Re: [ATM] Looking for information on a telescope design

["vladimir sacek" <vla@toast.net>]

Scott,

> When the refractor is well-corrected for both spherical & coma, however, I
> find that the most significant change in off-axis behavior is in fact, the
> addition of field curvature added by the Mersenne front end as I had
> predicted, although to credit your earlier point, if any residual 
> spherical
> is present, off-axis coma is still aggravated, just not as hugely as it is
> for the case when coma is not corrected to begin with.

The question is what is, specifically, the "well-corrected" requirement.
The 4" f/10 doublet apo I used has little over 1/4 wave p-v of 3rd order
coma (1/20 wave RMS) 1.2 degrees (20mm) off-axis, plus about half
as much of 5th order coma of the opposite sign, making the total coma
error roughly twice smaller. That definitely goes as well corrected when
used alone.

It also has about a wave p-v of 3rd order astigmatism that far off, and
no 5th order astigmatism. The total error is about 0.23 wave RMS,
similar to 3/4 wave of spherical aberration.

When the stop is displaced by about 1200mm after placing the apo into
a Mersenne arrangement, the 3rd order coma at 0.3
degrees (20mm) off-axis is doubled, with the sign reversed, and its
5th order coma is seven times stronger, also with sign reversal.
 At the same time, the astigmatism is actually slightly lower. The error
totals over 0.6 wave RMS (about 2 waves of spherical aberration equivalent).

And the 4" f/10 triplet apo, corrected for 3rd order coma, with very low
 residual 5th order coma (~1/60 wave RMS 1.2 degree, or 20mm off-axis)
and with similar level of 3rd order astigmatism with the stop at the 
aperture,
gets strong 3rd order coma, nearly twice as much of 5th order coma of the
opposite sign, no 3rd order astigmatism, and less than a wave of 5th order
astigmatism, when in the Mersenne at 0.3-degree (20mm) off-axis. Its total
error raises from 0.2 wave RMS to nearly 1 wave for the same linear field
radius of 20mm.

For the comparison, classical f/3.6/10 Cassegrain that far off axis would
have 0.3 wave RMS (combined 3rd order coma and astigmatism),
Dall-Kirkham nearly 0.6 wave RMS (mostly 3rd order coma), and
an f/4.5 Newtonian 1.7 wave RMS of mainly 3rd order coma.

Both apos have better spherical correction than one can realistically wish
 for: the doublet less than 1/30 wave p-v level, and the triplet less than
1/20 wave. But - and that may matter - the correction results from balancing
3rd and 5th order spherical roughly between 1/8 p-v and 1/4 p-v wave level.

As you said, lens astigmatism is independent of stop position when both
spherical aberration and coma are corrected. That means *corrected*,
and applies to both, 3rd and 5th order aberrations. Residual spherical
directly contributes to abaxial coma and astigmatism resulting from the
displaced stop, and it seems to be applying to its balanced residuals.

In other words, in order to avoid off-axis aberrations caused by stop
displacement in a Mersenne/refractor arrangement, the refractor needs to
be corrected for all three, spherical coma and astigmatism, both 3rd and
5th order.

It may be hard to find in an apo doublet or triplet. But, as Scott E. 
suggested,
I checked out the Petzval refractor. They were the two posted to the list by
Richard Snashall, and both fit the bill. The first, Ptz-04-29x, scaled down 
to
 an 4" f/7.5 system, shows as little as ~1/30 wave RMS 20mm (1.5 degree)
off-axis, and the second, Ptz08-53x, only slightly more, 1/23 wave. Both 
have
actually corrected the three aberrations mentioned - spherical, coma and
astigmatism - down to the 5th order.

 I don't know if this level of correction is typical for Petzval 
refractors - Richard
should have better insight into it - but it seems to be the preferred choice 
for the
Mersenne/refractor arrangement, if one wants to avoid the risk of a soft 
outer
field that can be worse than  in a relatively fast
(f/10) Dall-Kirkham (what would be the purpose of going through extra effort
and expense?).

With such Petzval refractor, the only added aberration in the Mersenne 
arrangement
would be, as you say, field curvature. Since the system astigmatism should 
be
very low, the resulting field curvature radius is well approximated by the 
Mersenne
Petzval curvature, given by Rc=kR1/2(1-k), with "k" being the minimum 
secondary
diameter in units of the aperture diameter, and R1 the primary radius of 
curvature.

Vlad


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