# Image Reconstruction

In order to interrogate the internal composition of shielded containers via the Coulomb scattering of cosmic-ray muons, knowledge of the muon path through the volume is essential. Once the space points are reconstructed in each of the four tracking modules (illustrated opposite), the incoming vector (denoted **A**) and the Coulomb-scattered vector (denoted **B**) are determined. These are projected into the voxelated (split into small, virtual elements) assay volume and their **P**oint **o**f **C**losest **A**pproach (**PoCA**) and the corresponding *voxel* are identified.

Within this voxel, the *scattering density* λ of that muon can be stored. This is calculated in the 2D (x and z directions only) example above as:

where θ_{x} is the scattering angle in the x direction, L_{1}+L_{2} is the 2D pathlength of the muon through the volume, and p_{0} is the normalised momentum of the muon as it enters the system. After many muons the average λ value in each voxel can be used to form an image.

For the imaging results published by this project, this simplistic method outline above has been extended to include sophisticated likelihood-based techniques.