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Quantitative concentration measurements in a turbulent helium jet using rainbow schlieren deflectometry
Rainbow schlieren deflectometry (RSD) is applied to acquire quantitative concentration measurements in a turbulent environment for the first time. RSD methodology is developed and validated using Rayleigh scattering data available in the literature. Experiments were performed in an initially laminar, momentum-driven helium jet injected into ambient air. Full-field measurements are acquired that span the laminar, transition, and fully turbulent regions of the jet. Furthermore, the RSD results are shown to provide accurate measurements in each region and also confirm the self-similar nature of the fully turbulent jet. Analysis shows that the transition from laminar to turbulent flow occurs across an axial span that decreases with increasing Reynolds number. Experiments with a long exposure time were conducted to evaluate the limitations of hardware averaging of the RSD signal in comparison with software averaging.
Static metrology of the meter-scale deformable heliostat
This paper describes a heliostat metrology system which is developed based on deflectometry, utilizing a static perforated panel instead of conventional dynamic monitor displays to provide incident rays. The developed method is named static screen deflectometry (SSD). This robust and scalable method is especially valuable for outdoor tests of large reflectors used in concentrating solar-thermal power (CSP) systems. The developed method has been successfully demonstrated on a 2.4 𝑚 × 3.3 𝑚 float glass deformable reflector bent to focus sunlight at 113 𝑚 distance throughout a day. From images obtained from a camera at 50𝑚 distance, the reflector surface was measured to an accuracy of less than 1 𝑚𝑟𝑎𝑑 rms slope error in the full test scope.
Collimated phase measuring deflectometry
Phase measuring deflectometry has been applied for free-form specular surface metrology, but its measured slope results are sensitive to the depth of sample positioning, which is also called the height-slope ambiguity. The objective of this work is to tackle this height-slope ambiguity problem. The main idea is to introduce collimated camera rays using a telecentric imaging lens and collimated structured-light illumination with a Fourier lens. This setup makes the fringe phases become only sensitive to the surface slopes and insensitive to the depth of the sample positioning. In this way, the slope calculation is theoretically independent of the sample depth. We call this new deflectometry technique Collimated Phase Measuring Deflectometry (CPMD). With our developed CPMD experimental setup, the measurement is insensitive to the depth of sample positioning, e.g., the measured height dispersion is less than 30 nm RMS within a 10 mm depth range when measuring a 50-mm-diameter spherical mirror with a 200 mm radius of curvature. In conclusion, the merits and limitations of the proposed CPMD technique are discussed, revealing its prospects in practical metrology applications and potential future investigations.
Proton deflectometry of a capacitor coil target along two axes
A developing application of laser-driven currents is the generation of magnetic fields of picosecond–nanosecond duration with magnitudes exceeding $B=10~\text{T}$. Single-loop and helical coil targets can direct laser-driven discharge currents along wires to generate spatially uniform, quasi-static magnetic fields on the millimetre scale. Here, we present proton deflectometry across two axes of a single-loop coil ranging from 1 to 2 mm in diameter. Comparison with proton tracking simulations shows that measured magnetic fields are the result of kiloampere currents in the coil and electric charges distributed around the coil target. Using this dual-axis platform for proton deflectometry, robust measurements can be made of the evolution of magnetic fields in a capacitor coil target.
Collimated phase measuring deflectometry II: Re-design of the optical layout for high-curvature surfaces
Collimated phase measuring deflectometry (CPMD) is an optical metrology technique developed to improve upon traditional phase measuring deflectometry (PMD). CPMD utilizes telecentric imaging and collimated structured light illumination to eliminate the height-slope ambiguity present in traditional PMD measurements. After the publication of the first CPMD paper, efforts began to optimize the optical layout of the CPMD system. The first proposed change, and the one detailed in this work, was to move the Fourier transform (FT) lens closer to the surface under test (SUT). Moving the FT lens closer to the SUT meant that for a given FT lens diameter, a larger range of surface slopes on the SUT could be measured. This change to the optical layout was not trivial and introduced at least two concerns that had to be addressed: telecentricity in the imaging path and possible ghost reflections from the re-located FT lens. Here, in this work, we examine how these concerns were addressed and present results showing that the revised optical layout is capable of measurement results at least as good as the original CPMD optical layout. We also demonstrate the increased slope measuring range of the revised optical layout.
Implementation of Talbot–Lau x-ray deflectometry in the pulsed power environment using a copper X-pinch backlighter
A Talbot–Lau x-ray deflectometer can map electron density gradients in high energy density plasmas, as well as provide information about plasma elemental composition through single-image x-ray refraction and attenuation measurements. A new adaptation to a pulsed power environment used backlighting from copper X-pinches, allowing for electron density mapping of a low-Z object. Even though the X-pinch backlighter is not properly optimized for emitting x-rays in terms of source size and photon fluence, Moire fringe patterns with contrast up to 14% and fringe shift due to refraction on a beryllium object are obtained. Due to the proximity of the deflectometer with the X-pinch (~6 cm), it is shown that a protective filter is required to avoid damage in the closest (i.e., source) grating due to both plasma debris and mechanical shock. Regarding grating survival, these did not show any damage due to the intense magnetic field or heating induced by plasma radiation. Electron density on beryllium was measured with a difference lower than 16%. The areal electron density mapping of the sample was limited by source size characteristics, in similarity to transmission radiography. These results show the potential of plasma electron density as well as material mapping through Talbot–Lau x-ray deflectometry in a pulsed power environment.
Proton deflectometry with in situ x-ray reference for absolute measurement of electromagnetic fields in high-energy-density plasmas
In this work, we report a technique of proton deflectometry that uses a grid and an in situ reference x-ray grid image for precise measurements of magnetic fields in high-energy-density plasmas. A D 3 He fusion implosion provides a bright point source of both protons and x-rays, which is split into beamlets by a grid. The protons undergo deflections as they propagate through the plasma region of interest, whereas the x-rays travel along straight lines. The x-ray image, therefore, provides a zero-deflection reference image. The line-integrated magnetic fields are inferred from the shifts of beamlets between the deflected (proton) and reference (x-ray) images. We developed a system for analysis of these data, including automatic algorithms to find beamlet locations and to calculate their deflections from the reference image. The technique is verified in an experiment performed at OMEGA to measure a nonuniform magnetic field in vacuum and then applied to observe the interaction of an expanding plasma plume with the magnetic field.
Measuring magnetic fields in laser-driven coils with dual-axis proton deflectometry
Abstract By driving hot electrons between two metal plates connected by a wire loop, high power lasers can generate multi-tesla, quasi-static magnetic fields in miniature coil targets. Many experiments involving laser-coil targets rely on proton deflectometry directed perpendicular to the coil axis to extract a measurement of the magnetic field. In this paper, we show that quantitative measurements using perpendicular probing are complicated by the presence of GV m −1 electric fields in the target that develop on sub-ns timescales. Probing parallel to the coil axis with fiducial grids is shown to reliably separate the electric and magnetic field measurements, giving current estimates of I ≈ 5 kA in 1 mm- and 2 mm-diameter wire loops. An analytic model of proton deflection in electric and magnetic fields is used to benchmark results from the particle-in-cell code and help deconvolve the magnetic and electric field deflections. Results are used to motivate a new experimental scheme that combines a single-plate target with axial proton probing and direct current measurements. This scheme has several important advantages over the traditional target and diagnostic set-up, enabling the robust measurement of coil magnetic fields and plasma properties, as well as making it easier to validate different theoretical models at a range of laser intensities.
Self-driven ion deflectometry measurements using MeV fusion-driven protons and accelerated deuterons in the deuterated hybrid x-pinch on the MAIZE LTD generator
Abstract We report on the results of point-projection ion deflectometry measurements from a mid-size university z-pinch experiment. A 1 MA 8 kJ LTD generator at the University of Michigan (called MAIZE) drove a hybrid x-pinch (HXP) with a deuterated polyethylene fiber load to produce a point-like source of MeV ions for backlighting. In these experiments, 2.7 MeV protons were generated by DD beam-target fusion reactions. Due to the kinematics of beam-target fusion, the proton energies were down-shifted from the more standard 3.02 MeV proton energy that is released from the center-of-mass rest frame of a DD reaction. In addition to the 2.7 MeV protons, strongly anisotropic beams of 3 MeV accelerated deuterons were detected by ion diagnostics placed at a radial distance of 90 mm from the x-pinch. Numerical reconstruction of experimental data generated by deflected hydrogen ion trajectories evaluated the total current in the vacuum load region. Numerical ion-tracking simulations show that accelerated deuteron beams exited the ion source region at large angles with respect to the pinch current direction.
Proton deflectometry analysis in magnetized plasmas: Magnetic field reconstruction in one dimension
Proton deflectometry is used in magnetized high-energy-density plasmas to observe electromagnetic fields. Here we describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The algorithm is verified against analytic solutions and applied to example data. Next, we study the role of source fluence uncertainty for 1-D reconstructions. We show that reconstruction boundary conditions can be used to constrain the source fluence profile and use this to develop a reconstruction using a specified pair of boundary conditions on the magnetic field. From these considerations, we experimentally demonstrate a hybrid mesh-fluence reconstruction technique where fields are reconstructed from fluence data in an interior region with boundary conditions supplied by direct mesh measurements at the boundary.
Design of proton deflectometry with in situ x-ray fiducial for magnetized high-energy-density systems
We report a design and implementation of proton deflectometry with an in situ reference x-ray image of a mesh to precisely measure non-uniform magnetic fields in expanding plasmas at the OMEGA and OMEGA EP laser facilities. The technique has been developed with proton and x-ray sources generated from both directly driven capsule implosions and short pulse laser–solid interactions. The accuracy of the measurement depends on the contrast of both the proton and x-ray images. Here we present numerical and analytic studies to optimize the image contrast using a variety of mesh materials and grid spacings. Our results show clear enhancement of the image contrast by factors of four to six using a high Z mesh with large grid spacing. This leads to further improvement in the accuracy of the magnetic field measurement using this technique in comparison with its first demonstration at the OMEGA laser facility [Rev. Sci. Instrum. 93, 023502 (2022) [CrossRef]].
OpenCSP Deflectometry Technical Description, Document Version 1.0
This document provides a technical description of algorithms used in the OpenCSP code repository that are common to deflectometry. This document is meant to be a technical reference that describes the internal algorithms of OpenCSP. An example program that uses these algorithms is SOFAST 2.0.
INVESTIGATION OF TURBULENT JETS, SPRAYS, AND SUPERCRITICAL MIXING BY TIME RESOLVED RAINBOW SCHLIEREN DEFLECTOMETRY
As technological advancements have enabled higher efficiency compression ignition (CI) engines (diesel engines) by operating at higher pressures and temperatures, the mechanisms of fuel-air mixing are postulated to change. Thus, there is a greater need for experimental data to develop and verify new phenomena. However, the fast time scales and harsh environments associated with CI engines present many experimental difficulties and requires high quality non-intrusive diagnostics to obtain useful data. The diagnostics itself must be validated prior to its implementation in an engine environment. The purpose of this research is to advance rainbow schlieren deflectometry (RSD) to study turbulent fuel sprays including the effects of supercritical mixing in CI engine environments. This objective is met by developing and applying quantitative RSD, for the first time, to three separate aspects of fuel sprays: 1) turbulent mixing, 2) phase boundaries, and 3) non-ideal gas mixing. First, quantitative RSD is demonstrated for turbulent mixing in a canonical helium jet. Rayleigh scattering data in the literature is used to validate the concentration measurements obtained by RSD. The results also provide explanations for phenomena occurring in the helium jet and provide data not yet present in the literature. Second, RSD is applied to high pressure multi-phase fuel sprays and new methodologies are developed to distinguish the liquid region from the vapor region and to quantify the in-between region on a probabilistic basis. Isolating liquid and vapor regions generally requires two separate diagnostics, e.g., Mie scattering (liquid region) and Rayleigh scattering (vapor region). However, the results of this study demonstrate that RSD can be used as a single diagnostic to measure both liquid and vapor boundaries. Third, the optical-to-thermodynamic relations associated with refrac-tometry are investigated under non-ideal gas mixing conditions to develop a generalized relationship valid for both ideal or non-ideal gas mixing. The last part of this research develops the theoretical tools to understand and experimentally realize supercritical mixing at diesel conditions. Guided by the theoretical analysis, RSD is applied to compare supercritical versus transcritical mixing at CI conditions using a constant pressure test rig. It is found that while fully supercritical mixing ers benefits in diesel engines, i.e, faster mixing times (50% higher velocities), the absence of droplets which cause high levels of particulate emissions, etc., it would be difficult to achieve in practice because of the requirements of fuels with low critical temperature and/or substantial fuel preheating.
Phase imaging of irradiated foils at the OMEGA EP facility using phase-stepping X-ray Talbot–Lau deflectometry
Abstract Diagnosing the evolution of laser-generated high energy density (HED) systems is fundamental to develop a correct understanding of the behavior of matter under extreme conditions. Talbot–Lau interferometry constitutes a promising tool, since it permits simultaneous single-shot X-ray radiography and phase-contrast imaging of dense plasmas. We present the results of an experiment at OMEGA EP that aims to probe the ablation front of a laser-irradiated foil using a Talbot–Lau X-ray interferometer. A polystyrene (CH) foil was irradiated by a laser of 133 J, 1 ns and probed with 8 keV laser-produced backlighter radiation from Cu foils driven by a short-pulse laser (153 J, 11 ps). The ablation front interferograms were processed in combination with a set of reference images obtained ex situ using phase-stepping. We managed to obtain attenuation and phase-shift images of a laser-irradiated foil for electron densities above ${10}^{22}\;{\mathrm{cm}}^{-3}$ . These results showcase the capabilities of Talbot–Lau X-ray diagnostic methods to diagnose HED laser-generated plasmas through high-resolution imaging.
Surface Metrology for X-ray Mirrors using Deflectometry (Final Report)
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Multi-Energy Differential Evolution Reconstruction (MEnDER 1D) for Proton Deflectometry
This code is designed to reconstruct magnetic field deflections, and thus the path-integrated magnetic field, from sets of proton images at two distinct proton probe energies. A differential evolution (DE) algorithm is used to iteratively update a population of solution candidates of the magnetic deflections of the protons for reconstructing the input images, selecting improved candidates as they are discovered. This algorithm was written using MATLAB (R2019a) and makes use of the Image Processing and Parallel Processing Toolboxes.
Phase contrast imaging of irradiated foils through Talbot Lau X ray Deflectometry on OMEGA EP.
Abstract not provided.