Hiroto Motoyama

Error analysis of ellipsoidal mirrors for soft X-ray focusing by wave-optical simulation

The ellipsoidal mirror is an ideal soft X-ray focusing optic that enables achromatic and highly efficient focusing to a nanometer spot size; however, a high-quality surface is necessary for ideal focusing. Knowledge of the required figure accuracy is important for fabrication. In this paper, we analyze the effects of figure errors on the focusing performance through wave-optical calculations based on the Fresnel?Kirchhoff diffraction theory, assuming coherent soft X-rays. Figure errors are classified into three types from the viewpoint of manufacturing. The effect of the alignment error is also investigated. The analytical results quantitatively indicate criteria regarding figure accuracy, which are expected to be essential for the development of high-performance ellipsoidal soft X-ray focusing mirrors.

Development of a numerically controlled elastic emission machining system for fabricating mandrels of ellipsoidal focusing mirrors used in soft x-ray microscopy

Ellipsoidal mirrors are one of the most promising types of X-ray mirror, because the mirror can focus X-rays to nanometer size with a large aperture and no chromatic aberration. However, so far ideal ellipsoidal mirrors cannot be realized by any manufacturing methods. One of the reasons is there is no fabrication method to process their inside surface with a diameter of several millimeters with nanometer-level accuracy. We propose and develop a manufacturing process of the ellipsoidal mirror. First, a master which has the reversed shape is prepared using grinding, polishing and Elastic Emission Machining (EEM). EEM can finish the surface shape to within 2nm (RMS). Then, the ellipsoidal mirror is produced by replicating the surface using an electroforming deposition method. By conducting the process without any stress at room temperature, replicating the surface roughness and shape with nanometer order accuracy is possible. In this paper, we report the current status of manufacturing of the ellipsoidal mirror.

Development of high-order harmonic focusing system based on ellipsoidal mirror

We have developed a focusing system for extreme ultraviolet light produced by high-order harmonic generation. An ellipsoidal mirror with a precise surface shape was fabricated and installed into the focusing system. A rigid mirror manipulator and a beam profiler were employed to perform precise and stable mirror alignment. As a demonstration of the focusing performance, high-order harmonics in the wavelength range of 13.5-19.5 nm were successfully focused into a 2.4 × 2.3 μm(2) spot.

Three-dimensional shape measurement for x-ray ellipsoidal mirror

An X-ray ellipsoidal mirror requires nanometer-level shape accuracy for its internal surface. Owing to the difficulty in processing the surface, electroforming using a high precision master mandrel has been applied to mirror fabrication. In order to investigate the replication accuracy of electroforming, a measurement method for the entire internal surface of the mirror must be developed. The purpose of this study is to evaluate the shape replication accuracy of electroforming. In this study, a three-dimensional shape measurement apparatus for an X-ray ellipsoidal mirror is developed. The apparatus is composed of laser probes, a contact probe, reference flats, a z-axis stage, and a rotation table. First, longitudinal profiles of a mandrel or mirror placed vertically on the rotation table are measured at several angular positions. Subsequently, without realignment of the measured sample, circularity at every height is measured at regular intervals of 0.1 mm. During each measurement, the effect of motion errors is calculated and subtracted from each profile by referring to the distances between the probes and reference flats. Combining the circularity data with the longitudinal profiles, a three-dimensional error distribution of the entire surface is obtained. Using a mandrel with nanometer-level shape accuracy and a replicated mirror, the performance of the measurement apparatus and the replication accuracy are evaluated. Measurement repeatability of single-nanometer order and replication accuracy of sub-100-nm order are confirmed.

Development of ellipsoidal focusing mirror for soft x-ray and extreme ultraviolet light

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.

Two-stage reflective optical system for achromatic 10 nm x-ray focusing

Recently, coherent x-ray sources have promoted developments of optical systems for focusing, imaging, and interferometers. In this paper, we propose a two-stage focusing optical system with the goal of achromatically focusing pulses from an x-ray free-electron laser (XFEL), with a focal width of 10 nm. In this optical system, the x-ray beam is expanded by a grazing-incidence aspheric mirror, and it is focused by a mirror that is shaped as a solid of revolution. We describe the design procedure and discuss the theoretical focusing performance. In theory, soft-XFEL lights can be focused to a 10 nm area without chromatic aberration and with high reflectivity; this creates an unprecedented power density of 1020 W cm−2 in the soft-x-ray range.

Optical design of soft x-ray focusing system with ellipsoidal mirror for laboratory-based 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.

Fabrication of a precise ellipsoidal mirror for soft X-ray nanofocusing

In X-ray focusing, grazing incidence mirrors offer advantages of no chromatic aberration and high focusing efficiency. Although nanofocusing mirrors have been developed for the hard X-ray region, there is no mirror with nanofocusing performance in the soft X-ray region. Designing a system with the ability to focus to a beam size smaller than 100 nm at an X-ray energy of less than 1 keV requires a numerical aperture larger than 0.01. This leads to difficulties in the fabrication of a soft X-ray focusing mirror with high accuracy. Ellipsoidal mirrors enable soft X-ray focusing with a high numerical aperture. In this study, we report a production process for ellipsoidal mirrors involving mandrel fabrication and replication processes. The fabricated ellipsoidal mirror was assessed under partial illumination conditions at the soft X-ray beamline (BL25SU) of SPring-8. A focal spot size of less than 250 nm was confirmed at 300 eV. The focusing tests indicated that the proposed fabrication process is promising for X-ray mirrors that have the form of a solid of revolution, including Wolter mirrors.

Ptychography simulations for precisely measuring wavefront profiles in soft x-ray focusing system based on ellipsoidal mirror

In synchrotron radiation facilities, soft X-ray nanofocusing with mirrors remains a hurdle due to difficulties in mirror fabrication. We have been researching the use of ellipsoidal mirrors for soft X-ray nanofocusing. Information on the wavefront errors of focused beams is helpful for improving the focusing system. This study presents ptychographic wavefront measurements for a nanofocusing system with an ellipsoidal mirror. We developed a ptychography program and performed several simulations at 300 eV to investigate the theoretical accuracy of the wavefront measurements. The simulation results indicate that wavefront measurements with high accuracy are possible.

Optical design of a sub-1-μm focusing system for soft x-ray free electron lasers

We present an optical design of a new focusing system for soft x-ray free electron lasers. The system is based on a two-staged focusing configuration that combines a Kirkpatrick-Baez focusing system with an ellipsoidal mirror so as to produce a sub-1-μm focal spot. A wave-optical simulation indicates that the power density at the focus exceeds 1018 W/cm2, which enables us to access exotic interactions between soft x-rays and matters.