ATM Re: More Spheroidalage

[Michael Peck <mpeck1@ix.netcom.com>]

Sorry, somehow the subject header got lost in my first post. So, to get it 
back to the proper thread I'm restoring it.

Anthony Stillman wrote:

>Rayleigh criterion references wavefront error, 1/4 wave wavefront error,
>which for a spheroid at the diffration focus amounts to 1/16 of a wave of
>transverse spherical abberration. And thus, a tolerably degraded image.
>The title to Texereau's table is just plane wrong and what the table itself
>implies, what Couder's formula implies is that 1/4 wave of transverse
>aberration, one wave of wavefront error is tolerable. Well, perhaps this

Sorry again, this is still wrong and getting wronger. The formula on page 
19 of Texereau (2nd edn.) is correct -- it correctly gives the relationship 
between focal length and diameter for a spherical mirror that just 
satisfies Rayleigh's criterion. The data in his Table I are accurate, and 
the table itself is appropriately titled.

I'm tempted to launch into a discourse on aberration theory, but it really 
shouldn't be necessary. A mirror that just satisfies Rayleigh's criterion 
does in fact have 1 wave of spherical aberration as measured at the 
paraxial (or marginal) focus. That same mirror does have 1/4 wave of 
spherical aberration as measured at the diffraction focus. And when you 
change the focus position of a telescope you are in fact changing your 
reference wavefront as the term is understood in aberration theory.

Talking about "waves of transverse aberration" really makes little sense. 
The linear diameter in waves of the Airy disk out to the first PSF minimum 
for a perfect unobstructed system is 2.44F where F is the focal ratio. At 
f/8 that is almost 20 waves diameter, or 11 microns. No matter how tightly 
you squeeze the "rays" the light is going to fill up that disk (and then 
some of course).

We really should try to move beyond 19th century physics one of these days.

Mike Peck

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Michael Peck
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