A few weeks ago, I was interviewing for a job working on electronic cameras, and was quite tickled that the interviewer asked me to explain how a Schmidt camera worked. I think he wanted to make sure that I really was an ATM. (I took a different job, though).
Anyway, one way that you might think about coma is to draw a picture of the light path going into a deeply parabolic mirror and coming to a focus. You can get a perfect focus at the center, but if you draw the parallel incoming light coming in at an angle with respect to the axis, the light doesn't "see" a radially symmetric parabola. It sees some really complicated shape that bounces the light around to all sorts of strange places.
Light coming into a spherical mirror, though, always experiences the same reflection no matter what angle it is it. A sphere doesn't have an axis (or rather, it has infinitely many axes; no axis is better than the others). So a spherical mirror will not have coma. It _will_ have spherical aberration, but this aberration will still be the same for all angles. It will be uniformly blurry.
The schmidt camera compromises between the two by placing a funny shaped lense at the center of curvature of the mirror. The lens' shape is generally the geometrical difference between the shape of a parabola and a sphere. The magnitude of this shape will depend on the index of refraction, but just as there are different ways to parabolize a mirror, there are different shapes of schmidt corrector plates that will work.
For a much broader range of angles, the refraction seen by an incoming plane wave is the same no matter what the angle. There is some astigmatism, though, as at the extremes the lens is seen to be a little tilted.
Mike_Crawford@QuickMail.Apple.Com