Sources of straylight in the post-focus imaging instrumentation of the Swedish 1-m Solar Telescope

Mats Löfdahl & Göran Scharmer, Astronomy & Astrophysics, 537:A80, 2012

Context. Recently measured straylight point spread functions (PSFs) in Hinode/SOT make granulation contrast in observed data and synthetic magnetohydrodynamic (MHD) data consistent. Data from earthbound telescopes also need accurate correction for straylight and fixed optical aberrations.
Aims. We aim to develop a method for measuring straylight in the post-focus imaging optics of the Swedish 1-m Solar Telescope (SST).
Methods. We removed any influence from atmospheric turbulence and scattering by using an artificial target. We measured integrated straylight from three different sources in the same data: ghost images caused by reflections in the near-detector optics, PSFs corresponding to wavefront aberrations in the optics by using phase diversity, and extended scattering PSF wings of unknown origin by fitting to a number of different kernels. We performed the analysis separately in the red beam and the blue beam.
Results. Wavefront aberrations, which possibly originate in the bimorph mirror of the adaptive optics, are responsible for a wavelength-dependent straylight of 20–30% of the intensity in the form of PSFs with 90% of the energy contained within a radius of 0."6. There are ghost images that contribute at the most a few percent of straylight. The fraction of other sources of scattered light from the post-focus instrumentation of the SST is only ∼10^−3 of the recorded intensity. This contribution has wide wings with FWHM ∼16" in the blue and ∼34" in the red.
Conclusions. The present method seems to work well for separately estimating wavefront aberrations and the scattering kernel shape and fraction. Ghost images can be expected to remain at the same level for solar observations. The high-order wavefront aberrations possibly caused by the AO bimorph mirror dominate the measured straylight but are likely to change when imaging the Sun. We can therefore make no firm statements about the origin of straylight in SST data, but strongly suspect wavefront aberrations to be the dominant source.

A tilted interference filter in a converging beam

Mats Löfdahl, Vasco Henriques & Dan Kiselman. Astronomy & Astrophysics, 533:A82, 2011.

Context. Narrow-band interference filters can be tuned toward shorter wavelengths by tilting them from the perpendicular to the optical axis. This can be used as a cheap alternative to real tunable filters, such as Fabry-Pérot interferometers and Lyot filters. At the Swedish 1-meter Solar Telescope, such a setup is used to scan through the blue wing of the Ca II H line. Because the filter is mounted in a converging beam, the incident angle varies over the pupil, which causes a variation of the transmission over the pupil, different for each wavelength within the passband. This causes broadening of the filter transmission profile and degradation of the image quality.
Aims.We want to characterize the properties of our filter, at normal incidence as well as at different tilt angles. Knowing the broadened profile is important for the interpretation of the solar images. Compensating the images for the degrading effects will improve the resolution and remove one source of image contrast degradation. In particular, we need to solve the latter problem for images that are also compensated for blurring caused by atmospheric turbulence.
Methods.We simulate the process of image formation through a tilted interference filter in order to understand the effects.We test the hypothesis that they are separable from the effects of wavefront aberrations for the purpose of image deconvolution. We measure the filter transmission profile and the degrading PSF from calibration data.
Results.We find that the filter transmission profile differs significantly from the specifications. We demonstrate how to compensate for the image-degrading effects. Because the filter tilt effects indeed appear to be separable from wavefront aberrations in a useful way, this can be done in a final deconvolution, after standard image restoration with Multi-Frame Blind Deconvolution/Phase Diversity based methods. We illustrate the technique with real data.

Evaluation of image-shift measurement algorithms for solar Shack-Hartmann wavefront sensors

Mats Löfdahl, Astronomy & Astrophysics, 524:A90, 2010.

Context. Solar Shack–Hartmann wavefront sensors measure differential wavefront tilts as the relative shift between images from different subapertures. There are several methods in use for measuring these shifts.
Aims. We evaluate the inherent accuracy of the methods and the effects of various sources of error, such as noise, bias mismatch, and blurring. We investigate whether Z-tilts or G-tilts are measured.
Methods. We test the algorithms on two kinds of artificial data sets, one corresponding to images with known shifts and one corresponding to seeing with different r0.
Results. Our results show that the best methods for shift measurements are based on the square difference function and the absolute difference function squared, with subpixel accuracy accomplished by use of two-dimensional quadratic interpolation. These methods measure Z-tilts rather than G-tilts.

Striation and convection in penumbral filaments

Henk Spruit, Göran Scharmer & Mats Löfdahl, Astronomy & Astrophysics, 521:A72, 2010.

Observations with the 1-m Swedish Solar Telescope of the flows seen in penumbral filaments are presented. Time sequences of bright filaments show overturning motions strikingly similar to those seen along the walls of small isolated structures in the active regions. The filaments show outward propagating striations with inclination angles suggesting that they are aligned with the local magnetic field. We interpret it as the equivalent of the striations seen in the walls of small isolated magnetic structures. Their origin is then a corrugation of the boundary between an overturning convective flow inside the filament and the magnetic eld wrapping around it. The outward propagation is a combination of a pattern motion due to the down flow observed along the sides of bright filaments, and the Evershed flow. The observed short wavelength of the striation argues against the existence of a dynamically significant horizontal field inside the bright filaments. Its intensity contrast is explained by the same physical effect that causes the dark cores of filaments, light bridges and `canals'. In this way striation represents an important clue to the physics of penumbral structure and its relation with other magnetic structures on the solar surface. We put this in perspective with results from the recent 3-D radiative hydrodynamic simulations.

High-order aberration compensation with multi-frame blind deconvolution and phase diversity image restoration techniques

Göran Scharmer, Mats Löfdahl, T.I.M. van Werkoven and Jaime de la Cruz Rodriguez, Astronomy & Astrophysics, 521:A68, 2010.

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 r0. 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.

Wavefront sensing and wavefront reconstruction for the 4m European Solar Telescope EST

Thomas Berkefeld, Dirk Soltau, Dario Del Moro & Mats Löfdahl, in Adaptive Optics Systems II, Proc. SPIE 7736:77362J, 2010

We give an overview of the Adaptive Optics (AO) and Multi-conjugate Adaptive Optics (MCAO) system of the planned 4m European Solar Telescope (EST). The parameter space and the problems of solar MCAO working in the visible are explained. The wavefront reconstruction schemes presently being considered are explained. First estimates of the expected MCAO performance for varying parameter sets are given.

Adaptive optics and MCAO for the 4-m European Solar Telescope EST

Dirk Soltau, Thomas Berkefeld, Sánchez Capuchino, Manuel Collados Vera, Dario Del Moro, Mats Löfdahl & Göran Scharmer, in Adaptive Optics Systems II, Proc. SPIE 7736:77360U, 2010.

A consortium of more than 20 European solar physics institution from 15 different countries is conducting a design study for a 4 m class solar telescope which shall be situated at the Canary Islands. In this paper we introduce the AO and MCAO design concept for EST. A ground layer deformable mirror is combined with an arrangement of four deformable layer mirrors. A combination of Shack-Hartmann wave front sensors with wide and narrow fields of view is used to control the system and to achieve a corrected field of view of one arcmin.

CRISP spectropolarimetric imaging of penumbral fine structure

Göran Scharmer, Gautam Narayan, Tomas Hillberg, Jaime de la Cruz Rodriguez, Peter Sütterlin, Mats Löfdahl, Michiel van Noort, Dan Kiselman & Andreas Lagg, published in Astrophysical Journal Letters, 689(1):L69-L72, 2008.

We discuss penumbral fine structure in a small part of a pore, observed with the CRISP imaging spectropolarimeter at the Swedish 1-m Solar Telescope (SST), close to its diffraction limit of 0.16". Milne-Eddington inversions applied to these Stokes data reveal large variations of field strength and inclination angle over dark-cored penumbral intrusions and a dark-cored light bridge. The mid-outer part of this penumbra structure shows ~0.3" wide spines, separated by ~1.6" (1200 km) and associated with 30° inclination variations. Between these spines, there are no small-scale magnetic structures that easily can be identified with individual flux tubes. A structure with nearly 10° more vertical and weaker magnetic field is seen midway between two spines. This structure is cospatial with the brightest penumbral filament, possibly indicating the location of a convective upflow from below.

Spectropolarimetry of Sunspots at 0.16 arcsec resolution

Göran Scharmer, Vasco Henriques, Tomas Hillberg, Dan Kiselman, Mats Löfdahl, Gautam Narayan, Peter Sütterlin, Michiel van Noort & Jaime de La Cruz Rodriguez, in Proc. 12th European Solar Physics Meeting, Freiburg, Germany, September, 8-12, 2008, p.2.5, 12:2, 2008

We present first observations of sunspots with the imaging spectropolarimeter CRISP, recently installed at the Swedish 1-m Solar Telescope (SST) on La Palma. This spectropolarimeter is based on a high-fidelity dual Fabry-Perot filter system.
Two liquid crystals and a polarizing beam splitter are used to reduce seeing induced I,Q,U,V crosstalk by simultaneously recording images with two 1kx1k back-illuminated Sarnoff CCD's. A third CCD simultaneously records broadband images through the pre-filter of the FPI filter system, allowing image reconstruction and co-alignment of images of different polarization states and at different wavelengths in Zeeman sensitive spectral lines.

The first data, recorded in April 2008, demonstrate the capability of this system to record high cadence, high S/N polarimetric data with a spatial resolution at or close to the diffraction limit of the SST at 630 nm, 0.16 arcsec. We discuss the analysis of first spectropolarimetric data for sunspots, based on Milne-Eddington inversion techniques.

SST/CRISP Magnetometry with Fe I 630.2 nm

Gautam Narayan, Göran Scharmer, Tomas Hillberg, Mats Löfdahl, Michiel van Noort, Peter Sutterlin & Andreas Lagg, in Proc. 12th European Solar Physics Meeting, Freiburg, Germany, September, 8-12, 2008, p.2.2-64, 12:120., 2008

We present recent full Stokes observations in the Fe I 630.2 nm line with CRISP, an imaging spectropolarimeter at the Swedish 1-m Solar Telescope (SST). The observations reach a spatial resolution of 0".16, close to the diffraction limit of the SST, representing a major improvement over any past ground based or space based spectropolarimetric data. We describe the data acquisition and reduction methods and present results of Milne-Eddington(ME) inversions applied on observations of plage.

Multi-frame deconvolution with space-variant point-spread functions by use of inverse filtering and fast Fourier transform

Mats Löfdahl, Applied Optics, 46(21):4686-4693, 2007.

A procedure for deconvolution of multiple images of the same object with space-variant point-spread functions (PSFs) is presented. It is based on expressing deconvolution with inverse filtering as convolution with kernels corresponding to inverse PSFs. Sets of basis functions are made from these inverse PSFs, given at discrete sample points, through Karhunen–Loève (K–L) decomposition. The entire field of view can then be convolved with the K–L kernels. Co-adding the results using continuous maps of expansion weights, interpolated for every pixel between the sample points, results in an image that is deconvolved with smoothly varying PSFs that match the discrete measurements. A demonstration data set is used to show how the transition between the grid points improves deconvolutions compared to piecewise deconvolution and mosaicking by avoiding the blending of discontinuities at the interfaces between adjacent subfields.

Solar Image Restoration

Mats Löfdahl, Michiel van Noort & Carsten Denker, invited review, in Proc. Modern Solar Facilities - Advanced Solar Science, workshop in Göttingen 27-29 September, 2006, Kneer, Puschmann & Wittmann, eds., 2007.

Image restoration is used to repair solar images degraded by the turbulence in Earth’s atmosphere. Restoration algorithms are based on models of the optical system that produce the images – from the solar source of radiation, through Earth’s atmosphere and telescope/instrument optics, to the detectors recording the data. In this review, these model components are discussed in the context of two very different classes of image restoration methods, i.e., Speckle Imaging and Phase Diversity/MultiFrame Blind Deconvolution, which have been successfully used during the last two decades. The strengths and weaknesses of these two approaches are discussed, as well as some variants and recent progress.

Observations of dark-cored filaments in sunspot penumbrae

Kai Langhans, Göran Scharmer, Dan Kiselman, & Mats Löfdahl, Astronomy & Astrophysics, 464:763-774, 2007

Context: The recent discovery of dark-cored penumbral filaments suggests that we are resolving the building blocks of sunspot penumbrae. Their properties are largely unknown but provide important clues to understanding penumbral fine structure.
Aims: Our observations provide new constraints for the different scenarios put forward to explain the structure of sunspot penumbrae.
Methods: We present an analysis of dark-cored penumbral filaments, based on intensity filtergrams (G-band, continuum and Ca II H line wing), magnetograms and Dopplergrams, obtained at heliocentric distances between 15° and 55°.
Results: In general, the visibility of dark cores degrades with increasing heliocentric distance. Based on Ca II H wing images we conclude that this is due to a geometrical 3D-effect and not due to a simple formation height effect. Only in the center-side penumbra are dark-cored filaments visible at all observed heliocentric distances. We observe that dark-cored filaments frequently split in the umbra, forming a Y-shape that disappears after a few minutes, leaving a shortened filamentary structure and a bright dot in the umbra. The dark-cored filaments have life times ≥ 90 min. The dark cores are related to a much weaker and a more horizontal magnetic field than their lateral brightenings. Where the dark-cored filaments appear in the umbra, the magnetic field is inclined by 40° with respect to the solar surface normal for both the dark core and the bright edges. With increasing distance from the umbra, the magnetic field inclination in the dark cores increases rapidly within a few thousand km. Both the magnetic field strength and inclination in the lateral brightenings show very small variations with spot-center radial distance. The velocity field possesses a strong horizontal component within the dark cores. The absolute line-of-sight (LOS) velocity is larger within the dark cores than in their lateral brightenings. The Evershed flow apparently is present primarily in the dark cores.

Recent high resolution observations and interpretations of sunspot fine structure

Göran Scharmer, Kai Langhans, Dan Kiselman & Mats Löfdahl, in New Solar Physics with Solar-B Mission, Proc. 6th Solar-B Science Meeting, Shibata, Nagata, & Sakurai, eds., Astronomical Society of the Pacific Conference Series, 369:71, 2007

We review analyses made of highly resolved filtergrams, magnetograms and Dopplergrams of sunspots, recorded with the Swedish 1-meter Solar Telescope (SST) on La Palma. Dark cores in penumbral filaments are shown to be directly linked to peripheral umbral dots and to dark lanes in light bridges, suggesting similar or related underlying physics. The visibility of dark cores is found to depend strongly on the azimuth angle already for spots located at small heliocentric distances. It is shown that dark cores are clearly visible close to the center of the Ca II H line, formed approximately 150--200~km above the photosphere. We conclude that the τ = 1 layer of dark-cored filaments outlines a strongly warped surface, consistent with the finding that the magnetic field strength is strongly reduced in dark cores. We show that several properties of dark-cored filaments derived from SSTSST data are consistent with results of inversions of low-resolution Stokes spectra, but also find important discrepancies with the interpretation that penumbral filaments can be identified with flux tubes. Our data are consistent with the model proposed by Spruit & Scharmer (2006), explaining dark cores as signatures of field-free convection occurring just below the visible surface of the penumbra. We discuss recent simulations of light bridges and umbral dots, providing additional support to that model.

What are 'Faculae'?

Thomas Berger, Alan Title, Ted Tarbell, Luc Rouppe van der Voort, Mats Löfdahl & Göran Scharmer, in New Solar Physics with Solar-B Mission, Shibata, Nagata, & Sakurai, eds., Astronomical Society of the Pacific Conference Series, 369:103, 2007

We present very high resolution filtergram and magnetogram observations of solar faculae taken at the Swedish 1-meter Solar Telescope (SST) on La Palma. Three datasets with average line-of-sight angles of 16, 34, and 53 degrees are analyzed. The average radial extent of faculae is at least 400 km. In addition we find that contrast versus magnetic flux density is nearly constant for faculae at a given disk position. These facts and the high resolution images and movies reveal that faculae are not the interiors of small flux tubes - they are granules seen through the transparency caused by groups of magnetic elements or micropores ``in front of'' the granules. Previous results which show a strong dependency of facular contrast on magnetic flux density were caused by bin-averaging of lower resolution data leading to a mixture of the signal from bright facular walls and the associated intergranular lanes and micropores. The findings are relevant to studies of total solar irradiance (TSI) that use facular contrast as a function of disk position and magnetic field in order to model the increase in TSI with increasing sunspot activity.

Contrast analysis of solar faculae and magnetic bright points

Thomas Berger, Luc Rouppe van der Voort & Mats Löfdahl, Astrophysical Journal, 661(2):1272-1288, 2007

The morphology and contrast of small-scale solar magnetic elements at four disk positions is analyzed. The data were obtained at the Swedish 1 m Solar Telescope (SST) over 3 yr (2003-2005). Two of the data sets have disk positions near disk center (average μ=cosθ>0.8) and show numerous ``magnetic bright points'' (MBPs), and two are sufficiently limbward to show prominent ``faculae'' (average μ<=0.6). The filtergrams are obtained in the 430.5 nm G band and 436.4 nm ``continuum'' bandpasses; the magnetograms are Fe I 630.25 nm Stokes V images taken with the Solar Optical Universal Polarimeter (SOUP) tunable filter. In all images we achieve nearly diffraction-limited resolution (~100 km in the G band). Analysis shows that MBPs and faculae are distinct radiative signatures of the magnetic field: MBPs have a constant or slightly decreasing contrast with increasing magnetogram signal, while facular contrast increases linearly with magnetogram signal. Faculae are much larger than MBPs, with an average radial width of 400 km. The observations support recent modeling showing that faculae are granules seen through the opacity reduction provided by magnetic elements (or groups thereof), while MBPs are caused by lateral radiation leakage scattering from deeper layers of the magnetic element.

Rapid temporal variability of faculae: High resolution observations and modelling

Bart De Pontieu, Mats Carlsson, Robert Stein, Mats Löfdahl, Michiel van Noort, Åke Nordlund, Luc Rouppe van der Voort & Göran Scharmer, Astrophysical Journal, 646:1405, 2006

We present high resolution G-band observations (obtained with the Swedish 1 m Solar Telescope) of the rapid temporal variability of faculae, which occurs on granular timescales. By combining these observations with magneto-convection simulations of a plage region, we show that much of this variability is not intrinsic to the magnetic field concentrations that are associated with faculae, but rather a phenomenon associated with the normal evolution and splitting of granules. We also show examples of facular variability caused by changes in the magnetic field, with movies of dynamic behavior of the striations that dominate much of the facular appearance at 0.1′′ resolution. Examples of these dynamics include merging, splitting, rapid motion, apparent fluting, and possibly swaying.

Solar image restoration by use of multi-frame blind de-convolution with multiple objects and phase diversity

Michiel van Noort, Luc Rouppe van der Voort & Mats Löfdahl, Solar Physics, 228(1-2):191-215, 2005.

An extension on Joint Phase Diversity Speckle image restoration is presented. Multiple realizations of multiple objects having known wavefront relations with each other can now be restored jointly. As the alignment of the imaging setup does not change, near-perfect alignment can be achieved between different objects, thus greatly reducing false signals in the determination of derived quantities, such as magnetograms, Dopplergrams, etc. The method was implemented in C++ as an image restoration server, to which worker clients can connect and disconnect randomly, so that a large number of CPUs can be used to speed up the restorations. We present a number of examples of applications of the restoration method to observations obtained with the Swedish 1-m Solar Telescope on La Palma.

Inclination of magnetic fields and flows in sunspot penumbrae

Kai Langhans, Göran Scharmer, Dan Kiselman, Mats Löfdahl & Thomas Berger, Astronomy & Astrophysics, 436(3):1087-1101, 2005

An observational study of the inclination of magnetic fields and flows in sunspot penumbrae at a spatial resolution of 0.2 arcsec is presented. The analysis is based on longitudinal magnetograms and Dopplergrams obtained with the Swedish 1-m Solar Telescope on La Palma using the Lockheed Solar Optical Universal Polarimeter birefringent filter. Data from two sunspots observed at several heliocentric angles between 12° and 39° were analyzed. We find that the magnetic field at the level of the formation of the Fe I-line wing (630.25 nm) is in the form of coherent structures that extend radially over nearly the entire penumbra giving the impression of vertical sheet-like structures. The inclination of the field varies up to 45° over azimuthal distances close to the resolution limit of the magnetograms. Dark penumbral cores, and their extensions into the outer penumbra, are prominent features associated with the more horizontal component of the magnetic field. The inclination of this dark penumbral component - designated B - increases outwards from approximately 40° in the inner penumbra such that the field lines are nearly horizontal or even return to the solar surface already in the middle penumbra. The bright component of filaments - designated A - is associated with the more vertical component of the magnetic field and has an inclination with respect to the normal of about 35° in the inner penumbra, increasing to about 60° towards the outer boundary. The magnetogram signal is lower in the dark component B regions than in the bright component A regions of the penumbral filaments. The measured rapid azimuthal variation of the magnetogram signal is interpreted as being caused by combined fluctuations of inclination and magnetic field strength. The Dopplergrams show that the velocity field associated with penumbral component B is roughly aligned with the magnetic field while component A flows are more horizontal than the magnetic field. The observations give general support to fluted and uncombed models of the penumbra. The long-lived nature of the dark-cored filaments makes it difficult to interpret these as evidence for convective exchange of flux tubes. Our observations are in broad agreement with the two component model of Bellot Rubio et al. (2003), but do not rule out the embedded flux tube model of Solanki & Montavon (1993).

Image Restoration

Carsten Denker, Alexandra Tritschler & Mats Löfdahl, in Encyclopedia of Optical Engineering, Driggers, ed., Marcel Dekker, Inc., 2005

Throughout the past two decades, digital image processing has made its way into today’s technology and computer driven society. Its applications encompass a wide variety of specialized disciplines including medical imaging, machine vision, remote sensing, and astronomy – even influencing the computer user at home. Personal images obtained with digital cameras can easily be manipulated by a variety of dedicated commercial and public domain image processing software packages. Image reconstruction has to be defined in this context. Whereas image enhancement strives to bring out certain features in an image to simplify the extraction of image information, image reconstruction is the attempt to retrieve information that has been lost or obscured in the imaging process itself. Therefore, image reconstruction requires a systems approach that takes into account the entire process of image formation including the propagation of light through inhomogeneous media, the properties of the optical system, and the characteristics of the detector. Here, solar astronomy will serve as an example of the image formation process. We will discuss various image reconstruction methods an the underlying mathematical models.

A comparative study of the contrast of solar magnetic elements in CN and CH

Vasily Zakharov, Achim Gandorfer, Sami Solanki & Mats Löfdahl, Astronomy & Astrophysics, 437:L43-L46, 2005

Photospheric bright points were investigated in three different wavelength bands using interference filters centered at 436.5 nm (continuum), 430.5 nm (Fraunhofer's G-band dominated by absorption due to CH), and 388.7 nm (absorption band of CN). Such bright points serve as proxies of small-scale solar magnetic elements. Near diffraction limited imaging was achieved by real-time frame selection and subsequent joint phase diverse speckle reconstruction. Comparison of the filtergrams of NOAA0670 taken in CH and CN shows that the contrast of bright points is on average 1.4 times higher in CN than in G-band, which is in good quantitative agreement with the predictions of Berdyugina et al. (2003, A&A, 412, 513) and Rutten et al. (2001, ASP Conf. Ser., 236, 445).

Penumbral structure at 0."1 resolution. I. General appearance and power spectra

Luc Rouppe van der Voort, Mats Löfdahl, Dan Kiselman and Göran Scharmer, Astronomy & Astrophysics, 414:717-726, 2004.

We analyse sunspot filtergrams of unprecedented quality obtained by Scharmer et al. (2002) with the Swedish 1-m Solar Telescope on La Palma. The observations comprise images in three different wavelength bands: 488, 436, and 430 nm (G-band). We find that there are still unresolved penumbral filaments which must have widths smaller than 80 km. The fine structuring along the filaments is limited. Penumbral grains have internal structure and look like they are split or crossed by narrow dark structures. We calculate intensity power spectra of the penumbra from images that are corrected for seeing using the Phase Diversity technique. The effects of high order aberrations that are not corrected for are estimated to be too low to be consistent with a flat power spectrum. The penumbral power spectra do not show any signs of bumps or peaks that could correspond to a preferred scale at 0."35 for the width of penumbral filaments. We argue that the power spectrum is not a very reliable source of information concerning preferred scales.

Solar magnetic elements at 0.1" resolution. General appearance and magnetic structure

Thomas Berger, Luc Rouppe van der Voort, Mats Löfdahl, Mats Carlsson, A. Fossum, Viggo Hansteen, Elin Marthinussen, Alan Title & Göran Scharmer, Astronomy & Astrophysics, 428:613-628, 2004

New observations of solar magnetic elements in a remnant active region plage near disk center are presented. The observations were obtained at the recently commissioned Swedish 1-m Solar Telescope on La Palma. We examine a single 430.5 nm G-band filtergram that resolves ˜70 km (0.1 arcsec) structures and find new forms of magnetic structures in this particular region. A cotemporal Ca II H-line image is used to examine the low-chromosphere of network elements. A cotemporal Fe I 630.25 nm magnetogram that resolves structures as small as 120 km (0.18 arcsec) FWHM with a flux sensitivity of approximately 130 Mx cm-2 quantifies the magnetic structure of the region. A Ni I 676.8 nm Dopplergram establishes relative velocity patterns associated with the network features with an accuracy of about 300 m s-1. We find that magnetic flux in this region as seen in both the magnetogram and the G-band image is typically structured into larger, amorphous, ``ribbons'' which are not resolved into individual flux tubes. The measured magnetic flux density in the ribbon structures ranges from 300 to 1500 Mx cm-2, the higher values occurring at localized concentrations embedded within the ribbons. The Dopplergram indicates relative downflows associated with all magnetic elements with some indication that higher downflows occur adjacent to the peak magnetic flux location. The mean absolute magnetic flux density of the remnant plage network is about 130 Mx cm-2; in the lowest flux regions of the field-of-view, the mean absolute flux density is approximately 60 Mx cm-2. Within these quiet regions we do not find evidence of pervasive kilo-gauss strength magnetic elements as seen in recent high resolution internetwork studies. In general, the observations confirm recent 3-dimensional numerical simulations which show that the magnetic field in high-density regions such as plage is concentrated in complex structures that are not generally composed of discrete magnetic flux tubes.

Svarta droppen

Dan Kiselman & Mats Löfdahl, Populär astronomi (2)38, 2004

– en liten kommentar till den förestående Venuspassagen 8 juni

Phase diverse speckle inversion applied to data from the Swedish 1-meter solar telescope

Mats Löfdahl & Göran Scharmer, in Innovative Telescopes and Instrumentation for Solar Astrophysics, Keil & Avakyan, eds., Proc. SPIE 4853:567-575, 2003

We report on the use of a new joint phase diverse speckle code, an implementation of a method where a single object and individual phases are estimated from several pairs of phase diverse data.  The code was used on 430.5 nm G-band data collected with the newly installed Swedish 1-meter solar telescope in La Palma, equipped with a low-order adaptive optics system. We describe the algorithm briefly, show wavefront statistics and object estimates from the processing and discuss the results.  We demonstrate a resolution of 0.12 arc seconds for a time sequence and a large field of view, which is a break-through for ground based solar telescopes.

Adaptive optics system for the new Swedish solar telescope

Göran Scharmer, Pete Dettori, Mats Löfdahl & Mark Shand, in Innovative Telescopes and Instrumentation for Solar Astrophysics, Keil & Avakyan, eds., Proc. SPIE 4853:370-380, 2003

The 1-meter Swedish solar telescope is a new solar telescope that was put in operation on the island of La Palma in the Canary Islands at the end of May 2002. The goal of this telescope is to reach its diffraction limited resolution of 0.1 arcsec in blue light. This has already been achieved by use of a low-order adaptive optics (AO) system.  This paper describes the AO system initially developed for the former 50-cm Swedish Vacuum Solar Telescope (SVST) and further improved for the new telescope.  Both systems use a combination of bimorph modal mirrors and Shack-Hartmann wavefront sensors. Unique to these systems are that they rely on a single workstation or a PC to do all the computations required to extract and pre-process the images, measure their positions using cross correlation techniques and for controlling the deformable mirror.  This is in the present system possible by using the PERR instruction available on Compaq's Alpha architecture and in the new system using the PSADDBW instruction, available on Pentium 4 and Athlon processors. We describe both these systems with an emphasis on the performance, the ease of support and upgrades of performance.

We also describe the optimization of the electrode geometry for the new 37-electrode bimorph mirror, supplied by AOPTIX Technologies, Inc., for controlling Karhunen-Loeve modes. Expected performance, based on closed-loop simulations, is discussed.

First results from the Swedish 1-m solar telescope

Göran Scharmer, Dan Kiselman, Mats Löfdahl & Luc Rouppe van der Voort, Proc. Third International Workshop on Solar Polarization, Trujillo Bueno & Sánchez Almeida, eds., Tenerife, ASP Conference Series 307, 2003

We describe the Swedish 1-m Solar Telescope (SST) on La Palma which has twice as large aperture as the previous SVST.  The un-obscured optics consists of a singlet lens used as vacuum window and secondary optics. The secondary optics uses a field mirror to re-image the pupil on a 25 cm corrector which provides a perfectly achromatic image, compensated also for atmospheric dispersion.  The adaptive optics system consists of a low-order bimorph modal mirror with 37 electrodes, allowing near-diffraction-limited imaging a reasonable fraction of the observing time on La Palma.  The new telescope became operational on 21 May 2002 and has quickly proven to be the most highly resolving solar telescope ever built. In this paper, we describe its design, the instrumentation in use or planned for this telescope and present first results based on observations made in May-July 2002.

Multi-frame blind deconvolution with linear equality constraints

Mats Löfdahl, in Image Reconstruction from Incomplete Data II, Bones, Fiddy, & Millane, eds., Proc. SPIE 4792:146-155, 2002

The Phase Diverse Speckle (PDS) problem is formulated mathematically as Multi Frame Blind Deconvolution (MFBD) together with a set of Linear Equality Constraints (LECs) on the wavefront expansion parameters. This MFBD--LEC formulation is quite general and, in addition to PDS, it allows the same code to handle a variety of different data collection schemes specified as data, the LECs, rather than in the code. It also relieves us from having to derive new expressions for the gradient of the wavefront parameter vector for each type of data set. The idea is first presented with a simple formulation that accommodates Phase Diversity, Phase Diverse Speckle, and Shack--Hartmann wavefront sensing. Then various generalizations are discussed, that allows many other types of data sets to be handled.

Background: Unless auxiliary information is used, the Blind Deconvolution problem for a single frame is not well posed because the object and PSF information in a data frame cannot be separated. There are different ways of bringing auxiliary information to bear on the problem. MFBD uses several frames which helps somewhat, because the solutions are constrained by a requirement that the object be the same, but is often not enough to get useful results without further constraints. One class of MFBD methods constrain the solutions by requiring that the PSFs correspond to wavefronts over a certain pupil geometry, expanded in a finite basis. This is an effective approach but there is still a problem of uniqueness in that different phases can give the same PSF. Phase Diversity and the more general PDS methods are special cases of this class of MFBD, where the observations are usually arranged so that in focus data is collected together with intentionally defocused data, where information on the object is sacrificed for more information on the aberrations. The known differences and similarities between the phases are used to get better estimates.

Dark cores in sunspot penumbral filaments

Göran Scharmer, Boris Gudiksen, Dan Kiselman, Mats Löfdahl & Luc Rouppe van der Voort, Nature, 420:151-153, 2002.

Sunspot umbrae - the dark central regions of the spots - are surrounded by brighter filamentary penumbrae, the existence of which remains largely inexplicable. The penumbral filaments contain magnetic fields with varying inclinations and are associated with flowing gas, but discriminating between theoretical models has been difficult because the structure of the filaments has not hitherto been resolved. Here we report observations of penumbral filaments that reveal dark cores inside them. We cannot determine the nature of these dark cores, but their very existence provides a crucial test for any model of penumbrae. Our images also reveal other very small structures, in line with the view that many of the fundamental physical processes in the solar photosphere occur on scales smaller than 100 km.

Two dual-wavelength sequences of high-resolution solar photospheric images captured over several hours and restored by use of phase diversity

Mats Löfdahl, Thomas Berger & John Seldin, Astronomy & Astrophysics, 377:1128-1135, 2001

The collection, seeing compensation, and temporal filtering of two high-resolution time-sequences of solar photospheric images are described. 44"x80" image sequences of co-spatial and co-temporal 430.5 nm G band and 436.4 nm continuum filtergrams, were obtained with the 47.5 cm Swedish Vacuum Solar Telescope. One data set covers 5 hours of photospheric evolution; the other covers 8 hours. The field-of-view contains both an enhanced network region, a large pore, and in the longer sequence, a pore forming event. The mean time between frames is <40 s. With a few exceptions, the G band frames are partitioned phase-diverse speckle (PPDS) restorations of three realizations of the atmospheric turbulence acquired rapidly in sequence. Due to strict simultaneity and closely spaced wavelengths, the G band wavefronts, compensated for fixed aberration differences, could also be used for deconvolving the corresponding continuum data. For some of the data, collected during periods of particularly bad seeing, restorations made with a related method, joint phase-diverse speckle, were substituted for the PPDS restorations.

Algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths

Mats Löfdahl & Henrik Eriksson, Optical Engineering, 40(6):984-990, 2001.

Measurement of differences in optical path length in monochromatic light with any interferometric method is insensitive to errors that are whole numbers of waves. If measurements are performed in several wavelengths, this ambiguity can be resolved. We present a general algorithm for finding the correct distance post facto, given multiple measurements in different wavelengths. Applied to piston measurements of a segmented mirror, the capture range of a wavefront sensor can be extended from +/- half a wave to several waves. The extended capture range can be calculated and depends on the selection of wavelengths used for measurements and the expected accuracy of the method used.

Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity

Mats Löfdahl, Göran Scharmer and Wang Wei, Applied Optics, 39(1):94, 2000.

Calibration experiments with a bimorph mirror are presented. Phase-diversity wave-front sensing is used for measuring the control matrix, nulling wave-front errors in the optical setup, including the mirror, and measuring Strehl ratios and residual higher-order aberrations. The Strehl ratio of the calibrated system is measured to be 0.975, corresponding to 1/40 wave rms in the residual wave front. The conclusion is that a phase-diversity wave-front sensor is easier to install and use than interferometers and can replace them in optical setups for testing adaptive optics systems.

A predictor approach to closed-loop phase-diversity wavefront sensing

Mats Löfdahl & Göran Scharmer, in UV, Optical, and IR Telescopes and Instrumentation VI, Breckinridge & Jacobsen, eds., Proc. SPIE 4013:737-748, 2000

We present a novel and fast method for utilizing wavefront information in closed-loop phase-diverse image data. We form a 2-dimensional object-independent error function using the images at different focus positions together with OTFs of the diffraction limited system. Each coefficient in an expansion of the wavefront is estimated quickly and independently by calculating the inner product of a corresponding predictor function and the error function. This operation is easy to parallelize. The main computational burden is in pre-processing, when the predictors are formed. This makes this method fast and therefore attractive for closed loop operation. Calculating the predictors involves error function derivatives with respect to the wavefront parameters, statistics of the parameters, noise levels and other known characteristics of the optical system. The predictors are optimized so that the RMS error in the wavefront parameters is minimized rather than consistency between estimated quantities with image data. We present simulation results that are relevant to the phasing of segmented mirrors in a space telescope, such as the NGST.

A workstation based solar/stellar adaptive optics system

Göran Scharmer, Mark Shand, Mats Löfdahl, Peter Dettori & Wang Wei, in Adaptive Optical Systems Technology, Wizinowich, ed., Proc. SPIE 4007:239-250, 2000

The microprocessors used in off-the-shelf workstations double in performance every eighteen months. The Swedish Vacuum Solar Tower (SVST) uses off-the-shelf workstations for all aspects of its on-line telescope control and data acquisition. Since 1995 workstation performance has been adequate for a correlation tracker of solar granulation controlling a tip–tilt corrector. In 2000 workstation performance permits the construction of a 20–50 subimage Shack–Hartmann based low latency adaptive optics system. It is argued that workstations provide a cost-effective, upgradable, low-risk and flexible means of construction of stellar and solar adaptive optics systems.

We give an overview of the adaptive optics system installed at the SVST in May 1999. The system uses a bimorph modal mirror with 19 electrodes from Laplacian Optics. For use with extended targets, such as solar fine structure, cross-correlations with 16x16-pixel sub-images are used. For use with point sources, a centroiding algorithm is implemented. The work station used is capable of completing all processing required by the adaptive optics system in 0.5 ms (cross-correlations) or 0.3 ms (centroiding), with potential for significant performance improvements.

Resolving piston ambiguities when phasing a segmented mirror

Mats Löfdahl & Henrik Eriksson, in UV, Optical, and IR Telescopes and Instrumentation VI, Breckinridge & Jacobsen, eds., Proc. SPIE 4013:774-782, 2000

Wavefront sensing in monochromatic light is insensitive to segment piston errors that are a whole number of waves. If the wavefront sensing is performed in several wavelengths, this ambiguity can be resolved. We give an algorithm for finding the correct phase, given multiple measurements in different wavelengths. Using this algorithm, the capture range of a wavefront sensor can be extended from on the order of
 2 in piston to several waves. This relaxes the demands on an initial, coarse alignment method. The extended capture range depends on the selection of wavelengths available for phase measurements and the expected accuracy of the wavefront sensing method used.

Experimental results from a multiple telescope imaging array

Rick Kendrick, Ray  Bell, Larry Benson, Pete Cuneo, Alan Duncan, B. Holmes, Mats Löfdahl, Keith Mitchell, Bob Reardon, R. Sigler, R. Stone, Dave Stubbs, Vasilis Zarifis, in 1999 IEEE Aerospace Conference, 5:415, 1999

A nine telescope imaging phased array is being demonstrated at the Lockheed-Martin Advanced Technology Center in Pale Alto. The array consists of nine afocal telescopes arranged in a y-formation that are combined to a common focus in a Fizeau interferometer configuration. We have demonstrated diffraction limited performance over a 150 micro-radian field of view with broadband (500 to 800 nm) illumination

Orthogonalization of basis functions for diagonalized wavefront sensing

Mats Löfdahl, in Proc. Nineteenth Sacramento Peak Summer Workshop, High Resolution Solar Physics: Theory, Observations, and Techniques, Rimmele, Radick, & Balasubramaniam, Eds., ASP Conf. Series 183:320-329, 1999

Phase diversity problems are usually solved by gradient search techniques or by non-linear least-squares optimization methods. In the latter case, when the wavefront is expanded in Zernike polynomials, a system matrix with significant off-diagonal elements is obtained. We can approximately diagonalize the system matrix by orthogonalizing the basis functions used to expand the wavefront. Using only the diagonal of the MxM resulting matrix, reducing the need for time-consuming inner products from ~M^2 to ~M, closed loop simulations converge to the same error level as full-matrix solutions. We show results with real solar data as well as with simulations corresponding to a closed loop adaptive optics system.

The multi aperture imaging array

Vasilis Zarifis, Ray Bell, Bob Benson, Pete Cuneo, Alan Duncan, B. Herman, B. Holmes, R. Sigler, R. Stone, Dave Stubbs, Rick Kendrick, Rick Paxman, John Seldin & Mats Löfdahl, in Working on the Fringe: Optical and IR Interferometry from Ground and Space, Unwin and Stachnik, eds, ASP Conf. Series 194:278, 1999

A multi-aperture telescope imaging phased array is being demonstrated at the Lockheed Martin Advanced Technology Center in Palo Alto. The sparse array consists of nine afocal telescopes that are combined to a common focus in a Fizeau interferometer configuration. We have demonstrated diffraction limited performance over a 150 micro-radian field of view with broad band (550 to 800 nm) illumination. The relatively high bandwidth closed loop phasing is achieved using phase diversity wavefront sensing techniques. Applications using a filled array for astronomical observations will also be discussed.

Measurements of Solar Magnetic Element Dispersal

Thomas Berger, Mats Löfdahl, Richard Shine & Alan Title, Astrophysical Journal, 506:439, 1998

The dispersal of magnetic elements in the solar photospheric flow field is studied by tracking individual ``magnetic bright points'' (MBPs) identified in a G-band 4305 Å filtergram time series obtained at the 50 cm Swedish Vacuum Solar Telescope on La Palma, Spain. The time series spans approximately 70 minutes with a field of view of 29" x 29" near disk center. All images in the time series are restored to near the telescope diffraction limit (~0.2" in the G band) using partitioned phase diverse speckle techniques. Regions of enhanced magnetic network and quiet Sun are examined. In the network region, automated tracking of individual MBPs reveals approximately Gaussian diffusion, with indications for slightly ``superdiffusive'' dispersal. The inferred Gaussian diffusion coefficient is 60.4 ± 10.9 km^2/s. In the quiet-Sun region, local correlation tracking velocity measurements show the dispersal of artificial tracers to be non-Gaussian over most of our data set with indications of an asymptotic approach to a 285 km^2/s Gaussian diffusion.

Preparation of a dual wavelength sequence of high resolution solar photospheric images using phase diversity

Mats Löfdahl, Thomas Berger, Richard Shine & Alan Title, Astrophysical Journal, 495:965, 1998

The collection, seeing compensation, and temporal filtering of a high-resolution time-sequence of solar photospheric images is described. A 70 minute time series of cospatial and cotemporal G band 4305 A and wideband 4686 A filtergrams was obtained with the 50 cm Swedish Vacuum Solar Telescope on the island of La Palma, Spain. The 29" x 70" field-of-view near disk center contains both an enhanced network region and an (apparently) nonmagnetic "quiet" region of granulation. The mean time between frames is 23.5 s. Each frame is created with partitioned phase-diverse speckle restoration of three realizations of the atmospheric turbulence acquired rapidly in sequence. The result is high-resolution movies of the solar photosphere, good enough to allow detection, tracking, and analysis of ~0."2 bright points. This analysis is the subject of a companion paper.

Measurements of Solar Magnetic Element Motion from high resolution filtergrams

Thomas Berger, Mats Löfdahl, Richard Shine & Alan Title, Astrophysical Journal, 495:973, 1998

Solar photospheric flowfield properties on sub-0."5 scales are measured using local correlation tracking (LCT) and object tracking of magnetic bright points (MBPs: photospheric bright points associated with magnetic elements). The dataset is a 70 minute time series of cospatial and cotemporal G-band 4305 Å and wideband 4686 Å filtergrams obtained with the 50 cm Swedish Vacuum Solar Telescope on the island of La Palma, Spain. We examine a 29" x 70" field of view (FOV) near disk center and compare a 29" x 29" magnetic network subfield and a 27" x 27" apparently nonmagnetic "quiet-Sun" subfield. The mean time between frames is 23.75 s. Each frame is created by partitioned phase-diverse speckle restoration of three image pairs acquired rapidly in sequence. Angular resolution is ~0."4 or less in all frames of the restored data set. From LCT on a 0."4 grid with 0."83 FWHM apodization, we find the flow speeds to be Rayleigh distributed with a mode of 550 m/s and an average of 950 m/s in the network FOV; in the quiet FOV the modal speed is 700 m/s with a mean of 1100 m/s. Within the network FOV, a "magnetic region" defined by the loci of tracked MBPs exhibit even greater alteration: rms contrast of the region is 8% higher in the G band compared to areas outside, LCT speeds are reduced by a factor of 1.6, and the convective flow structures are smaller and much more chaotic. Mesogranulation is entirely absent in the magnetic region. The modal and mean speeds of 534 tracked MBPs are 300 m/s and 1470 m/s, respectively. MBPs split and merge with mean times of 320 and 404 s respectively. The mean lifetime of MBPs in the data set is 9.33 minutes although approximately 5% of the objects can be tracked for the entire 70 minute duration of the time series.

Fine structures of magnetic field in solar quiet region

Hongqi Zhang, Göran Scharmer, Mats Löfdahl & Zhang Yi,, Solar Physics, 183:283, 1998

In this paper, we present a time series of Fe I lambda 5250.2 Å photospheric filtergrams and corresponding magnetograms in a quiet region. The relationship between fine structures of granulation and magnetic fields is analyzed. It is found that although most bright filigree features in photospheric filtergrams are related to corresponding magnetic features, they are generally not cospatial. It is also found that some bright features and their corresponding photospheric magnetic fields show fast changes within several minutes.

Dynamics of magnetic flux elements in the solar photosphere

Aad van Ballegooijen, Pete Nisenson, R. Noyes, Mats Löfdahl, Robert Stein, Åke Nordlund & V. Krishnakumar, Astrophysical Journal, 509, pp. 435, 1998

The interaction of magnetic fields and convection is investigated in the context of the coronal heating problem. We study the motions of photospheric magnetic elements using a time series of high-resolution G-band and continuum filtergrams obtained at the Swedish Vacuum Solar Telescope at La Palma. The G-band images show bright points arranged in linear structures (``filigree'') located in the lanes between neighboring granule cells. We measure the motions of these bright points using an object tracking technique, and we determine the autocorrelation function describing the temporal variation of the bright point velocity. The correlation time of the velocity is about 100 s. To understand the processes that determine the spatial distribution of the bright points, we perform simulations of horizontal motions of magnetic flux elements in response to solar granulation flows. Models of the granulation flow are derived from the observed granulation intensity images using a simple two-dimensional model that includes both inertia and horizontal temperature gradients; the magnetic flux elements are assumed to be passively advected by this granulation flow. The results suggest that this passive advection model is in reasonable agreement with the observations, indicating that on a timescale of 1 hr the flux tubes are not strongly affected by their anchoring at large depth. Finally, we use potential-field modeling to extrapolate the magnetic and velocity fields to larger height. We find that the velocity in the chromosphere can be locally enhanced at the separatrix surfaces between neighboring flux tubes. The predicted velocities are several km/s, significantly larger than those of the photospheric flux tubes. The implications of these results for coronal heating are discussed.

A phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II telescope

Mats Löfdahl, Rick Kendrick, Alex Harwit, Keith Mitchell, Alan Duncan, John Seldin, Rick Paxman & Scott Acton, in Space Telescopes and Instruments V, Bely & Breckinridge, eds., Proc. SPIE 3356:1190-1201, 1998

We are developing a technique to measure segment misalignment of large telescopes based on wavefront estimation using phase-diverse (in- and out-of-focus) images. We report the current results of an experiment to measure piston errors on the Keck II primary segmented mirror, through atmospheric turbulence, using phase-diverse phase retrieval. The segment piston errors are separated from the random turbulence by averaging phase estimates from many frames. Phase estimates from real data collected with segments intentionally moved in piston reproduce the observed speckle patterns well. However, average phase maps do not reveal the segment piston errors. Simulations show that the observed data were collected in a regime of turbulence where the current algorithm often fails, but would be expected to work very well when the adaptive optics system is operating. There is reason to believe that we can eventually make the algorithm work with these or similar data if apparent mismatches between the data and our current imaging model are removed.

Fast phase diversity wavefront sensing for mirror control

Mats Löfdahl, Alan Duncan & Göran Scharmer, in Adaptive Optical System Technologies, Bonnaccini & Tyson, eds., in Proc. SPIE 3353:952-963, 1998

We show with simulation experiments that closed-loop phase-diversity can be used without numerical guard-bands for wavefront sensing of low-order wavefronts from extended objects using broad-band filters. This may allow real- time correction at high bandwidth for certain applications. We also present a proper maximum likelihood treatment of Shack–Hartman data, which includes an imaging model to extract curvature information from the lenslet images. We demonstrate by simple simulations that this approach should allow higher-order wavefront information to be extracted than with with traditional Shack–Hartmann wavefront sensing for a given number of lenslets.

Evaluation of phase-diversity techniques for solar-image restoration

Rick Paxman, John Seldin, Mats Löfdahl, Göran Scharmer & Christoph Keller, Astrophysical Journal, 466:1087-1099, 1996

Phase-diversity techniques provide a novel observational method for overcoming the effects of turbulence and instrument-induced aberrations in ground-based astronomy. Two implementations of phase-diversity techniques that differ with regard to noise model, estimator, optimization algorithm, method of regularization, and treatment of edge effects are described. Reconstructions of solar granulation derived by applying these two implementations to common data sets are shown to yield nearly identical images. For both implementations, reconstructions from phase-diverse speckle data (involving multiple realizations of turbulence) are shown to be superior to those derived from conventional phase-diversity data (involving a single realization). Phase-diverse speckle reconstructions are shown to achieve near diffraction-limited resolution and are validated by internal and external consistency tests, including a comparison with a reconstruction using a well-accepted speckle-imaging method.

Phase diversity wavefront sensing and image restoration applied to high-resolution solar observations

Mats Löfdahl, PhD thesis, Stockholm University, 1996.

An implementation of a phase-diverse speckle imaging (PDS) technique for reducing the effects of aberrations in solar images is described. Such aberrations usually occur in the Earth's atmosphere and in telescopes. PDS is a post-processing technique for measuring such aberrations and for deblurring the images.

The code has been extensively tested. Realistic simulations indicate that the systematic errors are small. The wavefront and object estimates calculated from real solar data, collected with the Swedish Vacuum Solar Telescope (SVST), are spatially and temporally consistent with expectations for anisoplanatism and the assumption of no evolution of the solar features on the time scale of a few seconds. Implementation invariance is demonstrated by comparison of the output with that of a separately developed implementation. External reference for the wavefront determination is provided by comparison with theoretical predictions of temporal variation of the telescopic aberrations at the SVST. High-quality image restorations can be made with much less data than is needed by the more established method of speckle interferometry.

The usefulness of the technique for astronomical purposes is demonstrated by the successful restoration and analysis of a 29"x29" 70-minute time sequence of solar granulation and bright points. The resolution in the restored data is sufficient to allow the evolution and motion of bright points to be followed in detail.

En störande atmosfär

Mats Löfdahl, Akademiska Gobitar (1):29-31, 1996

Application of phase-diversity to solar images

Mats Löfdahl & Göran Scharmer, invited paper, in Image reconstruction and restoration, Schultz and Snyder, eds., Proc. SPIE 2302:254-267, 1994

We have implemented a least-squares technique for recovering phase information and alignment parameters from simultaneously obtained focused and defocused solar images. Small subfields are used, in order to deal with anisoplanatism. The method is applied to sequences of 100 8-bit solar granulation images. These data enable a number of consistency tests, all of which demonstrate that the technique works.

Alignment parameters derived from averaged images in a sequence are highly consistent and wavefronts derived from different subfields and different sequences recorded close in time are virtually identical. The wavefronts derived from averaged images are also virtually identical to the average of wavefronts derived from individual images. These aberrations vary with time in a way which is consistent with a major contribution from the moving elements of the alt-az tower telescope.

Independently derived wavefronts from single images show high correlation between neighbouring subfields and smooth variations across large fields-of-view, consistent with the impression that the image quality is more or less uniform across the image. Restored images in a sequence show a high degree of consistency and much more fine structure than the corresponding observed images.

Wavefront sensing and image restoration from focused and defocused solar images

Mats Löfdahl & Göran Scharmer, Astronomy & Astrophysics Supplement Series, 107:243-264, 1994

We have implemented a least-squares technique for recovering phase information from simultaneously recorded focused and defocused images. The inversions are made from small subfields in order to deal with anisoplanatic image formation, such as occurring through the Earth's atmosphere. Parameters corresponding to the alignment of the focused-defocused images are determined simultaneously with aberration parameters. Simulations show that the method can recover wavefronts of up to 1/2 wave rms and that 15-21 Zernike coefficients can be obtained from 3"x3"-5"x5" solar granulation images using a 50 cm telescope and with noise levels of 0.4% of the average intensity. In general, the accuracy of the restored images is better than expected from the number of Zernike polynomials used to represent the wave front. We have applied the method to sequences of 100 8-bit solar granulation images obtained with the Swedish Vacuum Solar Telescope (SVST) in La Palma using subfields of 3"x3"-5"x5". These data enable a number of consistency tests, all of which demonstrate that the technique works on real data. Using averaged images obtained from each sequence we find that derived alignment parameters are consistent to within 0.02" and that wavefronts derived from different subfields and different sequences recorded close in time are virtually identical. The wavefronts derived from averaged images are also virtually identical to the average of wavefronts derived from individual images. These measurements of telescope aberrations suggest that astigmatism and coma are the major aberrations. These aberrations vary with time in a way which is consistent with a major contribution from the telescope objective and/or the first folding mirror of the alt-az tower telescope. Wavefronts derived from individual images show 50-90% correlation between Zernike coefficients 4-14 derived from nearby but independent subfields. Mosaics of 13 x 11 independently derived wavefronts from single images show smooth variations across a 12"x10" field-of-view. These results are consistent with the impression that degradation of image quality is more or less uniform across the image. Restored images in a sequence show a high degree of consistency and much more fine structure than the corresponding observed images, but occasional fringe-like artifacts can be seen. Using the results of two inversions to restore the scene removes such artifacts. We conclude that this technique provides adequate wavefront information on telescopic and atmospheric wavefront aberrations and substantial improvements in image quality. The ease of implementation as well as its tolerance to experimental errors and low cost makes it an excellent complement to or even substitute for adaptive optics for many applications. The technique is particularly well-suited for solar telescopes, where wavefront sensing over a large field-of-view is important.

Phase-diversity restoration of solar images

M.G. Löfdahl and G.B. Schamer, in Proc. Thirteenth Sacramento Peak Summer Workshop, Real Time and Post Facto Solar Image Correction, Radick, Ed., pp. 89-104, 1993

We have implemented a least-squares linearization technique for recovering phase information from simultaneously recorded focused and defocused solar images. The inversion is made from small subfields, in order to deal with anisoplanatic image formation, such as occuring through the earth's atmosphere.

Simulations show that the method can recover wavefronts of approximately 1/4 wave rms and that noise levels corresponding to 8-bit images allow better reconstruction of the images than of the derived wavefronts. We find that cross-correlation techniques cannot be used to align the focused and defocused images because of cross-talk with coma and similar asymmetric aberrations. Therefore we simultaneously determine alignment and aberration parameters.

We have applied the method to 8-bit solar granulation images obtained with the Swedish Vacuum Solar Telescope in La Palma using subfields of 3".1x3".1. The least-squares fits indicate wavefronts of approximately 0.12--0.16 waves rms. Derived alignment parameters from different subfields and different images are consistent, indicating that the wavefront is well determined by the data. Wavefronts derived from different sub fields of a single image in general show similar aberrations whereas derived wavefronts from different images only show occasional similarities, indicating a significant wavefront aberration from the lower atmosphere. The reconstructed granulation images show enhanced fine structure and an increase of the rms contrast by ~2% as compared to the observed focused image, but the rms contrasts of consequtive images indicate small errors in the derived rms wavefronts.

The ROYACS user library

Mats Löfdahl, in Proc. LEST Mini-Workshop, Software for Solar Image Processing, Yi, Darvann & Molowny Horas, Eds., 1992

The main purpose with the ROYACS User Library is to provide ANA users at the Stockholm Observatory with suitable subprograms for data reduction of solar images. Other useful routines have also been included in order to improve the programming environment.

Swedish solar telescope: Short summary of instrumentation and observation techniques

Göran Scharmer & Mats Löfdahl, Advances in Space Research: Opening Frontiers in Solar Research, 11(5):129-132, 1991

A short summary of the design concepts of the Swedish Solar Telescope at La Palma is given along with the most important parts of the instrumentation and observing techniques. The experience from using high-speed read-out CCDs for solar observations is also discussed. The advantages of this data acquisition system are that it allows real-time frame selection for achieving high spatial resolution, that several cameras can be slaved by one seeing monitor, and that bursts of digital images can be recorded for full spatial coverage of small parts of active regions.

Diffuse reflection from rough surfaces

Mats Löfdahl, MSc thesis, Royal Institute of Technology, Stockholm, Sweden, 1989

A computer model is developed for the examination of electromagnetic wave scattering from rough surfaces. Conditions that would allow refraction and diffraction of the incident light are avoided, which makes the model limited to representing diffuse reflection from opaque surfaces. A ray tracing algorithm, that is designed to cover multiple reflections, calculates the reflection points of a set of rays that illuminate a bicubic interpolation surface. Jones matrix algebra is adapted to the treatment of multiple reflections and used to compute the intensity and polarization distribution of the reflected radiation. The procedures are coded in Pascal and demonstrated with a set of test surfaces and illumination angles. The results of the test executions are presented and compared with experimental measurements. Possible improvements in the model and of the programs are discussed and, finally, further examinations are suggested.