Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Seismic modelling and ava analysis of hidrocarbon traps

In this study, forward seismic modelling of four geological models with Hydrocarbon (HC) traps were performed by ray tracing method to produce synthetic seismogram of each model. The idea is to identify the Hydrocarbon Indicators (HCI‟s) such as bright spot, flat spot, dim spot and Bottom Simulating Reflector (BSR) in the synthethic seismogram. The modelling was performed in DISCO/FOCUS 5.0 seismic data processing programme. Strong positive and negative reflection amplitudes and some artifact reflection horizons were observed on produced seismograms due to rapid changes in subsurface velocity and geometry respectively Additionally, Amplitude-versus-angle (AVA) curves of each HCIs was calculated by the Crewes Zoeppritz Explorer programme. AVA curves show that how the reflection coefficients change with the density and the P and S wave velocities of each layer such as oil, gas, gas hydrate or water saturated sediments. Due to AVA curves, an increase in reflection amplitude with incident angle of seismic waves corresponds to an indicator of a hydrocarbon reservoir

First results obtained using the CENBG nanobeam line: performances and applications

A high resolution focused beam line has been recently installed on the AIFIRA (“Applications Interdisciplinaires des Faisceaux d’Ions en Région Aquitaine”) facility at CENBG. This nanobeam line, based on a doublet–triplet configuration of Oxford Microbeam Ltd. OM-50™ quadrupoles, offers the opportunity to focus protons, deuterons and alpha particles in the MeV energy range to a sub-micrometer beam spot. The beam optics design has been studied in detail and optimized using detailed ray-tracing simulations and the full mechanical design of the beam line was reported in the Debrecen ICNMTA conference in 2008. During the last two years, the lenses have been carefully aligned and the target chamber has been fully equipped with particle and X-ray detectors, microscopes and precise positioning stages. The beam line is now operational and has been used for its firstapplications to ion beam analysis. Interestingly, this set-up turned out to be a very versatile tool for a wide range of applications. Indeed, even if it was not intended during the design phase, the ion optics configuration offers the opportunity to work either with a high current microbeam (using the triplet only) or with a lower current beam presenting a sub-micrometer resolution (using the doublet–triplet configuration). The performances of the CENBGnanobeam line are presented for both configurations. Quantitative data concerning the beam lateral resolutions at different beam currents are provided. Finally, the firstresults obtained for different types of application are shown, including nuclear reaction analysis at the micrometer scale and the firstresults on biological samples

A Novel Method for Radio Propagation Simulation Based on Automatic 3D Environment Reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target regions, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. Our proposition reduces, or even eliminates, infrastructure cost and human efforts during the construction of realistic 3D scenes used in radio propagation modeling. In addition, the results obtained from our propagation model proves to be both accurate and efficient

Triple-junction solar cell performance under Fresnel-based concentrators taking into account chromatic aberration and off-axis operation

Concentration photovoltaic (CPV) systems might produce quite uneven irradiance distributions (both on their level and on their spectral distribution) on the solar cell. This effect can be even more evident when the CPV system is slightly off-axis, since they are often designed to assure good uniformity only at normal incidence. The non-uniformities both in absolute irradiance and spectral content produced by the CPV systems, can originate electrical losses in multi-junction solar cells (MJSC). This works is focused on the integration of ray-tracing methods for simulating the irradiance and spectrum maps produced by different optic systems throughout the solar cell surface, with a 3D fully distributed circuit model which simulates the electrical behavior of a state-of-the-art triple-junction solar cell under the different light distributions obtained with ray-tracing. In this study four different CPV system (SILO, XTP, RTP, and FK) comprising Fresnel lenses concentrating sunlight onto the same solar cell are modeled when working on-axis and 0.6 degrees off-axis. In this study the impact of non-uniformities on a CPV system behavior is revealed. The FK outperforms other Fresnel-based CPV systems in both on-axis and off-axis conditions.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Primary optics for efficient high-brightness LED color mixing

In SSL general illumination, there is a clear trend to high flux packages with higher efficiency and higher CRI addressed with the use of multiple color chips and phosphors. However, such light sources require the optics provide color mixing, both in the near-field and far-field. This design problem is specially challenging for collimated luminaries, in which diffusers (which dramatically reduce the brightness) cannot be applied without enlarging the exit aperture too much. In this work we present first injection molded prototypes of a novel primary shell-shaped optics that have microlenses on both sides to provide Köhler integration. This shell is design so when it is placed on top of an inhomogeneous multichip Lambertian LED, creates a highly homogeneous virtual source (i.e, spatially and angularly mixed), also Lambertian, which is located in the same position with only small increment of the size (about 10-20%, so the average brightness is similar to the brightness of the source). This shell-mixer device is very versatile and permits now to use a lens or a reflector secondary optics to collimate the light as desired, without color separation effects. Experimental measurements have shown optical efficiency of the shell of 95%, and highly homogeneous angular intensity distribution of collimated beams, in good agreement with the ray-tracing simulations.

Analytic free-form lens design for imaging applications with high aspect ratio

A new three-dimensional analytic optics design method is presented that enables the coupling of three ray sets with only two free-form lens surfaces. Closely related to the Simultaneous Multiple Surface method in three dimensions (SMS3D), it is derived directly from Fermat?s principle, leading to multiple sets of functional differential equations. The general solution of these equations makes it possible to calculate more than 80 coefficients for each implicit surface function. Ray tracing simulations of these free-form lenses demonstrate superior imaging performance for applications with high aspect ratio, compared to conventional rotational symmetric systems.

Inhomogeneous source uniformization using a shell mixer Köhler integrator

High flux and high CRI may be achieved by combining different chips and/or phosphors. This, however, results in inhomogeneous sources that, when combined with collimating optics, typically produce patterns with undesired artifacts. These may be a combination of spatial, angular or color non-uniformities. In order to avoid these effects, there is a need to mix the light source, both spatially and angularly. Diffusers can achieve this effect, but they also increase the etendue (and reduce the brightness) of the resulting source, leading to optical systems of increased size and wider emission angles. The shell mixer is an optic comprised of many lenses on a shell covering the source. These lenses perform Kohler integration to mix the emitted light, both spatially and angularly. Placing it on top of a multi-chip Lambertian light source, the result is a highly homogeneous virtual source (i.e, spatially and angularly mixed), also Lambertian, which is located in the same position with essentially the same size (so the average brightness is not increased). This virtual light source can then be collimated using another optic, resulting in a homogeneous pattern without color separation. Experimental measurements have shown optical efficiency of the shell of 94%, and highly homogeneous angular intensity distribution of collimated beams, in good agreement with the ray-tracing simulations.

Simulation Tool and Case Study for Planning Wireless Sensor Network

In this paper, a simulation tool for assisting the deployment of wireless sensor network is introduced and simulation results are verified under a specific indoor environment. The simulation tool supports two modes: deterministic mode and stochastic mode. The deterministic mode is environment dependent in which the information of environment should be provided beforehand. Ray tracing method and deterministic propagation model are employed in order to increase the accuracy of the estimated coverage, connectivity and routing; the stochastic mode is useful for large scale random deployment without previous knowledge on geographic information. Dynamic Source Routing protocol (DSR) and Ad hoc On-Demand Distance Vector Routing protocol (AODV) are implemented in order to calculate the topology of WSN. Hence this tool gives direct view on the performance of WSN and assists users in finding the potential problems of wireless sensor network before real deployment. At the end, a case study is realized in Centro de Electronica Industrial (CEI), the simulation results on coverage, connectivity and routing are verified by the measurement.

A novel method for radio propagation simulation based on automatic 3D environment reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target region, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. By comparing with other methods, the work presented in this paper makes contributions on reducing human efforts and cost in constructing 3D scene; moreover, the developed propagation model proves its potential in both accuracy and efficiency.

Optical systems design using the SMS method and optimizations

Resumen El diseño de sistemas ópticos, entendido como un arte por algunos, como una ciencia por otros, se ha realizado durante siglos. Desde los egipcios hasta nuestros días los sistemas de formación de imagen han ido evolucionando así como las técnicas de diseño asociadas. Sin embargo ha sido en los últimos 50 años cuando las técnicas de diseño han experimentado su mayor desarrollo y evolución, debido, en parte, a la aparición de nuevas técnicas de fabricación y al desarrollo de ordenadores cada vez más potentes que han permitido el cálculo y análisis del trazado de rayos a través de los sistemas ópticos de forma rápida y eficiente. Esto ha propiciado que el diseño de sistemas ópticos evolucione desde los diseños desarrollados únicamente a partir de la óptica paraxial hasta lo modernos diseños realizados mediante la utilización de diferentes técnicas de optimización multiparamétrica. El principal problema con el que se encuentra el diseñador es que las diferentes técnicas de optimización necesitan partir de un diseño inicial el cual puede fijar las posibles soluciones. Dicho de otra forma, si el punto de inicio está lejos del mínimo global, o diseño óptimo para las condiciones establecidas, el diseño final puede ser un mínimo local cerca del punto de inicio y lejos del mínimo global. Este tipo de problemática ha llevado al desarrollo de sistemas globales de optimización que cada vez sean menos sensibles al punto de inicio de la optimización. Aunque si bien es cierto que es posible obtener buenos diseños a partir de este tipo de técnicas, se requiere de muchos intentos hasta llegar a la solución deseada, habiendo un entorno de incertidumbre durante todo el proceso, puesto que no está asegurado el que se llegue a la solución óptima. El método de las Superficies Múltiples Simultaneas (SMS), que nació como una herramienta de cálculo de concentradores anidólicos, se ha demostrado como una herramienta también capaz utilizarse para el diseño de sistemas ópticos formadores de imagen, aunque hasta la fecha se ha utilizado para el diseño puntual de sistemas de formación de imagen. Esta tesis tiene por objeto presentar el SMS como un método que puede ser utilizado de forma general para el diseño de cualquier sistema óptico de focal fija o v afocal con un aumento definido así como una herramienta que puede industrializarse para ayudar al diseñador a afrontar de forma sencilla el diseño de sistemas ópticos complejos. Esta tesis está estructurada en cinco capítulos: El capítulo 1, es un capítulo de fundamentos donde se presentan los conceptos fundamentales necesarios para que el lector, aunque no posea una gran base en óptica formadora de imagen, pueda entender los planteamientos y resultados que se presentan en el resto de capítulos El capitulo 2 aborda el problema de la optimización de sistemas ópticos, donde se presenta el método SMS como una herramienta idónea para obtener un punto de partida para el proceso de optimización. Mediante un ejemplo aplicado se demuestra la importancia del punto de partida utilizado en la solución final encontrada. Además en este capítulo se presentan diferentes técnicas que permiten la interpolación y optimización de las superficies obtenidas a partir de la aplicación del SMS. Aunque en esta tesis se trabajará únicamente utilizando el SMS2D, se presenta además un método para la interpolación y optimización de las nubes de puntos obtenidas a partir del SMS3D basado en funciones de base radial (RBF). En el capítulo 3 se presenta el diseño, fabricación y medidas de un objetivo catadióptrico panorámico diseñado para trabajar en la banda del infrarrojo lejano (8-12 μm) para aplicaciones de vigilancia perimetral. El objetivo presentado se diseña utilizando el método SMS para tres frentes de onda de entrada utilizando cuatro superficies. La potencia del método de diseño utilizado se hace evidente en la sencillez con la que este complejo sistema se diseña. Las imágenes presentadas demuestran cómo el prototipo desarrollado cumple a la perfección su propósito. El capítulo 4 aborda el problema del diseño de sistemas ópticos ultra compactos, se introduce el concepto de sistemas multicanal, como aquellos sistemas ópticos compuestos por una serie de canales que trabajan en paralelo. Este tipo de sistemas resultan particularmente idóneos para él diseño de sistemas afocales. Se presentan estrategias de diseño para sistemas multicanal tanto monocromáticos como policromáticos. Utilizando la novedosa técnica de diseño que en este capítulo se presenta el diseño de un telescopio de seis aumentos y medio. En el capítulo 5 se presenta una generalización del método SMS para rayos meridianos. En este capítulo se presenta el algoritmo que debe utilizarse para el diseño de cualquier sistema óptico de focal fija. La denominada optimización fase 1 se vi introduce en el algoritmo presentado de forma que mediante el cambio de las condiciones iníciales del diseño SMS que, aunque el diseño se realice para rayos meridianos, los rayos skew tengan un comportamiento similar. Para probar la potencia del algoritmo desarrollado se presenta un conjunto de diseños con diferente número de superficies. La estabilidad y potencia del algoritmo se hace evidente al conseguirse por primera vez el diseño de un sistema de seis superficies diseñado por SMS. vii Abstract The design of optical systems, considered an art by some and a science by others, has been developed for centuries. Imaging optical systems have been evolving since Ancient Egyptian times, as have design techniques. Nevertheless, the most important developments in design techniques have taken place over the past 50 years, in part due to the advances in manufacturing techniques and the development of increasingly powerful computers, which have enabled the fast and efficient calculation and analysis of ray tracing through optical systems. This has led to the design of optical systems evolving from designs developed solely from paraxial optics to modern designs created by using different multiparametric optimization techniques. The main problem the designer faces is that the different optimization techniques require an initial design which can set possible solutions as a starting point. In other words, if the starting point is far from the global minimum or optimal design for the set conditions, the final design may be a local minimum close to the starting point and far from the global minimum. This type of problem has led to the development of global optimization systems which are increasingly less sensitive to the starting point of the optimization process. Even though it is possible to obtain good designs from these types of techniques, many attempts are necessary to reach the desired solution. This is because of the uncertain environment due to the fact that there is no guarantee that the optimal solution will be obtained. The Simultaneous Multiple Surfaces (SMS) method, designed as a tool to calculate anidolic concentrators, has also proved useful for the design of image-forming optical systems, although until now it has occasionally been used for the design of imaging systems. This thesis aims to present the SMS method as a technique that can be used in general for the design of any optical system, whether with a fixed focal or an afocal with a defined magnification, and also as a tool that can be commercialized to help designers in the design of complex optical systems. The thesis is divided into five chapters. Chapter 1 establishes the basics by presenting the fundamental concepts which the reader needs to acquire, even if he/she doesn‟t have extensive knowledge in the field viii of image-forming optics, in order to understand the steps taken and the results obtained in the following chapters. Chapter 2 addresses the problem of optimizing optical systems. Here the SMS method is presented as an ideal tool to obtain a starting point for the optimization process. The importance of the starting point for the final solution is demonstrated through an example. Additionally, this chapter introduces various techniques for the interpolation and optimization of the surfaces obtained through the application of the SMS method. Even though in this thesis only the SMS2D method is used, we present a method for the interpolation and optimization of clouds of points obtained though the SMS3D method, based on radial basis functions (RBF). Chapter 3 presents the design, manufacturing and measurement processes of a catadioptric panoramic lens designed to work in the Long Wavelength Infrared (LWIR) (8-12 microns) for perimeter surveillance applications. The lens presented is designed by using the SMS method for three input wavefronts using four surfaces. The powerfulness of the design method used is revealed through the ease with which this complex system is designed. The images presented show how the prototype perfectly fulfills its purpose. Chapter 4 addresses the problem of designing ultra-compact optical systems. The concept of multi-channel systems, such as optical systems composed of a series of channels that work in parallel, is introduced. Such systems are especially suitable for the design of afocal systems. We present design strategies for multichannel systems, both monochromatic and polychromatic. A telescope designed with a magnification of six-and-a-half through the innovative technique exposed in this chapter is presented. Chapter 5 presents a generalization of the SMS method for meridian rays. The algorithm to be used for the design of any fixed focal optics is revealed. The optimization known as phase 1 optimization is inserted into the algorithm so that, by changing the initial conditions of the SMS design, the skew rays have a similar behavior, despite the design being carried out for meridian rays. To test the power of the developed algorithm, a set of designs with a different number of surfaces is presented. The stability and strength of the algorithm become apparent when the first design of a system with six surfaces if obtained through the SMS method.

Radio propagation modeling and measurements for ZigBee based indoor wireless sensor networks

The deployment of nodes in Wireless Sensor Networks (WSNs) arises as one of the biggest challenges of this field, which involves in distributing a large number of embedded systems to fulfill a specific application. The connectivity of WSNs is difficult to estimate due to the irregularity of the physical environment and affects the WSN designers? decision on deploying sensor nodes. Therefore, in this paper, a new method is proposed to enhance the efficiency and accuracy on ZigBee propagation simulation in indoor environments. The method consists of two steps: automatic 3D indoor reconstruction and 3D ray-tracing based radio simulation. The automatic 3D indoor reconstruction employs unattended image classification algorithm and image vectorization algorithm to build the environment database accurately, which also significantly reduces time and efforts spent on non-radio propagation issue. The 3D ray tracing is developed by using kd-tree space division algorithm and a modified polar sweep algorithm, which accelerates the searching of rays over the entire space. Signal propagation model is proposed for the ray tracing engine by considering both the materials of obstacles and the impact of positions along the ray path of radio. Three different WSN deployments are realized in the indoor environment of an office and the results are verified to be accurate. Experimental results also indicate that the proposed method is efficient in pre-simulation strategy and 3D ray searching scheme and is suitable for different indoor environments.

Evaluation of angle-dependent absorption: Computer simulation and listening test for an objective and subjective evaluation

The aim of this thesis is the subjective and objective evaluation of angledependent absorption coefficients. As the assumption of a constant absorption coefficient over the angle of incidence is not always held, a new model acknowledging an angle-dependent reflection must be considered, to get a more accurate prediction in the sound field. The study provides information about the behavior of different materials in several rooms, depending on the reflection modeling of incident sound waves. An objective evaluation was run for an implementation of angle-dependent reflection factors in the image source and ray tracing simulation models. Results obtained were analysed after comparison to diffuse-field averaged data. However, changes in acoustic characteristics of a room do not always mean a variation in the listener’s perception. Thus, additional subjective evaluation allowed a comparison between the different results obtained with the computer simulation and the response from the individuals who participated in the listening test. The listening test was designed following a three-alternative forced-choice (3AFC) paradigm. In each interaction asked to the subjects a sequence of either three pink noise bursts or three natural signals was alternated. These results were supposed to show the influence and perception of the two different ways to implement surface reflection –either with diffuse or angle-dependent absorption properties. Results show slightly audible effects when material properties were exaggerated. El objetivo de este trabajo es la evaluación objetiva y subjetiva del coeficiente de absorción en función del ángulo de incidencia de la onda de sonido. La suposición de un coeficiente de absorción constante con respecto al ángulo de incidencia no siempre se sostiene. Por ello, un nuevo modelo considerando la reflexión dependiente del ángulo se debe tener en cuenta para obtener predicciones más certeras en el campo del sonido. El estudio proporciona información sobre el comportamiento de diferentes materiales en distintos recintos, dependientes del modelo de reflexión de las ondas de sonido incidentes. Debido a las dificultades a la hora de realizar las medidas y, por lo tanto, a la falta de datos, los coeficientes de absorción dependientes del ángulo a menudo no se tienen en cuenta a la hora de realizar las simulaciones. Hoy en día, aún no hay una tendencia de aplicar el coeficiente de absorción dependiente del ángulo para mejorar los modelos de reflexión. Por otra parte, para una medición satisfactoria de la absorción dependiente del ángulo, sólo hay unos pocos métodos. Las técnicas de medición actuales llevan mucho tiempo y hay algunos materiales, condiciones y ángulos que no pueden ser reproducidos y, por lo tanto, no es posible su medición. Sin embargo, en el presente estudio, los ángulos de incidencia de las ondas de sonido son conocidos y almacenados en una de base de datos para cada uno de los materiales, de modo que los coeficientes de absorción para el ángulo dado pueden ser devueltos siempre que sean requeridos por el usuario. Para realizar el estudio se llevó a cabo una evaluación objetiva, por medio de la implementación del factor de reflexión dependiente del ángulo en los modelos de fuentes imagen y trazado de rayos. Los resultados fueron analizados después de ser comparados con el promedio de los datos obtenidos en medidas en el campo difuso. La simulación se hizo una vez se configuraron un número de materiales creados por el autor, a partir de los datos existentes en la literatura y los catálogos de fabricantes. Los modelos de Komatsu y Mechel sirvieron como referencia para los materiales porosos, configurando la resistividad al aire o el grosor, y para los paneles perforados, introduciendo el radio de los orificios y la distancia entre centros, respectivamente. Estos materiales se situaban en la pared opuesta a la que se consideraba que debía alojar a la fuente sonora. El resto de superficies se modelaban con el mismo material, variando su coeficiente de absorción y/o de dispersión. Al mismo tiempo, una serie de recintos fueron modelados para poder reproducir distintos escenarios de los que obtener los resultados. Sin embargo, los cambios en las características acústicas de un recinto no significan variaciones en la percepción por parte del oyente. Por ello, una evaluación subjetiva adicional permitió una comparación entre los diferentes resultados obtenidos mediante la simulación informática y la respuesta de los individuos que participaron en la prueba de escucha. Ésta fue diseñada bajo las pautas del modelo de test three-alternative forced-choice (3AFC), con treinta y dos preguntas diferentes. En cada iteración los sujetos fueron preguntados por una secuencia alterna entre tres señales, siendo dos de ellas iguales. Éstas podían ser tanto ráfagas de ruido rosa como señales naturales, en este test se utilizó un fragmento de una obra clásica interpretada por un piano. Antes de contestar al cuestionario, los bloques de preguntas eran ordenados al azar. Para cada ensayo, la mezcla era diferente, así los sujetos no repetían la misma prueba, evitando un sesgo por efectos de aprendizaje. Los bloques se barajaban recordando siempre el orden inicial, para después almacenar los resultados reordenados. La prueba de escucha fue realizada por veintitrés personas, toda ellas con conocimientos dentro del campo de la acústica. Antes de llevar a cabo la prueba de escucha en un entorno adecuado, una hoja con las instrucciones fue facilitada a cada persona. Los resultados muestran la influencia y percepción de las dos maneras distintas de implementar las reflexiones de una superficie –ya sea con respecto a la propiedad de difusión o de absorción dependiente del ángulo de los materiales. Los resultados objetivos, después de ejecutar las simulaciones, muestran los datos medios obtenidos para comprender el comportamiento de distintos materiales de acuerdo con el modelo de reflexión utilizado en el caso de estudio. En las tablas proporcionadas en la memoria se muestran los valores del tiempo de reverberación, la claridad y el tiempo de caída temprana. Los datos de las características del recinto obtenidos en este análisis tienen una fuerte dependencia respecto al coeficiente de absorción de los diferentes materiales que recubren las superficies del cuarto. En los resultados subjetivos, la media de percepción, a la hora de distinguir las distintas señales, por parte de los sujetos, se situó significativamente por debajo del umbral marcado por el punto de inflexión de la función psicométrica. Sin embargo, es posible concluir que la mayoría de los individuos tienden a ser capaces de detectar alguna diferencia entre los estímulos presentados en el 3AFC test. En conclusión, la hipótesis de que los valores del coeficiente de absorción dependiente del ángulo difieren es contrastada. Pero la respuesta subjetiva de los individuos muestra que únicamente hay ligeras variaciones en la percepción si el coeficiente varía en intervalos pequeños entre los valores manejados en la simulación. Además, si los parámetros de los materiales acústicos no son exagerados, los sujetos no perciben ninguna variación. Los primeros resultados obtenidos, proporcionando información respecto a la dependencia del ángulo, llevan a una nueva consideración en el campo de la acústica, y en la realización de nuevos proyectos en el futuro. Para futuras líneas de investigación, las simulaciones se deberían realizar con distintos tipos de recintos, buscando escenarios con geometrías irregulares. También, la implementación de distintos materiales para obtener resultados más certeros. Otra de las fases de los futuros proyectos puede realizarse teniendo en cuenta el coeficiente de dispersión dependiente del ángulo de incidencia de la onda de sonido. En la parte de la evaluación subjetiva, realizar una serie de pruebas de escucha con distintos individuos, incluyendo personas sin una formación relacionada con la ingeniería acústica.