One a priori information for tomography is a magnetic field model, possibly constrained by stereoscopic triangulation, as we described in the previous section on magnetic stereoscopy. The subset of loops (or loop segments) than could be triangulated in an active region, serves then as a skeleton, while the magnetic field model can fill in an arbitrary set of auxiliary field lines to fill the entire coronal volume. In the case where no fitting theoretical magnetic field line can be found (or be trusted), auxiliary field lines can also be generated by 3D interpolation (Aschwanden et al., 2009c), although this method works only well for a sufficient number of reliably triangulated skeleton field lines, and may contain unphysical solutions that do not fulfill the Maxwell equation of divergence-freeness () in underpopulated regions. Once a full 3D magnetic field is established for some coronal volume, each field line can be populated with a hydrodynamic loop model of the electron temperature and electron density . The emission measure can then be integrated along each line-of-sight , convolved with a filter response function (Eqs. (4) and (5)), and EUV and soft X-ray images can be rendered for arbitrary instrument filters (Figure 14). Such simulations of coronal images with rendering for particular instrument filters were already simulated in the pre-STEREO era (Gary, 1997; Alexander et al., 1998) and forward-fitted to observed coronal images (Schrijver et al., 2004; Mok et al., 2005; Lundquist et al., 2008a,b), as well as to image pairs from STEREO in three wavelength filters (Aschwanden et al., 2009c).
Alternative methods of 3D reconstruction methods of coronal structures that use auxiliary information involve the line-of-sight velocity measurements of plasma flows in flare loops (Nitta et al., 1999) or in coronal loops (Alissandrakis et al., 2008), time-evolving tomographic 3D reconstruction of polar plumes (Barbey et al., 2008), and multiscale optical-flow methods applied to erupting filaments (Gissot et al., 2008).
Living Rev. Solar Phys. 8, (2011), 5
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