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The Development of a Small Scale Radio Astronomy Image Synthesis Array for Research in Radio Frequency Interference Mitigation

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The Development of a Small Scale Radio Astronomy Image Synthesis Array for Research in Radio Frequency Interference Mitigation Brigham Young University BYU ScholarsArchive Theses and Dissertations 2005-09-05 The Development of a Small Scale Radio Astronomy Image Synthesis Array for Research in Radio Frequency Interference Mitigation Jacob L. Campbell Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Electrical and Computer Engineering Commons BYU ScholarsArchive Citation Campbell, Jacob L., "The Development of a Small Scale Radio Astronomy Image Synthesis Array for Research in Radio Frequency Interference Mitigation" (2005). Theses and Dissertations. 673. https://scholarsarchive.byu.edu/etd/673 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. THE DEVELOPMENT OF A SMALL SCALE RADIO ASTRONOMY IMAGE SYNTHESIS ARRAY FOR RESEARCH IN RADIO FREQUENCY INTERFERENCE MITIGATION by Jacob Lee Campbell A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Department of Electrical and Computer Engineering Brigham Young University December 2005 Copyright c 2005 Jacob Lee Campbell All Rights Reserved BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a thesis submitted by Jacob Lee Campbell This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. Date Karl F. Warnick, Chair Date Brian D. Jeffs Date Michael A. Jensen BRIGHAM YOUNG UNIVERSITY As chair of the candidate’s graduate committee, I have read the thesis of Jacob Lee Campbell in its final form and have found that (1) its format, citations, and bibli- ographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date Karl F. Warnick Chair, Graduate Committee Accepted for the Department Michael A. Jensen Graduate Coordinator Accepted for the College Alan R. Parkinson Dean, Ira A. Fulton College of Engineering and Technology ABSTRACT THE DEVELOPMENT OF A SMALL SCALE RADIO ASTRONOMY IMAGE SYNTHESIS ARRAY FOR RESEARCH IN RADIO FREQUENCY INTERFERENCE MITIGATION Jacob Lee Campbell Department of Electrical and Computer Engineering Master of Science Radio astronomy synthesis imaging arrays are composed of many parabolic reflector antennas. These antennas are designed to be extremely sensitive to detect faint emissions from astronomical sources. Unfortunately, this also makes them sus- ceptible to radio frequency interference (RFI) from man made sources such as orbiting satellites. The radio astronomy research group at Brigham Young University (BYU) is investigating methods to mitigate the effects of RFI in radio astronomy synthesis imaging. Though real-time RFI mitigation has been demonstrated for a large single dish telescope, for synthesis imaging arrays our prior work has consisted solely of algorithm development and computer simulations. To test our algorithms on experi- mental data we need an image synthesis array at BYU. The primary contribution of this Master’s thesis is the design and construction of a working image synthesis array on the roof of the Clyde Building at BYU. This thesis describes the design of the antenna placement for the synthesis ar- ray. Antenna placement is the primary factor for determining image quality since the placement dictates the shape of the synthesized beam. Simulations were performed, prior to the array’s construction, to predict the quality of images from the array. Another contribution of this thesis is signal processing code to generate correlations of the signals from the antennas. Code was written to calibrate measured data and generate an image from the correlations. Code was also written to steer the antennas and track astronomical phenomena. The performance of the array is evaluated in this thesis. The culmination of this thesis is a radio image of the supernova remnant Cassiopeia A. This thesis concludes with simulations of an RFI mitigation experiment that can be performed with the new array (pending certain improvements to the array). ACKNOWLEDGMENTS Many people have helped me with my thesis. I want to thank Dr. Karl Warnick for his guidance through my research, this thesis, and through my graduate studies. I would also like to thank Dr. Brian Jeffs for recruiting me to this project, and for his advice in my research. I express my appreciation to Andy Poulsen, Chad Hansen, and Devin Pratt who helped me with my research and homework. I would also like to thank James Nagel and Micah Lilrose who helped me build and maintain the VSA. I leave the array in their capable hands. Above all I would like to thank my family and especially my parents for their love, prayers, and support. Thank you Rod, Janet, Jesse, Andrew, Mark, Lisa, Cari, and Sharon. This thesis is dedicated to Rod and Janet Campbell. Contents Abstract ix Table of Contents xv List of Tables xxi List of Figures xxiii 1 Masters Thesis Introduction 1 1.1 Radio Astronomy Synthesis Imaging . 1 1.2 Radio Interference in Radio Astronomy . 2 1.3 ThesisContributions ........................... 3 1.4 ThesisOrganization............................ 3 2 Mathematical Foundations and Background 5 2.1 Synthesis Imaging Formulation . 5 2.1.1 General Formulation of Observed Field . 5 2.1.2 Simplifying Assumption 1: Ignore Polarization . 7 2.1.3 Simplifying Assumption 2: Immense Distance to Source . 7 2.1.4 Simplifying Assumption 3: Celestial Sphere is Empty . 7 2.1.5 Measuring Spatial Coherence . 8 2.1.6 Simplifying Assumption 4: Spatial Correlation . 9 2.1.7 ObservedIntensity ........................ 10 2.1.8 Coordinate System for Imaging, Part I . 10 2.1.9 Coordinate System for Imaging, Part II . 11 2.1.10 Error Bounds for Small Field Imaging . 14 xv 2.1.11 ANoteonAntennaResponse . 14 2.2 The Interferometer and Measured Visibility . 15 2.3 Computinguandv............................ 17 2.4 FourierTransformImaging. 21 2.4.1 Measuring Spatial Frequency . 22 2.4.2 Samplingtheuvplane . 23 2.4.3 InvertingtheTransform . 24 3 Array Design 27 3.1 Introduction................................ 27 3.2 EarlyDesignDecisions .......................... 27 3.3 AntennaPlacement............................ 28 3.3.1 Placement Logistics . 28 3.3.2 Final Placement Concerns . 31 3.3.3 UVPlaneSampling ....................... 31 3.4 ReceivingandProcessing. 38 3.4.1 Analog Receiver . 38 3.4.2 SignalProcessing ......................... 39 4 Simulation and Analysis 41 4.1 Introduction................................ 41 4.2 The Noise Free Model: Dirty Beam and Resolution . 41 4.3 ModelwithNoise............................. 46 4.3.1 Noise in Radio Astronomy . 46 4.3.2 Simulations with Noise . 49 4.4 PhaseStabilitySimulations . 51 4.4.1 RandomPhaseError ....................... 55 4.4.2 CalibrationOffsetError . 55 4.4.3 LinearlyDriftingPhase. 56 xvi 5 Performance 61 5.1 Introduction................................ 61 5.2 TheCompletedVSA ........................... 61 5.2.1 TheAntennas........................... 61 5.2.2 Software.............................. 66 5.3 FirstFringeFunction........................... 69 5.4 ObservingaCalibratorwiththeVSA . 70 5.4.1 FlaggingandEditingData. 70 5.4.2 TemporalData .......................... 71 5.4.3 PhaseandAmplitudeAnalysis . 72 5.4.4 MeasuredversusPredicted. 73 5.4.5 CrossCoupling .......................... 74 5.4.6 DCOffsetCalibration . 76 5.4.7 PhaseOffsetCalibration . 77 5.5 AnImageofCassiopeiaA ........................ 77 6 RFI Experiments 87 6.1 Introduction................................ 87 6.2 SubspaceProjection ........................... 87 6.3 CrossSubspaceProjection . 89 6.4 SimulationofCSPfortheVSA . 90 7 Conclusions and Future Work 97 7.1 ImagingahighSNRSource ....................... 97 7.2 ImagingOtherAstronomicalPhenomena . 97 7.3 RFIScenarios............................... 98 7.4 ImprovementstotheArray. 99 7.5 Conclusions ................................ 100 A Operating Procedures and Guidelines 103 A.1 OutdoorEquipment ........................... 103 xvii A.2 EquipmentCheck............................. 105 A.3 PointingCalibration . 107 A.4 WeatherConditions. 109 A.5 UsingthePentekDSP .......................... 110 A.6 Checklist.................................. 110 A.7 AntennasTracking ............................ 112 B VSA Software 115 B.1 CodefortheDSP............................. 115 B.1.1 CSource.............................. 115 B.1.2 IntermediateandOutputFiles. 118 B.1.3 HelperCode............................ 119 B.1.4 Initial Data Analysis Code . 121 B.2 ObservationCode............................. 123 B.2.1 Astroandsatellite ........................ 123 B.2.2 Tracking and Steering Software . 124 B.2.3 Weather Software . 128 B.2.4 Management Scripts for Executables . 129 B.3 Analysis and Image Generation Code . 129 B.3.1 MakinganImage ......................... 129 B.3.2 InitialAnalysis .......................... 130 B.3.3 cruncher.m ............................ 130 B.3.4 gather.m.............................. 133 B.3.5 Tools for Imaging . 134 C Recommended Improvements 137 C.1 Problems.................................. 137 C.1.1 CrossTalk............................. 137 C.1.2 AntennaPositions
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