Phase Extraction from Single Interferogram Including Closed-Fringe Using Deep Learning

One step accurate phase demodulation from a closed fringe pattern with the convolutional neural network HRUnet

Retrieving a phase map from a single closed fringe pattern is a challenging task in optical interferometry. In this paper, a convolutional neural network (CNN), HRUnet, is proposed to demodulate phase from a closed fringe pattern. The HRUnet, derived from the Unet model, adopts a high resolution network (HRnet) module to extract high resolution feature maps of the data and employs residual blocks to erase the gradient vanishing in the network. With the trained network, the unwrapped phase map can be directly obtained by feeding a scaled fringe pattern. The high accuracy of the phase map obtained from HRUnet is demonstrated by demodulation of both simulated data and actual fringe patterns. Compared results between HRUnet and two other CNNS are also provided, and the results proved that the performance of HRUnet in accuracy is superior to the two other counterparts.

Fringe pattern demodulation using Zernike polynomials and a l1-norm regularized extended Kalman filter

A novel algorithm for closed fringe demodulation for an absolute phase estimation, to the best of our knowledge, is proposed. The two-dimensional phase is represented as a weighted linear combination of a certain number of Zernike polynomials (ZPs). Essentially, the problem of phase estimation is converted into the estimation of ZP coefficients. The task of ZP coefficient estimation is performed based on a state space model. Due to the nonlinear dependence of the fringe intensity measurement model on the ZP coefficients, the extended Kalman filter (EKF) is used for the state estimation. A pseudo-measurement model is considered based on the state vector sparsity constraint to improve the convergence performance of the EKF. Simulation and experimental results are provided to demonstrate the noise robustness and the practical applicability of the proposed method.

PhotoelastNet: a deep convolutional neural network for evaluating the stress field by using a single color photoelasticity image

Quantifying the stress field induced into a piece when it is loaded is important for engineering areas since it allows the possibility to characterize mechanical behaviors and fails caused by stress. For this task, digital photoelasticity has been highlighted by its visual capability of representing the stress information through images with isochromatic fringe patterns. Unfortunately, demodulating such fringes remains a complicated process that, in some cases, depends on several acquisitions, e.g., pixel-by-pixel comparisons, dynamic conditions of load applications, inconsistence corrections, dependence of users, fringe unwrapping processes, etc. Under these drawbacks and taking advantage of the power results reported on deep learning, such as the fringe unwrapping process, this paper develops a deep convolutional neural network for recovering the stress field wrapped into color fringe patterns acquired through digital photoelasticity studies. Our model relies on an untrained convolutional neural network to accurately demodulate the stress maps by inputting only one single photoelasticity image. We demonstrate that the proposed method faithfully recovers the stress field of complex fringe distributions on simulated images with an averaged performance of 92.41% according to the SSIM metric. With this, experimental cases of a disk and ring under compression were evaluated, achieving an averaged performance of 85% in the SSIM metric. These results, on the one hand, are in concordance with new tendencies in the optic community to deal with complicated problems through machine-learning strategies; on the other hand, it creates a new perspective in digital photoelasticity toward demodulating the stress field for a wider quantity of fringe distributions by requiring one single acquisition.

Deep learning in optical metrology: a review

With the advances in scientific foundations and technological implementations, optical metrology has become versatile problem-solving backbones in manufacturing, fundamental research, and engineering applications, such as quality control, nondestructive testing, experimental mechanics, and biomedicine. In recent years, deep learning, a subfield of machine learning, is emerging as a powerful tool to address problems by learning from data, largely driven by the availability of massive datasets, enhanced computational power, fast data storage, and novel training algorithms for the deep neural network. It is currently promoting increased interests and gaining extensive attention for its utilization in the field of optical metrology. Unlike the traditional "physics-based" approach, deep-learning-enabled optical metrology is a kind of "data-driven" approach, which has already provided numerous alternative solutions to many challenging problems in this field with better performances. In this review, we present an overview of the current status and the latest progress of deep-learning technologies in the field of optical metrology. We first briefly introduce both traditional image-processing algorithms in optical metrology and the basic concepts of deep learning, followed by a comprehensive review of its applications in various optical metrology tasks, such as fringe denoising, phase retrieval, phase unwrapping, subset correlation, and error compensation. The open challenges faced by the current deep-learning approach in optical metrology are then discussed. Finally, the directions for future research are outlined.

One-shot phase retrieval method for interferometry using a hypercolumns convolutional neural network

In three dimensional profilometry, phase retrieval technique plays a key role in signal processing stage. Fringe images need to be transformed into phase information to obtain the measurement result. In this paper, a new phase retrieval method based on deep learning technique is proposed for interferometry. Different from conventional multi-step phase shift methods, phase information can be extracted from only a single frame of an interferogram by this method. Here, the phase retrieval task is regarded as a regression problem and a hypercolumns convolutional neural network is constructed to solve it. Firstly, functions and each component of the network model are introduced in details; Then, four different mathematical functions are adopted to generate the training dataset; training and validation strategies are also designed subsequently; Finally, optimization processing is performed to eliminate local data defects in initial results with the help of polynomial fitting. In addition, hardware platform based on point diffraction interferometer is fabricated to support this method. Concluded from the experiment section, the proposed method possesses a desirable performance in terms of phase retrieval, denoising and time efficiency.

High-accuracy phase demodulation method compatible to closed fringes in a single-frame interferogram based on deep learning

Interferogram demodulation is a fundamental problem in optical interferometry. It is still challenging to obtain high-accuracy phases from a single-frame interferogram that contains closed fringes. In this paper, we propose a neural network architecture for single-frame interferogram demodulation. Furthermore, instead of using real experimental data, an interferogram generation model is constructed to generate the dataset for the network's training. A four-stage training strategy adopting appropriate optimizers and loss functions is developed to guarantee the high-accuracy training of the network. The experimental results indicate that the proposed method can achieve a phase demodulation accuracy of 0.01 λ (root mean square error) for actual interferograms containing closed fringes.

Random two-frame interferometry based on deep learning

A two-frame phase-shifting interferometric wavefront reconstruction method based on deep learning is proposed. By learning from a large number of simulation data based on a physical model, the wrapped phase can be calculated accurately from two interferograms with an unknown phase step. The phase step can be any value excluding the integral multiples of π and the size of interferograms can be flexible. This method does not need a pre-filtering to subtract the direct-current term, but only needs a simple normalization. Comparing with other two-frame methods in both simulations and experiments, the proposed method can achieve better performance.