[mturmon]

Alas, the above comment is quite mistaken. The microwave reflection from sunlight is too faint to detect. All the information shown comes from the radar beam from Goldstone.

The radar imaging process is complex, but suffice to say the shown "image" is not in physical coordinates. If it's a conventional radar image, the vertical coordinate of the shown image is "delay" (distance from observer). And also conventionally, the horizontal image coordinate is "doppler", which is the doppler shift given to the returned signal by the rotating asteroid.

So, stuff on the left side of the image was moving away from the observer, and stuff on the right side was moving towards the observer. And of course the brightness is essentially the "amount of stuff" at that delay-doppler locus.

The reason we can't plot an "image" in physical coordinates, and have to be content with the altered coordinates, is that all we get from the returned radar carrier signal is a delay, and a doppler shift. That's it - "delay-doppler" coordinates.

So any set of sites on the asteroid surface with the same distance and the same relative velocity (w/r/t the observer) will be binned into the same place in the radar image. There is no guarantee that these sites are near each other, and for complex geometries (rough asteroids), they often will not be.

If you want to get a real image in physical coordinates, you have a separate inversion problem to solve, and you'll probably need more images and some model constraints.

For much more, see this paper (http://mel.ess.ucla.edu/jlm/publications/Ostro02.AsteroidsII...), and in particular, see around Fig. 1, Fig. 4 (especially), and Fig. 6.

[hahajk]

Eh, your explanation makes it sound like the radar "image" is as divorced from physical coordinates as a spectrogram or a bar chart. Radar images are at least phyicalish... the asteroid does look similar to the image in real life. Doppler and range do roughly map to x/y. I hear it alot with SAR imagery as well - that we're not looking at a "physical representation". We are - there are just different anomalies to account for.

[mturmon]

I’d agree partway, and I appreciate the counterpoint, in that the delay coordinate is simple. But Doppler for a rotating, irregular asteroid is not simple. See Fig. 1 of the paper I linked for an example. It really is many-to-one.

Delay-Doppler for planar surfaces, like a remote sensing radar zipping along Earth’s surface, is pretty straightforward, as you note…and we get to set up the system parameters, like beam width, pulse rate and ground speed, so it works out nicely.

[derstander]

I'm not at all plugged into astronomy, though I have worked in radar for quite awhile.

Can you comment at all why a technique like Inverse Synthetic Aperture Radar (ISAR) is not used? That relies on the rotation of an object to generate cross-range resolution through sampling a diverse set of aspect angles (and is certainly useful for non-uniform, non-planar surfaces). If the rotation rates of the asteroids are known, then that minimizes one of the main challenges in forming quality ISAR imagery. For the use-cases I'm familiar with, we need to estimate the rotational motion because vehicles do unfortunate things like accelerate and turn while we're trying to look at them -- the nerve! And ISAR has certainly existed before the paper you linked in another comment was written (and also before the previous study the paper itself references).

As a side note, that paper by Ostro et al. is very interesting to me; it's like being familiar with Leibniz's notation for calculus and seeing something written using Newton's notation (or vice-versa). I skimmed the references and all of the ones I saw seemed to be from astronomy / astrophysics sources. It's almost as though we have two fields using similar methodologies to look at different objects that don't seem to talk at all and have developed different dialects.

Edit: maybe delay-Doppler imaging is akin to ISAR, like medical tomography and SAR were shown to be mathematically related?

[mturmon]

I know something about SAR and InSAR because I use radar (Earth) remote sensing in my day job, and I have a signal processing background. But I’m not a serious radar expert.

ISAR sounds like its operating principle is the same as the radar imaging technique used for these asteroid results. In general, it’s all radar imaging so you get reflectances in delay/Doppler coordinates as your observable.

One possible difference is the poor SNR of the asteroid problem — you have to average many radar images to beat down the noise. The velocity of the scattering elements on the asteroid is assumed to be the same across all these images (as far as I know). (After correcting for a known offset due to the Earth’s changing motion.)

This seems to be a little different than the ISAR “swaying boat” type of application in which the body is indeed accelerating and your radar image must be adjusted for that, or else the mast of the swaying boat will smear across the image.

It may also be worth saying that there is no synthetic aperture in the OP - it’s a physical aperture.