Did you use a cell phone camera to take the images? If so, congratulations for actually getting an image. That's not easy. In my experience, the simple camera lens can alter what is actually seen. How close are your images to what you actually saw? How does the image appear in focus, relatively sharp and high contrast? Is there something that gave you cause or simply curiosity? The reason I ask is because in focus images matter, and if you're not happy with it. If you are, great, it's just an exercise in curiosity.
I trust your at the same "shim" distance on either side of focus. For over correction, the shadow outside will be a bit larger than inside. You seem to show this, but only if you are very nearly the same distance on both sides of focus. However, the geometric size of the outside image is larger suggesting under correction. This happens because the edge comes to focus well before best focus and diverges more as you move outside focus providing an overall larger image. The edge defines the size of the pattern we see.
So, a few things can be happening in terms of spherical aberration. First, you could be a bit further outside focus in which case both the secondary shadow and the geometric size of the pattern will be larger as shown. If the outside image is a little smaller being closer to focus, both the shadow and the size will be more inline with your inside image showing better correction. So, ensuring both images are close to the same defocus is important.
Secondly, I'd like to see the ring patterns more clearly looking for a brighter central ring or edge ring on either side of focus. Use both the shadow and the ring brightness to confirm over or under correction. If the inner diffraction ring emerges from the shadow and it is brighter inside focus, that would confirm over correction generally. With pure over correction, the edge ring will be brighter outside focus and the geometric size of the pattern will be a little smaller with a larger shadow. That presumes a smooth correction error over the entire mirror surface, which may or may not be the case.
So, third, you could have a mix of correction error where the edge is steeper (under corrected) producing a larger geometric pattern outside focus and the center is over corrected showing a larger shadow outside focus. If your images are at the same defocus, this is what is indicated. This larger shadow happens because, as Suiter says, the energy at the center evacuates allowing the shadow to show up a little earlier and grow as we defocus outward. This is because the center comes to focus before best focus and diverges more outside focus allowing the shadow to emerge. So, it's possible to have a larger outside image and a larger shadow as you show. The star test becomes more difficult to interpret because we may not have a smooth correction error.
I'd like to see the edge and central ring brightness more clearly in conjunction with the shadow size to get a better feel for what's going on. In your images above, it does appear as if the central ring inside focus is a little brighter suggesting over correction (center focusing short and edge focusing long) as well as a hint of an edge ring outside focus possibly being brighter. The brightness of the ring is suggestive of how far you are from it's focal point. You can use relative ring brightness to kind of estimate where your edge and center are coming to focus. The brighter the ring, the closer you are to it's focal point. For example, if you're inside focus and the inner ring bordering the shadow is brighter, you are closer to the central focus point suggesting it is focusing short of best focus.
So, with over correction, inside focus you are closer to the central zone focus (focusing short) thus the central ring will be a little brighter. When outside focus, you are closer to the edge focal point (as it is focusing long) and the edge ring will be brighter (and the central ring relatively dimmer). But, at the same defocus distance, geometry matters, too. Also with over correction, inside focus and further from the edge focal point, the size of the pattern will be larger than outside focus because of convergence and divergence of the edge. You show just the opposite suggesting some under correction, at least at the edge (and hopefully no turned edge, which is a form of over correction at the edge). So, I see conflicting signals above.
I'm taken aback a little by the amount of space between the inner shadow and the edge of the pattern. There is room for more than one diffraction ring between the shadow and the edge suggesting you may be several waves further from focus than what we might expect. (Either that or the simple camera lens is "correcting" your image into something else, something different than what you see visually with the shim). Ideally, we want to see a bight inner ring bordering the shadow and a bright outer ring at the edge with one diffraction ring between them. If you see anything close to that, you're fine. That's pretty much perfect if the shadows are about the same size, too.
In my opinion, if the inner ring is broken out on both sides not too far from focus, that's a good sign. You want to see this inner ring not too far from focus on both sides, and probably by the amount of defocus provided by the shim. This suggests a more equal distribution of energy across the defocused pattern (the edge and the center have the roughly the same energy) because all zones are focusing close enough together and likely to offer better than 1/4 PV SA (as a reference point). The longer it takes the central ring to emerge, the less the energy distribution is equally distributed across the defocused pattern suggesting greater correction error. So, IMO, if it emerges early on both sides of focus, you're probably fine. How fine is anyone's guess. (Obstruction size matters, too, how large is your obstruction)?
If you can get cleaner images, that'd be great. To me, the images provided are a bit difficult to interpret other than the shadow size. As mentioned above, on the shadow alone, I see nothing egregious either. At 1/4 PV SA, the smaller shadow should be about 0.7x the larger shadow (according to Suiter's graphic). You might be near that eyeballing it. But, don't forget to check for astigmatism in focus and slightly out of focus. Look closely for a slight eccentricity of the defocused image being perpendicular on either side of focus and a + pattern in focus (if seeing allows).
Classic over correction: http://www.astrogene..._45ft_f10_c.jpg
Sorry for the length...just having morning coffee.
Edited by Asbytec, 18 August 2019 - 06:47 AM.