Adequate phase unwrapping based on 2π cycle invariant between shifted phase maps

To obtain an adequate unwrapping solution for reliable phase measurement under noisy circumstances, a novel unwrapping algorithm is proposed. This algorithm extracts abundant valid pixels and rejects noise based upon revealing a property of 2π invariant, which is implied between wrapped phase maps with shifted fringe patterns. Distinct from conventional algorithms that use residues or minimum norm solution to attenuate the impacts of noise affected areas, this technique is free from the uncertainties arising from inadequate resources or over-smoothing effects during the unwrapping process. The performance of the proposed algorithm is demonstrated and confirmed through both computer simulations and practical experiments carried out using a fringe projection system. Superior capability in handling noise affected phase images is then achieved. [Display omitted] •To obtain reliable and accurate unwrapped results from noisy interferograms, a new algorithm is proposed that extracts object characteristics while rejecting noise.•The algorithm investigates the affluence behind the arctan operation by adding a shifted wrapped phase map, providing a much deeper understanding of the Nyquist theorem that has been used with two thresholds −πandπ for a long time.•A significant property, referred to as the 2π invariant, is identified that distinguishes between fringe lines and noisy pixels among wrapped and underlying phases. This property is the main contribution of the paper and the key to the proposed unwrapping algorithm.•Distinct from conventional algorithms, this algorithm handles noise without using the theory of residues and thus avoids the complexity and inadequacy in establishing branch-cuts during the unwrapping process.•This algorithm also does not use any minimum linear norm to smooth over phase details, which are related to the object characteristics that should not be removed. Therefore, it is capable of providing a complete unwrapping result without reducing the spatial resolution under a high level of noise.