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At least 487 records · Page 27

Quantifying Leaf Chlorophyll Concentration of Sorghum from Hyperspectral Data Using Derivative Calculus and Machine Learning

Leaf chlorophyll concentration (LCC) is an important indicator of plant health, vigor, physiological status, productivity, and nutrient deficiencies. Hyperspectral spectroscopy at leaf level has been widely used to estimate LCC accurately and non-destructively. This study utilized leaf-level hyperspectral data with derivative calculus and machine learning to estimate LCC of sorghum. We calculated fractional derivative (FD) orders starting from 0.2 to 2.0 with 0.2 order increments. Additionally, 43 common vegetation indices (VIs) were calculated from leaf spectral reflectance factor to make comparisons with reflectance-based data. Within the modeling pipeline, three feature selection methods were assessed: Pearson’s correlation coefficient (PCC), partial least squares based variable importance in the projection (VIP), and random forest-based mean decrease impurity (MDI). Finally, we used partial least squares regression (PLSR), random forest regression (RFR), support vector regression (SVR), and extreme learning regression (ELR) to estimate the LCC of sorghum. Results showed that: (1) increasing derivative order can show improved model performance until certain order for reflectance-based analysis; however, it is inconclusive to state that a particular order is optimal for estimating LCC of sorghum; (2) VI-based modeling outperformed derivative augmented reflectance factor-based modeling; (3) mean decrease impurity was found effective in selecting sensitive features from large feature space (reflectance-based analysis), whereas simple Pearson’s correlation coefficient worked better with smaller feature space (VI-based analysis); and (4) SVR outperformed all other models within reflectance-based analysis; alternatively, ELR with VIs from original reflectance yielded slightly better results compared to all other models.

47 OTHER INSTRUMENTATION↗

A canonical purification for the entanglement wedge cross-section

In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analyzing LF/VLF Lightning Waveforms to Estimate D-region Electron Density Profiles

Lightning waveforms in the low frequency (LF; 30-300 kHz) and the very low frequency (VLF; 3-30 kHz) bands can be exploited to produce data-driven ionospheric D-region electron density profile (EDP) estimates with significantly higher spatial and temporal coverage than previously available. The lightning waveforms used in this paper are signals detected in the LF/VLF of negative cloud-to-ground lightning by the Earth Networks Total Lightning Detection Network. Each waveform contains a ground wave and a time-delayed ionospheric reflection. The time delay between the ground wave and ionospheric reflection has previously been used to estimate a single specular reflection altitude, where LF/VLF emissions are reflected by the ionosphere. Here, we expand upon previous methods to include filtering and spectral analysis, and account for oblique propagation to produce higher-order estimates for reflection altitudes and corresponding electron densities. Once estimated, reflection altitudes and corresponding electron densities can be used to derive parameters β and h’, which define an EDP for the D-region. In this study, the lightning waveform (LW) analysis is demonstrated using a single representative 24-hour dataset over the Southeast United States, and then extended to a total of 10 separate datasets with varying locations and ionospheric conditions. The LW-derived D-region EDPs are in agreement with predictions made by the Faraday International Reference Ionosphere model, and the LW EDPs β and h’ values are consistent with previous LF/VLF-derived estimates.

D-region ionosphere↗

Sequential Infiltration Synthesis of Bilayer Porous Alumina Nanostructures for Broad-Angle, Broadband Antireflective Coatings

Antireflective coatings (ARCs) are thin films engineered to reduce light reflections. Delivering broadband, wide-angle performance is essential for photovoltaics, imaging, and sensing, yet truly omnidirectional antireflection remains difficult due to angle-dependent optical paths and a narrow palette of suitable refractive indices. Here, in this study, we systematically investigate an emerging class of multilayer inorganic ARCs based on conformally coated nanoporous alumina templated by intrinsically microporous polymers (PIMs) and block copolymers (BCPs). We establish a design framework that maps thickness reflectance relationships to identify thickness pairs minimizing reflection across wavelength and incidence angle. We show that deliberately separating the local reflectance minima of the top and bottom layers in bilayer nanostructures broadens the antireflective bandwidth and angular range. We show that 235-nm single-side bilayer porous alumina nanostructures achieves under 2 % reflectance from 380–750 nm for incidence angles up to 45° with less than 0.6% reflectance for incidence angles under 20°. The approach is readily extensible to additional layers or materials with refractive indices tuned via templated nanoporosity and composition, enabling practical, etch-free ARC fabrication without HF or fluorinated precursors and advancing straightforward design of broadband, wide-angle (quasi-omnidirectional) ARCs for next-generation optical systems.

antireflective coatings↗

Broadband radiometric measurements from GPS satellites reveal summertime Arctic Ocean Albedo decreases more rapidly than sea ice recedes

Abstract New measurements from the Arctic ± 40 days around the summer solstice show reflected sunlight from north of 80°N decreases 20–35%. Arctic sea ice coverage decreases 7–9% over this same time period (as reported by the NSIDC) implying Arctic sea ice albedo decreases in addition to the sea ice receding. Similar Antarctic measurements provide a baseline to which Arctic measurements are compared. The Antarctic reflected sunlight south of 80°S is up to 30% larger than the Arctic reflectance and is symmetric around the solstice implying constant Antarctic reflectivity. Arctic reflected sunlight 20 days after solstice is > 100W/m 2 less than Antarctic reflected sunlight. For perspective, this is enough heat to melt > 1 mm/hour of ice. This finding should be compared with climate models and in reanalysis data sets to further quantify sea ice albedo’s role in Arctic Amplification. The measurements were made with previously unpublished pixelated radiometers on Global Positioning System satellites from 2014 to 2019. The GPS orbits give each radiometer instantaneous and continuous views of 37% of the Earth, two daily full views of the Arctic and Antarctic. Furthermore, the GPS constellation gives full-time full-Earth coverage that may provide data that complements existing limited field of view instruments that provide a less synoptic Earth view.

54 ENVIRONMENTAL SCIENCES↗

Deriving the Infrared Complex Refractive Indices of Organic Powders for Optical Modeling: Comparison of Methods

Identification of solids via infrared reflection spectroscopy requires a spectral library of all solids likely to be encountered. A confounding factor in populating such a spectral library is that the reflectance spectra of solids vary with their form, including particle size, film thickness, and substrate. To reduce the efforts of experimentally constructing such a library, an alternate strategy is to use the wavelength-dependent optical constants, n and k, of a solid to calculate a series of reflectance spectra corresponding to each scenario or morphology. Because most n/k measurements are best performed on mm-sized crystals, however, the challenge of determining the optical constants increases when a solid is only readily available as a powder, as is often the case. Some organic solids, such as caffeine, are both unavailable in large crystals and difficult to press into pellets. In this study, the infrared optical constants, or complex refractive indices, of caffeine were determined using three different methods: single-angle reflectance, infrared spectroscopic ellipsometry, and quantitative absorbance measurements of KBr pellets. The n and k values derived through each method were used to model the hyperspectral imaging reflectance spectrum of a caffeine film on a steel planchet. Over 1,110 – 870 cm-1, the single-angle reflectance-derived n and k had the best correlation with the experimental spectrum. These results suggest different organic solids may require different methods to determine the most accurate infrared complex refractive indices for synthetic spectral libraries.

FTIR, hyperspectral imaging, infrared, infrared (I↗

A Polarimetric Radar Analysis of Ice Microphysical Processes in Melting Layers of Winter Storms Using S-Band Quasi-Vertical Profiles

Quasi-vertical profiles (QVPs) obtained from a database of U.S. WSR-88D data are used to document polarimetric characteristics of the melting layer (ML) in cold-season storms with high vertical resolution and accuracy. A polarimetric technique to define the top and bottom of the ML is first introduced. Using the QVPs, statistical relationships are developed to gain insight into the evolution of microphysical processes above, within, and below the ML, leading to a statistical polarimetric model of the ML that reveals characteristics that reflectivity data alone are not able to provide, particularly in regions of weak reflectivity factor at horizontal polarization Z H . QVP ML statistics are examined for two regimes in the ML data: Z H ≥ 20 dB Z and Z H < 20 dB Z . Regions of Z H ≥ 20 dB Z indicate locations of MLs collocated with enhanced differential reflectivity Z DR and reduced copolar correlation coefficient ρ hv , while for Z H < 20 dB Z a well-defined ML is difficult to discern using Z H alone. Evidence of large Z DR up to 4 dB, backscatter differential phase δ up to 8°, and low ρ hv down to 0.80 associated with lower Z H (from -10 to 20 dB Z ) in the ML is observed when pristine, nonaggregated ice falls through it. Positive correlation is documented between maximum specific differential phase K DP and maximum Z H in the ML; these are the first QVP observations of K DP in MLs documented at S band. Negative correlation occurs between minimum ρ hv in the ML and ML depth and between minimum ρ hv in the ML and the corresponding enhancement of Z H (Δ Z H = Z H max - Z H rain ).

Meteorology & Atmospheric Sciences↗

Photothermal heterodyne imaging of micron-sized objects

Micron-sized dye-doped polymer beads were imaged using transmitted/reflected light microscopy and photothermal heterodyne imaging (PHI) measurements. The transmitted/reflected light images show distinct ring patterns that are attributed to diffraction effects and/or internal reflections within the beads. In the PHI experiments pump laser induced heating changes the refractive index and size of the bead, which causes changes in the diffraction pattern and internal reflections. This creates an analogous ring pattern in the PHI images. The ring pattern disappears in both the reflected light and PHI experiments when an incoherent light source is used as a probe. When the beads are imaged in an organic medium heat transfer changes the refractive index of the environment, and gives rise to a ring pattern external to the beads in the PHI images. This causes the beads to appear larger than their physical dimensions in PHI experiments. This external signal does not appear when the beads are imaged in air because the refractive index changes in air are very small.

Bhandari, Janak (ORCID:0000000188423259)↗

Nondestructive Evaluation (NDE) of Cable Anomalies using Frequency Domain Reflectometry (FDR) and Spread Spectrum Time Domain Reflectometry (SSTDR)

This report presents a comparative assessment of the performance of frequency domain reflectometry (FDR) and spread spectrum time domain reflectometry (SSTDR) in detecting a wide range of electrical cable anomalies. All tests and results reported herein were performed at the PNNL Accelerated and Real-Time Environmental Nodal Assessment (ARENA) cable and motor test bed. The primary objective of this work was to evaluate the effectiveness of SSTDR, a fledgling cable monitoring technique that shows promise for application in online monitoring of energized cable systems, against FDR, an offline technique widely employed in the nuclear power plant (NPP) industry. FDR tests are becoming more widely used in nuclear power plant cable aging management and test programs – particularly for low voltage cables. FDR capabilities for these kinds of tests have been reported by PNNL and others. The FDR test is performed on de-energized cables by connecting the FDR instrument to two of the cable conductors, or one conductor and the shield. A broad band low voltage (< 5 V) chirp is introduced in the cable, and any reflected response is captured in the frequency domain. The captured reflection is then processed by performing an inverse Fourier transform to a time domain response which can then be converted to a distance response based on the cable velocity of propagation (VoP). SSTDR measurements are functionally similar to FDR measurements in that a broad-band voltage signal composed of a square or sine wave modulated pseudo-random sequence of chips (< 5 volts), is injected onto one of the cable conductors. The injected signal will experience partial energy reflection and transmission at each impedance discontinuity along the transmission line. Any reflected response is detected by computing a cross-correlation between the reflected signals and a delayed copy of the incident SSTDR signal. the time delay for the reflected signal to experience the best matched correlation with the incident signal, indicates the travel time for the signal to reach a change in impedance. By knowing this time delay and velocity of propagation (VoP) of the signal, one can compute the physical distance. A big advantage that SSTDR measurements have over other methods is the ability to be connected to energized or live wires (currently up to 1kV) thereby enabling online monitoring of cables. SSTDR has been used successfully in several applications, e.g., aircraft, rail, and photovoltaic systems. In this work FDR and SSTDR cable assessment techniques were used to characterize a variety of cable anomalies and faults including: (1) Presence or absence of a motor; (2) Ground faults and short circuit faults; (3) Moist environments and water ingress faults; (4) Accelerated thermal aging. Both shielded and non-shielded cables were evaluated in this report. Offline measurements were made using FDR and online measurements were made by SSTDR for a range of test scenarios. Based on the results across all cable anomalies evaluated in this study, FDR displayed high sensitivity towards cable condition assessment, while SSTDR showed promise for future application in monitoring NPP cable systems. However, further developments are suggested to improve the resolution and sensitivity of SSTDR towards faults and anomalies in low voltage cables.rt presents a comparative

42 ENGINEERING↗

Integrated freeform optical couplers

Reflecting light beams off of microscale three-dimensional (3D) freeform surfaces can yield highly efficient coupling into and out of optical waveguides, optical fibers, and photonic chips. The structure of the 3D freeform reflective surface determines the shape of the reflected beam. This allows freeform reflectors to control the mode profile, rotation angle, and divergence angle of light beams. Control of beam shape enables mode matching between source output mode and target input mode, which results in low-loss optical coupling. An inventive freeform reflective surface can direct light beams in plane or out of plane via specular reflection or total internal reflection. A photonic integrated circuit with this type of freeform optical coupler can operate with a bandwidth range of at least 400 nm, potentially encompassing all visible or telecommunications wavelengths, and can be volume manufactured in photonic chips.

Yu, Shaoliang↗

Spectroradiometric detection of competitor diatoms and the grazer Poteriochromonas in algal cultures

To address challenges in early detection of pond pests, we have extended a spectroradiometric monitoring method, initially demonstrated for measurement of pigment optical activity and biomass, to the detection of algal competitors and grazers. The method relies upon measurement and interpretation of pond reflectance spectra spanning from the visible into the near-infrared. Reflectance spectra are acquired every 5 min with a multi-channel, fiber-coupled spectroradiometer, providing monitoring of algal pond conditions with high temporal frequency. The spectra are interpreted via numerical inversion of a reflectance model, in which the above-water reflectance is expressed in terms of the absorption and backscatter coefficients of the cultured species, with additional terms accounting for the pigment fluorescence features and for the water-surface reflection of sunlight and skylight. With this method we demonstrate detection of diatoms and the predator Poteriochromonas in outdoor cultures of Nannochloropsis oceanica and Chlorella vulgaris, respectively. Further, the relative strength of these signatures is compared to microscopy and sequencing analysis. Spectroradiometric detection of diatoms is then further assessed on beaker-contained mixtures of Microchloropsis salina with Phaeodactylum tricornutum, Thalassiosira weissflogii, and Thalassiosira pseudonana, respectively, providing an initial evaluation of the sensitivity and specificity of detecting pond competitors.

09 BIOMASS FUELS↗

Eco-friendly passive radiative cooling using recycled packaging plastics

Passive daytime radiative cooling, requiring zero external energy consumption, is a promising cooling strategy achieved by simultaneously reflecting solar irradiance and thermally radiating heat into the cold outer space (~3 K) through the atmospheric transparency window. However, current materials for passive radiative cooling face huge challenges, such as complicated fabrication approaches, expensive raw materials, and environmental requirements for practical applications. In line with the urgent need for plastic recycling to curb global environmental pollution, the recycled plastics are used to fabricate a passive radiative cooling material. Herein, the foam-paper composite (FPC) with excellent self-cooling capability is fabricated by a simple crushing-and-mixing procedure using recycled polystyrene (PS) foam and printer paper. The superhydrophobic PS foam particles not only protect the FPC from water damage for field applications but also reinforce its solar reflectivity via their porous structure. The cellulose fibers in printer paper can efficiently emit infrared thermal radiation into the cold outer space and bond dispersed PS foam particles together, further increasing its mechanical strength. The combination of highly diffusely reflective PS foam particles and fiber-based printer paper results in a reflectivity of 96% in the solar spectrum, a sub-ambient cooling performance of 8.4 degrees C, and a maximum radiative cooling power of 90 W/m2 during a 24-h cycle. Meanwhile, the FPC with high humidity can maintain its high solar reflectivity, which promotes its application in humid subtropical areas. Further, the low material cost and ease of fabrication will provide a path for effective daytime radiative cooling, especially in less developed areas.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

When can we detect lianas from space? Toward a mechanistic understanding of liana‐infested forest optics

Abstract Lianas, woody vines acting as structural parasites of trees, have profound effects on the composition and structure of tropical forests, impacting tree growth, mortality, and forest succession. Remote sensing could offer a powerful tool for quantifying the scale of liana infestation, provided the availability of robust detection methods. We analyze the consistency and global geographic specificity of spectral signals—reflectance across wavelengths—from liana‐infested tree crowns and forest stands, examining the underlying mechanisms of these signals. We compiled a uniquely comprehensive database, including leaf reflectance spectra from 5424 leaves, fine‐scale airborne reflectance data from 999 liana‐infested canopies, and coarse‐scale satellite reflectance data covering 775 ha of liana‐infested forest stands. To unravel the mechanisms of the liana spectral signal, we applied mechanistic radiative transfer models across scales, establishing a synthesis of the relative importance of different mechanisms, which we corroborate with field data on liana leaf chemistry and canopy structure. We find a consistent liana spectral signal at canopy and stand scales across globally distributed sites. This signature mainly arises at the canopy level due to direct effects of more horizontal leaf angles, resulting in a larger projected leaf area, and indirect effects from increased light scattering in the near and short‐wave infrared regions, linked to lianas' less costly leaf construction compared with trees on average. The existence of a consistent global spectral signal for lianas suggests that large‐scale quantification of liana infestation is feasible. However, because the traits responsible for the liana canopy‐reflectance signal are not exclusive to lianas, accurate large‐scale detection requires rigorously validated remote sensing methods. Our models highlight challenges in automated detection, such as potential misidentification due to leaf phenology, tree life history, topography, and climate, especially where the scale of liana infestation is less than a single remote sensing pixel. The observed cross‐site patterns also prompt ecological questions about lianas' adaptive similarities in optical traits across environments, indicating possible convergent evolution due to shared constraints on leaf biochemical and structural traits.

Environmental Sciences & Ecology↗

Potential annual daylighting performance of a high-efficiency daylight redirecting slat system

While the primary role of window attachments is often to moderate glare and solar heat gains, they are also able to provide additional daylight to interior spaces. For this purpose, a variety of daylight-redirecting window systems have been developed over the past 150 years. Fixed reflective systems (slats/light shelves) or prismatic systems that rely on total internal reflection work well under specific solar conditions, but generally sacrifice performance over a much wider range of incident solar angles and sky conditions. Dynamic systems - typically reflective slats - are more responsive to sun angles but have not been able to achieve optimal performance for glare and daylight redirection efficiency. A previous investigation into an adjustable, reflective blind concept first conceived of in the late 1970s showed promise but was not reduced to practice due to lack of adequate simulation and analysis tools. In this paper, this concept is further developed and its energy and visual comfort performance evaluated for four mid-latitude, temperate climates using ray-tracing simulation techniques. Overall, results indicate significant potential lighting energy savings when compared with conventional automated reflective blinds (2.1–4.9 kWh/(m 2 ·a), or 14%–42%, depending on climate and orientation) or, especially, manually-operated matte white venetian blinds (1.4–7.9 kWh/(m 2 ·a), or 9%–54%, depending on climate and orientation), while maintaining acceptable or better visual comfort conditions throughout the interior space.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Temporally and spatially resolved X-ray densitometry in a shock tube

Gas densities were measured by x-ray absorption spectroscopy to examine spatial inhomogeneity in density behind incident and reflected shock waves in a miniature (12.7 mm bore) high repetition rate shock tube. Shock waves were generated in argon. The pressure and temperature behind the incident shock were P 2 ~ 1.72 bar and T 2 ~ 800 K, while those behind the reflected shock were P 5 ~ 6.5 bar and T 5 ~ 1480 K. Time-resolved line-of-sight transmission measurements using x-rays at 9 keV photon energy were made along various axial and transverse locations covering the entire shock tube cross section. The x-ray transmission at each location was converted to pathlength-integrated densities, which in some conditions could be further converted to pathlength-averaged densities. The measured gas densities were compared with those calculated by the normal shock wave relations, and good agreement was found in the preshock and immediately behind the incident shock regions. Similar agreement was found for reflected shock conditions very near the endwall. However, increasingly large differences between the measured and calculated gas densities were found as distance from the endwall increased. Furthermore, reconstruction by Abel inversion allowed time and radially resolved densities to be obtained from the transverse measurements. While the profiles measured in this experiment are of insufficient signal-to noise level and resolution to definitively assign boundary layer thicknesses, future improvements may be able to do this. The radially resolved densities reveal growing sidewall thermal boundary layers in gases behind the reflected shock. These reconstructions were compared with a model of the thermal boundary layer and are consistent with values of the thermal boundary layer thickness being between 0.25 mm and 1 mm at 0.7 ms after shock reflection.

42 ENGINEERING↗

Active populations and growth of soil microorganisms are framed by mean annual precipitation in three California annual grasslands

Climate influences soil microbial composition and function, but the relative importance of a site's historic climate versus its more immediate environmental conditions is unclear. Using quantitative stable isotope probing (qSIP), we characterized actively growing soil microbial communities and soil properties in three California annual grasslands that span a rainfall gradient and have developed on similar parent material. The soils were assayed in the wet winter season, when environmental conditions are most similar across sites. Since growing populations might be expected to be most responsive to contemporary environmental conditions, we hypothesized that the structure of growing microbial communities would be more similar across the gradient than that of total communities (i.e., including non-growing populations). In addition, we hypothesized that population growth rates would be slowest in the driest site, reflecting a legacy effect of low soil moisture on microbial growth. Soils along the rainfall gradient differed in pH, texture, and cation exchange capacity, but not in total C, C:N or dominant minerals. The radiocarbon (14C) age of soil C (reflecting turnover time) increased with mean annual precipitation but soil respiration was uniformly modern, reflecting microbial reliance on recent C inputs across the sites. The structure of both total and growing microbial communities differed across sites. Across major microbial phyla, including the Actinobacteria, Acidobacteria, Bacteroidetes, Gemmatimonadetes and Proteobacteria, bacterial growth rates were consistently lower in the site with the lowest mean annual precipitation. Taxa that were growing at the dry site alone grew more slowly than taxa that grew at multiple sites. These results reflect the influence of climate history and point to the role of environmental filtering at the driest site in shaping its slower growing microbial community, possibly reflecting adaptation to repeated exposure to water stress. Lastly, across taxa, the growth rate of a taxon at one site was correlated with its growth rate in the other sites. Furthermore, this growth rate coherence is likely a consequence of genetically determined physiological traits and is consistent with the idea that evolutionary history constrains growth rate.

Environmental filtering↗

Characterization of flowing liquid films as a regenerating plasma mirror for high repetition-rate laser contrast enhancement

In this paper, we characterize a high repetition-rate regenerating plasma mirror produced by the thin film of liquid formed when two laminar streams collide. The use of a flowing liquid film is inexpensive and the interaction surface refreshes automatically, avoiding buildup of on-target debris. The composition of the liquid material and the relative angle of the film-generating nozzles was optimized for this application. Spectra measured in reflection from a water-based plasma mirror showed a blue shift but an optical reflectivity of up to 30%. The thickness of the film was found to be of the order of 2 μm, and the stability of the reflected spot was ≈1 mrad. The reflected beam profile was highly distorted but stable. Further optimization of the nozzles to affect the fluid flow should enable significant improvements in control of the fluid films and increase in the reflectivity of these mirrors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Topography of bent crystals with microradian resolution in one dimension

Optimum performance in x-ray imaging and spectroscopy of plasmas with bent crystals is achievable only when the crystal reflects the x rays theoretically perfectly across its entire surface. However, typical thin quartz (101̄1) crystal samples kept flat by direct attachment to a flat substrate reflect 8 keV x rays differently across their surface, on a scale comparable to the ideal rocking curve. Additional processing improves the uniformity. Irradiation of flat crystals with collimated, monochromatic x rays in rocking curve topography shows such problems directly, with microradian resolution. Nonuniform x-ray reflection is more difficult to document for strongly bent crystals because, then, monochromatic, collimated x rays satisfy the Bragg condition only along a narrow stripe that may be too narrow to resolve with the available cameras. However, it can be resolved with a knife edge that moves through the reflected x rays with the necessary spatial precision as demonstrated here for a bent silicon crystal. This shows qualitatively similar imperfections in the reflection as flat quartz and as the bent quartz analyzers reported on previously with lower resolution.

Pereira, N. R. (ORCID:0000000290569596)↗