A method for approximating the inverse error function involved in the determination of the radius of a Gaussian beam is proposed. It is based on a polynomial inversion that can be developed to any desired degree, according to an a priori defined error budget. Analytic expressions are obtained and used to determine the radius of a TEM(oo) He-Ne laser beam from intensity measurements experimentally obtained by using the knife edge method. The error and the interval of validity of the approximation are determined for polynomials of different degrees. The analysis of the theoretical and experimental errors is also presented.

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.

We derive a general, closed-form expression for the diffraction patterns including the aberrations that are due to off-axis alignment and positioning, of a paraboloid mirror. The diffraction patterns obtained in the focal plane of an off-axis paraboloidal mirror suffer modifications by the aberrations that are inherent in these surfaces: astigmatism and coma. Different magnifications in two perpendicular spatial directions indicate astigmatism. The Airy function, which affects a single spatial coordinate, describes the coma aberration. We identified the coma by the increased number of intensity zeros within adjacent lobules.

Resumen. Se realiza el análisis del desempeño de redes neuronales multicapa y SVM como clasificador para el reconocimiento de señas del LSM considerando tres conjuntos de características: Momentos de Hu, Momentos de Zernike e Histogramas de orientación del gradiente (HOG). Se creó un dataset de 21 señas y se le aplicó un preprocesamiento a las imágenes antes de extraer el conjunto de características, las técnicas aplicadas son: reducción de ruido, escalamiento de la imagen y eliminación del fondo de la imagen. Así mismo, se analizó el efecto de la reducción de dimensionalidad del conjunto de características con los algoritmos PCA y LDA. Los resultados indican que los momentos de Zernike junto con LDA ofrece la mejor exactitud en los resultados.Palabras clave: LSM, reconocimiento de imágenes, segmentación de piel, aprendizaje automático, momento de Hu, momento de Zernike, HOG.Abstract. We analyzed the perfomance of multilayer neural networks and SVM as classifier for the Mexican Sign Language (LSM) considering three diferent sets of features: Hu moments, Zernike moments and Histogram of oriented gradients (HOG). A 21-sign dataset was created and in order to extrac the features the images were pre-processed, the applied techniques were: noise reduction, image scaling, and image background removal. Likewise, we analyzed the dimensionality reduction of the set of features with PCA and LDA. The obtained results show that the moments of Zernike together with LDA offers the best accuracy in the classification using the features set.

Resumen. Debido a la dificultad de aprender la lógica necesaria para la programación se diseña y desarrolla un videojuego educativo que tiene como objetivo ayudar a niños a introducirse en el mundo de la programación. El videojuego busca desarrollar la lógica de los infantes en etapa de primaria y la forma en que se realiza es dando al jugador el control de un personaje el cual se maneja mediante líneas de pseudocódigo que deben ser escritas en un campo de texto de manera correcta. El videojuego consta de 20 niveles y su dificultad es incremental. La metodología de desarrollo utilizada es Scrum, además, se utilizaron herramientas de software, como el motor gráfico Unity 3D, Asesprite, Tiled y Adobe Photoshop para el diseño y desarrollo del videojuego.