Cell is a public domain program written originally as part of the design of the 24" equatorially mounted telescope Byron Melland and I built for the Pomona Valley Amateur Astronomers. An early form of the program in BASIC (for 9 and 18 point cells only) was published in ATM and has been used by a number of commercial telescope manufacturers for their mirror cells. Since then the program has been polished a bit and a new design has been added for 27 point cells. The current version of the program is available from SEDS Optics directory under the name cell.zip.
The design criteria implemented in Cell is to divide the mirror into sections of equal weight, each supported at its centroid. Groups of three adjacent support points are supported by triangles, which in turn are supported at their centroids.
For the 9 point assembly a base triangle supports three inward-pointing isosceles triangles which support mirror sections. The support points form an outer ring of six points and an inner ring of three points.
For the 18 point assembly a base triangle supports three crossbars, each of which supports two inward-pointing isosceles triangles. The support points form an outer ring of twelve points and an inner ring of six points.
For the 27 point assembly a base triangle supports three inward-pointing isosceles triangles, each of which supports three triangles which support mirror sections. The triangles that contact the mirror consist of an inner ring of three outward pointing isosceles triangles and an outer ring of six scalene triangles. The inner points of the scalene triangles are at the same radius as the outer point of the isosceles triangles. This yields three rings of support points: an inner ring of 6 points, a middle ring of 9 points, and an outer ring of 12 points.
The program computes the actual radii of the support rings, and gives the dimensions of the resulting triangles. It takes into account the curvature of the front surface and the existence of a central hole, if any. As inputs you specify the mirror diameter, its edge thickness, and the focal length, which determines the thickness of the mirror everywhere else. A text printout shows measurement specifications and an optional scale drawing in HPGL (resulting in drawings similar to those shown here), which will print out on HP Laserjet printers or HP Plotters only.
The DOS program is simple and reasonably user friendly, but there is no attempt to make this a polished commercial program.
I must point out that although Cell meets the stated design criterion quite well, the equal mass distribution is not the last word on the subject. Better design criteria would be to minimize the deviation from the theoretically ideal surface, or better yet, to minimize the deviations of the slope. This is a much more complex problem and Cell does not pretend to rigorously meet these criteria.
Toshimi Taki, a Japanese aircraft engineer and amateur astronomer who is also very interested in mirror cell design, has written several articles for Sky and Telescope about the design problem. In the April 1996 issue of Sky and Telescope he shows the results of a Finite Element Analysis (FEM) on 9 and 18 point designs generated with Cell. This analysis shows the resulting surface deformation due to flexure and shear. (Note the fact that the contour interval in the illustrations is 0.002 of a wavelength!) The FEM analysis vidicates both designs quite well. The 27 point design has not yet been tested with FEM, but Toshimi plans to do so soon.
You are free to use Cell for private or commercial mirror cells, but any commercial use should be accompanied by a credit in the documentation stating that the mirror cell design was computed using Cell by David Chandler and giving a reference to the David Chandler Company home page: http://www.DavidChandler.com.
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