CONVERSION FROM LINEAR TO CIRCULAR POLARIZATION IN FPGA IN REAL TIME Inaugural-Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultät der Universität zu Köln vorgelegt von Koyel Das aus Kolkata, West Bengal, Indien Köln 2013 Berichterstatter: Prof. Dr. Andreas Eckart Prof. Dr. Anton Zensus Tag der mündlichen Prüfung: 28.06.2013 CONTENT ACKNOWLEDGEMENT......................................................................................................................ix CONTRIBUTIONS IN WORK.............................................................................................................xi ZUSAMMENFASSUNG .....................................................................................................................xiii ABSTRACT..............................................................................................................................................1 1. INTRODUCTION................................................................................................................................2 1.1 Motivation to form circular polarization.............................................................................................2 1.2 Realization of circular polarization in analogue systems...................................................................3 1.3 The digital circular polarizer project...................................................................................................6 1.4 Aims of the project...........................................................................................................................8 2. THEORETICAL DEVELOPMENT..................................................................................................9 2.1 Significance of theoretical analysis..................................................................................................9 2.2 Method overview................................................................................................................................9 2.3 Instrumental phase and gain calibration..........................................................................................10 2.3.1 Phase equalization..........................................................................................................................10 2.3.2 Gain equalization...........................................................................................................................13 2.4 Windowing.........................................................................................................................................15 2.5 Forming circular polarization...........................................................................................................16 2.6 Performance limitations.....................................................................................................................16 2.7 Phase stability of the analogue receiver chain..................................................................................17 2.8 Expected polarization purity..............................................................................................................19 3. PRELIMINARY TEST OF ALGORITHM.....................................................................................20 3.1 Phase and gain equalization and windowing....................................................................................20 3.1.1 Experiment to collect test data........................................................................................................20 3.1.2 Description of spectral characteristics obtained by processing data in MATLAB....................21 3.1.3 Phase equalization...........................................................................................................................24 3.1.4 Gain equalization............................................................................................................................25 3.1.5 Windowing......................................................................................................................................27 3.2 Preliminary questions to be answered...............................................................................................28 3.3 Conclusion..................................................................................................................................... ...29 4. IMPLEMENTATION DETAILS......................................................................................................30 4.1 Overview of main logic blocks of the digital circular polarizer......................................................30 4.2 Conclusion.........................................................................................................................................32 5. EXPERIMENTS AND RESULTS....................................................................................................33 5.1 Design logic verification and simulation results................................................................................33 5.1.1 Lab setup for collecting test data....................................................................................................33 5.1.2 Time series obtained from the digital oscilloscope in the experiment...........................................34 5.1.3 Power spectra from the two channels in the experiment..............................................................34 5.1.4 Simulation results from the design logic.........................................................................................35 5.2 Verification of polarization purity.....................................................................................................41 5.2.1 Signal flow through the setup.........................................................................................................42 5.2.2 Measurement details.......................................................................................................................42 5.2.3 Results.............................................................................................................................................45 5.2.4 Discussion.......................................................................................................................................46 5.3 Conclusion.........................................................................................................................................48 6. APPLICATIONS IN RADIO ASTRONOMY.............................................................................49 6.1 Significance of the digital circular polarizer in radio astronomy.......................................................49 6.2 Different astronomical phenomena generating polarization.............................................................49 6.2.1 Cyclotron and synchrotron emission...............................................................................................49 6.2.2 Plasma frequency and plasma oscillations.....................................................................................50 6.2.3 Zeeman effect..................................................................................................................................50 6.2.4 Thompson scattering.......................................................................................................................50 6.2.5 Brewster angle effects...................................................................................................................51 6.3 Depolarization effects........................................................................................................................51 6.3.1 Depolarization due to Faraday rotation..........................................................................................51 6.3.2 Bandwidth depolarization...............................................................................................................51 6.3.3 Beam depolarization.......................................................................................................................51 6.4 Explorations and underlying techniques requiring polarimetric observations in VLBI..................52 6.4.1 Magnetic field studies by the SKA................................................................................................52 6.4.2 Studies of Sgr A*...........................................................................................................................56 6.4.3 Studies of circular polarization in AGN.......................................................................................59 6.4.4 Studies of the Perseus cluster......................................................................................................61 6.5 Conclusions......................................................................................................................................66 7. REMAINING TOPICS OF DISCUSSION.....................................................................................68 7.1 Brief overview of the antenna system in radio telescopes...............................................................68 7.2 Polarization ellipse: response of radio telescopes in ideal cases.................................................68 7.2.1 Retrieving linear polarization in the sky from elliptical response of antenna...............................71 7.3 Polarization ellipse: response from imperfectly oriented dipole elements......................................73