We developed an achromatic and high-resolution full-field X-ray microscope based on advanced Kirkpatrick-Baez mirror optics that comprises two pairs of elliptical mirrors and hyperbolic mirrors utilizing the total reflection of X-rays. Performance tests to investigate the spatial resolution and chromatic aberration were performed at SPring-8. The microscope clearly resolved the pattern with ~100-nm feature size. Imaging the pattern by changing the X-ray energy revealed achromatism in the wide energy range of 8–11 keV.
© 2015 Optical Society of America
The chromatic aberration of imaging optics is a phenomenon in which the image position changes along the optical axis and/or the image plane with a change in the wavelength. The colorful blurring introduced by the chromatic aberration must be removed to develop microscopes utilizing polychromatic light. Visible light microscopes can easily overcome the chromatic aberration owing to outstanding lens techniques.
Recently, many full-field microscopes with high resolution have been developed for the X-ray region because of the remarkable progress of Fresnel zone plates [1–3] and refractive lenses [4, 5]. However, the chromatic aberration in these devices remains unresolved. There are few reports on the development of an achromatic X-ray microscope. If such an X-ray microscope emerges, it will facilitate full-field imaging combined with X-ray absorption spectroscopy over a wide energy range and, together with a photon-counting area detector, will allow the production of multicolor X-ray images of objects. The latter will become a useful tool to obtain elemental distributions  of objects and diagnose plasmas , e.g., those produced by a high-power laser.
One possible way to eliminate the chromatic aberration in the X-ray region is the use of total-reflection mirrors, which are known to have little dependence on wavelength. Then, can total-reflection mirrors be used for achromatic image formation, particularly for high-resolution imaging? Indeed, total reflection also has a slight wavelength dependence caused by a phase-shift upon the reflection at an interface. Let us consider the trajectories of two rays at energies of 7 and 12 keV after reflection by a platinum-coated focusing mirror with a numerical aperture (NA) of 1.5 × 10−3. According to the precise wave optical calculation including the Fresnel equation, the discrepancy of the peak position between the two rays is only ~1 nm at the focal plane. In general, this is negligible because it is far smaller than the other blurring factors. Thus, total-reflection mirrors are highly suitable for achromatic imaging formation.
However, the challenge of high-resolution imaging remains. To achieve a high resolution with total-reflection mirrors, the wavefront aberration caused by the imperfections in the mirror fabrication should be eliminated. Therefore, a Wolter mirror  with extremely difficult fabrication is not currently suitable for high-resolution imaging, although it is ideal for imaging optics if perfectly finished. Kirkpatrick-Baez (KB) mirrors , often used as focusing optics, can overcome this difficulty because they comprise two nearly planar mirrors that can be finished with sub-2-nm accuracy . However, they cannot avoid comatic aberration, because they do not satisfy Abbe’s sine condition. To realize achromatic and high-resolution full-field X-ray microscopy, the use of an optical imaging system comprising four total-reflection mirrors (i.e., advanced KB mirror optics) has been proposed . The advanced KB mirror optics comprises two elliptical mirrors and two hyperbolic mirrors, which are nearly as planar as general KB mirrors. A pair comprising an elliptical mirror and a hyperbolic mirror can function as a part of a Wolter mirror. This can eliminate the wavefront aberration and satisfy Abbe’s sine condition [11, 12], which leads to the realization of achromatic and high-resolution full-field X-ray microscopy.
In this paper, we report the construction of an achromatic and high-resolution microscopy system based on advanced KB mirror optics comprising total reflection mirrors. The observation of a test pattern using this system demonstrates the system’s good performance. The relationship between the contrasts of the image and the spatial resolution is discussed. Moreover, the wavelength dependence of the image quality in the range of 8–11 keV is examined.
2. Advanced Kirkpatrick-Baez mirror optics
We have reported the development of advanced KB mirror optics before [11–13]. In our previous studies, staggered mirror geometry, in which two elliptical mirrors were placed after two hyperbolic mirrors, was employed to reduce mismatch of the magnifications in the vertical and horizontal directions. Consequently, the structure of the mirror manipulator was complex and the four-mirror alignment was difficult. Here, the advanced KB mirror optics was designed to align the mirror pairs (i.e., an elliptical mirror and a hyperbolic mirror), functioning as a one-dimensional objective, in series without staggered geometry. This arrangement makes the manipulator simpler and facilitates the four-mirror alignment. Table 1 shows the parameters of the developed advanced KB mirror optics. The NA was 1.5 × 10−3 to realize sub-50-nm resolution in the hard X-ray regions around 10 keV. Magnifications of 658 and 214 in the vertical and horizontal directions, respectively, can be obtained at BL29XUL of SPring-8, which has two experimental hutches with a separation as large as 45 m. The mismatched magnifications, resulting from the tandem arrangement of the mirrors, were corrected digitally after the images were taken. The four mirrors were figured on synthetic silica substrates by numerically controlled elastic emission machining (NC-EEM) . The figure errors were precisely measured using a microstitching interferometer (MSI)  and a relative angle determinable stitching interferometer (RADSI) . The figure errorsfrom the designed shape were confirmed to be less than 2 nm, which is sufficiently small to satisfy Rayleigh’s quarter-wavelength rule (Fig. 1) . Thus, the developed advanced KB mirror optics has the potential to provide a diffraction-limited resolution. Surface characterization using a microscopic interferometer (Zygo, NewView 200CHR) revealed a root-mean-square roughness better than 0.2 nm over an area of 64 × 48 µm2 (effective pixel size = 200 nm), which is sufficiently small that the reduction in the reflectivity caused by the roughness can be neglected. Subsequently, the surfaces were covered with a thin chrome binder layer and an 80-nm-thick platinum layer.
3. Experimental setup of full-field X-ray microscopy
Figure 2 shows the entire experimental setup of a full-field X-ray microscope constructed at BL29XUL. The incident X-rays are monochromatized by a double-crystal [Si(111)] monochromator (DCM). The objective mirrors are mounted on a specially developed mirror manipulator  to precisely adjust the four-mirror alignment. Prior to the experiment, the mirrors are aligned carefully according to the previously proposed alignment procedure [12, 18]. The condenser optics comprise a rotating diffuser, two platinum-coated plane mirrors, and two platinum-coated elliptical mirrors, aligned in the KB configuration. The elliptical mirrors, having NAs of 2.1 × 10−3 and 1.5 × 10−3 in the vertical and horizontal directions, respectively, collect X-rays on the sample plane. For broadened illumination, they are used in a defocus condition; the illuminated area was ~30 × ~160 μm2 (V × H). The two plane mirrors are placed upstream from the elliptical mirrors. This is because the beam direction reflected on the objective mirrors must be carefully made parallel to the beamline in order to successfully deliver the X-rays to the image plane placed deep within a long (~40 m) and narrow (minimum diameter of ~40 mm) vacuum duct. To reduce the speckle noise, a rotating diffuser comprising a motorized rotating stage and fine sandpaper is placed upstream from this system. An X-ray camera system (AA20MOD, Hamamatsu Photonics) is placed 45 m downstream from the objective to capture X-ray images. It comprises a thin scintillator (P43 with a thickness of 10 μm), a relay lens ( × 2), and a CCD. Two types of CCDs (ORCA-II Deep Cooling BTA 1024 and ORCA-R2, Hamamatsu Photonics) were used in the experiments.
4. Experimental results and discussion
Bright-field images were taken at an X-ray energy of 9.881 keV, which is slightly above the absorption edge of tantalum. The first sample used was a Siemens star chart (XRESO-50, NTT Advanced Technology Corporation) made of tantalum, with a thickness of 200 nm. The innermost region had the finest feature size of 50 nm (i.e., a half-period of 50 nm). The data analysis includes the flat-field correction, in which the obtained image data are normalized by image data taken without a sample, along with the magnification correction, in which an image stretched by mismatched magnifications is corrected to have a real aspect ratio. Figures 3 and 4(a) present the obtained image after the corrections and the line profiles along the tangential direction, respectively. The 100-nm feature in the inner side of the second donut-like island can be clearly resolved. Furthermore, the intermediate region of the innermost island, exhibiting a feature size of ~75 nm, is barely visible and only visible in the vertical direction.
To investigate the details of the contrast, an image modulation [19, 20] was plotted, as shown in Fig. 4(b). The image modulation was calculated according to the formula (Imax(r,θ)-Imin(r,θ))/Imax(r,θ), where Imax(r,θ) and Imin(r,θ) represent the maximum and minimum, respectively, of the modulated intensity, and r and θ are the radius from the center of the pattern and the azimuthal angle measured from the horizontal direction, respectively. The modulations were normalized by the ideal one calculated for the transmission of 200-nm-thick tantalum. The graph legends of “Vertical” and “Horizontal” represent the average image modulations between θ = 0 and 180 degrees and between θ = 90 and 270 degrees, respectively. A threshold modulation was set at 0.265, corresponding to the modulation at the Rayleigh criterion for a circular aperture . Thus, the minimum spatial resolution equivalent to the Rayleigh criterion is defined as the smallest half-period that can be resolved with an image modulation of 0.265. The modulation analysis indicates that the achieved minimum spatial resolutions were ~90 and ~120 nm in the vertical and horizontal directions, respectively.
Ideal image modulations were calculated in order to be compared with the experimental ones. The partial coherence factor  σ is defined as the ratio of the NA of the condenser to that of the objective (NAcondenser/NAobjective), corresponding to the degree of partial coherence of the illumination. The “σ = 0” and “σ = 1” in Fig. 4(b) represent image modulations calculated using our wave optical simulator according to the Fresnel-Kirchhoff integral [11, 12]. The wave propagation was one-dimensionally calculated from an object to an image plane through an objective, in which the vertical optical imaging system was assumed. For the calculation, the object used was a double slit with a width as large as the half-period. At σ = 0, a plane wave along the optical axis was illuminated on the object. At σ = 1, some plane waves were illuminated from the various directions within +/− 1.5 mrad, which corresponds to the NA of the objective. Then, the formed intensity images were summed up. These modulations were calculated in the same manner as the experimental ones. The achievable minimum spatial resolutions were found to be 49 and 40 nm at σ = 0 and 1, respectively. The experimental σ was estimated to be near 0 because the sample was placed at the defocus position of the condenser. Therefore, the achieved minimum resolution was found to be approximately twice as large as the ideal one.
The achromatism of the objective was confirmed. X-ray images were taken while the X-ray energy was changed (Fig. 5). For this experiment, the other test chart (XRESO-100, NTT Advanced Technology Corporation) was used, which has the finest feature size of 100 nm at the innermost side and a thickness of 1 micron. A 100-nm feature could be resolved in the region between 8 and 11 keV. For energies lower than 8 keV, strong attenuation of X-rays due to air absorption degraded the image quality (data not shown). Furthermore, at energies higher than 11 keV, the X-ray signals on the camera significantly dropped because of the decrease in the reflectivity of the mirrors (data not shown). These results are reasonable considering the path length in the atmosphere and reflectivity characteristics of the platinum-coated mirrors. Except for the low S/N ratio, energy dependence was not observed. To our knowledge, this result is the first demonstration of full-field hard X-ray microscopy achieving a wide energy acceptance and high spatial resolution.
On the other hand, the minimum resolution achieved was worse than expected. We consider why the expected minimum resolution could not be attained. The most dominant factor is a misalignment of the sample position. Advanced KB mirror optics, with a short focal length, suffer from a significant field curvature , leading to a relatively narrow field of view (FOV) for the system. The sample must be placed onto the focus and at the center of the FOV to obtain wide-field and high-resolution images. In the optical system, the tolerances to align a sample to obtain a 50-nm resolution and the maximum FOV are +/−25 μm along the optical axis and +/−12 μm (H) and +/−6 μm (V) along the transverse directions. Moreover, the gradual drift of the object plane, potentially caused by the misalignment of the relative angle between the elliptical and hyperbolic mirrors, seemed to increase the difficulty of positioning the sample. Such drift can cause a gradual change in the focal length and the center of the FOV without significantly degrading the point-spread function of the objective.
An achromatic and high-resolution full-field X-ray microscope has been realized for the first time. It achieved ~100 nm spatial resolution and achromatism in the wide energy range of 8–11 keV. In the near future, we will be able to realize high-resolution spectromicroscopy, such as full-field X-ray absorption fine structure spectroscopy and full-field X-ray fluorescence microscopy, to reveal elemental information and chemical states for a sample as well as the sample’s nanostructure.
This research was supported by the SENTAN project of JST. It was partially supported by JSPS KAKENHI (Grant Nos. 26286077, 23226004, 25600140), the CREST project of JST, the Global COE program (H08) from MEXT, Iketani Science and Technology Foundation, and Konica Minolta Imaging Science Foundation. The use of BL29XUL at SPring-8 was supported by RIKEN. We acknowledge K. Tamasaku for his valuable discussions and critical reading of the manuscript, as well as JTEC Corporation for helping to process the substrates.
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