Sub-photon accuracy noise reduction of a single shot coherent diffraction pattern with an atomic model trained autoencoder.

Single-shot imaging with femtosecond X-ray lasers is a powerful measurement technique that can achieve both high spatial and temporal resolution. However, its accuracy has been severely limited by the difficulty of applying conventional noise-reduction processing. This study uses deep learning to validate noise reduction techniques, with autoencoders serving as the learning model. Focusing on the diffraction patterns of nanoparticles, we simulated a large dataset treating the nanoparticles as composed of many independent atoms. Three neural network architectures are investigated: neural network, convolutional neural network and U-net, with U-net showing superior performance in noise reduction and subphoton reproduction. We also extended our models to apply to diffraction patterns of particle shapes different from those in the simulated data. We then applied the U-net model to a coherent diffractive imaging study, wherein a nanoparticle in a microfluidic device is exposed to a single X-ray free-electron laser pulse. After noise reduction, the reconstructed nanoparticle image improved significantly even though the nanoparticle shape was different from the training data, highlighting the importance of transfer learning.

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.

Soft X-ray ptychography system using a Wolter mirror for achromatic illumination optics.

A soft X-ray ptychography system using a Wolter mirror for the illumination optics has been developed. By taking advantage of the achromaticity of the optics, the system is capable of seamlessly imaging at half-period resolution of 50 nm with a broad photon-energy range from 250 eV to 2 keV while maintaining the focal position. Imaging a mammalian cell at various wavelengths was demonstrated, and high-resolution visualization of organelle was achieved. Stereo imaging was also performed with a long working distance of 20 mm. In combination with in-situ/operando and tomographic measurements, this system will be a powerful tool for observing biological and material targets with complex features.

Stable sub-micrometre high-flux probe for soft X-ray ARPES using a monolithic Wolter mirror.

A focusing optics that can provide a sub-micrometre high-flux probe for soft X-ray micrometre-scale angle-resolved photoemission spectroscopy (ARPES) is proposed. A monolithic Wolter-type mirror with a large acceptance, achromatism and small comatic aberration was designed and evaluated. A focused beam size of 0.4 µm (vertical) × 4 µm (horizontal), a high throughput of 59% and a high tolerance of 1.6 mrad to the pitching error were realized at a photon energy of 1000 eV. A Wolter-type mirror can be practically employed as a stable sub-micrometre focusing mirror with high throughput in ARPES applications.

Probing the spatial coherence of wide X-ray beams with Fresnel mirrors at BL25SU of SPring-8.

Probing the spatial coherence of X-rays has become increasingly important when designing advanced optical systems for beamlines at synchrotron radiation sources and free-electron lasers. Double-slit experiments at various slit widths are a typical method of quantitatively measuring the spatial coherence over a wide wavelength range including the X-ray region. However, this method cannot be used for the analysis of spatial coherence when the two evaluation points are separated by a large distance of the order of millimetres owing to the extremely narrow spacing between the interference fringes. A Fresnel-mirror-based optical system can produce interference patterns by crossing two beams from two small mirrors separated in the transverse direction to the X-ray beam. The fringe spacing can be controlled via the incidence angles on the mirrors. In this study, a Fresnel-mirror-based optical system was constructed at the soft X-ray beamline (BL25SU) of SPring-8. The relationship between the coherence and size of the virtual source was quantitatively measured at 300 eV in both the vertical and horizontal directions using the beam. The results obtained indicate that this is a valuable method for the optimization of optical systems along beamlines.

Ultracompact mirror device for forming 20-nm achromatic soft-X-ray focus toward multimodal and multicolor nanoanalyses.

Nanoscale soft-X-ray microscopy is a powerful analysis tool in biological, chemical, and physical sciences. To enhance its probe sensitivity and leverage multimodal soft-X-ray microscopy, precise achromatic focusing devices, which are challenging to fabricate, are essential. Here, we develop an ultracompact Kirkpatrick-Baez (ucKB) mirror, which is ideal for the high-performance nanofocusing of broadband-energy X-rays. We apply our advanced fabrication techniques and short-focal-length strategy to realize diffraction-limited focusing over the entire soft-X-ray range. We achieve a focus size of 20.4 nm at 2 keV, which represents a significant improvement in achromatic soft-X-ray focusing. The ucKB mirror extends soft-X-ray fluorescence microscopy by producing a bicolor nanoprobe with a 1- or 2-keV photon energy. We propose a subcellular chemical mapping method that allows a comprehensive analysis of specimen morphology and the distribution of light elements and metal elements. ucKB mirrors will improve soft-X-ray nanoanalyses by facilitating photon-hungry, multimodal, and polychromatic methods, even with table-top X-ray sources.

Abrasive slurry jet machining system using polyurethane@silica core-shell particles for internal surfaces of axisymmetric x-ray mirrors.

Abrasive machining has been used for inner surface processing of various hollow components. In this study, we applied an in-air fluid jet as a precision machining method for the inner surface of an axisymmetric x-ray mirror whose inner diameter was less than 10 mm. We employed an abrasive with a polyurethane@silica core-shell structure, which has a low density of about 1.2 g/cm3 and a relatively large particle size of about 15 µm. By using this abrasive, a practical removal rate and a smooth machined surface were simultaneously obtained. We performed figure corrections for an axisymmetric mirror and improved the circumferential figure accuracy to a sub-10 nm root mean square level. To evaluate the machining performance in the longitudinal direction of the ellipsoidal surface, we also performed periodic figure fabrication on the inner surface of a 114 mm-long nickel ellipsoidal mirror. X-ray ptychography, an optical phase retrieval method, was also employed as a three-dimensional figure measurement technique of the mirror. The wavefield of the x-ray beam focused by the processed ellipsoidal mirror was observed with the ptychographic system at SPring-8, a synchrotron radiation facility. The retrieval calculations for the wavefront error confirmed that a sinusoidal waveform with a period of 12 mm was fabricated on the mirror surface. These experimental results suggest that a nanoscale figure fabrication cycle for the inner surface consisting of jet machining and wavefront measurement has been successfully constructed. We expect this technique to be utilized in the fabrication of error-free optical mirrors and various parts having hollow shapes.

Fabrication of ultrashort sub-meter-radius x-ray mirrors using dynamic stencil deposition with figure correction.

This paper presents nanometer-scale production and metrology methods for elliptic-cylindrical x-ray mirrors with an unprecedentedly small tangential radius of curvature of 160 mm. Sub-millimeter-scale figure correction is conducted based on dynamic stencil deposition. The deposition flux through one or two shadow masks is examined by a comparison to a simple model. The masked deposition flux distribution is improved, leading to film thickness profiles that are 50 times sharper in terms of aspect ratio than those obtained using existing differential deposition approaches. Surface roughness deterioration is also effectively suppressed. A 2-mm-long 160-mm-radius mirror is produced with a width of 10 mm and measured using simple interferometry. The results are confirmed by conventional mirror metrology, contact profilometry, and x-ray ptychography. The x-ray focusing profile is diffraction-limited with a 142-nm focus size at a photon energy of 300 eV. The proposed methods have the potential to enhance the ultraprecise fabrication of highly curved mirrors, thus benefiting nanoscale photon-hungry x-ray techniques.

Fabrication of soft x-ray monolithic Wolter mirror based on surface scanning measurement using touch probe.

The monolithic Wolter mirror is an ideal optical device for focusing soft x rays to a submicron-sized spot, with the advantages of high efficiency, large acceptance, achromaticity, and robustness to alignment error. The fabrication process for this type of mirror has not been established because of the difficulty in highly accurate figure measurement of free-form surfaces with small radii of curvature and steep profiles. In this study, we employed tactile scanning measurement for surface characterization to fabricate a high-precision Wolter mirror. First, it was demonstrated that the touch probe measurement did not leave scratches on the raw surface of the mirror substrate. Next, the measurement capability of the surface profiler was assessed, and the data analysis conditions were determined. Finally, the Wolter mirror was fabricated through repeated figure correction based on the tactile measurement, and the figure error of the final surface was evaluated. Wave-optical simulations that used this error as reference suggested that the size of the beam focused by the mirror was equivalent to the theoretical value at 1000 eV. The reflected image with uniform intensity distribution obtained at SPring-8 also revealed the effectiveness of the present fabrication approach based on tactile measurement.

Copper electroforming replication process for soft x-ray mirrors.

We developed a copper electroforming replication (CER) process to fabricate precise ellipsoidal mirrors for soft x-ray focusing. Some applications of ellipsoidal mirrors in x-ray microscopy require that all components that are close to samples, including the mirrors, are made of non-magnetic materials. In this study, a non-magnetic copper ellipsoidal mirror was fabricated by replicating a figured and super-polished quartz glass mandrel using an electroforming technique. It was found that the CER process has a high replication accuracy of 8 nm. The focusing performance of the mirror was characterized using a soft x-ray free-electron laser with a photon energy of 100 eV. A small focus size of 370 × 400 nm2 was achieved with a high reflectivity of 65%.

Development of electroforming process for soft x-ray ellipsoidal mirror.

An x-ray ellipsoidal mirror is an ideal tool for focusing soft x-rays. Because nanometer-level shape accuracy is required in the internal surface of a mirror having a small diameter, it is difficult to fabricate the mirror by processing the surface directly. We developed a fabrication process for soft x-ray ellipsoidal mirrors in which the surface of a high-precision quartz mandrel with the inverted shape of the designed mirror is replicated by nickel sulfamate electroforming. In this study, an ellipsoidal mirror of 40-mm length was fabricated and the shape accuracy of the replicated surface was evaluated by a measurement method using a contact probe. The root mean square (RMS) of the replication error in the entire measured surface was 27.2 nm. When the evaluated area was half the replicated surface near the middle of the mirror, the RMS of the replication error was 14.7 nm. Wave-optical simulation suggested that it is possible to focus soft x-rays to a spot with a diameter of 400 nm.

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.