Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Amp\`ere Equations

We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target. Both problems can be modeled by strongly nonlinear second-order partial differential equations of Monge-Amp\`ere type. In [Math. Models Methods Appl. Sci. 25 (2015), pp. 803--837, DOI: 10.1142/S0218202515500190] the authors have proposed a B-spline collocation method which has been applied to the inverse reflector problem. Now this approach is extended to the inverse refractor problem. We explain in depth the collocation method and how to handle boundary conditions and constraints. The paper concludes with numerical results of refracting and reflecting optical surfaces and their verification via ray tracing.Comment: 16 pages, 6 figures, 2 tables; Keywords: Inverse refractor problem, inverse reflector problem, elliptic Monge-Amp\`ere equation, B-spline collocation method, Picard-type iteration; OCIS: 000.4430, 080.1753, 080.4225, 080.4228, 080.4298, 100.3190. Minor revision: two typos have been corrected and copyright note has been adde

Low-speed single-element airfoil synthesis

The use of recently developed airfoil analysis/design computational tools to clarify, enrich and extend the existing experimental data base on low-speed, single element airfoils is demonstrated. A discussion of the problem of tailoring an airfoil for a specific application at its appropriate Reynolds number is presented. This problem is approached by use of inverse (or synthesis) techniques, wherein a desirable set of boundary layer characteristics, performance objectives, and constraints are specified, which then leads to derivation of a corresponding viscous flow pressure distribution. Examples are presented which demonstrate the synthesis approach, following presentation of some historical information and background data which motivate the basic synthesis process

Space Shuttle flying qualities and flight control system assessment study

The suitability of existing and proposed flying quality and flight control system criteria for application to the space shuttle orbiter during atmospheric flight phases was assessed. An orbiter experiment for flying qualities and flight control system design criteria is discussed. Orbiter longitudinal and lateral-directional flying characteristics, flight control system lag and time delay considerations, and flight control manipulator characteristics are included. Data obtained from conventional aircraft may be inappropriate for application to the shuttle orbiter

Aeronautical Engineering: A special bibliography with indexes, supplement 64, December 1975

This bibliography lists 288 reports, articles, and other documents introduced into the NASA scientific and technical information system in November 1975

Target Mass Monitoring and Instrumentation in the Daya Bay Antineutrino Detectors

The Daya Bay experiment measures sin^2 2{\theta}_13 using functionally identical antineutrino detectors located at distances of 300 to 2000 meters from the Daya Bay nuclear power complex. Each detector consists of three nested fluid volumes surrounded by photomultiplier tubes. These volumes are coupled to overflow tanks on top of the detector to allow for thermal expansion of the liquid. Antineutrinos are detected through the inverse beta decay reaction on the proton-rich scintillator target. A precise and continuous measurement of the detector's central target mass is achieved by monitoring the the fluid level in the overflow tanks with cameras and ultrasonic and capacitive sensors. In addition, the monitoring system records detector temperature and levelness at multiple positions. This monitoring information allows the precise determination of the detectors' effective number of target protons during data taking. We present the design, calibration, installation and in-situ tests of the Daya Bay real-time antineutrino detector monitoring sensors and readout electronics.Comment: 22 pages, 20 figures; accepted by JINST. Changes in v2: minor revisions to incorporate editorial feedback from JINS

PhoSim-NIRCam: Photon-by-photon image simulations of the James Webb Space Telescope's Near-Infrared Camera

Recent instrumentation projects have allocated resources to develop codes for simulating astronomical images. Novel physics-based models are essential for understanding telescope, instrument, and environmental systematics in observations. A deep understanding of these systematics is especially important in the context of weak gravitational lensing, galaxy morphology, and other sensitive measurements. In this work, we present an adaptation of a physics-based ab initio image simulator: The Photon Simulator (PhoSim). We modify PhoSim for use with the Near-Infrared Camera (NIRCam) -- the primary imaging instrument aboard the James Webb Space Telescope (JWST). This photon Monte Carlo code replicates the observational catalog, telescope and camera optics, detector physics, and readout modes/electronics. Importantly, PhoSim-NIRCam simulates both geometric aberration and diffraction across the field of view. Full field- and wavelength-dependent point spread functions are presented. Simulated images of an extragalactic field are presented. Extensive validation is planned during in-orbit commissioning

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

Oceanus.

v. 38, no.1 (1995