[ATM] Re: Plop auto cell 36 and 54 points...

[Vladimir Sacek <vladis.2@juno.com>]

Mark Holm wrote:

>So, atms, making good mirrors 
for high quality observing want to hold surface errors to less than 
about 31 nM P-V, or, using the better criterion of RMS, about 9 nM. <

The Rayleigh 1/4 wave p-v wavefront criterion applies to spherical
aberration; 
for other forms of wavefront deformation the "diffraction limited" p-v
requirement 
is also different (usually lower). What is specific for spherical
aberration is that the
wavefront error at the best focus is not twice the surface error, but
half of it. For instance,
a 6" f/8.17 sphere has 1/4 wave p-v spherical aberration error at the
best focus, while 
its surface error vs. parabola of the same paraxial r.o.c. is 1/2 wave.
If the sphere surface is 
compared to a parabola that focuses at the best focus of the sphere (so
that parabola's r.o.c. is 
~0.6mm shorter) the surface error is zero; if compared to a parabola that
focuses at the circle of 
least confusion (nearly 0.9mm shorter r.o.c.) the surface error is 1/4
wave, and so on.
But as long as you work (test) at any given radius, all you need for 1/8
wave wavefront of spherical 
aberration is a smooth conic with 1/4 wave (138nm p-v, or 41nm RMS error
for the 550nm wavelength)
surface deviation from perfect parabola.

The 1/4 wave s.a. criterion should be actually called Conrady criterion,
not Rayleigh criterion. 
Lord Rayleigh hasn't been aware of the peculiarities of s.a. defocus, and
his original criterion 
was for the paraxial focus. Have we stayed with the original concept, the
wavefront=2x surface error 
would work just fine for spherical aberration too. A 6" f/8.17 sphere has
1 wave error at the paraxial focus.
But 1/4 wave criterion applied to the paraxial focus would imply 1/16
wave actual (best focus) error as a 
requirement. It would also be a more appropriate criterion for
"diffraction limited".

Vlad
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