TOMOGRAPHIC RECONSTRUCTION OF VECTOR-FIELDS

In this paper, the application of tomography to the reconstruction of vector fields is considered. Two different types of interaction between the radiation used for measurement and the investigated vector fields are discussed. As an introduction, the inverse transform for scalar quantities is outlined. Its extension to the reconstruction of vector fields is then discussed. It turns out that a complete reconstruction of a vector field can only be obtained if measurements based on both types of interaction are available. Otherwise, only curl-free or source-free components of the field can be reconstructed. In the case of nonhomogeneous boundary conditions, additional harmonic field components occur. Some experimental results are presented showing the reconstruction of flow velocity fields based on ultrasonic time-of-flight measurements.