Re: ATM 9 point cell

[Mark Holm <mdholm@telerama.com>]

Jim L. wrote:


> Yeah, I was looking at some site that touted Plop.  All the plans I
> remember seeing had nothing in the center - just a ring of points at one
> or two radii.  Didn't make sense to me.
> 
> 


Up to about 9 points, Plop tends to put all the points more or less in a ring. 
Although it may not be "intuitive", there is reason and good math behind it, so 
far as I can tell.

The reason is this.  Plop is designed to "ignore" any deformation of the mirror 
which results only in changing the focal length of the mirror, but not changing 
it from a paraboloid.  Single ring cells allow the mirror to sag more over all, 
but a large part of that deformation is parabolic in form.  The part that is not 
parabolic is smaller than the nonparabolic deformations from a cell with a ring 
of three and a ring of six points.

In Plop, the feature that "ignores" parabolic deformation is called refocusing. 
  Parabolic deformations change the focal length of the mirror slightly.  Plop 
calculates the deformations for the "new" mirror figure with the focal length 
shifted slightly.

So, the trade off with Plop, using refocusing, is: Gain the ability to use 
simpler cells with larger and thinner mirrors;  Lose the greater freedom from 
focal length shift.  For most ATM telescopes this is a good trade.

Plop displays the amount of focal length change that has been refocused.  It is 
also possible to turn off refocusing.

I have had some correspondence with Richard Schwartz regarding refocusing and 
the central point cells.  He says that the software he used to design those 
cells was not capable of the refocusing calculation.  He was, therefore 
minimizing total deformation, not just nonparabolic deformation.

BTW, the idea of allowing parabolic deformation is probably not new with Plop. 
The cell shown in Texerau for the 8-inch "standard" telescope has three support 
points close to the edge.  This arrangement results in considerable deformation, 
a lot of which is parabolic in nature.  The only problem is a lot of astigmatism 
near the edge.  If you were to mask off the outer 20% or so of this arrangement, 
the resulting non-parabolic deformations would be small.

My observations about Plop and refocusing are not original to me.  Richard 
Lewis, Plop's author, pointed them out explicitly in his S&T article on Plop.

Mark Holm
mdholm@telerama.com