"RKE" stands for "Rank Kellner Eyepiece". It is pretty much a standard Kellner reversed.
Rank, Kaspereit, Erfle, per filing for the RKE trademark ( click on document called UNCLASSIFIED ). Plus, when you look at a standard Kellner design it is a plano-convex doublet followed by a convex-plano singlet. And RKE is a double-convex singlet, followed by a convex-concave doublet. So both groups use different curve directions than the Kellner. When you look at the field doublet in an RKE, it is the same configuration as the field doublet in an Erfle or a Kaspereit design. The Kaspereit was developed from the Erfle. The upper 2 doublets of the Kaspereit are both double convex doublets. So the RKE is like removing one of those doublets, and replacing the other with a same curved singlet. So overall, looks much more like a hybrid of the Erfle and Kaspereit designs than it does at all like a reversed Kellner at all. The only common thing between the RKE and the Kellner is that they both are 3 elements in a 2-1 (or 1-2) configuration. The curves are all wrong between them, unlike the Erfle and Kaspereit.