Boundary conditions involving acoustic pressure waves and their normal derivatives are used to develop an acoustic imaging criterion. This criterion is actually a testing procedure which operates upon the sum of the incident and reflected acoustic waves associated with reflection from an unknown acoustic boundary. One of the outputs from this procedure is used to reconstruct the unknown acoustic reflector while a second output from this procedure estimates the acoustic wavespeed on the opposite (transmission) side of the boundary. The calculation of the reflected acoustic wave as a function of spatial position and temporal frequency (which is a prerequisite for applying the testing procedure) is analogous to the downward continuation calculation used in conventional migration of seismic data. After using some simple examples to demonstrate the concepts involved in this procedure, the method is applied to computer generated synthetic data.