Modern Solar Facilities: Advanced Solar Science, Proceedings of a Workshop held at Göttingen, September 27-29, 2006

Advances, challenges and limitations of speckle reconstruction and deconvolution

Modern Solar Facilities – Advanced Solar Science, 131–134 F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.) c  Universitätsverlag Göttingen 2007 Advances, challenges and limitations of speckle reconstruction and deconvolution K. Mikurda* , O. von der Lühe, F. Wöger, and W. Schmidt Kiepenheuer-Institut für Sonnenphysik, Freiburg, Germany * Email: kasia@kis.uni-freiburg.de Abstract. This paper presents the experiences with speckle imaging and deconvolution techniques we have made during the last five years at the Kiepenheuer-Institut für Sonnenphysik. We discuss our implementation of the above techniques, their tests and application ranges. In addition, we summarize our efforts in applying speckle techniques to the data taken with the support of the adaptive optics. 1 Introduction Speckle imaging and deconvolution methods have been widely applied to the solar data for over two decades now and have proven to be an excellent tool to increase the spatial resolution of images. Here, we summarize the progress recently made in this field at the Kiepenheuer-Institut für Sonnenphysik. We also discuss the performance test of speckle techniques and their limitations and the influence of the adaptive optics on the quality of reconstructed data. 2 Speckle reconstruction Speckle reconstruction techniques use a sequence of short-exposed images to obtain one high resolution (up to the diffraction limit) image. The most popular methods applied to solar data are the (Extended) Knox-Thompson (EKT, Knox & Thompson 1974; von der Lühe 1993; Mikurda & von der Lühe 2006) and the speckle masking (Weigelt 1977; de Boer & Kneer 1992) algorithms. The Kiepenheuer-Institut Speckle Imaging Package (KISIP) has been developed since the early 1980s. Recently, we have quantitatively evaluated its performance for different solar scenes and seeing conditions. For test purposes, we have created simulated data sets which allow to compare speckle reconstruction with input data. We have chosen five reconstructions of different solar scenes (e.g. granulation, pore, sunspot penumbra) taken at the German Vacuum Tower Telescope as input images (“truth images”). Then we have created five bursts of 100 frames each, for all five truth images. Individual frames are distorted by artificial random point spread functions, chosen to represent the atmospheric seeing characterized by values of the Fried parameter r0 corresponding to 5, 7, 10, 15 and 20 cm. Probably the most interesting question is how the quality of the reconstruction depends on the seeing conditions. The left panel of Fig. 1 compares the modeled and estimated values 132 K. Mikurda et al.: Speckle reconstruction and deconvolution techniques Figure 1. Left: estimated vs. modeled Fried parameter for all data sets and seeing qualities. The data sets represent: 1 – granulation with small scale structure, 2 – pore, 3 – edge of sunspot with penumbral filaments, 4 – active region granulation, 5 – quiet region granulation. Right: image distance D2 and linear regression error E2 for all data sets and seeing parameters. of the Fried parameter r0. The Fried parameter up to r0 = 10 cm seems to be very well recovered, but Fried parameters r0 > 10 cm are overestimated. It is caused by the fact that the spectral ratio technique (implemented in KISIP) is based on Korff’s STF theory (Korff 1973) that is best applicable for moderate seeing conditions (r0/D < 0.3). The right panel of Fig. 1 demonstrates the results of the Euclidean image distance D2 calculations for all the scenes and seeing conditions. The more similar the input and reconstructed images are, the smaller this parameter becomes. For our data set the image distance is systematically lower for the reconstructions with larger Fried parameters. The sunspot penumbra scene is characterized with the largest D2 , probably because of the complexity of the reconstructed structure. More information on the tests of KISIP can be found in the recent paper of Mikurda & von der Lühe (2006). The application of KISIP V to “real world” observational data was mostly successful and the range of atmospheric conditions which can be successfully treated by speckle imaging turned out to be very large. Even data with a Fried parameter in the order of a few cm could provide a decent reconstruction. The robustness of EKT is a particular advantage for the analysis of time series which requires constant quality of the data. 2.1 Speckle reconstruction and adaptive optics To date, most of the major solar ground-based telescopes are now equipped with adaptive optics (AO) systems. The AO, however, can effectively compensate only low orders of the wavefront distortions, leaving higher orders partially uncompensated. Moreover, an AO system loses efficiency with increasing distance from a lock point. A field dependent Speckle Transfer Function (STF) can correct this effect to the first order - this solution has been implemented in the IDL version of the KISIP package. The Fried parameters are calculated K. Mikurda et al.: Speckle reconstruction and deconvolution techniques 133 Figure 2. AO Speckle Transfer Function corresponding to different angles from a lock point, α=0, ..., 32 arcsec. individually in each isoplanatic subfield and the model STFs (Korff 1973) are applied accordingly . However, we have also studied the impact of the AO on the STF. The analytical models for the STF shown in Fig. 2 are also based on the work of Korff (1973). An AO system is taken into account in the new model presented here by subtracting phase terms that represent the AO’s correction, to modify the phase structure function (see also Wang & Markey 1978). The appearing four-dimensional integrals are numerically solved using Monte-Carlo integration algorithms. An arbitrary AO can be included in the model by using performance parameters that can be measured using wave front sensor data. The main difference in the reconstructions obtained with the Korff’s STF and AO-STF is that the first causes an overestimation of the image intensity contrast at and close to the lock point. The outer regions of the reconstructed images are less effected by the choice of the STF model, in fact the AO-STFs converge to the Korff’s STF in regions with large enough separation from the lock point (see Fig. 2). 3 Speckle deconvolution Two-dimensional spectroscopy has been gaining more importance in the last years and there are several tunable filter instruments operating currently at various solar observatories (for more details see e.g. Mikurda 2005). In general, they collect data by scanning across the spectral line and obtaining a two-dimensional filtergram at each wavelength step. The individual narrow-band filtergrams are then combined to a full 2-D spectrogram. The main limitation of this technique is the time needed to perform a scan, since the temporal evolution of the solar surface has to be taken into account. The time needed to take sufficiently large speckle bursts at every wavelength will in most cases exceed the interval of changes on the Sun and the conventional speckle reconstruction techniques cannot be applied. Speckle deconvolution techniques (Keller & von der Lühe 1992; Krieg et al. 1999; Mikurda et al. 2006) offer a solution to this problem: simultaneous broad-band and narrow-band images, close-by in wavelength, are taken and speckle imaging is only performed for the broad-band channel data. Combining the reconstruction and the single broad-band images gives infor- 134 K. Mikurda et al.: Speckle reconstruction and deconvolution techniques mation on the instantaneous state of the Earth’s atmosphere. This information is then used to correct the single narrow-band images. We compared the profiles of the Fe i line at 557.6 nm resulting from unrestored and speckle-deconvolved data in order to understand the influence of the speckle deconvolution on the spectral line profiles. The detailed description of this procedure is beyond the scope of this paper and can be found in Mikurda et al. (2006). We found that the changes of intensity on the small scales have the correct sign: the bright granules become brighter and the dark lanes - darker in the continuum. Moreover, the speckle deconvolution causes the decrease of the line width in the bright structures and its increase in the dark ones. The line asymmetry is in most cases not altered. The bandwidth of the tunable instruments is usually below 0.1 nm, so the signal-to-noise ratio at the spatial frequencies close to the diffraction limit is not always sufficient. It can result in a weak grainy pattern in the reconstructed filtergrams, with a stronger effect in the dark parts of the image. Usually, it can be reduced by taking more frames at each wavelength position. 4 Conclusions We have discussed the recent progress in the speckle techniques developed at the Kiepenheuer-Institut für Sonnenphysik. Our speckle imaging package - KISIP - delivers good results for a large range of atmospheric seeing conditions, and the tests made with the usage of simulated data demonstrated good photometric quality of the reconstructions. The usage of AO-STF helps to obtain even better estimation of the photometric intensities of reconstructed images. We have also investigated the influence of the speckle deconvolution on the 2-D solar spectra and demonstrated that this technique does not introduce artefacts to the line profiles. Thus, the speckle-deconvolved 2-D spectra can be used for quantitative spectroscopy. Acknowledgements. Part of this work (KM) was supported by the DFG under grant Schm 1168/3. The Vacuum Tower Telescope on Tenerife is operated by Kiepenheuer-Institut für Sonnenphysik, Freiburg, at the Spanish Observatorio del Teide of the Instituto de Astrofı́sica de Canarias. References de Boer, C. R. & Kneer, F. 1992, A&A, 264, L24 Keller, C. U. & von der Lühe, O. 1992, A&A, 261, 321 Knox, K. T. & Thompson, B. 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