1 Introduction

Stereoscopy (from Greek stereos = solid body and skopein = to see) includes a variety of methods to enable or enhance the depth perception that leads to a three-dimensional (3D) view of an object. Our eyes process stereoscopic information automatically when our brain correlates the visual inputs from the left and right eye, at near distances. Astronomical images, however, contain only two-dimensional (2D) brightness distributions, but can produce stereoscopic 3D information from two different aspect angles. Just by taking pictures of the night sky six months apart, we have a baseline change of two astronomical units (AU) and can triangulate the distance to the nearest stars that show a stereoscopic parallax with respect to the distant stars with no parallax. Here we are concerned with solar imaging, which can be stereoscopically processed by using either the solar rotation to change the aspect angle (≈ 13° per day) or multiple spacecraft that are spaced some significant fraction of 1 AU apart. The prime solar-dedicated space mission that is designed to exploit stereoscopic information to the fullest is the Solar TErrestrial RElations Observatory (STEREO) mission, launched in 2006. Solar stereoscopy became an important part of 3D geometric and physical modeling of solar dynamic phenomena, but still presents formidable challenges to construct detailed 3D models from two (or three) aspect angles only.

Tomography (from Greek tomos = cut, slice and graphein = to write) is a related 3D reconstruction method that uses images (or slices) from many aspect angles. Practically, tomography is accomplished by 2D imaging of different sections through a penetrating (X-ray or radio) wave, used in medical radiology, archeology, biology, geophysics, oceanography, material science, and astrophysics. Applications in solar physics include 3D reconstruction of the optically-thin plasma in the solar corona or in coronal mass ejections, using soft X-ray and extreme-ultraviolet (EUV) imagers or white-light coronagraphs. The solar-dedicated STEREO mission carries a set of coronagraphs onboard that can map the coronal plasma from two different directions, which represents a kind of minimum tomography. Alternatively, the solar rotation can be used to provide many slices from different viewing angles, but tomographic reconstruction is then challenged by dynamical changes during the observing period. 3D reconstructions inside the Sun (helioseismic tomography) or in the heliosphere, such as interplanetary coronal mass ejections (CMEs) or the solar wind, are not covered here.

In the following review we cover first the history of solar stereoscopy, which includes solar-rotation based stereoscopy, single- and multi-spacecraft stereoscopy in the pre-STEREO era, as well as a brief description of the STEREO mission. In Section 3 we describe the stereoscopic and tomographic methods that have been developed and applied to solar data. In Section 4 we provide applications of the methods described in Section 3, i.e., a systematic description of stereoscopic and tomographic observations of phenomena in the solar corona (active regions, flares, filaments, prominences, CME source regions, CME-triggered global waves). In the final Section 5 we summarize the main scientific results that were or could be obtained from stereoscopic and tomographic data analysis.

There exists no comprehensive review on STEREO results at this time, but STEREO-dedicated Topical Volumes have been published in the following four journal issues: Space Science Reviews Vol. 136 (2008), Solar Physics Vol. 256 and 259 (2009), and Journal of Atmospheric and Solar-Terrestrial Physics Vol. 73 (2011; Srivastava et al., 2011). Some minor reviews that cover partial aspects of solar stereoscopy include coronal regions (Wiegelmann et al., 2009Jump To The Next Citation Point; Aschwanden and Wülser, 2011Jump To The Next Citation Point), heliospheric coronal mass ejections (Howard and Tappin, 2009aJump To The Next Citation Point,b; Tappin and Howard, 2009; Harrison et al., 2009Jump To The Next Citation Point; Mierla et al., 2010), theoretical modeling (Khodachenko and Rucker, 2005; Aschwanden et al., 2008a), and short STEREO mission summaries (Schmidt and Bothmer, 1996Jump To The Next Citation Point; Davila, 1998Jump To The Next Citation Point; Kaiser, 2005Jump To The Next Citation Point; Staedter, 2006; Matthews and Culhane, 2007; Kaiser et al., 2008Jump To The Next Citation Point; Brown, 2009).

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