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Comment by derstander | Hacker News Reader

> I always wondered why most explainations of SAR take the frequency-domain approach of describing it in term of Doppler resolution instead of explaining the process of aperture synthesis in the spatial domain in terms of a sum of phase delayed signals.

A time-domain backprojection based approach as opposed to one of the Fourier Transform based approaches? My guess is that because you don’t see the backprojection based approaches much in real-time systems (at least I haven’t seen any). That might change as they’re easily parallelizable in comparison. So any conceptual understanding between a time based approach and a real-time (FFT based) implementation is a little harder to transfer.

Like you, I also find the time-based backprojection approach more conceptually straightforward and satisfying, though.

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Indeed I mean the time domain (or better yet, "space domain" backprojection. Besides being it easier to justify, it's easier to connect to the principles of other imaging system and it's much easier to generalise to non-linear geometries or even tomography, while if you operate in the frequency domain you need to perform all sorts of approximations to perform the FFT when you acquire samples on a non rectangular grid

All of what you said is true.

Yes: compensation is needed to account for non rectangular sampling (see the Polar reformat or the Stolt interpolator). Yes: non-straight and level flight paths result in degraded or even useless imagery unless the deviation is small or the FFT-based algorithm is specifically tweaked for it. Yes: various algorithms make assumptions that may be violated (e.g., planar wavefronts).

But again, I think it’s just the computational efficiency of the FFT-based algorithms for real-time use.

As a random thought, a lot of radar engineers that don’t start with SAR are perfectly comfortable reasoning about Doppler. Particularly with regard to detection of moving targets. Maybe that’s a factor, too.

I think you are right, and it seems the frequency domain aspect could also have won for historical reasons: the first "SAR" systems were effectively performing doppler beam sharpening by passing the output of a conventional radar through a filter bank and mapping the output of each filter to an off-track angle. But again, when I first got introduced to (modern) SAR I found the explanation through Doppler shifts to be more confusing and less physically understandable than a purely geometric approach

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