Hi Bradley,
I recently got to testing my function that extracts the Fourier components of the received pulse. In my linear simulation (2D, 3D) i transmit with a circular transducer and receive with a circular transducer. I was curious what conditions give me the best fit to the predicted analytical profile of the fundamental and also how i should analyze the received signals (specifically the Fourier transform). I was wondering if you could give me few tips? I have a couple of questions below.
1) When I look at some simulated data of the pressure fields in publications (e.g. demonstrating the diffraction pattern), i wonder if they analyze the whole signal (with the edge wave or without it?). If the pulse is short enough these components can be separated.
In my case, analyzing the central part of the first signal gave decent results, however, the fundamental profile is still somewhat far from the theoretically predicted one, even though i can see the main crests and valleys. On the other hand, If I give the whole signal to the Fourier function in matlab, the profile is much sharper, shows a very nice shape correspondence to the prediction, but, strangely, has a lag in it. Do you have an idea why this lag could occur? And when analyzing the received signal at a sensor point, would you advise selecting a part of it? Or taking the whole thing with/without the edge wave in the analyzed signal?
2) Another observation is that a shorter pulse gives a sharper fundamental profile, very close to the theoretically predicted one. I suppose that makes, sense since then we have better resolution. However, when the diffraction correction integral is derived, i never saw a mention that it can depend on the number of pulses in the sent signal. I suppose they assume a delta plane wave pulse? Do you perhaps know works when the number of cycles is also accounted for when deriving the diffraction pattern?
P.S. even for the 1 cycle pulse simulation the pressure profile is somewhat lagging for a small receiver, compared to the analytical solution. I was wondering if any comparison has been performed in you publications between the solutions offered by k-wave and the analytical solutions for the fundamental (Rayleigh integral or with the multigaussian beam model) for plane piston circular transducers?
Thank you in advance!