A system and method for sensing position of an oscillating moving element. The inventive position sensor includes a first arrangement for sampling the position of the element at first positions thereof and providing samples in response thereto and a second arrangement for calculating other positions of the element using the sample of the first position. In the illustrative application, the first arrangement includes an LED and a photodiode and the moving element is a piston of a long-life cryogenic cooler. A processor receives samples from the photodiode and solves an equation of motion therefor. The equation of motion is P(t)=Asin(.omega.t+.theta.)+B, where P(t)=the position of the element; A=position waveform amplitude; B=position waveform DC Offset; .omega.=angular frequency of operation; t=time; and .theta.=position waveform phase.