Mirror Cell Design Space at 2.5 nm Deformation

Mirror Cell Design Space

Each curve on this plot represents the design limit of Plop optimized cells with a given number of support points. Mirrors whose dimensions lie on or to the left of one of these curves will experience no more than 2.5 nanometers of non refocussable deformation when supported on a Plop optimized cell with the given number of support points.

The 3, 6, 9, 18 and 27 point cells used for this analysis are the default designs used in Plop's automatic cell design feature. The 9 point cells were optimized with variable angles and variable forces turned off. The 12 point designs use Tom Krajci's 12h layout. (Plop setup for the 12h layout.)

The three sloping lines indicate mirror thickness to diameter ratios. Note that, especially for smaller mirrors, the cell curves are nearly asymptotic to the 1:20 ratio line. This means that it is difficult to impossible to find a practical cell for a small mirror this thin and still have good, 2.5 nm, support.

The 2.5 nm deformation limit is based on these ideas.

For really fine images, one would like a Strehl ratio of 0.95, a demanding criterion.
A Strehl ratio of 0.95 implies a maximum combined, surface error of about 9 - 10 nm RMS.
If we assume a truly outstanding primary and secondary mirror with 5 nm RMS error each, the maximum allowable cell induced deformation is given by
Sqrt(10² - (5² + 5²)) = 7.1 nm
to
Sqrt(9² - (5² + 5²)) = 5.6 nm.
Plop simulations by Jeff Anderson Lee show that building tolerances of 1 - 2 mm, reasonable for careful work without expensive machine tools, can result in a factor of 2 to 4 worsening in cell induced deformation.