Re: [ATM] Diagonal Size

["vladimir" <svla@isp.com>]

Polaraligned wrote:

>The bottom line was that a scope
with a CO would perform as well as an unobstructed scope of
a diameter equal to the telescopes diameter minus the diameter
of the CO.<

This empirical rule is both, very approximative and very conditional.
It should be applicable to low-contrast details, but doesn't look good
under even very basic scrutiny. The low-contrast performance is basically
determined by the amount of energy transferred outside the Airy disc.
Very close approximation for it is given by a simple expression 1-(1-c^2)^2,
with "c" being the relative size of obstruction, and the ratio number 
indicating
what portion of the energy encircled within the Airy disc for a perfect
unobstructed aperture has been lost to the outer pattern.

A 20% c.o. (c=0.2) will transfer ~8% of energy outside of the Airy disc.
That is comparable to 1/6.6 wave p-v of spherical aberration. Is this much -
or little - of aberration going to reduce an aperture's low-contrast 
effectiveness
by 20%? I doubt it. According to a more thorough analysis in 
Rutten/Venrooij's
"Telescope Optics" (p215), it is only a partial truth: good portion of 
resolvable
details will have contrast level similar to that in a 20% smaller aperture 
(linearly),
but the contrast recovers for details closer to the resolution treshold, 
resulting
in a very small reduction in the low-contrast resolution limit. For smaller 
c.o.
there is no effect on resolution treshold at all.

Basically, there are two factors to consider: (1) contrast level within the 
range
of resolvable details, and (2) resolution treshold. The "rule" reflects 
contrast level
of details out of the treshold proximity. For the treshold itself, it errs 
less as
the size of obstruction increases, and begins to come close to the
actual effect for obstructions of over 40%.

Of course, this is only a standardized MTF scenario, but it is accepted as a 
good
general indicator. What pulls obstructed telescopes down, closer to the 
"rule" are
factors other than c.obstruction effect. In general, it is that all error 
sources tend to
increase with aperture (seeing error definitely does it), and also that some 
of error
sources happen to be more significant in obstructed apertures. It is only 
good
to be aware of the specifics influencing performance of obstructed vs. 
unobstructed systems,
instead of throwing all the "credits" to the size of central obstruction.

Vlad




_______________________________________________
ATM mailing list http://www.atmlist.net/