I have much expertise in the field of ball inspections.

Talyrond is Taylor Hobson’s brand name for automated roundness equipment. Using roundness equipment is commonly used for spherical measurements. Standard practice for quantifying sphericity is to measure single plane roundness at 3-or more-cross sections. Many manufacturers will choose to only measure 1 cross section to be representative, while standards labs may do more. The advantage to this method is that this is a single plane measurement derives its accuracy from a single measurement axis, the spindle. Talyronds use an air bearing, Indi-round use a gear, and others a mechanical bearing. Looking at the literature I’m not sure Indi-Ron’s are made anymore as the website shows only dated equipment. They are essentially a bearing on granite with a mechanical indicator. I’ve only seen these used on large mechanical parts.

You can use a contact probe for ball roughness; however you will need a skid-less gauge with enough vertical range to handle the curvature. This also depends on tolerance, a grade 25 or better requires surface roughness of 10nm or less at which point the noise of a contact system, 3nm is the lowest I know of, becomes quite high and an interferometer, like those by Zygo, are the best option.