ACCOUNTING FOR SPHERISITY OF PHASE WAVE FRONTS IN THE THEORY OF WAVE SCATTERING BY TURBULENT ATMOSPHERE - Bryukhovetski, A. S. (Видавничий дім «Академперіодика», 2014)
For the case of wave scattering by turbulent atmosphere, the asymtotics of three-fold integrals that determine the intensity of the scattered field are found. For nondegenerate scattering (hessian of phase being nonzero) the method of a stationary phase with respect to three integration variables has been used. For the degenerate scattering (hessian of phase being zero) the combined method has been applied, namely, the Fraunhofer approximation in one variable, and the method of stationary phase in two other variables. The correlation has been established with the results known from literature.Key words:  wave dispersion, oscillating function’s integral, stationary phase, Fresnel zone, Fraunhofer diffractionManuscript submitted 25.12.2013Radio phys. radio astron. 2014, 19(3): 217-228REFERENCES1. TATARSKI, V. I., 1967. Wave Propagation in a Turbulent Atmosphere. Moscow: Nauka Publ. (in Russian). 2. ISHIMARU, A., 1981. Wave Propagation and Scattering in Random Media. Vol. II. Moscow: Mir Publ. (in Russian). 3. ERDELYI, A. 1962. Asymptotic Expansions. Moscow: Phyzmatgiz Publ. (in Russian). 4. TATARSKII, V. I., 2003.Theory of Single Scattering by Random Distributed Scatterers. IEEE Trans. Antennas Propag. vol. 51, no. 10, pp. 2806–2813. DOI: https://doi.org/10.1109/TAP.2003.817980 5. KON, A. I. and TATARSKII, V. I., 1986. On the signal power at radio acoustic sounding of the atmosphere. Radiotekhnika i Elektronika. vol. 31, no. 10, pp. 1903–1908 (in Russian). 6. BRYUKHOVETSKI, A. S., 1970. Scattering of electromagnetic waves in the artificially created environments. PhD thesis ed. O.Ya. Usikov Institute for Radiophysics and Electronics of NASU, Kharkiv, Ukraine (in Russian). 7. BRYUKHOVETSKI, A. S., 2005. Radar reflection from acoustic pulse. Radio Phys. Radio Astron. vol. 10, no 4, pp. 432–441 (in Russian). 8. KRYUKOVSKI, A. S., LUKIN, D. S., PALKIN, E. A.and RASTYAGAEV, D. S., 2006. Wave catastrophes: types of focusing in diffraction and propagation of electromagnetic waves. Radiotekhnika i Elektronika. vol. 51, no. 10, pp. 1155–1192 (in Russian). 9. FELSEN, L. B. and MARKUVITZ, N., 1978. Radiation and Scattering of Waves. Vol. 1. Moscow: Mir Publ. (in Russian). 10. BRYUKHOVETSKI, A. S., 2010. Near-to-Far Zone Transition in the Problem of Wave Backscattering by a Statistically Rough Surface. Radio Phys. Radio Astron. vol. 15, no.4, pp. 408–424 (in Russian). 11. BRYUKHOVETSKI, A. S., 2012. Near-to-far zone transition in the problem of plane wave scattering by statistically rough surface. Radio Phys. Radio Astron. vol. 17, no. 2, pp. 157–170 (in Russian). 12. BRYUKHOVETSKI, A. S., 2013. Near-to-far zone transitionin a two-point wave scattering by a statistically rough surface. Radio Phys. Radio Astron. vol. 18, no 3,pp. 244–256 (in Russian). 13. BORN, M. and VOLF, E., 1970. Principles of Optics. Moscow: Nauka Publ. (in Russian). 14. ABRAMOWITZ, M. and STEGUN, I. A., 1979. Handbook of Special Functions. Moscow: Nauka Publ. (inRussian). 15. FEDORYUK, M. V., 1987. Asymptotics: Integrals and Series. Moscow: Nauka Publ. (in Russian).