Thomas Ruppel

Response analysis of holography-based modal wavefront sensor.

The crosstalk problem of holography-based modal wavefront sensing (HMWS) becomes more severe with increasing aberration. In this paper, crosstalk effects on the sensor response are analyzed statistically for typical aberrations due to atmospheric turbulence. For specific turbulence strength, we optimized the sensor by adjusting the detector radius and the encoded phase bias for each Zernike mode. Calibrated response curves of low-order Zernike modes were further utilized to improve the sensor accuracy. The simulation results validated our strategy. The number of iterations for obtaining a residual RMS wavefront error of 0.1λ is reduced from 18 to 3.

Feedforward Control of Deformable Membrane Mirrors for Adaptive Optics

In this paper, performance enhancements for deformable membrane mirrors based on model-based feedforward control are presented. The investigated deformable mirror consists of a flexible membrane and voice coil actuators. Feedback control of the distributed actuators cannot be implemented in these mirrors due to a lack of high speed internal position measurements of the membranes deformation. However, by using feedforward control, the dominant dynamics of the membrane can still be controlled allowing for faster settling times and reduced membrane vibrations. Experimental results are presented for an ALPAO deformable mirror with 88 distributed actuators on a circular membrane with a pupil of two centimeters in diameter.

Model-Based Feedforward Control of Large Deformable Mirrors

In this paper, a model-based feedforward control concept for fast set-point changes of large deformable mirrors is proposed. It takes into account local position control loops of excited actuators and mode-dependent stiffness variations of the mirror shell. Based on partial differential equations for the temporal and spatial behavior of the deformable mirror, a modal approximation of the mirror dynamics is performed. It is shown that a second order approximation of the eigenmode dynamics is appropriate for low-order modes even when additional system components as delays, digital-to-analog converters, current drivers, actuator-magnet efficiencies, capacitive sensors, and analog-to-digital converters are included. In particular, appropriate transfer functions with identified coefficients of the proposed modal models are presented for a 45-actuator prototype of the Large Binocular Telescope adaptive secondary mirror (P45). Additionally, experimental results with model-based feedforward control are presented. The identified dynamic model of the P45 is finally used to derive flatness based feedforward commands for chopping.

Kinodynamic planning - an analytical approximation with C n polynomials for industrial application

The need for n-times continuously differentiable trajectories arises when high speed, high precision control of dynamical systems is intended. Especially in mechanics, dynamical systems are usually limited in speed, acceleration and jerk. This paper introduces a strictly analytical method for generating Cn trajectories along given points under dynamic constraints and given maximum path deviations. Addressing the need for discrete time point evaluation in industrial application, a discrete time speed scheduling method is applied. By using higher order polynomials to interconnect given points along the trajectory it is shown that the resulting path complies with the given geometric and dynamic constraints. As an example, a trajectory for a given set of points is derived and the results are discussed in comparison to a computed time-optimal solution.

Suppressing low-order eigenmodes with local control for deformable mirrors

To improve the mechanical characteristics of actively controlled continuous faceplate deformable mirrors in adaptive optics, a strategy for reducing crosstalk between adjacent actuators and for suppressing low-order eigenmodes is proposed. The strategy can be seen as extending Saint-Venant’s principle beyond the static case, for small local families of actuators. An analytic model is presented, from which we show the feasibility of the local control. Also, we demonstrate how eigenmodes and eigenfrequencies are affected by mirror parameters, such as thickness, diameter, Young’s modulus, Poisson’s ratio, and density. This analysis is used to evaluate the design strategy for a large deformable mirror, and how many actuators are needed within a family.

Actuator placement for minimum force modal control of continuous faceplate deformable mirrors

A mechanically motivated strategy for determining actuator locations for minimum force modal control of continuous faceplate deformable mirrors in adaptive optics systems is proposed. It is shown that numerically or analytically derived eigenmodes of deformable mirrors can be used to determine optimal positions for a limited number of actuators. The actuators considered in this framework may either be of displacement type or of force type. Moreover, the presented methodology can be adapted to momentum actuators.

Modal Trajectory Generation for Adaptive Secondary Mirrors in Astronomical Adaptive Optics

The use of high speed adaptive secondary mirrors (AS) in cassegrain or Gregorian telescopes shows high optical efficiency as well as the possibility to make adaptive optics (AO) available at all foci. After 4 years of extensive and successful use of a 336-actuator AS (MMT336) at the multi mirror telescope (MMT), the need for faster control methods of the AS is arising. Recent wavefront sensors allow frame rates above 1 kHz and the dynamically limiting part in the telescopes closed loop AO system is the AS. The development of two 672-actuator (LBT672) AS for the large binocular telescope (LBT) underlines the need for accurate high speed control methods of AS systems with a large number of spatially distributed actuators in the near future. Currently, AS are controlled based on local position feedback for all actuators independently. Arising problems in this configuration are mode-dependent stiffness variations of the mirror shell, interacting actuators and the excitation of uncontrollable modal mirror modes in closed loop operation. Based on dynamic inversion of identified controllable modal eigenmodes of the deformable mirror shell we derive a feed-forward trajectory generator that excites only controllable modal mirror modes, compensates for the varying mirror stiffness, and the actuator interaction of the AS. Verified at the LBT672 prototype (P45), an experimental 45-actuator AS, we show the benefits of modal feed-forward control including faster settling times and less overshoot for a setpoint change in closed loop operation.

Analytical Multi-Point Trajectory Generation for Differentially Flat Systems with Output Constraints

Abstract In this paper, an analytical off-line multi-point trajectory generation scheme is presented for differentially flat systems. For control of dynamical systems along a given set of control points, multi-point trajectory generation is required when input and state constraints exist. It is assumed that differential constraints for flat coordinates can be formulated explicitly. The trajectory scheme is based on analytically solving a set of polynomial equations to parameterize n-times continuously differentiable segmented transition polynomials, that approximate time optimal trajectories. The computational effort for determining valid trajectories is low in comparison to numerical optimization. As an example, a multi-point trajectory generation problem for a 3-DOF gantry crane is presented.

Development of new concepts to minimize the impact of fast telescope vibrations seen by the E-ELT/MICADO wavefront sensors

We present our recently started eort to realize feedforward vibration control loops with a full adaptive optics (AO) testbed in the laboratory. A piezo-driven tip-tilt mirror unit introduces an arbitrary, but controllable, vibration power-spectrum to simulate telescope mirror vibrations of any kind on the wavefront sensor. Our ultimate goal is to demonstrate in realistic laboratory tests, how telescope vibrations faster than atmospheric tip-tilt can be measured by accelerometers, and controlled in real-time feedforward to allow for longer and more sensitive wavefront sensor (WFS) integrations.

Modelling the optical pathway of the Large Binocular Telescope

We dynamically model the Large Binocular Telescopes optical path using a linear system approach. The model is derived from experiments conducted at the telescope. These experiments will be described and we will explain the possibilities and difficulties in extracting a simulation model from measured data. The model also incorporates disturbances, such as wind forces and single excitations induced by vibrating machinery. We will show, why it is necessary to measure structural vibrations at the LBT and why we follow a model based approach in estimating the mirror’s oscillatory motions. Some simulation results will be presented and compared to measured time series and a conclusion will be drawn. An outlook will be given on how the observer can be implemented.