Tomographic reconstruction of 3-D vector fields

Inner product probe measurements are defined for tomographic reconstruction of 3-D vector fields. General conditions and formulas for reconstruction of an arbitrary vector field are given, as are the conditions and formulas for fields known to be either irrotational or solenoidal. Formulas to extract the irrotational or solenoidal component of an arbitrary vector field using special inner product probe measurements are also developed. It is shown that one set of measurements is required to reconstruct an irrotational field, that two are required to reconstruct a solenoidal field, and that special probes are required to reconstruct the components of an arbitrary field.<>