Examining the validity of using a Gaussian Schell Model for modeling an extended beacon on a rough perfectly reflecting surface

In military applications that use adaptive optics, an extended beacon instead of a point source beacon is created at the target due to atmospheric turbulence and other factors. These beacons, which have a finite spatial extent and exhibit varying degrees of coherence, are typically modeled in existing literature as a Gaussian Schell Model (GSM) due to its analytical tractability. Earlier, we used a full wave computational technique to evaluate the scattered field from a rough impedance surface in vacuum. The results showed some deviations from GSM behavior. The present work uses a simulation approach based on Physical Optics (PO) approximation to study the scattering behavior in presence of atmospheric turbulence. A fully coherent Gaussian beam is propagated through atmospheric phase screens to the rough surface target plane. The PO current is computed on the rough surface and the scattered field right above the surface is determined. The scattered light is propagated through a second set of atmospheric phase screens and thus the double passage through the atmosphere is realized. The rough surface is simulated using statistical parameters derived from profilometer measurements of standard targets. Through multiple realizations of the atmosphere and the rough surface, the statistics of the scattered field is determined. The simulations are done with different strengths of turbulence and different roughness scales of the target. The results are compared with a GSM. An effects model where the rough surface is modeled as a phase screen has also been implemented in order to verify the nature of the speckle returns.