A highly sensitive accelerometer for determining the acceleration of a structure includes a mass within a housing suspended by opposing support members. The support members are alternately wound around a pair of fixed mandrels and the mass in a push pull arrangement. At least a portion of one of the support members comprises a transducer capable measuring the displacement of the mass within the housing. An embodiment of the invention employs optical fiber coils as the support members for use in interferometric sensing processes. Arrays of such interferometer based accelerometers may be multiplexed using known techniques.