:)
Medical 3D ultrasounds are a thing:
https://en.wikipedia.org/wiki/3D_ultrasound
That doesn't take away anything from how cool this project is though!
The subjects have not been officially published. But here's a scanned copy:
https://www.cpge-paradise.com/Concours2021/PhysPSI.pdf
It's in French though!
But another reason (which would be valid for a resistive load as well) is that anything plugged into the emitter will have its impedance "reflected" to the base.
Even if you're talking about a digital circuit you need to think about transistor biasing. A pure capacitive load on the emitter means no biasing.
One of the ways you could work around this is to have an inductor in parallel with the transducer so it would resonate at the frequency you want https://en.wikipedia.org/wiki/LC_circuit (though not very practical to your case) - but ideally this would go on the collector, not on the emitter
Your 3 transistor solution is ok for the most part. Maybe it's doable with only one transistor but probably would need an inductor and/or wouldn't be too efficient.
(Not the best explanation, but this would require some trial and error and actually thinking a bit about the analog aspects of the circuit)
https://rusneb.ru/catalog/000224_000128_0000488231_19751015_...
-- click on "Skachat' PDF" (second from the top on the left). Unfortunately it is in Russian, not sure whether English translation exists.
This patent seems only for (X,Y) coordinate capture, but the same authors later worked on 3D setups as well.
EDIT: let me know if you need help with translation
https://en.m.wikipedia.org/wiki/Phased_array
Radar is at its simplistic sensing a pulse out and listening for a return. But then the engineers wanted more.. of course home radar would not be really safe.
Cool project by the way.
they definitely aren’t as cheap as Chinese offers but I always found them to be reasonably priced. They manufacture in Germany.
[0] https://en.wikipedia.org/wiki/Phased_array_ultrasonics