A modification to the extended Rytov theory

Abstract

This paper proposes a heuristic modification to the extended Rytov theory of strong scintillation [Andrews L, Phillips R. Laser beam propagation through random media. 2nd ed., Washington, USA: SPIE Press; 2005, Andrews LC, Al-Habash MA, Hopen CY, et al. Theory of optical scintillation: Gaussian-beam wave model. Waves Random Media. 2001;11(3):271–291]. This is done by dividing the large and small scales in the extended Rytov theory into further sub-scales. Expressions for the induced irradiance variance, and log-irradiance, due to each sub-scale are presented. The modified theory is used to derive and justify recent results in irradiance fluctuation modeling and hence answer a question initially proposed in [Shishter YM, Young RC, Ali FH. Irradiance probability density function for turbulence induced fading in free space optics. JOSA A. 2022;39(7):1267–1274, Shishter YM, Young RC, Ali FH. General statistical model of irradiance fluctuations in free space optics. JOSA A. 2023;40(1):53–63]. Plots of the irradiance pdf under the modified theory are in support of the theory. The validity of the theory presented would result in modifications to the classical scintillation analysis of waves in random media, with applications to the design of optical systems. Moreover, it is observed that the mathematical framework developed also follows from the assumption of variations in the turbulence along a horizontal path. The work presented in this paper suggests the need of further theoretical and experimental investigations into the effect of variations in atmospheric turbulence characteristics along horizontal paths in the received signal irradiance distribution.