Piston phase compensation of tiled apertures in the presence of turbulence and thermal blooming

With current phasing technology, the individual beamlets within a tiled aperture can be phased in piston to coherently combine at the target. In practice, this piston phasing of the optical beamlet trains is accomplished using a point-source target. The reflections from the point-source target act as an idealized beacon, which propagate from the target to the tiled aperture through aberrations induced within the optical beamlet trains. Thus, an ideal reference is achieved to perform piston phase compensation by exploiting high-bandwidth phase loops. This paper investigates piston phase compensation of tiled apertures in the presence of horizontal-path turbulence and thermal blooming by using wave-optics simulations. To represent different array fill factors in the source plane, both seven and 19 element hexagonal close-packed tiled apertures are used in the simulations along with both Gaussian and flat-top outgoing beamlets. Performance is evaluated by calculating peak Strehl ratio and power in the bucket in the target plane for all simulation setups and averaging these performance metrics for multiple realizations of turbulence and thermal blooming. The performance metrics are plotted as a function of the Fried coherence diameter, the log-amplitude variance, and the distortion number for comparison purposes. In general, the results show that piston phase compensation does not perform well when the subaperture diameter is greater than the coherence diameter and when the distortion number is greater than 21 rad. These results are intuitive; however, the trends are often nonlinear with distinct asymptotes. With this said, the results presented in this paper should help future conceptual designs.