> An off axis parabola will have a bit less coma than a
> mirror twice as fast. In other words, an f/9 off axis
> mirror will have coma almost as much as a f/4.5 one.
and what Chuck (grant@aretha.llnl.gov (Chuck Grant)) said:
> It is fairly easy to ray trace an off axis section of a paraboloid
> to get an idea of what is happening. Yes they have more coma than
> an on axis paraboloid the same diameter, and less coma than a full on axis
> paraboloid with a diameter large enough that your off axis section can
> be cut from it.
>
> The spot diagrams (showing the off axis abberations) are shaped differently
> than the usual spot diagrams from centered systems, so comparing them is
> not as straightforeward as it might be.
Of course ray-tracing is easy, once you have the program. Take away my fun, will you? <g>
I did a quick-and-dirty calculation* which showed that the length of the coma spot is exactly the same for the off-axis paraboloid as it is for a symmetric paraboloid that's twice as fast and twice the size *if* the edge of the off-axis mirror is right on the axis of symmetry. Obviously that's not a practical telescope. The spot length for a symmetric mirror is 3 r^2 alpha / (4 f), where r is the mirror's radius (not radius of curvature), alpha is the direction cosine of the incident rays, and f is the focal length. For a mirror which is a distance a from the symmetry axis, the spot size is 3 a r alpha / f. If I set a to r (edge of the mirror on the symmetry axis) in the latter and replace r with 2r in the former, I get the same thing. Notice that the coma gets worse as the piece of paraboloid gets farther from the axis, and does so linearly.
Like Chuck, I get a strange spot shape. Also, this is for objects that are in the plane defined by the symmetry axis and center of the mirror. I haven't treid it for things in the perpendicular direction, but I would think it's smaller.
*The usual third-order approximation in the angles of the rays ->relative to the axis of symmetry of the paraboloid<-. I could have expanded relative to the central ray.
Clay cspence@sarnoff.com