In general, in one aspect, the invention features a system including a light source, a plurality of interferometers configured to receive light from the light source and to form output light, each interferometer including a first optic and a second optic, the first and second optics configured to be mounted on a first object and a second object, respectively, where first object is moveable with respect to the second object, the first and second optics being configured introduce an optical path length difference (OPD) between two components of the light to form the output light, the OPD being related to the position of the first optic with respect to the second optic. The system further includes a plurality of detectors configured to detect the output light from the interferometers, a modulation apparatus in the optical path between the light source and the detectors, the modulation apparatus being configured to vary an OPD between the two components of the light over a range including OPDs for which a net OPD of the output light from at least one of the interferometers at the detectors is zero, a plurality of waveguides configured to direct light between the interferometers, the modulation apparatus, and the detectors, and an electronic controller in communication with the detectors, the electronic controller being configured to determine information about a position of the first object based on the detected output light from at least one of the interferometers.