Design of asynchronous phase detection algorithms optimized for wide frequency response

In many fringe pattern processing applications the local phase has to be obtained from a sinusoidal irradiance signal with unknown local frequency. This process is called asynchronous phase demodulation. Existing algorithms for asynchronous phase detection, or asynchronous algorithms, have been designed to yield no algebraic error in the recovered value of the phase for any signal frequency. However, each asynchronous algorithm has a characteristic frequency response curve. Existing asynchronous algorithms present a range of frequencies with low response, reaching zero for particular values of the signal frequency. For real noisy signals, low response implies a low signal-to-noise ratio in the recovered phase and therefore unreliable results. We present a new Fourier-based methodology for designing asynchronous algorithms with any user-defined frequency response curve and known limit of algebraic error. We show how asynchronous algorithms designed with this method can have better properties for real conditions of noise and signal frequency variation.