THE CELL
General The purpose of the cell is to mount the primary in the tube. The mirror usual rests completely free in the cell. I.e. it is not fixed. When the telescope is pointed at the zenith, the mirror weight rests on support points. The mirror just rests on these points, and is not fixed to it. Some people prefer to glue it to these points, but by means of a silicone glue that still allows a slight movement of the mirror. When the telescope is pointed at the horizon, it rests in a sling or on several points along it circumference. To secure the mirror against dropping out of the cell, a few clamps may be used that are not in contact with the mirror unless it would actually drop of. The reason for not fixing the mirror in place is that the surface deformations caused by mechanical stress due to fixation tension or thermal expansion can be strong enough to give a noticeable image degradation.
These type of cells are called "floating" cells.
Number of support points So called "full thickness mirrors" need only three support points, placed at 70 % of the radius as measured from the center. The thickness to diameter ratio is about 1:6 for these mirrors. This leads to very heavy mirrors for larger diameters. The "thin mirrors" have a thickness to diameter ratio of more than 1:6 sometimes to as much as 1:10. These need more support points; 9, 18 or 27.
If more than three support points are used, special care has to be taken that all points support the mirror equally. This is achieved by using triangles with can freely pivot on their center. For example the 9 point cell has three triangles, each triangle pivots on one of the points of the base triangle. The 18 point support cell has six paired triangles
The number of points should be chosen such, that no (or an acceptable amount of) mirror sagging occurs in between the points. Today we see a shift occurring in the way these points are found. Up till now, and probably for some time in the future, they were found by trial and error. Since computing power is ever increasing, it has now become feasible to find these points using finite elements analysis (FEM: Finite Element Modeling). FEM is very processing intensive since it also finds the support points by trail and error, however now with the computer simulating the mirror sagging. Since a number of people are working on this, it can be hoped that in the near future SW will be available to do your own FEM. For the time being the old "equilibrium approach" still yields good results.
Where to place the support points The equilibrium approach assigns each point the same amount of weight. To my knowledge it has not been proven to be the best solution, but it is generally accepted. Note in the formulas below, D refers to the mirror diameter.
3 Point Cell : The support points should be placed on a circle with 0.707D. They should be 120 degrees apart.9 Point Cell : The support points on the (isosceles) triangles should have the following distances between them : 0.408D, 0.253D, 0.253D. The triangles should be pointed toward the mirror center. The inner circle of support points on the triangles should have a diameter of 0.204D. The triangles should be supported on a circle with a diameter of 0.304D.
18 Point Cell : The support points on the (isosceles) triangles should have the following distances between them : 0.211D, 0.218D, 0.218D. The triangles should be pointed toward the mirror center. The inner circle of support points on the triangles should have a diameter of 0.204D. The triangles should be supported on a circle with a diameter of 0.331D. The rocker (which connects two triangles) should be supported on a circle with a diameter of 0.286D.
Note : There are more solutions for the 18 point support, the one above is a slightly improved proposal from John H. Hindle.
Ventilation The cell should allow rapid adjustment of the mirror to the environment temperature. Some people mount ventilators to speed this process.