Context. For accurately measuring intensities and determining magnetic field strengths of small-scale solar (magnetic) structure, knowledge of and compensation for the point spread function is crucial. For images recorded with the Swedish 1-meter Solar Telescope (SST), restoration with multi-frame blind deconvolution (MFBD) and joint phase diverse speckle (JPDS) methods lead to remarkable improvements in image quality but granulation contrasts that are too low, indicating additional stray light. Aims. We propose a method to compensate for stray light from high-order atmospheric aberrations not included in MFBD and JPDS processing. Methods. To compensate for uncorrected aberrations, a reformulation of the image restoration process is proposed that allows the average effect of hundreds of high-order modes to be compensated for by relying on Kolmogorov statistics for these modes. The applicability of the method requires simultaneous measurements of Fried's parameter r 0 . The method is tested with simulations as well as real data and extended to include compensation for conventional stray light. Results. We find that only part of the reduction of granulation contrast in SST images is due to uncompensated high-order aberrations. The remainder is still unaccounted for and attributed to stray light from the atmosphere, the telescope with its re-imaging system and to various high-altitude seeing effects. Conclusions. We conclude that statistical compensation of high-order modes is a viable method to reduce the loss of contrast occurring when a limited number of aberrations is explicitly compensated for with MFBD and JPDS processing. We show that good such compensation is possible with only 10 recorded frames. The main limitation of the method is that already MFBD and JPDS processing introduces high-order compensation that, if not taken into account, can lead to over-compensation.

Context.To evaluate site quality and to develop multi-conjugative adaptive optics systems for future large solar telescopes, characterization of contributions to seeing from heights up to at least 12 km above the telescope is needed. Aims. We describe a method for evaluating contributions to seeing from different layers along the line-of-sight to the Sun. The method is based on Shack Hartmann wavefront sensor data recorded over a large field-of-view with solar granulation and uses only measurements of differential image displacements from individual exposures, such that the measurements are not degraded by residual tip-tilt errors.Methods. The covariance of differential image displacements at variable field angles provides a natural extension of the work of Sarazin and Roddier to include measurements that are also sensitive to the height distribution of seeing. By extending the numerical calculations of Fried to include differential image displacements at distances much smaller and much larger than the subaperture diameter, the wavefront sensor data can be fitted to a well-defined model of seeing. The resulting least-squares fit problem can be solved with conventional methods. The method is tested with simple simulations and applied to wavefront data from the Swedish 1-m Solar Telescope on La Palma, Spain. Results. We show that good inversions are possible with 9−10 layers, three of which are within the first 1.5 km, and a maximum distance of 16−30 km, but with poor height resolution in the range 10−30 km. Conclusions. We conclude that the proposed method allows good measurements when Fried's parameter r 0 is larger than about 7.5 cm for the ground layer and that these measurements should provide valuable information for site selection and multi-conjugate development for the future European Solar Telescope. A major limitation is the large field of view presently used for wavefront sensing, leading to uncomfortably large uncertainties in r 0 at 30 km distance.

Context. The Kepler object KIC 12557548 shows irregular eclipsing behaviour with a constant 15.685 h period, but strongly varying transit depth. The object responsible for this is believed to be a disintegrating planet forming a trailing dust cloud transiting the star. A 1D model of an exponentially decaying dust tail was found to reproduce the average eclipse in intricate detail. Based on radiative hydrodynamic modelling, the upper limit for the planet mass was found to be twice the mass of the Moon. Aims. In this paper we fit individual eclipses, in addition to fitting binned light curves, to learn more about the process underlying the eclipse depth variation. Additionally, we put forward observational constraints that any model of this planet-star system will have to match. Methods. We manually de-correlated and de-trended 15 quarters of Kepler data, three of which were observed in short cadence mode. We determined the transit depth, egress depth, and stellar intensity for each orbit and search for dependencies between these parameters. We investigated the full orbit by comparing the flux distribution of a moving phase window of interest versus the out-ofeclipse flux distribution. We fit short cadence data on a per-orbit basis using a two-parameter tail model, allowing us to investigate potential dust tail property variations. Results. We find two quiescent spells of ∼30 orbital periods each where the transit depth is <0.1%, followed by relatively deep transits. Additionally, we find periods of on-off behaviour where >0.5% deep transits are followed by apparently no transit at all. Apart from these isolated events we find neither significant correlation between consecutive transit depths nor a correlation between transit depth and stellar intensity. We find a three-sigma upper limit for the secondary eclipse of 4.9 × 10 −5 , consistent with a planet candidate with a radius of less than 4600 km. Using the short cadence data we find that a 1D exponential dust tail model is insufficient to explain the data. We improved our model to a 2D, two-component dust model with an opaque core and an exponential tail. Using this model we fit individual eclipses observed in short cadence mode. We find an improved fit of the data, quantifying earlier suggestions by Budaj (2013, A&A, 557, A72) of the necessity of at least two components. We find that deep transits have most absorption in the tail, and not in a disk-shaped, opaque coma, but the transit depth and the total absorption show no correlation with the tail length.