Figuring Dall/Kirkham primary.

Hello all,I would appreciate any help in figuring the elliptical primary mirror for my Dall/Kirkham scope.I have figured parabolas in the past by reading about it.But this one is different,apparently it is figured to 70% of a parabola and I cannot find any literature on this subject that explains in laymans terms(thats me)how to approach that.I guess I should start with the design of the scope which was put together by someone else and this is what he came up with.I hope its right.
System...........F20
Primary dia..... 12.87"
Primary F/L..... 58.0"
System F/L...... 259.09"
Back F/L........ 8.0"
Distance secondary
from system focus 53.6175"
Distance secondary
from prime focus 12.0024"
Distance secondary
from primary.... 45.6175"
ROC of secondary 30.9284"
Primary conic... -0.7578
Secondary conic. 0.0
Extension factor 4.4671
Maybe someone with the expertise can double check the numbers on this design.I would greatly appreciate it.
Right now I have the mirror polished to a sphere with a ROC of 116" according to the focault test.I'm just a little confused about how to approach figuring it to only 70% of a parabola.I'm planning on using the everest stick pin method and will need to find the zones for an ellipse of -0.7578% of a parabola.Thats where I am confused.Also not sure if I start at the central zone during figuring and move away to what point like is done for a parabola?If anyone can help I would surely appreciate it.Thanks.-Joe-

Hi Joe,
Using the data from your Astromart forum posting I laid the design out in Zemax, and the system performance is good as expected. Although this is a reflective system I weighted the spot diagram below for the dark adapted (scoptopic) eye to get the Ary disk about the right size. There are geometric spot traces for on axis, 0.25” off axis and 0.5” off axis. This is the radial distance from the field center. As expected coma is the dominant aberration. Performance is good on axis and this will make a very good imaging instrument for planets, double stars, etc. as it is nearly diffraction limited over a 0.5” diameter full field. I get better performance with the primary secondary spacing of 45.900” and the modeling represents that very minor change…



For figuring this mirror, as you know it will be less correction than a parabola by a factor equal to the conic constant (K). For a parabola each knife edge position is calculated, K=-1 or 1.0*( r2 / R) where r is the zonal radius from the center of the mirror and R is the radius of curvature of the mirror. If moving both the knife edge and source use K*(r2/2R). For your scopes elliptical primary the conic constant K is -0.7578 and you’ll need to calculate the zones as 0.7578*(r2/R).

Conic Constant -0.7578
Radius of Curvature 116
Zonal increment 0.5
Parabola r^2/R
0 0
0.5 0.00163319
1 0.006532759
1.5 0.014698707
2 0.026131034
2.5 0.040829741
3 0.058794828
3.5 0.080026293
4 0.104524138
4.5 0.132288362
5 0.163318966
5.5 0.197615948
6 0.23517931
6.5 0.276009052

I looked at using the 2 foci of the ellipse as a null test but as expected the long focus (conjugate) of the ellipse is 895” almost 75 feet away with the short focus of the ellipse being 62” or 5 feet away. Thus if you placed a slit or point source 895” away and a knife edge 62” away you would cut the light uniformly across the aperture, i.e. it will null.

Well the images didn't make the posting and I couldn't attache a pdf so if you are interested send me an email to the address below and I'll forward the pdf to you...
Hope this helps…

Dave Erickson
[email protected]
www.hbastro.com

You could do the zones/knife-edge test modified for the ellipse, but I came across a diagram in one of Ingall's classic ATM books that showed an interesting test set up for a compound scope. The scope was pointed vertically down and tested in autocollimation for a null using a large pan of oil as an optical flat. This means you'd have to make the spherical secondary before figuring the primary, and build the tube assembly (or a test fixture).

Thanks for your help fellas.-Joe-