Convex optimization-based windowed Fourier filtering with multiple windows for wrapped-phase denoising

Fringe pattern analysis based on the two-dimensional synchrosqueezing transform

Windowed Fourier transform (WFT) is used to analyze fringe patterns observed from optical measurements. The space-frequency resolution of the WFT is limited, which affects the analyzing performance. In this Letter, we propose to apply the two-dimensional synchrosqueezing transform (SST) for analyzing fringe patterns. The SST is a technique used to overcome the limitation of the space-frequency resolution of the WFT, which sharpens the WFT representation using the derivative of the WFT phase. Numerical experiments confirm the effectiveness of the SST in denoising the fringe pattern and estimating the local frequency from the observed fringe pattern.

High-efficiency static speckle-suppression method based on a combination of beam splitting cavity and liquid-core fiber

Current static speckle suppression methods have an extremely large system size and unsatisfactory performance. This study proposes a device called beam-splitting cavity (BSC) and establishes a model of speckle suppression based on the combination of BSC and a liquid-core fiber. Subsequently, a passive static speckle suppression system is constructed and the key factors affecting the speckle contrast are studied. Consequently, the speckle contrast was reduced from 30.2% to 3.1%, which is below the human-eye speckle-discrimination limit (<4%). The scheme consists entirely of passive optical elements, which are more applicable to projectors than the traditional static and dynamic speckle-suppression methods.

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.

Strategies for reducing speckle noise in digital holography

Digital holography (DH) has emerged as one of the most effective coherent imaging technologies. The technological developments of digital sensors and optical elements have made DH the primary approach in several research fields, from quantitative phase imaging to optical metrology and 3D display technologies, to name a few. Like many other digital imaging techniques, DH must cope with the issue of speckle artifacts, due to the coherent nature of the required light sources. Despite the complexity of the recently proposed de-speckling methods, many have not yet attained the required level of effectiveness. That is, a universal denoising strategy for completely suppressing holographic noise has not yet been established. Thus the removal of speckle noise from holographic images represents a bottleneck for the entire optics and photonics scientific community. This review article provides a broad discussion about the noise issue in DH, with the aim of covering the best-performing noise reduction approaches that have been proposed so far. Quantitative comparisons among these approaches will be presented.

Time-directional filtering of wrapped phase for observing transient phenomena with parallel phase-shifting interferometry

Recent development of parallel phase-shifting interferometry (PPSI) enables accurate measurement of time-varying phase maps. By combining a high-speed camera with PPSI, it became possible to observe not only time-varying but also fast phenomena including fluid flow and sound in air. In such observation, one has to remove static phase (time-invariant or slowly-varying phase unrelated to the phenomena of interest) from the observed phase maps. Ordinarily, a signal processing method for eliminating the static phase is utilized after phase unwrapping to avoid the 2π discontinuity which can be a source of error. In this paper, it is shown that such phase unwrapping is not necessary for the high-speed observation, and a time-directional filtering method is proposed for removing the static phase directly from the wrapped phase without performing phase unwrapping. In addition, experimental results of simultaneously visualizing flow and sound with 42 000 fps are shown to illustrate how the time-directional filtering changes the appearance. A MATLAB code is included within the paper (also in https://goo.gl/N4wzdp) for aiding the understanding of the proposed method.

Reference-free metric for quantitative noise appraisal in holographic phase measurements

This paper presents a reference-free metric for quantitative appraisal of de-noising algorithms for phase measurements in digital holography. In the literature, quality metrics are not self-contained because they require a noise-free reference phase fringe pattern in order to be computed. In practical situations, no exact phase is available to evaluate the quality of processing. In order to bypass such limitations, one needs a metric directly capable of providing information on how efficient the filtering is, without any help from any reference measurements and by only considering the measured available phase data. This paper presents a novel reference-free metric, called estimated phase error for quantitative appraisal of de-noising algorithms for noisy phase data processing. This metric is based on the computation of an estimator of the standard deviation of the phase error between data processed with an external algorithm and that from the evaluated algorithm. A benchmark, including 37 different de-noising algorithms, demonstrates that the proposed metric is capable of producing the same rankings as those obtained with classical metrics, requiring a reference phase. Application to phase data from mechanical testing demonstrates that the ranking obtained from experimental phase data is similar to that obtained during the benchmarking with simulated data.

Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry

This paper presents a non-iterative phase retrieval method from randomly phase-shifted fringe images. By combining the hyperaccurate least squares ellipse fitting method with the subspace method (usually called the principal component analysis), a fast and accurate phase retrieval algorithm is realized. The proposed method is simple, flexible, and accurate. It can be easily coded without iteration, initial guess, or tuning parameter. Its flexibility comes from the fact that totally random phase-shifting steps and any number of fringe images greater than two are acceptable without any specific treatment. Finally, it is accurate because the hyperaccurate least squares method and the modified subspace method enable phase retrieval with a small error as shown by the simulations. A MATLAB code, which is used in the experimental section, is provided within the paper to demonstrate its simplicity and easiness.

Improving principal component analysis based phase extraction method for phase-shifting interferometry by integrating spatial information

Phase extraction methods based on the principal component analysis (PCA) can extract objective phase from phase-shifted fringes without any prior knowledge about their shift steps. Although it is fast and easy to implement, many fringe images are needed for extracting the phase accurately from noisy fringes. In this paper, a simple extension of the PCA method for reducing extraction error is proposed. It can effectively reduce influence from random noise, while most of the advantages of the PCA method is inherited because it only modifies the construction process of the data matrix from fringes. Although it takes more time because size of the data matrix to be decomposed is larger, computational time of the proposed method is shown to be reasonably fast by using the iterative singular value decomposition algorithm. Numerical experiments confirmed that the proposed method can reduce extraction error even when the number of interferograms is small.

Compensation of fringe distortion for phase-shifting three-dimensional shape measurement by inverse map estimation

For three-dimensional shape measurement, phase-shifting techniques are widely used to recover the objective phase containing height information from images of projected fringes. Although such techniques can provide an accurate result in theory, there might be considerable error in practice. One main cause of such an error is distortion of fringes due to nonlinear responses of a measurement system. In this paper, a postprocessing method for compensating distortion is proposed. Compared to other compensation methods, the proposed method is flexible in two senses: (1) no specific model of nonlinearity (such as the gamma model) is needed, and (2) no special calibration data are needed (only the observed image of the fringe is required). Experiments using simulated and real data confirmed that the proposed method can compensate multiple types of nonlinearity without being concerned about the model.