Super-resolution based number-theoretical phase unwrapping method applicable to 2D spiral fringe patterns

Spiral interferometry is a technique that accurately measures changes in 3D structures or refractive indices by converting phase changes into spiral fringe patterns. The spiral fringe patterns consist of phase distributions, which are wrapped from 0 to 2 pi, requiring phase unwrapping techniques. Phase unwrapping transforms a discontinuous phase image from 0 to 2 pi into a continuous phase image, which can ultimately be reconstructed into 3D information. The 3D reconstructed information is affected by the unwrapped phase information with noise. Among the phase unwrapping methods, the number-theoretical phase unwrapping method used in 1D structured light is a unique approach that unwraps the phase into a step function. Due to its insensitivity to noise, this method is an effective solution for improving phase unwrapping in noisy environments. However, due to the same characteristics, the resolution inevitably decreases. In this paper, we propose a super-resolution based numerical unwrapping method applicable to two-dimensional spiral patterns. Based on multi-wavelength interpolation, this method not only retains the advantage of the number-theoretical phase unwrapping method, which is insensitive to noise, but also compensates for its disadvantage of resolution degradation. The proposed method uses the basic concept of generating sub-step information by multi-wavelength interpolation and performing super-resolution based on this concept. We perform simulations and experiments to verify the validity. As a result of the verification, it is confirmed that the super-resolution effect of the number-theoretical unwrapping in the 2D spiral fringe patterns can be achieved by the proposed method.