If the state of polarization of a monochromatic light beam is changed in a cyclical manner, the beam acquires-in addition to the usual dynamic phase-a geometric phase. This so-called Pancharatnam-Berry phase, equals half the solid angle of the contour traced out on the Poincaré sphere. We show that such a geometric interpretation also exists for the Pancharatnam connection, the criterion according to which two beams with different polarization states are said to be in phase. This interpretation offers a new and intuitive method to calculate the geometric phase that accompanies non-cyclic polarization changes. We also present a novel setup that allows the observation of the geometric phase for such changes. The phase can depend in a linear or in a nonlinear fashion on the orientation of the optical elements, and sometimes the dependence is singular. Experimental results that confirm these three types of behavior are presented. The observed singular behavior may be applied in the design of optical switches. © 2010 Copyright SPIE - The International Society for Optical Engineering.