Comparative study of sampling moiré and windowed Fourier transform techniques for demodulation of a single-fringe pattern

Towards a more practical analysis of Newton's rings using deep learning

As a typical form of optical fringes with a quadratic phase, Newton's ring patterns play an important role in spherical measurements and optical interferometry. A variety of methods have been used to analyze Newton's ring patterns. However, it is still rather challenging to fulfill the analysis. We present a deep-learning-based method to estimate the parameters of Newton's ring patterns and fulfill the analysis accordingly. The experimental results indicate the excellent accuracy, noise robustness, and demodulation efficiency of our method. It provides another applicable approach to analyzing Newton's ring patterns and brings insights into fringe analysis and interferometry-based measurements.

Dual-angle rotation two-dimensional wavelet transform profilometry

The two-dimensional continuous wavelet transform (2D CWT) has been widely used in single-shot fringe projection profilometry (FPP) because of its multi-resolution characteristics and anti-noise ability. This Letter aims to develop a novel 2D wavelet transform model in FPP. Dual-angle rotation operation on a 2D wavelet is performed to improve the directional selectivity and frequency localization of the wavelet. The proposed method improves the accuracy of the phase calculation of wavelet transform profilometry (WTP) for higher accuracy reconstruction from the single-shot fringe. We present mathematical expressions, theoretical analysis, and the comparison to traditional 2D WTP. The experiments demonstrate the effectiveness of the proposed method.

Moire profilometry through simultaneous dual fringe projection for accurate phase demodulation: a comparative study

In optical metrology, fringe projection and moire techniques have been widely used to measure the topography of objects. We can combine the advantages of the two techniques by applying a configuration of simultaneous dual projection in the fringe projection technique, which generates a superimposed fringe pattern containing a moire pattern that is phase modulated according to the topography. In this work, we present an analytic and comparative study of three methods to demodulate the phase of the moire pattern: the spatial, spatial-temporal, and temporal methods. Those methods consist of two steps: first, the moire pattern is extracted from the superimposed fringe pattern; next, the phase of the moire pattern is demodulated. The analytical results show that the resulting phase map has double phase sensitivity compared to that of the classical fringe projection technique. Experimental and numeric results prove the feasibility of this technique.

One-shot dual-projection topography enhanced by phase-shifting logical moiré

In conventional dual-projection moiré topography, the additive-type moiré pattern has an amplitude modulated form, and therefore poor visibility, unable to be improved through low-pass filtering. To overcome this difficulty, this paper presents an enhanced dual-projection moiré topography by means of logical moiré. In its implementation, a couple of projectors project two fringe patterns of different colors onto the object simultaneously and then a color camera captures the deformed fringe pattern. Instead of directly processing the additive-type moiré fringes, we separate the deformed fringes of two chromatic channels, binarize them, and then calculate their exclusive OR (XOR) moiré pattern. By differentiating one of the two deformed fringe patterns, a second XOR moiré pattern having exactly a π/2-rad phase shift can also be generated, so that the phases are simply calculated by using an arctangent function after low-pass filtering to the XOR moiré patterns. By doing so, we can measure the three-dimensional shape of an object in an efficient way requiring a single-shot implementation. The validity of this method has been demonstrated through simulation and experimental results.

A Binocular Vision-Based 3D Sampling Moiré Method for Complex Shape Measurement

As a promising method for moiré processing, sampling moiré has attracted significant interest for binocular vision-based 3D measurement, which is widely used in many fields of science and engineering. However, one key problem of its 3D shape measurement is that the visual angle difference between the left and right cameras causes inconsistency of the fringe image carrier fields, resulting in the phase mismatch of sampling moiré. In this paper, we developed a phase correction method to solve this problem. After epipolar rectification and carrier phase introduction and correction, the absolute phase of the fringe images was obtained. A more universal 3D sampling moiré measurement can be achieved based on the phase match and binocular vision model. Our numerical simulation and experiment showed the high robustness and anti-noise ability of this new 3D sampling moiré method for high-precision 3D shape measurement. As an application, cantilever beams are fabricated by directed energy deposition (DED) using different process parameters, and their 3D deformation caused by residual stresses is measured, showing great potential for residual stress analyses during additive manufacturing.

Demodulation of noisy interferograms with rapid phase variations and amplitude fluctuations using a surrogate principle-based optimization method

This paper presents an optimization-based method for phase extraction from interferograms corrupted with noise, rapid phase variations, and localized amplitude fluctuations. In the proposed method, the phase retrieval problem is addresed by modeling a cost function using non-convex non-smooth total generalized variational regularization. Further, the surrogate principle is used to transform the cost function into convex form for convenient optimization framework. Simulation results demonstrate the performance of the method. We also show the experimental utility of the proposed method for onion cell imaging using digital holographic microscopy.

Wide-view and accurate deformation measurement at microscales by phase extraction of scanning moiré pattern with a spatial phase-shifting technique

A scanning-based second-order moiré method is proposed for high-accuracy deformation measurement in a large field of view (FOV) by analyzing the phase distribution of a single-shot scanning moiré fringe image using a spatial phase-shifting technique. In this method, the grating pitch can be as small as around one pixel in the scanning moiré image to ensure a wide FOV, while high-precision phase measurement is achievable. The strain measurement accuracy has been verified from simulations at different grating pitches, applied strains, and noise levels. The simulation results show that the closer the grating pitch is to the scanning pitch, the smaller the strain measurement error, and the recommended pitch ratio is 0.9∼1.1. Furthermore, the feasibility of this method has been verified from a tensile experiment on an aluminum specimen under a laser scanning microscope with scanning moiré images recorded. The microscale strains of aluminum measured at different tensile loads agree well with the strain gauge results. As an integration of the scanning and sampling moiré methods, this method has the advantages of a large FOV, high accuracy, strong noise immunity, and visualization of magnified deformation. Compared with the traditional phase-shifting scanning moiré method, this method only needs to record a single scanning moiré image and is suitable for dynamic deformation analysis.