The spherical shape is obtained by rotating a circle.
The formula for a spherical curve is:
Although the paraboloidal shape is the most used for newtonian, mirrors with a small aperture and long focal length may be left spherical without a noticeable performance degradation. When making your own mirror there is a small advantage, since a spherical mirror can be null-tested and it is (more or less) the result from the polishing stage. (So the figuring stage may be skipped)
The following table gives the minimum f/# for a given aperture that may be left spherical. The criteria is that the difference between the (ideal) paraboloidal and the sphere is maximal 0.14 micro meter. (1/4 of 560 nano meter)
D f/# mm inch 100 4 8.9 150 6 10.2 200 8 11.2 250 10 12.1
I know that the value's in this table are significantly different from the ones in Texereau's book (page 19). If anyone knows how A. Couder (Texereau used his formula) derived his formula, then please drop me an email. (For address see "Welcome" page)