Rayleigh Criterion and reflectors

I'm wondering how the Rayleigh Criterion for a certain aperture is affected by the central obstruction in a reflecting telescope, specifically a SCT.
Does the percentage of obstruction by the secondary reduce the expected figure? Obviously, the image of the star is tighter in a refractor. So do I have different Rayleigh limit for an 8" reflector vs an 8" refractor?
Thanks,
David

In general, obstructed telescopes need higher
wavefront quality than 0.8 Strehl to meet
1/4 wave p-v of spherical aberration level.
Needed rms error of spherical aberration is not hard to estimate: it is

rms=sq.rt.{[0.0055+0.058log(1-c^2)^2]/(1-c^2)^4}

where "c" is the relative size of c.obstruction.
For the p-v error it only needs to be multiplied
by 3.354. So 20% obstructed telescope (c=0.2)
needs rms=0.064 and pv=0.214 or 1/4.7 wave of
spherical aberration to achieve 0.8 Strehl level.

A 30% obstructed telescope needs 0.015 rms or
1/20 wave level. A 33% obstruction would require
better than perfect wavefront - unfortunately,
not an option.

Vlad