Don, thank you. It's interesting topic. IME, a difference can be noted, but why? Is it the inherent smoothness or is it the transverse aberration?
Yes, I suspect the Airy disc remains the same diameter (pending any article by Sirchz), but does it change appearance other than being dimmer? Does it get mushy and surrounded by faint light at lessor correction and more tight at better correction. If so, is this responsible for the improvement we can see? No reason to doubt that, really, but is a mushy appearance the reason?
The diffracted wavefront coming to focus is full of interference, some points on the disc are canceled while others are augmented (CO aside for the moment.) If the optic is perfect, then it adds no more disruption to the phase nor the pattern of interference. However, if the optic does not produce a spherical wavefront, then the greater optical path from different rays changes the pattern of interference.
But, the radii of the Airy disc, first minimum and second maximum, etc., should remain constant and based solely on the wavelength and aperture. So, as I understand it, the first minimum is a point of maximum interference cancelling all energy from that point (or at that radii) regardless of the figure. So, the Airy disc will still fall to zero at a set first minimum distance even as the peak intensity falls off. The PSF curve at the very edge of the Airy disc remains very steep, hence the Airy disc well defined. (I was wrong above thinking the slope toward minimum would be more shallow.)
So, I am not sure transverse error has a role in giving the Airy disc a mushy appearance. This diffracted and aberrated wavefront still cancels energy at the first minimum, just the pattern (at set radii determined by wavelength and aperture change in relative brightness.) However, it does redistribute the light across the pattern as the total energy must remain the same.
Similarly, micro ripple across the entire surface is an aberration, it sends rays here and there and induces some very fine changes in the wavefront. But they tend to cancel over the entire wavefront. Some points are, say, +1/10th and other points are -1/10th from the perfect reference sphere. Without doing the math, I think total RMS is not affected. In other words, what's left to affect the average is the overall wavefront deviation (back to transverse ray's again
) But, I think at focus ray's do not define the pattern seen, they are simply geometrical representations of self interfering wavefront and not a portion of the wave providing energy into the first minimum. As I can understand it, anyway.
So, what would give the in focus Airy pattern that washed out look and is this what makes the difference between a better optic and a lessor one? Or is it the redistribution of light across the pattern through interference induced by diffraction, surface deviation (phase), and the CO? I dunno, but I suspect it's the redistribution of light into the rings that makes the difference. CO induced diffraction would simply add to the wavefront's diffraction making the redistribution more pronounced (and a tiny bit more so if the secondary is not perfectly flat?)