Unfortunately my spherometer can only measure flats and concave surfaces and even then it's only to detect small differences in depth to a high accuracy. It might manage the shallower R1 and R4 but would need to be remade to measure R3 which is around f0.7.
I would be a bit anxious about scratching the valuable fluorite surfaces with the plain steel ball bearings.
David
Thanks David for pointing out these practical difficulties.
Setting the spherometer aside, might it instead be possible to measure the radius R2 (once your re-polishing is complete) via reflection off that surface, by locating its center of curvature?
For purposes of distinguishing between glass types for the negative element (based on the individual element powers needed for color correction with CaF2, as a function of the Abbe Number of the glass used for the negative element), I wonder if one could then just assume R3 = R2 (as in reality these are unlikely to be too dissimilar, even if they are unequal), such that given this estimate of R3 and measuring the focal length for the fluorite element alone would let one solve for R4, and having thus deduced values for R2, R3, and R4, knowing the focal length of the assembled doublet would let one solve for R1 (for an assumed refractive index of the negative first element). From here, the check via raytrace (or just hand-calc of L.Ch.A between the F and C foci ?) to assess overall color correction for various assumed mating glass types might then enable one to draw empirical+analytic conclusions on whether the [thusly approximated] lens radii are consistent, or else inconsistent, with the mating glass type being KzFS2, KzF5, K7, etc. ?
Granted there may be some slight amount of 'circular logic' involved since the derived value for R1 will differ for each assumed mating glass, but because the Abbe values (dispersions) of the candidate mating glass types vary much more than do their refractive indices, so I'm thinking that this empirical+analytic 'test' of candidate mating glass materials still ought to be perceptive in showing which mating glass type(s) can be ruled out as inconsistent with the measured R2 and the measured diopter power of the fluorite element, no ?
Food for thought, anyway ...
Cheers,
-- Jim