The counter ring fits exactly over the barrel adaptors and eyepieces. It is used to fix a specific position in the barrel adaptor. The counter ring is clamped using grub screws.
The stop ring is used to set the insertion depth of barrel adaptors or adaptors, for example if you want to have reproducible focus positions.
The adjustment ring is also often used to prevent tilting problems with locking grooves in ring clamps.
Similarly, several rings can be used to make the eyepieces absolutely parfocal with each other, eliminating the need for refocusing. Or you can adjust an eyepiece to be perfectly parfocal with a camera. This allows you to use the eyepiece to locate the object, focus and then start photographing immediately.
