Volume 82 VERY LONG BASELINE INTERFEROMETRY AND THE VLBA. J. A. Zensus, P. J. Diamond, and P. J. Napier

Transcription

1 ASTRONOMICAL SOCIETY OF THE PACIFIC CONFERENCE SERIES Volume 82 VERY LONG BASELINE INTERFEROMETRY AND THE VLBA Proceedings of a Summer School held in Socorro, New Mexico June 1993 NRAO Workshop No. 22 Edited by J. A. Zensus, P. J. Diamond, and P. J. Napier Vll

2 Very Long Baseline Interferometry and the VLBA ASP Conference Series, Vol. 82, 1995 J. A. Zensus, P. J. Diamond, and P. J. Napier (eds.) Contents FIGURES TABLES PREFACE DEDICATION CONTRIBUTORS xxi xxv xxvii xxix xxxi I Basic Theory 1 1 Theory 3 B. G. Clark 1.1 Introduction Basis and Textbooks Electromagnetic Field The Spatial Coherence Function of the Field Synthesis Imaging Spectroscopy Polarization Imaging Design of Radio Interferometers Element Gain Calibrating Element Gains Living with Uncalibrated Gains Conclusion 16 2 Theory of Correlation 17 J. D. Romney 2.1 Introduction Interfaces Background Correlation and Coherence VLBI Observations The Correlator Frontend Delay Compensation Phase Compensation The Lag Correlator Fractional-Sample Delay 25 ix

3 CONTENTS Phase Rotator Implementation Spectral Response The FX Correlator Fractional-Sample Delay Phase Rotator Implementation Spectral Response Segmentation Miscellaneous FX Topics FX and Lag Correlator Intercomparison Cost Summary of Other Advantages 36 Imaging Concepts 39 T. Cornwell 3.1 Introduction Fourier Inversion: Theory The Problem with /^-Sidelobes Computation The Convolution Equation The CLEAN Algorithm The Maximum Entropy Algorithm Comparison of the CLEAN and MEM Algorithms Non-Negative Least-squares Origin of Phase Errors Phase Closure Self-calibration Comparison of Phase Closure and Self-calibration 54 II The Very Long Baseline Array 57 4 VLBA Design 59 P. J. Napier 4.1 Introduction VLBA Design Goals Imaging with High Resolution and High Dynamic Range High Sensitivity Spectral Coverage From 300 MHz To 45 GHz Spectral Line Imaging Capability Support of Research in Geodesy and Astrometry User-Friendly and Reliable Operation Full-Time Operation with Low Down Time Compatibility with Other VLBI Antennas Antennas, Optics, and Feeds 66

4 CONTENTS. xi VLBA Sites Antennas Feed System Conclusion 72 5 VLBA: Antenna to Data Formatter 73 A. R. Thompson 5.1 Introduction Feeds and Polarizers Simultaneous, Multi-Frequency Observations Front Ends for Bands Below 1 GHz Front Ends for Bands Above 1 GHz IF and Baseband Signals in the Station Building Digital Sampling Local Oscillator and Timing System Calibration System Stability and Accuracy of Measurements Observing Bands and Radio Interference 90 6 VLBA: Formatter to Tape 93 A. E. E. R. Rogers 6.1 Introduction Why Magnetic Tape? VLBI Recording Systems The VLBA Data Format Longitudinal Format Transverse Track Format Data and Non-Data Replacement Track Width and Track Structure The VLBA Formatter Digital Switch Board Header Control Board Transport Driver Board Timing and Control Board Data Buffer Board Quality Analysis Board Magnetic Recording Fundamentals Recording Losses Wavelength Response Head-to-Tape Contact and Tribology The VLBA Recorder The Tape Transport The Headstack The Headstack Positioner 106

5 xii CONTENTS Control Electronics Signal Electronics and Eye Pattern Recorder Characteristics and Limitations Error Rate Versus Bit Density Tape Thickness-Interchange Head Flying Overwrite Tracking Errors Headlife and Humidity Thin Tape and Edge Damage by Frictional Heating... Ill Tape Reel and Shipping Canister Ill 6.7 Future VLBI Recording Systems Expansion Paths for the VLBA Formatter Recorder Improvements Thinner Tape Higher Data Rates Next Generation of Heads Mark IV Summary and Conclusfons The VLBA Correlator 117 J. M. Benson 7.1 Introduction Design Specification and History Technical Description The Playback Interface The Track Recovery Card The Deformatter The Cross-Bar Switch The FFT Engines The Cross-Multipliers The Correlator Backend The Correlator Computers and Software Software Architecture Database Management System Correlator Job Scheduling Data Archiving and Distribution The Correlator Model Model Calculation The Model Distribution Model Accountability The Pulsar Gate 130

6 CONTENTS xiii What the VLBA Can Do For You 133 R. C. Walker 8.1 Basic Capabilities of the VLBA Special Capabilities for Imaging Special Capabilities for Geodesy and Astrometry Operational Advantages of the VLBA Frequency Coverage Frequency Resolution (u, v) Coverage and Resolution Sensitivity System Temperature and Antenna Temperature Sensitivity of a Single-Baseline Interferometer Instrumental Losses Image Sensitivity Image Quality and Dynamic Range Sample VLBA Images 156 III VLBI Data Analysis Calibration techniques for VLBI 161 J. M. Moran and V. Dhawan 9.1 Introduction Delay Calibration Fringe-Rate Calibration Amplitude Calibration Antenna Calibration Atmospheric Opacity Phase Calibration Coherent and Incoherent Averaging Atmospheric Effects on Phase and Delay Phased Arrays as VLBI Elements The Impact of Calibration Errors in Images Summary Fringe Fitting 189 W. D. Cotton 10.1 Fringe Fitting Theory Correlator Model Delay Errors Fringe Fitting Techniques Baseline Baseline with Closure Constraints Global Solution Interval 192

7 xiv CONTENTS Calibration Sources Source Structure Phase Referencing Multi-band Data Phase-Cals Multi- vs. Single-band Delay Sidebands Filtering Establishing a Common Reference Antenna Smoothing and Interpolating Solutions Bandwidth Synthesis 196 lo.l.loweights Polarization Fringe Fitting Practice Phase Slopes in Time and Frequency Phase-Cals Sidebands Delay and Rate Fits Signal-tg-Noise Ratios Delay and Rate Windows Details of Global Fringe Fitting Multi- and Single-band Delays Phase-Cal Errors Calibrator Sources Solution Interval Weights Source Model Suggested Procedure Bandwidth Synthesis Spectral-Line VLBI 209 Mark J. Reid 11.1 Spectral Line VLBI Sources Basic Concepts Spectral-Line Calibration Instrumental Parameters Doppler Tracking Transforming from Delays to Frequencies Spectral Line Amplitude Calibration Clock and Coordinate Corrections Electronic Phase Shifts Phase Referencing Fringe-Rate Mapping 223

8 CONTENTS XV 12 VLBI Data Reduction in Practice 227 P. J. Diamond 12.1 Introduction.... ' Calibration Philosophy AIPS Calibration Tables and Data Structure The Data Processing Path Reading the Data Data Examination Lining up the Phases Bandpass Calibration Amplitude Calibration Fringe Fitting The Final Product Conclusion Practical VLBI Imaging 247 R. C. Walker 13.1 Introduction Editing and Calibration Controlling the Hybrid Mapping Self-Calibration Solution Mode Windowing Weights (u,v) Ranges and Tapers Natural vs. Uniform Weighting Cell Size and Image Size CLEAN Components Self-Calibration Parameters Imaging Parameters Antenna Subsets An Example Difference Mapping Advanced Techniques Non-Imaging Data Analysis 267 T. J. Pearson 14.1 Introduction Visibility Data Sampling Closure Quantities Non-Fourier Imaging Noise Model Fitting Imaging as an Inverse Process 270

9 xvi CONTENTS Uses of Model Fitting Practical Model Fitting Simple Models Inspecting Visibility Data Programs for Model Fitting Least-squares Fitting Algorithms Non-Linear Least Squares Algorithms Error Estimation Comparison of Observations 282 A Properties of the Fourier Transform 284 A.I Addition Theorem 285 A.2 Convolution 285 A.3 Shift Theorem 285 A.4 Similarity Theorem 285 B Simple Models 285 B.I Delta Function (Point Source) 285 B.2 Gaussian 286 B.3 Uniformly Bright Disk 286 B.4 Optically Thin Sphere 286 B.5 Ring '. 286 IV Advanced VLBI Topics Polarimetry 289 W. D. Cotton 15.1 Introduction Instrumental Response Interaction with Total Intensity Calibration Phase Delays and Rates Ellipticity-Orientation Model Leakage-Term Model Polarization Angle Phase Calibration Linearly Polarized Feeds Circularly Polarized Feeds Phase Rereferencing Phase-Cals Fringe Fitting Parallel-Hand Fringe Fits Right-left Delay Calibration Right-Left Coherence Ionospheric Faraday Rotation 299

10 CONTENTS xvii External Faraday Rotation Calibration Faraday Self-Calibration Instrumental Polarization Calibration Calibrator Polarization Model Fitting A Feed Model Iterative Calibration Polarization Angle Calibration Unresolved Calibrator Resolved Calibrator Imaging Asymmetric (u, v) Coverage Complex Deconvolution Spectro-Polarimetry Suggested Procedure Multi-Frequency Synthesis 309 J. E. Conway and R. J. Sault 16.1 Introduction Image Fidelity Multi-Frequency Synthesis Spectral Effects The Spectral Expansion Spectral Dirty Beams First Order Spectral Errors Second Order Spectral Errors The MFS Deconvolution Problem Nature of The Problem Map and Stack Direct Assault Data Weighting Methods Double Deconvolution The Sault Algorithm Multi-Frequency Self-Calibration Practical MFS Conclusions VLBI Phase-Referencing 327 A. J. Beasley and J. E. Conway 17.1 VLBI Phase Errors Geometric Errors Instrumental Errors Neutral Atmosphere Effects Ionospheric Effects Phase-Referencing 333

11 xviii CONTENTS 17.3 Imaging Residual Phase Errors A Priori Phase Calibration Temporal Phase Variations and Switching Time Angular Phase Variations and Switching Angle Calibrator Position Errors Hybrid Self-Calibration Imaging Relative Astrometry Prospects For Phase-Referencing Summary and Conclusions Geodesy 345 D. B. Shaffer 18.1 A Bit of History Size of Geodetic and Astrometric Effects Phase and Group Delays Observing Techniques and Calibrations Analysis Results Literature Astrometry 363 E. Fomalont 19.1 Types of Astrometry Absolute Astrometry Relative Astrometry The Basic Array Measurement The Total Phase Delay The Model Phase Delay Phase (Lobe) Ambiguities Absolute Astrometry The Fundamental Astrometric Equation Multi-element Arrays Common Non-dispersive Phase-Delay Terms Tropospheric Refraction Clock Errors Instrumental Path Lengths Common Dispersive Phase Delay Terms Ionospheric Phase Delay Visibility Phase Phase Changes Multi-Frequency Observations Reference Frames and the Motion of the Earth Celestial Coordinate Frame 375

12 CONTENTS xix Terrestrial Coordinate Frame Earth Orientation Polar Motion Time and Earth Rotation Plate Tectonics Earth Orbital Parameters VLBI Observations Phase Derivatives with Time and Frequency Solution Using the Phase Rate Solution Using the Group Delay Measuring the Group Delay Measuring the Ionosphere Delay Relative Accuracies of Phases and Delays Analyzing VLBI Data: SOLVE Relative Astrometry Nodding Observations Groups of Calibrators Nodding Errors and Supportive Astrometric Observations Simultaneous Observations of Source and Calibrators 391 V Other Networks and Global VLBI EVN and Global VLBI 397 R. T. Schilizzi 20.1 Introduction The World of VLBI The European VLBI Network (u, v) Coverage for the EVN Alone (u, v) Coverage for the EVN+VLBA EVN Sensitivity Current Performance Expected Performance by EVN Upgrade Data Processor Correlator User and Technical Support The Asia-Pacific Telescope Final Remarks 408

13 xx CONTENTS VI Planning a VLBI Observation VLBI Observing Strategies 411 J. M. Wrobel 21.1 Select a Target Desired Angular Resolution Desired Largest Angular Scale Desired Observing Frequency Desired Stokes Parameters Desired Recorded Bandwidth Select and Evaluate a Trial VLBI Array Special Needs Evaluation Geometric Evaluation Baseline Sensitivity Evaluation Image Sensitivity Evaluation Field-of-View Evaluation Optimal Times, Seasons, or Years to Observe? Submit an Observing Proposal Make Antenna and Tape Control Schedule Files Correlator Tolerance on» Target Positional Errors 425 ABBREVIATIONS 429 BIBLIOGRAPHY 431 INDEX 442 COLOPHON 453