Why does a mirror bent 'like a potato chip' allow space telescopes to be smaller and have a wider field of view? I was browsing NASA featured items and came across this - Out With the Old, In With the New: Telescope Mirrors Get New Shape


  Called freeform optics, this emerging mirror technology, brought about
  by advances in computer-controlled fabrication and testing, has
  triggered a sea change in optical engineering... the technology holds
  great promise for scientists who want to develop compact telescopes
  for CubeSat and other small satellites — an increasingly popular and
  cost-effective alternative to more traditional missions that are more
  expensive to build and launch.


Telescopes for cubesats?!

The article had this illustration, and I'm trying to figure out how that is converted into a clear image without distortions, and why they say it allows the telescope to be much more compact. 



It was a short article that didn't even try to explain this, and when I went looking for other articles on the topic for non-experts I found zip. Perhaps this is very challenging to explain, but I thought I'd ask anyhow. I told an enthusiastic youth just a few weeks ago that it wasn't possible to launch a telescope capable of anything useful on a cubesat. Oops...
Freeform optics are a response to the specific challenge of cramming a telescope in a very limited space. A traditional instrument would have all optics symmetrical and aligned on the same axis. It would waste a lot of space within the cubesat. Also, traditional designs tend to be much longer than they are wider; they don't fit well in a cube; it is very hard to make classic instruments that are as short as they are wide.

But with freeform optics you could bounce light in a few directions within the cube. You'd still achieve a decent focal length, and you would use all the volume available to you.



Since light is reflected from mirrors at angles different from normal, you cannot use the traditional symmetric shapes such as parabolic, spherical, etc. You need to basically take a paraboloid and squish it in one direction so that it works about the same like a parabolic mirror (I'm simplifying), but at an angle of reflection of, say, 45 degrees.

In such an instrument you could have multiple "potato chip" mirrors, as in the diagram above. You have to design the instrument as a whole; computer simulations will adjust the shape of each mirror until the performance of the whole instrument is close to a classic straight design.

As far as I can tell, the manufacturing precision is such that freeform optics are only usable at long wavelengths such as infrared, where less precise optics can be used. But technology improves all the time. It also depends on how much aberration you can tolerate in your image.

For usage from ground level this is less useful, unless you absolutely need a telescope in a very small form factor for some reason. Classic optics are still preferred when space and shape are not restricted.