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.

Comparative study of phase unwrapping algorithms based on solving the Poisson equation

Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point

The existing methods of contact respiration rate (RR) measurement can bring discomfort to the person being measured. However, RR is a human index that has to be monitored in clinical medicine. To overcome the limitations of contact measurement methods, a non-contact RR measurement method based on an infrared thermal camera is proposed. This is based on the phenomenon that human breathing causes periodic temperature changes around the nostrils. First, an infrared thermal camera is used to collect image sequences of the human face. And then, to track a region-of-interest (ROI) in moving image sequences, the You Only Look Once V3 deep learning method is used to track the nostril ROI from the recorded facial image sequences. The performance of the deep learning model is analyzed through experiments. The average temperature of the nostril ROI of the tracked image is calculated, and the temperature change value of the continuous image series can be obtained. The temperature change curve reflects the respiratory process. A Butterworth low-pass filter is used to filter the continuous temperature value to obtain robust respiratory signals, to improve the signal-noise ratio. Last, the respiratory rate is calculated by time-domain and frequency-domain methods. RR is calculated in different conditions, such as normal respiration, fast respiration, and slow respiration. Through the training, the training accuracy of the model reaches 97.9%. Experimental results show that the method can achieve high precision, and the maximum error is not more than 2%. Those indicate the proposed method can effectively measure the RR. Therefore, the proposed non-contact RR measurement method can be a useful reference for clinical RR measurement and other applications.

Non-contact measurement of human respiration using an infrared thermal camera and the deep learning method

• An emissivity measurement equipment by using an infrared camera is constructed and calibrated by a blackbody furnace with a suitable emissivity model. • By using an infrared camera with no filter (band wavelength range of 7.5 μm–13 μm), a 10.2 ± 0.1 μm filter, and a 10.8 ± 0.19 μm filter, the relationship between the temperature and emissivity of graphite and the residual between data and model are obtained respectively and compared. • The emissivity of graphite at different roughness is studied, and uncertainty quantification is used to provide an error estimate for the resulting curves. Due to the advantages of high-temperature resistance, low thermal expansion coefficient, and thermal shock resistance, etc., graphite is regarded as one of the materials for the first wall of nuclear fusion devices. The real-time monitoring of temperature distribution of the first wall based on an infrared camera is widely used to guarantee the stable operation of devices. To accurately measure the temperature of the first wall, it is important to measure the normal emissivity of graphite. However, the emissivity of graphite is affected by many factors. For example, the effect of the surface layers, like carbon-hydro layers-layers, will influence the measurement of the emissivity. The ambition of this work is to study the relationship between graphite emissivity and infrared camera with filters of different wavelengths and the roughness of graphite, and then give the proposed emissivity model to improve the accuracy of graphite surface temperature measurement. The experiment is carried out with a FLIR infrared camera and calibrated by using a blackbody furnace. The emissivity at given temperatures is systematically investigated. By using an infrared camera with no filter (band wavelength range of 7.5–13 μm), a 10.2 ± 0.1 μm filter, and a 10.8 ± 0.19 μm filter, this paper studies the relationship between the temperature and emissivity of graphite from 150 °C to 500 °C and calculates the relative error of temperature measurement respectively. A suitable fitting model which fits emissivity curves is selected. The measurement results show the use of a 10.2 μm filter to measure the graphite surface temperature has the smallest relative error, the range is 0.90%∼1.17%. The emissivity of graphite with different roughness is also studied. At the same temperature, the greater the roughness of the graphite surface, the higher the emissivity value. The uncertainty of the emissivity measurement is analyzed, and its value is 0.0099–0.0211. The graphite surface temperature measurement method based on the emissivity model proposed in this paper provides useful references for the non-contact temperature measurement of the first wall in nuclear fusion devices. The research results can be used as a reference for plasma experiments in some fusion devices and other similar applications. 

Research on the normal emissivity of Graphite between 150 and 500℃ by an infrared camera for nuclear fusion devices

Abstract Baseline drift and noise can blur or even drown out a signal and affect analysis results, especially in multivariate analysis. To address the problem of spectrum denoising and baseline correction, this paper proposes an improved dual asymmetric penalized least squares (IDAPLS) baseline correction method. The proposed method first changes the single parameter λ used for balancing fidelity and roughness in the traditional penalty least squares (PLS) method into a new diagonal matrix Λ and uses the fast convergent inverse tangent S-type penalty function to iteratively estimate the noise level. Then, the diagonal matrix Ψ is introduced into the fidelity of the updated energy spectrum, and the element ψi is updated iteratively by using the inverse tangent S-type penalty function. Finally, the baseline of the original signal is obtained when a preset number of iterations or termination criteria are reached. Compared with other methods, IDAPLS solves the problem of underfitted curves when dealing with additive noise that the asymmetric least squares method and adaptive iterative reweighted penalized least squares method would get. The proposed method also retains the advantage of fast PLS and realizes the further approximation of the fitting baseline to the real baseline. Especially, in the case of high noise, this method reduces the error of the traditional PLS method from 30% to less than 5%, which gives a useful reference for nuclear data analysis.

An Improved Dual Asymmetric Penalized Least Squares Baseline Correction Method for High-Noise Spectral Data Analysis

Tungsten is regarded as the baseline first wall material in tokamaks. This work provides a polarized method for measuring the emissivity and temperature of the tungsten using an infrared camera and a polarizer under simulating tokamak conditions. In the experiment, a polarizer with an adjustable polarization direction is set up in front of an infrared camera. A rotatable fixture is used to fix the sample and change the angle between the surface and the normal. The sample is rotated from 0° to 80°, and the polarized emissivity first increases and then decreases with increasing rotation angle. The uncertainty in emissivity resulting from this polarized method and non-polarized method is analyzed. To compare the effects of the polarized method and the non-polarized method, the rotation angle is adjusted to 0°, and a fitting model is used to describe the relationship between emissivity and temperature. Errors between the calculated temperature and measured temperature are used as a scale, and the polarized method improves the accuracy of temperature measurement. This polarized method provides a technical way to measure the emissivity and temperature in a tokamak and can be applied in other similar applications.

Hua-Rong Liang

Papers

Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point

Non-contact measurement of human respiration using an infrared thermal camera and the deep learning method

Research on the normal emissivity of Graphite between 150 and 500℃ by an infrared camera for nuclear fusion devices

An Improved Dual Asymmetric Penalized Least Squares Baseline Correction Method for High-Noise Spectral Data Analysis

Measurements of emissivity and temperature for polarized long-wavelength infrared light from tungsten under simulating tokamak conditions.