The basic idea is to calculate the theoretical paraboloid mirror shape (P) and compare this with the results from the test results using a Foucault tester (Pf). The difference (P-Pf) indicates what polishing is still to be done to achieve the theoretical paraboloid shape. It is then a case of deciding what polishing strokes are to be carried out to achieve the theoretical paraboloid shape. To help do this the mirror is separated into a numbers of bands or zone with the same area, and therefore each zone will have the same light gathering capacity.
The central radius of each zone, or band, is defined as ri.
The theoretical paraboloid mirror shape is given by P=ri2/R, where ri is the zone central radius and R is the mirror's centre of curvature (CoC). If the tester light source and knife edge move together then P=ri2/(2.R).
To get an idea of when figuring is finished limits (X) can be calculated either side of P. This shows how close the polished surface should be to the theoretical surface. X=p.R/(2.ri), where R and ri are as above and p=1.22.h.f/D where h is the wave length of light (0.217E-06 inches), f is the mirrors focal length, and D is the mirror diameter.
Applying these equations to a 6" mirror at f#8 and f#4 shows why it is easier to figure an f#8 mirror compared to a lower f# mirror;
As can be seen the upper and lower limits for the f#8 mirror are significantly greater and presumably allows larger errors in the final figure relative to an f#4 mirror.
Note that the graphs are only an approximation of the images seen through he Foucault tester.
1st Figuring Polish 2nd Figuring Polish
This produced a spherical surface, therefore not graph.
