Fast PSF reconstruction using the frozen flow hypothesis

When imaging space objects from ground-based telescopes, observed images are degraded by atmospheric blurring. If an accurate estimate of the point spread function (PSF) is known, then deconvolution algorithms can be used to restore the image. Wavefront sensors (WFS) collect gradients of the wavefront, which can then be used to estimate the PSF. However, the relatively coarse grid used by a typical WFS limits the accuracy of the PSF estimate, especially when there is severe atmospheric turbulence. Using the frozen flow hypothesis, it is possible to capture the inherent temporal correlations present in wavefronts in consecutive frames of data. Exploiting these correlations can lead to more accurate estimation of the PSF. Here we address the computational aspects of the problem. Specifically we show that the process of extracting additional information from the correlated WFS data can be done by solving a sparse linear least squares problem.