Re: ATM 19.5" mirror support?

["Mark D. Holm" <mdholm@telerama.com>]

Hi Mark,

Schott's web site gives the following data for Suprax 8488

Density 2.3 g/cm^3
Elastic Modulus (same as Young's Modulus) 67 x 10^3 N/mm^2
Poisson's Ratio 0.20

Refractive Index 1.484 @ 587.6 nm
Thermal Expansion Coefficient 4.3 x 10^-6  K^-1  (over the range 20 - 300, I
presume that is in C)

To use the elastic modulus in Plop, it need to be converted to KgF/mm^2.  The
result is 6832 KgF/mm^2.

To use the density in Plop it needs to be converted to Kg/mm^3.  The result is
2.3 x 10^-6 Kg/mm^3.

I will assume a diagonal minor axis of 75 mm.  Since Plop ignores the part of
the mirror shadowed by the diagonal, it is important to put in the diagonal
size.

When I do a 9-point cell using Automatic Cell Design and not checking "Allow
Angles to Vary" I get the following.

Inner three points at radius = 0.343995 of mirror radius
Outer six points at radius = 0.745598 of mirror radius
Triangle pivot points on circle of radius = 135.003 mm

Triangle dimensions in mm:
0, 0
92.324, 74.719
184.648, 0
Pivot point
92.324, 24.906

The mirror surface deformations for this cell are:
P-V 3.18486e-05 mm  = 1/16 wave  (Where 1 wave is defined as 500 nm.)
RMS 7.03932e-06 mm =  1/71 wave

This would result in a wavefront error of 1/8 wave P-V.  That seems like too
much to allow from the cell alone.

Doing the Plop design again, but allowing angles to vary I get:

Inner three points at radius = 0.450114 of mirror radius
Outer six points at radius = 0.679287 of mirror radius
Triangle pivot points on circle of radius = 130.634 mm

Triangle dimensions in mm:
0, 0
92.949, 28.745
185.897, 0
Pivot point
92.949, 9.582

The mirror surface deformations for this cell are:
P-V 2.45109e-05 mm  = 1/20 wave  (Where 1 wave is defined as 500 nm.)
RMS 4.26792e-06 mm =  1/117 wave

This would result in a wavefront error of 1/10 wave P-V.  To my way of thinking,
this may be good enough for many applications.  If you know your mirror has a
very high quality figure and you intend to use it for high magnification work,
you might want to improve on this amount of deformation by about a factor of 2.


Surprisingly, I actually get comparable result from a 6-point cell:

All six point lie on a circle of radius = 0.587983 x mirror radius

Each pair of points is on a pivoting bar.
Distance between points = 145.614 mm
bar pivots at 72.807 mm
pivot points lie on a circle of radius 126.106 mm

The mirror surface deformations for this cell are:
P-V 2.44146e-05 mm  = 1/20.5 wave  (Where 1 wave is defined as 500 nm.)
RMS 4.67654e-06 mm =  1/106 wave


An 8-point cell gives:

All eight point lie on a circle of radius = 0.587241 x mirror radius

Each pair of points is on a pivoting bar.
Distance between points = 111.308 mm
bar pivots at 55.654 mm
pivot points lie on a circle of radius 134.36 mm

The mirror surface deformations for this cell are:
P-V 2.10557e-05 mm  = 1/23.7 wave  (Where 1 wave is defined as 500 nm.)
RMS 3.93187e-06 mm =  1/127 wave

So, the eight point has four bars instead of three triangles and gives slightly
lower deformation than either of the nine point designs or the six point.  The
problem with the eight point is that at least two of the bars will themselves
have to be pivoted on top of another bar in order to let the mirror set evenly
on them all.  At least the way I ran it, Plop doesn't make this clear.  Part of
the problem is that I don't know yet how to set up Plop for more complicated
cases.  I think the analysis for this 8-point cell is probably OK so long as you
realize that another layer of pivoting is needed.


Anybody else have thoughts on the matter?

Mark Holm
mdholm@telerama.com