Interferometry and Synthesis in Radio Astronomy

by Thompson, A. Richard; Moran, James M.; Swenson, George W.

• ISBN13: 9780471254928
• ISBN10: 0471254924
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-04-25
• Publisher: Wiley-VCH

Summary

Interferometry and Synthesis in Radio Astronomy, Second Edition is comprehensive in that it provides an excellent overview of most radio astronomical instrumentation and techniques.

Author Biography

A. RICHARD THOMPSON, PhD, has been associated with the National Radio Astronomy Observatory in numerous capacities for more than 27 years.

Table of Contents

Preface to the Second Edition	xix
Preface to the First Edition	xxi
Introduction and Historical Review	1	(49)
Applications of Radio Interferometry	1	(2)
Basic Terms and Definitions	3	(9)
Cosmic Signals	3	(6)
Source Positions and Nomenclature	9	(1)
Reception of Cosmic Signals	10	(2)
Development of Radio Interferometry	12	(27)
Evolution of Synthesis Techniques	12	(1)
Michelson Interferometer	13	(3)
Early Two-Element Radio Interferometers	16	(2)
Sea Interferometer	18	(1)
Phase-Switching Interferometer	18	(3)
Optical Identifications and Calibration Sources	21	(1)
Early Measurements of Angular Width	21	(3)
Survey Interferometers and the Mills Cross	24	(2)
Centimeter-Wavelength Solar Mapping	26	(1)
Measurements of Intensity Profiles	27	(1)
Spectral Line Interferometry	28	(1)
Earth-Rotation Synthesis Mapping	28	(3)
Development of Synthesis Arrays	31	(2)
Very-Long-Baseline Interferometry	33	(4)
VLBI Using Orbiting Antennas	37	(2)
Quantum Effect	39	(11)
Introductory Theory of Interferometry and Synthesis Imaging	50	(18)
Planar Analysis	50	(3)
Effect of Bandwidth	53	(4)
One-Dimensional Source Synthesis	57	(7)
Interferometer Response as a Convolution	58	(2)
Convolution Theorem and Spatial Frequency	60	(1)
Example of One-Dimensional Synthesis	61	(3)
Two-Dimensional Synthesis	64	(4)
Projection-Slice theorem	65	(3)
Analysis of the Interferometer Response	68	(18)
Fourier Transform Relationship between Intensity and Visibility	68	(9)
Cross-Correlation and the Wiener---Khinchin Relation	77	(1)
Basic Response of the Receiving System	78	(8)
Antennas	78	(1)
Filters	79	(1)
Correlator	80	(1)
Response to the Incident Radiation	80	(2)
Mathematical Representation on Noise-Like Signals	82	(1)
Analytic Signal	82	(2)
Truncated Function	84	(2)
Geometric Relationships and Polarimetry	86	(36)
Antenna Spacing Coordinates and (u, v) Loci	86	(4)
(u', v') Plane	90	(1)
Fringe Frequency	91	(1)
Visibility Frequencies	92	(1)
Calibration of the Baseline	93	(1)
Antenna Mounts	94	(2)
Beamwidth and Beam-Shape Effects	96	(1)
Polarimetry	97	(25)
Parameters Defining Polarization	97	(2)
Antenna Polarization Ellipse	99	(3)
Stokes Visibilities	102	(3)
Instrumental Polarization	105	(4)
Matrix Formulation	109	(3)
Calibration of Instrumental Polarization	112	(5)
Conversion Between Hour Angle--Declination and Azimuth--Elevation Coordinates	117	(1)
Leakage Parameters in Terms of the Polarization Ellipse	117	(1)
Linear Polarization	118	(1)
Circular Polarization	119	(3)
Antennas and Arrays	122	(46)
Antennas	122	(4)
Sampling the Visibility Function	126	(3)
Sampling Theorem	126	(2)
Discrete Two-Dimensional Fourier Transform	128	(1)
Introductory Discussion of Arrays	129	(9)
Phased Arrays and Correlator Arrays	129	(3)
Spatial Sensitivity and the Spatial Transfer Function	132	(5)
Meter-Wavelength Cross and T Arrays	137	(1)
Spatial Transfer Function of a Tracking Array	138	(4)
Desirable Characteristics of the Spatial Transfer Function	140	(1)
Holes in the Spatial Frequency Coverage	141	(1)
Linear Tracking Arrays	142	(5)
Two-Dimensional Tracking Arrays	147	(14)
Open-Ended Configurations	148	(2)
Closed Configurations	150	(5)
VLBI Configurations	155	(3)
Orbiting VLBI Antennas	158	(1)
Planar Arrays	159	(2)
Conclusions on antenna Configurations	161	(1)
Other Considerations	162	(6)
Sensitivity	162	(1)
Long Wavelengths	163	(1)
Millimeter Wavelengths	163	(5)
Response of the Receiving System	168	(44)
Frequency Conversion, Fringe Rotation, and Complex Correlators	168	(15)
Frequency Conversion	168	(1)
Response of a Single-Sideband System	169	(2)
Upper-Sideband Reception	171	(1)
Lower-Sideband Reception	172	(1)
Multiple Frequency Conversions	173	(1)
Delay Tracking and Fringe Rotation	173	(1)
Simple and Complex Correlators	174	(1)
Response of a Double-Sideband System	175	(3)
Double-Sideband System with Multiple Frequency Conversions	178	(2)
Fringe Stopping in a Double-Sideband System	180	(1)
Relative Advantages of Double- and Single-Sideband Systems	181	(1)
Sideband Separation	181	(2)
Response to the Noise	183	(16)
Signal and Noise Processing in the Correlator	183	(5)
Noise in the Measurement of Complex Visibility	188	(1)
Signal-to-Noise Ratio in a Synthesized Map	189	(3)
Noise in Visibility Amplitude and Phase	192	(1)
Relative Sensitivities of Different Interferometer Systems	193	(6)
System Temperature Parameter α	199	(1)
Effect of Bandwidth	199	(6)
Mapping in the Continuum Mode	200	(4)
Wide-Field Mapping with a Multichannel System	204	(1)
Effect of Visibility Averaging	205	(7)
Visibility Averaging Time	205	(1)
Effect of Time Averaging	206	(2)
Partial Rejection of a Sideband	208	(4)
Design of the Analog Receiving System	212	(42)
Principal Subsystems of the Receiving Electronics	212	(9)
Low-Noise Input Stages	212	(2)
Noise Temperature Measurement	214	(3)
Local Oscillator	217	(1)
IF and Signal Transmission Subsystems	218	(1)
Optical Fiber Transmission	218	(2)
Delay and Correlator Subsystems	220	(1)
Local Oscillator and General Considerations of Phase Stability	221	(12)
Round-Trip Phase Measuring Schemes	221	(1)
Swarup and Yang System	222	(1)
Frequency-Offset Round-Trip System	223	(5)
Automatically Correcting System	228	(1)
Fiberoptic Transmission of LO Signals	229	(1)
Phase-Locked Loops and Reference Frequencies	230	(2)
Phase Stability of Filters	232	(1)
Effect of Phase Errors	233	(1)
Frequency Responses of the Signal Channels	233	(7)
Optimum Response	233	(2)
Tolerances on Variation of the Frequency Response: Degradation of Sensitivity	235	(1)
Tolerances on Variation of the Frequency Response: Gain Errors	235	(3)
Delay-Setting Tolerances	238	(1)
Implementation of Bandpass Tolerances	239	(1)
Polarization Mismatch Errors	240	(1)
Phase Switching	240	(8)
Reduction of Response to Spurious Signals	240	(1)
Implementation of Phase Switching	241	(5)
Interaction of Phase Switching with Fringe Rotation and Delay adjustment	246	(2)
Automatic Level Control and Gain Calibration	248	(6)
Sideband-Separating Mixer	248	(1)
Dispersion in Optical Fiber	249	(5)
Digital Signal Processing	254	(50)
Bivariate Gaussian Probability Distribution	255	(1)
Periodic Sampling	256	(4)
Nyquist Rate	256	(1)
Correlation of Sampled but Unquantized Waveforms	257	(3)
Sampling with Quantization	260	(18)
Two-Level Quantization	261	(3)
Four-Level Quantization	264	(7)
Three-Level Quantization	271	(2)
Quantization with Eight or More Levels	273	(3)
Quantization Correction	276	(1)
Comparision of Quantization Schemes	277	(1)
System Sensitivity	278	(1)
Accuracy in Digital Sampling	278	(4)
Principal Causes of Error	278	(1)
Tolerances in Three-Level Sampling	279	(3)
Digital Delay Circuits	282	(1)
Quadrature Phase Shift of a Digital Signal	283	(1)
Digital Correlators	283	(21)
Correlators for Continuum Observations	283	(1)
Principles of digital Spectral Measurements	284	(5)
Lag (XF) Correlator	289	(1)
FX Correlator	290	(3)
Comparison of Lag and FX Correlators	293	(4)
Hybrid Correlator	297	(1)
Demultiplexing in Broadband Correlators	297	(1)
Evaluation of Σ∞q=1 R2∞(qτs)	298	(1)
Probability Integral for Two-Level Quantization	299	(1)
Correction for Four-Level Quantization	300	(4)
Very-Long-Baseline Interferometry	304	(79)
Early Development	304	(2)
Differences Between VLBI and Conventional Interferometry	306	(2)
Basic Performance of a VLBI System	308	(18)
Time and Frequency Errors	308	(7)
Retarded Baselines	315	(1)
Noise in VLBI Observations	316	(3)
Probability of Error in the Signal Search	319	(4)
Coherent and Incoherent Averaging	323	(3)
Fringe Fitting for a Multielement Array	326	(6)
Global Fringe Fitting	326	(3)
Relative Performance of Fringe Detection Methods	329	(1)
Triple Product, or Bispectrum	330	(1)
Fringe Searching with a Multielement Array	331	(1)
Multielement Array with Incoherent Averaging	331	(1)
Phase Stability and Atomic Frequency Standards	332	(21)
Analysis of Phase Fluctuations	332	(8)
Oscillator coherence Time	340	(2)
Precise Frequency Standards	342	(4)
Rubidum and Cesium Standards	346	(2)
Hydrogen Maser Frequency Standards	348	(3)
Local Oscillator Stability	351	(1)
Phase Calibration System	352	(1)
Time Synchronization	353	(1)
Recording Systems	353	(4)
Processing Systems and Algorithms	357	(9)
Fringe Rotation Loss (nR)	358	(3)
Fringe Sideband Rejection Loss (nS)	361	(2)
Discrete Delay Step Loss (nD)	363	(2)
Summary of Processing Losses	365	(1)
Bandwidth Synthesis	366	(3)
Burst Mode Observing	368	(1)
Phased arrays as VLBI Elements	369	(4)
Orbiting VLBI (OVLBI)	373	(10)
Calibration and Fourier Transformation of Visibility Data	383	(43)
Calibration of the Visibility	383	(4)
Corrections for Calculable or Directly Monitored Effects	384	(1)
Use of Calibration Sources	385	(2)
Derivation of Intensity from Visibility	387	(12)
Mapping by Direct Fourier Transformation	387	(1)
Weighting of the Visibility Data	388	(5)
Mapping by Discrete Fourier Transformation	393	(1)
Convolving Functions and Aliasing	394	(4)
Aliasing and the Signal-to-Noise Ratio	398	(1)
Closure Relationships	399	(2)
Model Fitting	401	(3)
Basic Considerations for Models	402	(2)
Cosmic Background Anisotropy	404	(1)
Spectral Line Observations	404	(7)
General Considerations	404	(2)
VLBI Observations of Spectral Lines	406	(3)
Variation of Spatial Frequency over the Bandwidth	409	(1)
Accuracy of Spectral Line Measurements	409	(1)
Presentation and Analysis of Spectral Line Observations	410	(1)
Miscellaneous Considerations	411	(15)
Interpretation of Measured Intensity	411	(1)
Errors in Maps	412	(1)
Hints on Planning and Reduction of Observations	413	(1)
The Edge of the Moon as a Calibration Source	414	(3)
Doppler Shift of Spectral Lines	417	(4)
Historical Notes	421	(1)
Maps from One-Dimensional Profiles	421	(1)
Analog Fourier Transformation	422	(4)
Deconvolution, Adaptive Calibration, and Applications	426	(41)
Limitation of Spatial Frequency Coverage	426	(1)
The Clean Deconvolution Algorithm	427	(5)
Clean Algorithm	427	(2)
Implementation and Performance of the Clean Algorithm	429	(3)
Maximum Entropy Method	432	(6)
Mem Algorithm	432	(2)
Comparison of Clean and Mem	434	(1)
Other Deconvolution Procedures	435	(3)
Adaptive Calibration and Mapping With Amplitude Data Only	438	(7)
Hybrid Mapping	438	(2)
Self-Calibration	440	(4)
Mapping with Visibility Amplitude Data Only	444	(1)
Mapping With High Dynamic Range	445	(1)
Mosaicking	446	(7)
Methods of Producing the Mosaic Map	449	(2)
Some Requirements of Arrays for Mosaicking	451	(2)
Multifrequency Synthesis	453	(1)
Non-Coplanar Baselines	454	(5)
Further Special Cases of Image Analysis	459	(8)
Use of Clean and Self-Calibration with Spectral Line Data	459	(1)
Low-Frequency Mapping	459	(2)
Lensclean	461	(6)
Interferometer Techniques for Astrometry and Geodesy	467	(40)
Requirements for Astrometry	467	(3)
References Frames	469	(1)
Solution for Baseline and Source-Position Vectors	470	(10)
Connected-Element Systems	470	(2)
Measurements with VLBI Systems	472	(4)
Phase Referencing in VLBI	476	(4)
Time and the Motion of the Earth	480	(5)
Precession and Nutation	481	(1)
Polar Motion	482	(1)
Universal Time	482	(2)
Measurement of Polar Motion and UT1	484	(1)
Geodetic Measurements	485	(1)
Mapping Astronomical Masters	485	(22)
Least-Mean-Squares Analysis	490	(17)
Propagation Effects	507	(87)
Neutral Atmosphere	508	(35)
Basic Physics	508	(5)
Refraction and Propagation Delay	513	(5)
Absorption	518	(6)
Origin of Refraction	524	(4)
Smith--Weintraub Equation	528	(2)
Phase Fluctuations	530	(4)
Kolmogorov Turbulence	534	(5)
Anomalous Refraction	539	(2)
Water Vapor Radiometry	541	(2)
Atmospheric Effects at Millimeter Wavelengths	543	(11)
Site Testing by Opacity Measurement	543	(3)
Site Testing by Direct Measurement of Phase Stability	546	(4)
Reduction of Atmospheric Phase Error by Calibration	550	(4)
Ionosphere	554	(10)
Basic Physics	555	(4)
Refraction and Propagation Delay	559	(1)
Calibration of Ionospheric Delay	560	(2)
Absorption	562	(1)
Small- and Large-Scale Irregularities	562	(2)
Scattering Caused by Plasma Irregularities	564	(7)
Gaussian Screen Model	564	(5)
Power-Law Model	569	(2)
Interplanetary Medium	571	(5)
Refraction	571	(3)
Interplanetary Scintillation	574	(2)
Interstellar Medium	576	(18)
Dispersion and Faraday Rotation	576	(3)
Diffractive Scattering	579	(1)
Refractive Scattering	580	(14)
Van Cittert--Zernike Theorem, Spatial Coherence, and Scattering	594	(19)
Van Cittert--Zernike theorem	594	(8)
Mutual Coherence of an Incoherent Source	596	(1)
Diffraction at an Aperture and the Response of an Antenna	597	(3)
Assumptions in the Derivation and Application of the Van Cittert--Zernike Theorem	600	(2)
Spatial Coherence	602	(5)
Incident Field	602	(1)
Source Coherence	603	(3)
Completely Coherent Source	606	(1)
Scattering and the Propagation of Coherence	607	(6)
Radio Interference	613	(14)
General Considerations	613	(2)
Short- and Intermediate-Baseline Arrays	615	(6)
Fringe-Frequency Averaging	616	(4)
Decorrelation of Broadband Signals	620	(1)
Very-Long-Baseline Systems	621	(3)
Interference From Airborne and Space Transmitters	624	(3)
Regulation of the Radio Spectrum	625	(2)
Related Techniques	627	(28)
Intensity Interferometer	627	(5)
Lunar Occultation Observations	632	(4)
Measurements on Antennas	636	(5)
Optical Interferometry	641	(14)
Modern Michelson Interferometer	642	(2)
Sensitivity of Direct Detection and Heterodyne Systems	644	(2)
Optical Intensity Interferometer	646	(1)
Speckle Imaging	647	(8)
Principal Symbols	655	(12)
Author Index	667	(10)
Subject Index	677