Tomography and triangulation

Many earlier experiments have used multi-station measurements combined with triangulation techniques to estimate the height of the aurora (Section 1.1.1). Computer Tomography (CT) has its most well-known applications in the field of radiology^6.2 [Cormac, 1963a; Cormac, 1963b]. A similar method was applied by Solomon et al. [1984] to estimate the airglow distribution as measured by space-borne photometers. An emission distribution was characterised by Jones et al. [1991] by using data from a rocket and three ground-based scanning photometers. Na and Lee [1991] estimated ionospheric electron densities from radar measurements by the use of tomographic methods. McDade and Llewellyn [1994] presented methods to estimate airglow distributions from limb-scanning satellite measurements. By the use of image data from two monochromatic TV-cameras in Antarctica with a separation of 20 km Aso et al. [1990] studied the auroral emission distribution in slices.

Methods, initial studies and simulations

One primary scientific objective of ALIS was to provide the possibility to reconstruct the 3D auroral volume emission by applying tomographic inversion techniques on spectroscopic high-resolution images of aurora, airglow and related phenomena [Steen, 1989]. An initial study based on simulated ALIS-data was performed by Gustavsson [1992]. Later, the problems of auroral tomography were discussed during an auroral tomography workshop in Kiruna [Steen, 1993]. A more detailed model simulation study [Gustavsson, 1998] concluded that the capability to achieve results with acceptable horizontal and vertical resolution, exists. This paper also suggests a useful way to define a stopping criteria for iterative tomographic methods by combining adaptive low-pass filtering and feasibility tests, and concludes that ``it is possible to achieve feasible reconstructions with the modified Multiplicative Algebraic Reconstruction Technique (MART).'' An introductory overview of ground-based tomography, including a further investigation of resolution and error sensitivity is presented in Gustavsson [2000, Chap. 3] concluding that ``the result of the tomographic inversion cannot retrieve fine scale internal structures. However, estimates of the spatial distribution of ionospheric emissions which, in general, have a comparatively simple shape, can be accurately obtained''. The chapter also presents a strengthening of the statistical stopping criteria of Veklerov and Llacer [1989].

Summary of results from computer tomography of ALIS-data

At an early stage a close scientific and technical collaboration was established with colleagues at Kyoto University, and later at the National Institute for Polar Research (NIPR), Tokyo. During a joint campaign (ALIS-Japan 1) held in March 1996, the first results of auroral tomography were obtained as reported in Aso et al. [1998a]. At this time ALIS had only three imagers, and two additional intensified CCD-cameras were provided by our Japanese colleagues [Aso et al., 1993; Aso et al., 1994], resulting in a total of five imaging stations. A modified MART was used for tomographic analysis, presenting initial results of tomography for a folded arc, and a double-arc system [Aso et al., 1998a]. An auroral model with a folded arc is also discussed in this paper.

In Aso et al. [1998b] initial results and model comparisons using a modified version of a Simultaneous Iterative Reconstruction Technique (SIRT) [Gilbert, 1972] were applied to data from the March 1995 ALIS-Japan 1 campaign. The method was also verified by numerical simulations. An auroral fold occurring at 23:40:30 UTC on 26 March 1995 was selected for testing the tomographic analysis with the modified SIRT method assuming magnetic field-aligned auroral structures. Projecting back the reconstructed volume onto the original images reveals a disparity of about $10$% or less. The modified SIRT method was found to be a promising CT application in the field of auroral studies. In total, four joint ALIS-Japan campaigns have been undertaken so far, and some of these data are still in the analysis phase.

Aso et al. [2000] reports on tomographic analysis of auroral images by the modified SIRT method. Auroral images were obtained on 9 February 1997 at 19:46:00 UTC in the $O(^1S)$ 5577 Å emission line as well as at 18:31:30 UTC in the $N^+_{2}$ 1Neg. 4278 Å emission line. The latter case showed a bright folded arc south of Kiruna and a faint thin arc north of Kiruna. The peak height of the intense aurora appears lower than the faint arc. Given favourable conditions for auroral tomography, it is possible to study the basic auroral formation process. To demonstrate this Aso et al. [2000] also performed a numerical simulation for the reconstruction of a slightly folded auroral structure using data from seven stations. Furthermore, the authors report on initial triangulation results applied to the studies of nacreous clouds. Some more reports of ALIS observations of nacreous clouds are summarised in Section 6.6.1.

Triangulation and tomography-like methods were applied to the studies of HF pump-enhanced airglow (Section 6.4). A solution to the inverse problem for a particularly ill-posed problem, with data from only three stations south of the emission region, is discussed in Gustavsson et al. [2001a].

In Gustavsson et al. [2001b] a constrained tomographic inversion was used to estimate the $N^+_{2}$ 1Neg. 4278 Å altitude distribution, which allowed an estimate of the energy distribution of the electron flux (Section 6.5.1).

This section has provided a rather brief summary of a very large subject. For further, more detailed studies, the reader is encouraged to read the cited papers, and, in particular, the main reference for three-dimensional imaging with ALIS by Gustavsson [2000].

Future developments to be expected in this field include the investigation of smooth basis functions and approximated projection algorithms for faster tomography [Rydesäter and Gustavsson, 2001].