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Comment by kevin_thibedeau | Hacker News Reader

Atmospheric scattering puts a bound on the practical lower limit. It's not much less than 4".

Ah, I still remember this question from a high school physics exam around 1980. I think I remember it because I also remember not even attempting to answer it.

The exam was three questions, answer one. I only vaguely remember the one I did work on, but I remember this question well because I remember thinking "holy cow there isn't enough info in this problem to answer it", and also that apparently I was wrong!

Can that be overcome with computational photography?

I'm neither an astronomer nor an imaging expert, but I've read that ground-based telescopes use "lucky imaging" plus deformable mirrors to work around atmospheric distortion. Maybe something analogous works in the reverse direction.

For deformable mirrors they shine a control beam into the sky. A spy satellite would have to shine it downwards.

Can you use a known object which is illuminated by the sun?

Given that people have called this 'wavefront based correction' I would guess you need light source where all photons are 'in phase' like a laser. The sun is not such a source.

However, I do not know near enough about physics to say the above with any degree of confidence.

No matter what you do, you still have to deal with diffraction [1], which means the resolution is inversely proportional to the aperture. I think the Trump/Iran release was estimated to be pretty close to the diffraction limit.

[1] https://en.wikipedia.org/wiki/Angular_resolution#Explanation

How about optical interferometry? IIRC, this can beat the diffraction limit.

Optical interferometry means you have a wider telescope. Same limit formula.

Yes, but the aperture of the interferometer is no longer limited in the same way, so we could say that interferometry gets around the “naive” diffraction limit.

Well, but if you have a bunch of these in orbit, able to image the same site, at the same time...

Yep.

  angle = k (wavelength / diameter)

And the diameter is going to be limited by the launch vehicle. But multiple satellites could improve this.

Just took a radars course and we definitely spent a whole section on just atmospheric effects / defraction. My only guess about how you could maybe lower the error is by monitoring and measuring the condition of the atmophere and building a model that can use that data to apply corrections and reduce error to your image.

If there was a known object in an image could a high resolution image of the known object be used to compensate for atmospheric diffraction effects?

One example is a laser guide star: https://en.m.wikipedia.org/wiki/Laser_guide_star

Yes. Ssshhh.

As I mentioned above, there is a technique called lucky imaging, where you take lots of short exposures and only use the best ones. In astronomy, this can be used to reach the diffraction limit. You need a bright source, however, and it provides a narrow field of view.

Another technique is to use multiple camera sources spread out over an area. The angle between the cameras is known, so differences in the images caused by diffraction and atmospheric aberrations can be computed out to some degree.

Can you expand on "the Trump/Iran release was estimated to be pretty close to the diffraction limit"? What is this in reference to?

https://mobile.twitter.com/realDonaldTrump/status/1167493371...

https://www.npr.org/2019/08/30/755994591/president-trump-twe...

I think your question was misunderstood, as the other replies do not go into any details on diffraction limit at all.

I too would be interested in knowing if this image is showing all we got, or because someone else looked at it and said "sure you can release it, we've got better than that anyway."

Can multi-camera/multi-view photogrammetry defeat this limit and create super-resolution imagery?

Optical interferometry has been used to synthesize very large apertures in ground based experiments (e.g., https://en.wikipedia.org/wiki/Palomar_Testbed_Interferometer). That was in the mid 1990s.

Operational ground interferometers have obtained 5 mas resolution, which corresponds to sub-mm resolution from an orbital platform.

You still have atmospheric turbulence, but do we know how to get around the naive diffraction limit.

In astronomy a technique called lucky imaging can be used to reduce the effects of the atmosphere. You use a high frame rate and throw away all the frames where the atmospheric quality is poor. This technique produces a narrow field of view, however, and requires a lot of photons.

"Lucky imaging" is not a widely used technique in astronomy. There is generally no shortage of photons in earth observation, however, so it could work quite well on spy satellites.

A much more common technique is adaptive optics. A wavefront sensor measures the incoming signal from a reference star (or laser guide star) and deforms the mirror to compensate. I wouldn't be surprised if adaptive optics is also used on spy satellites though I can't imagine what they would use for a reference.

As other commenters have mentioned, you are always going to be limited by the diffraction limit of the telescope, which is a function of the mirror size and wavelength.

> "Lucky imaging" is not a widely used technique in astronomy

True, but it is very popular in astrophotography.

Also, there are many recent advances in super-resolution imaging, compressive sensing, and sub-diffraction-limit pixels, often based on results from Donoho, Candes, and friends. Taking advantage of signal sparsity (i.e. that the set of physically possible signals is much smaller than the set of all possible signals, and physical systems have many constraints upon them) has led to a lot of surprising results over the past 15 years or so. Another approach that has yielded results is aperture synthesis, which has been applied to optical systems for at least the past 15 years. And in some certain circumstances for spysats, optical heterodyne detection can also be used to great effect.

> you are always going to be limited by the diffraction limit of the telescope

While the diffraction limit of a system is definitely a constraint, it's not as simple as this anymore.

Aperture synthesis, aka interferometry, has been applied to optical systems for far more than 15 years. The Narrabri Stellar Intensity Interferometer[1] saw first light in 1963, for example. However, your resolving power is still fundamentally limited by the distance between your telescopes. The diffraction limit may be more of a fuzzy limit than a hard cut off, but it is fundamental physics. Optical interferometry is hard, and you don't get a image in the way that most people would think of it. To build up a detailed image with aperture synthesis requires measurements over a very large number of baselines.

[1] https://en.wikipedia.org/wiki/Narrabri_Stellar_Intensity_Int...

Yes, agreed. In fact, the first example I can think of is the Michelson stellar interferometer at the Mount Wilson Observatory, which was in operation in 1920.

However, there has been a major push recently to circumvent the limitations of optically connecting the telescope arrays; there are a few different approaches, of which I'm not aware of any fatal flaws. Seems likely it's a matter of time and physics and engineering; very difficult, but achievable.

See for example: https://dspace.mit.edu/bitstream/handle/1721.1/51042/Tegmark...

If they know the shape of buildings (or vehicles) near the area of interest, they could use those to guide correction.

"Lucky imaging" is not a widely used technique in astronomy.

There was a major announcement on Friday using just this technique: https://www.gemini.edu/pr/gemini-gets-lucky-and-takes-deep-d... It might become more popular now.

Yes, I saw it, and that was the first time I had heard the term in my years of studying and working in astronomy. Most astronomical sources of interest are not anywhere near as bright as Jupiter. It can take hours of integration to even detect many targets of interest. The technique is simply not possible for 99%+ of astronomy work.

Did I use the word "often" in my comment above? Anyway, as an astronomer, I've heard about lucky imaging quite a few times - it likely depends what other astronomers you are exposed to. Of course, it can currently only be used on some bright targets, but it's a fascinating method. Similar techniques are also now being used at other wavelengths, such as for the LOFAR low frequency radio telescope.

> I can't imagine what they would use for a reference

All the orbits are well known (to all interested parties at least) so I'd assume a downwards pointing laser guide wouldn't be much of an issue.

Can't put a drone high up, just under the satellite, and capture the higher fidelity image of what the satellite would have picked up, then train a model top automatically correct the satellite's original image?

Can we train a neural net to use it's "imagination" to fill in some extra details? Maybe. Would we want to?

I wouldn't like to participate in a military operation based on the imagination of a machine. Or any imagination whatsoever.

You can't extract any more information from the image than what the satellite originally acquired - you could make an "error correcting" model that creates an image that appears to have higher fidelity, but the additional detail is just a representation of what the model is filling in based on the other images it has been trained on, rather than an actual increase in resolution.

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