Aperture Synthesis: Methods and Applications to Optical Astronomy / Edition 1

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Overview

Over the years long baseline optical interferometry has slowly gained in importance and today it is a powerful tool. This timely book sets out to highlight the basic principles of long baseline optical interferometry.

The book addresses the fundamentals of stellar interferometry with emphasis on aperture synthesis using an array of telescopes particularly at optical/IR wavelengths. It discusses the fundamentals of electromagnetic fields, wave optics, interference, diffraction, and imaging at length. There is a chapter dedicated to radio and intensity interferometry corroborating with basic mathematical steps. The basic principle of optical interferometry and its requirements, its limitations and the technical challenges it poses, are also covered in depth.

Assisted by illustrations and footnotes, the book examines the basic tricks of the trade, current trends and methods, and it points to the potential of true interferometry both from the ground and space.

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Product Details

  • ISBN-13: 9781441957092
  • Publisher: Springer New York
  • Publication date: 10/21/2010
  • Series: Astronomy and Astrophysics Library Series
  • Edition description: 2011
  • Edition number: 1
  • Pages: 466
  • Product dimensions: 6.40 (w) x 9.40 (h) x 1.30 (d)

Meet the Author

Professor S. K. Saha is with the Indian Institute of Astrophysics in Bangalore, India. He has spent one year (1988-89) at the Observatoire de la Cote d'Azur (formerly C.E.R.G.A) in Caussols, France. During this year he conducted research on the high angular features of stars, using the long baseline topical interferometer with a pair of 1.5 meter telescopes. He has a strong interest in Experimental Physics and has developed various equipment in the area. He is the author of the book Diffraction-Limited Imaging with Large and Moderate Telescopes (World Scientific, 2007). Another book, 21st Century Astrophysics (Anita Publications, 2005, with V. K. Rastogi (Ed.)) was brought out to commemorate Einstein's "Year of Miracles," which contains a set of articles written by reputed scientists working at the various laboratories across the Globe. Saha has edited a special issue of Asian J. Physics on 'Astrophysics" in 2004.

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Table of Contents

1 Introduction to Wave Optics 1

1.1 Preamble 1

1.2 Complex Representation of Harmonic Waves 3

1.3 Polarized Waves 6

1.3.1 Stokes Parameters 9

1.3.2 Transformation of Stokes Parameters 12

1.4 Diffraction Fundamentals 14

1.4.1 Derivation of the Diffracted Field 14

1.4.2 Near and Far-Field Diffractions 16

1.4.3 Diffraction by a Circular Aperture 19

1.5 Image Formation 21

1.5.1 Optical Transfer Function 23

1.5.2 Influence of Aberrations 26

1.5.3 Resolving Power of a Telescope 27

2 Principles of Interference 31

2.1 Coherence of Optical Waves 31

2.1.1 Interference of Partially Coherent Beams 32

2.1.2 Source and Visibility 36

2.1.3 Power-spectral Density of the Light Beam 40

2.1.4 Mutual Intensity 43

2.1.5 Propagation of Mutual Coherence 44

2.2 Van Cittert-Zernike Theorem 46

3 Applications of Interferometry 51

3.1 Early Stellar Interferometry 51

3.1.1 Fizeau-Stéphan Interferometer 52

3.1.2 Michelson Stellar Interferometer 54

3.2 Radio Interferometry 57

3.2.1 The Radio Telescope 58

3.2.2 The Radio Interferometer 70

3.2.3 Very Long Baseline Interferometry 81

3.3 Intensity Interferometry 87

3.3.1 Derivation of the Separation of Two Points on a Star 90

3.3.2 Intensity Interferometer at Radio Wavelengths 93

3.3.3 Optical Intensity Interferometry 96

3.3.4 Intensity Correlations in Partially Coherent Fields 103

3.3.5 Correlation Between the Signals of the Photo-detectors 107

3.4 Interferometer for Cosmic Probe 109

4 Single-dish Diffraction-limited Imaging 115

4.1 Turbulence 115

4.1.1 Spectral Description of Turbulence 115

4.1.2 Structure Function for Deriving Kolmogorov Turbulence 118

4.1.3 Refractive Index Power-spectral Density 119

4.1.4 Turbulence and Boundary Layer 122

4.1.5 Statistics of the Amplitude and Phase Perturbations 123

4.1.6 Imaging Through Atmospheric Turbulence 130

4.2 Speckle Interferometry 137

4.2.1 Deciphering Information from Specklegrams 138

4.2.2 Benefit of Short-exposure Images 141

4.3 Adaptive Optics 142

4.3.1 Atmospheric Compensation 143

4.4 Required Components for an AO System 147

4.4.1 Wavefront Correcting Systems 148

4.4.2 Wavefront Sensors 152

4.4.3 Wavefront Reconstruction 157

4.4.4 Wavefront Controller 158

4.4.5 Laser Guide Star 160

4.4.6 Multi-conjugate Adaptive Optics 162

5 Diluted-aperture Stellar Interferometry 165

5.1 Methodology of Interferometry 165

5.1.1 Resolving Power of an Interferometer 167

5.1.2 Astrometry 170

5.1.3 Nulling Interferometry 171

5.2 Baseline Geometry 176

5.2.1 Celestial Coordinate System 176

5.2.2 Coordinates for Stellar Interferometry 181

5.2.3 (u, v)-plane Tracks 186

5.3 Imaging Interferometry 188

5.3.1 Phase-closure Imaging 190

5.3.2 Aperture-Synthesis Interferometry 192

6 Basic Tools and Technical Challenges 205

6.1 Requirements for the LBOI 205

6.1.1 Delay-line 206

6.1.2 Spatial Filtering 208

6.1.3 Beam Recombination in Reality 211

6.1.4 Phase and Group Delay Tracking 224

6.1.5 Coherence Envelope 227

6.1.6 Fringe Acquisition and Tracking 229

6.1.7 Effect of Polarization 235

6.1.8 Dispersion Effect 237

6.1.9 Calibration 238

6.1.10 Role of Adaptive Optics Systems 241

6.2 Limitations and Constraints 243

6.2.1 Instrumental Constraints 244

6.2.2 Field-of-view 246

6.2.3 Sensitivity 247

6.2.4 Bandwidth Limitations 249

6.2.5 Limitations due to Atmospheric Turbulence 250

6.2.6 Atmospheric Phase Errors 251

7 Discrete-Element Interferometers 253

7.1 Direct-Detection Interferometers 253

7.1.1 Interféromètre à deux Télescope 253

7.1.2 Grand Interféromètre à deux Télescope (GI2T) 255

7.1.3 Mark III Interferometer 257

7.1.4 Sydney University Stellar Interferometer 258

7.2 Spatial Interferometry in the Infrared (IR) Region 260

7.2.1 Heterodyne Detection 260

7.2.2 Plateau de Calern IR Interferometer 263

7.2.3 Infrared Spatial Interferometer 264

7.3 Arrays with Multiple Telescopes 265

7.3.1 Cambridge Optical Aperture Synthesis Telescope 266

7.3.2 Infrared Optical Telescope Array (IOTA) 267

7.3.3 Navy Prototype Optical Interferometer 268

7.3.4 Palomar Test-bed Interferometer 269

7.3.5 Keck Interferometer 270

7.3.6 Very Large Telescope Interferometer (VLTI) 270

7.3.7 Center for High Angular Resolution Astronomy Array 272

7.4 Interferometers Under Development 275

7.4.1 Large Binocular Telescopes 275

7.4.2 Mitaka Optical and Infrared Array 276

7.4.3 Magdalena Ridge Observatory Interferometer 277

7.5 Interferometry with Large Arrays 278

7.5.1 Optical Very Large Array (OVLA) 278

7.5.2 Hypertelescope Imaging 279

7.5.3 Carlina Array 282

7.5.4 High Resolution Coronagraphy 285

7.6 Space-borne Interferometry 288

7.6.1 Space Interferometry Mission 288

7.6.2 Terrestrial Planet Finder 289

7.6.3 Darwin Mission 290

7.6.4 Long-term Perspective 291

7.7 Reviving Intensity Interferometry 293

8 Image Recovery 299

8.1 Data Processing 299

8.1.1 Recovery of Visibility Functions 300

8.2 Reconstruction of Objects from Speckles 306

8.2.1 Knox-Thomson Method 306

8.2.2 Triple Correlation Technique 308

8.2.3 Blind Iterative Deconvolution (BID) Technique 311

8.3 Aperture Synthesis Mapping 313

8.3.1 CLEAN 315

8.3.2 Bayesian Statistical Inference 316

8.3.3 Maximum Entropy Method (MEM) 317

8.3.4 Self-calibration Method 320

9 Astronomy with Diluted Aperture Interferometry 325

9.1 Astronomical Measurements 325

9.1.1 Limiting Magnitude 326

9.1.2 Stellar Luminosity 329

9.1.3 Hertzsprung-Russell (HR) Diagram 330

9.1.4 Derivation of Effective Temperatures 332

9.1.5 Stellar Spectra 334

9.2 Stellar Parameters 336

9.2.1 Determining Stellar Distance 336

9.2.2 Evolution of Stars 338

9.2.3 Resolving Young Stellar Objects (YSO) 341

9.2.4 Diameter across Stellar Evolution 349

9.2.5 Stellar Rotation 355

9.2.6 Be Stars 357

9.2.7 Stellar Surface Structure 364

9.2.8 Stellar Atmospheres 366

9.2.9 Circumstellar Shells 369

9.2.10 Binary Systems 373

9.2.11 Multiple Systems 380

9.3 Exploding Stars 384

9.3.1 Novae 384

9.3.2 Supernovae 386

9.4 Extragalactic Sources 389

9.4.1 Active Galactic Nuclei 391

9.4.2 Star-Formation in Galaxies 397

9.5 Infrared Astronomy 400

9.5.1 Astronomy with IR Interferometry 402

9.5.2 Astrobiology 410

A Transfer Function of an Optical System 411

A.1 Linear System 411

A.2 Measures of Coherence 413

B Fourier Optics 415

B.1 Fourier Transform 415

B.1.1 Convolution and Cross-Correlation 423

B.1.2 Hankel Transform 425

C Spatial Frequency Response 429

C.1 Transfer Function 429

D Zernike Representation of Atmospheric Turbulence 433

E Celestial Coordinate System 437

References 439

Index 459

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