For the past three years, I've been on-and-off building an ultrasonic 3D scanner using an active phased array emitter. Just had the first successful results.
It images its surroundings by sending an ultrasonic wave train in a specific direction and listening for the echos. Linked to some photos in a first comment.
Currently, I'm just plotting in 3D all the points for which the intensity of the received signal is above a threshold. The problem with that is that my beam is large (a dozen centimeters at two meters, see my comment below) so one small detail of the scene gets a larger 3d representation because the beam is large. The scan looks like a blurred image.
I know this problem has already been solved. If I understand correctly, SAR radars create very long and blurry images of the ground from a satellite and then use an algorithm to "unblur" them. I guess that the blurred image my sonar generates is a sort of convolution of the scene that could be represented by a matrix, and that I just have to find the right inverse matrix, convolve it on my results to get a good image back.
I can't find any good and intuitive explanations on devoncolutions/sar algorithms. The only ressources I found are research papers of which I have trouble reading the maths and fail to apply to my own use case (I'm a 19yo in a French preparatory school, so I've only been doing real maths for 2 years).
How could I solve that problem? Am I completely misled to think that it's possible? (maybe the "blurring" transformation is irreversiblei.e. losing too much information)
Proper imaging requires keeping track of phase information, so you measure the distances more precisely.
It appears you're using 40Khz ultrasound transducers, so the wavelength should be about 8mm. You might want to try using less phase shift of the beam to tighten up the volume you're sweeping, and do it slower.
Try suspending a hard solid round object from 3 threads, and see how that responds. It should give you an idea of the "impulse" response in 3 dimensions, and thus a clue as to how to de-convolve the data.
the device and a few things I scanned - myself and the room I'm working in: https://imgur.com/a/kxSTn2J
gif of my beam: https://imgur.com/a/mLAhT2h