PLOP Mirror Cells
Below are some mirror cells optimized using PLOP written by David Lewis.  PLOP optimizations have a tendency to prefer ring supports from ~40%  ~60% of the mirror's radius, depending on the mirror diameter and thickness.  Using PLOP's Monte Carlo feature I found a ring with a center support was more forgiving of exact support point placement (manufacturing errors).  In some trials it pushed the support ring a bit further out along the mirror's radius.  This isn't necessarily a good thing, as much as it is a comfort thing.

So the next question is: How to support the center of the mirror on these cells?  Below is PLOP's Cell Parts diagram for each cell, the corresponding color relief diagrams and the PLOP text file for each cell.  The center support is integrated with 2 of the ring supports.  Does it work?  PLOP says it does.  I don't know yet in practice, but am working on the 7 point cell and the 9 point right after that.  Any corrections, misconceptions or errors I have, opinions or ideas are greatly appreciated.

Of particular interest too me is the 9 point cell, which blows away any traditional cell I could construct for PLOP to optimize.  The traditional configuration trials were sufficient for a 16" x 1.625" mirror, but just by a nm.  David Lewis recommends minimums of 1/128 RMS and 1/32 P-V surfaces.  PLOP indicates the 9 point cell below exceeds that with a comfortable margin.


 7 Point Cell
 16 inch x 1.625" thick Pyrex

  P-V   1.07542e-05          ~ 1/51 surface
  RMS   2.53803e-06      ~ 1/216 surface
 

     ;7 point cell with angles fixed
    diameter 406
    thickness 41
    density 2.45e-06
    modulus 6000
    poisson 0.22
    focal-length 1828
    n-mesh-rings 12
    rel-support-radii 0 0.681608 0.681608
    num-support 1 3 3
    support-angle 0 27.4616 87.4616
    basis-ring-size 1
    basis-ring-min 0
    obstruction-diam 67
    optimize rel-support-radii 1 0.01
    optimize rel-support-radii 2 0.01
                                           part triangle 1 point 0 0 point 1 0 point 2 0
                                           part bar 1 point 1 1 point 2 1
                                           part bar 1 point 1 2 point 2 2
 

     9 Point Cell
           16 inch x 1.625" thick Pyrex

            P-V   5.96718e-06        ~ 1/92 surface
            RMS   1.29611e-06    ~ 1/424 surface

 
    ;9 point cell with angles fixed
    diameter 406
    thickness 41
    density 2.23e-06
    modulus 6400
    poisson 0.2
    f-ratio 4.5
    n-mesh-rings 16
    rel-support-radii 0 0.640809 0.640809
    num-support 1 4 4
    support-angle 0 35.6104 80.6104
    basis-ring-size 4
    basis-ring-min 0
    obstruction-diam 79
    part triangle 1 point 0 0 point 1 0 point 2 0
    part triangle 1 point 1 1 point 2 1 point 1 2
                                          part triangle 1 point 2 2 point 1 3 point 2 3

Other 9 Point Cells
16 inch x 1.625" thick Pyrex

9 Point Kriege & Berry                9 Point Ring

 PV   1.47966e-05   ~1/37 surface                                                     PV   1.08699e-05   1/51 surface
 RMS   3.37246e-06   ~1/163 surface                                               RMS    1.80949e-06   1/304 surface
 

 Radius Inner 0.32625                                                                       Radius Inner 0.0
 Radius Outer 0.7775                                                                        Radius Outer 0.584769

                                                                    
                                                                    

11 Point Cell
16 inch x 1.625" thick Pyrex

P-V    4.57932e-06       ~ 1/120 surface
RMS    9.82256e-07    ~ 1/559 surface

 
    ;11 point cell with angles fixed
    diameter 406
    thickness 41
    density 2.23e-06
    modulus 6400
    poisson 0.2
    f-ratio 4.5
    n-mesh-rings 16
    rel-support-radii 0 0.640123 0.640124
    num-support 1 5 5
    support-angle 0 41.3792 77.3787
    basis-ring-size 5
    basis-ring-min 0
    obstruction-diam 79
    part triangle 1 point 0 0 point 1 0 point 2 0
    part bar 1 point 1 1 point 2 1
                                           part bar 1 point 1 2 point 2 2
                                           part bar 1 point 1 3 point 2 3
                                           part bar 1 point 1 4 point 2 4
                                           part bar 1 part 1 0 part 2 0
                                           part bar 1 part 3 0 part 4 0

Copywrite © December 2001, G.S. Vegos