Introduction

This section describes the data processing procedures which are applied in the data processing pipeline. For information about the telescope, its optical parameters, the camera system unit and the image acquisition techniques follow the links:

The data processing pipeline describes the work flow from the data acqusition to the final data repository in the archives and substantial processing steps. The methods and procedures are explained in the sections below:

Positional Information

Determination of the solar limb is crucial for deriving geometrical information from the solar images. Properties of the disk (center coordinates and radius) are needed for the shifting of the disks towards the center of the field of view and the actual image scale. They are given in the FITS headers of archives and synoptic level data.

The solar limb is commonly defined as the inflexion point of a radial intensity profile. A stable method which works also on images which show only a part of the disk (cf fig. 4) is to find limb points on a set of disk profiles parallel to the CCD y-axis. A profile is smoothed, the first derivative is calculated and again smoothed. The max and the min of the derivative should indicate the position of the inflexion point of the intensity profile. A circle (x₀, y₀, r) representing the disk is derived by fitting this set of limb points with the least squares method.

Figure 1: Position of the intensity profiles used for limb detection. Starting from column 200 to col. 1800 each ten pixel columns a profile is selected.

Figure 2: Limb profile of a continuum image. The dots represent the individual pixel values along the radial profile (in this plot parallel to the CCD x-axis), the solid line is a running average over 15 pixel values. The dashed line is the smoothed derivative (again running average over 15) of the intensity profile. The vertical line shows the max of the derivative and therefore the position of the solar limb.

In a second step the individual radial distances of the set of limb points to the fitted circle from the above described first approximation is calculated, limb points with distances above a certain threshold (e.g. 10 pix) are neglected for a new estimation of the limb circle. With this iteration we yield usually standard errors in radius (from the least squares method) of < 1 pixel.

In order to derive heliophysical coordinates of solar features on solar images one has to know the orientation of a pixel axis of the CCD with respect to celestial coordinates. The equatorial mounting of the telescope has the advantage of no image rotation during the diurnal movement of the Sun across the celestial sphere. Apart from small errors due to non-perfect telescope setup or bending of the optical axis (on the changing direction of the weight of the telescope during a day) the angle Θ between the pixel axis and e.g. the celestial E-W-direction should be constant as long as the system will not be disassembled for maintenance. If the tracking system of the telescope is switched off and one neglects the change of the solar declination and of the refraction during a few minutes the track of a solar feature or of the disk center will represent the celestial E-W-direction.

Figure 3: The principle of the determination of the E-W direction in the images. Inclination of the Solar rotation axis (P and B₀) is reckoned from celestial North which is perpendicular to the derived E-W track.

Therefore we obtain from time to time a series of about 20 images with no tracking having the solar disk moving across the field of view. Applying an edge detection filter, fitting circles through the solar limb points and calculating the center coordinates yield finally a track of the disk centers and the angle Θ.

Figure 4, top: Drift of the solar disk centers of an images series taken at 2007-08-01 around 6:50 UT. The + mark the calculated disk center coordinates of the individual images. Θ is derived by a linear fit from these positions y = tanΘ.x + d. Bottom: The image series taken at 2007-08-01 around 6:50 UT covers a range where about a half disk is visible at the eastern limb of the field of view until still a half disk is visible at the opposite end of the CCD field.

The standard error of this procedure was determined of about 0.02° for Θ and the daily variation due to the above described imperfections is in the order of 0.05°. The standard error for the deviation of individual limb pixels from the calculated circles is within one image less than 1 pixel, the observed variation of 2...3 pixels typically in the disk radii of about 930 pixels in image series is rather an influence of the seeing than an error in the fitting procedure. So the individual calculated disk radii have an error in the order 0.1% and we can estimate a reliability of better than 1° in heliographic positions in our images.

Figure 5: The derived radii of the images (gain from the series taken at 2007-08-01 around 6:50 UT) are relatively stable even when only a part of the disk is visible, the variation is mainly due to seeing effects.

Figure 6: The variation of Θ from 3 images series taken on 2007-08-01. The observation time (middle of each series) is indicated by the hour angle of the telescope at the observation time. We assume that the variation should depend on the geometrical position i. e. the hour angle of the parallactic telescope mounting. The dashed line is a second order polynomial fit which should be symmetric to noon.

Photometric Information

CCDs have basically a linear relation between the produced charge (and the output voltage) and the amount of the incident light, but there exists a level of saturation which limits the linear range. Therefore the amount of light during exposure has to be limited below that level (cf. » KPDC - Kanzelhöhe Photosphere Digital Camera). The TM--4100CL allows to set the gain and the lower level of the A/D converter, so that the full dynamic range (which corresponds to pixel value 0...1023) can be mapped into the linear part of the CCDs charge vs. incident light relation. The zero level is set properly when some noise floor (dark current) is visible. Signal noise limits the dynamic resolution of the pixels (the number of useful bits). For setting and checking of these properties we used a simple procedure which was proposed by ESO (see Deiries, S.: 1995, ESO Doc. No. VLT-INS-ESO-13670-0001).

Figure 7, left: Single dark current frame of the TM4100CL. The mean of the pixel values is dc = 4.3 counts with σ = 2.8. The read-out noise, defined as the standard deviation of the pixel differences of 2 dark current frames, is rmsnoise = 2.77 which yields a dynamic range of 51 dB or 8.5 significant bits. Right: Smoothed average of 17 dark current frames with integration times from less than 1 ms to about 10 ms. There are variations in the dark current of the individual taps of the dual tap CCD array visible, however we noticed that a general subtraction of such a smoothed average dark current frame did not improve the images.

In the lab the cam was illuminated with a stable and uniform light source (e.g. a LED with diffusor) and a set of paired frames (with identical exposure times) were taken in a wide range of exposure times. Sums and differences of individual pixel values of the 2 frames of each pair were used to calculate statistical properties (mean, standard deviation - for details see the ESO paper and the image captions). These statistics were made on sub-fields (e.g. of size 256x256 pixels) to avoid averaging over potentially non-uniform areas: The means of the pixel values as a function of the amount of incident light (i. e. of the exposure time) showed a non-linearity of 0.2%. The standard deviations of the difference of the equally exposed frame pairs give the noise in the data. The dark current proved to be fairly independent from the exposure time and is noise dominated (see fig. 7 and 8), probably produced by the electronics (read-out noise). The ratio between full scale and noise yields finally the useful dynamic range and can be expressed in the effective number bits.

Figure 8: Parameters for the TM4100 cam with the finally selected gain and lower level for the A/D converter, derived from the statistical evaluation of the pairs of frames uniformly illuminated as described in the text. The plots show the numbers for a 256x256 pixels area starting from pixel (1024,768), values for other sub-fields do not differ substantially, even on fields with double linear dimensions. Top left the variances of the individual pixel differences of the frame pairs which can be used for an estimation of the conversion factor (data units per absorbed electron/photon). Top, right: Linearity of the output signal as a function of the incident light, which is proportional to the exposure/integration time if we assume a stable light source. Bottom row: Dark current (mean and standard deviation) of the individual non-illuminated frames but with a variation of integration times. Right: The standard deviations of the individual pixel differences of the frame pairs of identical integration times. Both plots show that the values are integration-time independent and of the same order, therefore the dark current is rather a noise than a bias. As noise is unpredictable, it is an uncertaincy in the signal and cannot be subtracted. The methods are explained in detail in the mentioned ESO paper.

A flatfield frame can be considered as a multiplicative map of non-uniform gain of the individual pixels. It may origin from a real non-uniform gain or sensitivity of the pixels or may be a result of non-uniform illumination of the telescope, due to e.g. tilt lenses. This non-uniformity was investigated and calculated with 2 methods which deliver such maps and a center-to-limb variation/darkening (CLV) estimate as well:

• Method A) - denominated as Kuhn-Lin method - by a set 8-10 consecutively taken solar image frames which assume to show the same object but at shifted positions (see Kuhn, J. R., Lin, H., & Loranz, D.: 1991, Publ. Astr. Soc. Pacific, 103, 1097), any variation of the solar image in the set must origin from non-uniformity.
• Method B) - denominated as Burlov method - by assuming circular symmetry in a (spotless) solar disk image. The disk is split into concentric rings. The intensity function of each ring and therefore potential asymmetries are mapped by fitting polynomials. These polynomial represent the non-uni-formity and can be used to calculate a flatfield map and correct the images. Real asymmetries in the images, e. g. caused by active regions, are of smaller scale and should not be corrected. This can be handled by limiting the order of the polynomials. This method was basically developed by K. Burlov-Vasiljev and P. N. Brandt at KIS Freiburg in 1996 for the processing of RISE/PSPT images but never published.

Figure 9: Comparison of flatfield methods described in the text, left method A) and right method B), bottom row is a TV-representation where higher values are brighter. Clearly visible that in method A) the noise which is from nature variable from frame to frame produces more small-scale non-uniformity than any visible large scale variation. Method B) uses only a single frame and no differences, assumes large scale circular symmetry and stops compensation of the variation at a certain scale.

Both methods showed that the effect of noise dominates over non-uniformity which is in the single percent range (Fig. 9). Fig. 10 shows for comparison two very high contrast solar images of a spotless Sun where limb darkening is compensated by the CLV function which is a by-product of the both methods. It is clearly visible that both methods fail at the extreme limb regions, but method B) seems to be a little bit better (see left part of the disk), but it has to be further checked on images with sunspots.

Figure 10: Very high contrast images of the spotless Sun from 2007-08-01 to check the quality of the flat fielding methods. Left processed with method A) and right with method B). Limb darkening is compensated by applying the CLV function derived from the flat-fielding procedures. Between the black and white level there is only an intensity variation of 1%.

In practice the method B) has advantage that it can be applied as a post-processing on any archived image without any prerequisite at observation time, but needs some computing power for the calculation of the rings and the fitting of the polynomials. Method A) however needs a recording of the set of displaced images on a clear sky from time to time followed by a calculation of the flat-field frame, but allows then to apply this frame to a series of subsequently taken images.