Extracting hysteresis from nonlinear measurement of wavefront-sensorless adaptive optics system

Data-driven modeling and control of an X-ray bimorph adaptive mirror

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

Robust Control Design Based on Perturbation Cancellation for Micro-Positioning Design with Hysteresis

Based on the superiority of the piezoelectric elements, including lightweight, high electric mechanical transformation efficiency and a quick response time, a piezoelectric-based micro-positioning actuator is developed in this investigation. For eliminating the effects of hysteresis and modeling uncertainties that appeared in this micro-positioning actuator, a nonlinear adaptive fuzzy robust control design with a perturbation cancellation ability is proposed for this micro-positioning design to achieve a positioning resolution of 1 μm. Structurally, this proposed robust control methodology contains two particular parts: a universal fuzzy approximator and a robust compensator, which are employed to cancel the modeling uncertainties caused by the perturbed parts of the micro-positioning actuator and mitigate the approximation error between the modeling uncertainties and the universal fuzzy approximator, respectively. From both the numerical simulations and real validations, this proposed micro-positioning design performs a promising positioning performance in the micrometer level.

Accurate aberration correction in confocal microscopy based on modal sensorless method

Confocal microscopy has the advantages of high resolution and optical sectioning ability over conventional microscopy. However, aberration induced by the optical system can compromise these advantages and considerably reduce the energy reaching the pointlike detector. We propose an accurate aberration correction method with a liquid-crystal spatial light modulator (LCSLM) in the confocal system. Each coefficient of Zernike aberration modes is calculated by directly measuring the variance of the images with different bias aberration modes. Large-coefficient (>0.7 rad) aberration is compensated first by LCSLM, following which aberrations with small coefficients are measured precisely, minimizing the cross talk between different kinds of aberrations. With this predistortion strategy, the aberration correction is much more accurate, and maximum image intensity in the normal and nonconjugated systems is improved by 2.5 times and 4 times compared to the normal correction method, respectively, demonstrating the effectiveness of our method.

Tracking control of piezoelectric actuator using adaptive model

Piezoelectric actuators (PEAs) have been widely used in micro- and nanopositioning applications due to their fine resolution, rapid responses, and large actuating forces. However, a major deficiency of PEAs is that their accuracy is seriously limited by hysteresis. This paper presents adaptive model predictive control technique for reducing hysteresis in PEAs based on autoregressive exogenous model. Experimental results show the effectiveness of the proposed method.

Estimating the atmospheric correlation length with stochastic parallel gradient descent algorithm

The atmospheric turbulence measurement has received much attention in various fields due to its effects on wave propagation. One of the interesting parameters for characterization of the atmospheric turbulence is the Fried parameter or the atmospheric correlation length. We numerically investigate the feasibility of estimating the Fried parameter using a simple and low-cost system based on the stochastic parallel gradient descent (SPGD) algorithm without the need for wavefront sensing. We simulate the atmospheric turbulence using Zernike polynomials and employ a wavefront sensor-less adaptive optics system based on the SPGD algorithm and report the estimated Fried parameter after compensating for atmospheric-turbulence-induced phase distortions. Several simulations for different atmospheric turbulence strengths are presented to validate the proposed method.

Model-based aberration correction in a closed-loop wavefront-sensor-less adaptive optics system

In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N=9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N+5=14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N+4=13 intensity measurements.