Intensity-referenced phase unwrapping for shot reduction in multi-frequency fringe projection profilometry

Traditional multi-frequency fringe projection profilometry suffers from low efficiency, as it requires capturing multiple phase-shifted fringe pattern sequences at different frequencies-the highest frequency ensures measurement resolution, while low frequencies provide references for phase unwrapping. To improve measurement efficiency, this paper proposes an intensity-referenced phase-unwrapping technique, where only a single pattern needs to be captured at each low frequency, with its intensities serving as references for phase-unwrapping purposes. With this proposed technique, by using the wrapped phases, background intensities, and modulations calculated from the highest-frequency fringe patterns, the possible intensities of a low-frequency fringe pattern are reconstructed. Comparing these possible intensities with the captured intensities of the low-frequency reference pattern enables the determination of the low-frequency pattern's phases. However, ambiguities arise in this process. To resolve this issue, specific phase shifts are introduced into the reference fringe patterns, and a tri-frequency algorithm is deduced to uniquely determine low-frequency phases. Experimental results confirm the high efficiency and reliability of the proposed technique.