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Ask HN: Help on SAR/deconvolution for an ultrasonic phased array radar

7 points by belzebalex ↗ HN
This is as much a Ask HN as a Show HN of my first results:

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)

6 comments

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mikewarot
Do you physically move your scanner? If so, how do you measure displacement accurately? Synthetic aperture requires a moving scanner, which it doesn't see you are doing.

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.

belzebalex
The scanner is fixed, but the beam is moving. In a synthetic aperture, the beam is fixed but the scanner is moving, which should be equivalent for a first approximation. A "dot" like a hard solid round object returns a cardinal cosine in two dimensions centered on the object.

I don't understand. Having more points by using smaller phase-shifting steps won't make my beam narrower?

mikewarot
If your array is phase coherent, your maximum resolution is going to be about 1/4 wavelength end to end, as an angle. Estimate 2mm for that 1/4 wavelength, and 200mm end to end on the array, the angle should be about 1/100 radians, or about 40 minutes of arc, if everything is working perfectly.

Synthetic apertures start with phased arrays, such as yours, but take data from multiple positions, which are then correlated into virtual focus. If you were to attach your array to a board, butted up against a yardstick fixed to the desk, to keep the direction stable, you could move it sideways in 1cm intervals and collect enough data to do synthetic aperture, without spending a ton of money. 8)

belzebalex
Where is this 1/4 factor coming? I know that for a circular dish, the max resolution is 1.22lambda/(aperture size), so for my scanner it would be (1/4)lambda/(aperture size)

Scanner is 100mm large, so that would do 2/100 radians. Will check up if that matches my simulations.

Thanks for the infos on SAR! Will try doing that!

mikewarot
>Where is this 1/4 factor coming?

Guesswork... 40khz ultrasound has a wavelength of about 8mm. If your phase from end to end isn't at least 90 degrees, you don't have enough shift to form a beam with. I would imagine if you're clever, and your transducers don't drop off to fast on the sides, and you've got them fairly tightly constrained in X,Y,Z to a regular grid, you might be able to tweak out more resolution slightly off center, because the return phases will more quickly diverge as this angle increases.