A method is presented for tracing rays through a medium discretized as finite-element volumes. The ray-trajectory equations are cast into the local element coordinate frame, and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The finite-element methodology is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The procedure is applied to a finite-element model of an optic with a severe refractive-index gradient, and the results are compared to the closed-form gradient ray-path integral approach.
We investigate what can be learned from translating numerical algorithms into neural networks. On the numerical side, we consider explicit, accelerated explicit, and implicit schemes for a general higher order nonlinear diffusion equation in 1D, as well as linear multigrid methods. On the neural network side, we identify corresponding concepts in terms of residual networks (ResNets), recurrent networks, and U-nets. These connections guarantee Euclidean stability of specific ResNets with a transposed convolution layer structure in each block. We present three numerical justifications for skip connections: as time discretisations in explicit schemes, as extrapolation mechanisms for accelerating those methods, and as recurrent connections in fixed point solvers for implicit schemes. Last but not least, we also motivate uncommon design choices such as nonmonotone activation functions. Our findings give a numerical perspective on the success of modern neural network architectures, and they provide design criteria for stable networks.
This paper presents an overview of the development and capabilities of a space-traceable testbed developed for investigation of research issues related to deployable space telescopes. The Air Force Research Laboratory (AFRL) is developing the Deployable Optical Telescope (DOT), which upon completion will be a fully-deployable, sub-scale, space-traceable ground testbed for development and demonstration of critical technologies for the next-generation of space-optics systems. The paper begins with an overview of the DOT project's technology goals, including the specific performance objectives of the various technologies that are being incorporated into the DOT testbed. The paper presents an overview of the DOT design, including the central integrating structure, deployable primary mirror petals, deployable secondary tower, deployment mechanisms, lightweight mirror segments, metrology, and control systems. The paper concludes with a report on the cunent status of DOT activities as well as a view of the future research that is planned for the project.
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