Open Access
Add to BibSonomy
Abstract
The hard X-ray nanoprobe beamline is the first beamline to take advantage of the full coherent beam to attain the nanoscale focusing at the Shanghai Synchrotron Radiation Facility (SSRF). Here we introduce the beamline and specially go over the features of the multilayer Kirkpatrick-Baez focusing system and its supporting phase compensator system. The performance and stability of the phase compensator are also put to the test. By using the speckle scanning metrology, the wavefront of a focused beam was characterized and intensity distribution near the focus was reconstructed. The focusing performance was greatly enhanced by two phase compensations based on a global optimization technique, and a two-dimensional focal spot of 26 nm × 17 nm was achieved and maintained with good stability.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
It is well known that at the nanoscale, quantum confinements and interfacial effects lead a substance to exhibit a variety of unique properties that are distinct from those of macroscopic objects. The promotion of technological advancements is currently being led by nanotechnology in the sectors of information, energy, materials, environment, and biomedicine. The importance of X-ray nanofocusing and nanoimaging techniques on synchrotron radiation and free-electron laser devices has been intensively stressed to meet the requirement of nanoscale research. It makes it possible to see and examine materials at the atomic level, giving important information about their composition and structure. It also makes it possible to investigate the growth processes, crystal or interfacial structures, non-linear phenomenon and other properties of nanostructures such nanoparticles, nanocrystals, and thin films. In order to develop novel medications and treatments, it is capable of visualizing cellular structures, proteins, and viruses. With the development of next-generation advanced coherent light sources, the demand for ultra-high spatial resolution and ultrafast temporal resolution has also elevated the scientific significance of X-ray nanofocusing with ultra-high coherent flux density to a new stage.
Based on the broad applications of X-ray nanofocusing systems, researchers have been optimizing the focusing systems to achieve an ultra-small spot size, so that the important information such as elements, structures and atomic coordination of samples in a very small area can be obtained on the basis of ensuring high flux density. The spot size of a focusing system generally depends on the demagnification of the system and the size of the light source, but it has a theoretical diffraction limit and cannot be lowered indefinitely. Since practically in the hard X-ray regime, the refractive index 1-δ of almost all materials is close to unity, it is challenging to use the traditional refractive focusing method. In the past few decades, many hard X-ray focusing elements have been developed, including diffractive, refractive and reflective elements. Diffractive elements include Fresnel zone plate (FZP) [1], multilayer Laue lenses (MLL) [2], etc. Refractive elements include composite refractive lenses [3], Kinoform lenses [4], etc. Reflective elements include Kirkpatrick-Baez (K-B) focusing mirrors [5], ellipsoidal mirrors [6] and other focusing mirrors with different curved surfaces [7,8], polycapillaries [9], waveguides [10], and microstructured optical arrays [11]. The diffractive elements suffers from very limited aperture and working distance, while the refractive elements suffer from high absorption. In comparison, the significant advantage of reflective elements lies in increased aperture and reduced photon flux loss. It's easy to notice that only a small number of elements can successfully achieve the focal spot size at the nanoscale due to their focusing abilities and processing challenges. As seen in Fig. 1, we outline the key nanofocusing achievements made possible by various focusing optics over the past 15 years. The underlined cases represent the performances of current main synchrotron radiation nanoprobe beamlines.
The K-B mirror focusing system consists of two usually orthogonal grazing incidence mirrors. By combining two mirrors with the appropriate curvature and alignment, the X-rays can be focused down to a spot size approaching the diffraction limit and widely used as the two-dimensional nanofocusing system in synchrotron radiation facilities [12]. The grazing incidence angle of mirror θ is smaller than the critical angle of total reflection θc = 2δ of the coating materials and the incident X-ray beams can be reflected without chromatic aberration below the cut-off energy, but the total-reflection angle limits the numerical aperture (NA) of the focusing system. Over the years, one important development is the deposition of multilayer coatings onto the mirror. These coatings consist of alternating layers of low and high atomic number materials, which enhance the X-ray integrated reflectivity. Multilayer coatings can be optimized for different X-ray energies, enabling the system to achieve a better focusing performance by enlarging numerical aperture about 3-10 times of the total-reflection case [13]. Since multilayer focusing mirror is a quasi-monochromatic element, focusing condition can be satisfied only in the bandwidth (Δλ/λ ≈ 10−2) of a specific wavelength, where λ is the wavelength. The main constraints on the diffraction-limited focusing performance of K-B mirrors come from the mirror surface polishing processing technology. In 2005, the researchers from the Advanced Photon Source (APS) used differential polishing technology to prepare a short-focal-length K-B mirror focusing system and obtained the focal spot of 85 nm × 95 nm [14]. In the same year, researchers from the Osaka University produced an ultra-high-precision K-B focusing mirror with a peak-to-valley (PV) surface shape error of 2 nm, and realized a two-dimensional diffraction-limited focusing with a spot size of 36 nm × 48 nm under the energy of 15 keV [15]. In 2010, Mimura et al. combined a gradient multilayer K-B mirror with a grazing-incidence phase compensater to realize a two-dimensional focal spot size of 7 nm × 8 nm [16,17]. In 2015, researchers from the Taiwan Photon Source (TPS) used a Montel-type K-B focusing mirror to realize a two-dimensional focusing of 40 nm × 40 nm at the energy of 10 keV [18]. In 2016, the scientists from the European Synchrotron Radiation facility (ESRF) processed two fixed-faceted multilayer K-B focusing mirrors, and realized two-dimensional focusing of 23 nm × 37 nm and 27 nm × 21 nm at the energies of 17 and 33.6 keV, respectively [19]. Recently, researchers from the Osaka University used multilayer advanced K-B focusing system to obtain a focal spot of 5.8 nm in the vertical direction [20] and two-dimensional focusing of 6.5 nm × 6.9 nm [21] at the SACLA free-electron laser device.
However, it is worth noting that the surface polishing process of mirrors is close to the limitation so that it becomes very difficult to further improve their focal spot size. Focusing under diffraction-limited conditions places severe demands on the wavefront error Δψ. In order to maintain a perfect coherent wavefront, the wavefront error caused by various optical components needs to satisfy Rayleigh’s quarter-wavelength criterion of less than 1/4 (PV) of the wavelength. For focusing mirrors, the relationship between the wavefront error Δψ and the mirror unintended height error Δh is $\Delta \psi = 4\pi \Delta h\sin \theta /\lambda \le \pi /2$. In order not to destroy the beam coherence, the height errors of the focusing mirror with a large NA need to be controlled to smaller than 1 nm (PV) or even 0.5 nm which can not be achieved by the current polishing technique. More unpredictable surface errors will also be introduced due to the bending, clamping, or mounting of the mirror. In this case, the addition of phase compensation becomes a research hotspot. Static compensation of mirrors is performed by adding material (deposition, ion implantation) or reducing material (sputtering, etching) to create an opposite wavefront error. Active or adaptive phase compensation is another major way to realize the correction of the low- and medium- frequency wavefront error. There are various forms of active phase compensation mirrors for X-rays, including piezoelectric [22], magnetic [23], and heater [24] deformable mirrors which are widely used in the synchrotron radiation field. Piezoelectric deformable mirrors are specialized optical devices used to correct and manipulate X-ray wavefronts, commonly containing at least three parts, i.e., a mirror, piezoelectric ceramics and actuation mechanisms. Common ceramics include lead zirconate titanate (PZT) or lead magnesium niobate-lead titanate (PMN-PT). The piezoelectric ceramics and actuators are often pasted on the front, back, or side of the mirror. When an electric voltage is applied to the piezoelectric ceramic, a stretching effect occurs in the ceramic along the length of the mirror, allowing for deformations of the mirror body and producing concave or convex localized characteristics. The actuation mechanism consists of individual piezoelectric elements arranged in an array or several columns. Each element can be independently controlled to induce the desired deformation in the mirror surface. Typically, a closed-loop feedback control system is employed to achieve accurate wavefront correction. The relationship between the curvature of the piezoelectric deformation mirror surface shape and voltage is ${R_{\textrm{mirror}}} = {h^2}/({\beta {\textrm{d}_{31}}V} )$ [25], where h is the thickness of the deformation mirror, β is the constant related to the material of the deformation mirror, d31 is the piezoelectric constant of ceramics along the mirror length, and V is the input voltage. The curvature change caused by a change in unit voltage is called the piezoelectric response function (PRF). Bimorph or monomorph piezoelectric deformable mirrors have been widely used in prefocusing mirror and micro- and nano-focusing systems at beamlines. It is crucial for achieving optimal focus and minimizing aberrations. In the field of nanofocusing, the most successful example of the active compensation technique is that the scientists from Osaka University have achieved an ideal sub-10 nm focal spot by intervening a phase compensation mirror upstream of high-precision multilayer K-B mirrors to correct the wavefront errors [16]. Since the phase compensater works below the total-reflection angle, the tolerance of mirror processing is much greater than that of multilayer K-B mirrors. Through the phase compensation mirror such a slightly-lower-precision mirror can be highly accurate to compensate the downstream K-B mirror error and ultimately obtain the size of the spot for 7 nm. Matsuyama [26] used four piezoelectric deformation mirrors to obtain near-diffraction-limited focusing with variable spot size in the range of 0.1-1.4 µm.
About ten years ago, the design report of the nanoprobe beamline at the Shanghai Synchrotron Radiation Facility (SSRF) was reviewed. Over the years, the beamline has performed pre-research, construction, and commissioning. We developed a multilayer K-B nanofocusing system combined with a total-reflection phase compensater to achieve a diffraction-limited focusing. The paper reports the detailed design of our X-ray nanofocusing system and presents the initial focusing test results.
2. Nanoprobe beamline of SSRF
2.1 Beamline layout
The hard X-ray nanoprobe beamline at the SSRF was designed and constructed to explore cutting-edge scientific fields with nanometer spatial resolution. The beamline works in two modes of operation, high flux and high energy resolution modes, by switching the double multilayer monochromator (DMM) and double crystal monochromator (DCM). Ru/C and Ni/C multilayer stripes are switched for use, respectively, in 8.3-25 keV and 5-8.3 keV. The mircostructure and optical performance of multilayers under high thermal load and low temperature environment were investigated in previous studies [27,28]. The layout of the beamline can be found in Fig. 2(a), and the basic beamline design was presented in our previous paper [29]. The beamline adopts a two-stage focusing method by inserting a secondary source aperture (SSA, S3) at the focus of the prefocusing toroidal mirror that is 53 m downstream of the source.
Fig. 2. (a) Beamline layout of hard X-ray nanoprobe beamline at the SSRF. (b) Mechanical design sketch of the multilayer K-B focusing system.
The experimental hutch is a satellite building that is outside the storage ring building. The total-reflection K-B focusing system and the multilayer K-B focusing system are respectively settled at ∼125 m and ∼130 m downstream of the U20 undulator source. The total-reflection K-B focusing system would be removed from the beamline when the multilayer K-B focusing system is in use. The phase compensation system is located 2 m upstream of the multilayer K-B focusing system, as seen in the mechanical design sketch of Fig. 2(b). In order to ensure that the beam entering the multilayer K-B focusing system is fully coherent and meets the spatial coherence conditions, the size D of SSA is used to restrict the passage of the coherent beam by a more rigorous relationship $D \le \lambda L/4a$, where L is the distance between the SSA and the focusing mirror and a is the aperture of the focusing system. The multilayer K-B focusing mirror is used at a photon energy of 10 keV, and the size of SSA is about 40 µm × 11 µm.
2.2 Multilayer K-B focusing mirror system
The high-NA multilayer K-B mirrors with a steeply curved surface work at an energy of 10 keV. The ideal surface shape of multilayer K-B mirrors is an elliptic cylinder with the variable radii of curvature of a few meters. The numerical aperture satisfies $2NA \approx 4/3{\theta _0}$, where ${\theta _0}$ is the grazing incidence angle at the mirror center. For a one-dimensional nanofocusing system, the one-dimensional diffraction limit satisfies $s = \lambda /2NA = 3\lambda /4{\theta _0}$. If the goal spatial resolution is 10 nm, the calculated central grazing incidence angle of the mirror is 9.3 mrad. In order to make both ends of the mirror meet the spatial resolution, the grazing incidence angle should be appropriately enlarged, and the final design value of the central grazing incidence angle was set at 10.5 mrad and refer to Figs. 3(a) and (b) for more details. The substrate material is single-crystal silicon, and the surface accuracy needs to reach 1 nm (PV) to meet the requirements of coherent X-ray focusing. The mirror surface adopts a precise gradient thickness multilayer coating process to ensure the final surface accuracy. Some gold layers were deposited on top and side surfaces as the reflective surfaces for laser feedback to positioning the mirrors. The Ru/C multilayer K-B mirrors including the substrate were fabricated by JTec Company. The inspection based on the relative angle determinable stitching interferometry (RADSI) showed that the PV figure errors of substrates for VFM and HFM are respectively 0.99 ± 0.05 nm and 0.97 ± 0.04 nm, as seen in Fig. 3(c). The multilayer structures were characterized by the grazing incidence reflectivity technique, and the comparison of the measured and theoretical periodic thicknesses is shown in Fig. 3(d). The micro-roughness was measured by Zygo NewView (50×) and take the average of ten regions (0.14 mm × 0.11 mm) as the result. The specifications and test results of the multilayer K-B mirrors and substrate are listed in the Table 1.
Fig. 3. The mirror shape and the grazing incidence angle for (a) VFM and (b) HFM, (c) the metrology on VFM and HFM and (d) the periodic thickness of multilayers measured by grazing incidence reflectivity technique.
Table 1. The specifications and test results of vertical (VFM) and horizontal (HFM) focusing mirrors of the multilayer K-B focusing system and phase compensator mirror (PCM)
For a nanofocusing mirror, the focal spot size is modulated by three parts: demagnification, diffraction limit and wavefront errors and can be expressed as
where sde is the spot size calculated based on the demagnification, sdi is the diffraction limit and Δs is the spot broadening resulted from the mirror shape errors, other wavefront error from upstream optics and beam or mechanical vibrations. Based on the first two terms in the root sign, the theoretical minimum spot of the focusing mirror in this direction can be calculated. As can be seen in Fig. 4, the theoretical minimum spot size at the size of SSA of 40 µm × 11 µm is 10.52 nm in each direction. To approach the theoretical minimum spot, minimizing the spot broadening as much as possible is a key issue that needs to be addressed in the focusing system.Fig. 4. Theoretical minimum spot sizes as the function of aperture sizes in horizontal and vertical directions.
The K-B manipulators were designed based on the high-rigidity flexible hinges. Flexible hinges are different from the traditional spring mechanisms in that they have the advantages of no friction, light weight, high accuracy, and high reliability. In recent years, flexible hinges have been widely used in the field of nanopositioning of synchronous radiation facilities [30]. The VFM manipulator has two motion degrees of freedom, pitch angle and in/out of beam in the vertical direction. The HFM manipulator adopts an inverted design, with four degrees of motion including pitch angle, roll angle, in/out of beam in the horizontal direction and astigmatism adjustment along the beam propagation direction. All mechanisms are driven by piezoelectric motors. The manipulator and chamber of K-B mirrors were designed to minimize possible vibration and thermal drift. The vacuum of the chamber is better than 10−4 pa. Figure 5 shows the photographs of the whole K-B focusing system.
Fig. 5. The photographs of multilayer K-B focusing mirror system: (a) back view and (b) forward view.
2.3 Phase compensation system
The low-frequency figure errors broaden the focal spot, and higher-frequency figure errors produce sidelobe peaks far from the focused beam spot [29]. Large PV figure errors obviously decrease the focusing intensity. An additional total-reflection phase compensator is significantly necessary to correct the figure errors from the vertical focusing mirror and compensate the low- and medium-frequency wavefront errors from all upstream optics. The focusing system refers to the basic design and demo experiments from Osaka University [16,17].
The material of piezoelectric ceramics is PZT, and piezoelectric ceramics were symmetrically distributed on both sides of the long edge of the mirror surface and bottom. The size of each PZT is 150 mm × 15 mm × 1 mm. The electrode material is nickel. On each side, 18 pairs of electrodes were deposited at 0.5 mm intervals on the mirror surface, and the size of each electrode is 7.86 mm × 15 mm, as shown in Fig. 6(a). The 20th pair of electrodes was deposited on both sides of PZT materials. 20 independent voltages are output for controlling the electrodes driving the deformation of piezoelectric ceramic. The direct-current voltage range on PZT is from 0 to 1000 V. The 19th pair of electrodes is the cathode that connects to conductive adhesive between the PZT and substrate and its voltage is always set to 500 V. The actual voltages applying to PZT elements are the voltage differences between the surface electrodes (channels 1-18) and the intermediate electrode (channel 19). The PZT element deforms according to these voltages and bends the mirror. The resolution of voltage is better than 0.05 V. A sophisticated control system is required to manipulate the mirror surface shape to approach a target figure. This system receives the feedback from the wavefront sensors, and based on the measured wavefront errors, it adjusts the voltages applied to the piezoelectric elements. Advanced surface measurement and feedback algorithms and control techniques are employed to optimize the correction process. The phase compensator system mounted in the chamber can be seen in the photograph of Fig. 6(b).
Fig. 6. (a) The photograph of the mirror, (b) photograph of the phase compensator system and (c) mechanism model.
Figure 7(a) presents the piezoelectric response functions (PRF) of 18 small electrodes of the phase compensator measured by a Fizeau interferometer (Zygo VeriFire). The measured PRFs are similar to the simulated functions based on ANSYS analysis. The details of the simulation can be found in our previous study [31]. Figure 7(b) compares the full width at half maxima (FWHMs) and Fig. 7(c) compares the central positions of the measured and the simulated PRFs of the deformable mirrors. The central positions present good linearity, and the measured FWHM reveals a wider covering area of each electrode, about three electrodes.
Fig. 7. (a) The measured PRF of the phase compensator compared with the simulation results. Comparison of (b) the FWHMs and (c) the central positions of the measured and the simulated PRFs of the deformable mirrors.
Figure 8(a) shows the shape change of the phase compensator with the holder in 50 minutes. The mirror shape remained basically stable. Figure 8(b) shows the mirror height changes on the 1st, 3rd, 5th, 7th and 9th electrodes in 450 minutes when the voltage applied to all the electrodes was kept at 200 V measured by the Fizeau interferometer. The results reveal that a slight convex shape of several tens of nanometers was gradually generated, and the piezoelectric ceramics trended to shrink for a long time.
Fig. 8. (a) The stability of the height of phase compensator with holder in 50 minutes and (b) the height drifts of 1st, 3rd, 5th, 7th and 9th electrodes in 450 minutes when 200 V were applied to all electrodes.
The phase compensator was fixed into a holder, and then the holder was mounted on a manipulator. The manipulator of the phase compensator was designed and made by the Cinel company, as seen in Fig. 6(c). It can adjust the mirror in the dimensions of pitch, in/out of beam, stripe change, and roll (manual). The specifications and test results of the phase compensator and manipulator are listed in Tab.1. The first eigenfrequency of the phase compensator is around 98 Hz. An active control system made by the CAENels company, named Beamline Enhanced Stabilization Technology (BEST), based on the encoder readout of pitch angle was used to continuously monitor and correct the mirror pitch positions. This allows for robust performance and long-term stability of the mirror system.
Figures 9(a)-(c) present the open-loop pitch angle vibration results tested by the encoder as well as real-time temperature and humidity measurement across three days. The results demonstrate a substantial correlation between pitch angle values and temperatures. Every 0.1 degrees Celsius temperature drift causes an pitch angle drift of ∼900 nrad. The main environmental vibrations, according to the spectrum analysis, are at 0.3, 0.9, and 2.1 Hz. However, when the BEST was used to achieve closed-loop feedback of pitch angle, the low-frequency vibrations were clearly eliminated, as seen in Figs. 9(d) and (e). With and without the argon environment, the root mean square (rms) vibration of the pitch angle of the phase compensator in the chamber was 32.1 nrad and 8.2 nrad, respectively.
Fig. 9. (a) The relationship between the (a) open-loop pitch angle vibration, (b) temperature and (c) humidity. The closed-loop pitch angle vibrations during (d) 12 hours and (e) 0.1 hours.
2.4 Closed-loop feedback process
A full closed-loop feedback mechanism for phase compensation consists of three components: measurement, compensation, and monitoring, as seen in Fig. 10. The wavefront of the focused beams must first be measured. Based on the measured wavefront, the intensity profiles at the focus can be reconstructed. If the focusing spot size is not acceptable, an iterative technique will be employed to estimate the voltages supplied to all electrodes [31]. The piezoelectric ceramics then force the mirror to distort to a target shape. The Fizeau interferometer measures the actual distortion of the mirror shape. The preceding outlines the complete compensation process at once. Another wavefront test will be performed to confirm the effectiveness of phase adjustment. If the outcome is not satisfactory, additional compensation procedures will be implemented.
3. Speckle scanning metrology and focal spot reconstruction
3.1 Experimental layout
Figure 11(a) shows the layout of the hard X-ray nanofocusing system. A Fizeau interferometer was put on the phase compensator to monitor the mirror shape in real time. The reference mirror (λ/50) of the interferometer was inserted into the chamber of the phase compensator. Argon gas filled the chamber to protect the coating on the phase compensator. Figure 11(b) shows the photography of the phase compensator system. The K-B mirror system and the sandpaper manipulator were put into a vacuum chamber, as seen in Figs. 5. The sandpaper with a high-precision manipulator is located downstream of the focus.
Fig. 11. (a) Layout diagram of the hard X-ray nanofocusing system and the upper left small image shows the distribution of divergent focused beams and direct beam recorded in the far field; (b) the photograph of the phase compensation system.
The high-resolution detection system, a microscope objective lens system (Optique Peter) with a magnification of 2, coupled to a CMOS camera (Hamamatsu), was placed at 0.25 m downstream of the focus. The effective pixel size of the detector was p = 0.325 nm. The sandpaper was located at d = 0.245 m upstream of the detector and moved along the scanning direction with a step of 200 nm.
The photon flux was measured by using OKEN ionization chamber. The length of the ionization chamber electrode plate is 1880 mm, with a high voltage of 3 kV. For the flux measurement, the ionization chamber replaced the high-resolution detection system. After the gas in the ionization chamber was ionized by incident X-ray photons, the generated current was amplified by an amplifier and converted into a voltage signal.
3.2 Speckle scanning metrology
The local wavefront radius of curvature at the detector plane was acquired by in-situ speckle scanning metrology [32]. As can be seen in Fig. 12(a), a series of speckle patterns were collected, and the digital image correlation (DIC) method [33] was used to calculate the speckle displacement Δs between two stitched images, respectively, stitched from the ith and jth rows of these speckle patterns (Fig. 12(b)). Our group has developed the related method based on speckle [34,35] and analyzed the influence of experimental [36,37] and algorithm parameter choices [38]. Based on the speckle displacement calculated by DIC, the local wavefront curvature can be written by the following relation [32]:
where i and j are two different rows of speckle pattern, and Δτ is the speckle displacement. As is well known, the slope of the wavefront is twice that of the mirror. So the relationship between the curvatures of the mirror and the wavefront is ${C_{\textrm{mirror}}} = 0.5\sin \theta C$. The feedback process of a phase compensation system is based on a global optimization method [31]. Based on the wavefront radius of curvature acquired, the voltages to different actuators were calculated by the PRF of the phase compensator, as seen in Fig. 6, for wavefront compensation.Fig. 12. (a) The speckle pattern recorded in the detector plane and (b) two new speckle images stitched from the ith and jth rows of these sampled speckle patterns.
The essence of the deviation in the wavefront curvature is out of focus, and according to geometric relationships, the local broadening of the focal spot satisfies
where η is defined as the error of the offset in the experiment and s is the focal spot size. The error of this measurement system mainly includes algorithm error, sandpaper vibration error, etc. We adopt a subpixel algorithm based on a multi-point fitting algorithm, with an algorithm error of better than 0.025. The vibration amplitude of the sandpaper is about 1.7 nm with an error of the offset of 0.008. Based on error analysis, the total error η = 0.026.3.3 Focal spot reconstruction
The inverse Fresnel diffraction-based intensity propagation was used to reconstruct the intensity distribution near the focal spot [39,40]. The complex amplitude near the focus can be expressed as:
3.4 Photon flux test
The number of X-ray photons absorbed by the ionization chamber N, was determined by the incident X-ray photon flux N0, and the gas's absorption coefficient µ and the length of the ionization chamber plate l:$N = {N_0}(1 - {e^{ - \mu l}})$. Considering the relationship between the voltage and absorbed X-ray photons ${V_{\textrm{ion}}} = MNE\textrm{e}/\varepsilon$,where M is the gain of current amplifier, photon energy E, average ionization energy of gas molecules ε∼34.42 eV and the electron charge e, the incident X-ray photon flux N0 can be estimated by the formula:
4. Results
The wavefront radii were measured using the speckle scanning technique. Based on Eq. (3), the intensity distribution near the focus can be calculated. The goal mirror shape and its accompanying voltage values can be produced using a specific iterative global optimization procedure that considers the coupling effect of PRFs of various actuators described in the previous article [31]. New voltages can be applied to cause mirror deformation, and the mirror shape can be verified using the Fizeau interferometer located above. The new wavefront radii can be measured again after the initial optimization. A satisfactory focused spot can be obtained by testing the focus performance twice through iterative methods.
The wavefront radius is shown in Fig. 13(a) before and after two optimizations. The oscillation of the radii is greatly minimized. Figure 13(b) clearly compares the frequency signals of the wavefront radii. The phase compensation has a strong corrective effect on the medium frequency wavefront error. Figure 14(a) compares the residual curvature errors of the mirror after two optimizations. Although the phase compensator cannot completely correct the visible curvature oscillations recorded as the incident-beam wavefront curvature error [41], the lower-frequency alterations have been compensated. The final applied voltages after two optimizations are shown in Fig. 14(b).
Fig. 13. (a) Comparison of the wavefront radii before and after phase compensation and (b) their frequency distribution.
Fig. 14. (a) The residual curvature error and twice compensation approaching; (b) the final applied voltages of different actuators.
Figure 15(a) compares the central height profiles before and after two optimizations, and Fig. 15(b) presents the two-dimensional mirror surface measured by the Fizeau interferometer. The optimization procedure of the intensity distribution near the focus can be readily seen in Fig. 16. The separate focal spots converged dramatically into a single focus. Figure 17(a) compares the intensity profiles at the focal plane for VFM before and after phase compesations, while Fig. 17(b) records the intensity profile at the focal plane for HFM. For VFM, the intensity at the focus visibly increases, whereas the number and intensity of sidelobe peaks is greatly reduced. Because practically all of the beamline optics are horizontally deflecting, the more severe incident-beam wavefront curvature error compared to the vertical direction causes the focus to be more dispersed for HFM. The measured two-dimensional focal spot size was 26 nm × 17 nm. When the beam position at the secondary source slit is steady, the measured wavefront curvatures have strong measured repeatability, with an rms error of 0.3% in one hour and an rms error of focal spot size less than 1.0%.
Fig. 15. (a) The measured heights of phase compensator at the central line before and after deformations by Fizeau interferometer; (b) the measured surface after 2nd compensation by Fizeau interferometer.
Fig. 16. The intensity distribution near the focus reconstructed by inverse Fresnel diffraction based on the measured radius of curvatures (a) before, (b) after 1st compensation and (c) after 2nd compensation. The vertical axis is the vertical direction perpendicular to the beam.
Fig. 17. The intensity profiles at the focus (a) before and after phase compensation in the vertical direction and (b) in the horizontal direction.
Due to the ionization chamber being placed in the atmosphere, it is necessary to consider the influence of atmospheric absorption (transmittance of 78.5%) and beryllium window (thickness of 500 µm, transmittance of 94.2%) on the X-ray photon flux. The actual photon flux gathered into that focal spot is 1.94 × 109 phs/s@200 mA and the flux density is 4.4 × 106 phs/s/nm2@200 mA.
When the wavefront performances of VFM and HFM are compared, the main difference is caused by the incident-beam wavefront curvature errors, which result in a distorted and broadened focus in the horizontal direction. Considering the positions where these oscillations of wavefront curvature occur are consistent with the stripe [42] positions recorded on the detector, and combined with similar records from previous studies [41], it can be determined that these errors come from the optics before the secondary source, i.e., pre-focusing mirror and multilayer monochromators. Because all mirrors deflect horizontally, this explains why the oscillations in the horizontal direction are more pronounced than the oscillations in the vertical direction. According to the results, it can be seen that the phase compensation in the vertical direction has a very large improvement effect on the focal spot size, peak shape, and focused flux. In the future, phase compensation in the horizontal direction will also be required to compensate for incident-beam wavefront curvature errors. To steady the beam at the secondary source slit, a higher-resolution feedback mechanism must be devised. Intelligent system calibration and wavefront characterization methods are being developed to quickly achieve stability of the focusing system [43]. A two-dimensional focal spot close to 10 nm is also a significant future target to pursue.
5. Conclusion
We report the current state of the nanoprobe beamline at the SSRF, as well as the design and testing of the X-ray focusing system, in this paper. The beam wavefront was characterized using the speckle scanning technique. To address the wavefront errors, a phase compensator system was created. The vertical focusing performance was considerably improved by applying iterative global optimization. The reconstructed intensity distribution around the focus demonstrates that the first stable focal spot size of 26 nm × 17 nm at 10 keV photon energy was reached.
Funding
National Natural Science Foundation of China (12175294, 12235011); National Key Research and Development Program of China (2023YFA1608600); Natural Science Foundation of Shanghai (21ZR1471500).
Acknowledgments
Authors thank Hua Wang, Yuzhu Wang, Naxi Tian, Shuai Yan and other scientists and engineers from SSRF for help testing the focusing and useful discussions. We thank Professor Kazuto Yamauchi from Osaka University for kindly discussions in the design of nanofocusing system. We are also grateful to Hongchang Wang from Diamond light source, Qiushi Huang, Shengzheng Yi from Tongji University and Guangcai Chang from the Institution of High Energy Physics for giving suggestions in focusing optics and speckle-based metrology.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
References
1. Y. Suzuki, A. Takeuchi, H. Takano, et al., “Diffraction-limited microbeam with Fresnel zone plate optics in hard X-ray regions,” Jpn. J. Appl. Phys. 40(3R), 1508–1510 (2001). [CrossRef]
2. H. C. Kang, J. Maser, G. B. Stephenson, et al., “Nanometer linear focusing of hard X rays by a multilayer Laue lens,” Phys. Rev. Lett. 96(12), 127401 (2006). [CrossRef]
3. A. Snigirev, V. Kohn, I. Snigireva, et al., “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996). [CrossRef]
4. H. Yan, “X-ray nanofocusing by kinoform lenses a comparative study using different modeling approaches,” Phys. Rev. B 81(7), 075402 (2010). [CrossRef]
5. P. Kirkpatrick and A. V. Baez, “Formation of optical images by X-rays,” J. Opt. Soc. Am. 38(9), 766–774 (1948). [CrossRef]
6. H. Yumoto, T. Koyama, S. Matsuyama, et al., “Ellipsoidal mirror for two-dimensional 100-nm focusing in hard X-ray region,” Sci. Rep. 7(1), 16408 (2017). [CrossRef]
7. A. Elliott, “The use of toroidal reflecting surfaces in X-ray diffraction cameras,” J. Sci. Instrum. 42(5), 312–316 (1965). [CrossRef]
8. C. Sparks Jr, G. E. Ice, J. Wong, et al., “Sagittal focusing of synchrotron x-radiation with curved crystals,” Nucl. Instrum. Methods Phys. Res. 195(1-2), 73–78 (1982). [CrossRef]
9. D. Bilderback, S. Hoffman, and D. Thiel, “Nanometer spatial resolution achieved in hard X-ray imaging and Laue diffraction experiments,” Science 263(5144), 201–203 (1994). [CrossRef]
10. S. Lagomarsino, W. Jark, S. Di Fonzo, et al., “Submicrometer X-ray beam production by a thin film waveguide,” J. Appl. Phys. 79(8), 4471–4473 (1996). [CrossRef]
11. A. Michette, S. J. Pfauntsch, S. Sahraei, et al., “Active microstructured X-ray optical arrays,” Proc. SPIE 7360, 736007 (2009). [CrossRef]
12. W. Liu, G. Ice, L. Assoufid, et al., “Achromatic nested Kirkpatrick-Baez mirror optics for hard X-ray nanofocusing,” J. Synchrotron Rad. 18(4), 575–579 (2011). [CrossRef]
13. J. Underwood and T. Barbee, “Layered synthetic microstructures as Bragg diffractors for X-rays and extreme ultraviolet theory and predicted performance,” Appl. Opt. 20(17), 3027–3034 (1981). [CrossRef]
14. W. Liu, G. Ice, J. Tischler, et al., “Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe,” Rev. Sci. Instrum. 76(11), 113701 (2005). [CrossRef]
15. H. Mimura, S. Matsuyama, H. Yumoto, et al., “Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors,” Jpn. J. Appl. Phys. 44(4L), L539–542 (2005). [CrossRef]
16. H. Mimura, S. Handa, T. Kimura, et al., “Breaking the 10 nm barrier in hard-X-ray focusing,” Nature Phys. 6(2), 122–125 (2010). [CrossRef]
17. K. Yamauchi, H. Mimura, T. Kimura, et al., “Single nanometer focusing of hard X-rays by Kirkpatrick-Baez mirrors,” J. Phys.: Condens. Matter 23(39), 394206 (2011). [CrossRef]
18. G. Yin, S. Chang, B. Chen, et al., “Hard X-ray nanoprobe by Montel K-B mirrors at Taiwan Photon Source,” Proc. SPIE 9592, 959204 (2015). [CrossRef]
19. R. Barrett, R. Baker, P. Cloetens, et al., “Reflective optics for hard X-ray nanofocusing applications at the ESRF,” Synchrotron Radiat. News 29(4), 10–15 (2016). [CrossRef]
20. T. Inoue, S. Matsuyama, J. Yamada, et al., “Generation of an X-ray nanobeam of a free-electron laser using reflective optics with speckle interferometry,” J. Synchrotron Rad. 27(4), 883–889 (2020). [CrossRef]
21. J. Yamada, S. Matsuyama, I. Inoue, et al., “Ultimate condensation of hard X-ray free-electron laser reaching single-nanometre focus size and 1022 W/cm2 intensity,” Research SquareVersion 1 (2023). [CrossRef]
22. R. Signorato, “R&D program on multisegmented piezoelectric bimorph mirrors at the ESRF status report,” Proc. SPIE 3447, 20–31 (1998). [CrossRef]
23. C. Colldelram, N Gonzalez, J. Gonzalez, et al., “Adaptive optics bender with sub-nanometer correction and stability,” AIP Conf. Proc. 2054(1), 060013 (2019). [CrossRef]
24. D. Cocco, C. Hardin, D. Morton, et al., “Adaptive shape control of wavefront-preserving X-ray mirrors with active cooling and heating,” Opt. Express 28(13), 19242–19254 (2020). [CrossRef]
25. J. Susini, D. Labergerie, and L. Zhang, “Compact active adaptive X-ray mirror bimorph piezo electric flexible mirror,” Rev. Sci. Instrum. 66(2), 2229–2231 (1995). [CrossRef]
26. S. Matsuyama, H. Nakamori, T. Goto, et al., “Nearly diffraction-limited X-ray focusing with variable numerical-aperture focusing optical system based on four deformable mirrors,” Sci. Rep. 6(1), 24801 (2016). [CrossRef]
27. H. Jiang, W. Hua, N. Tian, et al., “In situ GISAXS study on the temperature-dependent performance of multilayer monochromators from the liquid nitrogen cooling temperature to 600°C,” Appl. Surf. Sci. 508, 144838 (2020). [CrossRef]
28. S. Yan, H. Jiang, H. Wang, et al., “Temperature-dependent thermal properties of Ru/C multilayers,” J. Synchrotron Radiat. 24(5), 975–980 (2017). [CrossRef]
29. A. Li, H. Jiang, H. Wang, et al., “Current status of the hard x-ray nanoprobe beamline at the SSRF,” Proc. SPIE 10389, 103890J (2017). [CrossRef]
30. D. Shu, W. K. Lee, W. Liu, et al., “Development and applications of a two dimensional tip tilting stage system with nanoradial level positioning resolution,” Nucl. Instrum. Methods Phys. Res., Sect. A 649(1), 114–117 (2011). [CrossRef]
31. H. Jiang, N. Tian, D. Liang, et al., “A piezoelectric deformable X-ray mirror for phase compensation based on global optimization,” J. Synchrotron Radiat. 26(3), 729–736 (2019). [CrossRef]
32. H. Wang, J. Sutter, and K. Sawhney, “Advanced in situ metrology for x-ray beam shaping with super precision,” Opt. Express 23(2), 1605–1614 (2015). [CrossRef]
33. B. Pan, K. Qian, H. Xie, et al., “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20(6), 062001 (2009). [CrossRef]
34. H. Jiang, S. Yan, N. Tian, et al., “Extraction of medium-spatial-frequency interfacial waviness and inner structure from X-ray multilayers using the speckle scanning technique,” Opt. Mater. Express 9(7), 2878–2891 (2019). [CrossRef]
35. H. Jiang, S. Yan, D. Liang, et al., “X-ray multilayer mid-frequency characterizations using speckle scanning techniques,” Proc. SPIE 10385, 25 (2017). [CrossRef]
36. N. Tian, H. Jiang, A. Li, et al., “Influence of diffuser grain size on the speckle tracking technique,” J. Synchrotron Radiat. 27(1), 146–157 (2020). [CrossRef]
37. N. Tian, H. Jiang, A. Li, et al., “High-precision speckle-tracking X-ray imaging with adaptive subset size choices,” Sci. Rep. 10(1), 14238 (2020). [CrossRef]
38. N. Tian, H. Jiang, L. Xue, et al., “Influence of photon beam and motor vibrations on at-wavelength X-ray speckle scanning metrology,” Front. Phys. 10, 864985 (2022). [CrossRef]
39. X. Huang, H. Yan, E. Nazaretski, et al., “11 nm hard X-ray focus from a large-aperture multilayer Laue lens,” Sci. Rep. 3(1), 3562 (2013). [CrossRef]
40. C. Kewish, P. Thibault, M. Dierolf, et al., “Ptychographic characterization of the wavefield in the focus of reflective hard X-ray optics,” Ultramicroscopy 110(4), 325–329 (2010). [CrossRef]
41. L. Hu, H. Wang, O. Fox, et al., “Two-dimensional speckle technique for slope error measurements of weakly focusing reflective X-ray optics,” J. Synchrotron Radiat. 29(6), 1385–1393 (2022). [CrossRef]
42. A. Rack, T. Weitkamp, M. Riotte, et al., “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synchrotron Rad. 17(4), 496–510 (2010). [CrossRef]
43. J. Xie, H. Jiang, A. Li, et al., “Deep learning for estimation of Kirkpatrick-Baez mirror alignment errors,” Nucl. Sci. Tech. 34(8), 122 (2023). [CrossRef]
