Perturbative approach to the small-scale physics of the interaction of thermal blooming and turbulence

Abstract

In the past the combined effects of thermal blooming and atmospheric turbulence in the wave-optics regime were considered analytically intractable and were treated heuristically or left to 1wave-optics codes. We demonstrate that, at least for uniform atmosphere and wind, the linearized problem for small-scale blooming is tractable and leads to considerable physical insight. We analytically solve the linearized equations of thermal blooming for uplink propagation of an infinite beam in uniform atmosphere and wind as a perturbation series in blooming for the case of compensated and uncompensated propagation. A Feynman diagram representation of the series is presented. Most importantly, the propagators are used to compute the mutual coherence function and the Strehl ratio also as a perturbation series in blooming. The dependence of the results on the actuator Fresnel number of the adaptive optics is discussed along with the relative roles of the phase-compensation instability and stimulated thermal Rayleigh scattering. A brief comparison is made with nonlinear numerical simulations in order to show that the nonlinearities may be neglected for realistic levels of atmospheric turbulence.