Darell,

Theoretically perfect is a lot more understandable to me than putting a bunch of variables into the equation. After assuming scope A has optical fault X and scope B has optical fault Y, it approaches blue smoke and mirrors, and you can skew the data to favor either viewpoint at the extreme end of the discussion.

Oversimplification is always easier. That doesn't make it

good. Understanding actual telescopes inevitably requires

inclusion of actual factors. It may surprise you, but it is

not complicated at all. Aberrations and other wavefront

deformations, c.obstruction, seeing - they all can be with ease incorporated into MTF as degradation factors. It results in a realistic MTF.

If you're saying that a larger aperture scope with a poor mirror won't beat a perfect smaller refractor, that's all well and good for the poor soul who deliberately goes shopping for a scope with a poor mirror. I don't see how it helps the rest of us.

Poor mirror (or optics) is not a prerequisite for poor telescope or performance.

Nobody goes shopping for a poor telescope, but not a few people do get it, sometimes with

claims of good or even excellent quality. Larger apertures

are prone to larger errors from all sources; even a perfect

primary is not a promise of good performance.

Some of routine extra error sources of a large

Newtonian are primary deformation induced by its cell, thermal imbalance,

miscollimation, diagonal inherent

error and cell/thermal deformations, seeing,

and, of course, central obstruction. Let it be 1/8 wave

p-v mirror (0.95 Strehl) to begin with. We can say it is

a very good mirror. What will, say, 20% c.obstruction do?

We can quantify this effect with the lowering of the energy

encircled within the Airy disc, given by (1-c^2)^2, "c"

being the c.obstruction relative size. In this case it gives

0.92 which, for the left-hand side of MTF graph (which is

what matters for planetary observing) can be taken

as an MTF degradation factor. Combined with the correction

error, it will result in ~0.87. Although not a Strehl,

strictly talking (since it doesn't all come from wavefront

deformation), it can be looked at as sort of it. It says

that average contrast loss over the range of MTF frequencies

is ~13%, resulting in performance level comparable to

~13% smaller (linearly) aperture.

Let's say that miscollimation is 1/20 wave RMS , and that cell induced and thermal error are 1/40 wave RMS on both

primary and diagonal. Let's throw in 1/50 wave RMS on each, primary and diagonal, on account of local surface irregularities. Since these are mostly uncorrelated errors, we can use the square root sum squared to obtain likely cumulative error. The square root of the sum of all the RMS

errors squared comes to 0.076, or 1/13.1 wave RMS combined

error. From S~1/2.72^(39.5RMS^2), the appropriate Strehl

comes to 0.79. This is the next degradation factor to add,

and it lowers the system Strehl-like figure to 0.69.

Adding a very moderate 1/14 wave RMS seeing error results

in 0.82 degradation factor, lowering system's figure to

0.57. Starting out with a very good mirror, we ended up with

a telescope performing at ~0.57 Strehl level, a 1/8.4 wave

RMS level (from RMS=0.241sq.rt(-logS)), an equivalent of

1/2.5 wave of spherical aberration.

If similar calculation would be done for a 4"-6" apo

with 1/8 wave objective, all the error sources would be considerably lower. Thus the nominal aperture difference

would shrink down to a considerably smaller actual

difference. The point is that c.obstruction alone,

even if we put it at 35%, would play only a small part in it.

Vlad