[ATM] Re:How much cell induced deformation is too much?

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

Steve Koehler wrote:

>...Of course, we also need to standardize on surface error
or wavefront error.  I don't know about others, but for me it seems more
natural to talk about wavefront error in waves and surface error in
nanometers.<

Standardizing wavefront error will be easier than standardizing surface
error.
The reason is that surface and wavefront error don't  have a constant
common denominator. Depending on what form of surface deviation
dominates, we'll go from the wavefront having anywhere from  1/2 to 2
times the surface error. On one side of the range, there is a pure figure
error, either rotationally symmetrical (conic error, resulting in
spherical aberration) or asymmetric (astigmatism). Any conic error "w" on
the surface will result in w/2 wavefront error at the best focus. This is
because every axial location within defocused section has slightly
different perfect reference wavefront, whose radius is determined by the
axial separation of such point from mirror's center. While surface error
doubles in the wavefront vs. perfect reference wavefronts for both
paraxial and marginal foci, it is only half of the surface error vs.
perfect reference wavefront for the location midway between these two -
which is what makes it best, or diffraction focus.

In the case of astigmatism, any surface error "w" will double in the
wavefront. However, due to the avearge error over the entire wavefrontof
being smaller than that with spherical aberration, it will in effect be
comparable to an error smaller by a factor 0.68 (for primary astigmatism
vs. primary s.a.), coming to the comparable wavefront error being
approximately 1.4 times the surface error, or nearly three times larger
than that resulting from a conic error.

And for  random surface irregularities of relatively small amplitude,
surface error will nearly double in the wavefront. This is because
defocus caused by such surface imperfections is not intense enough to
move best focus from its original location, and the perfect reference
wavefront is one for the paraxial focus. The effect of such surface
irregularities is given through MTF/Strehl degradation factor, closely
approximated by 
1/2.72^(39.5w^2), "w" being the RMS wavefront error. This factor can be
directly applied to the Strehl figure obtained for the figure error.

For an actual surface, with all three forms of deformation (and then some
likely) combined, it will be hard to come up with any sort of unified
surface standard. The competent error will inevitably be that measured at
the wavefront, vs. perfect reference wavefront.

In regard to cell induced surface error, it is important, but shouldn't
be taken to the extreme. Taking into account error contributions from the
atmosphere, local turbulence, thermal imbalances, miscollimation,
c.obstruction, TE, roughness, etc. 0.80 Strehl seems to be out of the
reach. For apertures ~16" and larger, seeing alone will take care of it
nearly 100% of the time. Considering this, an attempt to preserve
non-existent near-perfect optical quality by nearly elliminating cell
induced error seems pointless. If an effective Strehl is, say, 0.7 (which
can be considered very good), 4.4nm RMS surface, resulting in 0.99
degradation factor, would only degrade the Strehl to 0.693 - bellow the
level of perception. But this doesn't mean that error caused by cell
deformation shouldn't be kept as small as reasonably possible - just like
all other error sources than can be influenced.

Vlad
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