Gabriel Martínez-Niconoff

Impact of velocity distribution assumption on simplified laser speckle imaging equation.

Since blood flow is tightly coupled to the health status of biological tissue, several instruments have been developed to monitor blood flow and perfusion dynamics. One such instrument is laser speckle imaging. The goal of this study was to evaluate the use of two velocity distribution assumptions (Lorentzian- and Gaussian-based) to calculate speckle flow index (SFI) values. When the normalized autocorrelation function for the Lorentzian and Gaussian velocity distributions satisfy the same definition of correlation time, then the same velocity range is predicted for low speckle contrast (0 < C < 0.6) and predict different flow velocity range for high contrast. Our derived equations form the basis for simplified calculations of SFI values.

Modulation of coherence and polarization using liquid crystal spatial light modulators.

We propose a method for modulation of coherence and polarization of electromagnetic fields, employing two crossed zero-twisted nematic liquid crystal spatial light modulators. In contrast to a similar technique analyzed by Shirai and Wolf [J. Opt. Soc. Am A, 21, 1907, (2004)] our method provides a wide range simultaneous modulation of coherence and polarization. The dependence of the obtained results on different definitions of electromagnetic coherence is considered.

The van Cittert-Zernike theorem for electromagnetic fields

The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.

Coherent-Mode Representation of Propagation-Invariant Fields

The general coherent-mode structure of a propagation-invariant field is found as the solution of the differential equation for propagation of the coherent modes of said field. It is shown that three kinds of the propagation-invariant fields exist. Examples of propagation-invariant fields of the three kinds are discussed.

Caustics of diffraction fields

Abstract Caustics of diffraction fields are described for radiation passing through a binary screen with amplitude transmittance of the form t(x,y) = δ[y−f(x)]. The description is based on the geometrical properties of the function f(x). Experimental results are presented.

Simple correction factor for laser speckle imaging of flow dynamics

One of the major constraints facing laser speckle imaging for blood-flow measurement is reliable measurement of the correlation time (τ(C)) of the back-scattered light and, hence, the bloods speed in blood vessels. In this Letter, we present a new model expression for integrated speckle contrast, which accounts not only for temporal integration but spatial integration, too, due to the finite size of the pixel of the CCD camera; as a result, we find that a correction factor should be introduced to the measured speckle contrast to properly determine τ(C); otherwise, the measured bloods speed is overestimated. Experimental results support our theoretical model.

Generation of light string and light capillary beams

Abstract Recently we reported a new modal theory of propagation-invariant optical fields [Opt. Commun. 195 (2001) 27–34]. Within the framework of this theory we predicted the existence of so-called light string and light capillary beams. Here, we propose an optical technique for generating these beams and demonstrate it through experimental results.

Self-focusing transmittances

In this Letter, we describe the optical field associated with transmittances characterized by a slit-shaped curve. The influence of the curvature is that the diffraction field generates focusing regions. The focusing geometry corresponds to the geometry of the transmittance curve, except for scaling, rotations or translations. A relevant point is that the changes in the morphology of the diffraction field are bounded by the focusing regions. Our experimental and computational results are in good agreement with the theoretical predictions.

Description of phase singularities and their application to focusing design

We describe the focusing region associated with transmittances, analyzing its associated phase function. We show that generic features can be studied from the differential equation for focusing geometry, which is obtained through angular representation for diffraction fields. With the treatment, we recover the results for circular zone plates, and by introducing a linear transformation into the transmittance function we generate structures that keep the ability to generate focusing. According to the choice of the parameters involved, the diffraction field presents new focusing regions, whose three-dimensional geometry and spatial evolution can be described in a selective fashion with analysis of only the phase singularities associated with the diffraction field and avoidance of the integral representation. The treatment is also applied to a simple lens. We recover the theoretical predictions obtained by Berry and Upstill [M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. XVIII, p. 259], and these predictions are corroborated experimentally. The results obtained are shown.

Topological properties of the interaction between focusing regions kind cusped

We study here the cusped-cusped interaction between two kinds of Pearcey optical fields by analyzing its topological structure. We do it in two steps; the first one is an irradiance interaction that allows us to identify organization regions. The second one is an amplitude interaction, where it is shown that the interference fringes are organized around the irradiance distribution. The topological behavior of the optical field is analyzed identifying regions with different phase functions, one of them, corresponds with a catastrophe function which has associated a focusing region, the other region can be approximated by a quadratic function. The main consequence heritage from the phase structure is interference fringes emerge from focusing regions having similar features like a topological charges. We show computational and experimental results which are in very well agreement with the theoretical model.