Astron. Astrophys. 323, 599–605 (1997) ASTRONOMYAND

ASTROPHYSICS

Two-dimensional speckle spectroscopyof the moustache phenomenon on the SunC. Denker

Universitats-Sternwarte, Geismarlandstr. 11, D-37083 Gottingen, Germanypresent address: Big Bear Solar Observatory, California Institute of Technology, Pasadena, CA 91125, USA

Received 27 August 1996 / Accepted 9 January 1997

Abstract. This paper deals with a detailed morphological andphotometric investigation of solar small-scale features in thevicinity of an irregular sunspot group. The observations wereperformed with the Vacuum Tower Telescope at the Observato-rio del Teide/Tenerife on May 18, 1994. The speckle maskingmethod has been applied to reconstruct almost diffraction lim-ited filtergrams in two different wavelength regions. For thispurpose, we used the two-dimensional spectrometer of the Uni-versitats-Sternwarte Gottingen which was slightly modified forthe speckle observations. In the narrow-band filtergrams, westudied the intensity enhancement in the inner wings of thestrong chromospheric absorption line Na D2 (moustache phe-nomenon). The corresponding filtergrams in the white-lightchannel show a clear correlation of photospheric filigree and themoustache phenomenon. The bandwidth of the small-passbandchannel amounts to 0.014 nm. This is the highest spectral reso-lution reached with speckle masking imaging so far.

Key words: Sun: activity – granulation – sunspots – methodsobservational – techniques: interferometric

1. Introduction

The Sun is an ideal star to investigate exemplarily the surface ofmain sequence stars. Due to its proximity, we can resolve finestructures with sizes of about 100 km which corresponds ap-proximately to the density scale height. A variety of small-scalephenomena are related to active regions (Bray & Laughhead1974). Investigating filtergrams taken in the wings of strong ab-sorption lines, bright points appear in the vicinity of large com-plex sunspot groups and at the outer border of sunspot penum-brae. A brief review of this so called moustache phenomenon, itsspectral characteristics, appearance, temporal evolution, and itsrelation to magnetic fields is given by Denker et al. (1995a). Thebehaviour of the moustache phenomenon may be of relevancefor numerical simulations dealing with the dynamic interaction

of granular flows and small-scale magnetic fields as presentedby Steiner et al. (1994).

To extract as much information as possible from the Sunlight, we have to use modern solar telescopes, complex post-focus instruments, and refined methods of data reduction andanalysis. The two-dimensional spectrometer in the VacuumTower Telescope (VTT) at the Observatorio del Teide/Tenerife(Bendlin et al. 1992, Bendlin 1993, Bendlin & Volkmer 1995,Volkmer 1995) in combination with speckle interferometry (deBoer 1993, Denker et al. 1995a, 1995b, Denker 1996) presentsa powerful tool to obtain high spatial, spectral, and temporalresolution observations of solar fine structures. Speckle de-convolution techniques have previously been applied to two-dimensional polarimetric measurements (Keller & von der Luhe1992) and to spectrograms of a rapid scanning spectrograph(Keller & Johannesson 1995).

Besides speckle interferometric techniques, a number ofpost-processing methods have been developed and applied tosolar phenomena. The phase diversity technique tries to findthe best estimate of a real astronomical object from seeing dis-torted images. This technique has been proposed by Gonsalves& Childlaw (1979). Hogbohm (1989) showed independently thepossibility of restoring a seeing distorted object from simulta-neously recorded images around the telescope’s focal volume.The method of Gonsalves & Childlaw was extended by Paxmanet al. (1992) who used several diversity channels and realiza-tions of the turbulent atmosphere of the Earth. They called theirmethod phase-diverse speckle imaging indicating that it com-bines features of speckle interferometry and phase diversity.Phase diversity methods provide nowadays excellent imagesof solar small-scale phenomena (Lofdahl & Scharmer 1994,Berger et al. 1996, Paxman et al. 1996) and give new access tohigh resolution observations.

2. Observations

The investigation aims at a better comprehension of photo-spheric and chromospheric fine structures in active regions.Therefore, a part of a sunspot group (NOAA 7722, Mt. Wil-son No. 28103) was observed near the disc center of the Sun

600 C. Denker: Two-dimensional speckle spectroscopy of the moustache phenomenon on the Sun

2

SUN

PF

FS

CCD

L L BS IF GB2

1

NFIF

L FPI

II

CCD

ML1 3 4

Fig. 1. Experimental set-up of the modified two-dimensional spectrometer used for speckle imaging. FS: rectangular field stop, PF: primaryfocus, L1 – L4: achromatic lenses, BS: beam splitter, IF: interference filter, GB: glass bloc, FPI: Fabry-Perot-Interferometer, M: mirror, NF:neutral density filter, II: image intensifier, CCD1 and CCD2: slow-scan CCD cameras.

(cos θ = 0.99) in different spectral regions. Time series of white-light filtergrams were taken at λ = 550 ± 5 nm. In order tostudy the intensity enhancement in the inner line wings (mous-tache phenomenon) of strong chromospheric absorption lines,we took strictly simultaneous filtergrams in a small-passbandchannel at λ = 589.1±0.007 nm, 0.08 nm off the line centre ofNa D2. The observations have been performed with the VTT onMay 18, 1994 from 8:05 to 9:09 UT. The time series consists of32 burst with 142 short exposure (4 ms) images. Consecutiveframes were separated by 240 ms in time. The interval betweenone burst upon another was approximately 2 min. The entrancepupil of the VTT has a diameter of 70 cm. The correspondingdiffraction limited resolution amounts to 0.16′′ at 550 nm. Thefiltergrams were recorded on two 384 × 286 pixel slow-scanCCD cameras as 12-bit digital images. The corresponding spa-tial field of view amounts to 38.4′′ × 28.6′′ resulting in a slightundersampling with 0.1′′ per pixel.

The speckle imaging was performed with the optical set-upof the modified two-dimensional spectrometer as schematicallydepicted in Fig. 1 (a description of the original set-up is given byBendlin & Volkmer 1995). A rectangular field stop (FS) at theprimary focus (PF) reduces the scattered light in the followingoptical elements. The achromatic lenses L1 and L2 transfer thesolar image from the PF to the optical laboratory without chang-ing the image scale. A beamsplitter (BS) was inserted into thelight path to feed the slow-scan CCD camera (CCD1) with 5%of the light. These white-light images were observed through aneutral density and an interference filter (λ = 550±5 nm). Thefirst modification concerns the filter combination used to restrictthe wavelength region of the small-passband channel. The fil-ter combination used for speckle imaging consists only of aninterference filter (λ = 589±0.16 nm) and a Fabry-Perot inter-ferometer (FPI). The FWHM of the FPI amounts to 0.014 nm,and its free spectral range is about 0.7 nm. The Universal Bire-fringent Filter (UBF) used in the original experimental set-upwas replaced by a suitable block of glass (GB) simulating theoptical path length of the UBF. The second modification refersto the second pair of achromatic transfer lenses (L3 and L4).Since the original image scale of 0.2′′ per pixel is not conve-nient for speckle imaging, we chose another achromatic lens L4

so that the image scale remains at 0.1′′ per pixel. This results in

a longer focal length for L4 and requires folding the light pathbecause of the limited space in the optical laboratory.

In the scanning mode, the software control program for thespectrometer offers an option to stabilize automatically the line-core position of a spectral line (cf. Bendlin & Volkmer 1995).This option could not be applied to our speckle observations atone fixed wavelength position. Therefore, the wavelength driftof the FPI’s passband has to be corrected manually every 3 or 5bursts introducing short delays ≈ 20 s into the time series.

3. Data reduction

This section contains a short summary of the different steps ofdata reduction and image processing by means of speckle in-terferometry (a more detailed description is given e.g. by deBoer 1993, Denker et al. 1995a, Denker 1996). The first stepsof the data processing concern the subtraction of the averagedark image and the the correction by means of the flat field im-age. Intensities of pixels that strongly deviate from their neigh-bourhood are replaced by the median of adjacent pixels. Wenormalized the corrected images so that the mean value of theintensity for a region with granulation is unity. Yet I remindyou that the specklegrams of the small-passband channel weretaken in the red line wing of Na D2, i.e. they are not continuumimages. Furthermore, the image motion was removed in a crosscorrelation analysis and the aligned images were divided intopartially overlapping subfields with a size of 64 × 64 pixels.This area of 6.4′′ × 6.4′′ corresponds from our experience ap-proximately to the size of the isoplanatic patches at the site. Todetermine the atmospheric point-spread function, we derivedthe Fried parameter r0 by applying the spectral ratio technique(von der Luhe 1984) to the bursts of white-light images. Wecompared the observed spectral ratios with theoretical valuesderived from Korff’s (1973) model of the speckle transfer func-tion and Fried’s (1966) model of the average short-exposuremodulation transfer function. The classical method of Labeyrie(1970) was used to get the corrected amplitudes of the object’sFourier transform. Modulus and phase of the object’s Fouriertransform were derived with the speckle masking or triple cor-relation technique (Weigelt 1977, Weigelt & Wirnitzer 1983,Lohmann et al. 1983). Furthermore, a special noise filter for

C. Denker: Two-dimensional speckle spectroscopy of the moustache phenomenon on the Sun 601

Fig. 2a–d. Improvements of image quality attainable with the speckle masking method (Burst No. 29): a best single exposure with the highestcontrast of the white-light burst b corresponding speckle reconstruction c best single exposure with the highest contrast of the small-passbandchannel (Na D2 + 0.08 nm) and d corresponding speckle reconstruction. The frames are scaled individually; brightness and contrast are thus notcomparable. The tickmarks have a separation of 2′′.

high wavenumbers (de Boer 1993, 1996) was applied. Back-transformation into object space and accurate alignment of thereconstructed subfields yield high spatial resolution images ofoutstanding quality. The treatment of the white-light and narrowpassband filtergrams in the data reduction and image processingwas the same, but in both cases the atmospheric point-spreadfunction derived from the white-light burst has been used be-cause it is more reliable due to the lower noise level and highercontents of solar fine structures in the white-light images.

The average counts of the flat field image in the small-passband channel amounts to 1200. The flat field frames werederived from a quiet Sun area near the disc centre with a defo-cussed telescope. Halving this count rate yields still well-definedspeckle reconstructions. Prolonging the exposure time to 10 msgains 2.5 times more photons at the detector. Keeping these num-bers in mind, it should be possible in the future that adequatehigh-transmission optics (a second Fabry-Perot interferometer)will enable us to shrink the bandwidth of the two-dimensionalspectrometer in the speckle mode to approximately 3 pm.

4. Results

The best single exposures and speckle reconstructions of thewhite-light and small-passband specklegrams (Burst No. 29)are depicted in Fig. 2. The measured Fried-parameter used toreconstruct these images was r0 = 11.7 cm. The average Fried-parameter r0 = 9.8 ± 1.3 cm in the time-series demonstratesthe excellent seeing conditions at the Observatorio del Teide.Fig. 2 illustrates the improvements of image quality attainablewith speckle interferometric techniques. The quality of the bestsingle exposure is comparable to frame selection techniques (cf.Scharmer 1989). The visual improvements of image quality inthe speckle reconstructions are well related to the more quantita-

tive values of the rms-contrast, mean or peak feature intensitiesas well as image gradients. Small-scale features become moreconspicuous, and faint details hardly perceptible in the singleexposures are clearly discernible after the reconstruction proce-dure.

The first white-light and small-passband speckle reconstruc-tions of the time series have been chosen for a detailed investi-gation of the photometric characteristics of bright points. In thereconstructed white-light image, two pores at the lower rightpart of Fig. 3 are located close to the outer parts of an irreg-ular sunspot group. The pores are separated by two ropes ofelongated granules which are disconnected by a conspicuousintergranular lane. The contrast of the granulation was com-puted for a square area of 12′′× 12′′ extension in the lower leftcorner of Fig. 3. The raw rms-contrast Crms of the granular areain this white-light reconstruction amounts to 11.6%. The rawrms-contrast CNa D2 for the same area but in the small-passbandreconstruction was 9.1%. In Fig. 3b two rectangular areas aresurrounded by white outline. In these areas the intensity en-hancement in the inner line wings of strong chromospheric ab-sorption line (moustache phenomenon) is clearly discernible.Considering the corresponding locations in the granular pattern(Fig. 3a), it is obvious that a clear correlation exists betweenmoustaches and photospheric crinkles or filigree. The crinklesoften show a ring-like formation (de Boer & Kneer 1992), andtheir extensions are close to the telescopic diffraction limit of0.16′′.

In the white-light as well as in the small-passband recon-structions, penumbral filaments possess small-scale brighten-ings at the border of the penumbra and umbra (arrows A-Dresp. A′-D′ in Fig. 3). Following penumbral grains on their waytowards the umbra, time series show in some cases that the in-

602 C. Denker: Two-dimensional speckle spectroscopy of the moustache phenomenon on the Sun

Fig. 3a and b. Speckle reconstructions of Burst No. 1: a white-light channel and b small-passband channel (Na D2 + 0.08 nm). The tickmarkshave a separation of 2′′.

tensity of these small-scale features is rapidly increasing (cf.Sobotka et al. 1995). The photometric characteristics of thesebright points are summarized in Table 1. Ip describes the peakintensity of the bright feature. Ib is the mean background inten-sity. It is the average of the three neighbouring local intensityminima. Generally, it is a quite difficult procedure to identify allpixels belonging to a certain bright feature in an objective way.For this purpose, a smoothed background image was computedat the first place. The width of the square smoothing-windowwas 1′′. The second step is to establish an intensity limit that thepixel belonging to the feature should exceed with respect to thebackground image. This limit was chosen to half the intensitydifference of the peak intensity and the corresponding back-ground intensity. In this way, the mean feature intensity If andits standard deviation as well as the feature area af were char-acterized. Assuming that the brightenings are circular in shape,df denotes an equivalent diameter corresponding to af . The in-tensity values for the bright points A-D in Fig. 3a represent thefinal stage of their approach towards the umbra, i.e. when theirintensity reaches its maximum. The measured peak/background

ratio corresponds to the values for bright penumbral grains andfaint light bridges Ip/Ib = 1.99± 0.46 given by Sobotka et al.(1993). But the peak intensities given by Sobotka et al. reach notmore than 0.96 at maximum. In contrast to their measurements,we observe peak intensities up to approximately 1.5. In the in-vestigation of Sobotka et al., the equivalent diameter of brightfeatures amounts to df = 0.47′′ ± 0.11′′ which agrees withthe diameters given in Table 1. The photometric characteristicsfrom brightenings associated with moustaches (arrows α-ζ inFig. 3b) differ from bright penumbral grains (cf. Table 1). Thepeak intensities and the geometric extension of moustaches areobviously larger.

The so-called Local Correlation Tracking (LCT) Technique(November & Simon 1988, Molowny-Horas 1994a, 1994b,Molowny-Horas & Yi 1994) has been applied to a time series ofspeckle reconstructions. The horizontal proper motions of con-trast features in and around the outer parts of a sunspot have beenderived from the first 25 bursts of the time series, i.e. the dura-tion of this part of the time series was approximately 50 min.The flow vectors of this computation are depicted in Fig. 4 which

C. Denker: Two-dimensional speckle spectroscopy of the moustache phenomenon on the Sun 603

Table 1. Photometric characteristics of bright points

Ib If Ip Ip/Ib af df[arcsec2] [arcsec]

A 0.57 1.28±0.10 1.44 2.51 0.18 0.48B 0.80 1.34±0.09 1.48 1.85 0.18 0.48C 0.60 1.42±0.07 1.52 2.54 0.17 0.47D 0.70 1.40±0.11 1.57 2.25 0.23 0.54

A′ 0.60 1.10±0.05 1.20 2.00 0.26 0.58B′ 0.60 1.11±0.05 1.21 2.03 0.26 0.58C′ 0.55 1.14±0.08 1.28 2.34 0.42 0.73D′ 0.57 1.29±0.11 1.49 2.60 0.41 0.72

α 0.98 1.34±0.06 1.46 1.50 0.96 1.11β 0.88 1.33±0.07 1.44 1.63 1.11 1.19γ 0.94 1.35±0.06 1.49 1.58 1.45 1.36δ 0.89 1.32±0.06 1.43 1.61 0.44 0.75ε 0.88 1.34±0.06 1.47 1.68 0.45 0.76ζ 0.99 1.31±0.07 1.44 1.45 1.27 1.27

shows an averaged velocity map with a Gaussian sampling win-dow of FWHM = 1.5′′. The time interval separating consecutiveframes was 120 s. Reducing the width of the sampling windowresults in noisy maps of the velocity field, i.e. the LCT-routineswere restricted to track on contrast features with extensions ofapproximately the cell-size of the granulation. The mean veloc-ity of the granular area was vgran = 0.62±0.60 km/s with a maxi-mum value of vmax

gran = 4.4 km/s. The average velocity for the areacovered by the outlying parts of the sunspot and the two poreswas vspot = 0.27±0.16 km/s. The velocity reaches its maximumat vmax

spot = 1.0 km/s. These results are in good agreement withthe values published by Molowny-Horas (1994b). The large ve-locity vectors in the lower left corner of Fig. 4 originate from alarge exploding granule. Examination of the time series showsthat penumbral grains and elongated bright features are mov-ing from the upper left corner along the rudimentary penumbralfilaments. Their motion follows the extension of the sunspot inthe x-direction (see Fig. 4 at y-coordinate 20′′). Below this partof the figure, granules are pushed along the sunspot boundaryresulting in a horizontal shearing flow.

5. Discussion

The fact that moustaches are not restricted to Hα has been dis-cussed by Stellmacher & Wiehr (1991). Their results indicatethat moustaches are closely related to the magnetic field. It isvery suggestive that the magnetic field topology around a com-plex sunspot group causes the small-scale brightenings of themoustaches. Rust (1968) pointed out that they originate due toreconnection at the location of neutral points in the magneticfields. However, Kitai & Muller (1984) considered the heatingof elementary flux tubes as their origin. Furthermore, from in-specting the images depicted in Fig. 3 and their photometric in-vestigation it becomes clear that the moustache phenomenonis well-related to photospheric filigree. The peak intensities

Fig. 4. Large-scale velocity field superposed on a speckle reconstruc-tion of a sunspot (Burst No. 11).

of moustaches are close to the value where these small-scalebrightenings become emission features (cf. Denker et al. 1995a).Their equivalent diameter resp. the feature area increase withthe height of the atmospheric layers (cf. Table 1) if one assumesthat the wings of Na D2 were formed at the lower chromosphere.The funnel-like geometrical shape of moustaches, diverging up-ward from the photosphere to the lower chromosphere, was firstreported by Wilson (1981). From numerical simulations of thedynamic interaction of granular flows and small-scale magneticbrightenings, Steiner et al. (1994) have shown that flux sheetsare brighter than the average intensity of an area of the quiet Sunby a factor of 1.25. Their magnetic elements possess diametersof approximately 400 km and penetrate atmospheric layers upto 400 km above τ5000 = 1. In summary, the present findings arein good agreement with the statistical investigation of facularpoints, filigree, calcium bright points, and moustaches of Kitai& Muller (1984).

604 C. Denker: Two-dimensional speckle spectroscopy of the moustache phenomenon on the Sun

The motion of penumbral grains towards the umbra could beexplained by numerical simulations of flux tubes in the ‘thin fluxtube approximation’ (Schlichenmaier et al. 1996) embedded ina background described by the global magneto-static sunspotmodel of Jahn & Schmidt (1994). In Schlichenmaier’s model,the flux tube moves inwards and rises upwards resulting in anupflow in the subphotospheric layers. The flux tube is forcedto bend extending horizontally approximately 100 km abovethe photosphere at τ5000 = 1, and the upflow continues all theway to the canopy. Schlichenmaier derived typical velocitiesbetween 1 and 10 km/s for the outward flow reproducing theobserved phenomena of the Evershed effect. The motion of thepenumbral grains is caused by the intersection of the flux tubewith the layer at τ5000 = 1 moving inwards towards the umbra.The intersection point appears bright due to the persistent upflowof material which is hotter than the surroundings.

The high transmission optics of the two-dimensional spec-trometer allow us to reconstruct directly the images of the small-passband channel. This has advantages compared with speckledeconvolution techniques by Keller & von der Luhe (1992) andKeller & Johannesson (1995) since the individual point-spreadfunctions to deconvolve the small-passband images were de-rived from the average point-spread function of the white-lightresp. slit-jaw images so that errors due to the additional decon-volution will grow further.

The number of photons per resolution element, per wave-length, and time interval is constant, i.e. for short exposuresand narrow passbands photon noise becomes more dominant asone can see by comparing Fig. 2a with Fig. 2c. One advantageof the speckle masking method is the increased signal-to-noiseratio and reliability due to the high redundancy of the phaseinformation. Phase diversity methods have been applied only towhite-light images at the moment, and it is not clear how theycope with the limitations of photon noise. But photon noise is aserious problem for speckle interferometric methods, too (vonder Luhe 1994). The compensation of the photon bias in triplecorrelation imaging of stellar clusters has been discussed byPehlemann et al. (1992). The application of similar methods tosolar observations is of great importance for two-dimensionalsolar spectroscopy. The photometric error of the present ob-servations depends on different sources: speckle noise, photonnoise, the correction for the speckle transfer function, and aslight uncertainty due to a blend of the Na D2 line. The mostserious source of error is the dependence of the speckle trans-fer function on theoretical models. Phase diversity methods,however, do not rely on a priori assumptions concerning thebehaviour of the Earth’s atmosphere. Empirical speckle trans-fer function measurements from partial eclipse observations ofthe Sun (de Boer 1995) indicate that the spectral ratio method(von der Luhe 1984) overestimates the Fried parameter. In thepresent observations, the contrast and peak intensities of solarsmall-scale features derived with the theoretical models of Korff(1973) and Fried (1966) were estimated in a conservative way,i.e. they represents lower limits. The resulting photometric er-ror from the sources mentioned above is from our experience

(Denker et al. 1995a) smaller than 5% of the granular back-ground intensity.

6. Conclusions

In continuation of our previous investigations concerning themoustache phenomenon (Denker et al. 1995a, 1995b), this pa-per summarizes the first attempts to combine the abilities ofspeckle interferometry and two-dimensional spectroscopy. Itwas shown that high spatial and spectral resolution images couldbeen routinely obtained. Further improvements concerning thehigh-transmission optics will enable us to increase the spectralresolution by a factor of 4-5 without any loss of spatial infor-mation so that speckle spectroscopy in the scanning mode ofthe two-dimensional spectrometer becomes possible in the nearfuture.

Furthermore, from the photometric investigation of small-scale features located at the outer parts of a complex sunspotgroup it becomes clear that the moustache phenomenon is wellrelated to photospheric filigree. Both phenomena are of the samephysical origin, but they appear at different layers of the solaratmosphere. The present results confirm the statistical analysisof facular points, filigree, calcium bright points, and moustachesperformed by Kitai & Muller (1984).

Acknowledgements. I am very indebted to Dr. F. Kneer for fruitfuldiscussions and helpful comments. I am grateful to Dr. C.R. de Boerfor his assistance with these observations and for providing me with hisspeckle code. The provision of the Local Correlation Tracking routinesby Drs. R. Molowny-Horas and Z. Yi is gratefully acknowledged aswell. Part of this work was supported by the Deutsche Forschungs-gemeinschaft through grant Kn 152/12-1 and -2. The Vacuum TowerTelescope on Tenerife is operated by the Kiepenheuer-Institut fur Son-nenphysik in Freiburg at the Spanish Observatorio del Teide of theInstituto de Astrofısica de Canarias.

References

Bendlin C., 1993, Hochauflosende zweidimensionale Spektroskopieder solaren Granulation mit einem Fabry-Perot-Interferometer,PhD-Thesis, Gottingen

Bendlin C., Volkmer R., 1995, A&ASS 112, 371Bendlin C., Volkmer R., Kneer F., 1992, A&A 257, 817Berger T., Lofdahl M.G., Title A.M., Shine R.S., 1996, ApJ in pressBray R.J., Loughhead R.E., 1974, The Solar Chromosphere, Chapman

and Hall, London, 227de Boer C.R., 1996, A&ASS 120, 195de Boer C.R., 1995, A&ASS 114, 387de Boer C.R., 1993, Speckle-Interferometrie und ihre Anwendungen

auf die Sonnenbeobachtung, PhD-Thesis, Gottingende Boer C.R., Kneer F., 1992, A&A 264, L24de Boer C.R., Kneer F., Nesis A., 1992, A&A 257, L4Denker C., de Boer C.R., Volkmer R., Kneer F., 1995a, A&A 296, 567Denker C., de Boer C.R., Kneer F., 1995b, Speckle Masking Imaging

of Bright Points (Moustaches), in: Poster Proc. IAU Symp. No. 176on Stellar Surface Structure, ed. K.G. Strassmeier, Vienna, 51

Denker C., 1996, Untersuchung der Feinstruktur von Sonnenfleckenmit Methoden der Speckle-Interferometrie, PhD-Thesis, Gottingen

Fried D.L., 1966, J. Opt. Soc. Am. 56, 1372

C. Denker: Two-dimensional speckle spectroscopy of the moustache phenomenon on the Sun 605

Gonsalves R.A., Childlaw R., 1979, Wavefront Sensing by Phase Re-trieval, in: Teschner A.G. (ed.), Applications of Digital Image Pro-cessing III, Proc. SPIE, 32

Hogbohm J.A., 1989, Reconstruction from Focal Volume Information,in: Rutten R.J., Severino G. (eds.), Solar and Stellar Granulation,Kluwer Academic Publishers, 61

Jahn K., Schmidt H.U., 1994: A&A 290, 295Keller C.U., Johannesson A., 1995, A&ASS 110, 565Keller C.U., von der Luhe, O., 1992, A&A 261, 321Kitai R., Muller R., 1984, Sol. Phys. 90, 303Korff D., 1973, J. Opt. Soc. Am. 63, 971Labeyrie A., 1970, A&A 6, 85Lofdahl M.G., Scharmer G.B., 1994, A&ASS 107, 243Lohmann A.W., Weigelt G.P., Wirnitzer B., 1983, Appl. Opt. 22, 4028Molowny-Horas R., 1994a, Dynamics and structure of the solar chro-

mosphere, PhD-Thesis, OsloMolowny-Horas R., 1994b, Sol. Phys. 154, 29Molowny-Horas R., Yi Z. 1994, Oslo IDL Software for Image pro-

cessing and Data Analysis, Univ. Oslo, Inst. Theor. Astro., InternalRep. No. 31

November L.J., Simon G.W., 1988, ApJ 333, 427Paxman R.G., Schulz T.J., Fienup J.R., 1992, J. Opt. Soc. Am. A9,

1072Paxman R.G., Seldin R.H., Lofdahl M.G., Scharmer G.B., Keller C.U.,

1996, ApJ 466, 1087

Pehlemann E., Hofmann K.H., Weigelt G., 1992, A&A 256, 701Rust D.M., 1968, in: Kiepenheuer K.O. (ed.), Structure and Develop-

ment of Solar Active Regions, IAU Symp. 35, 77Scharmer G.B., 1989, High Resolution Granular Observations from La

Palma: Techniques and first Results, in: Rutten R.J., Severino G.(eds.), Solar and Stellar Granulation, Kluwer Academic Publishers,161

Schlichenmaier R., Jahn K., Schmidt H.V., 1996: Dynamics of a Mag-netic Flux Tube in the Penumbra, in: Astron. Ges. Abstr. Ser.No. 12, Tubingen, 90

Sobotka M., Bonet J.A., Vasquez M., 1993, ApJ 415, 832Sobotka M., Bonet J.A., Vasquez M., Hanslmeier A., 1995, ApJ 447,

L133Steiner O., Knolker M., Sch”ussler M., 1994: Dynamic Interaction of

Convection with Magnetic Flux Sheets. First Results. in: RuttenR.J., Schrijver C.J. (eds.), Solar Surface Magnetism, Kluwer Acad.Publ. Dordrecht, 441

Stellmacher G., Wiehr E., 1991, A&A 251, 675Volkmer R., 1995, Hochauflosende zweidimensionale Spektro-

Polarimetrie solarer Magnetfelder, PhD-Thesis, Gottingenvon der Luhe, O., 1994, A&A 281, 889von der Luhe O., 1984, J. Opt. Soc. Am. A1, 510Weigelt G.P., 1977, Opt. Comm. 21, 55Weigelt G.P., Wirnitzer B., 1983, Opt. Lett. 8, 389Wilson P.R., 1981, Sol. Phys. 69, 9

This article was processed by the author using Springer-Verlag LaTEXA&A style file L-AA version 3.