Re: ATM Change of Plans, F/2 -> F/3.2

[Aplanatic@aol.com]

Dan asks,

> Isn't coma invariant vs. focal ratio?

If we hold constant the off-axis angle and the focal length of a mirror (where the aperture of the system is the mirror itself), then third-order coma grows as the square of the diameter of the mirror.  Born and Wolf, page 214 gives (simplifying a little)

delta X(max) = -F*y0*rho^2

for comatic aberration where delta X is the ray's offset from the on-axis ray, F is the third-order Siedel coefficient for coma, y0 is proportional to the field angle, and rho is the aperture radius.  From this we see that coma grows as second power of the aperture and thus, inversely as the second power of the f/ratio.

We can also see that coma grows as the first power of the off-axis angle.

Spherical aberration grows as the third power of the aperture.

Astigmatism grows as the second power of the off-axis angle and the first power of the aperture.

If you start with a given mirror diameter and adjust the focal length of the mirror to get different focal ratios, then you will get a very different answer.

Dave Rowe