I don't really understand, perhaps I have missed some vital point.

The input is a standard sine wave, stepped to test each frequency?

The measurements are amplitude and phase at each known distance Xn?

The plane wave tube has a limit below which it cannot support a transverse mode.

Are the Xn sufficiently small that you measure within the near field of some evanescent wave caused by wave front non flatness?

If not then...?

Seems relevant to the thread topic but if this is obvious to everyone else then sorry, perhaps you could spare Earl the trouble and explain it to me.

Best wishes

David

One could use a sine wave, but that would be inefficient since we would want to know how the curvature varies with frequency. I would use a broadband signal and something like HOLM to find the transfer function for all frequencies. In a PWT, there is no need for a window, so there is no LF limit.

The transfer function is complex so yes both amplitude and phase are measured.

There is a cut-off effect for a PWT below which only evanescent wave will propagate, but these waves still contain the information necessary. To what extent one can get good resolution of the curvature from the evanescent wave will be determined by the numerics and the SNR in the measurements. This is an implementation problem, not a theoretical one. But remember that there is also a cut-off effect for the waveguide itself so the evanescent modes will not propagate in the waveguide either, making them less of an initial right off the bat.

Location of the "ideal" measurement points would need to be investigated, but I would say that, in general, one would want to be in the near field of the device, at least as it exists inside of the tube.

By rotating the driver on its mount, the first rocking mode - probable one of the most significant - could be determined. More rotations than just three, would allow for even higher non-axi modes to be determined.

The math and the calculations are not easy, but certainly doable.