Optical characterization of high speed microscanners based on static slit profiling method

Optical characterization of high-speed microscanners is a challenging task that usually requires special high speed, extremely expensive camera systems. This paper presents a novel simple method to characterize the scanned beam spot profile and size in high-speed optical scanners under operation. It allows measuring the beam profile and the spot sizes at different scanning angles. The method is analyzed theoretically and applied experimentally on the characterization of a Micro Electro Mechanical MEMS scanner operating at 2.6 kHz. The variation of the spot size versus the scanning angle, up to ±15°, is extracted and the dynamic bending curvature effect of the micromirror is predicted.     

A central limit theorem in nonlinear filtering

It is shown that the probability law of a diffusion process conditioned on weakly corrupted observations is asymptotically Gaussian when properly scaled. The method of proof involves Fisher information matrices and a Cramér-Rao inequality.     

Relation between Airy beams and triple-cusp beams

Airy beams and triple-cusp beams are two kinds of accelerating beams. The propagation characteristics and internal topological structures of accelerating Airy beams are well understood because of the developed mathematical theory about Airy function. However, limited information is available about the optical characteristics of accelerating triple-cusp beams. In this work, the relationship between Airy beams and triple-cusp beams is examined theoretically and experimentally. Results reveal some important optical characteristics of triple-cusp beams based on the optical characteristics of Airy beams. These findings are expected to provide a foundation for future applications of triple-cusp beams.     

Generation and Propagation of Optical Superoscillatory Vortex Arrays

Superoscillation is an intriguing wave phenomenon which enables subwavelength features propagating into far field and hence has potential applications in super‐resolution microscopy as well as particle trapping and manipulation. While previous demonstrations mostly concentrate on designing complicated nanostructures for generating uncontrollable superoscillatory functions, here a new technique which allows for creating polynomially shaped superoscillatory functions that contain phase singularity arrays is demonstrated both theoretically and experimentally. Such a technique is implemented in optical experiments for the first time and controllable superoscillatory lobes with feature much below the diffraction limit is achieved. More importantly, a general theoretical framework, which, to our knowledge, has not been reported before, is developed to show how the created superoscillations propagate to a distance of many Rayleigh ranges and eventually disappear when the distance is sufficiently larger. The validity of the model is confirmed by the experiments. The results may trigger further studies in light field shaping and manipulations in subwavelength scale.     

Diseño automático de tableros óptimos de puentes de carretera de vigas artesa prefabricadas mediante algoritmos meméticos híbridos

This paper deals with the minimum cost automatic design of precast bridge decks made of U-beams and an upper slab. It uses a hybrid memetic algorithm that combines the population search of solutions by genetic algorithms and a search by variable neighborhood. This algorithm is applied to a bridge made of two isostatic U-beams of 20-40 m of span and a width of 12 m. This example has 40 discrete variables. The evaluation module takes into account the service and ultimate limit states usually considered for these structures, i.e. flexure, shear, torsion, cracking, deflections, etc. The use of the memetic algorithm requires its previous calibration. Each of the heuristics is run 12 times, obtaining information about the minimum and average values, as well as the scatter. The parametric study showed a good correlation for the cost, the number of strands and the steel and concrete quantities with the span length. Savings have been found between 8 and 50% compared to other structures really executed. The presented procedure allows the practical application to the real design and its adaptation to the precast process.     

Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.