Nonlinear problems in fast tomography

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.