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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Advanced Wavefront Sensing and Control Testbed (AWCT)

The Advanced Wavefront Sensing and Control Testbed (AWCT) is built as a versatile facility for developing and demonstrating, in hardware, the future technologies of wave front sensing and control algorithms for active optical systems. The testbed includes a source projector for a broadband point-source and a suite of extended scene targets, a dispersed fringe sensor, a Shack-Hartmann camera, and an imaging camera capable of phase retrieval wavefront sensing. The testbed also provides two easily accessible conjugated pupil planes which can accommodate the active optical devices such as fast steering mirror, deformable mirror, and segmented mirrors. In this paper, we describe the testbed optical design, testbed configurations and capabilities, as well as the initial results from the testbed hardware integrations and tests.

active optics↗
NASA NTRS2008

Dependence of Adaptive Cross-correlation Algorithm Performance on the Extended Scene Image Quality

Recently, we reported an adaptive cross-correlation (ACC) algorithm to estimate with high accuracy the shift as large as several pixels between two extended-scene sub-images captured by a Shack-Hartmann wavefront sensor. It determines the positions of all extended-scene image cells relative to a reference cell in the same frame using an FFT-based iterative image-shifting algorithm. It works with both point-source spot images as well as extended scene images. We have demonstrated previously based on some measured images that the ACC algorithm can determine image shifts with as high an accuracy as 0.01 pixel for shifts as large 3 pixels, and yield similar results for both point source spot images and extended scene images. The shift estimate accuracy of the ACC algorithm depends on illumination level, background, and scene content in addition to the amount of the shift between two image cells. In this paper we investigate how the performance of the ACC algorithm depends on the quality and the frequency content of extended scene images captured by a Shack-Hatmann camera. We also compare the performance of the ACC algorithm with those of several other approaches, and introduce a failsafe criterion for the ACC algorithm-based extended scene Shack-Hatmann sensors.

wave-front sensing and control↗
NASA NTRS2014

Origins of the Lunar and Planetary Laboratory, University of Arizona

The roots of the Lunar and Planetary Laboratory (LPL) extend deep into the rich fabric of G. P. Kuiper's view of the Earth as a planet and planetary systems as expected companions to most stars, as well as the post-war emergent technology of infrared detectors suitable for astronomy. These concepts and events began with Kuiper's theoretical work at Yerkes Observatory on the origin of the Solar System, his discovery of two planetary satellites and observational work with his near-infrared spectrometer on the then-new McDonald 82-inch telescope in the mid- to late-1940s. A grant for the production of a photographic atlas of the Moon in the mid-1950s enabled him to assemble the best existing images of the Moon and acquire new photographs. This brought E. A. Whitaker and D. W. G. Arthur to Yerkes. Others who joined in the lunar work were geologist Carl S. Huzzen and grad student E. P. Moore, as well as undergrad summer students A. B. Binder and D. P. Cruikshank (both in 1958). The Atlas was published in 1959, and work began on an orthographic lunar atlas. Kuiper's view of planetary science as an interdisciplinary enterprise encompassing astronomy, geology, and atmospheric physics inspired his vision of a research institution and an academic curriculum tuned to the combination of all the scientific disciplines embraced in a comprehensive study of the planets. Arrangements were made with the University of Arizona (UA) to establish LPL in affiliation with the widely recognized Inst. of Atmospheric Physics. Kuiper moved to the UA in late 1960, taking the lunar experts, graduate student T. C. Owen (planetary atmospheres), and associate B. M. Middlehurst along. G. van Biesbroeck also joined the migration to Tucson; Binder and Cruikshank followed along as new grad students. Astronomy grad student W. K. Hartmann came into the academic program at UA and the research group at LPL in 1961. Senior faculty affiliating with LPL in the earliest years were T. Gehrels, A. B. Meinel, H. L. Johnson, and F. J. Low, each with their own grad students and associates. Work began on IR spectroscopy and a rectified lunar atlas. Kuiper and Johnson started the search for future observatory sites in N. America and Hawaii.

Planets↗
NASA NTRS2016

Multilayer Active Shell Mirrors for Space Telescopes

A novel active mirror technology based on carbon fiber reinforced polymer (CFRP) substrates and replication techniques has been developed. Multiple additional layers are implemented into the design serving various functions. Nanolaminate metal films are used to provide a high quality reflective front surface. A backing layer of thin active material is implemented to provide the surface-parallel actuation scheme. Printed electronics are used to create a custom electrode pattern and flexible routing layer. Mirrors of this design are thin (< 1.0 mm), lightweight (2.7 kg/m2 ), and have large actuation capabilities. These capabilities, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Such mirrors could be used as lightweight primaries for small CubeSat-based telescopes or as meter-class segments for future large aperture observatories. Multiple mirrors can be produced under identical conditions enabling a substantial reduction in manufacturing cost and complexity. An overview of the mirror design and manufacturing processes is presented. Predictions on the actuation performance have been made through finite element simulations demonstrating correct abilities on the order of 250−300× for astigmatic modes with only 41 independent actuators. A description of the custom metrology system used to characterize the active mirrors is also presented. The system is based on a Reverse Hartmann test and can accommodate extremely large deviations in mirror figure (> 100 µm PV) down to sub-micron precision. The system has been validated against several traditional techniques including photogrammetry and interferometry. The mirror performance has been characterized using this system, as well as closed-loop figure correction experiments on 150 mm dia. prototypes. The mirrors have demonstrated post-correction figure accuracies of 200 nm RMS (two dead actuators limiting performance).

Reverse Hartmann↗
NASA NTRS2021

The Acoustic Air-Jet Generator

This paper describes the development history, operation, and working principle of an acoustic air-jet generator, which can be used to produce high intensity, high frequency acoustic waves. Flow imaging experiments of the system are shown, and applications of the system for various fluid flows are presented. While previous articles on this system have been written in English by the author, this article provides the only documented explanation and implementation of the focusing schlieren system used for flow imaging of the system. This paper has been cited in early works on focusing schlieren as one of the first implementations of such a system, but has not been widely cited in the bulk of the literature on the focusing schlieren method (aside from a more recent M.S. thesis), perhaps due to the difficulty of accessing the paper or that no translation was available. The purpose of this translation is to provide an English version of the article for researchers interested in this work of Dr. Hartmann, and in particular the description of his focusing schlieren system and its application.

Julius Hartmann↗
DOE OSTI2023

Virtual prototyping of liquid metal blanket performance in fusion pilot plant

Liquid metal blanket is a dominant design option for the next step fusion devices responsible for harvesting energy from fusion reaction, and simultaneously producing fuel for the same reaction through tritium breeding. Liquid metal blankets introduce additional complexity to the design due to fluid motion, fluid structure interaction, and magnetohydrodynamic (MHD) effects arising from the motion of the conducting fluid through the magnetic field. They are also directly affected by the plasma heat flux and neutronic fluence. PPPL is currently developing a virtual prototyping system for numerical analysis of the liquid metal blankets for future fusion devices. The system has a customized 3D computational fluid dynamics (CFD) code in its core, allowing MHD flow and conjugate heat transfer analysis in blankets fluids and solids. The code was successfully used before for dual coolant blanket analysis [A. Khodak et al., Fusion Eng. and Des. 137 (2018)]. Recently the same code was modified to allow verified simulation of MHD flows at high Hartmann numbers of several thousand typical for blanket applications. CFD code receives volumetric heat source distribution from the neutronic analysis based on MCNP code. In addition, direct tritium breeding simulation will be performed allowing optimization of the blanket performance. 2D axisymmetric version of neutronics code will be used for rapid optimization, with 3D version employed for detailed analysis. The surface heat distribution on the plasma facing wall will be defined by the software HEAT allowing 3D modeling of the heat flux based on the magnetic field distribution including gyro-orbit effects. Results of thermal analysis are imported into structural analysis code also included in the system. Finally, direct import of CAD geometry will be used for analyzing all components and as a result design option can be efficiently optimized.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Construction of 3D MHD pressure drop correlation and flow characterization in the contraction region of a fusion blanket manifold

Inlet and outlet manifolds are typical components of liquid metal (LM) blanket designs of a fusion power reactor to be used to distribute the LM flow into breeding channels and collect it at the exit of the blanket. High pressure loss in the magnetohydrodynamic (MHD) flows featuring abrupt geometrical changes is one of the main feasibility issues of such designs. Recently, optimization studies were conducted to construct 3D MHD pressure drop correlations for a LM flow in an electrically insulating manifold with gradual expansion. Here, the 3D computational approach developed in that study is applied to the outlet manifold featuring gradual contraction. A systematic analysis was performed with a total number of 135 flow cases computed with COMSOL Multiphysics for Hartmann numbers 1000 < Ha < 10,000, Reynolds numbers 100 < Re < 12,000, and contraction angles 45° < θ < 75° for a fixed contraction ratio of 4. The effects of Ha, Re and θ on the flow recirculation, development length and the total pressure drop were carefully examined. A linear regression analysis was used to determine the power rule of pressure drop coefficient k related to Ha and Re, demonstrating a good match with the Ludford layer theory. Eventually, a correlation for the 3D MHD pressure drop coefficient was constructed as a function of Ha, Re and θ. Further, the results were compared against the inlet manifold. It was found that the flow in the inlet manifold exhibits larger recirculation zones. In the investigated range of Ha, Re and θ, the pressure drop coefficient k of the LM MHD flow in the gradual contraction is only slightly lower (< 8 %) than that in the gradual expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

The effects of advanced spectral line shapes on atmospheric carbon dioxide retrievals

Line shape effects such as speed-dependence and collisional (Dicke) narrowing are manifest in high signal-to-noise ratio laboratory spectra for a wide range of molecular species and sample conditions. However, these effects are usually neglected in spectroscopic models used in remote sensing of atmospheric greenhouse gases. Here, in this study, we examine the effects of line profile choice on laboratory spectra and XCO 2 values retrieved from Total Carbon Column Observing Network (TCCON) spectra. To this end, we utilize limiting cases of the Hartmann-Tran profile (HTP) with shape parameters recently measured by cavity ring-down spectroscopy. Significant differences highlighting the importance of including speed-dependence effects in forward models were observed both in scaling retrievals as well as profile retrievals. However, because of uncertainties associated with the atmospheric temperature gradient, it was not possible to extract accurate carbon column profiles even with inclusion of these new line shape parameters and advanced line profiles.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Broadband cross polarization for ultra-wideline magic-angle spinning NMR

Over the past decade, there has been a sustained interest in using frequency-swept (FS) pulses for the efficient acquisition of wideline and ultra-wideline (UW) NMR powder patterns. Such experiments are typically conducted under static conditions, employing both direct- and indirect-excitation methods (i.e., WCPMG and BRAIN-CP/WCPMG, respectively). Recently, Koppe et al. demonstrated that the WCPMG pulse sequence can be used to efficiently acquire wideline and UW NMR spectra with spinning sideband (SSB) manifolds under magic-angle spinning (MAS) conditions, capitalizing on the increased signal-to-noise ratios (SNR) afforded by MAS. To date, there have been only a few instances of broadband cross-polarization (CP) experiments using FS pulses under MAS conditions and no applications to systems exhibiting wideline and/or ultra-wideline powder patterns, despite the clear advantages these experiments could offer. Herein, we demonstrate that FS pulses selectively applied to a single sideband of the S spin can be used for efficient 1 H-S polarization transfer to S = 1/2 nuclides with large anisotropic chemical shift interactions at slow to moderate MAS rates. The Hartmann–Hahn matching conditions in BRAIN-CP/WCPMG-MAS experiments bear similarity to those of standard CP sequences, yet operate over UW frequency ranges and only require low-amplitude RF pulses on the S channel. Crucial to the success of the BRAIN-CP/WCPMG-MAS experiment is careful calibration of the RF amplitude, transmitter offset, and effective frequency sweep of the FS pulse applied to the S spins at a given MAS rate. Thus, by means of numerical simulations and experimental testing, we provide recommendations for the parameterization and setup of BRAIN-CP/WCPMG-MAS experiments for their most efficient use. Results showcasing the capability of the BRAIN-CP/WCPMG-MAS pulse sequence are presented, including applications to 119 Sn, 195 Pt, and 103 Rh NMR.

Kimball, James J. [Florida State University, Talla↗
DOE OSTI2025

FreeMHD: Validation and verification of the open-source, multi-domain, multi-phase solver for electrically conductive flows

The extreme heat fluxes in the divertor region of tokamaks may require an alternative to solid plasma-facing components, for the extraction of heat and the protection of the surrounding walls. Flowing liquid metals are proposed as an alternative, but raise additional challenges that require investigation and numerical simulations. Free surface designs are desirable for plasma-facing components, but steady flow profiles and surface stability must be ensured to limit undesirable interactions with the plasma. Previous studies have mainly used steady-state, 2D, or simplified models for internal flows and have not been able to adequately model free-surface liquid metal (LM) experiments. Therefore, FreeMHD has been recently developed as an open-source magnetohydrodynamics (MHD) solver for free-surface electrically conductive flows subject to a strong external magnetic field. The FreeMHD solver computes incompressible free-surface flows with multi-region coupling for the investigation of MHD phenomena involving fluid and solid domains. The model utilizes the finite-volume OpenFOAM framework under the low magnetic Reynolds number approximation. FreeMHD is validated using analytical solutions for the velocity profiles of closed channel flows with various Hartmann numbers and wall conductance ratios. Next, experimental measurements are then used to verify FreeMHD, through a series of cases involving dam breaking, 3D magnetic fields, and free-surface LM flows. These results demonstrate that FreeMHD is a reliable tool for the design of LM systems under free surface conditions at the reactor scale. Furthermore, it is flexible, computationally inexpensive, and can be used to solve fully 3D transient MHD flows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Peculiarities of adaptive phase correction of optical wave distortions under conditions of ‘strong’ intensity fluctuations

The reason for the loss of efficiency of adaptive phase correction in the propagation of optical waves in a turbulent atmosphere under conditions of ‘strong’ intensity fluctuations is experimentally explained for the first time. Based on the data from experiments conducted on both horizontal and vertical atmospheric paths, we have found that intensity fluctuations begin to significantly affect phase measurements when the coherence radius of the optical wave becomes less than the radius of the first Fresnel zone. Under these conditions, the main meter of adaptive optics systems, i. e. the Hartmann sensor, no longer provides correct measurements of the phase distribution in the presence of deep amplitude modulation. Based on the study of the behaviour of the mode components of the phase fluctuations reconstructed from the results of measurements in various operating regimes, we have found that, first of all, the amplitudes of the lowest modes of phase fluctuation expansion (tilts, defocusing, and astigmatism) are distorted, which, as the analysis shows, is very different from the regime of weak fluctuations. (atmospheric optics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Pressure drop in a prototypical 3D magnetohydrodynamic flow across contraction of a fusion blanket manifold

Predicting 3D magnetohydrodynamic (MHD) pressure losses associated with liquid metal flows in complex geometry ducts is required to design breeding blankets for fusion reactors. Of such components, manifolds exhibit major pressure losses. Recent correlations [T. Rhodeset al. Magnetohydrodynamic pressure drop and flow balancing of liquid metal flow in a prototypic fusion blanket manifold. Phys. Fluids. 2018; 30: 057101.] demonstrate promise for predicting pressure drops in electrically insulated inlet manifolds. In the present work, the extend to which these correlations can be applied to outlet manifolds, which feature sudden contractions, is investigated in both viscous-electromagnetic (VE) and inertial-electromagnetic (IE) regimes for Reynolds numbers 50 < Re < 1500, Hartmann numbers 2500 < Ha < 5475, and expansion/contraction ratio 10. Numerical computations have shown that the MHD pressure drops in the eutectic lead-lithium (PbLi) flows in contractions are almost identical to those in the flows featuring expansion with slightly higher magnitudes in the contraction cases. The small discripancy in the MHD pressure drop between contractions and expansions (<8%) suggests that the earlier obtained correlations for the 3D MHD pressure drop in a duct flow with a sudden expansion can also be applied to flows with a sudden contraction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Modeling of Transport Processes in Liquid-Metal Fusion Blankets: Past, Present, and Future

The successful development of robust breeding blanket systems will strongly rely on computational tools for predicting the complex behavior of the electrically conducting liquid-metal (LM) breeder flowing in the complex-shaped blanket ducts in the presence of a strong plasma-confining magnetic field, volumetric heating, and tritium generation. Associated transport processes involve magnetohydrodynamic (MHD) flows, heat transfer, corrosion, and tritium transport. This paper is an overview of past and present efforts in the development, application, and verification and validation (V&V) of such computational tools. As a result of the ongoing campaign on V&V of computer codes for LM blankets, the international fusion community has identified several candidates that promise to become real blanket design and analysis tools in the near future. Among them are HIMAG, MHD-UCAS, COMSOL Multiphysics, ANSYS FLUENT, ANSYS CFX, and OpenFOAM. The progress, over the last decade, in the application of such codes in blanket studies is tremendous. This is illustrated with two examples for a dual-coolant lead-lithium (DCLL) blanket: (1) integrated computer modeling for the recently designed DCLL blanket in the United States and (2) application of the code MHD-UCAS to the analysis of PbLi flows and heat transfer in a generic DCLL blanket prototype at high Hartmann (Ha ~ 10 4 ) and Grashof numbers (Gr ~ 10 12 ). Here, this paper also presents an approach to the development of a new integrated computational tool called the virtual dual-coolant lead-lithium (VDCLL) blanket, which elaborates the existing U.S. MHD code HIMAG.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

MHD Analysis of Dual-Coolant Lead-Lithium Blanket for Spherical Tokamak Advanced Reactor

The tritium breeding blanket is vital for future fusion power plants, with the Spherical Tokamak Advanced Reactor (STAR) project highlighting the dual-coolant lead-lithium (DCLL) design. The DCLL blanket performs shielding, energy exhaust, and tritium breeding using a lead-lithium alloy , with lithium as the breeder and lead as the neutron multiplier. It also serves as the primary coolant, with helium providing supplemental cooling. Reduced-activation ferritic/martensitic steel is used for the blanket structure. Magnetohydrodynamic (MHD) phenomena influence the liquid metal flow in a magnetic field, affecting heat transfer in the breeder affected by energetic neutrons. Understanding key flow parameters in such conditions is critical for efficient DCLL design. This study uses three-dimensional thermofluid MHD analysis with ANSYS CFX software, modified at Princeton Plasma Physics Laboratory, to simulate high Hartmann flows. The neutronics code MCNP, coupled with plasma equilibrium, provides heat source distribution. In conclusion, we examine electromagnetic interactions in adjacent fluid domains and analyze the magnetic field’s impact on flow distribution in the inboard and outboard blanket layout, using detailed mesh generation for accurate results.

DCLL↗
DOE OSTI2022

Toward full simulations for a liquid metal blanket: part 2. Computations of MHD flows with volumetric heating for a PbLi blanket prototype at Ha ~10 4 and Gr ~10 12

On the pathway toward full simulations for a liquid metal (LM) blanket, this part 2 extends a previous study of purely magnetohydrodynamic (MHD) flows in a DCLL blanket in reference Chen et al (2020 Nucl. Fusion 60 076003) to more general conditions when the MHD flow is coupled with heat transfer. The simulated prototypic blanket module includes all components of a real LM blanket system, such as supply ducts, inlet and outlet manifolds, multiple poloidal ducts and a U-turn zone. Volumetric heating generated by fusion neutrons is added to simulate thermal effects in the flowing lead–lithium (PbLi) breeder. The MHD flow equations and the energy equation are solved with a DNS-type finite-volume code ‘MHD-UCAS’ on a very fine mesh of 470 × 10 6 cells. The applied magnetic field is 5 T (Hartmann number Ha ~ 10 4 ), the PbLi velocity in the poloidal ducts is 10 cm s –1 (Reynolds number Re ~10 5 ), whereas the maximum volumetric heating is 30 MW m –3 (Grashof number Gr ~ 10 12 ). Four cases have been simulated, including forced- and mixed-convection flows, and either an electrically conducting or insulating blanket structure. Various comparisons are made between the four computed cases and also against the purely MHD flows computed earlier in reference Chen et al (2020 Nucl. Fusion 60 076003) with regards to the (1) MHD pressure drop, (2) flow balancing, (3) temperature field, (4) flows in particular blanket components, and (5) 3D and turbulent flow effects. The strongest buoyancy effects were found in the poloidal ducts. In the electrically non-conducting blanket, the buoyancy forces lead to significant modifications of the flow structure, such as formation of reverse flows, whereas their effect on the MHD pressure drop is relatively small. In the electrically conducting blanket case, the buoyancy effects on the flow and MHD pressure drop are almost negligible.

Physics↗
DOE OSTI2022

Characterisations of the HinOTORI telescope with a three-color imager at Ali Observatory in Western Tibet

HinOTORI is a new telescope supported by an international collaboration project between China and Japan. It is a 50 centimeter telescope equipped with simultaneous three-color imagers (u',R C , and I C bands). It is located at Ali Observatory at an altitude of 5100m. Thanks to the high altitude and extreme dryness, Ali site is one of the most suitable sites for optical astrometry. HinOTORI telescope aims at detecting optical transients such as the counterparts of gravitational wave (GW) sources, supernovae, gamma-ray bursts (GRB) and so on. This paper describes the site information, design of simultaneous three-color optical layout, system instruments and whole control system. We also report some telescope characterisations for three bands (u'/R C /I C ) respectively, such as Hartmann constant (0.49"/0.56"/0.60"), best focus position (3.922/3.920/3.903 mm), PSF FWHM size (3.755/3.328/3.167pixels), total transmittance and limiting magnitude (15.69/17.57/17.05mag, 10 σ 30 seconds exposure time). With different airmass observation data, the atmospheric extinction coefficients of three bands (0.366/0.061/0.026) were also derived.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

X-ray wavefront sensor development at the Advanced Light Source

At Lawrence Berkeley National Laboratory's Advanced Light Source, we are developing x-ray wavefront sensors to support the creation and operation of beamlines with diffraction-limited quality. Our new approach to rapid, intermittent wavefront sensing operates in reflection at glancing incidence angles and is compatible with the high-power densities of modern beamlines. For soft x-ray applications especially, the wavefront sensor can operate upstream of the exit slit in a vertically dispersed beam. This single-shot technique supports lateral shearing interferometry and Hartmann wavefront sensing; it can be adapted to speckle-based techniques as well. The reflected beam is directed to an off-axis YAG crystal that produces scintillated visible light. A small mirror reflects the light to a microscope and camera, and the measured wavefront shape information can be used as feedback to adaptive x-ray mirror elements. A compact array of gratings enables measurement across a broad range of photon energies or wavefront curvatures. We describe recent demonstrations at soft x-ray and hard x-ray wavelengths measuring an adaptive x-ray mirror, and a toroidal focusing mirror.

Goldberg, Kenneth A↗
DOE OSTI2026

FastrSHWFS Analysis

This code analyzes the reflection geometry of modified Shack-Hartmann Wavefront Sensor (SHWFS) masks, with a focus on the fastrSHWFS designs. It takes a height map of a reflective mask, divides it into sub apertures, removes the global focus term by referencing a central block, and fits local surface planes to each sub aperture. From these fits it computes reflection angles and propagates the corresponding rays downstream to determine spot positions and the overall reflected beam footprint as a function of distance. The implementation is parameterized in sub aperture size, number of sub apertures, focal length, and mask dimensions, so it can be adapted to different mask designs beyond the two current fastrSHWFS masks. The code: Converts mask bitmaps into physical height in microns and reconstructs a focus subtracted mask, divides the mask into a grid of sub apertures and assigns pixel and micron coordinates to each block, excludes user specified unused sub apertures from the analysis, fits a plane to each sub aperture to obtain local surface normals, propagates reflected rays to a range of z positions to compute ray spots and the full reflected beam width, computes the effective mask tilt angle with respect to the incoming beam as a function of propagation distance, and provides helper routines for plotting the grid over the mask and for visualizing the beam geometry. These tools are intended for iterating on fastrSHWFS mask designs and for planning downstream optical layouts, for example choosing lens positions and apertures that capture the reflected beam given known focal plane distances and beam widths.

Gerard, BenjaminL [Lawrence Livermore National Lab↗