Digital speckle pattern interferometry (DSPI) is widely used in many scientific and industrial applications. Besides its several advantages, one of the basic problems encountered in DSPI is the undesired speckle noise existing in the fringe pattern. In this paper, we demonstrate the performance of nonlocal means (NLM) and its related adaptive kernel-based filtering methods for speckle noise reduction in DSPI fringes. The NLM filter and its related kernel-based filters such as NLM-average, NLM-local polynomial regression, and NLM-shape adaptive patches are implemented first on simulated DSPI fringes, and their performances are quantified on the basis of peak signal-to-noise ratio (PSNR), mean square error (MSE), and quality index ($Q$). Further, their effectiveness and abilities in reducing speckle noise are compared with other speckle denoising methods. These filtering methods are then employed on experimental DSPI fringes. The obtained results reveal that these filtering methods have the ability to improve the PSNR and $Q$ of the DSPI fringes and provide better visual and quantitative results. It is also observed that the proposed filtering methods preserve the edge information of the DSPI fringes, which is evaluated on the basis of the edge preservation index of the resultant filtered images.

A digital four-step phase-shifting method for obtaining the optical phase distribution from a single fringe pattern is proposed in this Letter. By computing the first-, second-, and third-order Riesz transform components for a given fringe pattern, three $\pi /2$ phase-shifted fringe patterns are generated from the obtained Riesz components and, finally, the wrapped phase map is extracted. The validity of the proposed method is demonstrated on both the simulated and experimentally obtained fringe patterns. The performance of the proposed method is evaluated by using the image quality index and edge preservation index. Further, the performance of the proposed method is tested on speckled correlation fringes obtained from digital speckle pattern interferometry, and the resulting phase from the proposed method is compared with the phase obtained from three experimentally recorded phase-shifted fringe patterns. The obtained results reveal that the proposed method provides a simple and robust solution for optical phase extraction from a single fringe pattern with good accuracy and, therefore, make it suitable for real-time measurement applications.

In digital coherent imaging and measurement systems, the image/fringe pattern quality is severely degraded by multiplicative uncorrelated noise, called speckle, resulting due to the coherent nature of the light source, which restricts the development of several applications of these systems in various fields. Digital holography, holographic interferometry, speckle metrology, and shearography are the most revealing non-invasive imaging and measurement tools in many areas including scientific, engineering, biomedical, and industrial applications. However, the presence of undesired speckle noise in the processed image/phase distribution may lead to ambiguity in the observation or analysis of the associated physical parameters, and thus, limit their applications in many fields. To overcome this problem, a variety of algorithms/methods/techniques have been developed to eliminate the inherent speckle-noise introduced in the images/phase distribution obtained from these systems, depending on the requirement and the understanding of the noise characteristics. The speckle denoising is the pre-processing step in these systems and their performance determines the accuracy of the measurand physical parameter. This review article aims to cover some important state-of-art speckle denoising algorithms. For the purpose of demonstration, the performance and comprehensive study of these algorithms are evaluated on simulation and experimental data.

This study aims to demonstrate the performances of nonlocal means (NLM) and their variant denoising methods, mainly focusing on NLM-shaped adaptive patches and several NLM-reprojection schemes for speckle noise reduction in amplitude and phase images of the digital coherent imaging systems. In the digital coherent imaging systems such as digital speckle pattern interferometry, digital holographic interferometry, etc., the image quality is severely degraded by additive uncorrelated speckle noise, due to the coherent nature of the light source, and therefore limits the development of several applications of these imaging systems in many fields. NLM and its variant denoising methods are employed to denoise the intensity/phase images obtained from these imaging systems, and their effectiveness is evaluated by considering various parameters. The performance comparison of these methods with other existing speckle denoising methods is also presented. The performance of these methods for speckle noise reduction is quantified on the basis of two criteria matrices, namely, the peak-to-signal noise ratio and the image quality index. Based on these criteria matrices, it is observed that these denoising methods have the ability to improve the intensity and phase images favorably in comparison to other speckle denoising techniques, and these methods are more effective and feasible in speckle-noise reduction.

Wavelets shrinkage is the most illustrative of wavelets transform for speckle noise reduction. We aim to study the performance of a monogenic wavelet transform to reduce the speckle noise in digital speckle pattern interferometric fringes. The proposed method is implemented on simulated and experimental speckle fringe patterns and its performance is appraised on the basis of peak signal-to-noise ratio (PSNR) and quality index (Q). The ability to reduce the speckle noise by the proposed method is compared with other classical speckle denoising methods. The obtained results corroborate the effectiveness of the proposed method for speckle noise reduction in speckle fringes in terms of PSNR and Q. It is also observed that the method provides better qualitative and quantitative results. Furthermore, the proposed method preserves the edge information of the speckle fringes, a feature that is quantified by the edge preservation index.

A method for optical phase extraction based on two-dimensional discrete wavelets transform (2-DWT) decomposition is shown. From modulated fringe pattern, phase distribution is extracted by the ratio between detail and approximation. Modulation process is realized digitally by introducing high-frequency spatial carrier, and this process needs two $π/2$-shifted fringe patterns. We propose to use only single fringe and generate its quadrature by spiral phase transform (SPT). After validation by computer simulation, we apply the 2-DWT algorithm on experimental speckle fringe correlation taken for hard disk surface. The extracted phase using SPT quadrature was compared with that given using this time experimental quadrature, and we show a good performance by multiscale structural similarity metric.