The geometrical design of a CT scanner is relatively simple. As already described in the preliminary remarks on CT in Sects. 3.3 to 3.6, the development stages can be divided into four generations. Two of these generations – the first and the third one – are particularly interesting. The first generation – the pencil-beam concept – exactly reflects the Radon reconstruction process, since parallel beams define the slice plane (cf. Fig. 7.1, middle and right side). The second generation is just a temporary intermediate developmental step toward the third generation, the fan-beam concept. The third-generation scanners (Fig. 7.1, left side) are those most frequently implemented to date. For this reason, the focus of this chapter will be on the reconstruction mathematics based on fan-beam geometry. The fourth generation is again a stage of evolutionary progress that has not yet been frequently implemented. From a mathematical point of view, this generation is identical to the third generation and will therefore not be considered here separately. The fast backprojection methods will not be considered here either. A good summary on modern reconstruction methods is given in Ingerhed (1999).
KeywordsAttenuation Eter Convolution Radon Sine
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