The phase diversity technique is studied as a wave-front sensor to be implemented with widely extended sources. The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images (in focus and out of focus) by use of a maximum-likelihood approach. The propagation of the photon noise in the images on the estimated phase is derived from a theoretical analysis. The covariance matrix of the phase estimator is calculated, and the optimal distance between the observation planes that minimizes the noise propagation is determined. The phase error is inversely proportional to the number of photons in the images. The noise variance on the Zernike polynomials increases with the order of the polynomial. These results are confirmed with both numerical and experimental validations. The influence of the spectral bandwidth on the phase estimator is also studied with simulations.
In order to address the high throughput requested for both downlink and uplink satellite to ground laser links, Adaptive Optics (AO) has become a key technology. While mature, application of this technology to satellite to ground telecommunication faces however difficulties such as higher bandwidth, optimal operation for a wide variety of atmospheric conditions (daytime and nighttime) with potentially low elevations that might severely affect wavefront sensing because of scintillation. To address these specificities an accurate understanding of the origin of the perturbations is required, as well as operational validation of AO on real laser links. We report here on a Low Earth Orbiting (LEO) microsatellite to ground downlink with AO correction. We discuss propagation channel characterization based on Shack-Hartmann WaveFront Sensor (WFS) measurements. Fine modelling of the propagation channel is proposed based on multi-Gaussian model of turbulence profile. This model is then used to estimate the AO performance and validate the experimental results. While AO performance is limited by the experimental setup , it proves to comply with expected performance and further interesting information on propagation channel is extracted. These results shall help dimensioning and operating AO systems for LEO to ground downlinks.
Optical technologies are extremely competitive candidates to achieve very-high throughput links between ground and GEO satellites; however, their feasibility relies on the ability to mitigate channel impairments due to atmospheric turbulence. For that purpose, Adaptive Optics (AO) has already proved to be highly efficient on the downlink. However, for the uplink, anisoplanatism induced by point-ahead angle (PAA) compromises AO pre-compensation efficiency to an extent that depends on propagation conditions. The ability to properly assess the anisoplanatism impact in a wide variety of conditions is thus critical in designing the optical ground terminals. In this paper, we demonstrate the consistency of experimental coupled flux statistics with results coming from performance and end-to-end models, on an AO pre-compensated 13 km slant path in Tenerife. This validation is demonstrated in a wide variety of turbulence conditions, hence consolidating propagation channel models that are of critical importance for the reliability of future GEO feeder links. We then compare experimental results to theoretical on-sky performance, and discuss to what extent such slant path or horizontal path experiments can be representative of real GEO links.
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