Principles of Stellar Interferometry (eBook)

Principles of Stellar Interferometry 3
Preface 
7 
Contents 
9 
List of Symbols, Notations and Abbreviations 
13 
1 Introduction 18
Chapter 2 Propagation of Light 22
2.1 Preliminaries 23
2.1.1 Basic Properties of the Electromagnetic Wave 23
2.1.2 Young's Experiment 26
2.2 Scalar Diffraction Theory 30
2.2.1 The Rayleigh–Sommerfeld Diffraction Formula 30
2.2.2 Fresnel Approximation 33
2.2.3 The Airy Disk 36
2.3 The Coherence Function 42
2.3.1 Varieties of the Coherence Function 43
2.3.2 Generalised van Cittert–Zernike Theorem 49
2.3.3 Incoherent Sources of Light: Stars 51
2.3.4 Quasi-Monochromatic Approximation 54
2.4 Young's Experiment Revisited 61
2.4.1 The Coherence Function in Young's Experiment 62
2.4.2 ABCD Method 67
2.4.3 Power Spectrum of the Fringe Pattern 68
2.4.4 Heuristic Approach 73
2.5 Higher Order Correlation Functions: Intensity Interferometry 79
Chapter 3 Imaging Process: Propagation Through Optical Systems 90
3.1 Fourier Optics 91
3.1.1 The Optical Transfer Function 93
3.1.2 Optical Aberrations: The Zernike Polynomials 99
3.2 The Coherence Function 105
3.2.1 Image Intensity Distribution 105
3.2.2 Coherent Imaging 109
3.2.3 Coherence Properties in the Image Plane 116
3.3 Propagation Through Interferometers 120
3.3.1 Young's Experiment with a Lens 121
3.3.2 Apertures of Finite Size 127
3.3.3 Spectra of Finite Width 133
3.3.4 Objects of Finite Size 139
3.3.5 Considerations on the Interferometric Field of View 145
3.3.6 Masked Field of View 149
3.4 The uv-Plane 156
3.4.1 Large Apertures, Short Baseline: The LBT 158
3.4.2 Large Apertures, Long Baselines: The VLTI 161
3.4.3 Image Reconstruction: General Principles 166
Chapter 4 Atmospheric Turbulence 173
4.1 Kolmogorov Turbulence 174
4.1.1 First Principles 174
4.1.2 Index of Refraction Fluctuations 175
4.2 Statistical Properties of the Perturbed Complex Wave 180
4.2.1 Thin Layer Turbulence Model 180
4.2.2 Multiple Layers, the Fried Parameter 182
4.2.3 Anisoplanatic and Temporal Effects 188
4.3 Propagation Through Optical Systems 194
4.3.1 Fringe Motion 194
4.3.2 Image Motion 206
4.3.3 Zernike Representation of Atmospheric Turbulence 210
4.3.4 Scintillation 214
4.3.5 Speckle Pattern and Seeing Disk 216
4.4 Speckle Interferometry 224
Chapter 5 Instrumental Techniques 232
5.1 Combination of Two Telescopes 233
5.1.1 Fizeau Configuration 233
5.1.2 Michelson Configuration 237
5.1.3 Co-Axial Combination 241
5.2 Multi-Aperture Combination: Michelson Configuration 249
5.2.1 Multi-Axial and Co-Axial Combination 249
5.2.2 Aspects of Beam Combination 254
5.3 Multi-Aperture Combination: Direct Imaging 258
5.3.1 Fizeau Configuration 259
5.3.2 Hypertelescope 261
5.3.3 Interferometric Remapped Array Nulling: IRAN 264
5.3.4 Nulling Interferometer 272
5.4 Layout of Interferometer Arrays 278
5.4.1 Many Apertures 278
5.4.2 Few Apertures 283
5.4.3 Delay Lines 286
Chapter 6 Observing Through Atmospheric Turbulence 290
6.1 Visibility Measurement Through Atmospheric Turbulence 291
6.1.1 Power Spectrum of the Fringe Pattern 298
6.1.2 ABCD Method 302
6.2 Beating Atmospheric Turbulence 308
6.2.1 Fringe Tracking 308
6.2.2 Dual-Feed System 316
6.2.3 Closure Phase 321
6.3 Adaptive Optics 325
6.3.1 Wave Front Sensing 326
6.3.2 Closed Loop Operation 328
Chapter 7 Modern Interferometers 331
A Appendix 333
A.1 The Fourier Transform 333
A.2 Atmospheric Transmission Bands 336
References 338
Index 349