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Abstract
We have developed the new hybrid adaptive X-ray mirror based on mechanical and piezo-driven deformation to realize precise shape controllability on a long-length mirror. The mechanical bender approximately provides the required ellipse, while the piezoelectric actuators attached to the mirror correct very small residual errors to satisfy the diffraction-limited condition. The mechanical bender significantly reduces the role of the piezoelectric actuator, resulting in the suppression of accuracy degradation due to the drift and/or junction effect of the piezoelectric actuators. In addition, line focusing was demonstrated with two different numerical apertures at SPring-8, and the obtained beam sizes were 127 and 253 nm (FWHM), which agree well with the diffraction-limited sizes.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Third-generation synchrotron radiation X-ray sources and XFELs (X-ray free-electron lasers) play prominent roles as indispensable light sources for cutting-edge microscopy, offering excellent opportunities for exploring the frontiers of science. Optical devices for condensing X-rays can enhance the performance of microscopy from the viewpoints of spatial resolution, detection limit, and sensitivity. Reflective mirror devices, especially, play important roles because of their higher transmittance efficiency and lower chromatic aberration, compared with other diffractive and refractive devices such as lenses and Fresnel zone plates. In the last 20 years, owing to the significant improvements in optical fabrication and metrology methods such as ion beam figuring [1, 2], elastic emission machining [3], nanometer optical metrology [4, 5], RADSI (relative angle determinable stitching interferometry) [6], and microstitching interferometry [7], X-ray mirrors became to satisfy the Rayleigh’s quarter wavelength criterion to realize diffraction-limited operation [8]. Ultimate condensation down to a size of 7 nm was demonstrated by a multilayer mirror device at SPring-8 (Super Photon Ring-8 GeV) [9], and nearly 50-nm focusing was performed with a total reflection mirror at SACLA (SPring-8 Angstrom Compact Free-Electron Laser) [10]. However, until now, highly accurate X-ray mirrors have been limited to figured mirrors in which the optical parameters are fixed and have no adaptability. In XFEL facilities, where the light source is based on linear accelerators, the number of beamlines is somewhat limited, which is different from ring-based X-ray sources. The beam sizes provided are also limited to a few sizes because of the inadaptability of the condensation optics. Accordingly, the sample size employed for the XFEL experiment must be selected considering not only purely scientific requirements but also the provided beam sizes. Adaptive optics for changing the beam size is highly preferred in XFEL science. In contrast, when upgrading third-generation SR (synchrotron radiation) sources, the brilliance increases by more than 100 [11–13]. Consequently, the experimental throughputs are expected to drastically increase and the multiple analyses of precious samples will become possible within the limited experimental term. In multifunctional instruments for multiple analyses, the X-ray probe size should adaptively change for each method while maintaining the diffraction-limited performance. For scanning microscopy, diffraction-limited characteristics are strongly required for the ultimate condensation of X-rays. In addition, for the relatively large probe of coherent diffraction microscopy, the wavefront quality should be high for recovering the phase with sufficient accuracy. The adaptive optical system is the only candidate that satisfies these requirements in both XFEL and the next-generation SR sources, and we have already proposed and achieved adaptive beam-size change by controlling the numerical aperture of condensation optics while maintaining the diffraction-limited characteristics [14]. In this optical system, we developed a short deformable mirror with a length of 100 mm, which was driven by piezoelectric actuators [15]. The obtained spot sizes ranged from 100 nm to more than 1 μm, which was sufficient in meeting the experimental requirements, e.g., both in coherent diffraction imaging and scanning fluorescence microscopy. However, the working distance, which is a critical parameter for applying the optics to multifunctional beamlines for various experiments, is not sufficient when the mirror length is short. Moreover, in high-photon-energy beamlines, long-length mirrors are required for compensating the small critical angle of total reflection. Furthermore, in high-intensity beamlines of next-generation SR and/or XFELs, long-length mirrors are essential for reducing radiation damage to the mirror surface. However, until now, long-length deformable mirrors have not satisfied the diffraction-limited condition. Mechanical bending mirrors do not have sufficient deformation accuracy, especially at the high-spatial-frequency range. Piezo-driven deformable mirrors lack long-term stability because of the drift of the piezoelectric actuators, and they suffer from the junction effect [16], which induces deformation errors at the gaps between the actuators.
In this study, we focus on hybrid adaptive X-ray focusing mirror, based on mechanical and piezo-driven deformation, to realize diffraction-limited operation with a long-length deformable mirror. The mechanical mirror bender can provide different bending moments to both ends of the mirror, resulting in an approximate ellipse up to the third-order polynomial. The piezo-driven deformable mirror corrects the very small shape error remaining after the mechanical bending, which consists of polynomials higher than the fourth order. In this configuration, piezoelectric plates on the deformable mirror perform a very slight correction in the shape error after mechanical bending. Accordingly, the drift and junction effect of the actuators sufficiently decrease. A hybrid adaptive mirror with a length of 400 mm has already been reported [17]. However, the achievable deformation accuracy has not been discussed in detail.
In this study, we developed a long-length (400 mm) deformable mirror with a hybrid bending mechanism and demonstrated the deformation accuracy to realize diffraction-limited operation at BL29XUL of SPring-8.
2. Hybrid adaptive X-ray mirror
A schematic of the piezo-driven deformable mirror and its specifications are shown and listed in Fig. 1(a) and Table 1, respectively. The mirror is flat and has a length of 400 mm, width of 30 mm, and thickness of 30 mm. As shown in Fig. 1(b), ten piezoelectric plates composed of PZT (lead zirconate titanate) are glued and five of them consist of two 200-mm-long and three 100-mm-long plates attached on each side in two lines along the upper and lower surfaces. The gaps between neighboring piezoelectric plates are located at different positions in the two lines. Electrodes with sizes of 19 mm are deposited at 1-mm intervals on the upper surfaces of the piezoelectric plates. The total number of electrodes in each line is 20. The central area of the mirror with a width of 10 mm is coated with a 100-nm-thick molybdenum layer with a chromium binding layer, and is used as a reflective area.
Fig. 1 (a) Schematic of the piezo-driven deformable mirror. (b) Arrangement of PZT plates on the side face of the mirror.
Table 1. Parameters of Piezo-Driven Deformable Mirror
Figure 2 shows the hybrid adaptive X-ray mirror we developed. The mechanical mirror bender has a monolithic structure made by hollowing a stainless-steel block, as shown in Fig. 2(a). Figure 2(b) shows the technique used to apply the torque. The same structure is equipped at the other end of the mirror bender to apply a different torque. A flexure hinge is employed as the rotational center and has a radius of 2.5 mm, thickness of 1 mm, and width of 5 mm. To apply the appropriate bending moment, a commercially available preloaded piezoelectric linear actuator (P-841, Physic Instrumente) is employed. The load applied by the actuator is monitored by a load cell unit kinematically connected to the actuator.
Fig. 2 Schematics of (a) hybrid adaptive X-ray mirror, (b) torque applying system, and (c) end view.
The mirror is clamped by pushing it up to the spacers at both ends of the mirror. The spacer thickness is optimized to successfully suppress the mirror twist down to less than 3 μrad [Fig. 2(c)]. Electrodes on the piezoelectric plates were wired to bipolar power units by very weak metal coil springs. When the mirror is clamped at both ends, the gravitational sag reaches a PV (peak-to-valley) of 250 nm. Five compensation coil springs are equipped as additional supports to reduce the sag to less than 4 nm PV.
To investigate the hybrid adaptive X-ray mirror in detail, we estimated the deformation characteristics using finite element analysis, where we employed a simulation code of Creo 3.0 (Parametric Technology Corporation). The parameters of the target ellipse employed here are listed in Table 2. In Fig. 3(a), the black curve represents the target shape of the ellipse, while the red line represents the residual shape error after mechanical bending. The residual error becomes as small as 80 nm PV. Because of the prior bending with the mechanical bender, the maximum deformation depth of the piezoelectric plates is decreased from 25 μm to 80 nm. Figure 3(b) shows the estimated final shape errors. The red line shows the final shape error of the hybrid deformation and is expected to be less than 2 nm PV. Errors due to the junction effect are significantly reduced to less than 1 nm PV. Unless the mechanical bender is employed for prior deformation, the error reaches nearly 7 nm, as indicated by the black curve in Fig. 3(b). In addition, the drift of the piezoelectric plates can be suppressed with the decreasing deformation amount to be covered by the piezoelectric plates.
Table 2. Parameters of Ellipse Figure
Fig. 3 (a) Target elliptical shape and calculated deformation error using mechanical bender. (b) FEM analysis results of deformation errors caused by junction effects with and without the assistance of mechanical bending, when the mirror is deformed to the target ellipse.
3. Experimental setup and procedure
We attempted to confirm the performance of the hybrid adaptive X-ray mirror by X-ray line focusing at BL29XUL EH3 of SPring-8. Figure 4 presents the experimental setup and photograph of the optical system. The X-ray photon energy was 10 keV. The incident slit was placed upstream of the mirror. The beam position monitor developed by us, consisting of a thin YAG: Ce ceramic, lens, CMOS camera, and gold wire with a diameter of 200 μm, was placed at the focal point. An indirect X-ray imaging camera (AA20Mod and ORCA Flash 2.0, Hamamatsu Photonics) was placed at the downmost-stream position to record the reflection image. We designed two different ellipses, as shown in Fig. 5, of which the grazing angles of incidence were 1.5 and 3.0 mrad. In both ellipses, the working distance was sufficiently long, at 1200 mm. The target shapes were generated by online and offline procedures [14]. In the offline procedure, we obtained the mechanical bending conditions and voltage patterns for application to electrodes on the piezoelectric plate using RADSI as a high-precision offline shape measurement method. Then, as a first step of the online procedure, we deformed the mirror to the near-final shape using the parameters obtained offline. The reproduced shape has a deformation error of approximately 30 nm due to the slight difference in temperature conditions. Therefore, the remaining shape error was compensated using at-wavelength measurement methods, where we employed an X-ray pencil-beam scanning method [18, 19] as the precise slope error measurement method with an accuracy better than 10−7 rad [20, 21]. As can be seen in Fig. 4(a), the incident slit is used to generate an X-ray pencil-beam with a size of 30 μm square, and the beam is scanned by scanning the slit. The reflected beam is monitored by using the beam position sensor, which can detect the median point shift of the beam with accuracy better than 10 nm [20]. Finally, we slightly modified the applied voltages to compensate the shape error estimated by the pencil-beam scanning method.
Fig. 4 (a) Experimental setup of the X-ray line focusing system. (b) Photograph of the hybrid adaptive X-ray mirror.
4. Experimental results and discussion
The online deformation processes are shown in Figs. 6(a) and 6(b), which correspond to the different ellipses under the grazing angles of incidence of 3.0 and 1.5 mrad, respectively. The black and red curves denote the residual shape errors before and after the final correction after modifying the applied voltages along the at-wavelength wavefront measurements, respectively. Through the online procedures, the shape errors of the two ellipses were improved from 20 nm PV to 3 nm PV and 32 nm PV to 7 nm PV, respectively. In both cases, Rayleigh’s quarter wavelength criterion was satisfied for operation with diffraction-limited characteristics. Figures 7(a) and 7(b) show focused beam profiles finally obtained with the two different ellipses. The blue circles show the profiles measured with the wire scanning method. The black and red curves show the calculated profiles for the ideal mirror shapes and actual shapes, respectively, using the measured shape errors shown by the red curves in Fig. 6. As can be seen in the profiles, the obtained beam sizes are 127 and 253 nm, which are in good agreement with the calculated sizes. In the case of the ellipse that is more steeply curved at a grazing angle of incidence of 3 mrad, the X-ray reflection image and intensity profile were recorded with an X-ray camera placed at the downmost-stream position. As can be seen in Fig. 8, excluding the mirror-edge regions, significant speckles related to the junction effect were not observed. This implies that the unnecessary mirror deformation near the gap between the piezoelectric plates is suppressed to negligibility. The alignment procedure took less than 15 min to change the mirror shape to a different ellipse. These results are due to the prior bending by the mechanical bender, which significantly reduces the role of the piezo-driven deformable mirror from the maximum deformation depth of several tens of micrometers to less than 100 nm. In summary, by using the hybrid deformation mechanism, the long deformable mirror can achieve diffraction-limited operation.
Fig. 6 Online deformation performance of the adaptive X-ray mirror. The black and red lines show the shape error before and after the final online modification, respectively, using the X-ray pencil-beam scan method. The grazing angles of incidence of the adaptive X-ray mirror are (a) 3.0 and (b) 1.5 mrad.
Fig. 7 Intensity profiles of the focused beam at the grazing angles of incidence of (a) 3 and (b) 1.5 mrad.
Fig. 8 X-ray reflection image with the X-ray camera and intensity profile along the red line in the image. The glazing angle of incidence employed here is 3 mrad.
5. Conclusions
In this study, we developed a hybrid adaptive focusing mirror based on a combination of a mechanical mirror bender and piezo-driven deformable mirror to realize a deformable mirror with a length of 400 mm. Long-length mirrors can meet the requirements necessary for long working distances, usage of high-photon-energy X-rays, and reduction of radiation damage to the mirror surface, among others. We also demonstrated precise shape generation, which satisfied Rayleigh’s quarter-wavelength criterion, and achieved focal spot sizes of 127 and 253 nm at different numerical apertures. The drift of the mirror shape has been tested using the X-ray pencil-beam scanning method and found to be less than PV 0.4 nm/h. The possible deformation depth of the mirror is limited by the maximum tensile stress on the mirror surface. These results can lead to the realization of adaptable optics working under diffraction-limited conditions in next-generation X-ray sources.
Funding
JSPS KAKENHI (JP16H06358), JSPS KAKENHI (JP23226004), JSPS Fellow (JP15J00656), the CREST project of JST, and the JSPS Core-to-Core Program on International Alliance for Material Science in Extreme States with High Power Laser and XFEL.
Acknowledgments
The use of BL29XUL at SPring-8 was supported by RIKEN. This research was partially supported by the General Proposal Program of SACLA (Proposal Nos. 2016B8010, 2016B8017, and 2017A8033).
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