Muon tomography: from detectors development to inverse problem resolution

This thesis presents the development of Micromegas gaseous detectors for muon tomography. This technique use cosmic muons, resulting from interactions between cosmic rays and the atmosphere to image objects of large dimensions and opacity such as buildings, concrete slabs, volcanoes or pyramids such as the Khufu's pyramid in Egypt. By studying the attenuation of the muon flux through objects, we can access their internal structure. To image such structures and detect muons passing through them, muon telescopes using Micromegas detectors are used. Many efforts have been developed during this thesis to improve the spatial resolution and gas performance of the latter. One of the main goal of this thesis is to image a concrete slab, which dimensions were 2000 mm x 1000 mm x 500 mm. Firstly, a study on the detection of defects in this slab was carried out. Thanks to an algorithm developed during this thesis, a 15 cm wide default can be detected with a 98% confidence level from 4 h of data collection. Subsequently, a two-dimensional feasibility study, in the plan of the slab length, was carried out in order to reconstruct the density map of the concrete slab. To do this, we need to solve what is commonly referred to as the inverse problem: estimating the parameters of an object based on the data collected. Here the density of the concrete slab will play the role of parameters to be estimated and the flux of muons that have passed through the slab and collected by our detectors will play the role of data. After analysing the different systematic problem analyses, we can reconstruct the density of a concrete slab, with a thickness resolution of 125 mm and a length resolution of 437.5 mm, with a maximum relative error of 12%. (author)