There are several satisfactory ways of testing concave surfaces. We generally use the methods detailed below:-
For spherical mirrors, one method is to set up a point light source at the centre of curvature of the mirror (twice the focal length) and observe the image formed.
A laser pointer with the lens system removed is perfectly adequate as a light source.
These tests are quite practical for an enthusiastic amateur making his/her own mirror and telescope.
In practice the light source must be set up just off axis so the image is formed close to, but not coincident with the source so that it can be viewed accurately. The image is then viewed either with an eyepiece or on a knife edge and is interpreted to show defects in the mirror.
For non-spherical mirrors, like the Parabolic, as used in a Newtonian Telescope, the light source can be abberated to correct for the surface not being spherical.
For mirrors up to about 300mm diameter, this can be done very efficiently with a single Plano-convex lens placed close to the light source. The exact distance from the light source is measured as a result of the diameter, focal length and conic shape of the mirror under test.
A knife edge is placed close to the focus of the converging rays, and by small increments edged into the beam until the image seen begins to darken. In a perfect mirror, the smallest movement of the knife edge at this point will make the image go completely dark. In practice the dark area spreads over the mirror gradually as the knife edge is inclined. This test is known as the Dall Null Test after the Englishman who invented it - Horace Dall.
Pictures taken of "real mirrors" will always show some shading unless the mirror is incredibly perfect. The picture here is the null of a 500mm mirror to our normal minimum specification of PV 1/4λ Wavefront error.
The test is usually adequate for a final test for small mirrors up to 300mm Diameter and 1/4 Wave accuracy. It does become less accurate for larger mirrors and we use other tests to confirm accuracy for these.
If the knife edge is now moved forwards and backwards along the optical axis using a micrometer, individual readings of the micrometer can be taken as the shading spreads over the mirror. These can be used to calculate the RMS surface smoothness, - which for one of our normal specification mirrors will be less than 1/15λ.
For larger mirrors, we often use the Dall Null test as a preliminary test during the figuring as it is easy to set up, but we follow on with either a Double Pass, which is described below, or we may resort to the James test, which is similar in principle to the Dall Null, but uses a large spherical mirror to abberate the light source.
Regarding all main mirror testing, we generally use red light of 625nM wavelength as sources are now so readily available.
If we are providing a Certificate of Conformity, we usually convert the figures obtained at 625nM to equivalent values at Yellow light of 546nM.