KEYWORDS: Coronagraphy, Diffraction, Planets, Wave propagation, Radio propagation, Chemical elements, 3D modeling, Finite element methods, Waveguides, Light
In this work we study vector electromagnetic wave propagation in a visible-light coronagraph for applications to the design and analysis of Terrestrial Planet Finder (TPF). A visible light coronagraph in TPF requires detection of a terrestrial planet which is ~1010 dimmer than the central stellar source. Consequently, any theory used to design and analyze TPF requires accuracy better than 10-10 in intensity or 10-5 in electric field.
Current coronagraphic approaches to TPF have relied on scalar diffraction theory. However, the vector nature of light requires a vector approach to the problem. In this study we employ a time-harmonic vector theory to study the electromagnetic field propagation through metallic focal plane occulting mask on dielectric substrate. We use parallelized edge-based vector finite element model to compute the wave propagation in a three-dimensional tetrahedral grid representing the geometry of the coronagraph. The edge-based finite element method overcomes the problem of modal propagation and rigorously enforces the field divergence to be zero. The reflectivity and transmittivity in the geometry are computed through the gold metal in various shapes using a planar incident beam. Subsequently, the near-field beam diffraction around the mask is investigated.
Two novel approaches to texture classification based upon stochastic modeling using Markov Random Fields are presented and contrasted. The first approach uses a clique-based probabilistic neighborhood structure and Gibbs distribution to derive the quasi likelihood estimates of the model coefficients. Likelihood ratio tests formed by the quasi-likelihood functions of pairs of textures are evaluated in the decision strategy to classify texture samples. The second approach uses a least squares prediction error model and error signature analysis to model and classify textures. The distribution of the errors is the information used in the decision algorithm which employs K-nearest neighbors techniques. A new statistic and complexity measure are introduced called the Knearest neighbor statistic (KNS) and complexity (KNC) which measure the overlap in K-nearest neighbor conditional distributions. Parameter vectors for each model, neighborhood size and structure, performance of the maximum likelihood and K-nearest neighbor decision strategies are presented and interesting results discussed. Results from classifying real video pictures of six cloth textures are presented and analyzed.
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