Abstract
Analysis of the RHESSI and STIX data requires some novel tools, all tailored to, and indeed in many cases optimized for, the construction of an image from a sparse set of relatively noisy Fourier components obtained using either the temporally modulated count rates measured with RHESSI or the Moiré patterns measured with STIX. The raw data from both instruments used for all of the image reconstruction algorithms to be discussed in this chapter consist of count rates accumulated into a relatively large number (∼ 103 − 106) of short time bins of ∼0.5–100 ms each. The essence of many of these image reconstruction methods has been described by Hurford et al. (Solar Phys 210:61–86, 2002) for RHESSI and by Massa et al. (Astron Astrophys 624:A130, 2019) for STIX. Here we discuss several of them in some detail, and we add a discussion of methods that have been developed more recently. Example applications using solar flare data are presented.
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Notes
- 1.
See https://hesperia.gsfc.nasa.gov/rhessidatacenter/imaging/BPClean_changes.pdf for more details.
- 2.
Note that, in viewing the solar disk from the Earth, solar North is at the top, but the East→West motion of the Sun in the sky is from left to right, so that displacements to the right of the disk are Westward and those to the left are Eastward, contrary to one’s immediate intuition. In a sense, we are viewing the compass rose “from the inside.”
- 3.
In thermodynamics, the entropy is maximized subject to a set of specified physical constraints. In the simplest example, the p i correspond to different energies E i, and conservation of total energy requires \(U = \sum p_i E_i = \mathrm {constant}\), so that the variation \(dU=\sum E_i dp_i = 0\). The entropy is a maximum when \(dS = -\sum (\ln p_i + 1) \, dp_i = 0\) and, since \(\sum dp_i = 0\), it follows that \(dS^* = -\sum (\ln p_i + \alpha ) \, dp_i = 0\), where α is a Lagrange multiplier. Writing dS ∗− β dU = 0, where β is another Lagrange multiplier, gives \(\sum (\ln p_i + \alpha + \beta E_i) \, dp_i = 0\) and, since the individual variations dp i are arbitrary, each term in this sum must equal zero. This immediately gives the well-known Maxwell-Boltzmann distribution of energies \(p_i \propto e^{-\beta E_i}\)—cf. Eq. (1.1).
- 4.
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Piana, M., Emslie, A.G., Massone, A.M., Dennis, B.R. (2022). Count-Based Imaging Methods. In: Hard X-Ray Imaging of Solar Flares. Springer, Cham. https://doi.org/10.1007/978-3-030-87277-9_5
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