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Quasi-Optical Design and Analysis of Bolometric Interferometers for Cosmic Microwave Background Experiments

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Quasi-Optical Design and Analysis of Bolometric Interferometers for Cosmic Microwave Background Experiments Quasi-Optical Design and Analysis of Bolometric Interferometers for Cosmic Microwave Background Experiments Presented by Gareth Stanley Curran, M.Sc. A thesis submitted for the degree of Doctor of Philosophy Department of Experimental Physics, National University of Ireland, Maynooth, Maynooth, Co. Kildare, Ireland. December 2010 Head of Department Prof. J. Anthony Murphy Research Supervisor Dr.Créidhe O‟Sullivan To my family Table of Contents Abstract ......................................................................................................................... v Acknowledgements ..................................................................................................... vi Chapter 1 Introduction ............................................................................................... 1 1.1 Introduction .................................................................................................. 1 1.2 The Electromagnetic Spectrum .................................................................... 1 1.2.1 Overview of the Electromagnetic Spectrum ........................................ 1 1.2.2 Terahertz Radiation and Astronomy .................................................... 2 1.3 The Cosmic Microwave Background (CMB) .............................................. 6 1.3.1 The Big Bang and the CMB ................................................................. 7 1.3.2 Past, Present and Future CMB Experiments ...................................... 19 1.3.3 Other Applications of Terahertz Imaging .......................................... 29 1.4 Interference and Polarisation ..................................................................... 30 1.4.1 Interference and the Interferometer .................................................... 30 1.4.2 The Fizeau Interferometer .................................................................. 37 1.4.3 Polarisation ......................................................................................... 39 1.4.4 The Stokes Parameters ....................................................................... 44 1.5 Imaging versus Interferometry ................................................................... 47 1.6 The Millimetre-Wave Bolometric Interferometer ...................................... 50 1.6.1 Overview of the MBI Project ............................................................. 50 1.6.2 Science with MBI ............................................................................... 51 1.7 The QU Bolometric Interferometer for Cosmology................................... 54 1.7.1 Overview of the BRAIN and QUBIC Projects .................................. 54 1.7.2 Science and Challenges with QUBIC ................................................ 55 1.8 Synopsis and Thesis Outline ...................................................................... 56 Chapter 2 Analytical Tools for Modelling Quasi-Optical Systems ....................... 59 2.1 Introduction ................................................................................................ 59 2.2 Ray Tracing Analysis ................................................................................. 60 2.2.1 Background ........................................................................................ 60 i 2.2.2 Ray Tracing Through an On-Axis Cassegrain System ...................... 61 2.3 Fresnel Diffraction Analysis ...................................................................... 64 2.3.1 Background ........................................................................................ 64 2.3.2 The Fresnel Integral ........................................................................... 65 2.4 Gaussian Beam Mode Analysis ................................................................. 69 2.4.1 Background ........................................................................................ 69 2.4.2 Derivation of Gaussian Beam Modes ................................................ 70 2.4.3 Propagation of Gaussian Beam Modes .............................................. 76 2.4.4 Multi-Moded Gaussian Beams ........................................................... 78 2.4.5 ABCD Matrices .................................................................................. 80 2.4.6 GBM Analysis of a Two-Slit Interferometer ..................................... 84 2.5 Physical Optics Analysis ............................................................................ 87 2.5.1 Background ........................................................................................ 87 2.5.2 Physical Optics Analysis of an Aperture with Stop ........................... 91 2.6 Description of Modelling Software ............................................................ 92 2.7 Conclusions .............................................................................................. 108 Chapter 3 The Millimetre-Wave Bolometric Interferometer ............................. 110 3.1 Introduction .............................................................................................. 110 3.2 The Instrumentation of the MBI-4 System .............................................. 111 3.2.1 Observing Strategy and Telescope Mount ....................................... 112 3.2.2 Interference ...................................................................................... 113 3.2.3 Detectors and Signal Processing ...................................................... 115 3.2.4 Cryogenics ....................................................................................... 117 3.2.5 The Optical System .......................................................................... 118 3.3 Design of the MBI-4 Optical Beam Combiner ........................................ 122 3.3.1 The Design of the Optical System ................................................... 123 3.3.2 A First Approximation Using Geometrical Optics .......................... 123 3.3.3 Diffraction Analysis ......................................................................... 129 Chapter 4 Electromagnetic Modeling of Horn Antennas and Waveguides ...... 152 4.1 Introduction .............................................................................................. 152 4.2 Smooth-Walled and Corrugated Horn Antennas ..................................... 153 4.2.1 Smooth-Walled Conical Horns ........................................................ 153 ii 4.2.2 The Implementation of Smooth-Walled Horns in MODAL ............ 157 4.2.3 MBI-4 Phase Flattening Lenses ....................................................... 158 4.2.4 Corrugated Conical Horns................................................................ 166 4.3 Scatter Matrix Analysis of Quasi-Optical Systems .................................. 170 4.3.1 Scatter Matrix Methods .................................................................... 171 4.3.2 MBI-4 Back-To-Back Horn Antennas ............................................. 175 4.3.3 Truncation by MBI-4 Windows ....................................................... 181 4.3.4 Singular Value Decomposition Analysis ......................................... 184 4.4 Mode Scattering at Rectangular-Circular Junctions ................................ 194 4.4.1 Rectangular Waveguide Modes ....................................................... 195 4.4.2 Circular Waveguide Modes.............................................................. 201 4.4.3 Scattering at a Rectangular-Circular Discontinuity ......................... 211 4.5 Beam Distortion in Closely Packed Waveguide Arrays .......................... 216 4.5.1 Circular Waveguide Arrays.............................................................. 216 4.5.2 Rectangular Waveguide Arrays ....................................................... 223 Chapter 5 Quasi-Optical Analysis of MBI-4 ........................................................ 233 5.1 Analysis of the Fizeau Optical System Using MODAL .......................... 233 5.1.1 Defining the System in MODAL ..................................................... 233 5.1.2 Evaluation of Propagation Techniques ............................................ 238 5.1.3 Calculating the System Scattering Matrix........................................ 244 5.1.4 The Effects of Truncation on the System ......................................... 256 5.1.5 Mechanical Tolerances in MBI-4..................................................... 261 5.1.6 Frequency Dependence of the Instrument........................................ 281 5.1.7 Simulating Lab Measurements ......................................................... 284 5.2 Conclusions .............................................................................................. 289 Chapter 6 Quasi-Optical Design and Analysis of QUBIC ................................... 291 6.1 Introduction .............................................................................................. 291 6.2 Science and Challenges with QUBIC ...................................................... 292 6.3 The QUBIC Instrument ............................................................................ 293 6.4 Design and Analysis of the Beam Combiner ........................................... 294 6.4.1 Optical System Design Contraints ................................................... 294 6.4.2 Physical Optics Analysis of the Mirror Configurations ................... 295 iii 6.4.3 The Implementation of Lenses ........................................................
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