Assessment of multifractal analysis in dynamic laser speckle signals using a spatial light modulator.

We assess and discuss several technical aspects of the multifractal statistical analysis applied to time series of dynamic speckle intensity signals. Due to the complexity of this goal, we implemented an optical setup that mimics the light scattering effect from the illuminated object using a spatial light modulator. The multifractal spectrum of the obtained dynamic speckle intensity signals is quantified by utilizing a mathematical framework based on the decomposition of wavelet leaders' functions.

Experimental evaluation of a 3D wavelet-based phase recovery method in temporal speckle pattern interferometry.

We test the performance of a phase recovery method based on a three-dimensional directional wavelet transform applied to the intensity signal measured by temporal speckle pattern interferometry (TSPI). We present and discuss several sources of uncertainty by analyzing experimental datasets recorded for an in-plane interferometer without introducing a temporal carrier. The dynamic phase data measured with the proposed method are compared with those obtained from the well-known one-dimensional Fourier transform phase recovery technique.

Comparative analysis of nanometric inspection methods in fringeless speckle pattern interferometry.

In digital speckle pattern interferometry, fringeless speckle pattern interferograms are obtained when the object field deformation is insufficient to produce local phase variations higher than 2π. Therefore, the use of the well-known phase recovery algorithms based on fringe processing is not adequate. In this work, distinct algorithms based on the application of a straightforward arccosine function to a filtered interferogram and the correlation of intensity images and implicit smoothing splines are proposed, analyzed, and compared for the fast inspection of nanometric displacement fields, avoiding the acquisition of several images.

Comparison of real-time phase-reconstruction methods in temporal speckle-pattern interferometry.

Three real-time methods for object-phase recovery are implemented and compared in temporal speckle-pattern interferometry. Empirical mode and intrinsic time-scale decompositions are used and compared as real-time nonstationary and nonlinear filtering techniques for the extraction of the spatio-temporal evolution of the object phase. The proposed real-time methods avoid the application of the Hilbert transform and improve the accuracy of the measurement by filtering under-modulated pixels using Delaunay triangulation.

Amplitude and phase retrieval in simultaneous π/2 phase-shifting heterodyne interferometry using the synchrosqueezing transform.

This paper presents a method for amplitude and phase retrieval in simultaneous π/2 phase-shifting heterodyne interferometry. The used optical setup admits the introduction of a temporal carrier and simultaneously verifies the two-beam interferometry equation for each intensity signal, which are π/2  rad out of phase (quadrature). The spatiotemporal recovering process is obtained by isolating the object amplitude and phase using wavelet transform analysis of the temporal series composed by the difference between the measured pixel intensities corresponding to each quadrature signal.

Simplified phase-recovery method in temporal speckle pattern interferometry.

A simplified method for object phase recovering is implemented in temporal speckle pattern interferometry when the employed interferometer admits the introduction of a temporal carrier, and the well-known two-beam interferometry equation is verified. The spatiotemporal evolution of the object phase is isolated by modulating the acquired interferometric intensity signals with a known temporal carrier in order to carry out its analysis by using a bivariate empirical mode decomposition framework that avoids the application of the Hilbert transform, which is not suitable for intensity signals with abrupt fluctuations. The advantages and limitations of this technique are analyzed and discussed by comparing computation time and phase recovery capability with well-known phase-retrieval methods by means of numerical simulations and experimental data.

Continuous phase estimation from noisy fringe patterns based on the implicit smoothing splines.

We introduce the algorithm for the direct phase estimation from the single noisy interferometric pattern. The method, named implicit smoothing spline (ISS), can be regarded as a formal generalization of the smoothing spline interpolation for the case when the interpolated data is given implicitly. We derive the necessary equations, discuss the properties of the method and address its application for the direct estimation of the continuous phase in both classical interferometry and digital speckle pattern interferometry (DSPI).

Measurement of in-plane displacements using the phase singularities generated by directional wavelet transforms of speckle pattern images.

We present a method to determine micro and nano in-plane displacements based on the phase singularities generated by application of directional wavelet transforms to speckle pattern images. The spatial distribution of the obtained phase singularities by the wavelet transform configures a network, which is characterized by two quasi-orthogonal directions. The displacement value is determined by identifying the intersection points of the network before and after the displacement produced by the tested object.

Phase-recovery improvement using analytic wavelet transform analysis of a noisy interferogram cepstrum.

We evaluate the extension of the exact nonlinear reconstruction technique developed for digital holography to the phase-recovery problems presented by other optical interferometric methods, which use carrier modulation. It is shown that the introduction of an analytic wavelet analysis in the ridge of the cepstrum transformation corresponding to the analyzed interferogram can be closely related to the well-known wavelet analysis of the interferometric intensity. Subsequently, the phase-recovery process is improved.

Measurement of nanometric displacements by correlating two speckle interferograms.

This paper presents a method to measure nanometric displacement fields using digital speckle pattern interferometry, which can be applied when the generated correlation fringes show less than one complete fringe. The method is based on the evaluation of the correlation between the two speckle interferograms generated by both deformation states of the object. The performance of the proposed method is analyzed using computer-simulated speckle interferograms.

Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition.

We propose a phase measurement technique to retrieve optical phase distributions coded in noisy temporal speckle pattern interferometry signals presenting regions of adjacent low-modulated pixels, which is based on the bidimensional empirical mode decomposition and the Hilbert transform. It is shown that this approach can effectively remove noise and minimize the influence of large sets of adjacent nonmodulated pixels located in the time series of speckle interferograms. The performance of the phase retrieval approach is analyzed using computer-simulated speckle interferograms modulated with a temporal carrier.

Sensitivity evaluation of dynamic speckle activity measurements using clustering methods.

We evaluate and compare the use of competitive neural networks, self-organizing maps, the expectation-maximization algorithm, K-means, and fuzzy C-means techniques as partitional clustering methods, when the sensitivity of the activity measurement of dynamic speckle images needs to be improved. The temporal history of the acquired intensity generated by each pixel is analyzed in a wavelet decomposition framework, and it is shown that the mean energy of its corresponding wavelet coefficients provides a suited feature space for clustering purposes. The sensitivity obtained by using the evaluated clustering techniques is also compared with the well-known methods of Konishi-Fujii, weighted generalized differences, and wavelet entropy.

Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform.

We evaluate a data-driven technique to perform bias suppression and modulation normalization of fringe patterns. The proposed technique uses a bidimensional empirical mode decomposition method to decompose a fringe pattern in a set of intrinsic frequency modes and the partial Hilbert transform to characterize the local amplitude of the modes in order to perform the normalization. The performance of the technique is tested using computer simulated fringe patterns of different fringe densities and illumination defects with high local variations of the modulation, and its advantages and limitations are discussed.

Robust phase recovery in temporal speckle pattern interferometry using a 3D directional wavelet transform.

We propose an approach based on a 3D directional wavelet transform to retrieve optical phase distributions in temporal speckle pattern interferometry. We show that this approach can effectively recover phase distributions in time series of speckle interferograms that are affected by sets of adjacent nonmodulated pixels. The performance of this phase retrieval approach is analyzed by introducing a temporal carrier in the out-of-plane interferometer setup and assuming modulation loss and noise effects.

Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier.

We evaluate a method based on the two-dimensional directional wavelet transform and the introduction of a spatial carrier to retrieve optical phase distributions in singular scalar light fields. The performance of the proposed phase-retrieval method is compared with an approach based on Fourier transform. The advantages and limitations of the proposed method are discussed.

Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier.

We present an optical phase measurement method based on the Hilbert transform for the analysis of a time series of speckle interferograms modulated by a temporal carrier. We discuss the influence of nonmodulating pixels, modulation loss, and noise that affect the bias and modulation intensities of the interferometric signal and propose the application of the empirical mode decomposition method for its minimization. We also show the equivalence between the phase recovery approaches that are based on the Hilbert and the Fourier transforms.

Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition.

We propose a bidimensional empirical mode decomposition (BEMD) method to reduce speckle noise in digital speckle pattern interferometry (DSPI) fringes. The BEMD method is based on a sifting process that decomposes the DSPI fringes in a finite set of subimages represented by high and low frequency oscillations, which are named modes. The sifting process assigns the high frequency information to the first modes, so that it is possible to discriminate speckle noise from fringe information, which is contained in the remaining modes.

Phase recovery in temporal speckle pattern interferometry using the generalized S-transform.

We propose a novel approach based on the generalized S-transform to retrieve optical phase distributions in temporal speckle pattern interferometry. The performance of the proposed approach is compared with those given by well-known techniques based on the continuous wavelet, the Hilbert transforms, and a smoothed time-frequency distribution by analyzing interferometric data degraded by noise, nonmodulating pixels, and modulation loss. The advantages and limitations of the proposed phase retrieval approach are discussed.

Denoising in digital speckle pattern interferometry using wave atoms.

We present an effective method for speckle noise removal in digital speckle pattern interferometry, which is based on a wave-atom thresholding technique. Wave atoms are a variant of 2D wavelet packets with a parabolic scaling relation and improve the sparse representation of fringe patterns when compared with traditional expansions. The performance of the denoising method is analyzed by using computer-simulated fringes, and the results are compared with those produced by wavelet and curvelet thresholding techniques.

Multiscale analysis of the intensity fluctuation in a time series of dynamic speckle patterns.

We propose the application of a method based on the discrete wavelet transform to detect, identify, and measure scaling behavior in dynamic speckle. The multiscale phenomena presented by a sample and displayed by its speckle activity are analyzed by processing the time series of dynamic speckle patterns. The scaling analysis is applied to the temporal fluctuation of the speckle intensity and also to the two derived data sets generated by its magnitude and sign.

Speckle activity images based on the spatial variance of the phase.

We propose the display of the local spatial variance of the temporal variations of the phase as an activity descriptor in dynamic speckle images. The spatial autocorrelation of the speckle intensity is calculated in sliding windows, and an estimation of the variance of the phase variations in each region of the sample is determined. The activity images obtained in this way depict some interesting features and in some cases they could be related to physical magnitudes in the samples.

Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes.

We propose a novel approach to retrieving the phase map coded by a single closed-fringe pattern in digital speckle pattern interferometry, which is based on the estimation of the local sign of the quadrature component. We obtain the estimate by calculating the local orientation of the fringes that have previously been denoised by a weighted smoothing spline method. We carry out the procedure of sign estimation by determining the local abrupt jumps of size pi in the orientation field of the fringes and by segmenting the regions defined by these jumps.

Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines.

We evaluate the use of smoothing splines with a weighted roughness measure for local denoising of the correlation fringes produced in digital speckle pattern interferometry. In particular, we also evaluate the performance of the multiplicative correlation operation between two speckle patterns that is proposed as an alternative procedure to generate the correlation fringes. It is shown that the application of a normalization algorithm to the smoothed correlation fringes reduces the excessive bias generated in the previous filtering stage.

Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution.

We evaluate the use of a smoothed space-frequency distribution (SSFD) to retrieve optical phase maps in digital speckle pattern interferometry (DSPI). The performance of this method is tested by use of computer-simulated DSPI fringes. Phase gradients are found along a pixel path from a single DSPI image, and the phase map is finally determined by integration.