Reconstructed Potential Functions in Bounded Domain Vector Tomography
نویسندگان
چکیده
The tomographic imaging of vector elds on bounded domains is considered. Reconstruction formulas for the probe transform are rst shown to be valid on bounded domains. It is then shown that potential functions reconstructed from these formulas include a component that arises from the harmonic component of the vector eld, which is due to boundary conditions alone. Closed form expressions for the harmonic eld contribution to the reconstructed scalar and vector potential functions are derived. The harmonic component is not imaged equally into the irrotational and solenoidal elds, as had been previously speculated, but contributes unequally as a function of both the boundary shape and the vector eld values deened on the boundary.
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