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Ultraprecise imaging optics, which consists of two sets of elliptical mirrors and hyperbolic mirrors aligned perpendicular to each other (i.e., advanced Kirkpatrick–Baez mirrrors), is developed to realize high-resolution and achromatic full-field hard-X-ray microscopy. Experiments to form a demagnified image (with horizontal and vertical demagnification factors of 385 and 210, respectively) are conducted to evaluate the optical system at an X-ray energy of 11.5 keV at SPring-8. Results show that the imaging system can form a demagnified image with nearly diffraction-limited resolutions of ~50 nm in the horizontal and vertical directions. The field of view is also experimentally estimated to be ~12 × ~14 μm2 when used as a magnification imaging system.
©2012 Optical Society of America
1. Introduction
X-ray microscopy can ultimately attain sub-nanometer resolution, which is far beyond that of optical microscopes, owing to the very short wavelength. In addition to resolution, X-ray microscopy has unique advantages for various applications, compared with other methods. The high penetrating power of X-rays makes it possible to observe samples that are too thick to observe by transmission electron microscopy or that are too opaque to observe by visible microscopy, enabling 3D imaging by tomography. X-ray microscopy is suitable for observation in various environments (e.g., in aqueous solutions and gaseous atmospheres), which is useful for in situ measurements. It does not require special sample preparation techniques such as sectioning and coating, which are often necessary for electron microscopy. In addition, incorporating X-ray analysis techniques, such as X-ray fluorescence analysis and X-ray absorption spectroscopy, can reveal not only electron density distributions but also local bonding state and element distributions. Therefore, X-ray microscopy is strongly expected to be developed for various scientific fields.
There are various types of X-ray microscopies such as the full-field type [1,2], scanning type [3,4] and lensless type [5,6]. In this paper, full-field microscopy, which can yield magnified X-ray images using an optical imaging device, is discussed. Unlike other techniques, it has the potential to image polychromatic X-rays in one shot by incorporating an achromatic optical imaging device and a photon-counting CCD camera, which is compatible with X-ray fluorescence analysis [7].
Promising candidates for optical imaging devices to realize full-field X-ray microscopy are Fresnel zone plates [1,4], compound refractive lenses [2,8], Kirkpatrick–Baez (KB) mirrors [3,9], and Wolter mirrors [7]. Fresnel zone plates and compound refractive lenses can be fabricated sufficiently precisely to realize sub-50 nm resolution. However, they suffer from inherent chromatic aberrations due to refraction and diffraction, which makes them unsuitable for polychromatic imaging. KB mirrors are achromatic since they employ total reflection. However, they suffer from comatic aberration because single reflection in grazing-incidence optics cannot satisfy the Abbe sine condition; this aberration reduces the resolution and the field of view (FOV). Wolter mirrors are ideal X-ray imaging devices since they do not suffer from chromatic or comatic aberration. However, even when using state-of-the-art ultraprecise machining techniques, it is too difficult to fabricate Wolter mirrors with the figure accuracy required to realize diffraction-limited resolution because their mirror surfaces are located on the inner surface of ellipsoidal and hyperboloidal figures of revolution. Furthermore, the shape must be figured to an accuracy of one nanometer order. Thus, serious figure errors are currently unavoidable for Wolter mirrors.
Kodama et al. proposed overcoming the problems of chromatic, comatic, and wave aberrations by using advanced KB mirrors, which consist of two elliptical mirrors and two hyperbolic mirrors oriented perpendicular to each other as in KB mirrors [10]. Consequently, they satisfy the Abbe sine condition. Furthermore, they use nearly planar mirrors that can be fabricated with a figure accuracy of one nanometer order using existing techniques. Thus, advanced KB mirrors have the potential to realize full-field X-ray microscopy with no chromatic aberration and with diffraction-limited resolution.
In previous studies, we developed techniques for fabricating X-ray mirrors that can figure an aspherical shape with a figure error of only 1 nm [11–13]. A total-reflection mirror that had been elliptically figured using these developed techniques realized diffraction-limited X-ray focusing with a full width at half-maximum (FWHM) of 25 nm at an X-ray energy of 15 keV [14]. In addition, a one-dimensional imaging optics consisting of an elliptical mirror and a hyperbolic mirror were constructed to demonstrate the potential of advanced KB mirror optics [15]. Imaging tests conducted at SPring-8 with an X-ray energy of 11.5 keV realized hard X-ray imaging with a resolution of better than 50 nm and an FOV of 12 μm.
In this study, we demonstrated advanced KB mirror optics developed to realize an achromatic full-field X-ray microscope with a sub-50 nm resolution. The point spread functions (PSFs) of the imaging system were directly evaluated using a demagnifying geometry. By comparing the experimental results with those predicted using a wave-optical simulator [16], we confirmed that the four total-reflection mirrors function as an imaging system with a resolution of ~50 nm under a nearly diffraction-limited condition at an X-ray energy of 11.5 keV.
2. Advanced Kirkpatrick–Baez mirror optics
Our advanced KB mirror optics were designed to give magnification factors of 385 × 210 (H × V) between the first (EH1) and second experimental hutches (EH2) at BL29XUL [17] of SPring-8. The hutches are 45 m apart. In addition, the following conditions were considered when designing the optical imaging system: the microscope should have a diffraction-limited spatial resolution of 43 nm at 11.5 keV and a working distance of 50 mm. To increase the total reflectivity of the system, elliptical mirrors were designed to have a small glancing angle. To compensate for this small incident angle, long elliptical mirrors were employed. Table 1 lists the design parameters of the mirrors.
Table 1. Designed Mirror Parameters
The four mirrors were figured on synthetic silica substrates by numerically controlled elastic emission machining (NC-EEM) [11] with peak-to-valley figure accuracies of better than 2 nm (Fig. 1 ). The figure errors were measured using a microstitching interferometer (MSI) [12] and a relative angle determinable stitching interferometer (RADSI) [13]. Surface characterization using a phase-shift interference microscope (Zygo, NewView 200CHR) confirmed that the processed surfaces have a root mean square roughness of better than 0.2 nm over an area of 64 × 48 μm2, which is sufficiently small to neglect any reduction in the reflectivity caused by roughness. After figuring their shapes, the mirrors were coated with a thin chrome binder layer and a 30-nm-thick platinum layer by magnetron sputtering.
3. Wave-optical calculations
To investigate the behavior of the complex optical imaging system with four mirrors, a simulator that can accurately calculate the image shape for nearly diffraction-limited conditions is essential. We have developed a wave-optical simulator based on the Fresnel–Kirchhoff integral that can calculate the wave field reflected from flat and elliptical mirrors for hard X-rays [16,18]. In the present study, we extend this simulator to calculate intensity maps after X-rays are reflected from the four mirrors. The simulator calculates the propagation of the wave field from the object to the first mirror and from the mirror to the next mirror in series. Finally, it obtains the wave field in the image plane.
To evaluate the performance of the imaging system, we calculate a demagnified image of a point source, which represents the PSF of the imaging system and corresponds to the experiments described below. The point source is modeled using a single data point with an intensity of 1 and an initial phase of 0 rad. An X-ray energy of 11.5 keV was assumed. An opposite geometric arrangement to that for magnifying geometry (see Table 1) was employed to model the demagnifying geometry with demagnification factors of 385 × 210 (H × V). The arrangement is the same as the experimental one described below. Astigmatism can be ignored in this arrangement because the positions of the two image planes for vertical and horizontal imaging are consistent. Approximately 2,000,000 data points were used for each mirror.
To confirm that the fabricated mirrors satisfied the criteria for realizing a diffraction-limited resolution, the PSF was calculated on the basis of actually measured shapes (Fig. 2 ). The calculated PSF has a similar shape and width as an ideal PSF. The simulator revealed that the fabricated mirrors are capable of forming images without degradation due to figure errors. In addition, the effect of misalignment was investigated by calculating the PSFs for various misalignments. The results have been reported in detail elsewhere [19]. They reveal that the relative angle and distance between an elliptical mirror and a hyperbolic mirror should be aligned to accuracies of ~10 μrad and ~2 μm, respectively, and that rolling (i.e., rotation about an optical axis) between two mirrors should be adjusted to an accuracy of ~40 μrad. The obtained results were utilized in designing an alignment system and planning a strategy for aligning the four mirrors.
Fig. 2 PSFs calculated using (a) ideal mirror shapes and (b) measured shapes (area: 800 × 800 nm2; mesh size: 2 nm). Cross-sectional profiles of (a) and (b) in the (c) vertical and (d) horizontal directions are shown under the maps. The coordinate axes correspond to those in Fig. 4. The color bars have a linear scale.
4. Mirror alignment
Procedures to align KB mirrors are based on trial and error. We cannot apply this approach to advanced KB optics owing to the complexity of aligning the four mirrors and the limited experimental time at the synchrotron radiation facility. Thus, an off-line alignment procedure to precisely align four mirrors without using X-rays is desirable. We employed a two-step procedure to precisely align the four mirrors. This procedure requires a mirror manipulator that can be used to adjust all the degrees of freedom of the mirrors according to the above-mentioned alignment tolerances. It also requires an alignment monitoring system that can monitor the shape and slopes of the mirrors. The procedure consists of an initial off-line alignment and a final on-line alignment. In the off-line alignment, the relative positions of the four mirrors are finely adjusted using the mirror manipulator and the alignment monitoring system. After this off-line alignment, minimal effort is required to align the mirrors to the incident X-rays using the X-rays in the beamline.
Figure 3 shows a 3D diagram of the mirror manipulator. The alignment of the incident angle and the relative angle requires particularly careful adjustment using the adjustment system. It consists of flexure hinges and a high-resolution linear actuator and is based on previously developed KB manipulators [20]. The angular adjustment has a resolution of ~0.2 μrad, which is sufficiently fine. For rolling, angular adjustments using a differential micrometer head and a flexure hinge with a ~5 μrad resolution were used. For yawing (i.e., rotation about the vertical axis through the center of the mirror), simple angular adjustments using a micrometer head and a pivot point with a ~500 μrad resolution were used. In addition, the manipulator has XYZ translation axes under the mirrors to adjust the relative positions of each pair of mirrors.
The alignment monitor system consists of a translation stage, a laser displacement meter (resolution: 0.5 μm), and an autocollimator (resolution: 19 μrad). The sensors are scanned using the stage to measure the mirror shapes and the slopes. To eliminate the influence of the waviness of the stage and misalignment of the autocollimator, the systems are calibrated using a glass block (flatness of top and side: < 300 nm peak-to-valley; perpendicularity between top and side: + 3 arcsec) as a standard for aligning mirrors parallel and orthogonal.
After off-line alignment, the imaging system including the alignment system was installed in a beamline. Prior to performing experiments, only the incident angles and focal lengths were adjusted to accuracies of approximately 10 μrad and 25 μm, respectively, without changing the adjusted relative positions. The focal lengths for vertical and horizontal imaging were carefully matched to eliminate astigmatism.
5. Experiment and results
Figure 4 schematically depicts the experimental setup installed at BL29XUL (EH1 and EH2) of SPring-8. A demagnification imaging system was constructed to evaluate the performance of the imaging optics. This allows us to easily generate a practical point source and to precisely evaluate the experimental PSFs. By evaluating the experimental PSFs of the demagnification imaging system, the performance of the magnification imaging system (which is what we aim to develop) can be determined. A cross slit placed at EH1 is used to generate a point source. The slit size is 10 × 5 μm2 (H × V), which is sufficiently small to be considered a point source. A demagnified image of the slit is observed at EH2 placed 45 m downstream from the object. A wire scanning method with a 200-μm-diameter gold wire, an XZ stage (Sigma Tech, FS-1050SPXY; positioning resolution: 1 nm), and a PIN photodiode was used to evaluate the line profiles of the image shape in the vertical and horizontal directions. In the experiment, to eliminate the influence of position offset of the vertical and horizontal wires, the wires were shifted by an appropriate distance along the optical axis to match the image plane when scanning the vertical and horizontal wires, respectively. X-rays were generated by a standard undulator at SPring-8 and monochromatized at 11.5 keV by a double-crystal [Si(111)] monochromator (DCM).
The total reflectivity was first evaluated using a PIN photodiode. The reflectivity after correcting for absorption by air was 62%. This is consistent with the ideal reflectivity (65.7% at 11.5 keV) theoretically estimated with surface roughness neglected. The PSF of the imaging system at the center of the FOV was then carefully investigated. One-dimensional profiles of the image in the vertical and horizontal directions were measured separately. Figure 5 shows the experimental results together with those of the simulations. (In this paper, the coordinate axes in all the graphs correspond to those shown in Fig. 4.) The simulation results (solid red line) correspond to the cross-sectional profiles at the center on the intensity maps in Fig. 2(a). The FWHMs of the experimental PSFs were obtained by fitting with Gaussian functions. The experimental FWHM was 47 × 41 nm2 (H × V), which agrees well with the calculated FWHM (43 × 43 nm2). In contrast, the experimental PSFs have relatively long tails. They seem to originate from the accumulation of multiple minor factors, such as misalignment of the rolling, twisting of the mirrors, parasitic scattering from the unprocessed area on the mirrors, and measurement errors in the wire scanning method.
Fig. 5 Line profiles of images formed in the image plane. They were measured several times (vertical: three times, horizontal: four times) with different scanning intervals. All the experimental results obtained are plotted. The calculations correspond to the cross-sectional profiles at the center on the intensity maps shown in Fig. 2(a). The solid black curve was obtained by fitting Gaussian functions to the measured points.
The FOV of the imaging system was also evaluated by measuring a series of PSFs while inclining the whole imaging system horizontally and vertically. Here, the FWHM of a PSF with multiple peaks was defined as the maximum width (including satellite peaks) at half-maximum. Figure 6 shows the relationship between the FWHMs of the PSFs and the incident glancing angles together with the simulated results. These results show that the imaging system has a large FOV, which is the same as the simulated FOV. The FOV is ~12 μm × ~14 μm in the horizontal and vertical directions as estimated from the obtained angular distances of 120 μrad × 80 μrad. These results demonstrate that the four mirrors function as an accurate imaging system. On the other hand, FWHMs that are smaller than the simulated one were obtained on the outside of the vertical FOV. The PSF on the outside of the FOV tends to havea complex structure with multiple satellite peaks and a small flux density. It is generally difficult to measure such an image precisely by the wire scanning method. In addition, the FWHM as defined in this study is strongly influenced by the height of satellite peaks. Thus, the discrepancy between the FWHMs on the outside seems to result from measurement errors, particularly in measuring the satellite peaks. To investigate the PSFs on the outside of the FOV (–70 and 80 μrad in Fig. 6) in detail, the obtained PSFs were compared directly with the simulated ones (Fig. 7 ). The characteristics of the beam profiles including the satellite peaks were found to be in reasonable agreement with the simulated ones, in spite of the discrepancy between the FWHMs.
Fig. 6 Relationship between the angular distance from the field center and the FWHM in (a) horizontal and (b) vertical directions. The top horizontal axes indicate the FOV equivalent to the angular distance. The calculations were conducted only for the one-dimensional case.
Fig. 7 Line profiles (upper) and 2D profiles (lower) of the image formed for the off-axis condition. The 2D profiles (area: 800 × 800 nm2; mesh size: 2 nm) were calculated using the simulator. The calculation results in the upper graphs correspond to the line profiles along the dashed white lines in the 2D profiles below the graphs. The angular values shown in the graph represent angles corresponding to the angular distance in Fig. 6. The color bars have a linear scale.
6. Summary
For the first time, we developed an imaging system with four mirrors that has nearly diffraction-limited resolution owing to the ultraprecise fabrication of X-ray mirrors, performance prediction using the wave-optical simulator, and precise alignment. A resolution of ~50 nm and an FOV of ~12 × ~14 μm2 (H × V) were achieved. These results, which are also consistent with theoretically expected ones, indicate that the four mirrors were fabricated and aligned almost perfectly. We intend to construct a full-field hard-X-ray microscope by adding illumination optics to the imaging system. This will enable us to obtain magnified polychromatic X-ray images, such as X-ray fluorescence images. The high-resolution optical imaging system without chromatism will definitely become a new tool for spectromicroscopy, not only for synchrotron radiation X-rays, but also for the X-ray free-electron laser with extremely brilliant and ultrashort pulses [21,22].
Acknowledgments
This research was mainly supported by Sentan from the Japan Science and Technology Agency (JST). It was also partially supported by a Grant-in-Aid for Specially Promoted Research (18002009) and the Global COE Program “Center for Excellence for Atomically Controlled Fabrication Technology” from the Ministry of Education, Culture, Sports, Science and Technology, Japan, CREST from JST, and the Iketani Science and Technology Foundation. The use of BL29XUL at SPring-8 was supported by RIKEN. We are grateful to Mr. Masaki Fujii and Mr. Toshiyuki Wakioka for their support.
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