When A-Priori Information Cannot Resolve Tomogram Ambiguities

Abstract

The goal of scanning tomographic acoustic microscopy (STAM) is to image unambiguously at least a portion of a 3-dimensional object. In STAM, a source is always on one side of the object at different locations for different projections and a scanning sensor on the other. STAM is a limited angle tomographic system and the scanning does not necessarily pass over an edge of the object. The authors show that under these conditions it is mathematically impossible to compute an unambiguous map of the absolute transmissivity of the layers of interest in the object and that a priori information can often be used to resolve the ambiguities. However in actual practice the variations in the transmissivity may be too small to be discerned.

We demonstrate the existence of these ambiguities with tomographic simulations and show that in some cases we can remove the ambiguities by invoking the a priori constraint that transmission coefficients cannot be greater than unity or by scanning past an edge of the object.

A similar ambiguity exists for phase information within an object. While multifrequency scanning can reduce the effects, it does, of course, come at increased computational cost.