3.1.

Guider-Assisted Cross-Correlation

The optimal alignment, between two neighboring images, can be determined using a cross-correlation algorithm. The fastest way is using fast Fourier transforms (FFT) to reduce the cross-correlation to a simple multiplication in Fourier space. This, also, efficiently allows a convolution filter to be applied.¹⁰ A high-pass filter is recommended to remove any intensity gradients caused by the telescope optics. After transforming the result back, the position of the intensity peak, in the resulting correlation image, corresponds to the most likely shift between the two images. This position can be estimated, with subpixel accuracy, by fitting a 2D Gaussian curve to a $3\times 3$ pixel region around the intensity peak.¹¹ The problem with the FFT based method is that the peak is not uniquely defined, instead, it is the position of the true peak modulo, the image width, and height. For example, for a $1024\times 1024$ pixel image, if the position of the intensity peak is at coordinates (40, 1000) then, assuming that the two images do really overlap, the true peak could be at ($-984$, 1000), or at (40, $-24$), or at ($-984$, $-24$). The ambiguity can be removed by choosing the coordinate that is closest to the coordinates from the guider log.

3.2.

Spring Relaxation

There are several types of springs that represent the relation between individual images:

For an $N_x\times N_y\times N_t$ image mosaic movie, where $N_x$ is the number of images in the horizontal direction, $N_y$ in the vertical direction, and $N_t$ the number of mosaics in the mosaic movie, there will be approximately 3 $N_x\times N_y\times N_t$ springs.

For each image $i$, we keep track of the estimated position $\overrightarrow{r_i}$, that initially is set to be equal to the position according to the guider log. For each of these springs, the spring force between images $i$ and $j$ is $\overrightarrow{F_{ij}}=k_{ij}(\overrightarrow{r_{ij}}-\overrightarrow{R_{ij}})$ , where $\overrightarrow{r_{ij}}=\overrightarrow{r_i}-\overrightarrow{r_j}$ is the estimated distance vector between the two images, $\overrightarrow{R_{ij}}$ is the optimal distance between the two images according to the cross-correlation algorithm, and $k_{ij}$ is the spring constant for this pair. After calculating all the forces, we calculate an improved estimate of the position of the images: $\overrightarrow{r_i^{\prime }}=\overrightarrow{r_i}+c\sum _j\overrightarrow{F_{ij}}$ , where $c<<1$ is a small constant that limits the amount of movement in a single relaxation step and ensures the algorithm will converge smoothly to a solution. We repeat this a fixed number of steps or until the total force on each image, $\sum _j\overrightarrow{F_{ij}}$, is lower than a certain threshold.

3.3.

Seamless Blending

After calculating the optimal positions of all the images in the mosaic movie, the images, within each mosaic of the movie, must be blended together. Simply overlaying the images on top of each other will result in sharp, visible seams between the individual images. This can be avoided by making the images partly transparent in the overlapping region, such that, they are blended gradually into each other. While that avoids a sharp seam, it can still result in image artifacts when the images are not perfectly aligned. A much better way is to use “seam-line optimization”, an algorithm where an optimal curve is determined in the overlapping region that minimizes visual artifacts. Along the curve, the width of the blending region is varied depending on the intensity gradient of the image across the curve. In areas with small gradients (and thus low contrast), a wide region is used to blend, whereas, areas with large gradients (high contrast) use short region to blend. The off-the-shelf, open source program “Enblend”⁸ implements this algorithm. As input, this program expects a set of images the size of the whole mosaic, each input image containing the original image already aligned, and with an alpha layer that is opaque where the original image is, and transparent everywhere else.

4.1.

Description of the System

The observer uses the whole-sun image of the telescope guider to choose the place of interest and its size by drawing a rectangle around the desired region. Subsequently, the program calculates the required number of telescope fields-of-view and the coordinates of each field to be successively observed.

Figure 3 shows an example on an image from the guider telescope of the DOT. The guider telescope is equipped with an $H\alpha$ filter and electronic enhancement of contrast, of the image, for good visibility of filaments and prominences. Bright-yellow lines indicate the chosen rectangle. In this example, the calculated number of fields is 12 in the east-west direction six, and in the south-north direction two (north is on top, east at the left, like in the hand-control panel on the left side of the image). The calculated centers of the fields are indicated by bright-yellow points.

Fig. 3

Guider-telescope images of the whole sun with a mosaic field of six by two fields. Image (a) taken during the observation of the first sub-field of the mosaic. Image (b) taken during the second subfield observation. The array of bright points indicates the subfield centers.

During its exposure, the first mosaic field is shown in the bottom-left corner of the total mosaic field in Fig. 3(a). The boundaries of this field are indicated by a dark-red rectangle corresponding with the smallest camera field currently in use of $91\times 72$ arcsec, being $1300\times 1030$ pixels, hence, pixel size $0.07\times 0.07$ arcsec. The small dark-purple circle indicates the target position for tracking.

The DOT is equipped with a multi-channel system. The channels, at the blue side of the spectrum, are equipped with KPF100 Hitashi Denshi cameras. At present, the wavelengths of these channels are (i) G-band 430.5 nm, width 1.0 nm, (ii) blue continuum 431.9, width 0.6 nm, (iii) Ca II-H 396.87 nm, width 0.13 nm tunable to blue by tilt, (iv) Ba II 455.4 nm, width 0.008 nm tunable $-/+0.2\mathrm{nm}$ birefringent Irkutsk filter^12,13 and (v) near Barium blue continuum 450.48 nm, width 0.54 nm or H-beta prominence 486.23 nm, width 0.15 nm tunable to blue by tilt. The channels, at the red side of the spectrum, are equipped with ES4020 MegaPlusII Redlake cameras with a field of $113\times 113$ arcsec, $2048\times 2048$ pixels binned $2\times 2$ to effective $1024\times 1024$ pixels of $0.11\times 0.11$ arcsec. These channels are (i) $H\alpha$ 656.28 nm, width 0.025 nm tunable $-/+0.8\mathrm{nm}$ birefringent Zeiss filter¹⁴ and (ii) red continuum 655.05 nm, width 0.24 nm or $H\alpha$ prominence 656.35 nm, width 0.23 nm tunable to blue by tilt.

The image $b$, in Fig. 3(b), shows the guider image during the exposure of the second mosaic field. The dark-red boundary of the rectangular field is shifted one position to the right, to the west. The observer can follow how the field is moving along the programmed path starting at the bottom-left corner, then moving one-by-one to the right, in this case, six positions then one position upward, followed by moving back one by one to the left. In this example, there only are two rows. In case of more rows, the field continues by going up one position at the left side followed by going step by step to the right and so on, as already explained in Fig. 1. When the last field is reached, the telescope automatically moves to the first field at the bottom-left corner.

Originally, the program was developed with a square region of interest in mind, such as $2\times 2$, $3\times 3$ or $4\times 4$ fields. In the case of an elongated region, it would be better to go step by step along the shortest side of the region instead of along the longest side. This will give the best fit of the field boundaries to each other because the maximum time difference, between neighboring fields, is minimized. The program will be improved in this way for future observations.

The DOT has an equatorial mount. Consequently, the boundaries of the camera fields do not rotate relative to the solar image. This is comfortable, especially during long-term mosaic movies over several hours. Alt-azimuth mounts show relatively fast image rotation in the neighborhood of the zenith position. Hence, such rotation will be maximal during the hours around noon in summer. Of course, this could be overcome by an image rotator which requires additional optical surfaces and a precision drive system. The camera-field boundaries at the DOT are oriented east-west and north-south. This is convenient both for east-west strips (as in our example) and for north-south strips. In practice, these strips can be valuable for filament observations with the $H\alpha$ filter tuned to several spectral-line wing positions (a certain distance to the $H\alpha$ line center corresponds to a certain line-of-sight velocity). Flows, parallel to the solar surface, have a line-of-sight and transverse component except under specific limited circumstances when the flows are entirely in the plane of the sky. The selection of a line-of-sight velocity value can be helpful to find gas streams with certain velocities along the solar surface.

The large dark-red circle along the rim (see Fig. 3) indicates that the main telescope is precisely following the Sun, by use of an active system, which processes the solar rim position information of the guider. The guider image can be observed in full screen, see Fig. 4, to allow a better observation of objects of possible interest on the solar disk and at the rim. Before the start of the mosaic observations, the main telescope can follow the sun passively by use of only coordinates. The broad red ring disappears and what remains is a thin bright ring which is due to electronic enhancement of the region outside the rim for a better visibility of the prominences. Exactly at the rim, a narrow green ring of the solar coordinate system is visible. The position of the main telescope is visible in Fig. 4 at the disk center indicated by the purple circle and red camera-field boundary.

Fig. 4

Full-screen guider image for a better visibility of objects of interest. The dark red ring at the rim is absent because active guiding is switched off. Details outside the rim, like prominences, are better visible by use of electronic enhancement. The main telescope is pointed to the disk center.

4.2.

Application Examples

The mosaic-movie technique is extremely useful in correctly identifying and analyzing the dynamics of solar features as we illustrate by referring to common solar features seen in Fig. 5. This mosaic consists of 12 fields from a mosaic movie in the $H\alpha$ line center, as described above. It was recorded during the 2010 DOT Prominence Project by a team of collaborating solar researchers (PROM) coordinated by Helio Research¹⁵ in La Crescenta, California. Successive mosaics, of this area, were recorded during 10 days for the purpose of observing filament channels and filaments forming around the periphery of two relatively new, small active regions. One new filament channel is designated by three arrows and a label in Fig. 5 at the left (eastern) side of the mosaic. This filament channel contains a small filament in its initial stage of formation. Several other filaments are shown by arrows and labels. All are in filament channels, or zones, where the magnetic field of the central part of the channel is parallel with the long axis of the filament. The pattern of fibrils, typical of a filament channel, can be seen in the filament channel in the left side of the mosaic image in Fig. 5. The fibrils align end-to-end along boundaries where the line-of-sight component of the magnetic field direction changes sign from outward to inward. This is seen when Fig. 5(a) is compared to Fig. 5(b). Similar major channels, of realigned fibrils, are expected to form between the two active regions over the course of several days and later between the sunspots within each active region.

Fig. 5

(a) Mosaic of $6\times 2$ images in the $H\alpha$ line center from a mosaic movie over 5.5 h on this same area. This image was taken at 11:29 UT (10:19 local solar time) 0.2 h after the start of the mosaic sequences of images. Movies are an important asset to correct identifications of all of these dynamic solar features which change at different rates. The main subjects are two “active regions,” one left of center, and the other right of center. Each active region consists of bright areas called “plage.” Within these brightened areas, are sunspots which are the compact, nearly round, dark areas. Everywhere around the plage and sunspots are elongated, thread-like structures known as “fibrils” which are organized in patterns around the plage and sunspots because they follow the direction of the local magnetic field. The organized fibril patterns enable the identification of the boundaries of the active regions which are often also marked by dark “filaments.” Mosaic movies were taken of these two regions to study the formation and evolution of filaments that develop in and around the active regions. The filaments are designated by arrows with the exception of the arrow furthest to the right side of the image which points to a short-lived feature called a “surge.” In a single image, a narrow “surge” of mass along the local magnetic field can appear similar to a filament, but a surge is a temporary ejection of mass lasting minutes whereas filaments are longer-lived dynamic structures that develop specifically at boundaries where the local magnetic field has a sharp reversal from positive to negative polarity. (b) Magnetogram of same region at same time with SDO (Solar Dynamics Observatory) in space. Noticeably the DOT mosaic has a higher resolution: pixel size 0.1 arcsec at DOT, 0.5 arcsec at SDO.

An example of a surge is shown by the arrow that is furthest to the right in Fig. 5. Surges are short-lived ejections that emanate from specific locations that are often close to flare footpoints in the $H\alpha$ chromosphere. Their curved trajectories indicate that their flows follow the local magnetic field and reveal the degree of local field curvature. The example, in Fig. 5, has little obvious curvature as it follows the nearly radial fibrils around the periphery of the closest sunspot. As in this case, in a single image, a surge can roughly resemble a filament, however, in the movie, this surge is readily distinguished from filaments because its flows are more rapid and shorter-lived than the typical flows in filaments. It is seen, that the surge is no longer present in the series of three images, shown in Fig. 6, at a later time during the same day.

Fig. 6

Three successive images from the same set of 12 fields-of-view as in Fig. 5 at 4.7 h after the start of the observations on this day. The fibrils between the sunspots are one of the special subjects of interest. If they are dark and are changing rapidly, as within the plage to the left of the large sunspot in the active region in the right side of these images, they will have larger Doppler shifts than other fibrils. These large Doppler shifts are a characteristic property of locations where new magnetic flux is welling up beneath the fibrils. The dark fibrils are called “arch filament systems.” All active regions begin as “emerging flux regions” beneath arch filament systems which frequently recur within existing active regions. The interactions of the new and pre-existing magnetic fields frequently produce flares. The new bright structure seen only in the third images is a solar flare first seen in its early stage of development in the middle image.

The time between successive images is 6 min and 36 s, as shown in Fig. 6. The contrast of the structure, in the field around the flare, is seemingly lower in the bottom mosaic than in the two previous ones. This is because the program, to represent the mosaic on the screen, has an automatic contrast adaption to be able to clearly show the full range of intensities in the image, especially during a solar flare.

The time interval between successive mosaic images in this example, 6 min 36 s, comes about as follows. The $H\alpha$ line was sampled at seven spectral positions which are the line center and alternating at three positions in the red and blue line wing. At each spectral position, 20 short exposures were made. Strictly simultaneous, there were $7\times 20=140$ exposures in the nearby red continuum and other channels, in this case the G-band, blue continuum and Ca II-H. The red continuum images are used for Keller-Von der Lühe speckle reconstruction¹⁶ of the $H\alpha$ images leading to images with diffraction limited resolution of 0.3 arcsec. This process is computer-time consuming for movies and has not yet been carried out. The frame-selected images, that are shown here, are the best of each sample of 20 images. The time required for the 140 exposures per field position is 30 s including the time needed for tuning the $H\alpha$ filter. The repositioning time of the telescope is 3 s. Hence, the cycle time per subfield is 33 s, in this case, and mosaic cycle time is $12\times 33=396$ $\sec =6\min$ 36 s. The additional time needed for the longer way from the last image to the first image of the next mosaic is so small that it is taken within the redundancy time built in the 3 s motion time per step. All motions are shock-free with gradual increase and decrease of the accelerations by the servo system. Longer slew distances can be obtained in short time by reaching high velocities without shocks. The same technique is used for fast tuning of the $H\alpha$ filter.

The Keller-Von der Lühe speckle reconstruction requires at least 20 images at each $H\alpha$ tuned position and about 100 images in the red continuum. This results in the following other often used tuning modes of the Hα filter including five spectral positions with each 20 images for a total of 100 images with $22+3=25\mathrm{s}$ cycle time per subfield, 3 positions with each 34 images for a total of 102 images with $19+3=22\mathrm{s}$ per subfield, 2 positions with each 50 images for a total of 100 images with $16+3=19\mathrm{s}$ per subfield, and direct 100 images with $13+3=16$ s per subfield.

Surges and small flares frequently occur in and around sites where new magnetic flux is developing. It is now common knowledge that sites of new magnetic flux are marked, in $H\alpha$ images, by sets of closely spaced dark fibrils such as the set on the opposite side of the sunspot from the surge and below the filament in the right side of Figs. 5 and 6. These fibrils are much darker and are changing more rapidly than the fibrils between the sunspots in the active region in the left half of Figs. 5 and 6. The sets of dark fibrils are named “arch filament systems.”^17,18 These arch filament systems, in the active region in the right side of Fig. 6, are dark because they are Doppler-shifted in varying degrees in relation to the magnetic flux emerging beneath them. They are seen as Doppler-shifted features, in Fig. 7, which shows two pair of images at wavelengths a little greater and lesser than the $H\alpha$ centerline images in Figs. 5 and 6. The first pair is at $H\alpha$ $-0.04$ and $+0.04\mathrm{nm}$ from the line center wavelength of the $H\alpha$ line at 656.28 nm. On average, the Doppler shift, seen at $-0.04$ and $+0.04\mathrm{nm}$, is $18\mathrm{km}/\mathrm{s}$ toward Earth and $18\mathrm{km}/\mathrm{s}$ away from Earth. The second pair shows higher velocities which on average are $-32$ and $+32\mathrm{km}/\mathrm{s}$, respectively, toward and away from Earth. Some of the arch filaments are seen to have these higher velocities which distinguish them from ordinary fibrils.

Fig. 7

The mosaic at the time of the brightening in four wing positions of the $H\alpha$ filter, from top to bottom at $+0.04$, $-0.04$, $-0.07$, and $+0.07\mathrm{nm}$. The flare in Fig. 6 is seen here in the near wings of $H\alpha$ in the upper pair of images below the dark arch filaments system. The flare is not seen further into the wings in the pair of images at $-0.07$ and $+0.07\mathrm{nm}$ but a few arch filaments and filaments are visible due to their relatively high velocities.

Small solar flares often occur around arch filament systems, especially around sites where one polarity of the new magnetic fields pushes into the surrounding magnetic field of opposite polarity. Such a flare is seen in the bottom image of Fig. 6 on and around the periphery of the arch filament system. The flare is a newly brightened area on and below the arch filament system. The flare is also seen in the top pair of images in Fig. 7. The flare is nearly identical in both images and this is evidence that the flare brightening is spectrally broadened and does not reveal Doppler shifts. Figure 8 contains the set of images that immediately preceded those in Fig. 7 for each wavelength and no flare is seen in this set. Figure 8, in comparison with Fig. 7, also reveals the Doppler shifts in the filaments quite clearly. Unlike the flare, we do not see the same filament structure in the two wings of $H\alpha$. This is typical because filaments have continuous mass motions and, therefore, their structure is slightly different in each set of images separated in time by minutes. The movies, from which the images of Figs. 6–8 are taken, can be found on the following website: http://dotdb.strw.leidenuniv.nl/ftp/DOT/2010/2010-11-13/mosaic/.

Fig. 8

The mosaic 6.6 min earlier does not show the flare seen also in the $H\alpha$ wings in Fig. 7. $H\alpha$ wings from top to bottom: $+0.04$, $-0.04$, $-0.07$, and $+0.07\mathrm{nm}$.

Among the direct eye-catching features are those with the greater visibility of the brightening in the blue (negative) wings, which means in the gas streams toward us. The positions, in the wings farthest away from the line center at $+$ and $-0.07\mathrm{nm}$, show the small-sized foot points of the gas streams originating low in the solar atmosphere, low-chromosphere and photosphere. The brightenings are eye catching but the longer-term development of the region is important and can be followed by the dark structures of the gas streams along the magnetic field lines. The farther away from the line center, the higher the velocities are. The wing positions, at $+$ and $-0.07\mathrm{nm}$, also show as dark structures the smaller-sized regions with higher velocities, respectively, down and upward for $+$ and $-$ wing positions. Also, some higher-up gas streams, with high velocity, are visible. The fast change of the far-wing structures is notable and typical. The time of 6.6 min between successive mosaics is too long to follow these fast changes in time in detail. Smaller mosaics would take less time. Figure 9 shows the choice on the guider disk of two smaller regions. In Fig. 9(a), a region of three by one fields and in Fig. 9(b), an image of two by two fields. It is the task of the observer to choose the best combination of field size and time resolution depending on the intended science.

Fig. 9

Choice of two smaller mosaic regions on the guider image. (a) Region of $3\times 1$ camera fields. (b) Region of $2\times 2$ camera fields.

Figure 10 shows an example in which the choice was to make a mosaic after a high-time-cadence single-field movie of an interesting part of the filament where many of its threads appear to connect to small-sized areas with strong magnetic fields. Figure 10(a) shows a long filament in a mosaic of a north-south strip which, in this case, is speckle reconstructed. The gap in the center part is interesting because of the many filament threads going downward into the gap and to the sides, the so-called barbs of the filament, where the small brightenings hint at small-scale magnetic reconnections in the lower atmosphere. The eruption of this filament was observed the next day, 7 October 2004, at Helio Research in La Crescenta, California and the eruption appeared to begin at the site of the gap. Movies, at the DOT in time cadence of 30 s, were made of a single camera field centered on this filament gap. Movies from 08:47 till 09:42 UT were speckle reconstructed. Three successive image combinations are shown in Fig. 10(b) at 09:32:00, 09:32:30 and 09:33:00 UT. Each image combination consists of a G-band image at top-left, a Ca II-H image at top-right, an $H\alpha$ core image at bottom-right, and an $H\alpha$ blue wing image at $-0.08\mathrm{nm}$ of line center at bottom-left. The $H\alpha$ wing images show the very fast changes in the high-velocity gas streams in the solar atmosphere. The movie is available in avi, mov and mpeg at the DOT website: http://www.staff.science.uu.nl/~rutte101/dot/ or http://www.dot.iac.es.

Fig. 10

(a) Mosaic of whole filament, top is north. (b) Three successive image combinations with time intervals of 30 s.

Choose then “solar movies.” Direct link in, for example, avi: http://www.staff.science.uu.nl/~rutte101/dot/albums/movies/2004-10-06-filament-gb+ca+haw+hac.avi.

A possibility, for very high time cadence, is to split a full burst of 100 to 140 images of the red continuum in not only spectral positions of the $H\alpha$ line but also in small time intervals. For instance, the burst of 100 images in 13 s, without tuning the $H\alpha$ filter, can be split into five successive subbursts of 20 images, each in a period of 2.6 s.

When two high-resolution telescopes are available, it is possible to combine a single camera field showing unusually fast changes in high spatial resolution and high time cadence by one of the two telescopes with simultaneous mosaics of a whole filament region around this single camera field by the other telescope. An example of such a co-observing by the SST¹⁹ and DOT is shown in Fig. 11. These two neighboring telescopes can take advantage of good seeing at the same time for these combined observations.

Fig. 11

(a) Mosaic including whole filament channel with interesting fast changes in high resolution but lower time cadence than for smaller field-of-view, observed by DOT. (b) Single camera field of same interesting fast changes in high resolution and high time cadence, simultaneously by SST.