During my time as a PhD student at the Physics of Medical Imaging group at KTH, I have taken part in the work of developing a photon counting spectrally resolved silicon detector for clinical computed tomography. This work has largely motivated the direction of my research, and is the main reason for my focus on certain issues. Early in the work, a need to quantify and optimize the performance of a spectrally resolved detector was identified. A large part of my work have thus consisted of reviewing conventional methods used for performance quantification and optimization in computed tomography, and identifying which are best suited for the characterization of a spectrally resolved system. In addition, my work has included comparisons of conventional systems with the detector we are developing. The collected result after a little more than four years of work are four publications and three conference papers. This compilation thesis consists of five introductory chapters and my four publications. The introductory chapters are not self-contained in the sense that the theory and results from all my published work are included. Rather, they are written with the purpose of being a context in which the papers should be read. The first two chapters treat the general purpose of the introductory chapters, and the theory of computed tomography including the distinction between conventional, non-spectral, computed tomography, and different practical implementations of spectral computed tomography. The second chapter consists of a review of the conventional methods developed for quantification and optimization of image quality in terms of detectability and signal-to-noise ratio, part of which are included in my published work. In addition, the theory on which the method of material basis decomposition is based on is presented, together with a condensed version of the results from my work on the comparison of two systems with fundamentally different practical solutions for material quantification. In the fourth chapter, previously unpublished measurements on the photon counting spectrally resolved detector we are developing are presented, and compared to Monte Carlo simulations. In the fifth and final chapter, a summary of the appended publications is included. / <p>QC 20150303</p>