Ray and Wave Aberrations Revisited: A Huygens-Like Construction yields Exact Relations

The optical aberrations of a system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersection measured in the image plane. The classical connection between the two descriptions is an approximation, the error of which has, so far, not been quantified analytically. We derive exact analytical equations for computing the wavefront surface, the aberrated ray directions, and the transverse ray aberrations in terms of the wave aberrations (OPD) and the reference sphere. We introduce precise conditions for a function to be an OPD function, show that every such function has an associated wavefront, and study the error arising from the classical approximation. We establish strict conditions for the error to be small. We illustrate our results with numerical simulations. Our results show that large numerical apertures and high-frequency OPD functions yield larger approximation errors.Comment: 12 pages, 10 Figures, JOSA A, vol. 33, no.

Aportes para la formación de ciudadanos desde la clase de estadística

El siguiente trabajo de investigación, es una reflexión que surge de una propuesta que se enfoca al cómo contribuir a la formación de ciudadanos desde la clase de estadística, para ello se brindan unos elementos para diseñar situaciones que favorezcan la formación de ciudadanos desde esta área del conocimiento, para realizar esta propuesta se deben tener en cuenta unos referentes teóricos que aluden a la formación de ciudadanos, a la importancia de la estadística dentro de un contexto escolar y la relación que existe entre ellos dos

El lado oscuro de la democracia. Michel Mann

No es la primera vez que Michael Mann, un ilustre profesor de sociología de la Universidad de California, se supera a sí mismo. Sus libros son tratados académicos, recursos sociológicos de frontera, tesis doctorales y pólvora para impulsar balas de cañón. El lado oscuro de la democracia, es una apuesta arriesgada que se soporta en un trágico registro que no ocurre de forma azarosa. Tiene una lógica propia y sistemática que se alimenta de las condiciones inherentes de la democracia para demolerla o para negarla

Preliminary Study Using Forward Reaction Control System Jets During Space Shuttle Entry

Failure or degradation of the flight control system, or hull damage, can lead to loss of vehicle control during entry. Possible failure scenarios are debris impact and wing damage that could result in a large aerodynamic asymmetry which cannot be trimmed out without additional yaw control. Currently the space shuttle uses aerodynamic control surfaces and Reaction Control System jets to control attitude. The forward jets are used for orbital maneuvering only, while the aft jets are used for yaw control during entry. This paper develops a controller for using the forward reaction control system jets as an additional control during entry, and assesses its value and feasibility during failure situations. Forward-aft jet blending logic is created, and implemented on a simplified model of the space shuttle entry flight control system. The model is validated and verified on the nonlinear, six degree-of-freedom Shuttle Engineering Simulator. A rudimentary human factors study was undertaken using the forward cockpit simulator at Johnson Space Center, to assess flying qualities of the new system and pilot workload. Results presented in the paper show that the combination of forward and aft jets provides useful additional yaw control, in addition to potential fuel savings and the ability to balance the use of the fuel in the forward and aft tanks to meet availability constraints of both forward and aft fuel tanks. Piloted simulation studies indicated that using both sets of jets while flying a damaged space shuttle reduces pilot workload, and makes the vehicle more responsive

Kinematic identification of parallel mechanisms by a divide and conquer strategy

This paper presents a Divide and Conquer strategy to estimate the kinematic parameters of parallel symmetrical mechanisms -- The Divide and Conquer kinematic identification is designed and performed independently for each leg of the mechanism -- The estimation of the kinematic parameters is performed using the inverse calibration method -- The identification poses are selected optimizing the observability of the kinematic parameters from a Jacobian identification matrix -- With respect to traditional identification methods the main advantages of the proposed Divide and Conquer kinematic identification strategy are: (i) reduction of the kinematic identification computational costs, (ii) improvement of the numerical efficiency of the kinematic identification algorithm and, (iii) improvement of the kinematic identification results -- The contributions of the paper are: (i) The formalization of the inverse calibration method as the Divide and Conquer strategy for the kinematic identification of parallel symmetrical mechanisms and, (ii) a new kinematic identification protocol based on the Divide and Conquer strategy -- As an application of the proposed kinematic identification protocol the identification of a planar 5R symmetrical mechanism is simulated -- The performance of the calibrated mechanism is evaluated by updating the kinematic model with the estimated parameters and developing simulationsInstitute for Systems and Technologies of Information, Control and Communication, International Federation of Automatic Contro

Análisis cluster como método estadístico en estudio de tipo didáctico (una aplicación para la investigación de rutas)

El siguiente trabajo presenta una aplicación del método multivariado denominado Análisis Cluster (AC) en una de las etapas de la investigación que desarrolla actualmente el grupo Crisálida de la Universidad Distrital Francisco José de Caldas entorno a las rutas de estudio y aprendizaje, REA, seguidas por los estudiantes de grado séptimo de algunas instituciones educativas del Distrito Capital con respecto al objeto matemático proporcionalidad inversa y dirigido por el profesor Pedro Gerardo Rocha Salamanca

Next Generation NASA Hazard Detection System Development

The SPLICE project is continuing NASAs efforts to develop precision landing GN&C technologies for future lander missions. One of those technologies is the next generation Hazard Detection (HD) System, which consists of a new HD Lidar and HD Algorithms. The HD System is a modular system that will be adapted to meet specific mission needs in the future. This paper presents the design approach, the nominal concept of operations for which the first prototype is being designed, and the expected performance of the system

Pattern Recognition for a Flight Dynamics Monte Carlo Simulation

The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time

Rediscovery of Passiflora danielii Killip, 1960 (subgenus Passiflora): a threatened narrow endemic species of Colombia

Passiflora danielii, an endemic species to Colombia, which is threatened, was rediscovered in the Department of Antioquia, where it has not been reported since 1938. The species was only known from the type locality (Municipality of Cocorná). Now, four new locations are added near it. The current study further presents a revised morphological description of P. danielii based on fresh material, along with an updated distribution map. Finally, following the IUCN Red List Criteria, P. danielii was classified as Critically Endangered (CR) species