Generalized frequency-shifting fringe projection technique

Traditional phase-shifting (PS) techniques and its variants often follow a two-stage pipeline for absolute phase retrieval, which retrieves the wrapped phase in the first stage, followed by unwrapping. By contrast, the recent frequency-shifting (FS) technique provides a more concise alternative to PS. It directly obtains the absolute phase in only a single stage without phase unwrapping, thus significantly simplifying the phase retrieval process. We further extend the traditional FS to a generalized version, termed generalized frequency-shifting (GFS). Instead of a constant frequency shift, we introduce a temporally varying frequency shift in GFS, to further eliminate frequency ambiguity, especially for pixels with large projector image coordinates. We provide both non-uniform discrete Fourier transform and least square-based algorithms for absolute phase retrieval from GFS patterns. After extensive experimental validation, our method has demonstrated improved stability and accuracy compared with previous methods, even with fewer projection patterns.