High-speed adaptive optics using bimorph deformable x-ray mirrors

Piezo-electric deformable “bimorph” mirrors¹ have been used for more than two decades to focus X-rays on many synchrotron radiation (SR) beamlines around the world. Almost 100 such mirrors have been manufactured over the past 20 years. In recent times, bimorph mirrors have also been utilized at free electron laser (FEL) sources. The tangential curvature of a bimorph mirror used on a typical X-ray beamline is only changed every few hours, days, or even weeks. This operation can take up to tens of minutes and often requires expert guidance if re-optimisation is needed. Following a large change in curvature, numerous metrology studies have shown that bimorph mirrors take more than 15 min to fully stabilize on the single-digit nanometre scale. This can cause the size and shape of the reflected X-ray beam to gradually drift. For these reasons, and historically due to the lack of demand from beamline users, the dynamic capabilities of “active” X-ray optics have not been exploited at synchrotrons. This is in stark contrast to the ultra-fast adjustments made to “adaptive” optics in other scientific fields. For example, in astronomy, aberrations caused by atmospheric turbulence are corrected in real-time, albeit at a reduced level of surface control compared to synchrotron X-ray mirrors.

However, many SR beamlines, especially those dedicated to macromolecular crystallography, now routinely analyze hundreds of samples per day. Such beamlines would greatly benefit from the ability to quickly modify the X-ray beam profile in only a few seconds to match to the size of small samples or to vary the illuminated region of larger samples. In the future, this requirement could potentially be further extended to rapidly change the size of the X-ray beam as small samples are raster scanned through the beam at 10’s of Hz.

The first study of the time-dependent behavior of a series of micro-focusing, deformable bimorph mirrors for synchrotron X-ray beamlines was performed recently using Fizeau interferometry in the Optical Metrology Lab at Diamond Light Source.² Two, novel “speedy” bimorph mirrors were developed by making improvements to their opto-mechanical holders. In conjunction with utilising a new high-voltage power supply, the magnitude of curvature drift after applying a large voltage shift to the piezo-electric actuators was significantly reduced compared to a traditional bimorph mirror [Fig. 1(a)]. The small amount of residual curvature drift, caused by piezo-electric creep, was found to be repeatable and could readily be minimized by applying small, dynamic, corrective voltage pulses to the bimorph’s electrodes. These innovations enabled the speedy bimorph mirrors to be repeatably driven quickly to a given curvature and then remain stabilized indefinitely without the need for continuous metrology feedback. Once installed on the Microfocus Macromolecular Crystallography (I24) beamline at Diamond, it was confirmed that the KB pair of speedy bimorphs could simultaneously focus the X-ray beam in the vertical and horizontal directions in less than 10 s.³ Of equal importance, compensating the piezo-electric creep ensured that the size of the X-ray beam remained stable for more than 1 h after making a major change [Fig. 1(b)]. This enables continuous “adaptive” shaping of the X-ray beam in almost real-time. It is hoped that such innovations could lead to significant technical improvements in how active X-ray optics are utilized by the scientific communities at SR and FEL sources.

Can X-ray bimorphs work even faster? If so, how much faster? What will be the limiting factor(s) for the maximum speed that can be attained whilst satisfying the stringent nanometer accuracy control required for shaping the optical surface? To investigate, we used three different metrology instruments, including a novel array of high-speed, nano-distance measuring sensors.

The bimorph mirror used for this proof-of-principle study was a decommissioned, first-generation, horizontal micro-focusing mirror (with piezoceramics glued behind the optical substrate), formerly installed on the I24 beamline at Diamond Light Source. As with many 1st generation bimorph mirrors, it exhibits the “junction effect:”⁴ a degradation of the optical surface caused by defects occurring post-production at each glued junction between adjacent piezoceramics. To resolve such issues, substrates can either be repolished at Thales-SESO (France) or replaced by a 2nd generation bimorph mirror.⁵ The old I24 HFM has a 240 mm long, fused silica substrate with 8 independent piezo-electric electrodes (Fig. 2). Two, metal coatings provide enhanced reflectivity at higher X-ray energies compared to the central, uncoated, fused silica region. The mirror can be tangentially bent from a radius of curvature of ∼125 m to >600 m by globally applying ±1500 V to all piezo-electric electrodes. This old, decommissioned bimorph does not have an optimized holder or soft wire connectors, which limits its dynamic performance over extended periods, as highlighted in our previous studies. However, for this study, these detrimental issues are advantageous as the optic has a more complicated time response to driving voltage variations.

Many bimorph mirrors at Diamond are controlled using high voltages provided by using an HV-Adaptos bipolar power supply from CAEN (Italy). Over the past few years, we have worked closely with CAEN and Riccardo Signorato (S.RI. Tech) to help improve the software and enable efficient and fast communication via EPICS (the open-source control system used by all of Diamond’s beamlines). For this specific work, the HV-Adaptos was reprogrammed and extra features were added by Matteo Fusco and others at CAEN to create faster, user-defined voltage pulses. Dynamic voltages as a function of time were read in from a file and simultaneously applied to all electrodes of the mirror at a given time. Voltage shifts with a resolution of 0.1 V are now possible at a refresh rate of 1 Hz. Further programming at the firmware level is necessary to output voltages more rapidly, although the onboard electronics are inherently capable of providing a dynamic voltage output at a refresh rate of 100’s of Hz.

Our previous study of the dynamic bending effects of bimorph X-ray mirrors using ex situ metrology instruments was limited to a few seconds per measurement by the acquisition rate of the MiniFiz150 Fizeau interferometer (∼10 s per 4 scans averaged together). Although the Diamond-NOM (Nanometre Optical Metrology) slope profiler⁶ has sub-nm measuring capabilities and enhanced mechanical and thermal stability for reliably measuring over extended periods of time, its acquisition rate of several minutes per scan makes it unsuitable for recording rapid changes in the surface profile of bimorph mirrors. Therefore, to extend our earlier work, we utilized an array of novel, high speed, ZPS^TM absolute displacement sensors from Zygo.^7–10 Each ZPS probe [Fig. 3(a)] is ∼27 mm long and operates in the Fizeau configuration. Light from an external source operating at ∼1550 nm is fed via optical fiber to each of the sensors. The same fiber also carries the return optical signal from the sensor back to the measurement electronics. Optical interference occurs between the reflections from the sensor’s reference surface R_R and the measured target R_T [Fig. 3(b)]. The change in phase of the reflection from the target, relative to the reflection from the reference, is used by the measurement electronics to derive the displacement of the target. The sensor initially establishes the absolute distance d to the target using a multi-wavelength approach and then tracks displacements ∆d relative to this position. This gives the sensor the ability to recover the position of the target in the event that the photon beam is inadvertently or intentionally interrupted. ZPS sensors, mounted on a custom-built metrology frame, are designed to measure displacements over a range of 1.2 mm with sub-nm noise levels and a long-term stability of <1 nm per day. Direct registration of each sensor to the metrology frame, under the influence of an axial preload, is established by a well-defined, physically accessible, reference surface [Fig. 3(b)].

As seen in Fig. 4, a chamfer at the front edge of the sensor is held against a spherical cup in the metrology frame. Direct contact between the sensor’s reference surface and the cup provides an ultra-stable mount and constrains the sensor in the axial and radial directions. A spring mechanism (not shown) at the far end of the sensor provides an axial preload and a frictionless radial constraint. The ring contact between the sensor and the cup also allows angular adjustment of the sensor’s pointing vector by manipulating the far end of the sensor. The sensor beam exits the metrology frame through an aperture in the cup. A preload mechanism absorbs any thermal expansion of the sensor’s body without perturbing the location of the sensor’s reference surface. The controller unit receives the optical output from up to 64 ZPS sensors and outputs the measured displacements at up to 104 kHz.

Table I summarizes the major specifications of the ZPS system.

The compact nature of each sensor (only 3 mm in diameter) allows densely packed 1D or 2D arrays of sensors to be constructed in the metrology frame. Such arrays can simultaneously record the dynamic displacement of multiple targets, including numerous locations on an active optic. In this manner, the ZPS probes can monitor the optical surface of a bimorph X-ray mirror whilst voltages are applied to the piezo-electric electrodes to purposefully deform it. Aside from measuring changes in the tangential curvature of a bimorph, additional rows of sensors could also monitor sagittal twist and translational/rotational rigid body motions of the mirror.

A custom-built apparatus was designed and manufactured by Zygo to securely hold twenty-two ZPS probes in close proximity to the optical surface of a bimorph mirror. The old, I24 bimorph mirror was mounted to a robust, right-angled bracket [Fig. 5(a)]. The metrology frame, holding the array of ZPS sensors, was mounted to the right-angled bracket using three flexure bipods [Fig. 5(b)]. Each bipod constrains two degrees-of-freedom (DOF). Together, the three bipods function as the frictionless flexure equivalent of a type II Kelvin clamp.¹¹ This strategy decouples the metrology frame from deformations in the rest of the structure, such as differential expansion of the metrology frame and the mounting bracket, and limits the transfer of any deformations in the mirror’s holder to the metrology frame during operation. Three lockable, fine-pitch adjustment screws, accessible from behind the mounting bracket, enable tip, tilt, and height adjustment of the bimorph relative to the fixed sensor array. This enables the mirror’s surface to be positioned at a standoff distance of 3.5 mm from the sensors and within their angular capture range. The bipod design simultaneously limits the frame deformations to <1 nm for a 0.1 K temperature differential between the frame and mounting bracket and also provides a first resonance of ∼335 Hz for the entire setup. The latter is critical to minimizing the influence of seismic vibrations upon the measurement. While Zerodur^® or another material with a low coefficient of thermal expansion (CTE) seems like a natural choice for the metrology frame, a cost-effective solution of aluminum was found, based on the ratio of thermal conductivity λ to the CTE α. Maximizing this ratio helps identify a material with a suitably high thermal conductivity to minimize the formation of gradients (which are primarily responsible for shape change) and a low CTE (which minimizes dimensional changes causing shape change). Despite its high CTE, aluminum 6061-T6 was chosen for all components of the setup as it performs very favorably compared to low CTE materials due to its extremely high thermal conductivity. Two parallel, linear arrays of 11 ZPS sensors each straddle a rectangular aperture in the metrology frame to measure the upper or lower coated stripes of the bimorph. Due to their symmetric construction, one of the key advantages of bimorph mirrors is their insensitivity to isothermal changes in temperature. Unless severely constrained by thermal deformations from its mechanical holder, a bimorph mirror is intrinsically stable and will remain largely immune to the influence of large temperature fluctuations. This means that it will retain its calibration and bending range, even when exposed to variations of several °C.

A clear, line-of-sight aperture between the two rows of ZPS sensors enables another metrology instrument, such as the Diamond-NOM or a MiniFiz150 Fizeau interferometer (Fig. 6), to simultaneously measure the optical surface along the midpoint line between the two ZPS arrays. Taking the pairwise average of the readings of a ZPS sensor in one horizontal row, and the corresponding sensor in the other row, enables an effective measurement midway between the two sensor arrays. Thus, the two measurements can be compared in compliance with the Abbe principle.¹² The 2D array also provides information about the mirror’s pitch, roll, and twist during bimorph bending. A spacing of 18 mm between adjacent sensors provides coverage over most of the ∼210 mm length of the mirror’s active surface.

The mirror and the frame holding the ZPS probes were installed on the Diamond-NOM operating in a face-sideways configuration. All components were allowed to thermally and mechanically stabilize for several hours prior to data acquisition. With both metrology systems operational, an impulse of −1500 V was applied to the mirror. At hourly increments, the HV-Adaptos power supply was instructed, via EPICS, to automatically apply relative increments of +500 V to all piezo-electric electrodes, until the limit of +1500 V was reached. The Diamond-NOM was similarly synchronized to begin a new scan 20 min after each bimorph voltage change. The ZPS controller continuously recorded the displacement from the 22 probes over the full time period. MATLAB^® scripts automatically calculated the change in tangential radius of curvature. The ZPS data were converted to an absolute curvature by comparing with the initial Diamond-NOM measurement of the mirror at 0 V. Figure 7 shows a comparison of the mirror’s curvature as measured by the two different metrology instruments. Each Diamond-NOM scan (horizontal, blue bar) took ∼30 min and provides a single, averaged measurement of the radius of curvature throughout this period. The rapid acquisition time of the ZPS system (red dots) enables the observation of initial changes in curvature immediately after each voltage increment was applied to the mirror. Good agreement in the steady-state magnitude of radius change is observed between the two instruments over the full bending range of the mirror. Note that the ZPS probes see inverted drift at −1500 V compared to the other voltage steps. This is because the mirror was driven with a negative voltage change (0 to −1500 V) for the first step, compared with positive voltage changes (+500 V) for all subsequent steps.

A complementary measurement was also made by installing and operating the bimorph mirror on the Fizeau interferometer whilst simultaneously monitoring its optical surface using the ZPS probes. Figure 8 shows the relative height change in the optical surface of the bimorph, as measured by using ZPS probes (solid lines) and the Fizeau interferometer (dashed lines), as ±1500 V are applied to its piezo-electric electrodes. The Fizeau interferometer, with its planar transmission flat, was unable to reliably measure the strongly concave curvature of the optical surface when negative voltages were applied to the bimorph. The radius of curvature of the bimorph mirror was ∼200 m at 0 V and ∼125 m at −1500 V. For such curvatures, without any zoom, the Fizeau fringes become very closely spaced and the phase-shifting algorithm cannot accurately reconstruct the height profile across the desired region of the bimorph mirror. The Diamond-NOM data (dotted lines) are also added to Fig. 8 for comparison.

Finer details of the dynamics of the bimorph’s radius of curvature changes, as measured by using the Fizeau interferometer (black squares) and the ZPS probes (red dots), during voltage shifts of +500 V and −500 V, are presented in Fig. 9. Fizeau scans were collected at ∼0.1 Hz, and ZPS data were acquired at 4 Hz. However, the 4 Hz was imposed by the acquisition software and is not an inherent limitation of the ZPS system. Multiple points in the ZPS data are visible during the transition between the two bending states of the mirror. These higher speed data confirm a very smooth and regular response of the mirror to the driving voltages. Such temporal details cannot be captured by using the Fizeau.

Starting with all piezo-electric electrodes at their negative voltage limit (−1500 V), an extreme +3000 V impulse was applied to all electrodes to drive the mirror through its full bending range to its positive voltage limit (+1500 V). Over a ∼17 h period, the Diamond-NOM and ZPS probes both measured that the inverse radius of curvature of the bimorph drifted by several percent (Fig. 10). This is consistent with many previous observations of older bimorph mirrors clamped in their original opto-mechanical holders. Such drifts are eliminated using the upgraded hardware and techniques described in Refs. 2 and 3.

After completing stability tests, and with the mirror’s piezo-electric electrodes maintained at +1500 V for many hours to guarantee a stable curvature of the optical surface, small voltage increments were applied to the mirror each hour, in steps of −5, −5, −10, and −30 V. Diamond-NOM scans were initiated 20 min after each voltage change. As before, Fig. 11 shows that the ZPS probes accurately track the curvature change in the bimorph mirror and reveal extra information about how the mirror bends dynamically during and immediately after each voltage change.

Figure 11 demonstrates that curvature changes of <1% can reliably be made if the mirror starts from a stable configuration. In the above case, voltages had not been changed for many hours prior to applying the first, small voltage increment. However, can small changes still be observed if the mirror has recently experienced a major change in curvature? To investigate, the mirror was driven from 1500 V to 0 V, followed immediately by small sequential voltage steps of 5 V, 5 V, 10 V, 30 V, and 50 V. Taken in isolation, the Diamond-NOM data in Fig. 12 are puzzling: they show that the mirror’s curvature increases for the first few steps in response to each positive voltage change, but then bizarrely the curvature decreases for subsequent positive voltage steps. However, the ∼30× higher temporal resolution of the ZPS probes clearly explains this anomaly: the mirror’s curvature decreases by a small amount at each voltage step, but the overall curvature of the mirror is dominated by long term drifts during the first few hours following the initial voltage jump of −1500 V.

Very small voltage corrections, to induce sub-nm corrections to the mirror’s surface, could be required to perfectly focus an X-ray beam or correct wavefront deformations. To investigate the measurement sensitivity limit for curvature changes, very small voltage steps (0.5 V–3 V) were applied to the bimorph mirror whilst monitoring its optical surface using the ZPS probes at 4 Hz. Figure 13 confirms that curvature changes in the mirror’s surface caused by applying steps of only 0.5 V to all piezo-electric electrodes can reliably be measured. This corresponds to a change in the sagitta (depth of the mirror at its centre) of only 3 nm or alternately a radius of curvature change of >1000 km.

To push the boundaries even further, we repeated the above tests but now with voltage steps approaching the minimal increment of 0.1 V that can be applied by the HV-Adaptos. Figure 14 shows the displacement, measured as a function of time by the ZPS probe, at the centre of the bimorph mirror for extremely small voltage changes. The 0.2 V steps (Time ∼160 and 200 s) and 0.3 V step (Time ∼260 s) are clearly discernable in the raw ZPS data. For the 0.1 V steps, applied at Time ∼50, 75, and 115 s, the noise levels of the measurement (∼0.5 nm rms at each step) start to become comparable to the step change. This makes it difficult to clearly resolve each step. However, low pass filtering of the raw data and/or operating the ZPS at a higher sampling rate and performing suitable averaging will certainly improve the visibility of these extreme features. The above data provide evidence of the excellent sensitivity of the ZPS probes and clearly show that they are capable of measuring sub-nm changes in the optical surface of bimorph X-ray mirrors.

Currently, the control software for the high voltage power supply does not have the functionality for a high speed change in the voltage applied to an individual piezo-electric electrode. This means that we were unable to perform any dynamic characterization of single piezoactuators moving at high speed. However, in the future, it would certainly be beneficial to understand how individual piezoactuators, driven at high speed, can influence the mirror’s optical profile. This would be analogous to the traditional measurement of the steady-state behavior of piezo-response-functions.¹³ 

To further investigate the high-speed dynamics of the mirror, a sinusoidal voltage profile (with a period of 20 s and an amplitude of 50 V) was applied to all piezo-electric electrodes of the bimorph at a refresh rate of 1 Hz. Simultaneously, the ZPS probes monitored the optical surface for ∼100 s at an acquisition rate of 100 Hz. The upper plot of Fig. 15 shows a snapshot of the height profile of the optical surface at a given time. In the lower plot of Fig. 15, the dynamic displacement is plotted as measured by using the three ZPS probes at the ends and centre of the mirror. Aside from the sinusoidal voltage oscillations (with a period of 20 s), we can also see the ∼1 s period of the power supply’s voltage refresh rate. In the future, it is hoped that this 1 Hz limitation can be removed by reprogramming the power supply.

Using an upgraded HV power supply and high-speed ZPS displacement sensing probes, we have shown that bimorph X-ray mirrors can be driven and measured much more rapidly than ever before. This could be exploited at synchrotron and FEL beamlines to rapidly change the size of the X-ray beam at 1 Hz. We have shown that the ZPS displacement sensing probes can readily measure changes of <1 nm in the optical surface, induced by applying <0.5 V to the bimorph’s piezo-electric electrodes. To the best of our understanding, using the existing HV power supply, bimorph X-ray mirrors could potentially be driven at 10’s of Hz and possibly at 100’s of Hz. Most likely, the refresh rate could be significantly improved as we have not reached the intrinsic limit imposed by the electrical circuits inside the power supply. This would then be comparable to the refresh rates used for bimorph deformable mirrors in other scientific disciplines including astronomy. Developing high-speed “adaptive” optics for X-ray beamlines could profoundly change how focusing elements are dynamically utilized at synchrotron radiation and X-ray Free Electron Laser (XFEL) sources and aid novel scientific discoveries in the future.

See supplementary material for a video that is available online showing the real-time sinusoidal bending of the bimorph mirror at a voltage refresh rate of 1 Hz as measured by using the ZPS probes. The snapshot shown in Fig. 15 is derived from this video. The lower chart displays the instantaneous height profile along the optical surface of the bimorph mirror. Each diamond symbol shows the average height measured by each of the 11 pairs of ZPS probes. The upper chart shows the temporal evolution of the optical surface at its two ends (green and black curves) and at the centre (blue curve). The instantaneous time in the lower chart corresponds to the position of the red, vertical bar along the time axis of the upper chart. Note that the centre of the mirror is moving up and down by approximately ±500 nm, which corresponds to a significant change in its focusing power. This video demonstrates that major changes can be made to the surface of deformable bimorph mirrors at 1 Hz and likely much faster. We hope that this will spark new ideas about how bimorph mirrors are utilised at synchrotron and XFEL beamlines.

This work was carried out with the financial support of Diamond Light Source Ltd, UK.

Reference to any commercial product mentioned in this paper does not constitute or imply its endorsement, recommendation, or favouring by Diamond Light Source Ltd.