LUCKY IMAGING: BEYOND BINARY STARS Thesis submitted for the degree of Doctor of Philosophy by Tim Staley Institute of Astronomy & Emmanuel College arXiv:1404.5907v1 [astro-ph.IM] 23 Apr 2014 University of Cambridge January 21, 2013 DECLARATION I hereby declare that this dissertation entitled Lucky Imaging: Beyond Binary Stars is not substantially the same as any that I have submitted for a degree or diploma or other qualification at any other University. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualification. This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. I note that chapter 1 and the first few sections of chapter 6 are intended as reviews, and as such contain little, if any, original work. They contain a number of images and plots extracted from other published works, all of which are clearly cited in the appropriate caption. Those parts of this thesis which have been published are as follows: • Chapters 3 and 4 contain elements that were published in Staley and Mackay (2010). However, the work has been considerably expanded upon for this document. • The planetary transit host binarity survey described in chapter 5 is soon to be submitted for publi- cation. This dissertation contains fewer than 60,000 words. Tim Staley Cambridge, January 21, 2013 iii ACKNOWLEDGEMENTS 1 2 This thesis has been typeset in LATEX using Kile and JabRef. Thanks to all the former IoA members who have contributed to the LaTeX template used to constrain the formatting. It is a dark art. Many thanks to the Cambridge lucky imaging team. Firstly my supervisor Craig Mackay, ever on hand with sound advice and helpful input. Much hard effort has gone in behind the scenes to make LuckyCam work, and for that my thanks go to Craig, David King, Frank Suess and Keith Weller. Thanks also to all the administrative and student support staff at the IoA, for making my PhD experi- ence a remarkably well organised and content one. Thanks to my parents for their unfailing support, and all my friends in Cambridge for making my time here immensely enjoyable. Special thanks to Lindsey, for putting up with me throughout the write up, and to the windsurf club for making sure I get out enough. I acknowledge with gratitude the support of an STFC studentship. This thesis is based on observa- tions made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. This research has made use of NASAs Astrophysics Data System Bibliographic Services, as well as the SIMBAD database and VizieR catalogue access tools operated at CDS, Strasbourg, France. A few of the results were based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Institute. Tim Staley Cambridge, January 21, 2013 1http://kile.sourceforge.net/ 2http://jabref.sourceforge.net/ v vi Acknowledgements The LuckyCam observing team, shortly after assembling the camera for the observing run at the Nordic Optical Telescope, La Palma, in July 2009. From left to right: myself, LuckyCam, David King and Craig Mackay. SUMMARY Lucky Imaging: Beyond Binary Stars Tim Staley Lucky imaging is a technique for high resolution astronomical imaging at visible wavelengths, utilis- ing medium sized ground based telescopes in the 2–4m class. The technique uses high speed, low noise cameras to record short exposures which may then be processed to minimise the deleterious effects of atmospheric turbulence upon image quality. The key statement of this thesis is as follows; that lucky imaging is a technique which now benefits from sufficiently developed hardware and analytical techniques that it may be effectively used for a wide range of astronomical imaging purposes at medium sized ground based telescopes. Furthermore, it has proven potential for producing extremely high resolution imaging when coupled with adaptive optics systems on larger telescopes. I develop this argument using new mathematical analyses, simulations, and data from the latest Cambridge lucky imaging instrument. The first half of this thesis develops new models and algorithms for general purpose reduction of lucky imaging data. Imaging of faint astronomical objects is achieved through careful calibration and analysis of the data, and utilisation of faint guide stars is improved. An analytic model for predicting Strehl ratio in reduced images is proposed. The second half covers scientific results and applications, analysis techniques, and implementation of simulations and the data reduction pipeline. Results from a binarity survey of planetary transit hosts are given, demonstrating improved detection limits compared to previous publications. Wide field lucky images produced from the synchronised four CCD mosaic camera are demonstrated and analysed for image quality across the field. Preliminary investigations of hybrid lucky imaging adaptive optics sys- tems through simulation and experimental data are presented. Finally, the challenges of dealing with high volumes of image data in an accurate and timely fashion are covered and solutions discussed. Cambridge, January 21, 2013 vii CONTENTS Declaration . iii Acknowledgements . v Summary . vii Contents viii List of Figures xii 1 Introduction 1 1.1 Atmospheric turbulence and light propagation . 1 1.1.1 Basic turbulence modelling . 1 1.1.2 Image propagation . 3 1.2 Characterising wavefront aberrations and image quality . 4 1.3 Adaptive optics . 7 1.3.1 Field of view and isoplanatic angle . 7 1.3.2 Sky coverage . 9 1.3.3 Observation wavelengths . 11 1.4 Lucky imaging . 12 1.4.1 A very brief history . 12 1.4.2 Pros and cons . 13 1.4.3 Current status of lucky imaging techniques . 14 1.5 New hardware: The quad-CCD LuckyCam . 14 1.6 Statement of thesis . 17 1.7 Chapter summaries . 18 2 Calibration of electron multiplying CCDs 21 2.1 The physics of electron multiplying charge-coupled devices . 21 2.2 Basics of CCD calibration . 22 2.3 Motivation and comparison with previous work on EMCCD calibration . 24 2.4 Probability distribution models for EMCCDs . 24 2.4.1 Clock induced charge . 26 2.5 Histogram analysis algorithms . 27 2.5.1 Bias determination at low pixel counts for the purpose of single frame bias esti- mation . 27 2.5.2 Electron multiplication gain . 29 2.6 Calibrating the Cambridge e2v CCD201 . 31 viii Contents ix 2.6.1 Spatial gradient in bias pedestal . 33 2.6.2 Bias pedestal drift . 33 2.6.3 Internally generated signal levels . 34 2.6.4 Clock induced charge levels . 35 2.6.5 Flat fielding and gain uniformity . 35 2.6.6 Bad pixels and pixel weighting . 37 2.7 Results . 37 3 Lucky imaging of faint sources: Thresholding techniques 39 3.1 Summary and comparison with literature . 39 3.2 Signal to noise ratio for conventional and electron multiplying CCDs . 41 3.3 Thresholded signal to noise equation . 42 3.4 Choosing the best detector mode for an observation . 42 3.5 Threshold optimization . 42 3.6 Combining thresholded and linear data . 44 3.7 Results of applying thresholding techniques to real data . 46 4 Optimising and predicting the image formation process 49 4.1 Background — Sampling theory and image combination . 49 4.2 Background: Speckle patterns and speckle imaging . 51 4.3 Frame registration overview . 54 4.4 Registration methods . 55 4.4.1 Implementation details . 56 4.5 Simulation methods used for testing . 57 4.6 Testing registration algorithms . 58 4.6.1 Results from comparison via simulation . 58 4.6.2 Comparison using real data . 59 4.7 Image formation processes . 60 4.7.1 Instantaneous Strehl ratio probability distribution function . 62 4.7.2 Strehl estimation error . 62 4.7.3 Frame registration positional error . 64 4.8 Image formation model . 69 5 Scientific applications of lucky imaging 71 5.1 Binarity of planetary transit hosts . 72 5.1.1 Planetary transit surveys and the need for follow-up observations . 72 5.1.2 General techniques for detecting faint secondary sources . 73 5.1.3 Primary star PSF modelling and subtraction . 75 5.1.4 Applying a matched filter . 76 5.1.5 Automated companion candidate detection . 77 5.1.6 Companion candidate analysis . 78 x Contents 5.1.7 Results . 79 5.2 High temporal resolution photometry with EMCCDs . 79 5.2.1 Cygnus X-1 . 81 5.2.2 Estimating a lower bound to signal variance . 83 5.2.3 Fast photometry data reduction techniques . 84 5.2.4 Results . 87 5.2.5 Future work . 88 5.3 General high resolution imaging in the visible . 89 5.3.1 Faint limits . 89 5.3.2 High resolution across a wide field of view . 90 5.4 Science with lucky imaging-enhanced adaptive optics: Probing the binary star distribu- tion in globular clusters . 91 5.4.1 Globular clusters . 92 5.4.2 Metric: star separations detected vs. random positioning model . 95 5.4.3 Probing the binary distribution of M13 with LAMP . 96 6 Modelling of lucky imaging systems 99 6.1 End-to-end Monte Carlo simulation of atmospheric effects and optical systems . 100 6.1.1 Atmospheric phase screens . 101 6.1.2 End-to-end Monte Carlo simulation packages . ..