. Putaud, F. Ravetta, V. Rizi, V. Simeonov, N. Spinelli, T. Trickl, U. Wandinger, and M. Wiegner, “EARLINET for long term observations of aerosol over EUROPE,” in Reviewed and Revised Papers Presented at 24th International Laser Radar Conference, M.Hardesty and S.Mayor, eds. (Organizing Committee of the 24th International Laser Radar Conference, 2008), pp. 711–714.

V. Freudenthaler, “Optimized background suppression in near field lidar telescopes,” in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP 2003), U.Wandinger, R.Engelmann, and K.Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 243–245.

V. Freudenthaler, “The Telecover Test: a quality assurance tool for the optical part of a lidar system,” in Reviewed and Revised Papers Presented at 23th International Laser Radar Conference, C.Nagasawa and N.Sugimoto, eds. (Organizing Committee of the 23th International Laser Radar Conference, 2006), pp. 145–146.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2008).

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Coaxial and biaxial lidar configurations showing the overlap between the receiver FOV and the transmitted beam.

Fig. 2
Fig. 2

Schematic depiction of a lidar receiver optical system using a field lens.

Fig. 3
Fig. 3

Schematic depiction of the rays emerging from the input pupil and passing through the CC. Axes and circles drawn in the same shade (black or gray) are in the same plane perpendicular to the Z axis.

Fig. 4
Fig. 4

Overlap of the three circles limiting the overlap function in the focal plane of the telescope.

Fig. 5
Fig. 5

Overlap function as a function of range for various values of the far-field laser-beam divergence with and without a field lens.

Fig. 6
Fig. 6

Overlap function with a field lens with and without NA limitation ( 0.25 mrad beam divergence).

Tables (1)

Tables Icon

Table 1 All Possible Combinations of the Relative Positions of the Three Circles with Centers Falling on the Same Straight Line (Excluding Those in which the Circle of Confusion Does Not Overlap the Field-Lens Surface Circle) a

Equations (16)

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

F O V = D o f f t ,
1 f t + 1 d = 1 f f l ,
f t D o f d > D t ,
x = x C C + x d 2 f t d 2 ,
y = y C C + y d 2 f t d 2 ,
1 d 2 + 1 z = 1 f t .
x = x C C + x f t z ,
y = y C C + y f t z .
tan α x = x f f l + ( x x ) f t = x f t + ( 1 f t 1 f f l ) x .
tan α y = y f t + ( 1 f t 1 f f l ) y .
tan α 0 = tan 2 α x + tan 2 α y = [ ( x f t + x d ) 2 + ( y f t + y d ) 2 ] 1 2 .
tan α 0 = ( z f t 2 + 1 d ) [ ( x x C C 1 + f t 2 z d ) 2 + ( y y C C 1 + f t 2 z d ) 2 ] 1 2 .
D NA = 2 f t 2 z 1 1 + f t 2 z d NA 1 NA 2 ,
( x NA , y NA ) = ( x C C 1 + f t 2 z d , y C C 1 + f t 2 z d ) .
w ( z ) = ( λ π θ ) 2 + ( z θ ) 2 ,
O ( z ) = 4 z 2 f t 2 w 2 ( z ) A C C ( z ) 0 D C C ( z ) + D f l 2 A int ( z , r ) exp ( 2 r 2 + s 2 ( z ) f t 2 w 2 ( z ) ) I 0 ( 4 z 2 r s ( z ) f t 2 w 2 ( z ) ) r d r ,

Metrics