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Photometric Correction of Hayabusa2's NIRS3 Spectra of Asteroid 162173 Ryugu Using Empirical Photometric Models

In 2018, Japanese Aerospace Exploration Agency’s spacecraft Hayabusa2 began a near infrared spectroscopic imaging survey of near-Earth asteroid 162173 Ryugu. Hayabusa2 is a successful sample-return mission with an overarching goal to provide a better understanding of the origin and evolution of our solar system. The target, Ryugu, is a low-albedo carbonaceous asteroid (Cb-type) that is linked to carbonaceous chondrite meteorites. It is thought to have originated in the main asteroid belt and migrated inward to become a near-Earth asteroid, and therefore reachable by spacecraft. Preliminary findings from processed NIRS3data have shown that hydroxyl-bearing minerals are present on the surface of Ryugu, and it is likely the result of impact fragments from an aqueously altered parent body.In this project, we have used newly calibrated and processed NIRS3 data using updated shape models of Ryugu. NIRS3 spectra have both a thermal and reflectance component. The thermal component (beyond 2.5 microns) was modeled and removed from all NIRS3 spectra. Ryugu spectra were taken at different viewing geometries, and a photometric model needed to be developed to normalize all of the spectra at a common geometry for each mission phase. We have used three empirical models: Minnaert, Lommel-Seeliger, and ROLO (RObotic LunarOrbiter). These models were chosen for their ability to relate the surface reflectance to the viewing geometry, as well as their compatibility with the asteroid’s albedo range. The three models provide the global light scattering properties of Ryugu’s surface and subsequently enable us to calculate the geometric albedo, phase integral, spherical bond albedo, and the average surface normal albedo for Ryugu.

Lucille Grace Williamson↗

Velocity and Temperature Measurements in High-speed Flows with Naturally Present Dust Particles Using Rayleigh and Mie Scattering

Dust particles and occasional moisture condensations are unavoidable reality of all wind tunnels. On the path to pursue a goal of velocity and temperature measurements in high-speed wind tunnels we have created a tabletop, spectrally resolved, Rayleigh-Mie scattering setup around a small jet fed by ambient and air with different particle concentration to determine the accuracy of the technique. The other reality of a wind tunnel setup is the spurious reflection and scattering of the incident laser beam by solid surfaces (flare light), which contaminates the Rayleigh-Mie scattered light. This is simulated by backgrounds with different reflectivity towards the collection optics. Light from a CW laser is delivered via an optical fiber and the scattered light from a point on the laser path is spectrally resolved using a stabilized Fabry-Perot interferometer, followed by imaging on an EMCCD camera. A model of the combined background glare, Mie scattering, and the Rayleigh spectrum was fitted to the camera image using maximum likelihood estimation. It was observed that the present modeling approach can extract velocity and temperature with reasonable accuracy when the intensity of the Mie scattered light is less than or comparable to that of the Rayleigh scattered light; beyond that error in velocity measurement remains reasonable ±12m/s but the temperature measurement becomes progressively more inaccurate. Increasingly the flare light is found to cause a bias error in velocity. Similar trend is observed in the presence of both the flare light and the Mie scattered light. The setup has provided a set of data for the future improvement of the modeling procedure, and demonstrated that even in the case of large amount of dust particles and large flare light the present technique can provide measurement of velocity with reasonable accuracy.

Rayleigh scattering↗

Ultraviolet Molecular Rayleigh Scattering Used to Measure Velocity in High-Speed Flow

Molecular Rayleigh scattering offers a means to measure gas flow parameters including density, temperature, and velocity. No seeding of the flow is necessary. The Rayleigh scattered power is proportional to the gas density, the spectral width is related to the gas temperature, and the shift in the frequency of the spectral peak is proportional to one component of the fluid velocity. Velocity measurements based on Rayleigh scattering are more suitable for high-speed flow, where the bulk fluid velocity is on the order of, or larger than, the molecular thermal velocities. Use of ultraviolet wavelengths for Rayleigh scattering diagnostics is attractive for two reasons. First, the Rayleigh scattering cross section is proportional to the inverse 4th power of the wavelength. And second, the reflectivity of metallic surfaces is generally less than it is at longer wavelengths. This is of particular interest in confined flow situations, such as in small wind tunnels and aircraft engine components, where the stray laser light scattered from the windows and internal surfaces in the test facility limits the application of Rayleigh scattering diagnostics. In this work at the NASA Lewis Research Center, molecular Rayleigh scattering of the 266-nm fourth harmonic of a pulsed, injection seeded Nd:YAG (neodymium:yttriumaluminum- garnet) laser was used to measure velocity in a supersonic free air jet with a 9.3- mm exit diameter. The frequency of the Rayleigh scattered light was analyzed with a planar mirror Fabry-Perot interferometer used in a static imaging mode, with the images recorded on a cooled, high-quantum-efficiency charge-coupled discharge (CCD) camera. In addition, some unshifted light from the same laser pulse was imaged through the interferometer to generate a reference. Data were obtained with single laser pulses at velocities up to Mach 1.3. The measured velocities were in good agreement with velocities calculated from isentropic flow relations. Our conclusion from this study was that ultraviolet Rayleigh scattering is preferable in confined flow situations because of the increase in the ratio of Rayleigh scattering signal to stray laser light. On the other hand, in open flows, such as free jets and larger wind tunnels where stray laser light can be controlled, visible Rayleigh scattering is preferable.

Seasholtz, Richard G.↗

High-Contrast Near-Infrared Imaging Polarimetry of the Protoplanetary Disk around RY Tau

We present near-infrared coronagraphic imaging polarimetry of RY Tau. The scattered light in the circumstellar environment was imaged at H-band at a high resolution (approx. 0.05) for the first time, using Subaru-HiCIAO. The observed polarized intensity (PI) distribution shows a butterfly-like distribution of bright emission with an angular scale similar to the disk observed at millimeter wavelengths. This distribution is offset toward the blueshifted jet, indicating the presence of a geometrically thick disk or a remnant envelope, and therefore the earliest stage of the Class II evolutionary phase. We perform comparisons between the observed PI distribution and disk models with: (1) full radiative transfer code, using the spectral energy distribution (SED) to constrain the disk parameters; and (2) monochromatic simulations of scattered light which explore a wide range of parameters space to constrain the disk and dust parameters. We show that these models cannot consistently explain the observed PI distribution, SED, and the viewing angle inferred by millimeter interferometry. We suggest that the scattered light in the near-infrared is associated with an optically thin and geometrically thick layer above the disk surface, with the surface responsible for the infrared SED. Half of the scattered light and thermal radiation in this layer illuminates the disk surface, and this process may significantly affect the thermal structure of the disk.

protoplanetary disks↗

Optical Polarization of Light from a Sorghum Canopy Measured Under Both a Clear and an Overcast Sky

Introduction: We tested the hypothesis that the optical polarization of the light reflected by a sorghum canopy is due to a Fresnel-type redirection, by sorghum leaf surfaces, of light from an unpolarized light source, the sun or overcast sky, toward the measuring sensor. If it can be shown that the source of the polarization of the light scattered by the sorghum canopy is a first surface, Fresnel-type reflection, then removing this surface reflected light from measurements of canopy reflectance presumably would allow better insight into the biochemical processes such as photosynthesis and metabolism that occur in the interiors of sorghum canopy leaves. Methods: We constructed a tower 5.9m tall in the center of a homogenous sorghum field. We equipped two Barnes MMR radiometers with polarization analyzers on the number 1, 3 and 7 Landsat TM wavelength bands. Positioning the radiometers atop the tower, we collected radiance data in 44 view directions on two days, one day with an overcast sky and the other, clear and sunlit. From the radiance data we calculated the linear polarization of the reflected light for each radiometer wavelength channel and view direction. Results and Discussion: Our experimental results support our hypothesis, showing that the amplitude of the linearly polarized portion of the light reflected by the sorghum canopy varied dramatically with view azimuth direction under a point source, the sun, but the amplitude varied little with view azimuth direction under the hemispherical source, the overcast sky. Under the clear sky, the angle of polarization depended upon the angle of incidence of the sunlight on the leaf, while under the overcast sky the angle of polarization depended upon the zenith view angle. These results support a polarized radiation transport model of the canopy that is based upon a first surface, Fresnel reflection from leaves in the sorghum canopy.

cloud cover↗

Study of density distribution in a near-critical simple fluid (19-IML-1)

This experiment uses visual observation, interferometry, and light scattering techniques to observe and analyze the density distribution in SF6 above and below the critical temperature. Below the critical temperature, the fluid system is split up into two coexisting phases, liquid and vapor. The spatial separation of these phases on earth, liquid below and vapor above, is not an intrinsic property of the fluid system; it is merely an effect of the action of the gravity field. At a fixed temperature, the density of each of the coexisting phases is in principle fixed. However, near T sub c where the fluid is strongly compressible, gravity induced hydrostatic forces will result in a gradual decrease in density with increasing height in the sample container. This hydrostatic density profile is even more pronounced in the one phase fluid at temperatures slightly above T sub c. The experiment is set up to study the intrinsic density distributions and equilibration rates of a critical sample in a small container. Interferometry will be used to determine local density and thickness of surface and interface layers. The light scattering data will reveal the size of the density fluctuations on a microscopic scale.

Michels, Teun↗

Non-Lambertian effects on remote sensing of surface reflectance and vegetation index

This paper discusses the effects of non-Lambertian reflection from a homogeneous surface on remote sensing of the surface reflectance and vegetation index from a satellite. Remote measurement of the surface characteristics is perturbed by atmospheric scattering of sun light. This scattering tends to smooth the angular dependence of non-Lambertian surface reflectances, an effect that is not present in the case of Lambertian surfaces. This effect is calculated to test the validity of a Lambertian assumption used in remote sensing. For the three types of vegetations considered in this study, the assumption of Lambertian surface can be used satisfactorily in the derivation of surface reflectance from remotely measured radiance for a view angle outside the backscattering region. Within the backscattering region, however, the use of the assumption can result in a considerable error in the derived surface reflectance. Accuracy also deteriorates with increasing solar zenith angle. The angular distribution of the surface reflectance derived from remote measurements is smoother than that at the surface. The effect of surface non-Lambertianity on remote sensing of vegetation index is very weak. Since the effect is similiar in the visible and near infrared part of the solar spectrum for the vegetations treated in this study, it is canceled in deriving the vegetation index. The effect of the diffuse skylight on surface reflectance measurements at ground level is also discussed.

Lee, T. Y.↗

Chapter 10 - Remote Sensing Measurements of Aerosol Properties

Satellite instruments have proven especially capable at monitoring the quantity of airborne particles in columns of atmosphere, globally. This chapter describes the principles of satellite measurements and retrieval algorithms, and surveys current instruments and their capabilities. We outline the issues associated with retrieval algorithms, such as surface characterization and aerosol proximity to clouds, and the challenges with interpretation of the results. The relationship between measured aerosol properties and climate-relevant aerosol properties simulated in models is outlined, as well as how measurements are used to evaluate models. Most space-based aerosol instruments are passive sensors that measure reflected sunlight at multiple wavelengths, some at multiple viewing angles. A few are active sensors that send out their own laser light and measure the returned signal. Except when clouds are present, the excess amount of light scattered back to space, beyond that expected from the surface and atmospheric gas, is attributed to aerosol. Satellite measurements are used in many ways in aerosol research. They often provide the only method for monitoring hazardous phenomena such as major wildfire and volcanic eruption plumes, especially in remote areas. Stable, long-term, near-global-scale satellite data records make it possible to identify regional and global aerosol trends. Aerosol radiative effects on climate can be quantified on a near-global scale and used to estimate the strength of aerosol–radiation and aerosol–cloud interactions as well as to evaluate climate model simulations of these interactions. Aerosol-type mapping from satellite imagery is helpful for source attribution, model validation, and to constrain particle light-absorption properties that are essential for radiative forcing calculations. The range of aerosol properties retrieved from satellite observations has grown considerably since the first global estimates of aerosol optical depth (τ a) over ocean were made in the late 1970s. Methods for retrieving particle size and light-absorption properties were explored in the 1990s using multispectral, multi-angle observations, and polarization in visible and near-infrared wavelengths. Sensitivity to particle light absorption, primarily from black or brown carbon content, improved with the inclusion of UV channels, and sensitivity to very thin aerosol layers in the upper troposphere and lower stratosphere was advanced with the use of limb-sounding instruments and active sensors. There are limitations to every measurement technique, including satellite aerosol remote sensing. For wide-swath, passive instruments, aerosol retrievals near clouds can present substantial challenges as far as 15 km away due to cloud-scattered light contaminating the signal. In nearly all cases, retrievals over bright snow and ice surfaces are precluded because surface reflectance uncertainties can overwhelm the aerosol signal. Similarly, meteorological cloud is identified and masked out where possible. Data from passive sensors also lack vertical resolution except those that view toward the limb or where multi-angle imagery is acquired over plumes from wildfires, erupting volcanoes, and wind-blown dust. Yet, passive sensors provide vastly more coverage than the active instruments that mitigate these issues. Particle microphysical information is qualitative from all remote sensing techniques, relying on proxies to infer particle composition, hygroscopicity, and the amount of light-absorbing material. Further, particles smaller than about 200 nm diameter cannot be distinguished from atmospheric gas molecules with remote sensing, which hinders studies of cloud condensation nuclei and their effects on clouds. Most satellite instruments dedicated to aerosol observations are in low-Earth, near-polar, sun-synchronous orbits, which means they cross the equator at the same local time each day. Most are set on cycles that repeat approximately every 16 days, which makes it difficult to monitor aerosol evolution locally. Geostationary satellites make it possible to observe changes occurring from minutes to hours over regions up to 8000 km in size, but lack coverage of high latitudes, and often provide more limited constraints on aerosol properties. Ground-truth data are vital for satellite aerosol-retrieval validation. The AErosol RObotic NETwork (AERONET) of sun photometers was created in 1993 and has become an established global network of over 350 instruments for validating satellite measurements. The network, as well as global networks of ground-based lidars, solar flux radiometers and other sun photometers, are widely used for evaluating global satellite retrievals and model simulations. NASA's Earth Observing System (EOS) program beginning in 1999 led to improvements in reliability, spatial resolution, and spectral resolution (and hence, to improved particle size discrimination and light absorption properties). Satellite payloads include advanced broad-swath and multi-angle imagers, along with the first space-based active sensor focused largely on long-term aerosol monitoring. Since about 2002, Europe's SENTINEL and operational meteorological satellite fleets are also providing sustained aerosol observations, with planned continuation until at least 2030. Satellite remote sensing instruments offer valuable data for evaluating aerosol representations in global climate models. They have been used to assess aerosol optical and physical properties, trends and distributions, and are applied increasingly as direct model constraints in data assimilation to create global aerosol reanalysis products. Aerosol optical depth is the most common quantity adopted for routine model evaluation, including multiwavelength data to loosely constrain particle-size distributions. These evaluations of multiple models have revealed general biases in their regional aerosol amounts and seasonal patterns of transport and removal. Although satellite measurements have near-global coverage, substantial errors can be introduced into the model observation comparison unless attention is paid to spatial and temporal collocation, cloud screening, subgrid-scale variability, and measurement uncertainties that vary with retrieval conditions.

aerosol properties↗

VUV-induced degradation of FEP Teflon aboard LDEF

Examination of fluorinated ethylene propylene (FEP) copolymer materials recovered from the Long Duration Exposure Facility (LDEF) reveals differing damage characteristics on leading edge (ram-facing) versus trailing edge (wake-facing surfaces). Silver/Teflon (Ag/FEP) thermal control materials on ram facing surfaces of the LDEF exhibited obvious degradation, with an apparent increase in diffuse light scattering, whereas identical materials on the wake facing surfaces showed little apparent damage with cursory inspection. Microscopic examination of both types of surfaces reveals the nature and extent of environment induced degradation of materials. The ram facing surfaces were clearly eroded by atomic oxygen impingement, while the wake facing material developed a thin, highly embrittled surface layer.

Brinza, David E.↗

Colorimetry and magnitudes of asteroids

In the present paper, 1500 UBV observations are analyzed by a new rather general multiple scattering theory which provided clear insight into previously poorly-recognized optical nature of asteroid surfaces. Thus, phase curves are shown to consist of a surface-texture controlled component, due to singly scattered light, and a component due to multiple scattering. Phase curve shapes can be characterized by a single parameter, the multiple scattering factor, Q. As Q increases, the relative importance of the opposition effect diminishes. Asteroid surfaces are particulate and strikingly similar to texture, being moderately porous and moderately rough on a scale greater than the wavelength of light. In concequence, Q (and also the phase coefficient) correlate well with geometric albedo, and there exists a purely photometric means of determining albedos and diameters.

Bowell, E.↗

Nighttime observations of thunderstorm electrical activity from a high altitude airplane

Photographs from a NASA U-2 airplane flying over nocturnal thunderstorms show frequent lightning activity in the upper part of the cloud. In some cases, unobscured segments of lightning channels 1 km or longer are visible in clear air around and above the cloud. Multiple images of lightning channels indicate multiple discharges in the same channel. Photographs taken through a diffraction grating show that the lightning has a spectrum similar to that observed in the lower troposphere. Lightning spectra obtained with a slitless line-scan spectrometer show strong singly ionized nitrogen emissions at 463.0 and 500.5 nm. Field changes measured with an electric field-change meter correlate with pulses measured with a photocell optical system. Optical signals corresponding to dart leader, return stroke, and continuing current events are readily distinguished in the scattered light emerging from the cloud surface. The variation of light intensity with time in lightning events is consistent with predicted modification of optical lightning signals by clouds. It appears that satellite based optical sensor measurements cannot provide reliable information on current rise times in return strokes. On the other hand, discrimination between cloud-to-ground and intracloud flashes and the counting of ground strokes is possible using the optical pulse pairs which have been identified with leader, return-stroke events in the cloud-to-ground flashes studied.

Brook, M.↗

Images of star-forming regions. II - The circumstellar environment of L1551 IRS 5

The circumstellar environment of L 1551 IRS 5 is investigated based on high-resolution 8000 A (i) and 9000 A (z) broadband CCD images. A small conical reflection nebula extending from a bright semistellar knot located near the cusp of the nebula is noted. It is suggested that the point-like structure at lambda of less than about 3.7 microns may represent a bright knot of dust-scattered light located on the inner surface of a flattened circumstellar disk surrounding the radio source. Evidence is found of sharp changes in the position angle of the jet emanating from IRS 5, possibly resulting from precession of the jet nozzle provided by a dense inner disk which has dynamically decoupled from the much larger flattened molecular structure.

Campbell, Bel↗

Searching for Faint Companions to Nearby Stars with the Hubble Space Telescope

A search for faint companions (FC's) to selected stars within 5 pc of the Sun using the Hubble Space Telescope's Planetary Camera (PC) has been initiated. To assess the PC's ability to detect FCs, we have constructed both model and laboratory-simulated images and compared them to actual PC images. We find that the PC's point-spread function (PSF) is 3-4 times brighter over the angular range 2-5 sec than the PSF expected for a perfect optical system. Azimuthal variations of the PC's PSF are 10-20 times larger than expected for a perfect PSF. These variations suggest that light is scattered nonuniformly from the surface of the detector. Because the anomalies in the PC's PSF cannot be precisely simulated, subtracting a reference PSF from the PC image is problematic. We have developed a computer algorithm that identifies local brightness anomalies within the PSF as potential FCs. We find that this search algorithm will successfully locate FCs anywhere within the circumstellar field provided that the average pixel signal from the FC is at least 10 sigma above the local background. This detection limit suggests that a comprehensive search for extrasolar Jovian planets with the PC is impractical. However, the PC is useful for detecting other types of substellar objects. With a stellar signal of 10(exp 9) e(-), for example, we may detect brown dwarfs as faint as M(sub I) = 16.7 separated by 1 sec from alpha Cen A.

Schroeder, Daniel J.↗

Algorithm for Atmospheric and Glint Corrections of Satellite Measurements of Ocean Pigment

An algorithm is developed to correct satellite measurements of ocean color for atmospheric and surface reflection effects. The algorithm depends on taking the difference between measured and tabulated radiances for deriving water-leaving radiances. 'ne tabulated radiances are related to the measured radiance where the water-leaving radiance is negligible (670 nm). The tabulated radiances are calculated for rough surface reflection, polarization of the scattered light, and multiple scattering. The accuracy of the tables is discussed. The method is validated by simulating the effect of different wind speeds than that for which the lookup table is calculated, and aerosol models different from the maritime model for which the table is computed. The derived water-leaving radiances are accurate enough to compute the pigment concentration with an error of less than q 15% for wind speeds of 6 and 10 m/s and an urban atmosphere with aerosol optical thickness of 0.20 at lambda 443 nm and decreasing to 0.10 at lambda 670 nm. The pigment accuracy is less for wind speeds less than 6 m/s and is about 30% for a model with aeolian dust. On the other hand, in a preliminary comparison with coastal zone color scanner (CZCS) measurements this algorithm and the CZCS operational algorithm produced values of pigment concentration in one image that agreed closely.

Fraser, Robert S.↗

A Quantitative Test of the Applicability of Independent Scattering to High Albedo Planetary Regoliths

To test the hypothesis that the independent scattering calculation widely used to model radiative transfer in atmospheres and clouds will give a useful approximation to the intensity and linear polarization of visible light scattered from an optically thick surface of transparent particles, laboratory measurements are compared to the independent scattering calculation for a surface of spherical particles with known optical constants and size distribution. Because the shape, size distribution, and optical constants of the particles are known, the independent scattering calculation is completely determined and the only remaining unknown is the net effect of the close packing of the particles in the laboratory sample surface...

Goguen, Jay D.↗

Performance of the Dot Product Function in Radiative Transfer Code SORD

The successive orders of scattering radiative transfer (RT) codes frequently call the scalar (dot) product function. In this paper, we study performance of some implementations of the dot product in the RT code SORD using 50 scenarios for light scattering in the atmosphere-surface system. In the dot product function, we use the unrolled loops technique with different unrolling factor. We also considered the intrinsic Fortran functions. We show results for two machines: ifort compiler under Windows, and pgf90 under Linux. Intrinsic DOT_PRODUCT function showed best performance for the ifort. For the pgf90, the dot product implemented with unrolling factor 4 was the fastest. The RT code SORD together with the interface that runs all the mentioned tests are publicly available from ftp:maiac.gsfc.nasa.govpubskorkinSORD_IP_16B (current release) or by email request from the corresponding (first) author.

polarized radiative transfer↗

Effects of levitated dust on astronomical observations from the lunar surface

It is believed that a substantial population of levitated dust is present in the terminator region of the moon. Stray light scattered by this dust layer may contaminate astronomical observations made from the lunar surface using infrared, visible, and ultraviolet light. The evidence for dust levitation stems from: Surveyor vidicon images of horizon glow; anomalous brightness in photographs of the solar corona taken by Apollo astronauts while the spacecraft was just inside the moon's shadow; and observations by Apollo astronauts of streamers just prior to lunar orbital sunrise or just after lunar orbital sunset. It has been proposed that the differential charging of the lunar surface in the terminator region due to photoemission and the consequent strong local electric fields comprise the mechanism responsible for this levitation. Although quantitative data on the levitated lunar dust distribution are meager, it is possible to estimate column densities and sizes. In this paper we summarize the estimates of particulate sizes and number densities of previous authors, and construct a nominal terminator dust distribution, as a function of particulate radius and altitude above the lunar surface. Using the model we estimate the brightness of scattered sunshine for three wavelength bands. For the results in the visible wavelengths, we compare the estimated brightness with the known brightness of selected astronomical objects and discuss the implications for lunar-based astronomy.

Murphy, D. L.↗

Fabricating Radial Groove Gratings Using Projection Photolithography

Projection photolithography has been used as a fabrication method for radial grove gratings. Use of photolithographic method for diffraction grating fabrication represents the most significant breakthrough in grating technology in the last 60 years, since the introduction of holographic written gratings. Unlike traditional methods utilized for grating fabrication, this method has the advantage of producing complex diffractive groove contours that can be designed at pixel-by-pixel level, with pixel size currently at the level of 45 45 nm. Typical placement accuracy of the grating pixels is 10 nm over 30 nm. It is far superior to holographic, mechanically ruled or direct e-beam written gratings and results in high spatial coherence and low spectral cross-talk. Due to the smooth surface produced by reactive ion etch, such gratings have a low level of randomly scattered light. Also, due to high fidelity and good surface roughness, this method is ideally suited for fabrication of radial groove gratings. The projection mask is created using a laser writer. A single crystal silicon wafer is coated with photoresist, and then the projection mask, with its layer of photoresist, is exposed for patterning in a stepper or scanner. To develop the photoresist, the fabricator either removes the exposed areas (positive resist) of the unexposed areas (negative resist). Next, the patterned and developed photoresist silicon substrate is subjected to reactive ion etching. After this step, the substrate is cleaned. The projection mask is fabricated according to electronic design files that may be generated in GDS file format using any suitable CAD (computer-aided design) or other software program. Radial groove gratings in off-axis grazing angle of incidence mount are of special interest for x-ray spectroscopy, as they allow achieving higher spectral resolution for the same grating area and have lower alignment tolerances than traditional in-plane grating scheme. This is especially critical for NASA Constellation- X project that will utilize hundreds of gratings all of which need to be precisely aligned for x-ray observation of space.

Iazikov, Dmitri↗