The 18-point cells described here all use six isosceles triangles. Two triangles are located at the ends of each of three bars. The three bars' centers are located at 120 degree intervals. Each triangle has three support points that contact the mirror.
Plop allows designs where the angles between support points and the relative forces on the support points are varied. This differs from "conventional" designs in which the forces on the support points are usually equal. I have used both of these options for the 18-point cells. One result is that the triangle pivot points are not necessarily located at the "centroid" of each triangle.
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.)
r1 = Radius of circle on which inner six mirror support points lie as a fraction of mirror blank radius.
r2 = Radius of circle on which the bar pivot points lie as a fraction of mirror blank radius
r3 = Radius of circle on which the twelve outer mirror support points lie as a fraction of the mirror radius.
L = Length of each bar.
B = Base of each triangle as a fraction of the mirror blank radius.
A1 = Altitude of each triangle.
A2 = Altitude of pivot point on each triangle.
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)
Focus Shift = Change in focal length due to cell induced deformation. (In millimeters)
V.A. = Was PLOP's Variable Angle feature turned on for this cell? Y= Yes, N = No
V.F. = Was PLOP's Variable Force feature turned on for this cell? Y= Yes, N = No
See below
for correspondence with cell dimensions in The Dobsonian Telescope by
Kriege and Berry.
| Pyrex | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Diameter | Thickness | f/ | Obs. Dia. | r1 | r2 | r3 | L | B | A1 | A2 | P-V | RMS | Focus Shift |
V.A. | V.F. |
| 13.7 | 0.75 | 4.34 | 3.5 | 0.406 | 0.570 | 0.813 | 0.659 | 0.434 | 0.368 | 0.221 | 6.0nm | 0.83nm | -0.014mm | N | N |
| 16 | 2 | 6 | 2.6 | 0.384 | 0.535 | 0.761 | 0.618 | 0.394 | 0.351 | 0.117 | 1/147 | 1/1072 | -0.016mm | N | N |
| 16.50 | 0.75 | 4.6 | 2.5 | 0.398 | 0.578 | 0.832 | 0.668 | 0.438 | 0.405 | 0.135 | 1/35 | 1/250 | Y | Y | |
| 17.50 | 1.00 | 4.5 | 4.0 | 0.4017 | 0.5682 | 0.8108 | 0.6560 | 0.4197 | 0.3815 | 0.1272 | 1/61 | 1/391 | -0.023mm | N | N |
| 24.00 | 1.625 | 5 | 3.5 | 0.3435 | 0.5453 | 0.7536 | 0.6297 | 0.3950 | 0.3838 | 0.09757 | 1/51 | 1/327 | Y | Y | |
| 24.00 | 1.875 | 5 | 3.5 | 0.3457 | 0.5420 | 0.7522 | 0.6262 | 0.3951 | 0.3801 | 0.09960 | 1/57 | 1/376 | Y | Y | |
| 24.00 | 2.125 | 5 | 3.5 | 0.3478 | 0.5398 | 0.7511 | 0.6233 | 0.3954 | 0.3769 | 0.1014 | 1/62 | 1/415 | Y | Y | |
| Plate Glass | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Diameter | Thickness | f/ | Obs. Dia. | r1 | r2 | r3 | L | B | A1 | A2 | P-V | RMS | Focus Shift |
V.A. | V.F. |
| 16.00 | 0.875 | 5 | 2.6 | 0.3952 | 0.6559 | 0.8139 | 0.6559 | 0.4213 | 0.3910 | 0.1304 | 1/67 | 1/411 | -0.0221mm | N | N |
| 16.00 | 0.875 | 5 | 2.6 | 0.3417 | 0.6359 | 0.7561 | 0.6359 | 0.3914 | 0.3888 | 0.0945 | 1/114 | 1/586 | -0.053mm | Y | Y |
| 18.00 | 1.625 | 5 | 3.1 | 0.3920 | 0.5460 | 0.7775 | 0.6304 | 0.4124 | 0.3576 | 0.1192 | 1/83 | 1/566 | Y | Y | |
| 20.00 | 0.875 | 5 | 3.1 | 0.3386 | 0.5561 | 0.7587 | 0.6422 | 0.3963 | 0.3938 | 0.0902 | 1/43 | 1/258 | Y | Y | |
| 20.00 | 1.625 | 5 | 3.1 | 0.3898 | 0.5527 | 0.7906 | 0.6382 | 0.4181 | 0.3726 | 0.1242 | 1/63 | 1/473 | Y | Y | |
| 20.00 | 2.125 | 5 | 3.1 | 0.351 | 0.536 | 0.750 | 0.619 | 0.396 | 0.372 | 0.104 | 1/95 | 1/670 | Y | Y | |
| 30.00 | 2.125 | 5 | 4.5 | 0.3448 | 0.5433 | 0.7533 | 0.6287 | 0.3951 | 0.3822 | 0.0983 | 1/34 | 1/220 | Y | Y | |
| BVC | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Diameter | Thickness | f/ | Obs. Dia. | r1 | r2 | r3 | L | B | A1 | A2 | P-V | RMS | Focus Shift |
V.A. | V.F. |
| 20.00 | 2.000 | 5 | 3.1 | 0.350 | 0.537 | 0.750 | 0.621 | 0.396 | 0.373 | 0.103 | 1/93 | 1/648 | Y | Y | |
In their book, The Dobsonian Telescope, Kriege and Berry
give dimensions for 18 point mirror cells. One should not use the dimensions
they give, because they were designed before the use of PLATE and
PLOP. Their diagrams and detailed mechnical design are however
still quite useful. Their diagram and table for 18-point mirror cells is Table
5-5 found on page 123 of the first edition, ©1977. They use different
descriptions for the cell dimensions. The following table lists the
correspondence between Kriege & Berry's terms and the terms used in this web
site.
Note: r = radius of mirror. This is the diameter / 2, not the
radius of curvature. The asterix (*) means the arithmetic multiply operation.
| Kriege & Berry | This site |
| Radius of outer support points | r * r3 |
| Radius of inner support points | r * r1 |
| Base of triangle (isosceles) | r * B |
| Altitude of triangle | r * A1 |
| Balance Point from vertex | r * (A1 - A2) |
| Length of bar connecting triangles | r * L |
| Radius to center point of bar | r * r2 |
© 2002 Mark D. Holm