54-Point Cells

Diagram of 54 point cell
Map of mirror deformations on a 54 point cell

John Dudgeon used more brain power than I can muster to generate the setup for this cell and then used Plop to optimize it. John is working on a 1 inch thick, 30 inch diameter, f/6 mirror. He plans to use it in a classical Cassegrain, with Nasmyth folding to avoid perforating the mirror. At the center, the mirror is only about 10 mm thick!

Plop indicates this cell will produce only 1/42 wave P-V non-parabolic deformation and 1/272 wave RMS.

I think this is the first cell design I have seen that is rotationally assymetric. It isn't the same going clockwise as going counterclockwise!

Instead of trying to tabulate the dimensions for all the parts, I will give the Plop setup that John has kindly given permission to post here. Instead of making a downloadable file, I will just give the text here. Copy it into a text editor. Save it with a .gr extension and open it from the File menu in Plop. Go to the Design tab. Change all the Optimize selections to Fixed. Then click Run, Run Plop, Start. Generating the matrix will take a few minutes, but when that is done, the figures will be generated even though no further optimization is done. You will be able to get the dimensions from the Cell Design tab and the Graphic Plots, Part Dimensions menu item.

If you wish to optimize for different mirror dimensions, change the appropriate dimension entries, leave the choices on the Design tab set to Optimize and click Run, Run Plop, Start.

Here is the Plop Setup.



;This is a conventional 54 point cell with support radii and angles optimized by PLOP.
;Plate glass mirror diameter (762 mm), thickness (25.4 mm), focal length (4572 mm),
;and secondary size (170 mm) are fixed design elements.
diameter 762
thickness 25.4
density 2.45e-06
modulus 6000
poisson 0.22
focal-length 4572
n-mesh-rings 30
rel-support-radii 0.237432 0.502689 0.704679 0.883565
num-support 6 12 12 24
support-angle 1.4577e-07 30 15 30
basis-ring-size 6
basis-ring-min 0
obstruction-diam 170
optimize rel-support-radii 0 0.1
optimize rel-support-radii 1 0.1
optimize rel-support-radii 2 0.1
optimize rel-support-radii 3 0.1
optimize support-angle 0 0.1
optimize support-angle 1 0.1
optimize support-angle 2 0.1
optimize support-angle 3 0.1
part triangle 6 point 0 0 point 1 0 point 1 11
part triangle 12 point 2 0 point 3 0 point 3 23
part triangle 6 part 0 0 part 1 0 part 1 11
part bar 3 part 2 0 part 2 1

Now that John has done the hard part, even I can use Plop to design 54-point cells!

Here is a 54-point Plop setup for the largest hand made telescope mirror in the world, Dan Bakken's Hercules. This cell design would allow only 1/40 wave P-V, 1/287 wave RMS deformation for this 41.2 inch (1.05 meter) diameter, 2.125 inch thick (54 millimeter), f/4 mirror using a 6.25 inch diagonal. This setup is already optimized.



;This setup is for Dan Bakken's "Hercules" mirror.  It is 41.2 inch diameter
; by 2.125 inch thick, f/4 with 6.25 inch diagonal.  This cell gives
; 1/40 wave P-V and 1/287 wave RMS.
;
;This is a conventional 54 point cell with support radii and angles optimized by PLOP.
;Pyrex glass mirror diameter 1046.48 mm), thickness (53.975 mm), focal length (4185.92 mm),
;and secondary size (158.75 mm) are fixed design elements.
diameter 1046.48
thickness 53.975
density 2.23e-06
modulus 6400
poisson 0.2
focal-length 4185.92
n-mesh-rings 30
rel-support-radii 0.235693 0.50289 0.702689 0.880069
num-support 6 12 12 24
support-angle -3.56846e-05 30 15 30
basis-ring-size 6
basis-ring-min 0
obstruction-diam 158.75
optimize rel-support-radii 0 0.1
optimize rel-support-radii 1 0.1
optimize rel-support-radii 2 0.1
optimize rel-support-radii 3 0.1
optimize support-angle 0 0.1
optimize support-angle 1 0.1
optimize support-angle 2 0.1
optimize support-angle 3 0.1
part triangle 6 point 0 0 point 1 0 point 1 11
part triangle 12 point 2 0 point 3 0 point 3 23
part triangle 6 part 0 0 part 1 0 part 1 11
part bar 3 part 2 0 part 2 1


© 2002 Mark D. Holm