Para obtener la distribución de tamaños de partículas presentes en una muestra analizada, a partir de la función de autocorrelación media de intensidades obtenida
experimentalmente, es necesario resolver la ecuación integral $eq:integral$ teniendo en cuenta la relación de Siegert $eq:siegert$.
4
Si bien existen muchos métodos que proponen distintos acercamientos al problema, su solución no es un tema cerrado debido a las características del núcleo de la
ecuación integral que lo convierten en un problema mal condicionado. Esto implica que aunque el ajuste de los datos experimentales sea muy bueno, no se asegura que
la solución converja a la verdadera. Existen muchas soluciones dispares que reproducen esencialmente los mismos datos, dentro de un margen de error muy pequeño.
5
Esto hace que no sea posible invertir directamente el sistema, sino que sea necesario emplear algún tipo de regularización. Es decir, incorporar en el algoritmo las
propiedades deseables o información a priori que uno espera tenga la solución buscada, de manera de poder acotar el espacio de búsqueda.
6
7
$Breve reseña de distintos algoritmos$
8
9
El algoritmo propuesto en este trabajo intenta evitar el problema con el cual se encuentran la mayoría de los algoritmos que es establecer criterios de soluciones
suaves y parsimonia para penalizar soluciones no deseadas. En nuestro caso, en lugar de generar posibles soluciones y luego quedarnos con las que cumplen
ciertos criterios, proponemos trabajar en un espacio en donde la base elegida con la cual se construyen las soluciones lleve naturalmente a soluciones con las
propiedades que buscamos.
10
El algoritmo consiste en una heurística basada en el grupo de los algoritmos evolutivos.
La dispersión de luz en un medio se debe a fluctuaciones en el índice de refracción del medio. Analizando la luz dispersada es posible obtener información acerca de estas fluctuaciones y de las propiedades del medio.
3
Si se ilumina con luz coherente un medio con fluctuaciones de índice de refracción que varían con el tiempo, se obtiene un patrón de speckle que fluctúa con el tiempo. Este patrón de speckle surge debido a la interferencia de haces dispersados en distintas regiones del volumen de dispersión. Este volumen de dispersión está definido por la intersección entre el haz incidente y el haz dispersado que llega al detector.
4
El detector sensa las fluctuaciones de intensidad del patrón de speckle y un análisis de estas fluctuaciones de intensidad permiten obtener información acerca de la dinámica en el volumen de dispersión.
5
Las fluctuaciones se estudian analizando la función de autocorrelación de la intensidad dispersada.
6
Sea $A(t)$ una propiedad de un sistema de muchas partículas en un tiempo $t$, que depende de la posición y el momento de todas las partículas del sistema. Debido a movimientos térmicos aleatorios, la posición y el momento de las partículas cambia continuamente y esto se refleja en la fluctuación aleatoria de la magnitud $A(t)$ alrededor de su valor medio temporal $<A>$. El valor medio $<A>$ se define como
El objetivo del presente trabajo es la puesta a punto de la técnica dinámica de dispersión de luz para poder caracterizar satisfactoriamente distribuciones de tamaños de
muestras de micropartículas.
4
El objetivo del presente trabajo es la puesta a punto de la técnica dinámica de dispersión de luz para poder caracterizar satisfactoriamente distribuciones de tamaños de
muestras de micropartículas.
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\section{Algoritmos de inversión} \label{sec:alg}\section{Algoritmos de inversión} \label{sec:alg}\chapter{Conceptos teóricos} \label{sec:introduccion}\chapter{Teoría} \label{sec:Teoría}La dispersión de luz en un medio se debe a fluctuaciones en el índice de refracción del medio. Analizando la luz dispersada es posible obtener información acerca de estas fluctuaciones y de las propiedades del medio.Si se ilumina con luz coherente un medio con fluctuaciones de índice de refracción que varían con el tiempo, se obtiene un patrón de speckle que fluctúa con el tiempo. Este patrón de speckle surge debido a la interferencia de haces dispersados en distintas regiones del volumen de dispersión. Este volumen de dispersión está definido por la intersección entre el haz incidente y el haz dispersado que llega al detector.El detector sensa las fluctuaciones de intensidad del patrón de speckle y un análisis de estas fluctuaciones de intensidad permiten obtener información acerca de la dinámica en el volumen de dispersión.Las fluctuaciones se estudian analizando la función de autocorrelación de la intensidad dispersada.Sea $A(t)$ una propiedad de un sistema de muchas partículas en un tiempo $t$, que depende de la posición y el momento de todas las partículas del sistema. Debido a movimientos térmicos aleatorios, la posición y el momento de las partículas cambia continuamente y esto se refleja en la fluctuación aleatoria de la magnitud $A(t)$ alrededor de su valor medio temporal $<A>$. El valor medio $<A>$ se define como\begin{equation}<A(t)> = \lim_{T\to\infty}\frac{1}{T}\int^{T}_{0}A(t)dt\label{eq:meanValue}\end{equation}donde $T$ es el tiempo total de medición durante el cual se registra el valor de $A$. Si suponemos $<A> = 0$, la función de autocorrelación temporal\chapter{Introducción} \label{sec:intro}\section{Objetivos} \label{sec:objetivos}\section{Objetivos} \label{sec:objetivos}@Book{ bernepecora,%@Book{ born,%@Book{ born,\@writefile{toc}{\select@language{spanish}}\@writefile{toc}{\select@language{spanish}}\@writefile{lof}{\select@language{spanish}}\@writefile{lof}{\select@language{spanish}}\@writefile{lot}{\select@language{spanish}}\@writefile{lot}{\select@language{spanish}}\newlabel{sec:abstract}{{}{1}{\contentsname \@mkboth {\MakeUppercase \contentsname }{\MakeUppercase \contentsname }\relax }{chapter*.1}{}}\@writefile{toc}{\contentsline {chapter}{\numberline {1}Introducci\'on}{2}{chapter.1}}\@writefile{toc}{\contentsline {chapter}{\numberline {1}Introducci\'on}{2}{chapter.1}}\@writefile{lof}{\addvspace {10\p@ }}\@writefile{lof}{\addvspace {10\p@ }}\@writefile{lot}{\addvspace {10\p@ }}\@writefile{lot}{\addvspace {10\p@ }}\newlabel{sec:intro}{{1}{2}{Introducción\relax 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10000000)\BOOKMARK [0][]{chapter.1}{Introducci\363n}{}\BOOKMARK [0][]{chapter.1}{Introducci\363n}{}\BOOKMARK [1][]{section.1.1}{Resumen}{chapter.1}\BOOKMARK [1][]{section.1.1}{Objetivos}{chapter.1}\BOOKMARK [1][]{section.1.2}{Objetivos}{chapter.1}\BOOKMARK [0][]{chapter.2}{Teor\355a}{}\BOOKMARK [0][]{chapter.2}{Conceptos te\363ricos}{}\BOOKMARK [1][]{section.2.1}{Dispersi\363n de luz}{chapter.2}\BOOKMARK [1][]{section.2.1}{Dispersi\363n de luz}{chapter.2}\BOOKMARK [1][]{section.2.2}{Din\341mica de las part\355culas}{chapter.2}\BOOKMARK [1][]{section.2.2}{Din\341mica de las part\355culas}{chapter.2}\BOOKMARK [1][]{section.2.3}{T\351cnica DLS}{chapter.2}\BOOKMARK [1][]{section.2.3}{T\351cnica DLS}{chapter.2}(Resumen)(Objetivos)<< /S /GoTo /D (section.1.2) >><< /S /GoTo /D (chapter.2) >>(Objetivos)(Teor\355a)<< /S /GoTo /D (chapter.2) >><< /S /GoTo /D (section.2.1) >>(Conceptos te\363ricos)(Dispersi\363n de luz)<< /S /GoTo /D (section.2.1) >><< /S /GoTo /D (section.2.2) >>(Dispersi\363n de luz)(Din\341mica de las part\355culas)<< /S /GoTo /D (section.2.2) >><< /S /GoTo /D (section.2.3) >>(Din\341mica de las part\355culas)(T\351cnica DLS)<< /S /GoTo /D (section.2.3) >><< /S /GoTo /D (subsection.2.3.1) >>(T\351cnica DLS)(Distribuciones monodispersas)<< /S /GoTo /D (subsection.2.3.1) >><< /S /GoTo /D (subsection.2.3.2) >>(Distribuciones monodispersas)(Distribuciones polidispersas)<< /S /GoTo /D (subsection.2.3.2) >><< /S /GoTo /D (subsection.2.3.3) >>(Distribuciones polidispersas)(T\351cnica DLS con CCD)<< /S /GoTo /D (subsection.2.3.3) >><< /S /GoTo /D (chapter.3) >>(T\351cnica DLS con CCD)(Desarrollo experimental)<< /S /GoTo /D (chapter.3) >><< /S /GoTo /D (section.3.1) >>(Desarrollo experimental)(Montaje experimental)<< /S /GoTo /D (section.3.1) >><< /S /GoTo /D (section.3.2) >>(Montaje experimental)(Protocolo de medici\363n)<< /S /GoTo /D (section.3.2) >><< /S /GoTo /D (section.3.3) >>(Protocolo de medici\363n)(Preparaci\363n de muestras)<< /S /GoTo /D (section.3.3) >><< /S /GoTo /D (chapter.4) >>(Preparaci\363n de muestras)(Procesado y an\341lisis de los datos)<< /S /GoTo /D (chapter.4) >><< /S /GoTo /D (section.4.1) >>(Procesado y an\341lisis de los datos)(Autocorrelaci\363n)<< /S /GoTo /D (section.4.1) >><< /S /GoTo /D (section.4.2) >>(Autocorrelaci\363n)(Algoritmos de inversi\363n)<< /S /GoTo /D (section.4.2) >><< /S /GoTo /D (subsection.4.2.1) >>(Algoritmos de inversi\363n)(Pruebas con simulaciones)<< /S /GoTo /D (subsection.4.2.1) >><< /S /GoTo /D (chapter.5) >>(Pruebas con simulaciones)(Resultados y an\341lisis)<< /S /GoTo /D (chapter.5) >><< /S /GoTo /D (section.5.1) >>(Resultados y an\341lisis)(Monodispersos)<< /S /GoTo /D (section.5.1) >><< /S /GoTo /D (section.5.2) >>(Monodispersos)(Polidispersos)<< /S /GoTo /D (section.5.2) >><< /S /GoTo /D (section.5.3) >>(Polidispersos)(Comparaci\363n con otras t\351cnicas)<< /S /GoTo /D (section.5.3) >><< /S /GoTo /D (chapter.6) >>(Comparaci\363n con otras t\351cnicas)(Conclusiones)<< /S /GoTo /D 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