Robust phase unwrapping in the presence of high noise remains an open issue. Especially, when both noise and fringe densities are high, pre-filtering may lead to phase dislocations and smoothing that complicate even more unwrapping. In this paper an approach to deal with high noise and to unwrap successfully phase data is proposed. Taking into account influence of noise in wrapped data, a calibration method of the 1st order spatial phase derivative is proposed and an iterative approach is presented. We demonstrate that the proposed method is able to process holographic phase data corrupted by non-Gaussian speckle decorrelation noise. The algorithm is validated by realistic numerical simulations in which the fringe density and noise standard deviation is progressively increased. Comparison with other established algorithms shows that the proposed algorithm exhibits better accuracy and shorter computation time, whereas others may fail to unwrap. The proposed algorithm is applied to phase data from digital holographic metrology and the unwrapped results demonstrate its practical effectiveness. The realistic simulations and experiments demonstrate that the proposed unwrapping algorithm is robust and fast in the presence of strong speckle decorrelation noise.

Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise.

Robust phase unwrapping algorithm based on least squares

A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm’s performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.

Phase-unwrapping algorithm by a rounding-least-squares approach

The physical visualisation of a three-dimension (3D) stress field is a promising method for quantitatively analysing and revealing the stress distribution and evolution of a porous solid, and it significantly contributes to the understanding of the governing effects of stress fields on the mechanical behaviours of complex porous solids. However, experimental limitations regarding the manufacture of complex porous models and the extraction of the stress distributions in matrices inhibit the accurate visualisation of the 3D stress fields of porous structures. This paper presents a method of experimentally visualising and elucidating the 3D structures and stress fields of porous solids using photopolymer materials, 3D printing, the frozen-stress method, and photoelastic tests. Transparent thick discs containing various randomly distributed pores were produced using photopolymer materials and 3D printing technology. Experimental measures, including the frozen-stress method, photoelastic testing, and the phase-shifting method, were applied to quantitatively characterise the 3D stress fields distributed throughout the porous discs under radial-direction compressive loads. The temperature for ‘freezing’ stresses in the photopolymer materials was experimentally determined. The effects of pore distribution and population on the stress-field characteristics were investigated. The experimental results were used to validate the numerical analysis of the stress-field characteristics of the porous models. The visualisation test results agreed well with those of the numerical simulations. The proposed method can be used to visually quantify the characteristics and evolution of the 3D stress fields of porous solids.

Experimental Visualisation Methods for Three-Dimensional Stress Fields of Porous Solids

Phase unwrapping is a crucial process to obtain the absolute phase profile in many optical phase measurement techniques such as interferometry, holography, profilometry, etc. In this paper, we have studied several phase unwrapping algorithms based on solving the discrete Poisson equation. The differences among those algorithms lie in two aspects: one is the way to calculate the input for the Poisson equation using the wrapped phase data and the other is the way to compute the output (unwrapped phase data) using the corresponding input. Firstly, the method to compute the input for the Poisson equation was investigated using the finite difference (FD) and fast Fourier transform(FFT) method. Then different methods, based on FFT or discrete cosine transform (DCT), were employed to calculate the unwrapped phase, and their performances were compared in terms of accuracy and efficiency. To enhance the precision of those algorithms, an iteration strategy was introduced and its performance was investigated under different noise conditions. Finally, several real phase data were tested by using the direct and iterative methods. The detailed software package can be found in https://www.mathworks.com/matlabcentral/fileexchange/71810-phase- unwrapping-algorithms-by-solving-the-poisson-equation.

Fu-You Lao

Papers

Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point