Abstract
The notion of the adjoint operator/field is introduced, and its general importance in physical sciences briefly discussed. The applications of the adjoint in the solutions of inverse scattering problems for plane-wave excitation are overviewed for both obstacles and inhomogeneities. The method is then illustrated by applying it to a specific problem, namely the volume reconstruction of an acoustic object by inverse scattering. Calculations of noise propagation from the data to the reconstructed image in inverse scattering using the adjoint field algorithm are presented. These calculations are then specialized to the case of Born approximation. Finally, the similarities and differences between inverse scattering and X-ray tomographic covariance are pointed out.
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