Research Article Fast shaping control of x ray beams using a closed-loop adaptive bimorph deformable mirror Simon G. Alcock,1, * Ioana-Theodora Nistea,1 Vivek G. Badami,2 Riccardo Signorato,3 Matteo Fusco,4 Lingfei Hu,1 Hongchang Wang,1 AND Kawal Sawhney1 1 Diamond Light Source Ltd, Harwell Science & Innovation Campus, Didcot, Oxfordshire, OX11 0DE, UK Zygo Corporation, Middlefield, Connecticut 06455, USA 3 S.RI. Tech, Vigonza, Italy 4 CAEN, Viareggio, Italy *Corresponding author: [email protected] 2 Received 22 September 2022; revised 18 November 2022; accepted 8 December 2022; published 25 January 2023 High-speed adaptive correction of optics, based on real-time metrology feedback, has benefitted numerous scientific communities for several decades. However, it remains a major technological challenge to extend this concept into the hard x ray regime due to the necessity for active mirrors with single-digit nanometer height errors relative to a range of aspheric forms. We have developed a high-resolution, real-time, closed-loop “adaptive” optical system for synchrotron and x ray free electron laser (XFEL) applications. After calibration of the wavefront using x ray speckle scanning, the wavefront diagnostic was removed from the x ray beam path. Non-invasive control of the size and shape of the reflected x ray beam was then demonstrated by driving a piezoelectric deformable bimorph mirror at ∼1 Hz. Continuous feedback was provided by a 20 kHz direct measurement of the optical surface with picometer sensitivity using an array of interferometric sensors. This enabled a non-specialist operator to reproduce a series of pre-defined x ray wavefronts, including focused or non-Gaussian profiles, such as flattop intensity or multiple split peaks with controllable separation and relative amplitude. Such changes can be applied in any order and in rapid succession without the need for invasive wavefront diagnostic sensors that block the x ray beam for scientific usage. These innovations have the potential to profoundly change how x ray focusing elements are utilized at synchrotron radiation and XFEL sources and provide unprecedented dynamic control of photon beams to aid scientific discoveries in a wide range of disciplines. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. https://doi.org/10.1364/OPTICA.476449 1. INTRODUCTION A series of fixed-curvature or bendable optics is used on each experimental “beamline” at synchrotron light or free electron laser (XFEL) facilities to focus or collimate ultra-intense x ray beams from the source to the sample under test [1]. Due to the typical grazing angle of incidence of a few milliradians needed for efficient total external reflection of x ray photons, coupled with typical beam widths of a few millimeters, x ray mirrors are typically cuboids with lengths spanning from 25 to 1500 mm, and widths and depths between 20 and 100 mm. The optical face of the single-crystal silicon or fused silica substrate is pre-polished to a range of profiles, including cylinders or ellipses, and is often coated with metallic layers to enhance x ray reflectivity. The optical layout of each synchrotron or XFEL beamline is bespoke to suit a range of experimental techniques, including combinations of x ray diffraction, spectroscopy, ptychography, and imaging. Each beamline can be reconfigured to vary multiple experimental parameters, including changes in x ray wavelength, and the size or location of the focal spot. 2334-2536/23/020172-11 Journal © 2023 Optica Publishing Group Bimorph deformable mirrors have been extensively used by many optical communities for several decades [2]. Such optics are often operated in closed-loop at a refresh rate of hundreds or even thousands of cycles per second, based on feedback from a variety of metrology sensors. However, since hard x rays (10 keV = 0.124 nm) have a wavelength ∼5000 times smaller than red light (633 nm), tuning and stabilizing the surface of an x ray bimorph mirror is several orders of magnitude more demanding than 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 originally developed at the ESRF, France, in the 1990s [3,4], then at Spring-8, Japan [5], before being commercialized by Thales-SESO, France. X-ray bimorphs are now deployed on many beamlines around the world [6–8]. Their achromatic nature provides beam shaping control over a wide range of x ray wavelengths. Over the past decade, there has been an extensive collaborative research project [9] to advance the performance of bimorph mirrors at Diamond Light Source (Diamond), the United Kingdom’s national fa

Research Article When compared to mechanically bent mirrors (typically employing one or two independent bending motors [11]), which can only achieve cylindrical or elliptical profiles, the extra degrees of bending freedom and zonal control of bimorph x ray mirrors (typically with between 8 and 32 electrodes) permit more sophisticated control of the optical surface and the reflected x ray wavefront. This includes correcting opto-mechanical clamping of the mirror, photon-induced heat bumps [12], thermal deformation due to ambient temperature changes, residual polishing errors [13,14], and higher-order...

Research Article Fig. 2. Exploded view of the metrology frame and bimorph system. Bimorph mirror (yellow) is mounted into a holder (blue), which is attached to the base plate (dark gray) containing three bipod flexures. The metrology frame (light gray), holding an array of ZPS interferometric sensors, is mated with the three bipods. This arrangement securely holds the ZPS sensors ∼3.5 mm above the optical surface of the bimorph mirror whilst allowing line-of-sight access for grazing angle of incidence x rays. The bipod flexures ensure that the metrology frame is largely insensitive to thermal changes...