Quasi-Optical Design and Analysis of a Bolometric Interferometer for Cosmic Microwave Background Radiation Experiments Maynooth University Department of Experimental Physics Stephen Scully BSc (Eng) HDip (App Phy) A thesis submitted for the degree of Doctor of Philosophy February 2016 Department Head Prof. J. Anthony Murphy Supervisor Dr. Créidhe O’Sullivan TABLE OF CONTENTS 1 INTRODUCTION ....................................................................................................................... 1 1.1 COSMOLOGY AND THE CMB ........................................................................................................ 1 1.1.1 Historical........................................................................................................................... 1 1.1.2 The Big Bang Theory ......................................................................................................... 3 1.1.3 Inflation ............................................................................................................................ 7 1.1.4 Angular power spectrum of the CMB ............................................................................... 7 1.2 MEASURING THE CMB ............................................................................................................... 8 1.2.1 Temperature ..................................................................................................................... 9 1.2.2 Polarisation..................................................................................................................... 13 1.2.3 Constraining cosmological models ................................................................................. 19 1.2.4 Measurements ................................................................................................................ 21 1.3 INTERFEROMETRY .................................................................................................................... 23 1.3.1 Interferometry basics ..................................................................................................... 23 1.3.2 Interferometry operation ............................................................................................... 23 1.4 SUMMARY .............................................................................................................................. 33 1.5 THESIS OUTLINE ....................................................................................................................... 34 2 OPTICAL AND ELECTROMAGNETIC MODELLING ..................................................................... 36 2.1 FEED HORN ANALYSIS TECHNIQUES ............................................................................................. 38 2.1.1 TE and TM modes ........................................................................................................... 38 2.1.2 Mode matching techniques ............................................................................................ 44 2.1.3 Singular value decomposition......................................................................................... 51 2.1.4 Dispersion curves ............................................................................................................ 54 2.1.5 Hybrid modes .................................................................................................................. 56 2.2 FREE-SPACE ANALYSIS TECHNIQUES ............................................................................................. 59 2.2.1 Geometrical optics (GO) and geometric theory of diffraction (GTD) .............................. 60 2.2.2 Physical optics (PO) and theory of diffraction (PTD) ....................................................... 62 2.2.3 Gaussian beam modes (GBM) ........................................................................................ 65 2.3 SYSTEM ANALYSIS TOOLS .......................................................................................................... 83 2.3.1 Overview ......................................................................................................................... 84 2.3.2 Model system components ............................................................................................. 85 2.3.3 Propagating the aperture field ....................................................................................... 88 2.3.4 Sampling density ............................................................................................................ 89 2.3.5 Extracting data from the simulations ............................................................................. 90 2.3.6 Automation of simulations ............................................................................................. 92 2.3.7 Comparing MODAL and GRASP ...................................................................................... 93 ii 2.4 CONCLUSION .......................................................................................................................... 95 3 QUBIC .................................................................................................................................... 97 3.1 PATHFINDERS .......................................................................................................................... 97 3.1.1 MBI ................................................................................................................................. 97 3.1.2 BRAIN............................................................................................................................ 103 3.2 QUBIC DESIGN ..................................................................................................................... 105 3.2.1 Overview ....................................................................................................................... 105 3.2.2 QUBIC v1.0 .................................................................................................................... 107 3.2.3 QUBIC design v2.0 ........................................................................................................ 121 3.3 QUBIC V2.0 DETAILS OF MIRROR DESIGN................................................................................... 125 3.3.1 Definition of global reference frame ............................................................................ 125 3.3.2 Definition of primary mirror ......................................................................................... 127 3.3.3 Definition of secondary mirror ..................................................................................... 130 3.3.4 Definition of input feed horn array ............................................................................... 132 3.4 PRELIMINARY QUBIC MODELLING ............................................................................................ 134 3.4.1 Gaussian beam mode analysis ..................................................................................... 134 3.4.2 PO analysis ................................................................................................................... 137 3.5 CONCLUSION ........................................................................................................................ 142 4 QUBIC ANALYSIS AND OPTIMISATION ................................................................................. 144 4.1 SPILLOVER AND BEAM TRUNCATION ........................................................................................... 144 4.1.1 Visualisation of 400 beams ........................................................................................... 144 4.1.2 Beam truncation by the primary mirror ....................................................................... 147 4.1.3 Beam truncation by the secondary mirror .................................................................... 149 4.1.4 Beam truncation at the detector plane ........................................................................ 151 4.1.5 Bolometer detector array ............................................................................................. 154 4.2 MIRROR TOLERANCE ANALYSIS ................................................................................................. 157 4.3 POLARISER AND SIDE DETECTOR ................................................................................................ 160 4.3.1 Orientation of polariser and side detector ................................................................... 160 4.3.2 Separation of polariser and side detector .................................................................... 168 4.3.3 Determination of polariser dimensions ........................................................................ 177 4.3.4 Polariser optical surface imperfections ........................................................................ 183 4.4 COLDSTOP ............................................................................................................................ 196 4.5 MANUFACTURING LIMITATIONS ................................................................................................ 201 4.5.1 Source relocation .......................................................................................................... 201 4.5.2 Truncation (420 mm limit) ............................................................................................ 208 4.6 CONCLUSION .......................................................................................................................