Strehl correlates very strongly with RMS wavefront error - for the simple reason that both are calculated from the same measurements - ie both are essentially measurements of smoothness, and effectively equivalent..
The correlation between Strehl and P-V wavefront error isn't so perfect, however. The graph below is from scope test results for SCT and mak scopes 7" or more aperture, published on the Russian lab website I found a while back. I've discarded the worst of the scopes (below strehl 0.75). The curves are just least squares fits to the data using Excel, not based on the theory, and that they don't intercept at 0 is most likely due to limitations in the test equipment, more than anything else.
When looking at the test results its possible for example to have optics showing a bad turned edge that normally would be rejected (bad P-V measurement) yet is smooth and has a good strehl value. Conversely systems can have a poor smoothness (low strehl under 0.85) and yet have an acceptable P-V wavefront error under 0.3.
In this respect both P-V and RMS (or strehl) values are relevant.
Nirvana is theoretically possible - you could be lucky enough to acquire a scope with P-V under 0.1 wave and strehl above 0.985... in 20 years I have seen only two examples that good and neither were SCTs.
If the surface of a mirror were a plowed field an acre wide, it could be smooth or rough on several scales:
--from edge to edge (which we call wedge normally, but we'll call "figure" in this example)
--height variations from side to side in the form of small hills (which we call zones)
--piles of dirt in rows (which we call micro-ripple)
--rocks and clods of dirt (which we call surface roughness)
The question is, which level of smoothness has the greatest impact?
Well, just about everyone would say figure is the most important.
But what is critical beyond that?
That's where you get into a grey area. Zones certainly throw light in different places, but micro ripple can scatter light all over the place.
When you see two mirrors of 1/8 wave P-V on the wavefront, which mirror would you rather have, the one with a perfectly smooth surface but
one 1/16 wave deep pit, or a mirror with a coarse, rough surface that never exceeds +/- 1/16 wave from the ideal surface.
Both have he same P-V, but the 2nd mirror will be obviously poorer in the field than the first one.
And that is where RMS comes in because it describes a weighted average for the surface. In this case, the first mirror would have a higher RMS than the second,
which would calculate out to a higher Strehl ratio, too.
Yet, there isn't a mirror exactly like the first, that is perfect except for one tiny flaw in one spot. The 2nd example is far more likely to be the case in practice.
So what we care about is P-V and RMS and smoothness on the micro level as well. CZ is right that smoothness on all levels is important.
A mirror maker that makes a mirror with a low P-V error, and a smooth surface on both the larger and smaller scales is one I want to do business with.