Low-order representation of dynamic aero-optic distortions

When a laser beam traverses a turbulent fluid, the fluid imposes a phase disturbance on the beam's wavefront. This phenomenon, known as aero optics, is due to variations in the fluid's index of refraction, which is proportional to fluid density. One way of correcting the resulting aberrations employs adaptive optics, in which a conjugate phase pattern is imposed on the beam before it traverses the flow, making the emerging wavefront again planar.; At the present time the spatial and temporal frequencies associated with aero optics are too high to allow for adaptive-optic corrections. Recent developments in measuring dynamic aberrations now make it possible to contemplate applying adaptive optics, but the amount of optical information that must be processed makes the problem intractable.; This dissertation explores reducing the optical information to be manipulated by applying Proper Orthogonal Decomposition (POD) to index-of-refraction data from an acoustically-forced, heated jet. Each resulting index-of-refraction eigenmode was found to have an associated optical-path-difference (OPD) contribution function, which could then be used in the reconstruction of wavefront error.; The POD analysis was also applied directly to the wavefront error. The temporal coefficients of the wavefront decomposition were found to be surprisingly similar to those of the index-of-refraction decomposition. Even more surprising was the similarity between the OPD-contribution functions and the wavefront eigenmodes. These similarities suggested that a wavefront could be decomposed by projection onto just the first few OPD-contribution functions.; Fourier-optic simulations of adaptive-optic corrections indicated that wavefront reconstructions of lower dimension maintained a high fidelity to actual far-field patterns using the full wavefronts. An adaptive-optic system, using a deformable element preprogrammed with OPD-contribution functions, and driven by lower-dimensional coefficients, was successfully simulated.; The dimension of the problem was lowered further when wavefront-slope contribution functions were found to be associated with the OPD-contribution functions. Slope information was successfully projected onto these slope-contribution functions, indicating that a real-time, adaptive-optic correction for aero-optic flows could be driven directly by a small number of raw, slope signals.