Fourier-based design of asynchronous phase detection algorithms

Abstract

Phase detection is an important issue when dealing with optical metrology techniques for which the magnitude to be measured is encoded through the phase of a given fringe pattern. Asynchronous phase detection techniques are employed when the rate of phase change (frequency) it is not known. These techniques always present a variable frequency response, in other words, their ability to recover properly the phase depends strongly on the local frequency. In many experiments, it is possible to have a rough knowledge about the range of frequencies involved. Therefore, it constitutes a great advantage to have a procedure to design an asynchronous demodulation method which is suited to a particular frequency response for a given experiment. In this way, we get a better behaviour against noise which leads to more accurate and reliable phase extraction. In this work we present a technique to design asynchronous demodulation algorithms with a desired frequency response using a Fourier-based technique. The method allows the design of algorithms with a limited algebraic error in the recovered phase which have better properties than standard asynchronous phase detection techniques as it is shown in numeric and real experiments.