For example a secondary might have corrections that null out errors from the primary. You could have two mirrors with Strehls of 0.8 whose combinatiion yields Strehl 1.0. So the whole formula to me is bogus.
Glenn, thanks for pointing that out. It dawned on me later, as well. I think you're spot on.
Also the argument an obstruction improves resolution should be qualified. Yes it can help separate equal magnitude stars, but that effect is only worthwhile for fairly massive obstructions, like 50% or more. At that level you do not have a visual friendly system.
Glenn, Wilfried has some empirical results that much over 40% is actually detrimental to resolution and certainly for contrast. He's observing at a minimum magnification required for a split and at large CO's he's less successful. I suspect it's because the first ring is interfering with his relatively low power observation, as I understand his explanation, giving a mere notched split, as he describes it and IIRC. In any case, he's finding that much above 30%, resolution is not as clean. But, I think it's in his method of minimal power observing according to his acuity.
In my own experience, I've bested Dawes on a couple of occasions and attribute that to a 30% CO as the lab math seems to work in the real world. Now, there are errors in measurements and calculations, but something is happening allowing nearly equal doubles (STT 507 granted 7th magnitude pair) to be resolved. Not so much a test of Strehl, but attesting to CO effects of higher resolution in accord with 1 - co^2. I dunno how to explain it otherwise, unless one magnitude fainter made the tight split possible.
A real stunner was observing a crater form (unbelievable, I know) at a mere 1.4 km in diameter near lunar apogee. The math suggests this small crater subtended a mere ~0.71" arc (give or take due to errors in the calculation.) Using the small angle formula as an approximation, 0.71" arc = 206,265 * 1.4/400,000 (kilometers). It turns out, more accurate measurements of that crater are slightly smaller but I'd have to find the thread where David Knisely gave a better measure along with the known distance to the moon that night. The point being, that crater should not have been observable, but it was...plain as day and exactly three times on a superb night. This is what sent me on a rampage trying to understand how in the heck...
Also, other close equal binaries such as 31 and 7 Tau, both very close to Dawes pairs, were easily split. Even 7 Tau, the closer of the two and advertised at less than Dawes, had a clear grey space diving it suggesting a slightly tighter split is possible with less contrast between them. But, what are we talking about here, mere hundredths of an arc second. Very tiny and prone to errors of measurement. But, for some reason, resolution below the standard Dawes separation is occurring on several objects.
I dunno, Glenn, I am uneasy about disagreeing with you as I have so much respect for your views. Unless I am missing something, my own experience tells me the obstruction is making a difference albeit a very tiny but exiting difference exceeding the limits. Oh, and elongation of Chi Aql at 0.42" arc (again, given errors in measurement) or about Raleigh/2 is another example of another observation that should not be possible, but it was. Not easy, but with some patients over two or three nights, the (very nearly) correct PA could be determined. Oh, and the "apparent" elongation of Io and albedo on Ganymede /might/ be additional anecdotal evidence.
Something is allowing better resolution than I could have ever expected. It's not my aging eyes, it might be the seeing. I doubt it's the performance of the scope being simply diffraction limited (best I can tell) and not premium quality surely. It has to be the CO. (Well, it does not have to be, but it seems to be.)
If it came from a text I would like to know which one.
See Neptune's post above.
Great!! ...some folks will be bothered by this though
Had I read that before I posted, I would not have bothered. But, in fact, I'm excited, having the observing experience of a lifetime.