Limitations of beam-control compensation

In this paper, we use wave-optics simulations to explore the limitations of beam-control compensation. We evaluate performance in terms of the normalized power in a diffraction-limited bucket for the cases of no beam-control compensation, perfect phase compensation, and perfect full-field compensation. From these results, we are able to arrive at the following conclusions: (1) without any form of beam-control compensation, performance begins to degrade when D/r₀ > 1; (2) with perfect phase compensation, performance begins to degrade when D/r₀ > 1 and (λ/r₀)/θ₀ > 1; and (3) with perfect full-field compensation, performance begins to degrade when D/r₀ > 1 and (λ/D)/θ₀ > 1. Here, D is the aperture diameter, r₀ is the Fried parameter, λ is the wavelength, and θ₀ is the isoplanatic angle. We show (1)–(3) to be true for varying aperture diameters, uniformly distributed turbulence, and varying turbulence profiles. These findings will inform the development of future laser systems that need to sense and correct for the effects of atmospheric turbulence.