The Laser Interferometer Space Antenna (LISA) is an ESA mission designed to detect gravitational waves from space. To initiate the science phase, six test masses (TMs) are precisely handled and released into near-perfect free fall by dedicated mechanisms known as the Grabbing, Positioning, and Release Mechanisms (GPRMs). The stringent requirements on the noise level affecting the TMs’ release acceleration are extremely ambitious, motivating the need to experimentally verify the feasibility of achieving such performance. To this end, a dedicated precursor mission, LISA Pathfinder (LPF), flew from 2015 to 2017 to test key technologies. However, during the LPF mission, most release tests exhibited anomalous release velocities, often exceeding the requirements. In addition, the TM repositioning tests also revealed a bi-stable behavior in the TM rotations, which depend on the repositioning direction. This effect is produced by an unexpected non-rectilinear motion of the GPRM end effector, characterized by a micrometric side motion at the reversal of its axial motion. The bi-stable behavior also contributes to a TM-GPRM end effector misalignment, producing unwanted contacts and increasing the probability of a non-compliant TM release. Previous analyses identified asymmetric friction forces in the side-guiding system of the GPRM end effector as the primary cause of this behavior. Starting from the LPF flight experience, the GPRM delta development project in view of LISA led to a redesign of the mechanism architecture, supported by numerical analyses and multi-body models. Since the rectilinearity of the end-effector motion has been identified as critical for flight operation, alternative side-guiding concepts are developed, analyzed, and tested experimentally to evaluate their impact on the overall mechanism performance. The correlation of the models with ground and flight experimental data strengthens the understanding of the guiding system behavior, providing pivotal insights for selecting the GPRM design baseline for LISA.

Lithium niobate has emerged as a promising substrate material for adaptive X-ray mirrors. Heat treatment induces ferroelectric domain inversion, yielding two oppositely poled, layered regions that enable lithium niobate to behave as a monolithic bimorph in the presence of an applied electric field. In addition to fabrication simplicity, this well known material has favorable actuation and shape-control properties without hysteresis, creep, and drift. Following Timoshenko's approach to the bi-metallic strip thermostat, we derive an analytic description of shaping continuous electrode widths to produce a spatially varying surface curvature when a voltage is applied. Through comparison with finite-element analysis, the method is demonstrated for uniform electrode widths that produce cylindrical surfaces, and for varying electrode widths that produce plane-parabolic and plane-elliptical surfaces from initially flat substrates. A proposed longitudinally continuous, compound electrode pattern shows how a single flat mirror could be shaped to achieve multiple profiles with a single applied voltage.

For adaptive mirrors on X-ray beamlines and optical systems, we describe a strategy for arranging a small number of tangentially continuous electrodes with varying electrode widths tailored to improve mirror shape control. This approach, with patterned, compound electrodes, is well suited to the emerging class of lithium niobate mirrors that act as monolithic piezo-bimorphs, without the need for additional bonded or grown actuator elements. The proposed electrodes span the length of the mirror's clear aperture and have width profiles defined by polynomial shapes. Using a limited number of channels derived from Chebyshev polynomials, the actuators provide access to shape controls and correction modes of increasing polynomial order. We derive an analytic approach to optimize control voltages based on Euler–Bernoulli beam theory, and we show how the modeled characteristic response functions can be applied to fit arbitrary surfaces. Comparison with a conventional, linear array of 12 electrodes shows the relative benefit of each approach.

Recent advances in deformable mirrors based on monolithic piezoelectric substrates, such as lithium niobate, have the potential to improve the image quality of X-ray optical systems on synchrotron and free-electron laser beamlines and microscopes. However, the quantitative relationship between design parameters and the deformed shape has not been readily available in the literature. We present an analytical model, validated through finite element analysis, enabling calculation of tangential and sagittal curvatures based on mirror dimensions, crystallographic orientation, and applied voltage. We demonstrate that through the selection of material orientation, it is possible to achieve different deformed shapes (sphere, cylinder, or hyperbolic paraboloid). This methodology can be generalized to other piezoelectric materials and substrate-integrated actuator systems.