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Interferometry and Synthesis in Radio Astronomy.

Bibliographic Details
Main Author: Thompson, A. Richard.
Other Authors: Moran, James M., Swenson Jr., George W.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2017.
Edition:3rd ed.
Series:Astronomy and Astrophysics Library
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Preface to the Third Edition
  • Preface to the Second Edition
  • Preface to the First Edition
  • Contents
  • Abbreviations and Acronyms
  • Principal Symbols
  • 1 Introduction and Historical Review
  • 1.1 Applications of Radio Interferometry
  • 1.2 Basic Terms and Definitions
  • 1.2.1 Cosmic Signals
  • 1.2.2 Source Positions and Nomenclature
  • 1.2.3 Reception of Cosmic Signals
  • 1.3 Development of Radio Interferometry
  • 1.3.1 Evolution of Synthesis Techniques
  • 1.3.2 Michelson Interferometer
  • 1.3.3 Early Two-Element Radio Interferometers
  • 1.3.4 Sea Interferometer
  • 1.3.5 Phase-Switching Interferometer
  • 1.3.6 Optical Identifications and Calibration Sources
  • 1.3.7 Early Measurements of Angular Width
  • 1.3.8 Early Survey Interferometers and the Mills Cross
  • 1.3.9 Centimeter-Wavelength Solar Imaging
  • 1.3.10 Measurements of Intensity Profiles
  • 1.3.11 Spectral Line Interferometry
  • 1.3.12 Earth-Rotation Synthesis Imaging
  • 1.3.13 Development of Synthesis Arrays
  • 1.3.14 Very-Long-Baseline Interferometry
  • 1.3.15 VLBI Using Orbiting Antennas
  • 1.4 Quantum Effect
  • Appendix 1.1 Sensitivity of Radio Astronomical Receivers (the Radiometer Equation)
  • Further Reading
  • Textbooks on Radio Astronomy and Radio Interferometry
  • Historical Reviews
  • General Interest
  • References
  • 2 Introductory Theory of Interferometry and Synthesis Imaging
  • 2.1 Planar Analysis
  • 2.2 Effect of Bandwidth
  • 2.3 One-Dimensional Source Synthesis
  • 2.3.1 Interferometer Response as a Convolution
  • 2.3.2 Convolution Theorem and Spatial Frequency
  • 2.3.3 Example of One-Dimensional Synthesis
  • 2.4 Two-Dimensional Synthesis
  • 2.4.1 Projection-Slice Theorem
  • 2.4.2 Three-Dimensional Imaging
  • Appendix 2.1 A Practical Fourier Transform Primer
  • A2.1.1 Useful Fourier Transform Pairs
  • A2.1.2 Basic Fourier Transform Properties.
  • A2.1.3 Two-Dimensional Fourier Transform
  • A2.1.4 Fourier Series
  • A2.1.5 Truncated Functions
  • References
  • 3 Analysis of the Interferometer Response
  • 3.1 Fourier Transform Relationship Between Intensityand Visibility
  • 3.1.1 General Case
  • 3.1.2 East-West Linear Arrays
  • 3.2 Cross-Correlation and the Wiener-Khinchin Relation
  • 3.3 Basic Response of the Receiving System
  • 3.3.1 Antennas
  • 3.3.2 Filters
  • 3.3.3 Correlator
  • 3.3.4 Response to the Incident Radiation
  • Appendix 3.1 Mathematical Representation of Noiselike Signals
  • A3.1.1 Analytic Signal
  • A3.1.2 Truncated Function
  • References
  • 4 Geometrical Relationships, Polarimetry, and the Interferometer Measurement Equation
  • 4.1 Antenna Spacing Coordinates and (u,v) Loci
  • 4.2 (u',v') Plane
  • 4.3 Fringe Frequency
  • 4.4 Visibility Frequencies
  • 4.5 Calibration of the Baseline
  • 4.6 Antennas
  • 4.6.1 Antenna Mounts
  • 4.6.2 Beamwidth and Beam-Shape Effects
  • 4.7 Polarimetry
  • 4.7.1 Antenna Polarization Ellipse
  • 4.7.2 Stokes Visibilities
  • 4.7.3 Instrumental Polarization
  • 4.7.4 Matrix Formulation
  • 4.7.5 Calibration of Instrumental Polarization
  • 4.8 The Interferometer Measurement Equation
  • 4.8.1 Multibaseline Formulation
  • Appendix 4.1 Hour Angle-Declination and Elevation-Azimuth Relationships
  • Appendix 4.2 Leakage Parameters in Terms of the Polarization Ellipse
  • A4.2.1 Linear Polarization
  • A4.2.2 Circular Polarization
  • References
  • 5 Antennas and Arrays
  • 5.1 Antennas
  • 5.2 Sampling the Visibility Function
  • 5.2.1 Sampling Theorem
  • 5.2.2 Discrete Two-Dimensional Fourier Transform
  • 5.3 Introductory Discussion of Arrays
  • 5.3.1 Phased Arrays and Correlator Arrays
  • 5.3.2 Spatial Sensitivity and the Spatial TransferFunction
  • 5.3.3 Meter-Wavelength Cross and T-Shaped Arrays
  • 5.4 Spatial Transfer Function of a Tracking Array.
  • 5.4.1 Desirable Characteristics of the Spatial Transfer Function
  • 5.4.2 Holes in the Spatial Frequency Coverage
  • 5.5 Linear Tracking Arrays
  • 5.6 Two-Dimensional Tracking Arrays
  • 5.6.1 Open-Ended Configurations
  • 5.6.2 Closed Configurations
  • 5.6.3 VLBI Configurations
  • 5.6.4 Orbiting VLBI Antennas
  • 5.6.5 Planar Arrays
  • 5.6.6 Some Conclusions on Antenna Configurations
  • 5.7 Implementation of Large Arrays
  • 5.7.1 Low-Frequency Range
  • 5.7.2 Midfrequency and Higher Ranges
  • 5.7.2.1 Phased-Array Feeds
  • 5.7.2.2 Optimum Antenna Size
  • 5.7.3 Development of Extremely Large Arrays
  • 5.7.4 The Direct Fourier Transform Telescope
  • Further Reading
  • References
  • 6 Response of the Receiving System
  • 6.1 Frequency Conversion, Fringe Rotation,and Complex Correlators
  • 6.1.1 Frequency Conversion
  • 6.1.2 Response of a Single-Sideband System
  • 6.1.3 Upper-Sideband Reception
  • 6.1.4 Lower-Sideband Reception
  • 6.1.5 Multiple Frequency Conversions
  • 6.1.6 Delay Tracking and Fringe Rotation
  • 6.1.7 Simple and Complex Correlators
  • 6.1.8 Response of a Double-Sideband System
  • 6.1.9 Double-Sideband System with Multiple Frequency Conversions
  • 6.1.10 Fringe Stopping in a Double-Sideband System
  • 6.1.11 Relative Advantages of Double- and Single-Sideband Systems
  • 6.1.12 Sideband Separation
  • 6.2 Response to the Noise
  • 6.2.1 Signal and Noise Processing in the Correlator
  • 6.2.2 Noise in the Measurement of Complex Visibility
  • 6.2.3 Signal-to-Noise Ratio in a Synthesized Image
  • 6.2.4 Noise in Visibility Amplitude and Phase
  • 6.2.5 Relative Sensitivities of Different Interferometer Systems
  • 6.2.6 System Temperature Parameter α
  • 6.3 Effect of Bandwidth
  • 6.3.1 Imaging in the Continuum Mode
  • 6.3.2 Wide-Field Imaging with a Multichannel System
  • 6.4 Effect of Visibility Averaging
  • 6.4.1 Visibility Averaging Time.
  • 6.4.2 Effect of Time Averaging
  • 6.5 Speed of Surveying
  • Appendix 6.1 Partial Rejection of a Sideband
  • References
  • 7 System Design
  • 7.1 Principal Subsystems of the Receiving Electronics
  • 7.1.1 Low-Noise Input Stages
  • 7.1.2 Noise Temperature Measurement
  • 7.1.3 Local Oscillator
  • 7.1.4 IF and Signal Transmission Subsystems
  • 7.1.5 Optical Fiber Transmission
  • 7.1.6 Delay and Correlator Subsystems
  • 7.2 Local Oscillator and General Considerationsof Phase Stability
  • 7.2.1 Round-Trip Phase Measurement Schemes
  • 7.2.2 Swarup and Yang System
  • 7.2.3 Frequency-Offset Round-Trip System
  • 7.2.4 Automatic Correction System
  • 7.2.5 Fiberoptic Transmission of LO Signals
  • 7.2.6 Phase-Locked Loops and Reference Frequencies
  • 7.2.7 Phase Stability of Filters
  • 7.2.8 Effect of Phase Errors
  • 7.3 Frequency Responses of the Signal Channels
  • 7.3.1 Optimum Response
  • 7.3.2 Tolerances on Variation of the Frequency Response: Degradation of Sensitivity
  • 7.3.3 Tolerances on Variation of the Frequency Response: Gain Errors
  • 7.3.4 Delay and Phase Errors in Single- and Double-Sideband Systems
  • 7.3.5 Delay Errors and Tolerances
  • 7.3.6 Phase Errors and Degradation of Sensitivity
  • 7.3.7 Other Methods of Mitigation of Delay Errors
  • 7.3.8 Multichannel (Spectral Line) Correlator Systems
  • 7.3.9 Double-Sideband Systems
  • 7.4 Polarization Mismatch Errors
  • 7.5 Phase Switching
  • 7.5.1 Reduction of Response to Spurious Signals
  • 7.5.2 Implementation of Phase Switching
  • 7.5.3 Timing Accuracy in Phase Switching
  • 7.5.4 Interaction of Phase Switching with Fringe Rotation and Delay Adjustment
  • 7.6 Automatic Level Control and Gain Calibration
  • 7.7 Fringe Rotation
  • Appendix 7.1 Sideband-Separating Mixers
  • Appendix 7.2 Dispersion in Optical Fiber
  • Appendix 7.3 Alias Sampling
  • References
  • 8 Digital Signal Processing.
  • 8.1 Bivariate Gaussian Probability Distribution
  • 8.2 Periodic Sampling
  • 8.2.1 Nyquist Rate
  • 8.2.2 Correlation of Sampled but UnquantizedWaveforms
  • 8.3 Sampling with Quantization
  • 8.3.1 Two-Level Quantization
  • 8.3.2 Four-Level Quantization
  • 8.3.3 Three-Level Quantization
  • 8.3.4 Quantization Efficiency: Simplified Analysis for Four or More Levels
  • 8.3.5 Quantization Efficiency: Full Analysis, Three or More Levels
  • 8.3.6 Correlation Estimates for Strong Sources
  • 8.4 Further Effects of Quantization
  • 8.4.1 Correlation Coefficient for Quantized Data
  • 8.4.2 Oversampling
  • 8.4.3 Quantization Levels and Data Processing
  • 8.5 Accuracy in Digital Sampling
  • 8.5.1 Tolerances in Digital Sampling Levels
  • 8.6 Digital Delay Circuits
  • 8.7 Quadrature Phase Shift of a Digital Signal
  • 8.8 Digital Correlators
  • 8.8.1 Correlators for Continuum Observations
  • 8.8.2 Digital Spectral Line Measurements
  • 8.8.3 Lag (XF) Correlator
  • 8.8.4 FX Correlator
  • 8.8.5 Comparison of XF and FX Correlators
  • 8.8.6 Hybrid Correlator
  • 8.8.7 Demultiplexing in Broadband Correlators
  • 8.8.8 Examples of Bandwidths and Bit DataQuantization
  • 8.8.9 Polyphase Filter Banks
  • 8.8.10 Software Correlators
  • Appendix 8.1 Evaluation of ∞q=1R2∞(qτs)
  • Appendix 8.2 Probability Integral for Two-Level Quantization
  • Appendix 8.3 Optimal Performance for Four-Level Quantization
  • Appendix 8.4 Introduction to the Discrete Fourier Transform
  • A8.4.1 Response to a Complex Sine Wave
  • A8.4.2 Padding with Zeros
  • Further Reading
  • References
  • 9 Very-Long-Baseline Interferometry
  • 9.1 Early Development
  • 9.2 Differences Between VLBI and Conventional Interferometry
  • 9.2.1 The Problem of Field of View
  • 9.3 Basic Performance of a VLBI System
  • 9.3.1 Time and Frequency Errors
  • 9.3.2 Retarded Baselines
  • 9.3.3 Noise in VLBI Observations.
  • 9.3.4 Probability of Error in the Signal Search.

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