Why does a mirror bent 'like a potato chip' allow space telescopes to be smaller and have a wider field of view?
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.