Experimental measurement of the geometric phase of non-geodesic circles

We present and implement a method for the experimental measurement of geometric phase of non-geodesic (small) circles on any SU(2) parameter space. This phase is measured by subtracting the dynamic phase contribution from the total phase accumulated. Our design does not require theoretical anticipation of this dynamic phase value and the methods are generally applicable to any system accessible to interferometric and projection measurements. Experimental implementations are presented for two settings: (1) the sphere of modes of orbital angular momentum, and (2) the Poincar\'e sphere of polarizations of Gaussian beams.