Re: [ATM] astigmatism as seen via ronchi?

[Richard <cnc@cncservo.co.uk>]

Hi Mitch,

Tuesday, March 4, 2008, 2:18:12 PM, you wrote:

MCc> ummmm....COG of the mirror from front edge = (t/2) - (0.707S) .... ??

First off, by grinding out a spherical concave hole you are removing
mass from the front of the mirror, therefore its centre of mass must
move toward the rear of the mirror. Therefore I disagree with the
negative sign. If the centre of mass is measured from the front
edge surface of the mirror, then it must be greater than t/2 from the
front. I am defining the front as being the outside rim - maybe that
is not what is intended here, but the optical vertex is intended?. If
the latter, then that is not a very convenient measuring point.

My maths is rusty, so I constructed a mirror in a CAD package which
has the ability to give you centre of mass of any part. I started with
a 400mm diameter blank, 40mm thick, positioned so that its dead centre
was at the centre of the CAD coordinate system. Centre of Mass
correctly shown to be X=0.0, Y=0.0, Z=0.0.

Then I hogged out a spherical concave hole with a sagitta of 5.003mm.
CAD now shows the centre of mass as Z=-1.2232mm. This is 21.2232mm
from what I have called the front of the mirror (the outer rim) or
16.2202mm from the optical vertex, the centre of the concave face. The
formula above yields (20/2 - 5.003*0.5*sqrt(2)) = 16.4623mm, so it is
an approximation at best.

-- 

Best regards,
  Richard in the UK

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