Abstract
Asymptotic solutions for the problem of retrieving the distribution of the structure characteristic of refractive index fluctuations from measurement data on the backscattering enhancement factor have been found. The solutions are written in terms of fractional derivatives of the enhancement factor in the case of receivers with a small aperture or via usual derivatives in the case of receivers with a large aperture. Properties of the kernel of the integral equation from which the asymptotic formulas follow have been studied in detail. Attention is paid to the fact that the kernel is oscillating in the general case. The kernel oscillations slightly affect the magnitude of the enhancement factor; however, their effect on derivatives of this factor can be significant.
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References
A. G. Vinogradov, Yu. A. Kravtsov, and V. I. Tatarskii, “The effect of intensification of back scattering by bodies that are situated in a medium having random inhomogeneities,” Radiophys. Quantum Electron. 16 (7), 818–823 (1973).
A. G. Vinogradov, A. S. Gurvich, S. S. Kashkarov, Yu. A. Kravtsov, and V. I. Tatarskii, USSR Inventor’s Certificate no. 35, Byull. Izobret., No. 21 (1989).
V. A. Banakh, I. N. Smalikho, and Ch. Werner, “Numerical simulation of effect of refractive turbulence on the statistics of a coherent lidar return in the atmosphere,” Appl. Opt. 39 (33), 5403–5414 (2000).
V. A. Banakh and I. N. Smalikho, “Determination of optical turbulence intensity by atmospheric backscattering of laser radiation,” Atmos. Ocean. Opt. 24 (5), 457–465 (2011).
I. N. Smalikho, “Calculation of the backscatter amplification coefficient of laser radiation propagating in a turbulent atmosphere using numerical simulation,” Atmos. Ocean. Opt. 26 (2), 135–139 (2013).
V. A. Banakh, “Enhancement of the laser return mean power at the strong optical scintillation regime in a turbulent atmosphere,” Atmos. Ocean. Opt. 26 (2), 90–95 (2013).
A. S. Gurvich, “Lidar sounding of turbulence based on the backscatter enhancement effect,” Izv., Atmos. Ocean. Phys. 48 (6), 585–594 (2012).
A. S. Gurvich, “Lidar positioning of higher clear-air turbulence regions,” Izv., Atmos. Ocean. Phys. 50 (2), 143–151 (2014).
A. S. Gurvich and M. I. Fortus, “Lidar sounding of the optical parameter of atmospheric turbulence,” Izv., Atmos. Ocean. Phys. 52 (2), 165–175 (2016).
V. A. Banakh, I. A. Razenkov, and I. N. Smalikho, “Aerosol lidar for study of the backscatter amplification in the atmosphere. Part I. Computer simulation,” Opt. Atmos. Okeana 28 (1), 5–11 (2015).
V. A. Banakh and I. A. Razenkov, “Aerosol lidar for study of the backscatter amplification in the atmosphere. Part II. Construction and experiment,” Opt. Atmos. Okeana 28 (2), 113–119 (2015).
V. A. Banakh and I. A. Razenkov, “Lidar measurements of atmospheric backscattering amplification,” Opt. Spectrosc. 120 (2), 326–334 (2016).
V. V. Vorob’ev and A. G. Vinogradov, “Effect of background turbulence in lidar investigations of clear air turbulence,” Atmos. Oceanic Opt. 27 (2), 134–141 (2014).
V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Nauka, Moscow, 1967) [in Russian]; (Dover Publications, New York, 1967).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Izd-vo Fiz. Mat. Lit., Moscow, 1963) [in Russian].
A. V. Manzhirov and A. D. Polyanin, Methods for Solution of Integral Equations: Handbook (Faktorial, Moscow, 1999) [in Russian].
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Some Applications (Nauka i tekhnika, Minsk, 1987) [in Russian].
V. V. Vorob’ev, “On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: II–Results of numerical simulation,” Atmos. Ocean. Opt. 30 (2), 162–168 (2016).
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Original Russian Text © V.V. Vorob’ev, 2016, published in Optika Atmosfery i Okeana.
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Vorob’ev, V.V. On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: I–equations. Atmos Ocean Opt 30, 156–161 (2017). https://doi.org/10.1134/S1024856017020130
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DOI: https://doi.org/10.1134/S1024856017020130