[danaliv]

I don’t understand this at all. Is there a side-by-side comparison of radar and visible wavelength somewhere? Or maybe a version of the geometric diagrams with example objects and the imagery they’d produce?

EDIT: Ok, after Googling this a little I think I get it. The skyscrapers are upside-down. (I think?) The radar is measuring slant-range distance, and due to the viewing angle, the tops of the skyscrapers are closer to the radar than the bases. So the tops of the buildings are closer to the bottom of the image.

Since the skyscrapers are in the “wrong” place in the image, they get blended with ground features that are in the “right” place.

Is that right?

[aimor]

You have the right idea. It can also help to think of it as a projection problem.

The image is displayed as if it were taken from a camera directly above the ground, but the radar is actually located at some other location. In order to create the image an assumption is made that everything is located at the same height. So when something like a skyscraper is actually hundreds of meters above the ground, the radar detections from that object are projected to the wrong location in the image. The term to look up is "foreshortening".

This is similar to (but not exactly) what happens when aerial photography is used to make maps. Building in Google Maps get flattened and the roofs are translated to someplace other than where they should be.

What also helps is to look for "shadows" in the SAR imagery. The shadow tells you where the radar is located. From that you can intuit what side of objects the radar is actually seeing.

A great example used in textbooks is this image of the Washington Monument. You can tell from the shadow that the radar is located to the north^. So even though it looks like you're seeing the south side of the monument, the image is actually showing the north side. The north face of the monument has been projected onto the ground in the direction of the radar. http://image.slidesharecdn.com/radar-2009-a18-synthetic-aper...

So looking at the Tokyo image again. The tree shadows are south of the trees, so the radar is located to the north. The tops of the skyscrapers are closer to the radar than the bottoms, so the tops of the skyscrapers will be shifted to the north towards the radar. However, because the radar is located to the north, what we see is actually the north side of the skyscrapers. The false perspective makes it seem like we should be seeing the south side of the skyscrapers, but that's an illusion.

^ I'm just assuming that "up" is north.

[Jach]

You can build your own SAR system pretty easily, but of course the really cool stuff results from being able to fly a plane or in this case have some satellites. The PDF for Experiment 3 here https://ocw.mit.edu/resources/res-ll-003-build-a-small-radar... shows an example of using a weak 2.4 GHz system on the ground taking snapshots every two inches for 10 feet or so, facing down a road towards a warehouse. A visualization algorithm is overlayed on top of a satellite image to show that the system can at least detect front surfaces. The professor has also built other hobbyist high-frequency systems before, including demonstrating through-wall capabilities for some of them. This PDF (others on his site) has some good examples of what the environment looks like with a camera, and what you get when you process some SAR data with matlab into a 2D image: http://glcharvat.com/website%20pdfs/Charvat_MIT_Haystack_DIY...

[gaudat]

There is a proper-looking scan of high-rise buildings in the linked SAR 101 article: https://capellaspace.wpengine.com/wp-content/uploads/2020/02...

See how only the 2 near sides of the buildings got imaged. The skyscrapers in that Tokyo image only have the 2 far sides imaged.

So I guess the image was acquired upside-down on the satellite. The team fliped the 2D image and called it a day.

Now if Capella can release raw range information of their scans and let us play with it...

[srtjstjsj]

That a much better explanation than the OP article.

It's like an isometric view of a video game. (But not exactly, since the angles are different)

A tall thing and a lower thing nearby it are protected onto the same spot. (Usually in a video game the tall thing blocks the behind thing, instead of blending with it.) Blending the two images makes the front-looking thing look transparent, when in really you are seeing around one object (since the observation angle is not the same as the imaginary viewing angle of the image) and then drawing both objects in the same pixel.

[galangalalgol]

Yes, and you said it much better than the article.