  This paper describes polarimetric strategies based on measuring the light's
geometric phase, which results from the evolution of the polarisation state
while traversing an optical system. The system in question is described by a
homogeneous Jones matrix, which by definition, contains mutually perpendicular
eigenpolarisations. Our leading theory links the system's Jones matrix
parameters (eigenvalues and eigenvectors) with the input polarisation state and
the geometric phase. We demonstrate two interferometric techniques. The first
one measures the geometric phase based on the relative lateral fringe
displacement between the interference pattern of two mutually-orthogonal
polarisation states. The second technique uses the visibility of the
interference fringes to determine the eigenpolarisations of the system. We
present proof-of-principle experiments for both techniques.
