Renaud Bastaits

Modular bimorph mirrors for adaptive optics

This paper examines the possibility of constructing deformable mirrors for adaptive optics with a large number of degrees of freedom from silicon wafers with bimorph piezoelectric actuation. The mirror may be used on its own, or as a segment of a larger mirror. The typical size of one segment is 100 to 200 mm; the production process relies on silicon wafers and thick film piezoelectric material deposition technology; it is able to lead to an actuation pitch of the order of 5 mm, and the manufacturing costs appear to grow only slowly with the number of degrees of freedom in the adaptive optics.

Synchronized switch damping on inductor and negative capacitance

This article presents a strategy for enhancing the performance of the synchronized switch damping on inductor technique used for the semiactive control of structural vibrations. This enhancement is achieved by adding a negative capacitance to the resonant circuit that dissipates the energy converted by a piezoelectric transducer embedded in the structure. A unidimensional spring-mass system shunted synchronously to a resonant circuit is studied analytically, and the main parameters governing the performances of the system are highlighted. Experimental results obtained with a synthetic negative capacitance demonstrate the enhancement of the performance of synchronized switch damping on inductor and confirm the parametric dependencies identified analytically.

Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures

This paper considers the RL shunt damping of rotationally periodic structures with an array of regularly spaced piezoelectric patches. The technique is targeted to the damping of a specific mode with nodal diameters. For this particular case, one can take advantage of the shape of the targeted mode to organize the piezoelectric patches as a modal filter (in parallel loops) which reduces the demand on the inductors of the tuned inductive shunt. In the case of a perfectly rotationally periodic structure, it is possible to organize 4 piezoelectric transducers (PZT patches) in two parallel loops of 2 patches each. In this way, the demand on the inductors is reduced by as compared to independent loops, which may allow a fully passive integration of the RL shunt in a turbomachinery application. The method is first illustrated experimentally on a circular plate; it is then applied to a prototype of an industrial bladed drum. The influence of blade mistuning is investigated.

Active Optics of Large Segmented Mirrors: Dynamics and Control

This paper examines the active optics of future large segmented telescopes from the point of view of dynamic simulation and control. The first part of the paper is devoted to the modeling of the mirror. The model has a moderated size and separates the quasi-static behavior of the mirror (primary response) from the dynamic response (secondary or residual response). The second part of the paper is devoted to control. The control strategy considers explicitly the primary response ofthe telescope through a singular value controller. The control-structure interaction is addressed with the general robustness theory of multivariable feedback systems, where the secondary response is considered as uncertainty. This approach is very fast and allows extensive parametric studies. The study is illustrated with an example involving 90 segments, 270 inputs, and 654 outputs.

Multi-layer adaptive thin shells for future space telescopes

This paper examines the morphing capability of doubly curved elastic shells with various layers of active materials with strain actuation capability. The equivalent piezoelectric loads of an orthotropic multi-layer shell is established and it is demonstrated that a set of four active layers offer independent control of the in-plane forces and bending moments, which guarantees optimum morphing with arbitrary profile. This is illustrated by a numerical example which compares a unimorph configuration (single layer of active material) with a twin-bimorph (two pairs of symmetrical layers of active material with orthotropic properties). Numerical simulations indicate that the optical (Zernike) modes with shapes where the curvatures in orthogonal directions have opposite signs (e.g. astigmatism, trefoil, tetrafoil) are fairly easy to control with both configurations and that substantial amplitudes may be achieved. However, the optical modes with shapes where the curvatures in orthogonal directions have the same sign (e.g. defocus, coma, spherical aberration) are difficult to control with the unimorph configuration, and they lead to the appearance of slope discontinuities at the interface between the independent electrodes. As expected, a much better morphing is achieved with a twin-bimorph configuration.

Segmented bimorph mirrors for adaptive optics: segment design and experiment

We discuss the concept of lightweight segmented bimorph mirrors for adaptive optics. The segment consists of a monocrystal silicon substrate actuated by an array of in-plane piezoceramic (PZT) actuators with honeycomb electrodes. We focus on technological aspects of the segment design that are critical for space applications and describe a single segment demonstrator. The morphing capability of the segment is evaluated experimentally. We also discuss the local deformations (dimples) associated with the shape of the electrodes acting on the PZT array.

Segmented bimorph mirrors for adaptive optics: morphing strategy

This paper discusses the concept of a light weight segmented bimorph mirror for adaptive optics. It focuses on the morphing strategy and addresses the ill-conditioning of the Jacobian of the segments, which are partly outside the optical pupil. Two options are discussed, one based on truncating the singular values and one called damped least squares, which minimizes a combined measure of the sensor error and the voltage vector. A comparison of various configurations of segmented mirrors was conducted; it is shown that segmentation sharply increases the natural frequency of the system with limited deterioration of the image quality.

Morphing of Segmented Bimorph Mirrors

Atmospheric turbulence compensation for the next generation of terrestrial telescopes (30–40 m diameter) will require deformable mirrors of increasing size and a number of actuators reaching several thousands. However, the mere extrapolation of existing designs leads to complicated and extremely expensive mirrors. This article discusses an alternative solution based on the use of segmented identical hexagonal bimorph mirrors. This allows to indefinitely increase the degree of correction while maintaining the first mechanical resonance at the level of a single segment, and shows an increase in price only proportional to the number of segments. Extensive simulations using random turbulent screens show that the segmentation produces only moderate reductions of the Strehl number, compared to a monolithic bimorph mirror with the same number of actuators (S = 0.86 instead of S = 0.89 in this study).

Structural Response of Extremely Large Telescopes

This paper is concerned with the extrapolation of the dynamic response of the primary mirror of current 10-meter class telescopes to the next generation of 30 to 40 m extremely large telescopes and future, even larger, ones. A numerical study is conducted on a family of primary mirrors of increasing size, and the results are compared with analytical scaling laws derived earlier from a much simpler analysis. The correlation between the numerical and the analytical results is quite good and, to a large extent, independent of the boundary conditions. This confirms that the analytical scaling laws can be used in confidence to conduct parametric studies in the preliminary design phase of extremely large segmented mirrors. Copyright

Large lightweight segmented mirrors for adaptive optics

This paper examines the possibility of constructing deformable mirrors for adaptive optics with a large number of degrees of freedom, by assembling segmented silicon mirrors with bimorph piezoelectric actuation. The production process relies on silicon wafers and thick film PZT deposition technology; it is able to lead to an actuation pitch of the order of 5 mm, and the manufacturing costs appear to grow only slowly (linearly or less) with the number of degrees of freedom in the adaptive optics.