All mirrors will be tested using the tests indicated below.
The Foucault test is particularly being used to determine the shape of the parabolic curve across the mirror. This is done by measuring the focal length of mirror sectors as a function of the distance to the center. This is very convenient for mirrors that have a light parabolic shape.. Let's say f/5.
When mirrors become severely parabolic the number of sectors increases rapidly. Consequently the Foucault test becomes less accurate as the many sectors tend to overlap..
The Ronchi test is used to check the shape of the curve after the mirror has been polished. During the polishing phase this test provides information on how spherical the mirror is. In particular the curve shape around the edge can be checked for deviations.
The overall mirror curve has to be sufficiently spherical to continue with the figuring process. The Ronchi test is a relatively easy test that has proven its value many times.
The interferometer test uses the interference pattern between a laser source and the reflected signal from the mirror. This test is a bit more difficult because for averaging out data and calibrating the setup many pictures of the interferogram have to be taken.
The result is a total overview of the mirror surface up to an accuracy of 1/10 Lambda. Because of it's accuracy, this test is predominantly used for fast mirrors <f/4.