In general, in one aspect, the invention features methods that include using an interferometer to produce an output beam having a phase related to an optical path difference between a path of a first beam and a path of a second beam, wherein the first beam contacts a measurement object and either the measurement object or the interferometer are coupled (e.g., directly attached) to a stage that is moveable within a reference frame. The methods further include monitoring variations in the phase while both varying an orientation of the stage with respect to at least one degree of freedom in the reference frame and keeping a reference mark on the stage in a common position with respect to the reference frame, and determining information based on the monitored variations, the information being related to a contribution to the optical path difference caused by a deviation of the path of the first or second beam from a nominal beam path.