Tomographic Imaging of Vector Fields

In the last decade or so several papers have introduced and developed the area of tomographic imaging of vector fields. Johnson et al. [1] began the investigation by studying the imaging of flow fields using acoustic time-of-flight measurements. In this measurement, the time of flight is influenced by the component of the field in the direction of propagation, and is not influenced by the orthogonal component. This type of measurement is called a longitudinal measurement. Norton [2] concluded that longitudinal measurements allow the reconstruction of the solenoidal (divergence-free) field component, but not the irrotational (curl-free) component. He suggested using boundary measurements to reconstruct the irrotational component. Braun and Hauck [3] then discovered that a new type of tomographic measurement called the transverse measurement (sensitive to the orthogonal component of flow) allows one to reconstruct the irrotational component without boundary measurements. Prince synthesized these discoveries and extended the results to three dimensions in [4]. New algorithms for reconstruction using convolution backprojection have also been proposed in [5].