Re: [ATM] Re: Satisfying "Mililes-Lacroix" is neither necessarynorsufficient for "diffaction-limited" performance

["Nils Olof Carlin" <nilsolof.carlin@telia.com>]

Vladimir and Mike,

> >The next question I have is, does satisfying "M-L" do anything more than
> force you to work a little harder? Maybe you would do just as well by
> setting your standards for measured RMS wavefront error higher while
> completely ignoring slope errors. I think that's the route Jim Burrows
> has advocated taking for some time.

One thing to keep in mind is that what Rayleigh said (about low-order sph.
aberration) of the 1/4 wave P-V is that this was when aberrations begin to
be "decidedly prejudicial" - as I interpret it, a criterion to tell lousy
from mediocre, not to tell excellent from good. So, a wavefront error of say
20 nm RMS would satisfy the Maréchal criterion but not the amateur that will
work, or pay, for excellence.

On another list have been shown some nice simulations of diffraction images
for identical RMS errors but widely different transverse aberrations(RTA).
My simplified view is that the RMS says how much of the light is within the
Airy disk and how much in the rings, but the RTA says something about how
wide the light is scattered in the rings. A small amount that is widely
scattered may be objectionable in much the same sense that the spikes from
the spider vanes are. One other consequence is that turbulence seems to
affect a high RTA mirror by increasing the "spikiness".

> As you said, blur at the location of the circle of least confusion nearly
> equal to the Airy disc implies
> 0.046  waveront RMS error at the best focus, but only if the case of pure
> spherical aberration.
> That is, only for a surface that is near-perfect conic. Actual mirrors
> will likely be more or less deviant,
> which means that we can't count on that "best focus" anymore. Actual best
> focus can be better,
> but chances are it will be worse than that. I don't know how Texereau
> arrived at the RTA~1 or less standard,
> but him being so meticulous, it likely resulted from a number of
> practical tests. That is exactly what we are
> missing here, in order to come up with a specific conclusion on the
> ralation - at least statisitical - between
> the RTA~1 standard and 1/4 wave criterion: results of analysis of a
> number of actual mirrors with known Foucault
> test data and (reliable) RMS surface error.

See above - perhaps I can help making these simulations available to this
list. They are not actual measurements of course, but they serve to
illustrate the ideas. I guess it wasn't Texereau, but rather Couder and/or
Danjon whose criterion #1 deals with RTA. My guess is that the Airy disk
radius is a convenient, invariant reference length, and Texereau (as opposed
to others) does not interpret it in a physically doubtful way (e.g."...does
not divert light rays outside the diffraction disk"!).

Nils Olof


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