When talking about optical resonators for lasers I found on several places that confocal resonator is defined as "two spherical mirrors of the same radius of curvature R and separated by a distance L such that the mirror foci F1 and F2 are coincident". This definition is from the book "Principles of Lasers" by Orazio Svelto.
Is this correct definition or should it instead contain word "parabolic" instead of "spherical"? Parabolic mirrors (eg. cross section is parabola) have focus that is a single point in space but that is not the case for spherical mirrors (cross section is sphere) because of their spherical aberration. So how can two spherical mirrors have the same foci if focus is not well defined for each of them?
Also it seems to me that spherical mirrors are used as synonyms for parabolic mirrors in many places. For example here: http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mireq.html