Even the simplest problem of monochromatic scalar absorption tomography becomes non linear when the source and detectors elements are no longer treated as points. This has variously been described as non-linear partial volume effect or exponential edge effect. We show that the nonlinearity is significant in practical fast tomography systems such as the Bergen gamma tomography system used for inspection of flows in pipes. We describe an iterative reconstruction algorithm for reconstruction using this model and present numerical results. Other non- linear problems arise in rich tomography methods and as a simple example we describe the non-Ableian problem of neutron spin tomography used for imaging magnetic domains.
A high-speed motionless-gantry x-ray CT machine has been designed to allow for 3D images to be collected in real time. By using multiple, switched x-ray sources and fixed detector rings, the time consuming mechanical rotation of conventional CT machines can be removed. However, the nature of this design limits the possibility of detector collimation since each detector must now be able to record the energy of x-ray beams from a number of different directions. The lack of collimation has implications in the reconstructed image due to an increase in the number of scattered photons recorded. A Monte Carlo computer simulation of the x-ray machine has been developed, using the Geant4 software toolkit, to analyse the behaviour of both Rayleigh and Compton scattered photons when considering airport baggage and medical applications. Four different scattering objects were analysed based on 50kVp, 100kVp and 150kVp spectra for a tungsten target. Two suitcase objects, a body and a brain phantom were chosen as objects typical of airport baggage and medical CT. The results indicate that the level of scatter is negligible for a typical airport baggage application, since the majority of space in a suitcase consists of clothing, which has a low density. Scatter contributes to less than 1% of the image in all instances. However, due to the large amounts of water found in the human body, the level of scatter in the medical instances are significantly higher, reaching 37% when the body phantom is analysed at 50kVp.