Spherical Gratings Research Articles

Soft x-ray high diffraction efficiency and spectral flux laminar-type W/B4C multilayer diffraction grating for 300-1000 eV.

Multilayer diffraction gratings are designed to improve the detection limit and sensitivity of soft x-ray flat-field spectrographs in the region of 300-1000eV, placing emphasis on Fe-L (705eV), Cu-L (930eV), and Zn-L (1012eV) emissions. For this purpose, spectral flux was used as the performance index, which is proportional to the amount of optical flux incident into a detector and correlated with detection sensitivity. A super-mirror-type W/B4C multilayer coating [Koike et al., Rev.Sci. Instrum. 94, 045109 (2023)] was employed to improve diffraction efficiency in a wide energy region. The unique feature of the multilayer structure is that the average refractive index and the period length of W/B4C layer pairs are increased from the bottom to top layers. In addition, the incidence angle was reduced to 86.03° from 88.65° and the nominal groove density was increased to 3200 lines/mm from 2400 lines/mm of our previous design, to improve spectral flux while maintaining dispersion and spectral resolution. A holographic varied-line-spacing spherical grating and a soft x-ray flat-field spectrograph were designed, using the aspherical-wavefront-recording method, assuming the nominal grating constant and incident angle described above. The numerical simulation results showed that the spectrograph employing the newly designed grating with the W/B4C multilayer indicated 3.2-8.2 times higher spectral flux compared with those using the previously designed grating while keeping the same spectral resolution.

Laminar-type gratings overcoated with carbon-based materials to enhance analytical sensitivity of flat-field emission spectrograph in the VUV region.

Laminar-type spherical diffraction gratings overcoated with carbon-based materials were designed, fabricated, and evaluated for the purpose of enhancing the analytical sensitivity of the flat-field spectrograph in a vacuum ultraviolet region of 35-110 eV. As the design benchmark for numerical calculations, diffraction efficiency (DE) and spectral flux, which are defined by the product of the DE and numerical aperture and correlate with the analytical sensitivity of the spectrograph, were used. To simplify the feasibility study on the overcoating effects, we assumed a laminar-type grating having a grating constant of 1/1000 mm and coated with a Au layer of 30.0 nm thickness and an incidence angle of 84.0°. The optimized groove depth and duty ratio were 30.0 nm and 0.3, respectively. In addition, the optimum thicknesses of the overcoating layer were 44, 46, 24, and 30 nm for B4C, C, diamond-like-carbon, and SiC, respectively. Based on these results, we have fabricated a varied-line-spacing holographic grating overcoated with B4C with a thickness of 47 nm. For the experimental evaluation, we used the light source of Mg-L and Al-L emissions excited by the electron beam generated from an electron microscope, an objective flat-field spectrograph, and a CCD imaging detector. The experimental results showed that the spectrograph employing a new grating overcoated with the B4C layer indicated almost the same spectral resolution and 2.9-4.2 times higher analytical sensitivity compared with those obtained with a previously designed Au-coated grating having a grating constant of 1/1200 mm and used at an incidence of 86.0°.

Ultrashort X-ray Free Electron Laser Pulse Manipulation by Optical Matrix

Free electron laser (FEL) is capable of producing ultra-short X-ray pulses. The estimation of X-ray pulse propagation is the key process of X-ray FEL beamline design. By using the Kostenbauder matrix approach, the evolution of an ultra-short pulse in a beamline system can be calculated. Therefore, it is of significant importance to investigate the Kostenbauder matrices of different kinds of X-ray optics. In this work, we derive a unified 6 × 6 optical matrix to describe various kinds of X-ray optical elements, including varied-line-spacing (VLS) toroidal grating, VLS spherical grating, VLS cylindrical grating, VLS plane grating, toroidal grating, spherical grating, cylindrical grating, plane grating, toroidal mirror, spherical mirror, cylindrical mirror, and plane mirror. These optics are usually adopted in soft X-ray regime. We apply this method to describe the transverse focusing, pulse front tilt, and pulse stretching after an X-ray pulse going through a VLS plane grating monochromator (VLS-PGM). We also use this approach to simulate a grating compressor which can be used to compress chirped soft X-ray pulse. This work is helpful in the design and optimization of X-ray beamline systems.

Efficient low-density grating setup for monochromatization of XUV ultrafast light sources.

Ultrafast light sources have become an indispensable tool to access and understand transient phenomenon in material science. However, a simple and easy-to-implement method for harmonic selection, with high transmission efficiency and pulse duration conservation, is still a challenge. Here we showcase and compare two approaches for selecting the desired harmonic from a high harmonic generation source while achieving the above goals. The first approach is the combination of extreme ultraviolet spherical mirrors with transmission filters and the second approach uses a normal-incidence spherical grating. Both solutions target time- and angle-resolved photoemission spectroscopy with photon energies in the 10-20 eV range but are relevant for other experimental techniques as well. The two approaches for harmonic selection are characterized in terms of focusing quality, photon flux, and temporal broadening. It is demonstrated that a focusing grating is able to provide much higher transmission as compared to the mirror+filter approach (3.3 times higher for 10.8 eV and 12.9 times higher for 18.1 eV), with only a slight temporal broadening (6.8% increase) and a somewhat larger spot size (∼30% increase). Overall, our study establishes an experimental perspective on the trade-off between a single grating normal incidence monochromator design and the use of filters. As such, it provides a basis for selecting the most appropriate approach in various fields where an easy-to-implement harmonic selection from high harmonic generation is needed.

Ultra-Precision Cutting and Characterization of Reflective Convex Spherical Blazed Grating Elements.

In this work, based on the diffraction principle of reflective blazed grating, the structure size of the convex spherical blazed grating unit is determined, the machining accuracy of the convex spherical blazed grating is formulated, the effects of tool nose radius and Poisson burr on the diffraction efficiency of the convex spherical blazed grating are analyzed, and the performances of cutting convex gratings with microcrystalline aluminum RSA6061 and RSA6061+ chemically plated NiP for two workpiece materials are compared. A convex spherical blazed grating with a radius of curvature R = 41.104 mm, substrate diameter 14 mm, grating density 53.97 line/mm, and blaze angle of roughly 3.8° is turned by a four-axis ultra-precision machining system by adjustment of the cutting tool, workpiece material, and cutting parameters, as well as modification of the layouts of the blazed grating on the convex sphere. The results of the testing of convex spherical blazed grating elements in both layouts show that the size error of the grating period is close for both layouts, the size error of grating height is smaller in the equal-along-arc layout, the blaze angle error in the equal-along-projection layout is only 0.74%, and the average roughness of the blazed surface is less than 5 nm to meet the processing quality requirements of the reflective convex spherical blazed grating. The greater the blaze angle accuracy of the blazed grating, the higher its diffraction efficiency, so the grating element with an equal-along-projection layout has a higher diffraction efficiency than the grating element with an equal-along-arc layout. RSA6061+ chemically plated NiP material is superior to RSA6061 material in Poisson burr height and blazed surface roughness, which is more suitable for Offner-type imaging spectrometers in the spectral range 0.95–2.5 μm (SWIR).

Space-resolved vacuum-ultraviolet spectroscopy for measuring impurity emission from divertor region of EAST tokamak

The measurement of impurity distribution in the divertor region of tokamaks is key to studying edge impurity transport. Therefore, a space-resolved vacuum-ultraviolet (VUV) spectrometer is designed to measure impurity emission in the divertor region on EAST. For good spectral resolution, an eagle-type VUV spectrometer with 1 m long focal length with spherical holograph grating is used in the system. For light collection, a collimating mirror is installed between the EAST plasma and the VUV spectrometer to extend the observing range to cover the upper divertor region. Two types of detectors, i.e. a back-illuminated charge-coupled device detector and a photomultiplier-tube detector, are adopted for the spectral measurement and high-frequency intensity measurement for feedback control, respectively. The angle between the entrance and exit optical axis is fixed at 15°. The detector can be moved along the exit axis to maintain a good focusing position when the wavelength is scanned by rotating the grating. The profile of impurity emissions is projected through the space-resolved slit, which is set horizontally. The spectrometer is equipped with two gratings with 2400 grooves/mm and 2160 grooves/mm, respectively. The overall aberration of the system is reduced by accurate detector positioning. As a result, the total spectral broadening can be reduced to about 0.013 nm. The simulated performance of the system is found to satisfy the requirement of measurement of impurity emissions from the divertor area of the EAST tokamak.

Potential approaches for fabricating non-classical ruled diffraction gratings with large apertures

Principles for the design of pendulum-type ruling engines and their potential application for the fabrication of non-classical ruled diffraction gratings with large apertures are considered. For spherical diffraction gratings, the derivation of the analytical dependences for the determination of the geometrical shape of the curvilinear projections of their grooves, their curvature radii, and variable pitch is presented. Expressions for the coefficients of first–third-order aberrations are obtained.

Highly efficient soft x-ray spectrometer for transient absorption spectroscopy with broadband table-top high harmonic sources.

We present a novel soft x-ray spectrometer for ultrafast absorption spectroscopy utilizing table-top femtosecond high-order harmonic sources. Where most commercially available spectrometers rely on spherical variable line space gratings with a typical efficiency on the order of 3% in the first diffractive order, this spectrometer, based on a Hettrick–Underwood design, includes a reflective zone plate as a dispersive element. An improved efficiency of 12% at the N K-edge is achieved, accompanied by a resolving power of 890. The high performance of the soft x-ray spectrometer is further demonstrated by comparing nitrogen K-edge absorption spectra from calcium nitrate in aqueous solution obtained with our high-order harmonic source to previous measurements performed at the electron storage ring facility BESSY II.

Development and preliminary test of a space-resolved vacuum-ultraviolet spectroscopy in EAST.

The impurity radiation from the divertor region of the EAST tokamak is dominantly in the wavelength range of vacuum ultraviolet (VUV) due to the elevated edge electron temperature. A space-resolved VUV spectroscopy is developed to measure impurity radiation in the divertor region. An eagle-type VUV spectrometer with a focal length of 1m is adopted in this system, equipped with a spherical grating and a charged-coupled device (CCD) detector. The performance of the VUV spectrometer is preliminarily tested on a synchrotron radiation facility. The wavelength calibration is conducted near 65nm. It is found that the wavelength range observed by the CCD detector is about 11.07nm around the central wavelength of about 65nm. With a linear dispersion of 0.0053 nm/pixel, it is possible to measure the ion temperature lower than 20eV at the edge region by analyzing the Doppler broadening of a carbon line. These test results show that the performance of the VUV spectrometer is capable of measuring divertor radiation and analyzing the ion temperature of edge impurity ions.

Nonnull interferometric testing of spherical gratings under Littrow conditions with opposite diffraction orders.

Diffracted wavefront measurements are qualitative and comprehensive verifications for the spherical grating that was manufactured to specifications. Direct interferometric testing of the diffracted wavefront is convenient and implemented by tilting the spherical grating at a Littrow angle to obtain autoreflection and then results in a nonnull interferometric testing configuration. The diffracted wavefront of the spherical grating contains not only wavefront errors induced by the manufacturing imperfections but also inherent wavefront contributions from the autoreflection testing setup. The magnitudes of the latter are affected by both the spherical substrate and the groove pattern. Through the analysis of geometric aberrations of spherical gratings, the groove pattern contributions are demonstrated to be contrary for the opposite diffraction orders. A nonnull interferometric testing of spherical gratings is proposed without foreknowledge of the groove pattern, in which the wavefront errors contributed only by the manufacturing imperfections are derived from dual measurements under Littrow conditions with opposite diffraction orders. Simulations are implemented for varied line spacing (VLS) spherical gratings with an F-number slower than 1.5 and groove density varying from 150 to 300 lp/mm, and the residual error less than 0.004λ RMS is obtained. The residual misalignment error after conventionally removing defocus and tilt is further analyzed and discussed. A VLS grating in which the NA is 0.13 and groove density is 200 lp/mm is chosen as an experimental sample, and the diffracted wavefront error with 0.018λ RMS is obtained.

Aberration-reduced spherical concave grating holographically recorded by a spherical wave and a toroidal wave for Rowland circle mounting.

We propose a new recording system that employs a spherical wave and a toroidal wave to holographically record an aberration-reduced Rowland-circle spherical grating. Two more variables in this recording system are available for the design compared with a conventional symmetric dual-plane-wave recording system, which allows both the astigmatism and sagittal coma of the grating to be corrected to minimum. We derive the aberration coefficients of such grating and give the universal design principles for the recording system. An aberration-reduced grating used in a spectrometer equipped with linear array CCDs is then specifically designed and fabricated. The performances of the aberration-reduced grating and that of the conventional grating recorded by dual plane waves are compared in terms of the ray-tracing spot diagrams, and the photographed spectral images. The experimental results show that the spectral intensity of the aberration-reduced grating is about 4.5 times that of the conventional grating, while the resolution of the aberration-reduced grating is close to that of the conventional grating.

Normal-Incidence Imaging Spectrograph Based on an Aperiodic Spherical Grating for the Vacuum Spectral Region

The possibility of astigmatism compensation in a wide wavelength range in normal incidence schemes based on a spherical diffraction grating with variable groove density has been considered. Two schemes imaging spectrographs with dimensions of about 1 and 5 m for the wavelength ranges 820–1690 and 980–1520 A that operate in the first external and first internal diffraction orders, respectively, have been calculated. It has been shown that the advantage of the external order of diffraction is a wide (more than an octave) spectral range at relatively compact sizes of the device. Schemes operating in internal orders of diffraction have better imaging characteristics, but large dimensions of the device are required to maintain the width of the wavelength range at the octave level. A comparison of the above schemes with schemes based on gratings with curvilinear grooves has been carried out. It has been shown that the variable line-spaced gratings yield a gain in the limiting spatial resolution, while the gratings with curvilinear grooves allow the achievement of a better limiting spectral resolution. The schemes of the considered type can be applied in the soft X-ray range when using diffraction gratings with a multilayer coating.

Astigmatism-reduced spherical concave grating holographically recorded by a cylindrical wave and a plane wave for Rowland circle mounting.

We propose a new recording system that employs a cylindrical wave and a plane wave to holographically record astigmatism-reduced Rowland-circle spherical gratings. We find that the astigmatism of the grating can be sharply reduced, so that the spectral intensity is improved. Meanwhile, its defocus aberration and meridional coma remain zero throughout the working spectrum, meaning the spectral resolution is similar to that of a conventional grating recorded by symmetric dual plane waves. We designed and made one astigmatism-reduced grating and one conventional grating for an actual Rowland-circle spherical-grating spectrometer. Our experimental results showed that the spectral intensity of the astigmatism-reduced grating is about five times that of the conventional grating, while the resolution of the astigmatism-reduced grating is close to that of the conventional grating.

The variable polarization undulator beamline UE52 SGM at BESSY II

UE52 SGM is an open port beamline with a monochromator containing 3 spherical gratings covering the energy range of 100 to 1500 eV and allows for variable polarization (circular and in any orientation linear) with a focus of about 20 - 60 μm (horizontal) x beamline slit (vertical) spot in focus.

System for time-discretized vacuum ultraviolet spectroscopy of spark breakdown in air.

A system for time-discretized spectroscopic measurements of the vacuum ultraviolet (VUV) emission from spark discharges in the 60-160 nm range has been developed for the study of early plasma-forming phenomena. The system induces a spark discharge in an environment close to atmospheric conditions created using a high speed puff value, but is otherwise kept at high vacuum to allow for the propagation of VUV light. Using a vertical slit placed 1.5 mm from the discharge the emission from a small cross section of the discharge is allowed to pass into the selection chamber consisting of a spherical grating, with 1200 grooves/mm, and an exit slit set to 100 μm. Following the exit slit is a photomultiplier tube with a sodium salicylate scintillator that is used for the time discretized measurement of the VUV signal with a temporal resolution limit of 10 ns. Results from discharges studied in dry air, Nitrogen, SF6, and Argon indicate the emission of light with wavelengths shorter than 120 nm where the photon energy begins to approach the regime of direct photoionization.

2D XAFS-XEOL Spectroscopy – Some recent developments

The use of optical photons to measure the modulation of the absorption coefficient upon X-ray excitation, or optical XAFS, is of particular interest for application to the study of light emitting semiconducting nanomaterials due to the additional information that may be gained. The potential for site-selectivity, elemental and excitation energy specific luminescence decay channels, and surface vs. bulk effects all make the use of X-ray excited optical luminescence (XEOL) desirable as a detection method. Previous experiments have made use of a monochromator to select the optical emission wavelength used to monitor optical XAFS. This method of detection suffers from the primary limitation of only being able to monitor the optical response at one emission wavelength. By combining the high resolution soft X-ray Spherical Grating Monochromator beam-line at the Canadian Light Source with an Ocean Optics QE 65000 fast CCD spectrophotometer and custom integration software we have developed a technique for collecting 2D XAFS-XEOL spectra, in which the excitation energy is scanned and a XEOL spectra is collected for every energy value. Herein we report the development of this technique and its capabilities using the study of the luminescence emitted from single crystal zinc oxide as an example.

In situ calibration of an extreme ultraviolet spectrometer for attosecond transient absorption experiments

We report a method for calibrating an extreme ultraviolet spectrometer based on a flat-field grazing incidence spherical grating in the energy range of 20-30 eV. By measuring absorption lines corresponding to singly excited states in helium atoms and autoionizing states in argon atoms, the photon energy of the detected light was determined. The spectral resolution of the spectrometer, 60 meV, was obtained by deconvolving the Fano resonance profile of argon autoionizing states from the measured absorption line profiles.

Exploration for the Gratings Used for Auto-Stereoscopic Three-Dimensional Printing

In this paper, parallax-barrier gratings, lenticular lens gratings and spherical crown gratings which are the three kinds of main gratings for auto-stereoscopic three-dimensional printing are introduced. Besides, the principle for these three kinds of gratings is explored. According to the analysis, when different gratings are used for auto-stereoscopic three-dimensional printing，different effects will be obtained. The principle of parallax-barrier gratings is transmission pinhole imaging formation, and the presswork looks comfortable but transmission of light is worse as used parallax-barrier grating. The correspondence principle of lenticular lens gratings is convex lens imaging due to refraction and reflection. Therefore, the stereoscopic images can be only seen in the orientation perpendicular to the array of lenticular lens. While, as the principle of scatter of spherical crowns, the stereoscopic images can be seen in each azimuth when used spherical crown gratings for auto-stereoscopic three-dimensional printing. In the end, a series of further measures are raised to improve the common grating used for auto-stereoscopic three-dimensional printing.

Approaching ultimate resolution for soft x-ray spectrometers

We explore the potential performance of soft x-ray spectrometers based on the use of varied-line-spacing spherical diffraction gratings (VLS-SG). The quantitative assessment is based on an optimization procedure to obtain both negligible optical aberrations at full illumination of the grating and a quasi linear focal curve. It involves high-order optical aberration cancellation to calculate the focal curves. We also examine the validity of small divergence closed-form formulas describing the light path function. Optimizing the optical and geometric parameters gives an ultimate resolving power, at 930 eV, of between 10,800 for a 3 m long instrument and 34,000 for an 11 m spectrometer according to the Rayleigh criterion. Typical fabrication tolerances would scale these values down by about 10%. The findings are validated by ray-tracing simulations.

Laminar and blazed type holographic gratings for a versatile soft x-ray spectrograph attached to an electron microscope and their evaluation in the 50–200 eV range

Laminar and blazed type holographic varied-line-spacing spherical gratings for use in a versatile soft x-ray flat-field spectrograph attached to an electron microscope are designed, fabricated, and evaluated. The absolute diffraction efficiencies of laminar (or blazed) master and replica gratings at 86.00° incidence evaluated by synchrotron radiation show over 5% (or 8%) in the 50-200 eV range with the maxima of 22% (or 26%-27%). Also the resolving power evaluated by a laser produced plasma source is in excess of 700 at the energy near the K emission spectrum of lithium (~55 eV) for all gratings. Moreover, the K emission spectrum of metallic Li with high spectral resolution is successfully observed with the spectrograph attached to a transmission electron microscope.