Alejandro Federico

Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes

This paper presents a comparative study of different thresholding methods for speckle noise reduction in electronic speckle pattern interferometry fringes using several wavelet bases. An approach based on the removal of the wavelet subbands of the transformed image is presented. The performance of this method is analyzed and compared with the results obtained with the denoising techniques that use wavelet shrinkage. It is shown that the wavelet subband removal method reduces speckle noise and maintains image features more effectively than the wavelet shrinkage techniques based on soft and hard thresholding.

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. The proposed method is a fully data-driven technique, therefore neither fixed basis functions nor operator intervention are required. The performance of the BEMD method to denoise DSPI fringes is analyzed using computer-simulated data, and the results are also compared with those obtained by means of a previously developed one-dimensional empirical mode decomposition approach. An application of the proposed BEMD method to denoise experimental fringes is also presented.

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. Finally, the performance of the normalization approach in processing real data is also illustrated.

Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes

Universidad Nacional de RosarioInstituto de Fi´sica de Rosario(CONICET-UNR)andDepartamento de Fi´sicaFacultad de Ciencias ExactasIngenieri´a y AgrimensuraBoulevard 27 de Febrero 210 bisS2000EZP RosarioArgentinaAbstract. We present an evaluation of the continuous wavelet trans-form method when it is used to measure the phase distribution encodedby electronic speckle pattern interferometry (ESPI) fringes. The evalua-tion is performed using computer-simulated fringes, an approach thatallows knowing precisely the phase map contained in the pattern. It isshown that only ESPI fringes that verify the stationary phase approxima-tion and its analytic asymptotic limit can be analyzed with the continuouswavelet transform method. The influence of the filtering process tosmooth the ESPI fringes and the method used to extend the fringe pat-tern edges is also analyzed. Finally, additional drawbacks that emergewhen this phase evaluation method is applied 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. An application of the proposed method to reduce speckle noise in experimental data is also presented.

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. This technique does not need the application of a phase unwrapping algorithm or the introduction of carrier fringes in the interferometer. It is shown that a Wigner-Ville distribution with a smoothing Gaussian kernel gives more-accurate results than methods based on the continuous wavelet transform. We also discuss the influence of filtering on smoothing of the DSPI fringes and some additional limitations that emerge when this technique is applied. The performance of the SSFD method for processing experimental data is then illustrated.

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. Finally, we present a numerical comparison between these methods using computer-simulated speckle interferograms modulated with a temporal carrier.

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. The evaluation is carried out by use of computer-simulated fringes that are generated for different average speckle sizes and intensities of the reference beam, including decorrelation effects. A comparison with filtering methods based on the continuous wavelet transform is also presented. Finally, the performance of the smoothing method in processing experimental data is illustrated.

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. The results are also compared with those given by a technique based on the one-dimensional empirical mode decomposition. The advantages and limitations of the proposed approach are finally 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. The advantages and limitations of this approach are finally discussed.