Coronagraphic data post-processing using projections on instrumental modes by Yeyuan (Yinzi) Xin B.S., California Institute of Technology (2018) Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2020 c Massachusetts Institute of Technology 2020. All rights reserved. ○ Author...................................................................... Department of Aeronautics and Astronautics May 18, 2020 Certified by. Kerri Cahoy Associate Professor Thesis Supervisor Accepted by................................................................. Sertac Karaman Chair, Graduate Program Committee Coronagraphic data post-processing using projections on instrumental modes by Yeyuan (Yinzi) Xin Submitted to the Department of Aeronautics and Astronautics on May 18, 2020, in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics Abstract High contrast astronomy has yielded the direct observations of over a dozen exoplanets and a multitude of brown dwarfs and circumstellar disks. Despite advances in coronagraphy and wavefront control, high contrast observations are still plagued by residual wavefront aber- rations. Post-processing techniques can provide an additional boost in separating residual aberrations from an astrophysical signal. This work explores using a coronagraph instru- ment model to guide post-processing. We consider the propagation of signals and wavefront error through a coronagraphic instrument, and approach the post-processing problem us- ing "robust observables." We model and approximate the instrument response function of a classical Lyot coronagraph (CLC) and find from it a projection that removes the dominant error modes. We use this projection to post-process synthetically generated data, and as- sess the performance of the new model-based post-processing approach compared to using the raw intensity data by calculating their respective flux ratio detection limits. We extend our analysis to include the presence of a dark hole using a simulation of the CLC on the High-contrast imager for complex aperture telescopes (HiCAT) testbed. We find that for non-time-correlated wavefront errors, using the robust observables modestly increases our sensitivity to the signal of a binary companion for most of the range of separations over which our treatment is valid, for example, by up to 50% at 7:5휆/퐷. For time-correlated wavefront errors, the results vary depending on the test statistic used and degree of correla- tion. The modest improvement using robust observables with non-time-correlated errors is shown to extend to a CLC with a dark hole created by the stroke minimization algorithm. Future work exploring the inclusion of statistical whitening processes will allow for a more complete characterization of the robust observables with time-correlated noise. We discuss the dimensionality of coronagraph self-calibration problem and motivate future directions in the joint study of coronagraphy and post-processing. Thesis Supervisor: Kerri Cahoy Title: Associate Professor 2 Acknowledgments I want to thank Kerri Cahoy, my advisor, for supporting me and my various research interests throughout these couple of years, and for the genuine care and support she has for me and all of her students. I want to thank Laurent Pueyo for somehow believing in this project from the moment I (basically a stranger at the time) mentioned it, for sponsoring my work on it at STScI, and for all of the great mentorship and guidance he has provided since. I want to thank Ewan Douglas for teaching me much of what I know about optics and what real astronomy is like, for maintaining the perfect balance of interest and skepticism for my half-baked ideas, and for being a supportive mentor both for this project and in general. I want to thank Romain Laugier for taking the time to help me with many of the topics involved in this investigation, for his valuable suggestions for directions to explore, and for enlightening me about the term "coronagram." Thank you as well to Ben Pope, Frantz Martinache, Mamadou N’Diaye, and Alban Ceau for our helpful conversations on this topic. I want to acknowledge Rachel Morgan and Greg Allan, my labmates and friends at MIT, as well as the rest of the MIT DeMi team, with whom I’ve shared many fun experiences and many stressful experiences, and who have made those experiences memorable. Thank you also to the Stuffed Animal Party: Jules Fowler, Iva Laginja, Scott Will, Theo Jolivet, Kelsey Glazer, Evelyn McChesney, and Remi Soummer, who have made me feel incredibly welcome at STScI. Software: This research made use of PROPER, an optical propagation library [1]; hicat- package, the software infrastructure that models and runs the HiCAT testbed; POPPY, an open-source optical propagation Python package originally developed for the James Webb Space Telescope project [2]; HCIPy, an open-source object-oriented framework written in Python for performing end-to-end simulations of high-contrast imaging instruments [3]; As- tropy [4, 5]; NumPy [6]; SciPy [7]; and Matplotlib [8]. 3 Contents 1 Introduction and Background 12 1.1 Introduction . 12 1.2 Instrumentation . 13 1.2.1 Coronagraphy . 14 1.2.2 Wavefront Sensing and Control (WFSC) . 15 1.3 Post-processing . 17 1.3.1 Self-calibration, Robust Observables, and Kernel Methods . 17 1.3.2 Coronagraphic Post-processing . 19 1.3.3 Compatibility of Methods . 20 1.4 Thesis Contributions . 20 2 Signals and Wavefront Error in Coronagraphs 22 3 Classical Lyot Coronagraph (Simulation) 26 3.1 Optical Model . 26 3.2 Coronagraph Properties . 27 3.3 Building Response Matrices . 31 3.4 Singular Value Decomposition, Singular Modes, and the Projection K . 33 3.5 Synthetic Data Analysis . 35 3.5.1 Synthetic Data Generation . 35 3.5.2 Processing Synthetic Data . 36 3.5.3 Detection Tests . 38 3.5.4 Receiver Operating Characteristic Curves . 39 4 3.5.5 Detection Limits . 40 3.5.6 Time-correlated Wavefront Errors . 42 3.6 Summary of Results . 42 4 Classical Lyot Coronagraph with Dark Hole (HiCAT Simulation) 46 4.1 Background . 46 4.2 Optical Model . 47 4.3 Dark Holes with Stroke-Minimization . 49 4.4 Building a Response Matrix . 51 4.5 Singular Value Decomposition, Singular Modes, and the Projection K . 52 4.6 Synthetic Data Analysis . 53 4.6.1 Synthetic Data Generation . 53 4.6.2 Synthetic Data Analysis . 55 4.6.3 ROCs and Detection Limits . 55 4.7 Summary of Results . 58 5 Discussion 59 5.1 Lack of Statistical Whitening . 59 5.2 Kernel-Nulling . 60 5.3 Connection with PASTIS Formalism . 60 5.4 Dimensions for Continuous Coronagraphy . 61 6 Future Work and Conclusions 65 A Heuristic Details of Robust Observables with the CLC 67 5 List of Figures 1-1 a) The nominal coronagram (in log10 scale) of a central star with an off-axis point source at 7:5휆/퐷 with a contrast of 4 10−4. b) An example of phase × errors (nm) in the wavefront at the primary telescope pupil. c) A coronagram if the same system in a) in the presence of the wavefront errors shown in (b). 15 1-2 A typical AO system with a deformable mirror and wavefront sensor in closed loop control, and a downstream science instrument such as a high-resolution camera. [9] . 16 1-3 Pictorial representation of kernel phases. The operator A휑 injects phase aber- rations 휑 into a subspace of baseline phases Φ. There is another subspace of baseline phases, K휑Φ0, which are not affected by these phase aberrations, and we call these kernel phases. [10] . 19 3-1 Optical model for the Lyot coronagraph, included as an example in the PROPER optical propagation library [1]. The coronagraph operates at 585 nm. The occulter is a circular obscuration with radius 0.561 휇m, and the Lyot stop is a circular aperture with radius 2:02 m. The Fraunhofer regime is assumed, so the model consists of only 2D Fourier transforms and masks, and resizing and propagation distances are not considered. 27 3-2 The nominal coronagram of just a central star in log10 scale of arbitrary in- tensity units. 28 3-3 A radial slice of the nominal coronagraph residuals on a central star. 29 6 3-4 a) The radial slices of a mostly linear, a mostly quadratic, and an in-between sinusoidal speckle in the detector plane plotted against the coronagraph resid- uals. b) The intensity with a predominantly linear speckle, which mostly interferes with the nominal star PSF. c) The intensity with a predominantly quadratic speckle that is mostly the square-amplitude of the wavefront error itself. d) The intensity with a speckle that is neither dominantly linear nor quadratic, but somewhere in-between. 30 3-5 The throughput of an off-axis point source as a function of its spatial sepa- ration, indicated by the solid line. The inner working angle is the separation at which the throughput is 50% (indicated by the dashed line), which in this case is 5휆/퐷. ................................... 31 3-6 The singular values of the transfer matrix A. We choose the 102nd through 10,000th singular modes to make up our projection matrix K, which will project out the first 101 modes from our data and result in Nk = 9899. 34 3-7 The first 10 singular modes of AZ as represented in the the detector plane intensity basis. 35 3-8 Top left: A single aberrated snapshot (in linear scale) with a companion with a flux ratio of 4 10−4 at 7:5휆/퐷. Top right: The data frame with the model × coronagram subtracted. Bottom left: The mean of 20 frames of data, with the companion "location" (visible by eye) marked with the red box. Bottom right: The standard deviation of 20 frames of data.