Solving the Monge-Amp\`ere Equations for the Inverse Reflector Problem

The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the target, e.g., a projected image on a screen. This optical problem can mathematically be understood as a problem of optimal transport and equivalently be expressed by a secondary boundary value problem of the Monge-Amp\`ere equation, which consists of a highly nonlinear partial differential equation of second order and constraints. In our approach the Monge-Amp\`ere equation is numerically solved using a collocation method based on tensor-product B-splines, in which nested iteration techniques are applied to ensure the convergence of the nonlinear solver and to speed up the calculation. In the numerical method special care has to be taken for the constraint: It enters the discrete problem formulation via a Picard-type iteration. Numerical results are presented as well for benchmark problems for the standard Monge-Amp\`ere equation as for the inverse reflector problem for various images. The designed reflector surfaces are validated by a forward simulation using ray tracing.Comment: 28 pages, 8 figures, 2 tables; Keywords: Inverse reflector problem, elliptic Monge-Amp\`ere equation, B-spline collocation method, Picard-type iteration; Minor revision: reference [59] to a recent preprint has been added and a few typos have been correcte

Box truss analysis and technology development. Task 1: Mesh analysis and control

An analytical tool was developed to model, analyze and predict RF performance of box truss antennas with reflective mesh surfaces. The analysis system is unique in that it integrates custom written programs for cord tied mesh surfaces, thereby drastically reducing the cost of analysis. The analysis system is capable of determining the RF performance of antennas under any type of manufacturing or operating environment by integrating together the various disciplines of design, finite element analysis, surface best fit analysis and RF analysis. The Integrated Mesh Analysis System consists of six separate programs: The Mesh Tie System Model Generator, The Loadcase Generator, The Model Optimizer, The Model Solver, The Surface Topography Solver and The RF Performance Solver. Additionally, a study using the mesh analysis system was performed to determine the effect of on orbit calibration, i.e., surface adjustment, on a typical box truss antenna

Phased array-fed antenna configuration study

The scope of this contract entails a configuration study for a phased array fed transmit antenna operating in the frequency band of 17.7 to 20.2 GHz. This initial contract provides a basis for understanding the design limitations and advantages of advanced phased array and cluster feeds (both utilizing intergral MMIC modules) illuminating folded reflector optics (both near field and focused types). Design parametric analyses are performed utilizing as constraints the objective secondary performance requirements of the Advanced Communications Technology Satellite (Table 1.0). The output of the study provides design information which serves as a data base for future active phased array fed antenna studies such as detailed designs required to support the development of a ground tested breadboard. In general, this study is significant because it provides the antenna community with an understanding of the basic principles which govern near field phased scanned feed effects on secondary reflector system performance. Although several articles have been written on analysis procedures and results for these systems, the authors of this report have observed phenomenon of near field antenna systems not previously documented. Because the physical justification for the exhibited performance is provided herein, the findings of this study add a new dimension to the available knowledge of the subject matter

Light in Power: A General and Parameter-free Algorithm for Caustic Design

We present in this paper a generic and parameter-free algorithm to efficiently build a wide variety of optical components, such as mirrors or lenses, that satisfy some light energy constraints. In all of our problems, one is given a collimated or point light source and a desired illumination after reflection or refraction and the goal is to design the geometry of a mirror or lens which transports exactly the light emitted by the source onto the target. We first propose a general framework and show that eight different optical component design problems amount to solving a light energy conservation equation that involves the computation of visibility diagrams. We then show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power diagram with a planar or spherical domain. This allows us to propose an efficient and fully generic algorithm capable to solve these eight optical component design problems. The support of the prescribed target illumination can be a set of directions or a set of points located at a finite distance. Our solutions satisfy design constraints such as convexity or concavity. We show the effectiveness of our algorithm on simulated and fabricated examples

Optimal design of measurement network for neutronic activity field reconstruction by data assimilation

Using data assimilation framework, to merge information from model and measurement, an optimal reconstruction of the neutronic activity field can be determined for a nuclear reactor core. In this paper, we focus on solving the inverse problem of determining an optimal repartition of the measuring instruments within the core, to get the best possible results from the data assimilation reconstruction procedure. The position optimisation is realised using Simulated Annealing algorithm, based on the Metropolis-Hastings one. Moreover, in order to address the optimisation computing challenge, algebraic improvements of data assimilation have been developed and are presented here.Comment: 24 pages, 10 figure

Large Deployable Reflector Science and Technology Workshop. Volume 3: Systems and Technology Assessment

The results of five technology panels which convened to discuss the Large Deployable Reflector (LDR) are presented. The proposed LDR is a large, ambient-temperature, far infrared/submillimeter telescope designed for space. Panel topics included optics, materials and structures, sensing and control, science instruments, and systems and missions. The telescope requirements, the estimated technology levels, and the areas in which the generic technology work has to be augmented are enumerated

Proceedings of the Large Deployable Reflector Science and Technology Workshop. Volume 1: Executive Summary

A large ambient temperature, for infrared submillimeter telescope in space was discussed. The results of the scientific and technical activities were summarized. The scientific effort consisted of reviewing the science rationale for the Large Deployable Reflector (LDR) and arriving at a concensus set of scientific requirements. The telescope requirements were then compared to the current and anticipated state of the various technologies involved, and the technological shortfalls identified

The eleven antenna: a compact low-profile decade bandwidth dual polarized feed for reflector antennas

A novel dual polarized ultrawide-band (UWB) feed with a decade bandwidth is presented for use in both single and dual reflector antennas. The feed has nearly constant beam width and 11 dBi directivity over at least a decade bandwidth. The feed gives an aperture efficiency of the reflector of 66% or better over a decade bandwidth when the subtended angle toward the sub or main reflector is about 53°, and an overall efficiency better than 47% including mismatch. The return loss is better than 5 dB over a decade bandwidth. The calculated results have been verified with measurements on a linearly polarized lab model. The feed has no balun as it is intended to be integrated with an active 180° balun and receiver. The feed is referred to as the Eleven antenna because its basic configuration is two parallel dipoles 0.5 wavelengths apart and because it can be used over more than a decade bandwidth with 11 dBi directivity. We also believe that 11 dB return loss is achievable in the near future