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Vol. 29, issue 10, article # 12

Vorob'ev V. V. The validity of asymptotic formulas for recovery of "optical" turbulence parameters from data of the lidar sensing. I. Equations. // Optika Atmosfery i Okeana. 2016. V. 29. No. 10. P. 862–869. DOI: 10.15372/AOO20161012 [in Russian].
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Abstract:

Asymptotic solutions of the problem of reconstructing the distribution of the structural characteristics of the refractive index fluctuations from the measurement data of the backscatter enhancement effect are derived. Solutions are expressed through fractional derivatives of the backscattering gain in the case of small aperture receiver, or through the ordinary derivatives in the case of receivers with a large aperture. The properties of the integral equation kernel are studied in detail, from which the asymptotic formulas follow. Attention is drawn to the fact that the kernel is oscillating in general. Kernel oscillations little impact the value of the backscattering enhancement, but their impact can be significant on the derivatives of this factor.

Keywords:

lidar, turbulence, backscattering enhancement, Volterra equations and Abel equations

References:

  1. Vinogradov A.G., Kravcov Ju.A., Tatarskij V.I. Jeffekt usilenija obratnogo rassejanija na telah, pomeshhennyh v sredu so sluchajnymi neodnorodnostjami // Izv. vuzov. Radiofiz. 1973. V. 16, N 7. P. 1064–1070.
  2. Vinogradov A.G., Gurvich A.S., Kashkarov S.S., Kravcov Ju.A., Tatarskij V.I. «Zakonomernost' uvelichenija obratnogo rassejanija voln». Svidetel'stvo na otkrytie N 359. Prioritet otkrytija: 25 august 1972 year v chasti teoreticheskogo obosnovanija i 12 august 1976 year v chasti jeksperimental'nogo dokazatel'stva zakonomernosti. Gosudarstvennyj reestr otkrytij SSSR // Bjull. izobretenij. 1989. N 21.
  3. Banakh V.A., Smalikho I.N., Werner Ch. Numerical simulation of effect of refractive turbulence on the statistics of a coherent lidar return in the atmosphere // Appl. Opt. 2000. V. 39, N 33. P. 5403–5414.
  4. Banah V.A., Smaliho I.N. Opredelenie intensivnosti opticheskoj turbulentnosti po obratnomu atmosfernomu rassejaniju lazernogo izluchenija // Optika atmosf. i okeana. 2011. V. 24, N 4. P. 300–307; Banakh V.A., Smalikho I.N. Determination of optical turbulence intensity by atmospheric backscattering of laser radiation // Atmos. Ocean. Opt. 2011. V. 24, N 5. P. 457–465.
  5. Smaliho I.N. Raschet kojefficienta usilenija obratnogo rassejanija lazernogo izluchenija, rasprostranjajushhegosja v turbulentnoj atmosfere, s ispol'zovaniem chislennogo modelirovanija // Optika atmosf. i okeana. 2012. V. 25, N 9. P. 796–800; Smalikho I.N. Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation // Atmos. Ocean. Opt. 2013. V. 26, N 2. P. 135–139.
  6. Banah V.A. Usilenie srednej moshhnosti obratno rassejannogo v atmosfere izluchenija v rezhime sil'noj opticheskoj turbulentnosti // Optika atmosf. i okeana. 2012. V. 25, N 10. P. 857–862; Banakh V.A. Enhancement of the laser return mean power at the strong optical scintillation regime in a turbulent atmosphere // Atmos. Ocean. Opt. 2013. V. 26, N 2. P. 90–95.
  7. Gurvich A.S. Lidarnoe zondirovanie turbulentnosti na osnove jeffekta usilenija obratnogo rassejanija // Izv. RAN. Fiz. atmosf. i okeana. 2012. V. 48, N 6. P. 655–665.
  8. Gurvich A.S. Lidarnoe pozicionirovanie oblastej povyshennoj turbulentnosti jasnogo neba // Izv. RAN. Fiz. atmosf. i okeana. 2014. V. 50, N 2. P. 166–174.
  9. Gurvich A.S., Fortus M.I. Lidarnoe zondirovanie opticheskoj harakteristiki turbulentnosti v atmosfere // Izv. RAN. Fiz. atmosf. i okeana. 2016. V. 52, N 2. P. 187–199.
  10. Banah V.A., Razenkov I.A., Smaliho I.N. Ajerozol'nyj lidar dlja issledovanija usilenija obratnogo atmosfernogo rassejanija. I. Komp'juternoe modelirovanie // Optika atmosf. i okeana. 2015. V. 28, N 1. P. 5–11.
  11. Banah V.A., Razenkov I.A. Ajerozol'nyj lidar dlja issledovanija usilenija obratnogo atmosfernogo rassejanija. II. Konstrukcija i jeksperiment // Optika atmosf. i okeana. 2015. V. 28, N 2. P. 113–119.
  12. Banah V.A., Razenkov I.A. Lidarnye izmerenija usilenija obratnogo rassejanija // Optika i spektroskopija. 2016. V. 120, N 2. P. 339–348.
  13. Vorob'ev V.V., Vinogradov A.G. Vlijanie fonovoj turbulentnosti v lidarnyh issledovanijah turbulentnosti jasnogo neba // Optika atmosf. i okeana. 2013. V. 26, N 12. P. 1015–1022; Vorob’ev V.V., Vinogradov A.G. Effect of background turbulence in lidar investigations of clear air turbulence // Atmos. Ocean. Opt. 2014. V. 27, N 2. P. 134–141.
  14. Tatarskij V.I. Rasprostranenie voln v turbulentnoj atmosfere. M.: Nauka, 1967. 548 p.
  15. Gradshtejn I.S., Ryzhik I.M. Tablicy integralov, summ, rjadov i proizvedenij. M.: Izd-vo fiz. mat. lit., 1963. 1100 p.
  16. Manzhirov A.V., Poljanin A.D. Metody reshenija integral'nyh uravnenij: Spravochnik. M.: Faktorial, 1999. 272 p.
  17. Samko S.G., Kilbas A.A., Marichev O.I. Integraly i proizvodnye drobnogo porjadka i nekotorye ih prilozhenija. Minsk: Nauka i tehnika, 1987. 688 p.
  18. Vorob'ev V.V. O primenimosti asimptoticheskih formul vosstanovlenija parametrov «opticheskoj» turbulentnosti iz dannyh impul'snogo lidarnogo zondirovanija. II. Rezul'taty chislennogo modelirovanija // Optika atmosf. i okeana. 2016. V. 29, N 11 (v pechati).