Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There, speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster.Comment: 4 pages, 5 figures, 1 algorith

Modeling and multiresolution characterization of micro/nano surface for novel tailored nanostructures

Nanofabrication is state of the art technology. Various chemical, mechanical, biochemical and semiconductor products have characteristics controlled by the nanostructures of the surface and interphase. Surface microscopic imaging is generally used to capture different surface features. By properly analyzing the surface image, valuable information regarding manufacturing process and product performance can be extracted. While microscopy measurements can offer very accurate qualitative information about surface features, for many applications, it is critical to obtain a quantitative description of the surface morphology. Various statistical features can be used to characterize the surface in quantitative way. Such an analysis can be done by the multi-resolution capabilities of wavelet transforms (WT). A multi-scale molecular simulation can help to investigate the physical and chemical mechanism in manufacturing process. Multiresolution characterization was performed on the model structure to compare with image analysis. In our research, we have used a soft polymeric surface used in microfabrication application and a hard surface used for catalysis, and applied multiresolution characterization for surface feature extraction and multiscale modeling for optimizing system variables to get desired surface characteristics. In microfabrication, the efficiency of the product reduced by line-edge roughness (LER) created on the polymer surface. Off-line LER characterization is usually based on the top-down SEM image. We have shown a wavelet based segmentation method for edge searching region. There was no external decision involved in the wavelet based edge detection and characterization. Ab-initio atomistic based simulations are generally used for polymer material design in atomic scale. For mesoscale modeling we use the coarse graining of the molecules and use the Flory-Huggins mean field interaction parameters of the clusters of atoms or molecules obtained from ab-initio simulations. In our research we have used coarse grained lattice based important sampling Monte Carlo (MC) and kinetic Monte Carlo (kMC) methods for mesoscale simulation. We have identified the phase separation by spinodal decomposition resulting in the formation of LER. The kinetics of the process is found and the process variables are identified that can reduce the roughness. Surface of a transition metal have been analyzed in a similar way for enhanced catalytic performance

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Learning Wavefront Coding for Extended Depth of Field Imaging

Depth of field is an important factor of imaging systems that highly affects the quality of the acquired spatial information. Extended depth of field (EDoF) imaging is a challenging ill-posed problem and has been extensively addressed in the literature. We propose a computational imaging approach for EDoF, where we employ wavefront coding via a diffractive optical element (DOE) and we achieve deblurring through a convolutional neural network. Thanks to the end-to-end differentiable modeling of optical image formation and computational post-processing, we jointly optimize the optical design, i.e., DOE, and the deblurring through standard gradient descent methods. Based on the properties of the underlying refractive lens and the desired EDoF range, we provide an analytical expression for the search space of the DOE, which is instrumental in the convergence of the end-to-end network. We achieve superior EDoF imaging performance compared to the state of the art, where we demonstrate results with minimal artifacts in various scenarios, including deep 3D scenes and broadband imaging