AURORAL TOMOGRAPHY
The background
Tomography ( from greek: tomos cut, slice ) is a the methods to determine inner structure from measurements made from the outside. One of the purposes with ALIS is to determine the full 3D spatial structure of the aurora
It is obvisiously so that the intensities in our images are weighted integrals of the volume emissions along a ray for each pixel that makes the image:
It is not equally obvious how to determine the volume emission intensity I(x,y,z) from a set of images that are the result from a measurement with ALIS stations. In 1917 Radon showed that it is possible to exactly determine the function I(x,y) from projections:
provided that:
is known for l > 0 and 0 <= theta < 2*Pi. Tomography for ALIS is a task in three-dimensional space but there exists a similar lemma that states that provided that You have projections g(l,taeta,fi) for all taeta and fi and l is a curve such that all planes through all (x,y,z) where f(x,y,z) is nonzero cross l.
With the current ALIS setup we are far from fullfilling the above requierments, so we have to settle for the best possible solution for the emission intensity I(x,y,z), which means some restrictions on the spatial resolution. The current method to solve the inverse problem is a modified Algebraich Reconstruction Technique an itterative method that changes the volume emission rate to minimise the deviation between the measured images and the projected images from the reconstructed estimate of the volume emission. Then the itteration is stopped as soon as the deviation between the measured images and the projected images from the reconstruction can be considered as stochastical variations arising from the underlying physical processes that caused the emission and model the imaging.
Bjoern Gustavsson Last modified: Thu Oct 24 13:07:11 UTC