Windowed Fourier ridges for demodulation of carrier fringe patterns with nonlinearity: a theoretical analysis

Accurately extracting phase or phase derivative is the most important requirement in optical metrology. However, in practice, there are many error sources, among which nonlinear distortion in fringe patterns is often encountered. Several techniques have been proposed over time to remove the nonlinearity error. Among these techniques, the windowed Fourier ridges (WFR) algorithm has been shown to be an effective solution insensitive to nonlinearity, but it lacks a theoretical justification. In this paper, we theoretically analyze the local frequency estimation error and phase extraction error, which not only proves the mentioned insensitivity, but also supports the performance prediction and error control, and thus is very important and useful in optical measurement. The theoretical results have been verified by computer simulations. Other error sources such as model error and noise are also compared and discussed.