To do interference testing all you need to do is flash polish the concave tool used to grind the convex one and polish it spherical. When the interference fringes are straight then the convex surface is also spherical.
Dave, the problem today is that most people don't use solid glass tools but rather ceramic tile
tools which, obviously, cannot be used for contact interference. Purchasing extra glass disks just to turn them into matching test plates makes a one-time project really costly and wasteful, so it is no surprise ATMs shun away from such techniques and seek alternative ways to get the job done.
That's why picking a well-thought-through design from the start, one that matches your skills and tooling, is so critical. For ATMs, refracting objectives or compound correctors with as many matching surfaces as possible is the most economical approach. One such example is the Houghton corrector, where the rear element is biconcave and the front element biconvex where R1 = -R3, and R2 = -R4.
Almost symmetrical telescope objectives are also possible, especially with modern glass melts. If one can devise an objective where three out of four surfaces are known to be spherical, either by Foucault or by contact interference of matching surfaces, then the system can be nulled by DPAC by working on the front surface of an otherwise finished objective. Also, configurations with very long, almost flat R4 can be advantageous.
Unfortunately, Jim here is working in the dark, except for R2 (which can be contact tested against R3). Short of making two additional test plates his engima will not be easily solved. Assuming he determines R2 is spherical, then it would be a matter of judgment whether R1 or R4 or both are the culprits.
I would guess it's probably R1 because its relative power (shorter radius of curvature) is more likely to affect the overall wavefront error, than the weaker R4 surface, and is morel like to distort the wavefront even with smaller figure errors than R4.
I don't have time to do this right now, but this can be illustrated easily using a simple raytrace analysis of wavefront variation over different conic constant values for for R1 and R2. Maybe later on tonight I can find some time to do this analysis.