Resonant inelastic x-ray scattering (RIXS) is a widely used spectroscopic technique for analyzing elementary excitations. However, this process is inefficient and thus difficult to apply to imaging. We propose to stimulate the RIXS (SRIXS) process using a soft x-ray free-electron laser (SXFEL), increasing the photon yield by up to 6 orders of magnitude [Higley, Commun. Phys. 5 83 (2022)]. By designing a new achromatic full-field twin Wolter mirror microscope and multi-aperture grating, it should become possible to measure SRIXS by imaging the full x-ray spectrum at many spatial points simultaneously.
To test the feasibility of SRIXS imaging, we simulate the SRIXS signal strength with a three-level Maxwell-Bloch model. Using the parameters of the SACLA BL1 SXFEL, we show that SRIXS imaging is feasible, requiring a peak intensity of 1016 W/cm2 and sub-micron focus size, readily achievable with the proposed microscope.
A Kirkpatrick-Baez (KB) mirror is a reflective focusing device that sequentially positions a pair of crossed mirrors in a grazing-incidence setup. Typically, this type of device offers a relatively long working distance of 20 mm or longer, which allows specimens to be installed in various configurations. However, there is a tradeoff between the long working distance and both the numerical aperture and demagnification factor, resulting in drawbacks for KB mirrors for a sub-micron focus size in a soft-X-ray region. This research explores an ultrashort KB mirror composed of 2- and 8-mm-long mirrors with focal lengths of 2 and 8 mm, respectively. Its demagnification is designed to be up to 10000 and its focus size can theoretically be below 50 nm at a photon energy of 1 keV. To demonstrate an X-ray nanoprobe based on this focusing device for X-ray microscopy, the low energy X-ray fluorescence (LEXRF) technique is incorporated into the focusing system. The aim of this LEXRF system is to observe light elements in biological specimens. After X-ray fluorescence yields were estimated, the experimental setup was examined for a forward- and side-scattering configuration. Preliminary studies examined the fluorescence detector performance and the fluorescence detection of biological and pharmaceutical specimens in the traditional backscattering configuration. Compared with diffractive focusing devices, which condense approximately 10% of the incident X-rays, the reflective ultrashort KB mirror can benefit LEXRF by more efficiently collecting X-rays to its nanoprobe, thus enhancing the fluorescence signals from specimens.
Axisymmetric mirrors, such as ellipsoidal mirrors, are used as nanoscale focusing elements for soft X-rays. High figure accuracy is required to prevent distortion of the wavefronts of reflected X-ray beams. Although a mirror fabrication technique based on electroforming has been developed, figure correction of the inner surface of the mirror with most of the conventional machining methods is difficult. In this study, we constructed a processing system specialized for the inner surface of axisymmetric mirrors. This system is based on a fluid jet processing method. A fluid containing abrasives flows out from a very small nozzle placed inside the mirror and impinges against its inner surface. The surface layer of the mirror is locally removed with a spatial resolution of about 2 mm using this system. Abrasives used in our system contain organic resin and silica; therefore, they have a sufficient machining rate and a good dispersibility in water. We also applied X-ray ptychography to measure the 3-dimensional figure error of the mirror surface. We performed numerically controlled processing and measured the surface figure of the mirror with both a contact-type roundness measurement machine and a soft X-ray ptychographic system. The result of X-ray ptychography agreed well with the profile obtained by contact measurement.
Focusing x-rays is a key technology for x-ray microscopic techniques. In a soft-x-ray region, focusing systems with achromaticity and a high numerical aperture have long been desired as a substitute for Fresnel zone plates. Ellipsoidal mirrors are promising focusing optics for such systems. However, two technical problems have to be overcome to allow practical application of these mirrors: their low efficiency due to their hollow shapes and strict requirements for their alignment. A novel focusing system using two reflective mirrors was proposed for this purpose. The downstream mirror is a quasi-Wolter mirror with a hollow shape similar to an ellipsoidal mirror and has a high numerical aperture of more than 0.1. The tolerance of the setting angle error of the quasi-Wolter mirror is significantly large compared to that of the ellipsoidal mirror because a quasi-Wolter mirror reflects the incident rays twice. The upstream mirror is a ring-focusing mirror, which produces an x-ray beam with a ring-shaped intensity profile, ensuring the entire beam reflects onto the quasi-Wolter mirror and reaches the focus of the system. The proposed system is ideal for soft-x-ray focusing. The design procedure and formulas are described in the present study. A prototype of the system is designed for BL25SU-A of SPring- 8. The ideal focusing spot size is estimated by numerical simulation to be 10 nm at 300 eV. The influence of alignment errors of the two mirrors is also simulated and summarized.
X-ray focusing optics are essential for acquiring high-quality X-ray microscopy images. Fresnel zone plates (FZPs) are conventionally used to focus soft X-rays via diffraction. The use of Kirkpatrick-Baez (KB) mirrors for nanofocusing in the soft X-ray region is limited because a KB mirror is a reflective X-ray focusing optic that has a pair of perpendicular mirrors in a grazing-incidence configuration, which lowers the numerical aperture due to the long focal length. KB mirrors with a short focal length have been proposed for hard X-ray focusing. This paper presents the design of an ultrashort KB mirror for soft X-ray focusing that has an extremely short focal length, which is achieved by reducing its mirror length. Moreover, a large grazing angle is employed to utilize total-reflection-based focusing. An ultrashort KB mirror is proposed for pilot studies at beamline BL25SU-A, SPring-8, Japan. A ray-tracing simulator is used to determine the misalignment tolerance in terms of roll and yaw for each mirror in the KB geometry. Based on the results, a mirror manipulator and other equipment are designed to precisely position the mirrors. Although this strategy, commonly used for FZPs, leads to a short working distance and a small beam acceptance, we believe that it can be applied to ultrashort KB mirrors for X-ray microscopy applications with achromaticity and strong demagnification.
Ellipsoidal mirrors are ideal focusing optics for soft x-rays because of advantages that include high numerical aperture, high efficiency, and no chromatic aberrations. Shape accuracy of nanometer order is required on the internal surface of a mirror with a diameter of around 10 mm. Because of the difficulty of processing the internal surface, ellipsoidal mirrors are fabricated by replication of the shapes of master mandrels. In previous studies, a fabrication process was developed for x-ray ellipsoidal mirrors involving mandrel fabrication and nickel electroforming. 40-mm-long ellipsoidal mirrors were fabricated and a focused beam with full width at half maximum (FWHM) of 240 nm was obtained. For better focusing performance and expansion of the applicable energy range, we designed and fabricated a 120-mm-long ellipsoidal mirror from the master mandrel with a shape accuracy of 3.8 nm (root mean square). A focusing experiment was also performed at the synchrotron radiation facility, SPring-8 (BL25SU). A focused beam with FWHM of 1 μm was obtained.
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