From a mathematics standpoint it makes sense that a len's image quality at any particular radius in the image plane might change continuously with f-stop.
It also makes sense that if the image quality is best in the center of the image plane at some f-stop, it will also be best at f-stops not too far from that.
Certainly this is what happens with simple spherical surface lenses. More complex lenses are evolved form such simple lenses so it makes sense that they share these characteristics.
But it isn't necessary that they do so; smear a circle of vaseline the center of a good lens & see what happens to center-vs edge quality for proof of that!
Dave
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