Mario Garavaglia

Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time–frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932–940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schurmann, E. Basar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65–75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71–78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1<α<1) and fractional Brownian motion (1<α<3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.

Investigation of a pulsed molecular nitrogen laser at low temperature.

Accurate wavelength measurements in the molecular nitrogen pulsed laser have been made. Four new ir laser bands were discovered. In addition, about two hundred new stimulated emission lines belonging to the first and second positive systems were obtained and identified as to rotational quantum number. An analysis of the possible pumping mechanisms in accordance with experimental results is given.

Wavelet entropy and fractional Brownian motion time series

We study the functional link between the Hurst parameter and the normalized total wavelet entropy when analyzing fractional Brownian motion (fBm) time series—these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes [L. Zunino, D.G. Perez, M. Garavaglia, O.A. Rosso, Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform, Fractals 12(2) (2004) 223–233]. The aim of this work is to understand the differences in the information obtained from them, if any.

Fraunhofer diffraction by Cantor fractals with variable lacunarity

Abstract Optical diffraction by fractal openings is increasingly being studied because it allows the properties and parameters that characterize these objects to be determined. Allain and Cloitre published the first results showing that the resulting analysis of the distribution of intensity obtained from diffraction experiments through fractal deterministic pupils permits the self-similar dimension and other geometrical characteristic of these structures to be obtained directly. In this work the lacunarity effect ε, dimension d and order k of growth of the Cantor fractal about the distribution of intensities of the diffraction pattern are studied, solved analytically and characterized. In particular we note the influence of lacunarity because this is one of the first studies in which this geometric fractal parameter is taken into consideration. The selfsimilarity of the diffraction figure at different orders is also proved. The results of this study allow us to say that an intimate relation exists between the distribution of the diffracted waves and the parameters that describe this kind of fractal geometry.

Modeling turbulent wave-front phase as a fractional Brownian motion: a new approach.

We introduce a new, general formalism to model the turbulent wave-front phase by using fractional Brownian motion processes. Moreover, it extends results to non-Kolmogorov turbulence. In particular, generalized expressions for the Strehl ratio and the angle-of-arrival variance are obtained. These are dependent on the dynamic state of the turbulence.

CHARACTERIZATION OF LASER PROPAGATION THROUGH TURBULENT MEDIA BY QUANTIFIERS BASED ON THE WAVELET TRANSFORM

The propagation of a laser beam through turbulent media is modeled as a fractional Brownian motion (fBm). Time series corresponding to the center position of the laser spot (coordinates x and y) after traveling across air in turbulent motion, with different strength, are analyzed by the wavelet theory. Two quantifiers are calculated, the Hurst exponent, H, and the mean Normalized Total Wavelet Entropy,

Application of the structured illumination method to study the topography of the sole of the foot during a walk

\tilde{S}_{\rm WT}

A speckle method of gray level pseudocoloring

. It is verified that both quantifiers give complementary information about the turbulence.

Walsh Functions: Analysis of Their Properties under Fresnel Diffraction

The structured illumination technique consists of projecting a fringe system onto a 3D object from a well defined space point, which results in a pattern that depends on the characteristic of the projected fringes, the viewpoint and the illuminated object morphology. Therefore, the structured illumination method enables to determine the topography of 3D objects. To implement this technique we set up an optoelectronic array that allows studying the sole of the foot during a walk. The method consists of projecting a Ronchi grid and capturing the images generated on the foot by a CCD camera. These obtained images are graphically processed and fringes converted into vectors. A depending algorithm on the experimental setup allows obtaining, from those vectors data, cotes for a discrete profile plotting of the studied object. The method enables the quantitative determination of the sole topography during the walk. Qualitatively, it can be used for diagnosis and control of deformation and injuries caused by accidents or illnesses. It can be introduced in the primary attention health system to study a great number of patients, due to its simplicity and low cost installation, and for being a non-invasive technique.

Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: Dynamic study

Abstract A simple method of pseudocoloring gray level images is proposed. It is based on Youngs fringes modulated speckle encoding of images. Reconstruction from a photographic register is obtained using two light beams with different wavelengths at the same time. Pseudocoloring is produced by the superposition of a (diffracted) direct image in one color and a (directly transmitted) contrast reversed image in another color.