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Methods for Controlling Deformable Mirrors with Hysteresis Delft University of Technology Methods for controlling deformable mirrors with hysteresis Kazasidis, O. DOI 10.4233/uuid:3647c9bb-97d1-442a-9d3e-49cd1c9e3baf Publication date 2021 Document Version Final published version Citation (APA) Kazasidis, O. (2021). Methods for controlling deformable mirrors with hysteresis. https://doi.org/10.4233/uuid:3647c9bb-97d1-442a-9d3e-49cd1c9e3baf Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10. METHODS FOR CONTROLLING DEFORMABLE MIRRORS WITH HYSTERESIS METHODS FOR CONTROLLING DEFORMABLE MIRRORS WITH HYSTERESIS Dissertation for the purpose of obtaining the degree of doctor at Delft University of Technology by the authority of the Rector Magnificus, Prof. dr. ir. T. H. J. J. van der Hagen, chair of the Board for Doctorates to be defended publicly on Monday 1 March 2021 at 10:00 o’clock by Orestis KAZASIDIS Master of Science in Photonics, FH Münster University of Applied Sciences, Germany born in Athens, Greece This dissertation has been approved by the promotors. Composition of the doctoral committee: Rector Magnificus, chairperson Prof. dr. ir. M. Verhaegen Delft University of Technology, promotor Prof. dr. rer. nat. U. Wittrock FH Münster University of Applied Sciences, Germany, promotor Independent members: Prof. dr. B. Rieger Delft University of Technology Prof. dr. W. M. J. M. Coene Delft University of Technology Prof. dr. ir. N. J. Doelman TNO Dr. N. Devaney National University of Ireland Galway, Ireland Other member: Prof. dr. ir. G. V. Vdovine Delft University of Technology Keywords: active optics, adaptive optics, wavefront sensing, hysteresis, mathe- matical optimization Front: Design by the author, inspired by the drawings accompanying the es- say „Tanzkurven: Zu den Tänzen der Palucca“ by Wassily Kandinsky, Das Kunstblatt, Akademische Verlagsgesellschaft Athenaion, Potsdam, vol. 10, no. 3 (1926). Copyright © 2021 by O. Kazasidis ISBN 978-94-6384-169-6 An electronic version of this dissertation is available at http://repository.tudelft.nl/. v TÐ θὰ peῖ φῶς; Νὰ koitᾶς μὲ ἀθόlwto μάτι ὅla tὰ skotάδια. NÐkoc Καζαντζάκης What is meant by light? To gaze with undimmed eyes on all darknesses.* Nikos Kazantzakis *Translated by Kimon Friar CONTENTS Summary ix Samenvatting xi 1 Introduction1 1.1 Adaptive and active optics.........................2 1.1.1 Beginnings..............................2 1.1.2 Present and way ahead........................5 1.2 Wavefront representation..........................7 1.3 Unimorph deformable mirrors.......................9 1.3.1 Description and operation......................9 1.3.2 Characteristics and applications................... 12 1.4 Hysteresis.................................. 13 1.5 Motivation of the thesis........................... 14 1.5.1 Residual from open-loop compensation............... 14 1.5.2 Closed-loop control......................... 16 1.6 Organization and outline of the thesis................... 17 1.6.1 Extended-image-based aberration correction............ 18 1.6.2 Sensor for dynamic focus control.................. 19 References.................................... 21 2 A testbed for image-based correction 31 2.1 Introduction................................ 32 2.2 Testbed................................... 34 2.3 Deformable mirror control......................... 36 2.4 Merit function............................... 38 References.................................... 40 3 Merit function landscape 43 3.1 Introduction................................ 44 3.2 Simulation method............................. 44 3.2.1 PSF simulation............................ 44 3.2.2 Image simulation.......................... 45 3.3 Image-sharpness metric.......................... 46 3.4 Balancing an aberrated system....................... 47 3.5 Object-dependent aberration balancing.................. 50 3.6 Experimental verification.......................... 52 3.7 Conclusions................................. 54 References.................................... 56 vii viii CONTENTS 4 Extended-image-based correction 59 4.1 Introduction................................ 60 4.2 Aberration correction algorithm...................... 60 4.3 Results and discussion........................... 62 4.3.1 Merit function sensitivity...................... 62 4.3.2 Hysteresis compensation...................... 65 4.3.3 Correction of Zernike aberrations.................. 67 4.3.4 Correction of aberrations produced by random voltages....... 69 4.4 Summary and conclusions......................... 70 References.................................... 73 5 Sensor for dynamic focus control 75 5.1 Introduction................................ 76 5.2 Astigmatic method............................. 76 5.3 Experimental setup............................. 77 5.4 Defocus sensor............................... 78 5.4.1 Step response............................ 80 5.4.2 Calibration.............................. 80 5.4.3 Performance............................. 83 5.4.4 Accuracy and noise......................... 84 5.5 Conclusion................................. 85 References.................................... 86 6 Conclusions and recommendations 87 6.1 Conclusions................................. 88 6.1.1 Extended-image-based aberration correction............ 88 6.1.2 Sensor for dynamic focus control.................. 89 6.2 Recommendations for future work..................... 90 6.2.1 Extended-image-based aberration correction............ 90 6.2.2 Sensor for dynamic focus control.................. 90 References.................................... 92 Acknowledgements 95 Curriculum Vitæ 97 List of Publications 99 SUMMARY Fast adaptive optics and comparatively slower active optics are cornerstones of modern- day astronomy. Such systems are installed on most current large ground-based observa- tories in the visible or infrared and are included in the design of all future observatories. Their role is twofold; first, to compensate for astronomical seeing, and second, to cor- rect for design and manufacturing errors, as well as thermal and mechanical distortions. What’s more, the science goals of future large space observatories in the visible or in- frared rely on active and adaptive optics systems for reaching the required wavefront accuracy and stability, with imminent examples the folded segmented primary mirror of the James Webb Space Telescope (JWST) and the deformable mirrors of the Roman Space Telescope, previously called the Wide Field Infrared Survey Telescope (WFIRST). Besides astronomy, adaptive optics find laser applications, for aberration correction and for beam shaping. This thesis was set to explore methods for controlling deformable mirrors with hys- teresis, specifically for controlling unimorph deformable mirrors developed and manu- factured at the Photonics Laboratory of the FH Münster University of Applied Sciences in Germany. The technology for manufacturing unimorph deformable mirrors has been developed in the past at the Photonics Laboratory and has been expanded in a series of industrial and research projects, both for astronomical and for laser applications. Uni- morph deformable mirrors are a promising technology for adaptive and active optics systems, thanks to their paramount mechanical properties and their versatility. How- ever, their piezoelectric actuators exhibit higher hysteresis than most other actuators. The focus of this thesis lies in accurate and precise wavefront control with unimorph deformable mirrors despite their intrinsic hysteresis. Hysteresis can be compensated with two different approaches. In the feedforward scheme, a mathematical model of the hysteresis is constructed and its inverse model is used in open-loop to drive the deformable mirror. In the feedback scheme, the wave- front deviation – including the hysteresis influence – is measured by a wavefront sensor and the deformable mirror is controlled in closed-loop. These two approaches can be combined for optimal performance. The open-loop compensation using the Prandtl- Ishlinskii formalism has previously been implemented at the Photonics Laboratory and was found to reduce the hysteresis from 15% to about 2%. Nevertheless, the residual un- compensated hysteresis still limits the performance of optical systems that have to be almost diffraction-limited. This thesis consists of two parts that manifest the two activ- ities carried out during this PhD project. The first is image-based aberration correction using extended scenes. This aspires to complement existing technologies for the wave- front control in future space telescopes using active optics. The second is fast defocus sensing for the implementation of a closed-loop focus-shifter, with potential application in laser micromachining. ix x SUMMARY In the first part, the feedback for controlling the unimorph deformable mirror is gen- erated from the imaging detector. This
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