Because studies employing d′ and η are based on the theory of signal detectability, the theory is reviewed in sufficient detail for the purposes of definition. The efficiency, η, is defined as the ratio of the energy required by an ideal receiver to the energy required by a receiver under study when the performance of the two is the same. The measure d′ is that value of (2E/N0)12 necessary for the ideal receiver to match the performance of the receiver under study, where E is the energy of the signal, and N0 is the noise power per unit band width. The measure is extended to include the recognizability of two signals. Every set of signals is described by a Euclidean space in which distances are the square roots of the energy of the difference signal, (EΔ)12. The unit of measure is the square root of one-half of the noise power per unit band width (N0/2)12.