3-Point Cells
Diameter = Mirror Blank Diameter in Inches
Thickness = Mirror Blank Edge Thickness in Inches
f/ = Focal Length in Inches / Diameter
Obs Dia. = Central Obstruction Diameter in Inches (This is usually the diagonal mirror minor axis.)
r = Radius of circle on which support points lie as a fraction of mirror blank radius
P-V = Peak to Valley Mirror Deformation with this cell in Waves (1 wave = 500nm)
RMS = Root Mean Square Mirror Deformation with this cell in Waves (1 wave = 500nm)
| Pyrex |
|---|
| Diameter | Thickness | f/ | Obs. Dia. | r | P-V | RMS |
| 3 | 1 | 12 | 0 | 0.392 | 1/840 | 1/5000 |
| 3 | 1 | 8 | 0.75 | 0.369 | 1/929 | 1/5000 |
| 3 | 1 | 6 | 0.75 | 0.338 | 1/1068 | 1/6000 |
| 4.25 | 0.625 | 12 | 0 | 0.406 | 1/236 | 1/1120 |
| 4.25 | 0.625 | 8 | 1.0 | 0.381 | 1/246 | 1/1111 |
| 4.25 | 0.625 | 6 | 1.0 | 0.383 | 1/239 | 1/1083 |
| 4.25 | 1 | 12 | 0 | 0.398 | 1/348 | 1/2000 |
| 4.25 | 1 | 8 | 1.0 | 0.377 | 1/375 | 1/1990 |
| 4.25 | 1 | 6 | 1.0 | 0.378 | 1/370 | 1/1967 |
| 6 | 0.8 | 12 | 0 | 0.407 | 1/107 | 1/486 |
| 6 | 0.8 | 8 | 1.3 | 0.387 | 1/108 | 1/476 |
| 6 | 0.8 | 6 | 1.3 | 0.390 | 1/105 | 1/462 |
| 6 | 1.2 | 12 | 0 | 0.401 | 1/157 | 1/851 |
| 6 | 1.2 | 8 | 1.3 | 0.384 | 1/164 | 1/837 |
| 6 | 1.2 | 6 | 1.3 | 0.385 | 1/161 | 1/824 |
| 8 | 1.1 | 12 | 0 | 0.406 | 1/62 | 1/256 |
| 8 | 1.1 | 8 | 1.3 | 0.399 | 1/62 | 1/279 |
| 8 | 1.1 | 6 | 1.52 | 0.396 | 1/61 | 1/272 |
| 8 | 1.35 | 12 | 0 | 0.404 | 1/76 | 1/385 |
| 8 | 1.35 | 8 | 1.3 | 0.397 | 1/77 | 1/378 |
| 8 | 1.35 | 6 | 1.52 | 0.393 | 1/76 | 1/371 |
| 10 | 1.3 | 12 | 0 | 0.407 | 1/37 | 1/167 |
| 10 | 1.3 | 8 | 1.52 | 0.401 | 1/37 | 1/163 |
| 10 | 1.3 | 6 | 1.83 | 0.398 | 1/36 | 1/158 |
| 10 | 1.85 | 12 | 0 | 0.402 | 1/53 | 1/228 |
| 10 | 1.85 | 8 | 1.52 | 0.397 | 1/53 | 1/269 |
| 10 | 1.85 | 6 | 1.83 | 0.394 | 1/53 | 1/268 |
| 12.5 | 1.5 | 12 | 0 | 0.408 | 1/21 | 1/94 |
| 12.5 | 1.5 | 8 | 1.83 | 0.403 | 1/20 | 1/91 |
| 12.5 | 1.5 | 6 | 1.83 | 0.406 | 1/20 | 1/88 |
| 12.5 | 1.5 | 5 | 2.14 | 0.405 | 1/19 | 1/86 |
| 12.5 | 2.2 | 12 | 0 | 0.403 | 1/32 | 1/167 |
| 12.5 | 2.2 | 8 | 1.83 | 0.399 | 1/32 | 1/164 |
| 12.5 | 2.2 | 6 | 1.83 | 0.400 | 1/32 | 1/161 |
| 12.5 | 2.2 | 5 | 2.14 | 0.398 | 1/32 | 1/158 |
| Plate Glass |
|---|
| Diameter | Thickness | f/ | Obs. Dia | r | P-V | RMS |
| 4.25 | 0.7 | 12 | 0 | 0.404 | 1/265 | 1/1320 |
| 4.25 | 0.7 | 8 | 1.0 | 0.380 | 1/278 | 1.1309 |
| 4.25 | 0.7 | 6 | 1.0 | 0.382 | 1/275 | 1/1281 |
| 4.25 | 1 | 12 | 0 | 0.398 | 1/349 | 1/2006 |
| 4.25 | 1 | 8 | 1.0 | 0.377 | 1/375 | 1/1990 |
| 4.25 | 1 | 6 | 1.0 | 0.378 | 1/370 | 1/1967 |
| 6 | 0.375 | 6 | 1.3 | 0.406 | 1/23 | 1/105 |
| 6 | 0.5 | 6 | 1.3 | 0.398 | 1/43 | 1/193 |
| 6 | 0.75 | 6 | 1.3 | 0.390 | 1/81 | 1/354 |
| 6 | 0.8 | 12 | 0 | 0.407 | 1/107 | 1/484 |
| 6 | 0.8 | 8 | 1.3 | 0.387 | 1/109 | 1/475 |
| 6 | 0.8 | 6 | 1.3 | 0.390 | 1/105 | 1/462 |
| 6 | 1 | 12 | 0 | 0.404 | 1/134 | 1/673 |
| 6 | 1 | 8 | 1.3 | 0.385 | 1/139 | 1/664 |
| 6 | 1 | 6 | 1.3 | 0.387 | 1/136 | 1/650 |
| 8 | 0.75 | 6 | 1.52 | 0.405 | 1/25 | 1/113 |
| 8 | 0.875 | 12 | 0 | 0.409 | 1/43 | 1/195 |
| 8 | 0.875 | 8 | 1.3 | 0.401 | 1/42 | 1/189 |
| 8 | 0.875 | 6 | 1.52 | 0.399 | 1/41 | 1/183 |
| 8 | 1.1 | 12 | 0 | 0.406 | 1/62 | 1/286 |
| 8 | 1.1 | 8 | 1.3 | 0.399 | 1/62 | 1/279 |
| 8 | 1.1 | 6 | 1.52 | 0.396 | 1/61 | 1/272 |
| 8 | 1.375 | 12 | 0 | 0.404 | 1/77 | 1/395 |
| 8 | 1.375 | 8 | 1.3 | 0.396 | 1/78 | 1/387 |
| 8 | 1.375 | 6 | 1.52 | 0.393 | 1/77 | 1/380 |
| 10 | 0.875 | 12 | 0 | 0.411 | 1/18 | 1/83 |
| 10 | 0.875 | 8 | 1.52 | 0.406 | 1/17 | 1/80 |
| 10 | 0.875 | 6 | 1.83 | 0.405 | 1/17 | 1/76 |
| 10 | 1.3 | 12 | 0 | 0.407 | 1/37 | 1/167 |
| 10 | 1.3 | 8 | 1.52 | 0.401 | 1/37 | 1/163 |
| 10 | 1.3 | 6 | 1.83 | 0.398 | 1/36 | 1/158 |
| 10 | 1.75 | 12 | 0 | 0.403 | 1/50 | 1/259 |
| 10 | 1.75 | 8 | 1.52 | 0.398 | 1/51 | 1/254 |
| 10 | 1.75 | 6 | 1.83 | 0.394 | 1/50 | 1/249 |
| 12.5 | 1.5 | 12 | 0 | 0.407 | 1/18 | 1/80 |
| 12.5 | 1.5 | 8 | 1.83 | 0.403 | 1/20 | 1/91 |
| 12.5 | 1.5 | 6 | 1.83 | 0.406 | 1/20 | 1/88 |
| 12.5 | 1.5 | 5 | 2.14 | 0.405 | 1/19 | 1/86 |
| 12.5 | 2.125 | 12 | 0 | 0.403 | 1/27 | 1/135 |
| 12.5 | 2.125 | 8 | 1.83 | 0.398 | 1/27 | 1/133 |
| 12.5 | 2.125 | 6 | 1.83 | 0.400 | 1/26 | 1/130 |
| 12.5 | 2.125 | 5 | 2.14 | 0.398 | 1/26 | 1/128 |
| | | | | | |
| BVC |
|---|
| Diameter | Thickness | f/ | Obs. Dia | r | P-V | RMS |
| 8 | 1 | 6 | 1.52 | 0.398 | 1/51 | 1/226 |
| 10 | 1.25 | 6 | 1.83 | 0.399 | 1/33 | 1/148 |
| 12 | 1.5 | 6 | 1.83 | 0.407 | 1/22 | 1/100 |
| 12.5 | 1.5 | 6 | 1.83 | 0.409 | 1/19 | 1/86 |
The following table shows a slightly different approach to arranging the 3-point cell data. This table gives support radii optimised for a range of mirror diameters and thicknesses. These were calculated for plate glass mirrors, but the differences for Pyrex or BVC are small enough to be ignored. All of these designs result in no more than 2.5 nm RMS deformation of the mirror surface (1/200 wave). This allows some room for construction tolerances with a reasonable probability that the finished cell - mirror combination will perform well, even for high resolution work. The designs assume that focal ratio is 5 and a reasonably sized diagonal is present. Moderate changes in focal ratio will not have large effects, except perhaps on very thin mirrors.
| Plop Optimized Radii for 3-Point Cells |
|---|
| | Thickness (mm) |
| Diameter (mm) |
| 100 |
| 150 |
| 200 |
| 250 |
| 317.5 |
|
| 6 |
10 |
15 |
20 |
25 |
33.3 |
37 |
42 |
53 |
| 20.2 |
19.3 |
19 |
18.8 |
18.65 |
|
|
|
|
| |
|
29.1 |
28.72 |
28.5 |
|
|
|
|
| |
|
|
|
38.9 |
38.5 |
|
|
|
| |
|
|
|
|
|
47.88 |
47.75 |
|
| |
|
|
|
|
|
|
|
61.60 |
|
© 2002 Mark D. Holm
Revised January 21, 2005 |
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