Methods Of Sxt Image Processing And Analysis

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From the earlier analysis of the best high resolution flare X-ray images (Herant et al. 1991) and results of theoretical considerations (Gomez, Martens, & Golub 1993) it follows that the structuring and most of physical processes operating in solar flares act on small sub-arcsecond scales, i.e. below the nominal resolution of SXT images on Yohkoh. As the SXT pixel dimension and the FWHM of the point spread function (PSF) of the grazing incidence mirror are of similar sizes it is then possible to increase the effective resolution of the images by using image reconstruction techniques. A number of methods have been worked out and presented in the literature which allow the instrumental blurring to be removed. However, there was no well documented method (except the work of Roumeliotis 1995) which allows deblurring and over sampling to be performed simultaneously. Oversampling means that the recovered (deconvolved) picture contains more resolution elements than the original one. In the case of SXT images we have found that a fortunate compromise between FWHM and pixel size allows for subdivision of each SXT pixel into 5x5 subpixels. Such an oversampling scheme results in the formal numerical increase of the nominal resolution of the SXT image down to ~ 1 arcsec (the over-sampled size of subpixel is ~ 0.5 arcsec). We developed an algorithm called ANDRIL (Accelerated Noise Damped Richardson-Lucy) for SXT image processing. In constructing the algorithm we followed the ideas used for the reconstruction of images from the Hubble Space Telescope prior to its refurbishment. The details of ANDRIL can be found in the papers by Sylwester et al. (1996a) and Sylwester & Sylwester (1998a, 1999a) where extensive tests of the algorithm for various synthetic input models and various shapes of the PSF have been performed. An example of the application the ANDRIL algorithm to real SXT data is shown in Figure 1, where the comparison of original and deconvolved images is presented for two flares (17 April 1992, during the decay phase, and 24 March 1993, during the rise phase). The advantage of using ANDRIL image processing is obvious. Many fine structures of sub-arcsecond sizes

17 April 1992 23:31:32 UT 24 March 1993 03:21:59 UT

Fig. 1. Comparison of original and deconvolved AI12 images for two flares. The original and deconvolved images have been compressed in the same way in order to reveal weaker sources. The sizes of the original images are 18x18 SXT pixels which correspond to 90x90 subpixels after the deconvolution.

are revealed in the deconvolved images. Their physical reliability can be established when comparing the evolution on sequences of consecutive deconvolved images taken with different filters. Near the limb the looptop kernel of the relatively simple Ml.l flare on 17 April 1992 reveals a double structure during the decay phase. The structure of the limb C6.6 flare observed on 24 March 1993 looks more complicated. Deconvolution reveals a cusp-like structure with the main emission concentrated in one (south) foot during the rise phase.

A common interpretation of flare intensities as measured in a pair of images taken in slightly different energy bands provides information on the average temperature distribution of emitting plasma when the images are taken at the same time and the same plasma regions contribute to both bands. It is known that when image ratios are interpreted for regions of strong intensity gradients, derived values of temperatures are very sensitive to the exact co-alignment of the images in a pair. In order to better understand the dependence of the derived temperature distribution on possible small misalignments of Bell9 and A112 images due to fixed accuracy of spacecraft attitude information, Sylwester (1995) investigated to what extent derived T-maps depend on the possible inaccuracy of co-alignment. Siarkowski et al. (1996) have shown that the alignment procedures used in the standard SXT image co-alignment and processing routines may be inadequate when the temperature maps are in question. In order to improve the determination of the temperature pattern in the investigated structures, three numerical methods of Additional Pointing Corrections (APC) settlement have been proposed and investigated.

The uncertainty of temperature determination is much larger when deconvolved SXT images are to be used as the angular resolution is increased five-fold. In the paper by Sylwester & Sylwester (2001a) a method of co-alignment of deconvolved images has been proposed for flares partially occulted by the solar disc. For these flares the limb of the solar atmosphere occults the X-ray source at the very same location for images taken using individual filters. The description of modelling of X-ray occultation process can be found in Sylwester & Sylwester (2002). Taking these results into account it is possible to co-align the images to better than 0.1 arcsec accuracy which allows for temperature determinations on subpixel scales. We will refer to this method of co-alignment as the Limb Position Adjustment (LPA), as it is based on the limb as a reference. We have checked that the agreement between A112 and Bell9 images improves by using the LPA method so we have decided to adopt it routinely wherever possible.

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