Speckle demonstration movie. The comparison movie is available with 1 fps play rate as 2005-10-19-QS-hac-speckledemo.avi and as 2005-10-19-QS-hac-speckledemo.mov, both in the DOT movie album. The original 24 fps movie is available as 2005-10-19-QS-hac-speckledemo.mpg in the DOT mpg directory.
The movie was made from an 1.2-hour data sequence obtained on October 19, 2005. The target was a very quiet area near disk center. At the request of P. Gömöry, the DOT was programmed by P. Sütterlin to sequentially switch the Halpha speckle burst collection between the two modes, i.e., taking complete 100-frame bursts at Halpha line center alternated by 5-wavelength Halpha profile scans using 20 frames/burst in KvdL mode. The storage of the full-burst results as FITS files in the DOT database has the standard DOT format, containing not only the reconstruction (first FITS-file image) but also the sharpest frame of the full burst (second image) and the burst average after alignment (third image). This switched data set enabled the construction of a demonstration movie comparing frame selection, full speckle reconstruction, and KvdL reconstruction.
The movie shows only Halpha line-center data. The movie has four submovies, of which each is bytescaled separately for maximum display contrast. They cover only a 36x27 arcsec cutout of the full field of view in order to maintain the DOT pixel resolution (the other 4-panel DOT movies in the DOT movie album are 2x2 binned).
The first submovie shows the best frame of each full 100-frame burst. These bursts took 30 sec, but the movie cadence is 1 minute since the other 30 sec were used for the KvdL mode. The second panel shows the same sharpest frames, but co-aligned using the 100-frame averages per burst. This is only full-frame alignment, comparable to tip-tilt correction in active optics. There is still much rubber-sheet frame-to-frame warping visible.
The third panel clockwise shows the results from the full speckle reconstruction for the same bursts, after cube alignnment. For each, the superimposed Fried parameter specifies the seeing quality determined from the synchronous burst in the blue continuum. It varied from 6 cm to 11 cm, with an overall increase as seen on the corresponding G-band seeing quality plot taken from the chronological DOT data index. The improvement over the sharpest-frames movies is striking. Above Fried = 10 cm the restoration quality becomes very good, reliably resolving fine structure at the 0.3 arcsec diffraction limit.
The fourth panel clockwise shows the line-center results from the KvdL reconstructions of the 20-frame/burst wavelength-scans collected in the first half of each minute, also after cube alignment. The quality is significantly lower than for full reconstruction, but still much better than what is obtained by frame selection. The KvdL advantage is that these images can be directly compared with, or subtracted from, the companion images sampling the same scene in the other four Halpha wavelengths and in the red-continuum images. In addition, all of these can be precisely co-aligned with the simultaneously taken blue continuum and G-band image sequences via the red-continuum sequence.
Explanation. The DOT speckle reconstruction starts by aligning all frames per burst with the sharpest one through cross-correlation, and then obtain their average. The field of view covered by the camera is then tesselated into about 1000 overlapping isoplanatic patches of 64x64 px or 4.4x4.5 arsec (for the blue cameras). Each subfield is speckle-reconstructed independently, obtaining speckle transfer functions from atmospheric turbulence modeling using spectral-ratio Fried parameter evaluation and applying statistical bi-spectral phase estimation in speckle masking, as developed over the years by Weigelt, von der Lühe, de Boer, and others. The restored patches are then assembled by cross-correlation of their overlaps, using the burst average as template, into the full-field speckle-reconstructed image. This diagram by P. Sütterlin illustrates the scheme. The isoplanatic tesselation is an key part of speckle reconstruction that makes it wide-field in nature, in contrast to on-axis adaptive optics. The matching errors in the re-assembly are usually far smaller than the original rubber-sheet deformations. The resulting sequence of speckle-reconstructed images is then often aligned into a 3D (x,y,t) data cube to facilitate analysis and movie production.
In the case of full speckle reconstruction each camera registers speckle bursts of about 100 short-exposure frames, and each such burst is reconstructed independently. Since all cameras start their exposures synchronously, the resulting multiple-camera sequences are simultaneous. However, at each wavelength the wavefront corrections are determined and applied independently. In particular, when the Lyot filters for Halpha and Ba II 4554 are sequentially tuned to sample these lines at different wavelengths, the successive bursts undergo independent restoration. Each wavelength sample then has had its own seeing with its own restoration. The resulting data cubes must yet be aligned with each other. This is difficult when the scenes differ much, as between Halpha line center and red continuum.
In the case of two-channel KvdL registration and restoration with a tunable filter, only the parallel wide-band continuum camera registers full speckle bursts of 100 frames that undergo full speckle reconstruction. Within the same time, the tunable-filter camera takes shorter bursts, down to only 20 frames/burst, and is tuned in between taking these. For example, a five-wavelength "scan" through Halpha is taken at 20 frames/burst per profile sampling, while the wide-band red-continuum camera collects a full 100-frame burst in synchronous 20-frame segments. The exposure pairs are strictly synchronous between the two cameras, starting and ending simultaneously, and so they saw exactly the same seeing. The KvdL restoration then consists of normal speckle reconstruction for the complete wide-band burst, followed by application of the resulting wavefront deformation matrix as a deconvolution operator for the five retuned narrow-band bursts. The resulting narrow-band images have considerably lower quality than for full-burst reconstruction, but since they share the same wavefront deformation matrix they "have seen the same seeing" and can, for example, be subtracted to produce Dopplergrams. KvdL splitting into subbursts can also be used to speed up the cadence, at the DOT to as fast as 2 sec when sampling a single wavelength without tuning waits.
Note that the common KvdL wavefront correction also shares the rubber sheet correction inherent in the isoplanatic patch tesselation and re-assembly of the wide-band burst. The different profile samplings are therefore perfectly co-aligned and so are the resulting data cubes. Halpha line center and the other profile samplings are then easily aligned to the G-band data via the red-continuum images and to Ba II 4554 Dopplergrams using the barium broad-band continuum images, since these all show the granulation in common. Only the alignment with Ca II H remains difficult since its scene differs much from all others.
Further remarks. The movie also demonstrates how terribly (or beautifully) fast the quiet-Sun Halpha scene changes. The slow movie cadence obviously undersamples the intrinsic dynamical time scales. For comparison see this 1-sec cadence movie, presented in 2008ESPM...12..7.1R and made from data taken a year later by L. Rouppe van der Voort at the twice larger SST. Traditional estimates of the solar change time specified the 7 km/s sound speed as limiter, yielding 30 sec for the DOT diffraction limit at Halpha. This is a comfortable duration, much in excess of the seeing freezing time of 10 msec and so permitting collection of complete seeing statistics. However, 30 sec cadence appears much too slow for Halpha scenes. Their faster time scales imply that only KvdL restoration can be used to make Dopplergram movies; full bursts take too long and sample inconstant solar-tmosphere conditions.
The demonstration movie therefore also displays the major limitation of speckle reconstruction for chromospheric imaging. Its advantages are that it is a robust method and corrects the whole field of view, but its disadvantage is that it requires a large number of frames per burst that must independently sample the seeing to ensure validity of the assumed Kolmogorov statistics. Too many frames, so taking too long, for chromospheric imaging. The sound speed is a better solar change time estimator in the deeper atmosphere, making speckle reconstruction a better option for photospheric imaging. But the action is higher up. The short chromospheric time scales make the resulting photon need of fast narrow-band imaging a prime driver for larger solar telescope aperture.
The MOMFBD restoration method developed by Van Noort et al. (2005) for the SST requires far fewer frames per burst, but takes far more subsequent processing and is less robust, necessitating adaptive optics as well. It inherently (via the MO standing for Multi Object) entails multi-channel co-registration as in KvdL restoration. Larger telescopes than the DOT must combine adaptive optics with MOMFBD for chromospheric imaging.
Rob Rutten 2018-07-22