Using Closed-Loop Adaptive Bimorph Deformable Mirror for the Fast Shaping Control of X-Ray Beams

For decades, high-speed adaptive optics correction has greatly benefited various scientific communities. This technology is based on real-time metrology feedback, but its application in the hard X-Ray regime has been a major challenge. This is due to the need for active mirrors with single-digit nanometer height errors, which must be relative to a range of aspheric forms.  

A high-resolution, real-time, closed-loop “adaptive” optical system has been developed for synchrotron and X-Ray-free electron laser (XFEL) applications. The system uses X-Ray speckle scanning for wavefront calibration. Once calibrated, the wavefront diagnostic is removed from the X-Ray beam path.

By controlling a piezoelectric deformable bimorph mirror at 1 Hz, the size and shape of the reflected X-Ray beam may be altered non-invasively. A 20 kHz direct measurement of the optical surface with picometer sensitivity offers continuous feedback through an array of interferometric sensors. 

A non-specialist operator may use this non-invasive method to recreate a succession of pre-defined X-Ray wavefronts. Focused or non-Gaussian profiles, such as flattop intensity or numerous split peaks with controlled separation and relative amplitude, are among the pre-defined wavefronts.

Without the need for intrusive wavefront diagnostic sensors that obstruct the X-Ray beam, the wavefronts may be adjusted in any sequence and quick succession.

These advancements can significantly alter how X-Ray focusing elements are used at synchrotron radiation and XFEL sources. Furthermore, they provide extraordinary dynamic control of photon beams, facilitating scientific discoveries across various fields.

Introduction

At synchrotron light or free electron laser (XFEL) facilities, a series of fixed-curvature or bendable optics is utilized on each experimental “beamline” to focus or collimate ultra-intense X-Ray beams from the source onto the sample under test.¹

X-Ray mirrors are typically cuboids with lengths ranging from 25 to 1500 mm, widths and depths between 20 to 100 mm due to the necessary grazing angle of incidence of a few milliradians for efficient total external reflection of X-Ray photons, coupled with typical beam widths of a few millimeters.

The optical surface of the single-crystal silicon or fused silica substrate is pre-polished to a range of profiles, such as cylinders or ellipses, and often coated with metallic layers to enhance X-Ray reflectivity.

The optical layout of each synchrotron or XFEL beamline is customized to suit various experimental techniques, including combinations of X-Ray diffraction, spectroscopy, ptychography, and imaging.

Each beamline can be reconfigured to vary multiple experimental parameters, such as X-Ray wavelength changes and the focal spot's size or location. Bimorph deformable mirrors have been widely used in the optical community for decades.²

Such optics are frequently operated in a closed loop at a refresh rate of hundreds or thousands of cycles per second based on feedback from various metrology sensors.

However, since the wavelength of hard X-Rays (10 keV=0.124 nm) is about 5000 times smaller than that of red light (633 nm), tuning and stabilizing the surface of an X-Ray bimorph mirror is significantly more challenging than that for visible light.

Typically, the optical surface of an X-Ray mirror needs to be optimized to the desired profile with single-digit nanometer height errors.  

Piezoelectric deformable bimorph X-Ray mirrors were initially developed at the ESRF, France, in the 1990s, then at Spring-8, Japan, before being commercialized by Thales-SESO, France.^3,4,5 X-Ray bimorphs are currently being deployed on numerous beamlines worldwide^.6-8

The achromatic nature of bimorph mirrors enables control of beam shaping across a broad range of X-Ray wavelengths. Diamond Light Source (Diamond), the United Kingdom's national facility for synchrotron radiation science, has collaborated extensively over the last decade to enhance the performance of bimorph mirrors.^9,10

Compared to mechanically bent mirrors that utilize one or two independent bending motors, bimorph X-Ray mirrors offer additional degrees of bending freedom and zonal control, thanks to their typically 8-32 electrodes.¹¹

This allows for advanced optical surface and reflected X-Ray wavefront control, including correction of optomechanical clamping of the mirror, photon-induced heat bumps, thermal deformations resulting from ambient temperature changes, residual polishing errors, and higher-order aberrations in the wavefront from other imperfect optics in the photon delivery system.^12,13,14,15

X-Ray optics have a rich history, and a recent article provides an extensive review of the state-of-the-art wavefront preservation techniques required for achieving diffraction-limited performance.¹⁶

The demand for such techniques is growing as synchrotrons, and XFEL facilities upgrade their particle accelerators to produce brighter, more coherent X-Ray beams.

The quasi-static, open-loop mode has traditionally driven active X-Ray optics for synchrotron and XFEL beamlines. Changes to the mirror's profile shape occur every few hours or days and, in some cases, not for several months or years.

However, advances in detector technology and data processing, coupled with increasingly brighter X-Ray sources, have significantly increased sample throughput in recent years.

Beamlines devoted to macro-molecular crystallography routinely process hundreds or thousands of samples daily. As such, these beamlines require a way to adjust the size and shape of the X-Ray beam rapidly without losing flux to suit the size of each crystal or illuminate different-sized regions of more extensive samples.

Rapidly implementing significant changes to the photon beam can be intrinsically problematic because, when operated in an open loop, the curvature of X-Ray bimorph mirrors can drift by several percent over many hours following a significant voltage change.¹⁷

This leads to corresponding time variations in the size and shape of the reflected X-Ray beam, with a significant time lag between the operator's request and the system's reaction.

Such parasitic drifts become more problematic as facilities generate smaller, brighter X-Ray sources and employ stronger focusing geometries.

There is a need to develop a fast, non-invasive, closed-loop "adaptive" bimorph system based on accurate nano-metrology feedback, which can make significant and frequent changes to the X-Ray beam's size. To maximize the scientific utilization of X-Rays, the closed-loop system should not attenuate or block the beam.

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References and Further Reading

1. S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8, 17440 (2018).
2. C. Kettenbeil, J. Jewell, J. K. Wallace, and J. Steeves, “Picometer wavefront sensing using the phase-contrast technique,” Optica 7, 1267–1274 (2020).
3. R. Signorato, “R&D program on multisegmented piezoelectric bimorph mirrors at the ESRF: status report,” Proc. SPIE 3447, 20–31 (1998).
4. R. Signorato, “R&D program on multisegmented piezoelectric bimorph mirrors at the ESRF–status report: II,” Proc. SPIE 3773, 50–59 (1999).
5. R. Signorato and T. Ishikawa, “R&D on third generation multi-segmented piezoelectric bimorph mirror substrates at Spring-8,” Nucl. Instrum. Methods Phys. Res. A 467–468, 271–274 (2001).
6. A. Erko, F. Schäfers, A. Firsov, W. B. Peatman, W. Eberhardt, and R. Signorato, “The BESSY X-ray microfocus beamline project,” Spectrochim. Acta B Atom. Spectros. 59, 1543–1548 (2004).
7. R. Signorato, D. Hausermann, M. Somayazulu, and J.-F. Carré, “Performance of an adaptive u-focusing Kirkpatrick-Baez system for high-pressure studies at the Advanced Photon Source,” Proc. SPIE 5193, 112–123 (2004).
8. S. Matsuyama, H. Nakamori, T. Goto, T. Kimura, K. P. Khakurel, Y. Kohmura, Y. Sano, M. Yabashi, T. Ishikawa, Y. Nishino, and K. Yamauchi, “Nearly diffraction-limited X-ray focusing with variable-numericalaperture focusing optical system based on four deformable mirrors,” Sci. Rep. 6, 24801 (2016).
9. J. P. Sutter, S. G. Alcock, I. T. Nistea, H. Wang, and K. Sawhney, “Active and adaptive X-ray optics at diamond light source,” Synchrotron. Radiat. News 35(2), 8–13 (2022).
10. “Diamond light source,” https://www.diamond.ac.uk.
11. M. Vannoni, I. Freijo Martín, and H. Sinn, “Characterization of an X-ray mirror mechanical bender for the European XFEL,” J. Synchrotron. Radiat. 23, 855–860 (2016).
12. M. Sanchez Del Rio, A. Wojdyla, K. A. Goldberg, G. D. Cutler, D. Cocco, and H. A. Padmore, “Compensation of heat load deformations using adaptive optics for the ALS upgrade: a wave optics study,” J. Synchrotron Rad. 27, 1141–1152 (2020).
13. L. Huang, J. Xue, and M. Idir, “Controlling X-ray deformable mirrors during inspection,” J. Synchrotron Rad. 23, 1348–1356 (2016).
14. M. Vannoni, I. F. Martín, V. Music, and H. Sinn, “Calibration and optimization of an X-ray bendable mirror using displacement-measuring sensors,” Opt. Express 24, 17292–17302 (2016).
15. K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425, 052026 (2013).
16. D. Cocco, G. Cutler, M. Sanchez del Rio, L. Rebuffi, X. Shi, and K. Yamauchi, “Wavefront preserving X-ray optics for synchrotron and free electron laser photon beam transport systems,” Phys. Rep. 974, 1–40 (2022).
17. S. G. Alcock, J. P. Sutter, K. J. S. Sawhney, D. R. Hall, K. McAuley, and T. Sorensen, “Bimorph mirrors: the good, the bad, and the ugly,” Nucl. Instrum. Methods Phys. Res. A 710, 87–92 (2013).

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