Rigorous calculations and synchrotron radiation measurements of diffraction efficiencies for tender X-ray lamellar gratings: conical versus classical diffraction

Abstract

When reflection gratings are operated at grazing incidence in the extreme offplane configuration and the incident beam trajectory is parallel to the grooves, the diffraction into the first order can be more efficient than in the classical orientation. This situation is referred to as the conical diffraction case. In the classical configuration the grooves are perpendicular to the incident beam and thus an efficiency-reducing shadowing effect will be observed at very grazing angles. It was recently shown that a laminar grating could provide symmetric and relatively high efficiencies in conical diffraction for diffraction even of photons with large energies of the order of 4 and 6 keV. For photon energies in the tender X-ray range, accurate computing tools for the calculation of diffraction efficiencies from gratings with simple coatings have not been available. Promising results for this spectral range now require the development of tools for modelling the diffraction efficiency expected in optical instrumentation, in which the provision of high efficiency in the indicated spectral range is mandatory. This is the case when weak sources are to be investigated, like in space science. In this study it will be shown that scalar calculations are not appropriate for this purpose, while newly introduced rigorous calculations based on the boundary integral equation method, implemented in the PCGrate 1 code, can provide predictions that are in agreement with observed diffraction efficiencies. The agreement is achieved by modelling the exact surface profile. This applies for both the conical diffraction configuration and for the classical inplane configuration, in which a significantly lower efficiency was obtained. Even though the profile of the presented grating was not perfect, but significantly distorted, the calculations show that efficiency-wise the structure provided already more than 75% of the ideally expected efficiency for conical diffraction. This is a very promising result for further optimization of diffraction gratings for use in the tender X-ray range. research papers J. Synchrotron Rad. (2018). 25, 1683-1693 Goray, Jark and Eichert Diffraction efficiencies for tender X-ray lamellar gratings 1685 research papers 1690 Goray, Jark and Eichert Diffraction efficiencies for tender X-ray lamellar gratingsFigure 8Comparison of the measured grating efficiencies for a photon energy of 4 keV ( = 0.307 nm) for different orders (zeroth to third) in the conical diffraction scheme as measured by Jark & Eichert (2015) with the calculations using the rigorous approach accounting for the real grating profile (solid line). The prediction by the scalar theory is shown by the dashed line.

Оптимизация технологии изготовления дифракционных Si-решеток треугольного профиля для мягкого рентгеновского и экстремального ультрафиолетового излучения

“…Наши дальнейшие усилия будут направлены на оптимизацию условий сглаживающего−полирующего травления для получения наилучших параметров рабочей грани, от которых зависит дифракционная эффективность, а также исследованию зависимости дифракционных свойств Si-решетки от параметров рабочей грани. Кроме того, должна быть выполнена оптимизация расчетной эффективности для дифракционных решеток с измеренным профилем штрихов, работающих в различных диапазонах спектра, порядках и схемах дифракции (классической и конической) [14][15][16]. Измерения эффективности должны подтвердить правильность и надежность выбранных оптимизационных процедур.…”

A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence

“…The GIXRF intensities were obtained for the N-Kα fluorescence emission under various incidence angles α and azimuthal sample orientation angles φ (see Fig. 1b); φ = 0 • corresponds to the conical orientation 27 of the sample grating. The recorded spectra from the silicon drift detector were deconvoluted using detector response functions in order to isolate the fluorescence signal from N-Kα from other spectral contributions.…”

Blazed Diffraction Gratings on Si --- First Results

“…For mid-frequency and high-frequency diffraction gratings the classical (in-plane) diffraction gives the acceptable values of the working order efficiency only in the soft-X-ray (SXR) and extreme ultraviolet (EUV) ranges [1]. However, the mount of grazing-incidence conical (off-plane) diffraction has large advantages in efficiency when such gratings are used in short-wave regions of the X-ray range (hard X-ray and " tender X-ray"), including high orders, and for achieving the high dispersion and resolution.…”