A method for reconstructing the complex index of refraction of a bound
ed inhomogeneous object from measured scattered field data is presente
d. The index and the unknown fields within the object are simultaneous
ly reconstructed in an iterative algorithm. The method is a refinement
of earlier work which incorporates a more effective way to update the
unknowns at each stage of the iteration. Considerable efficiency in t
he algorithm is achieved. Some numerical examples are given indicating
the limits on the contrasts which can be reconstructed. These limits
show that the range of contrasts that may be reconstructed is extended
over that achievable with the earlier work.