Abstract We describe a general model for the behaviour of a sensor based on a Fabry–Perot interferometer placed between crossed polarizers. Compared to single-pass polarimeters, the sensitivity for the measurement of intracavity anisotropies is shown to be enhanced by a factor of the order of the square of the finesse compared to single-pass polarimeters. Our model, based on a vectorial spatial description of the cavity, predicts the response of the system to circular and/or linear intracavity anisotropies. It also gives the ultimate sensitivity and takes into account the spurious backgrounds. Experimental illustrations are presented for different types of reciprocal and non-reciprocal anisotropies. Moreover, it is shown that the insertion of an optical bias combined with a modulation of the intracavity anisotropies leads to experimental sensitivities limited only by the shot noise level, in agreement with theoretical predictions. We discuss further improvements and potential applications for the polarimeter.