[APML]: Laser Beam Test Spherical Aberration

[Steve Bell <sb635@delphi.com>]

Well, I've derived the equation for the spherical aberration seen from a
spherical mirror, along its optical axis, when a straight line laser
beam hits it at various zone distances. The results are not encouraging.
You can see the workup at:

http://people.delphi.com/sb635/spher.gif

I'll post the final result here in FORTRAN lingo:

s.a. = (R*sin(pi/2-theta)/sin(2*theta) - R/2

where

theta = atan(R/r - r/(2*R)), in radians,

and R = the sphere's Radius of Curvature, r = the distance to the zone,
and pi = 3.141.

The largest spherical aberration (s.a.) will be seen when the laser beam
strikes the very edge of the mirror. Let's say that we have a 12" f/6
sphere, so that the very edge is r = 6". The Radius of Curvature R =
144", and the focal length is R/2 = 72", The above equation gives s.a. =
0.06", so the edge laser beams would reflect and intersect along the
optical axis 0.06", or about 1.5mm, closer to the mirror than the focal
point of the center. I admit, that's pretty small. In order to use the
test as a null test, one would have to be able to quantify differences
between the intersection points of the laser beams to at least 10 times
that small, and preferably 100 times. I don't imagine one couldn't just
"eyeball" this. But, if a CCD camera was mounted in a JMI NGF focuser,
with its drawtube co-aligned along the optical axis, and if the focuser
had a JMI Digital ReadOut (DRO) attached, then it just might be
possible. The DRO's optical encoder can accurately read translational
distances to 0.01mm. And the CCD camera could give a very accurate
sensing of when the two laser dots fell on top of each other by
searching for the maximum pixel count. This would occur when the light
from both dots maximally co-add, which is when they have maximum
overlap. It just might be possible. Of course, all this added hardware
adds hundreds of dollars to the cost of the setup, but I just happen to
have all the pieces.

-- 
Clear skies,
Steve Bell
email: sb635@delphi.com
Astrophoto page: http://people.delphi.com/sb635