The existing algorithm used to calculate the bore profile of an object from the measured input impulse response assumes plane wave propagation. The possibility of including the frequency dependence of primary reflections derived from multimodal theory within the bore reconstruction algorithm has been discussed. Projection matrices have been derived which allow projection of forward and backward going multimodal pressure waves across discontinuities and cylinders. Deducing the cross-section changes is complicated by the frequency dependence of the reflections, even when the forward and backward going waves are known from multimodal calculation. This problem is an area suitable for further work. A large increase in computational load is another problem.
An iteration procedure could be an alternative option. The multimodal impedance method could be used to calculate the input impulse response of the bore profile obtained by the plane wave bore reconstruction. Comparison with the actual measured input impulse response would then give a useful estimate of the error in the bore reconstruction calculated using the plane wave algorithm. The bore could then be corrected to compensate for this difference and the process of correction repeated iteratively until a bore is obtained for which the input impulse response agrees with that measured experimentally.