Simulation of concave-convex imaging mirror system for development of a compact and achromatic full-field x-ray microscope

A multi-objective improved horse herd optimizer based on convex lens imaging for stochastic optimization of wind energy resources in distribution networks considering reliability and uncertainty

In this study, stochastic multi-objective allocation of wind turbines (WTs) in radial distribution networks is performed using a new multi-objective improved horse herd optimizer (MOIHHO) and an unscented transformation (UT) method for modeling the uncertainties of WTs power and network load. The objective function aims to minimize power loss, improve reliability, and reduce the costs associated with wind turbines (WTs), presenting these goals as a three-dimensional function. The Multi-Objective Improved Horse Herd Optimizer (MOIHHO) is derived from an enhanced version of the traditional horse herd optimizer. This enhancement utilizes mirror imaging based on convex lens principles to address issues of premature convergence. Additionally, the decision-making process is designed to identify the final fuzzy solution among the non-dominant solutions within the Pareto front set. The simulation results are presented with and without considering uncertainty in two scenarios of deterministic and stochastic WT allocation on 33- and 69-bus distribution networks and different objectives are compared. Also, the effect of incorporating uncertainties are evaluated on power loss and reliability using the MOIHHO. Moreover, the superiority of the MOIHHO is investigated in achieving better objective function value compared with conventional MOHHO, multi-objective particle swarm optimization (MOSPO), multi-objective gray wolf optimizer (MOGWO), and multi-objective gazelle optimization algorithm (MOGOA). The obtained results demonstrated that considering the UT-based stochastic scenario, the power losses cost is increased, and the reliability is weakened for 33- and 69-bus networks in comparison with the deterministic scenario.

Soft-X-ray nanobeams formed by aberration-reduced elliptical mirrors with large numerical aperture

X-ray focusing mirrors often employ the Kirkpatrick-Baez (KB) geometry, which sequentially crosses two elliptic-cylindrical mirrors in grazing-incidence configurations. However, KB mirrors do not satisfy the Abbe sine condition and thus potentially expand the focus size with severe coma aberration. Satisfying the Abbe sine condition complicates mirror shapes or increases the number of ultraprecision mirrors required. The present study shows that the focal length and mirror length of KB mirrors have to be shortened to simultaneously achieve a large numerical aperture and reduced aberration. Such ultracompact KB (ucKB) mirrors are examined using a simulation that combines ray tracing and wave propagation. The focus intensity distributions show that ucKB mirrors suppress the aberration produced by their rotation errors and that they robustly achieve diffraction-limited focusing. The simulation results are confirmed in a synchrotron radiation experiment. ucKB mirrors can be advantageous for soft-X-ray nanoprobes, which require focusing devices to achieve a large numerical aperture.

Wide field-of-view x-ray imaging optical system using grazing-incidence mirrors

A field-curvature-corrected imaging optical system for x-ray microscopy using only grazing-incidence mirrors is proposed. It combines a Wolter type I (WO1) mirror pair, which forms a real image, with field curvature correction (FCC) optics-a convex hyperbolic mirror pair-that form a virtual image; compensation of the field curvatures realizes a wide field-of-view (FOV) and high magnification. Ray-tracing and wave-optics simulations verified the efficacy of the design, for which a FOV width was 111 µm-4.7 times larger than that for the uncorrected WO1 design. The addition of FCC optics also produced a 2.3-fold increase in magnification.

X-Ray Single-Grating Interferometry for Wavefront Measurement and Correction of Hard X-Ray Nanofocusing Mirrors

X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than λ/72 in root-mean-square value.

Full-field X-ray fluorescence microscope based on total-reflection advanced Kirkpatrick-Baez mirror optics

A novel full-field X-ray fluorescence microscope based on total-reflection advanced Kirkpatrick-Baez mirror optics was developed. The total-reflection imaging mirror optics arrangement, with four reflections, has the advantage of being able to function both as a powerful low-pass energy filter, completely rejecting incident excitation X-rays, and as an achromatic optical imaging system. Isolated X-ray fluorescence signals can be imaged, avoiding imaging-detector saturation, with low background noise. A prototype fluorescence microscope constructed at SPring-8 demonstrated the capability to simultaneously image elemental distributions using various X-ray fluorescence signals (Ni, Cu, Zn, Ge, and Bi). A half-period spatial resolution of ~0.5-1 µm (1000-500 LP/mm) was achieved, owing to the achromaticity of the imaging mirrors and the photon-counting scheme of the CCD camera used for fluorescence detection.

Compact reflective imaging optics in hard X-ray region based on concave and convex mirrors

We demonstrated that the combination of a hyperbolic convex and elliptical concave mirrors works as a compact reflective X-ray imaging system with a short optical focal length and large magnification factor. We performed an experiment to form a one-dimensional demagnified image with a demagnification factor of 321 within an approximately 2-m-long optical setup at an X-ray energy of 10 keV. The results showed that this imaging optics system is capable of providing a resolution of ~40 nm. From wavefront analysis, it was confirmed that the optics possessed a wide field-of-view with a significant reduction of comatic aberration.

Development of an x-ray eight-image Kirkpatrick-Baez diagnostic system for China's laser fusion facility

This article presents the development of an x-ray eight-image Kirkpatrick-Baez diagnostic system to be used at China's Shenguang-III (SG-III) laser facility in aspects of the optical design, multilayers, and online/offline tests. Six pieces of concave spherical substrates are used for constituting a special optical structure. Dual-periodic tungsten/carbon (W/C) multilayers are used for high reflectivity and large angular bandwidth of ∼0.1°. The global spatial resolution is ∼5  μm in the ±100  μm range. The schemes of system installation, transport, collimation, and image acquisition at China's SG-III facility are also discussed.