KEYWORDS: X-ray optics, X-rays, Rockets, Calibration, Solar processes, Mirrors, Solar radiation models, Point spread functions, Hard x-rays, X-ray imaging
We have been developing X-ray optics for a fourth FOXSI (Focusing Optics X-ray Solar Imager) sounding rocket experiment, FOXSI-4. We fabricated two types of X-ray optics, soft X-ray optics (SXR) and hard X-ray optics (HXR), specified for soft and hard X-ray observations. We conducted X-ray irradiation tests to evaluate X-ray performances such as angular resolution and effective area. For the Flight Model (FM) SXR, the resultant angular resolution in Half Power Diameter (HPD) is 16 ± 2 / 14 ± 2 arcseconds at 2.7 / 4.5 keV for the best images, respectively and no significant energy dependence in HPD is seen. The observed effective area was reproduced within an accuracy of 10% by using our original ray-tracing simulator considering all of the SXR components in the 1.5-16 keV range at the smallest off-axis angle. Subsequently, both FM mirror module assemblies were integrated into a sounding rocket in combination with detectors and the vibration tests were performed for the whole sounding rocket system. Finally, FOXSI-4 was successfully launched on April 17, 2024 (UTC), and the sounding rocket and the data were also recovered successfully.
We have been developing our original space X-ray optics by combining space- and ground-based technologies for a solar sounding rocket experiment, FOXSI-4. We completed two Flight Models (FM), soft and hard X-ray optics. Vibration tolerance is one of the most important launch environmental tolerance and thus we established our experimental setup for the two FMs. The imaging quality was evaluated before and after the vibration tests. As a result, no significant changes were detected. In addition, we checked the effect of shims needed for the angle alignment between the optics and detectors integrated into the sounding rocket. We confirmed that the shims do not affect the angle alignment significantly before and after vibration tests.
We have been developing high-resolution space X-ray optics by using high-precision electroforming technology which has been refined through the development of ground-based X-ray focusing systems. Our optics have been on board the Japan-U.S. joint NASA sounding rocket experiment, the 4th Focusing Optics X-ray Solar Imager (FOXSI-4), which succeeded in the world's first X-ray imaging and spectroscopic observation of solar flares. So far, we have conducted ground calibration tests on these onboard items. We have been building our own ray-tracing simulator in order to model the data and finally construct a response function which is essential for obtaining physical parameters in imaging and spectroscopic analysis accurately. In this paper, we modeled the uncertainty of the reflection angle due to the surface shape error in the axial direction and implemented it in this simulator for the first time. As a result, we succeeded in reproducing the point spread function up to ~50 arcsec assuming a Cauchy distribution and confirmed the consistency between simulations and the data in terms of FWHM and HPD for the on-axis direction. Additionally, we optimized parameters of a Cauchy distribution also for the off-axis data and investigated the dependence of the parameters on the off-axis angles.
High-precision monolithic mirrors are used in the soft x-ray beamlines of synchrotron radiation facilities. A figure measurement technique is essential for the fabrication of high-precision mirrors. In recent years, mirrors of various shapes have been proposed, and a versatile figure measurement technique is required. Tactile measurements are one of the most suitable methods for evaluating the figure errors of x-ray mirrors with steep and complex geometries. Because a tactile measurement probe has a wide range of measurable depths and angles and can eliminate measurement errors depending on the sample curvature, tactile measurements have been applied to the fabrication of monolithic mirrors for soft x-ray focusing. In this study, a soft x-ray focusing mirror with concave and convex freeform surfaces on its monolithic substrate was fabricated based on tactile measurements for figure correction. The high- and mid-spatial-frequency roughness were 0.14-0.17 nm and 0.8 nm in RMS, respectively. Furthermore, the figure error evaluated using the tactile measurement was 2.64 nm in RMS.
Wolter mirrors work as imaging optics of X-ray telescopes. We have been developing a Wolter mirror for the FOXSI-4 project in 2023 using a high-precision Ni electroforming process. The figure accuracy of mirrors is one of the main factors determining the spatial resolution in X-ray imaging. In this study, we optimized the electrodeposition conditions from the viewpoint of the uniformity of film thickness. The simulation model was developed to correctly predict the film thickness distribution before fabrication, whose parameters and boundary conditions were determined through electrochemical experiments. The model calculates the distribution of current density on the surface of the cathode by finite element analysis. In this paper, we report the current status of the electroforming process specializing in Wolter mirrors in X-ray telescopes.
In the soft x-ray region, the demand for focusing x-rays into a spot of nanometer order size with high efficiency has been increasing. Ellipsoidal and Wolter mirrors, which are representative of ideal reflective focusing optics for soft x-rays, have optical advantages such as achromaticity, large acceptance, high efficiency and high numerical aperture, which are suitable to fully utilize the next-generation synchrotron light sources. Recently, the fabrication process of soft x-ray mirrors of replication type using nickel electroforming was developed, and several focusing experiments with ellipsoidal and Wolter mirrors were reported. The experimental environment of these mirrors, however, was limited due to the magnetism of the nickel body. We are currently developing the diamagnetic mirror fabrication process using copper electroforming technique to expand its application. In order to prevent oxidization of the replicated surface, this study demonstrates electroforming of copper mirror that has the reflective surface of gold. The surface roughness replicated from a flat substrate was 0.321 nm in root-mean-square in 0.1 mm × 0.1 mm area. The circularity of the gold inner surface of a copper electroformed mirror was evaluated at 26 nm in peak-to-valley.
For many years, Wolter mirrors have been used as imaging elements in X-ray telescopes. The shape error of Wolter mirrors fabricated by replicating the shape of a mandrel originates from the replication error in electroforming. We have been developing an X-ray focusing mirror for synchrotron radiation X-rays, as well as a high-precision electroforming process. In this paper, we report on the application of the advanced electroforming process to the fabrication of Wolter mirrors for the FOXSI Sun observation project. We also discuss the figuring accuracy of the mandrel.
We had been developing replicated aluminum foil optics for previous missions such as ASCA, Suzaku, and, Hitomi. This sort of X-ray optics can be lighter but the angular resolution is limited to on the order of arcminutes. Thus, to improve the angular resolution with light performances, we have started developing electro formed X-ray optics. Electroforming is a technology that can transfer to a substrate with high accuracy by plating the nano-level structure of a super-precision master and makes it easier to fabricate Wolter type-I shaped two-stage full-shell mirrors.
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.
Since a replication-type of the Wolter mirror is obtained as the negative shape of its mandrel via shape replication represented by electroforming, a high precision mandrel fabrication process is essential for nano-focusing with the mirror at synchrotron radiation facilities. In particular, three-dimensional shape measurement technique for the mandrel is required. In this study, we developed the high precision three-dimensional shape measurement system dedicated for the Wolter mandrels. First, the shape error distributions of the ellipsoidal surface and the hyperboloid surface were measured independently. The geometrical relation between the surfaces was constrained by the longitudinal profiles which include the intersection measured by a profilometer. The diameter was also measured and finally the three-dimensional shape distribution was obtained. Applying this system, we fabricated a high precision Wolter mandrel.
For vortex beams, characterization and optimization of the optical system are important. However, wavefront measurements on focused vortex beams are difficult because they have complex phase and intensity distributions. As a measurement method, we proposed the use of ptychography, in which the intensity and phase of the beams are retrieved using several far-field diffraction patterns. We constructed an optical system with a He-Ne laser light source to clarify the usefulness of ptychography. Test vortex beams were produced by a spatial light modulator (SLM) and focused by a plano-convex lens. A pinhole was scanned on the focal plane for collection of the diffraction intensity profiles. The phase and intensity of the vortex beams on the focal plane were retrieved so that the calculated beams were consistent with the intensity data. The retrieved intensity and phase distributions were compared with distributions predicted using the inputs for the SLM. They agreed well, indicating that the ptychographic phase retrieval method can be used for precise characterization of vortex beams. This method is valuable for improving the performance of applications using vortex beams.
Focusing and imaging optics can be characterized by evaluating the wavefront error of the focused beam. We have bean developing a ptychographic phase retrieval method using a visible laser to measure the wavefront error. In this study, the measurement accuracy of the method is increased by improving both the phase retrieval algorithm and the experimental setup. The system is applied to the characterization of an ellipsoidal mirror used for the focusing of soft X-rays. The posture of the mirror can be measured with a resolution of 1.4 μrad. The wavefront error originating from the surface profile error can be detected with an accuracy of 0.01λ (root mean square).
Mirrors are key devices for creating various systems in optics. Focusing X-ray and extreme ultraviolet (EUV) light requires mirror surfaces with an extremely high accuracy. The figure of an ellipsoidal mirror is obtained by rotating an elliptical profile, and using such a mirror, soft X-ray and EUV light can be focused to dimensions on the order of nanometers without chromatic aberration. Although the theoretical performance of ellipsoidal mirrors is extremely high, the fabrication of an ideal ellipsoidal mirror remains problematic. Based on this background, we have been working to develop a fabrication system for ellipsoidal mirrors. In this proceeding, we briefly introduce the fabrication process and the soft X-ray focusing performance of the ellipsoidal mirror fabricated using the proposed process.
It is possible to achieve soft X-ray nanofocusing with a high efficiency and no chromatic aberration by using an ultraprecise ellipsoidal mirror. Surface figure metrology is key in the improvement of surface figure accuracy. In this study, we propose a ptychographic phase retrieval method using a visible light laser to measure the surface figure error profile of an ellipsoidal mirror. We introduce a simple experimental system for ptychographic phase retrieval and demonstrate the basic performance of the proposed system. Obtainable wavefront information provides both the figure error and the alignment of the ellipsoidal mirror that yield the best focusing. This developed method is required for offline adjustments when an ellipsoidal mirror is installed in the beamline of synchrotron radiation or X-ray free-electron laser light sources.
The ellipsoidal mirror is one of the most effective achromatic focusing optic with large aperture and nanofocusing ability.
Because of the large aperture of mm-order size, this optic is suitable for a laboratory-based light source that has a large
divergence angle. Recently, soft X-rays produced by high-order harmonics have become available. Such a beam has high
spatial coherency but relatively large divergence angle. This light in combination with an ellipsoidal mirror will generate
a highly intense focusing nanobeam that will contribute to various experiments and analyses such as those of
photoelectron spectroscopy and nonlinear optical phenomena. In this paper, we present the optical design for a lab-based
soft X-ray beamline and the results of optical simulation considering the parameters of the source. Finally, we introduce
a two-stage focusing system with an axisymmetric mirror as a promising soft X-ray focusing system.
An ellipsoidal mirror is a promising type of X-ray mirror, because it can focus X-rays to nanometer size with a very
large aperture and no chromatic aberration. However, ideal ellipsoidal mirrors have not yet been realized by any
manufacturing method. This is partly because there is no evaluation method for its surface figure profile. In this paper,
we propose and develop a method for measuring surface figure profile of ellipsoidal mirrors using phase retrieval. An
optical design for soft X-ray focusing, the employed phase retrieval method and an experimental optical system
specialized for wavefront measurement using a He-Ne laser are reported.
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