# High resolution

We study the dynamic behaviour and the temporal variability of the smallest observable magnetic features in "quiet" and active regions of the solar atmosphere, by applying image reconstruction techniques to high-spatial resolution observations.

### Sunrise/IMaX observations of convectively driven vortex flows in the Sun

We characterize the observational properties of the convectively driven vortex ﬂows recently discovered on the quiet Sun, using magnetograms, Dopplergrams, and images obtained with the 1 m balloon-borne Sunrise telescope. By visual inspection of time series, we ﬁnd some 3.1 × 10^{−3} vortices Mm^{−2} minute^{−1} , which is a factor of ∼1.7 larger than previous estimates. The mean duration of the individual events turns out to be 7.9 minutes, with a standard deviation of 3.2 minutes. In addition, we ﬁnd several events appearing at the same locations along the duration of the time series (31.6 minutes). Such recurrent vortices show up in the proper motion ﬂow ﬁeld map averaged over the time series. The typical vertical vorticities are 6 × 10^{−3} s^{−1} , which corresponds to a period of rotation of some 35 minutes. The vortices show a preferred counterclockwise sense of rotation, which we conjecture may have to do with the preferred vorticity impinged by the solar differential rotation.

Horizontal velocity maps derived by the LCT, from the proper motions of the parameters shown in Figure 1. The velocities are averaged over the lifetime of the event (∼6.7 minutes). Horizontal scales are given in Mm. The length of the black bar at coordinates (0,0) corresponds to 1.8 km s−1 . The 1 Mm radius circles centered in the sinkhole are included for reference. (Click to see the launch of the Sunrise mission).

Bonet, J. A., et al. 2010, ApJ, 723, L13

### Image reconstruction with analytical point spread functions

The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto

image reconstruction techniques, even when observing with adaptive optics systems. These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computational burden. We generalize the extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function when the wavefront is described using Zernike functions. We present a linear expansion of the point spread function in terms of analytic functions, which, in addition, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique, which is demonstrated in terms of some applications. We propose that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use that are based on blind deconvolution.

Example of unique basis functions for representing the PSF, including terms up to the Noll index j = 7. These functions are calculated for a telescope of 100 cm diameter at a wavelength of 5250 Å, a typical situation in present-day telescopes. The spatial dimensions are in units of pixels, that we choose to be of size 0.055 , also typical of present observing conditions. The upper panel shows the results for the focused image while the lower panel shows the results for the defocused image.

Asensio Ramos, A., & López Ariste, A., 2010, A&A, 518, A6

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