Publications

The radiative transfer equation is used in many applications, including the simulation of nuclear weapons. Opacity is a term that is often used in conjunction with the radiative transfer equation along with mean opacities. For someone new to the subject, there may be confusion over various parts of the radiative transfer equation or why opacities and mean opacities are so important to solving certain problems. This report aims to give a brief introduction to the radiative transfer equation as well as an explanation to why opacities and mean opacities are important. We also derive the Planck and Rosseland mean opacities, which are the most common mean opacities used in applications. At the end of the report are references that can be used to learn more about the subject.

The structures that surround and support optical components play a key role in the performance of the overall optical system. For aerospace applications, creating an opto-mechanical structure that is athermal, lightweight, robust, and can be quickly developed from concept through to hardware is challenging. This project demonstrates a design and fabrication method for optical structures using origami-style folded, photo-etched sheetmetal pieces that are micro-welded to each other or to 3d printed metal components. Thin flexures, critical for athermal mounting of optics, can be thinner with sheetmetal than from standard machining, which leads to more compact designs and the ability to mount smaller optics. Building a structure by starting with the thinnest features, then folding that thin material to make the ''thicker'' sections is the opposite of standard machining (cutting thin features from thicker blocks). A design method is shown with mass savings of >90%, and stiffness to weight ratio improvements of 5x to 10x compared to standard methods for space systems hardware. Designs and processes for small, flexured, actively aligned systems are demonstrated as are methods for producing lightweight, structural, Miura-core sandwich panels in both flat and curved configurations. Concepts for deployable panels and component hinges are explored, as is a lens subcell with tunable piston movement with temperature change and an ultralight sunshade.

The Spiking/Processing Array (spARR) is a novel photonic focal plane that uses pixels which generate electronic spikes autonomously and without a clock. These spikes feed into a network of digital asynchronous processing elements or DAPES. By building a useful assemblage of DAPES, and connecting them together in the correct way, sophisticated signal processing can be accomplished within the focal plane. Autonomous self-resetting pixels (AsP) enable SPARR to generate electronic response with very small signals--as little as a single photon in the case of Geiger mode avalanche photodiodes to as few as several hundred photons for in-cmos photodetectors. These spiking pixels enable fast detector response, but do not draw as much continuous power as synchronous clocked designs. The spikes emitted by the pixels all have the same magnitude, the information from the scene is effectively encoded into the rate of spikes and the time at which the spike is emitted. The spiking pixels, having converted incident light into electronic spikes, supply the spikes to a network of digital asynchronous processors. These are small state machines which respond to the spikes arriving at their input ports by either remaining unchanged or updating their internal state and possibly emitting a spike on one or more output ports. We show a design that accomplishes the sophisticated signal processing of a Haar spatial wavelet transform with spatial-spectral whitening. We furthermore show how this design results in a data streams which support imaging and transient optical source detection. Two simulators support this analysis: SPICE and sparrow. The CMOS SPICE simulator Cadence provides accurate CMOs design with accounting for effects of circuit parasitics throughout layout, accurate timing, and accurate energy consumption estimates. To more rapidly assess larger networks with more pixels, sparrow is a custom discrete event simulator that supports the non-homogeneous Poisson processes that lie behind photoelectric interaction. Sparrow is a photon-exact simulator that nevertheless performs SPARR system simulator for large-scale systems.

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplified problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other, verifying the method.

This SAND report investigates the electron transport equation in the upper atmosphere and how it relates to auroral light emissions. The electron transport problem is a very stiff boundary value problem, so standard numerical methods such as symmetric collocation and shooting methods will not succeed unless if the boundary conditions are altered with unrealistic assumptions. We show this to be unnecessary and demon- strate a method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method can be verified by showing that under certain restrictive as- sumptions, the electron transport equation has an exact solution that can be written as an integral. The connection between electron transport and the aurora is made explicit and a kinetic model for calculating auroral light emissions is given.

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