Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization

Micro Fourier transform profilometry (μFTP) is a recently developed computational framework for high-speed dynamic 3D shape measurement of transient scenes based on fringe projection. It has been demonstrated that by using high-frame-rate fringe projection hardware, μFTP can achieve accurate, denser, unambiguous, and motion-artifact-free 3D reconstruction at a speed up to 10,000 Hz. μFTP utilizes a temporal phase unwrapping algorithm, so-called projection distance minimization (PDM), in which multiple wavelengths are used to solve the phase ambiguity optimally in the maximum-likelihood sense. However, it has been found that the choice of the wavelengths is essential to the unambiguous measurement range as well as the unwrapping reliability in the presence of noise. In this work, the relations between the wavelength combination and the noise resistance ability of PDM are analyzed and investigated in detail by analytical, emulational, and experimental means. This leads to a qualitative conclusion that the noise resistance ability of PDM is fundamentally determined by the value of each item in wavelength ratio: a smaller value of each item in wavelength ratio means better noise resistance ability in phase unwrapping. Our result provides a guideline for optimal wavelengths selection in order to improve the noise resistance ability of a practical fringe projection system. Simulations and experiments based on a microscopic fringe projection system are demonstrated to validate the correctness of our conclusion.