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I have been examining stripmap SAR algorithms, mainly Range Migration Algorithm. When I check the textbook examples so far I always saw the data trajectory is larger than scene that is observed. An example from Melvin, Scheer et. al page 309. RMA

As you can see, the platform trajectory roughly travels -20 to 20 and scene is half of it. Similarly, if you check this RMA implementation, this RMA Matlab implementation from the book "Spotlight SAR" by Carrara et. al., you can see the along-track axis of the reconstructed image is actually some subset of trajectory points. Just like the case above.

My question is, what happens in the opposite scenario? For instance in image above, we travel a small distance [-5 to 5] and try to produce, maybe not so precise, the image of the scene [-10 10]. If our antenna does not have high directivity, we should also able to get reflections from targets that are not directly in front of the antenna, but how we should map the frequencies in RMA?

I know that in Stolt mapping of RMA, we shift and strech each azimuth column, but in that case I should retrieve more azimuth columns than I have.. I don't know, if there is a such imaging type in SAR literature, please refer me to correct terminology, I am new to that area so I might be missing correct nomenclature.

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It's so that the cross-range (along-track) resolution is consistent for all targets in the scene. There is no reason why you could not use the flight path between [-5,5] to form the same size image. However, in that case, the targets on the edge of the scene will have been illuminated for a smaller angle than the targets in the middle of the scene, which will given them a smaller region of support in the frequency domain and, hence, a coarser resolution.

When choosing the first and last sensor locations that are used to form the image, it's common to select the first point to be that where the beam first enters the imaged scene and the last point to be when it leaves it. Picture the footprint of the beam on the ground as the sensor flies by; it's usually an oval or cone or something like that. At -20 is where the edge of the oval (or whatever shape it is) begins to intersect the imaged scene. At +20 is where it stops intersecting it.

I should add that, in general, the size of the imaged scene is limited only by the PRF of the sensor.

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  • $\begingroup$ Thanks for the answer, I was expecting such an answer. Indeed, when I simulated such stuff using backprojection algorithm I saw fine details when antenna is close to scene and blurry images when far away. However, I am having hard time figuring out how to do this in RMA. In that algorithm shift and scale every range column, which gets converted to a cross-range column in the image. But in this example basically I have less columns in azimuth than the one in the scene. How can we re-map this.. Can you help me on that? I.e. should we determine kx vector before Stolt interpolation? $\endgroup$ – tokmaklarim Feb 25 at 18:38
  • $\begingroup$ I am not sure I follow. You have less columns in azimuth than the one in the scene? Can you rephrase that? $\endgroup$ – AnonSubmitter85 Feb 25 at 18:51
  • $\begingroup$ Sorry, I will try to be clearer. I have assigned to produce SAR images with a mmWave radar (automotive radar). In this scenario I am able to send pulses at every 0.5mm as the speed of the platform is low enough. But in current hardware there are silent periods for sending data, synchronizing etc. So I have regular around100 pulses 0.5mm spaced and no pulses in next say 10cms.. I am trying to figure out can I produce healty images at least, sub-images from regularly spaced pulses $\endgroup$ – tokmaklarim Feb 25 at 19:53
  • $\begingroup$ I am so sorry, I just started working on this problem and since I am just getting into the terminology, I have no clear idea of stuff I am doing, I wanna be doing and I should have be doing.. $\endgroup$ – tokmaklarim Feb 25 at 19:55
  • $\begingroup$ So what is the issue exactly? From what you said above, you have 100 regularly-spaced pulses and you want to form an image from them using RMA. Is there some reason why you cannot? $\endgroup$ – AnonSubmitter85 Feb 25 at 20:54

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