New spin filters for interferometric fringe patterns and grating patterns

DeepOrientation: convolutional neural network for fringe pattern orientation map estimation

Fringe pattern based measurement techniques are the state-of-the-art in full-field optical metrology. They are crucial both in macroscale, e.g., fringe projection profilometry, and microscale, e.g., label-free quantitative phase microscopy. Accurate estimation of the local fringe orientation map can significantly facilitate the measurement process in various ways, e.g., fringe filtering (denoising), fringe pattern boundary padding, fringe skeletoning (contouring/following/tracking), local fringe spatial frequency (fringe period) estimation, and fringe pattern phase demodulation. Considering all of that, the accurate, robust, and preferably automatic estimation of local fringe orientation map is of high importance. In this paper we propose a novel numerical solution for local fringe orientation map estimation based on convolutional neural network and deep learning called DeepOrientation. Numerical simulations and experimental results corroborate the effectiveness of the proposed DeepOrientation comparing it with a representative of the classical approach to orientation estimation called combined plane fitting/gradient method. The example proving the effectiveness of DeepOrientation in fringe pattern analysis, which we present in this paper, is the application of DeepOrientation for guiding the phase demodulation process in Hilbert spiral transform. In particular, living HeLa cells quantitative phase imaging outcomes verify the method as an important asset in label-free microscopy.

Fringe direction weighted autofocusing algorithm for gear tooth flank form deviation measurement based on an interferogram

When measuring the form deviation of the gear tooth flank with laser interferometry, due to the limitation of the depth of field of the lens, focused and defocused regions exist in the interferogram simultaneously. The introduced errors that were generated by these defocused regions decrease the measurement accuracy. Therefore, the evaluation of definition for interferograms is necessary for image processing. However, the gradient of gray, which performs by fringes, makes it difficult for traditional algorithms to evaluate its definition. This paper proposes a method based on nonsubsampled contourlet transformation (NSCT) combined with fringe direction as weighting coefficients to solve the problem. First, the information about the directions of these fringes in interferograms was evaluated. Then, the NSCT method was applied to interferograms so that several sub-images in different scales and directions can be achieved. Based on these sub-images and directions information, an improved function for definition evaluation was conducted. Lastly, a series of simulations and experiments was carried out to verify its feasibility and accuracy.

General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition

Filtering off speckle noise from a fringe image is one of the key tasks in electronic speckle pattern interferometry (ESPI). In general, ESPI fringe images can be divided into three categories: low-density fringe images, high-density fringe images, and variable-density fringe images. In this paper, we first present a general filtering method based on variational image decomposition that can filter speckle noise for ESPI fringe images with various densities. In our method, a variable-density ESPI fringe image is decomposed into low-density fringes, high-density fringes, and noise. A low-density fringe image is decomposed into low-density fringes and noise. A high-density fringe image is decomposed into high-density fringes and noise. We give some suitable function spaces to describe low-density fringes, high-density fringes, and noise, respectively. Then we construct several models and numerical algorithms for ESPI fringe images with various densities. And we investigate the performance of these models via our extensive experiments. Finally, we compare our proposed models with the windowed Fourier transform method and coherence enhancing diffusion partial differential equation filter. These two methods may be the most effective filtering methods at present. Furthermore, we use the proposed method to filter a collection of the experimentally obtained ESPI fringe images with poor quality. The experimental results demonstrate the performance of our proposed method.

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns

It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis

Hybrid single shot algorithm for accurate phase demodulation of complex fringe patterns is proposed. It employs empirical mode decomposition based adaptive fringe pattern enhancement (i.e., denoising, background removal and amplitude normalization) and subsequent boosted phase demodulation using 2D Hilbert spiral transform aided by the Principal Component Analysis method for novel, correct and accurate local fringe direction map calculation. Robustness to fringe pattern significant noise, uneven background and amplitude modulation as well as local fringe period and shape variations is corroborated by numerical simulations and experiments. Proposed automatic, adaptive, fast and comprehensive fringe analysis solution compares favorably with other previously reported techniques.

Principal-vector-directed fringe-tracking technique

Fringe tracking is one of the most straightforward techniques for analyzing a single fringe pattern. This work presents a principal-vector-directed fringe-tracking technique. It uses Gaussian derivatives for estimating fringe gradients and uses hysteresis thresholding for segmenting singular points, thus improving the principal component analysis method. Using it allows us to estimate the principal vectors of fringes from a pattern with high noise. The fringe-tracking procedure is directed by these principal vectors, so that erroneous results induced by noise and other error-inducing factors are avoided. At the same time, the singular point regions of the fringe pattern are identified automatically. Using them allows us to determine paths through which the "seed" point for each fringe skeleton is easy to find, thus alleviating the computational burden in processing the fringe pattern. The results of a numerical simulation and experiment demonstrate this method to be valid.

Speckle-noise-reduction method of projecting interferometry fringes based on power spectrum density

The fringe projection technique plays an important role in surface inspection, due to its noncontact, full-field acquisition and high resolution. When using projecting interferometry fringes, one of the basic problems encountered is the speckle noise existing in the fringe pattern. In this paper, a novel method is proposed to reduce the speckle noise based on power spectrum density (PSD) thresholding, which consists of three steps: first, PSD is calculated according to the frequency spectrum obtained by Fourier transform; second, a filter is constructed by a PSD thresholding to filter the frequency content of the speckle noise; and finally inverse Fourier transform is used to obtain the noise-reduction image. Experimental results prove the feasibility and effectiveness of the presented method.

Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe

In this paper, we introduce the radial basis function (RBF) interpolation method to electronic speckle pattern interferometry (ESPI) and propose the RBF interpolation method to obtain unwrapped phase values based on a skeleton map. Because of the excellent approximation properties of the RBF interpolation, the proposed method can extract accurate phase values from a single fringe pattern effectively, even using a simple 3×3 mean filter as preprocessing. Using our method, both special filtering methods for ESPI fringes as preprocessing and postprocessing, including a dilatation and erosion algorithm for pruning and connecting and the smooth algorithm for improving the phase values are not needed. We test our method on a computer-simulated and two experimentally obtained poor-quality fringe patterns. The results have demonstrated that our RBF interpolation method works well even under a seriously disconnected skeleton map where it is impossible to apply the widely used, Matlab function grid data interpolation or the backpropagation neural networks method [Appl. Opt. 46, 7475 (2007)].

Comparative analysis on some spatial-domain filters for fringe pattern denoising

Fringe patterns produced by various optical interferometric techniques encode information such as shape, deformation, and refractive index. Noise affects further processing of the fringe patterns. Denoising is often needed before fringe pattern demodulation. Filtering along the fringe orientation is an effective option. Such filters include coherence enhancing diffusion, spin filtering with curve windows, second-order oriented partial-differential equations, and the regularized quadratic cost function for oriented fringe pattern filtering. These filters are analyzed to establish the relationships among them. Theoretical analysis shows that the four filters are largely equivalent to each other. Quantitative results are given on simulated fringe patterns to validate the theoretical analysis and to compare the performance of these filters.

Tangent least-squares fitting filtering method for electrical speckle pattern interferometry phase fringe patterns

An efficient method is proposed to reduce the noise from electrical speckle pattern interferometry (ESPI) phase fringe patterns obtained by any technique. We establish the filtering windows along the tangent direction of phase fringe patterns. The x and y coordinates of each point in the established filtering windows are defined as the sine and cosine of the half-wrapped phase multiplied by a random quantity, then phase value is calculated using these points' coordinates based on a least-squares fitting algorithm. We tested the proposed methods on the computer-simulated speckle phase fringe patterns and the experimentally obtained phase fringe pattern, respectively, and compared them with the improved sine/cosine average filtering method [Opt. Commun. 162, 205 (1999)] and the least-squares phase-fitting method [Opt. Lett. 20, 931 (1995)], which may be the most efficient methods. In all cases, our results are even better than the ones obtained with the two methods. Our method can overcome the main disadvantages encountered by the two methods.

In-plane electronic speckle pattern of interference (ESPI) with optical fibre system applied to the study of the human jaw

The standard illumination set-up for measurement of in-plane displacement in electronic speckle pattern of interference (ESPI) requires the use of two oblique coherent beams for the illumination of the object. These two beams define a direction in the plane perpendicular to the optical axis in which the displacement can be measured, while in the perpendicular direction the interferometer has no sensitivity. In this paper, a new ESPI system for the measurement of in-plane displacements is used. The novelty presented by this assembly is the use of optical fibres to split and guide the light beams. In this way, it is possible to vary with great precision and ease the direction of the projected beams and, consequently, the direction of the plane in which the displacements undergone by the object can be studied. This set-up makes possible the study of objects with complex geometries, which have deformations with unknown symmetry. We present results obtained with this interferometer applied to the study of the mechanical behaviour of the human jaw.

Spin filtering with curve windows for interferometric fringe patterns

Filtering off noise from fringe patterns is important for the processing and analysis of interferometric fringe patterns. Spin filters proposed by the author have been proven to be effective in filtering off noise without blurring and distortion to fringe patterns with small fringe curvature. But spin filters still have problems processing fringe patterns with large fringe curvature. We develop a new spin filtering with curve windows that is suitable for all kinds of fringe pattern regardless of fringe curvature. The experimental results show that the new spin filtering provides optimal results in filtering off noise without distortion of the fringe features, regardless of fringe curvature.

Fringe-orientation estimation by use of a Gaussian gradient filter and neighboring-direction averaging

We analyze the effect of image noise on the estimation of fringe orientation in principle and interpret the application of a texture-analysis technique to the problem of estimating fringe orientation in interferograms. The gradient of a Gaussian filter and neighboring-direction averaging are shown to meet the requirements of fringe-orientation estimation by reduction of the effects of low-frequency background and contrast variances as well as high-frequency random image noise. The technique also improves inaccurate orientation estimation at low-modulation points, such as fringe centers and broken fringes. Experiments demonstrate that the scales of the Gaussian gradient filter and the direction averaging should be chosen according to the fringe spacings of the interferograms.

Automatic processing in moiré deflectometry by local fringe direction calculation

An algorithm for accurately extracting the local fringe direction is presented. The algorithm estimates, in the neighborhood of n x n points, the direction of the gradient that points normal to the local fringe direction. The performance of four different derivative kernels is also compared. Since this method is sensitive to noise and variations in background and amplitude, a preprocessing step is used to limit these error sources. The method has been applied to the moiré deflectogram of a spherical and a progressive addition ophthalmic lens, resulting in a map of the refractive power of these lenses. The results are compared with the data obtained with a commercial focimeter. This technique is useful for analyzing the fringe patterns where the fringe direction is variable and must be obtained locally.

Generalized spin filtering and an improved derivative-sign binary image method for the extraction of fringe skeletons

Generalized spin filters, including several directional filters such as the directional median filter and the directional binary filter, are proposed for removal of the noise of fringe patterns and the extraction of fringe skeletons with the help of fringe-orientation maps (FOM's). The generalized spin filters can filter off noise on fringe patterns and binary fringe patterns efficiently, without distortion of fringe features. A quadrantal angle filter is developed to filter off the FOM. With these new filters, the derivative-sign binary image (DSBI) method for extraction of fringe skeletons is improved considerably. The improved DSBI method can extract high-density skeletons as well as common density skeletons.

Noise-free normalized fringe patterns and local pixel transforms for strain extraction

Noise reduction is one of the most exciting problems in automatic fringe processing. We propose a two-dimensional (2-D) envelope transform for normalization of fringe patterns, coupled with spin filtering, to construct so-called noise-free normalized fringe patterns. The 2-D envelope transform uses correct fringe intensity envelopes for normalization of fringe patterns, i.e., for making the fringe background and amplitude constant over the whole field. Spin filtering is applied to fringe patterns for removal of random noise taking into account fringe flow. With spin filtering and the 2-D envelope transform, a noise-free normalized fringe pattern is constructed for postprocessing. Based on this improved fringe pattern, two local pixel transforms for strain extraction from a single moiré pattern are developed, in which the digital pure secondary moiré method is improved and the strain-field image method with division is developed.

Fringe-orientation maps and fringe skeleton extraction by the two-dimensional derivative-sign binary-fringe method

The fringe-orientation information of an interferometric fringe pattern is provided in the form of a fringe-orientation map by spin filtering. The fringe-orientation information is an important feature of fringe patterns and is helpful in many fringe-pattern processing algorithms. With the help of a fringe-orientation map the two-dimensional derivative-sign binary-fringe method is developed to extract fringe skeletons from a fringe pattern with an arbitrary fringe distribution. This fringe skeleton extraction method does not require thresholds and a thinning process. It is relatively robust and highly accurate.