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 = a · sin + b , where p = the position of the element ; a = position waveform amplitude ; b = position waveform dc offset ; ω = angular frequency of operation ; t = time ; and θ = position waveform phase .