An analysis based on the comparison between singularities of speckle phase and pseudophase in the practice of optical vortex metrology is carried out by measuring the phase map of the speckle pattern obtained from the transmitted light through binary diffusers. In the characterization of the core structure of both phase singularities, the variation of the measured parameters is produced by means of in-plane linear displacements and rotations of the scattered speckle fields. These fields are addressed by using similar displacements of the binary phase masks recorded in a spatial light modulator (SLM). We complete these comparisons by measuring out-of-plane variations of the core structure parameters. In addition, we verified that the phase map of the transmitted light beam through the binary diffusers recorded in SLMs is actually characterized by a speckle phase with vortices of unitary charge. The presented analysis would be helpful for understanding the scope and limitations of the use of the singularities of speckle phase and pseudophase as position marking, and also for speckle measurement of in-plane rigid-body displacements of binary diffusers dynamically controlled by means of SLMs.
Using data sets recorded from a speckle interferometer with in-plane sensitivity, we compare the performance of a
recently proposed temporal phase evaluation technique based on the three-dimensional directional wavelet transform
with the one given by the one-dimensional Fourier transform method. The obtained results are compared for different
phase distributions, and the advantages and limitations of both temporal phase recovery approaches are also discussed.
We compare the performance of various recently-developed phase recovery approaches when they are applied
in temporal speckle pattern interferometry. The phase retrieval methods to be evaluated are based on the 1D
continuous wavelet, the Hilbert-Huang and the S-transforms, and the smooth time-frequency distribution. It
is shown that the 3D directional wavelet transform approach outperforms the use of these 1D phase recovery
techniques when sets of adjacent non-modulating pixels, modulation loss and noise effects are present in the
recorded data.
We present an introduction to the Bidimensional Empirical Mode Decomposition (BEMD) and its application to
the denoising of DSPI fringes. The BEMD is based on the decomposition of an image in high and low frequency
zero-mean oscillation modes, called intrinsic mode functions (IMFs). The decomposition is carried out through
a sifting process which produces many few basis functions than the ones generated by the Fourier or the wavelet
transforms. The denoising approach is based on the removal of the first IMFs, so that the filtered image is given
by the residue. A normalization algorithm is then applied to the denoised fringes to reduce the oversmoothing
caused by the filtering. The performance of this denoising approach was evaluated using computer-simulated
DSPI fringes with different fringe density and speckle size, in order to calculate a figure of merit through the
comparison with the noise-free fringes. The obtained results are also compared with those produced by other
smoothing methods, and the advantages and limitations of the proposed approach are finally discussed.
When the speckle pattern produced by a scattering surface shows some type of activity, the speckle distribution changes in time. This paper presents a method to locally estimate the spatial variance of the temporal variation of the phase as an activity descriptor in a sequence of dynamic speckle. This method is based on the computation of the spatial autocorrelation of the speckle intensity using a sliding window. The image obtained from the resulting spatial variance matrix reveals areas of the sample with different speckle activity. Results obtained for both simulated and experimental data are also shown.
In recent years, the fractal theory has been applied to a wide variety of scientific problems. However, this approach
has not been used to study dynamic processes through the analysis of temporal sequences of speckle patterns. In
this work we present a study of the dynamic speckle phenomenon based on the multifractal theory. This study
is carried out by calculating the Hausdorff dimension of the set of singularities of the Holder exponent. These
parameters are determined from the maxima of the wavelet transform modulus of the scattered light intensity
along the time axis, for each pixel of the sequence of speckle images. Calculations conducted on experimental
data evidence a multifractal structure in the case of a fast drying paint and a bruised fruit. We extend this result
by using a synthetic model, which reproduces quite well the first and second spatial statistics of the speckle
intensity as well as the correlation coefficient evaluated from a temporal sequence of speckle patterns.
This presentation reviews recent developments carried out by the authors to evaluate phase distributions in digital speckle pattern interferometry (DSPI) using wavelet analysis. The advantage of this approach is that it requires only one interferogram to be analyzed and does not need the application of a phase unwrapping algorithm neither the introduction of carrier fringes in the interferometer. In particular, it is presented an approach that takes into account the second order contribution of the phase map. It is also presented the application of a smoothed time-frequency distribution which improves the accuracy of the results obtained in the neighborhood of stationary phase points and also when the generated DSPI fringes present discontinuities in the first derivative of the phase map.
We evaluate the application of the Wigner-Ville distribution (WVD) to
measure phase gradient maps in digital speckle pattern interferometry (DSPI),
when the generated correlation fringes present phase discontinuities.
The performance of the WVD method is evaluated using computer-simulated fringes. The influence
of the filtering process to smooth DSPI fringes and additional drawbacks
that emerge when this method is applied are discussed. A comparison with the
conventional method based on the continuous wavelet transform in the stationary
phase approximation is also presented.
In this paper we analyze the application of a chirped Gaussian wavelet transform to retrieve the phase distribution in digital speckle pattern interferometry (DSPI). The performance of this method is evaluated using computer-simulated fringes, approach that allows an accurate determination of the phase map encoded by the fringe pattern. It is shown that the local chirp-based approximation does not give good results in the neighborhood of stationary phase points. To overcome this limitation, we compare the wavelet analysis by applying a smoothed time-frequency distribution. We show that the application of this distribution allows the determination of the phase map where the local chirp-based approximation fails. We also discuss the influence of the filtering process to smooth the DSPI fringes and some additional limitations that emerge when these methods are applied.
The Fourier transform method has become a popular technique to retrieve the phase map encoded by Digital Speckle Pattern Interferometry (DSPI) fringes. When closed fringes need to be analyzed, carrier fringes must be introduced in the pattern to eliminate the sign ambiguity that appears in the phase distribution. Recently, a method based on the application of the continuous wavelet transform (CWT) has been reported to evaluate phase maps in SPI. The CWT method does not produce ambiguities in the phase sign even when carrier fringes are not introduced in the interferometer. In the present paper the performance of the CWT phase-extraction method is evaluated using computer-simulated fringes, approach that allows knowing precisely the phase map contained in the pattern. It is shown that only DSPI fringes that verify the stationary phase approximation and its analytic asymptotic limit can be processed with this method. The influence of the filtering process to smooth the DSPI fringes and of the method used to extend the fringe pattern edges is also analyzed. Additional drawbacks that emerge when this method is applied are finally discussed.
KEYWORDS: Wavelets, Speckle, Image filtering, Speckle pattern, Fringe analysis, Denoising, Linear filtering, Interferometry, Wavelet transforms, Signal to noise ratio
Several papers have recently been published in the field of speckle interferometry to evaluate the phase distribution contained in the correlation fringes using continuous wavelet transform. Even though this approach has the advantage of avoiding the complex fringe analysis step of phase unwrapping, no studies were carried out to determine the accuracy of the retrieved phase map and the influence of the most common error sources. This paper present an evaluation of the continuous wavelet transform method when it is used to determine the phase information contained in Electronic Speckle Pattern Interferometry fringes. It is shown that only fringe patterns that verify the stationary phase approximation and its asymptotic limit can be analyzed with the wavelet method. The evaluation is performed using computer-simulated fringes, approach which allows knowing precisely the phase distribution encoded by them. It is shown that the us of continuous wavelet transform strongly depends on the filtering process used to smooth the fringes and also on the process utilized to extend the fringe pattern edges.
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