Wikipedia's 2021 Suez Canal obstruction links to the Sentinel-1 synthetic aperture radar (SAR) image of the

Traffic jam in the Gulf of Suez caused by the obstruction as seen by the Sentinel-1 satellite

SAR is a rapidly expanding earth observation technology and business model, partly because it can see through clouds and is day/night agnostic. As long as there is enough solar+battery power, local (spacecraft) computing power and bandwidth to the ground it is highly competitive with optical Earth observation for logistics (Where is all the stuff?) and topography (Has the ground risen or lowered a little bit?). See all the answers to How can ICEYE-X1 capture 2D high resolution SAR images in "tens of seconds"? for more, and How (the heck) was coherent synthetic aperture radar (SAR) implemented using photographic emulsion aboard Apollo 17? and How do radio astronomers avoid having their receivers burned out by ground-imaging radar from satellites? for fun.

There are several bright spots in the images; this is probably due to certain configurations of metal surfaces on the ships that either produce specular reflection (glint off of a mirror) or a corner-reflector like effect (the opposite of stealth aircraft shape design).

Question: But why are the star-like artifacts on certain very bright reflections star-like in shape? We see artifacts like this in optical telescopes (like the Hubble (optical) space telescope) with four vanes holding the secondary mirror (for more on that see below), but there are no secondary mirrors or vanes in SAR. What exactly causes this effect?

cropped detail from ESA multimedia via Wikimedia: Suez_Canal_traffic_jam_seen_from_space

ESA multimedia via Wikimedia: Suez_Canal_traffic_jam_seen_from_space

Source and original ESA source

[...] The two identical Copernicus Sentinel-1 satellites carry radar instruments to provide an all-weather, day-and-night supply of imagery of Earth’s surface, making it ideal to monitor ship traffic.

The sea surface reflects the radar signal away from the satellite, and makes water appear dark in the image. This contrasts with metal objects, in this case the ships in the bay, which appear as bright dots in the dark waters.

From What produces all of the small radial striations in this very overexposed image of a star by Hubble's WFC2? (the four big ones are from the vanes) in Astronomy SE

New shot of Proxima Centauri, our nearest neighbour enter image description here

left: "New shot of Proxima Centauri, our nearest neighbour" Source right: from Does this telescope only have a 4 blade aperture? in Photography SE, originally from 20 years of Hubble Space Telescope optical modeling using Tiny Tim (paywalled, also available here and see this page) Note that the lines in the image going one way are produced by the vanes going the other way in the telescope.

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    $\begingroup$ Glare on a metal surface. Probably. $\endgroup$ – A. Rumlin Mar 28 at 6:14
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    $\begingroup$ SAR uses the Fourier transform, and the image artifact looks like what you get when a wrong value is put into a 2-D Fourier transform. However, I don't know what is causing the error in the first place. $\endgroup$ – DrSheldon Mar 28 at 6:22
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    $\begingroup$ If it is indeed related to the FT, it is possible the folks over at dsp.stackexchange.com can help. This is a really intriguing question. $\endgroup$ – Polygnome Mar 28 at 8:31
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    $\begingroup$ Not going to write a full answer... Sentinel-1 traveled north-to-south in this image, along the vertical arm of the star. Therefore, one arm is in the azimuthal direction and the other is in the range direction of the SAR measurement. The contrast between sea and ships is huge causing this glare effect. In other words, a bit of the returned signal comes through even if the radar points a bit off the ship. One could adjust the image generation in a way to suppress this, but would lose detail in "ordinary" areas with less contrast. $\endgroup$ – asdfex Mar 28 at 9:57
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    $\begingroup$ What math to prose ratio are you looking for? $\endgroup$ – Craeft Mar 29 at 22:48

Discrete Fourier techniques introduce errors in their terms that track with the sinc function. Any target in the image will produce side lobes like those in the following graph.

Strong reflections will create side lobes that have a higher amplitude than the background of the image. This is why the target appears to have a larger spatial extent than it really does. The reason it looks like a star, is that the side lobes spread in the direction of the grid used to process the image, as in the next image which is from this paper.

This dissertation discusses how to remove these artifacts.


From the abstract:

The PSF [Point Spread Function] of a SAR system can be defined in different ways. For example, it can be defined in terms of the SAR system including the image processing algorithm. By using this definition, the PSF is an algorithm-specific sinc-like function and produces the bright, star-like artifacts that are noticeable around strong reflectors in the focused image.

  • $\begingroup$ Thank you for your answer! "Discrete Fourier techniques introduce errors in their terms that track with the sinc function." As shown in this answer a rectangular or "top-hat" shape and $\DeclareMathOperator{\sinc}{sinc}$ $\sinc$ are mathematical Fourier transforms of each other. You don't need to talk about DFT to get $\sinc$, all you need are finite limits, which real world data will always tend to have. $\endgroup$ – uhoh Mar 30 at 9:27
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    $\begingroup$ I think the sentence you quoted should probably be the first sentence of the answer, and everything before it should get deleted. When I started writing the answer, I was going to show the similarities between aperture size in optical and RF systems, but I ended up focused on the DFT, which is the dominant source of error here. Thoughts? $\endgroup$ – Craeft Mar 30 at 12:22
  • $\begingroup$ I think that there is no "error" at all, instead it's just a natural result of any finite sampling which is what we do in the real world. All systems that make images have some kind of aperture; telescopes have circular apertures and central obstructions and the point-spread functions are Airy disk-like (e.g. this) and Fourier apertures (in this case time in cross-track direction and number of samples in the along-track direction of the spacecraft) make 4 spikes just like a 12-segment iris in a camera lens makes 12 spikes. $\endgroup$ – uhoh Mar 30 at 12:32
  • $\begingroup$ I think your answer is perfectly fine, no problem at all! Maybe just don't say it's the "D" for "discreet" in DFT that create "errors" and instead just say apodization in Fourier space leads to funky spikes in real space, and it doesn't matter if the Fourier transform is discreet like in SAR, or continuous like in Fourier optics analysis of a camera or telescope. The discreteness of the FT here is in no way responsible; if you put a square aperture in front of an optical telescope you'd have exactly the same sinc-shaped point spread function. Most telescopes are round, so we see Airy disks $\endgroup$ – uhoh Mar 30 at 12:34
  • $\begingroup$ The star shaped artifacts in optical and RF systems are caused by different processes. I apologize for giving the impression that they are related. $\endgroup$ – Craeft Mar 30 at 12:48

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