Abstract We develop a theoretical model that shows that the overlap integral of two counterpropagating waves is an invariant along propagation in a reciprocal optical system. We use this property to implement a method that allows a quantitative measurement of the conjugation fidelity of a phase conjugate mirror. Applied to the double phase conjugate mirror (DPCM) this invariant can be rewritten as an equality between the ratio of the conjugation fidelity of the two ports of the DPCM and the ratio of the phase conjugate transmission of the two beams. If restricted to a plane wave case this relation becomes the well known equality of the diffraction efficiencies in both directions. We use the model to implement an experimental characterization of the DPCM, measuring its conjugation fidelity, and demonstrating that it is a reciprocal optical system.