The judgement of null zones is for me an area that I am having a hard time trying to learn.
John, David ("One of largest sources is judging were each zone nulls"), and Ivor ("The depth of focus at the center is many times that of the outer zone.") hit the nail on the head.
To get a "feel" of what they're saying, you need to be able to calculate what is know as the defocus tolerance.
Defocus tolerance (s) for each zone (z) is
s = λ/(2Nsin2Uz)
N = refractive index of the medium (in this case N = air, which RI is ≈ 1.00)
λ = wavelength of the light used
in this case sinUz = Dz/2R.
Dz = the mirror zonal aperture diameter
R is the radius of curvature of the mirror.
The defocus tolerance formula above gives you a focal range within which the error will not exceed 1/4 wavelength. It's intimately related to the f-ratio of the test beam. The slower the beam the greater the tolerance.
The best way to think of defocus tolerance is the case of a Foucault test is as an uncertainty range within which you can not know when the zone is nulled.
As an example, let's look at the defocus range for a 222 mirror with radius of curvature of 2000 mm. The mirror is tested at R. Let's say that you use a geren LED for light source, so λ ≈ 0.00055 mm.
Testing the 90% zone so D200 = 200, R = 2000, sinU = 0.1, sin2U = 0.01, N = 1.00, λ = 0.00055
defocus range = 0.00055/(2*1*0.01) = ±0.0275 mm
For a 20 mm central zone D20 = 20, sinU = 20/2000 =0.01, sin2U = 0.0001
defocus range = 0.00055/(1*1*0.0001) = ±2.75 mm
What does this mean? This means that for the marginal zone your uncertainty will be ±0.03 m, but for the central zone your uncertainty will be ±3 mm -- a 100-fold increase in uncertainty where the null is! So, if you start nulling the zone near the center you can be off by as much as 6 mm and not know it! Clearly such a large error will throw everything off.
This is one (of several) problems with the Foucault test. Sure, we can all make the numbers appear right, but unless we know exactly where the zonal nulls are we're creating a "fantasy mirror." This is where the need for alternative tests comes in as a sanity check. Chances are that for slower mirrors the results will be better then for very large an fast ones. Much of it also depends on experience of the maker.
Autocollimation with a full aperture flat mirror using a Ronchi test, and finishing with a knife-edge null is a better alternative then the Foucault because there are no zones to measure and the test is entirely qualitative.
If you wish to know your mirror like with no other available test to ATMs, then I strongly suggest you make a giant step and joint the interferometry group https://groups.io/g/Interferometry, build your own interferometer and get verifiable quantitative results.
Edited by MKV, 25 April 2018 - 03:12 PM.