Re: [ATM] Re: Weird Foucault readings

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

Vladimir Sacek wrote:


> Yes, I did run into that article some time ago. Nils tried to determine
> at what point of zonal defocus the zonal null is likely to be most
> "convincing" visually.

Not quite. I determined the point on the axis where the diffraction peak
falls from a given zone (of a perfect paraboloid), and from that, determined
the center of the zone in question as the point whose normal intersects the
optical axis at this point. This to ensure that the best estimate of the
zonal center is used. This is not exact with KE readings, but simulations
show (could you think of a better method?) that this a better approximation
than either Couder's or Texereau's radii.


> Both, "non-linearity" (uneven illumination across
> the zone) and reversed illumination change for the two opposite zones
> result from the zonal defocus, which causes different areas of the zone
> to be affected differently (illumination-wise) for any given position of
> the KE.

Here, it seems you assume that you can treat the zone as having separate
areas - this is simply not possible, for good wave-optical reasons. The
profile of the diffraction pattern is formed from the profile across the
whole zone aperture.

> All three suggestions for the correct zonal radius are around the
> best focus (also called diffraction focus) location. Couder is right on
> with (h^2+z^2)/2R, while Texereau and Carlin are slightly off.

The diffraction peak is placed according to my formula (given the zone is
part of a parabola). When you say that Couder is "right on", what other
criterion do you use?

> But the difference is rather negligible: for a 16" f/4.5 it would come to
less
> than 1/40 wave wavefront error at ~70% zone. Much more substantial error
> is already built in by averaging out the entire zone to its mean radius.

I don't quite see what you mean by "averaging out the entire zone" - could
you clarify?
I agree that the error from an unsuitable choice of zonal center is often
small, but not necessarily negligible with a small, slow mirror, using few
zones.
>
> What the article doesn't address is what is the error margin in dermining
> the most convincing null that is imposed by the objective perception
> limitations of an average individual (with necessary skills assumed) in
> real-life conditions.

Mathematically modelling an average Joe isn't easy, but Mike Peck and Jim
Burrows have done extensive work on how uncertainties in KE readings will
affect the estimate of the mirror profile. You might go from there.

> Part of those real-life conditions is less than
> perfect mirror, with less than symmetrical zonal surfaces which changes
> defocus structure and affects zonal illumination in an unpredictable
> manner.

By no means unpredictable - knowing the profile, the light distribution can
be calculated numerically to high accuracy. But a mirror with small-scale
irregularities can't really be measured to much accuracy by any method, and
going from light profile back to actual zonal profile is not possible in
general, I guess. However, a light distribution that isn't as even as
expected should be a warning that the zone can't be accurately evalued - by
Foucault or otherwise - this would apply to e.g. a turned down edge.

> Consequently, while we could try to approximate error margin for a
> perfect or near perfect mirror, it seems to be pretty much unpredictable
> for other - and rather common - scenarios.

Conclusion - don't bother to measure your mirror unless it *is* perfect -
and if it is, why bother? <G>

Nils Olof

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