A paraboloid has the same ROC as a particular sphere at its center/bottom, and then the ROC continuously increase as you move away from the center/bottom.

The slider below the surface error plot in FigureXP is nice - when you drag the ROC slider to the left, you shorten the ROC of the calculated paraboloid that you are comparing with the (reconstructed) shape of the mirror you are testing.

On a smaller, slower mirror, you can drag the slider far enough to make the outer zone "flat". This means you have shortened the ROC of the mirror shape you are "shooting for", so it is necessary to remove material inside the outer zone to match this shape. See image below, this is a 10" f/5 mirror that requires about 3.3 waves of center deepening. )This size and f/# is just about perfect, because dragging the slider all the way left or right matches the ROC at the edge and the center of the mirror, respectively.)

Try it. Pick some zones, and use the same ROC and a diameter of 10".

With respect to your original image that you posted, the sphere that you drew matches the ROC of the parabola at the center of the parabola. To make it match at the edge, move the sphere downward and increase its diameter (ROC) so that the slope matches where it meets the parabola at the edge of the imaginary mirror.

Note the green text below the FigureXP error plot - when you first go to the (F4) Surface Error Analysis screen, FigureXP automatically calculates the best fit ROC, which is 0.06216" shorter than the ROC. This makes the error plot flat at the 70% zone, or 3.5" radius, and this minimizes the P-V error when comparing a sphere to the ideal parabola. If you drag the slider all the way to the left (for the 10" f/5 mirror I use), you shorten the ROC by another -0.058". So, the total reduction is ~0.120", which is the same as the measured correction difference from center to edge when measuring with a moving source tester (r^2 / (2R)). So, you have to reduce the ROC of the center of the mirror by 0.120" compared to the edge in order to fully correct the mirror.

This is what you would get if you could measure the ROC of the exact center of the mirror and the very outer edge, but we can't. You measure at the center of zones with Foucault, so the difference beween readings between the center of the outer zone and the center of a zone that does not include the center will be less, I think it was ~0.093" for this mirror.

I've always wanted to explain this - think I might make a short article up about it......