Coherent x-ray optics

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Title:

Personal Author:

Paganin, David

Publication Information:

Oxford, NY : Oxford University Press, 2006

Physical Description:

xii, 411 p. : ill. ; 24 cm.

ISBN:

9780198567288

Subject Term:

X-ray optics -- Standards

X-rays -- Diffraction

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010178198	TA1775 P33 2006	Open Access Book	Book	Searching... Unknown

This book gives a thorough treatment of the rapidly-expanding field of coherent x-ray optics, which has recently experienced something of a renaissance with the availability of third-generation synchrotron sources. It is the first book of its kind. The author begins with a treatment of the fundamentals of x-ray diffraction for both coherent and partially coherent radiation, together with the interactions of x-rays with matter. X-ray sources, optics elements and detectors are then discussed, with an emphasis on their role in coherent x-ray optics. Various facets of coherent x-ray imaging are then discussed, including holography, interferometry, self imaging, phase contrast and phase retrieval. Lastly, the foundations of the new field of singular x-ray optics are examined. Most topics are developed from first principles, with numerous references given to the contemporary research literature. This book will be useful to x-ray physicists and students, together with optical physicists and engineers who wish to learn more about the fascinating subject of coherent x-ray optics.

Author Notes

David M. Paganin is a Lecturer at the School of Physics, Monash University, Australia.

1 X-ray wave-fields in free space	p. 1
1.1 Vacuum wave equations for electromagnetic fields	p. 2
1.2 Spectral decomposition and the analytic signal	p. 5
1.3 Angular spectrum of plane waves	p. 6
1.4 Fresnel diffraction	p. 10
1.4.1 Operator formulation	p. 11
1.4.2 Convolution formulation	p. 12
1.5 Fraunhofer diffraction	p. 16
1.6 Kirchhoff and Rayleigh-Sommerfeld diffraction theory	p. 18
1.6.1 Kirchhoff diffraction integral	p. 18
1.6.2 Rayleigh-Sommerfeld diffraction integrals	p. 23
1.7 Partially coherent fields	p. 26
1.7.1 Random variables and random processes	p. 26
1.7.2 Intermediate states of coherence	p. 29
1.7.3 Spatial coherence	p. 30
1.7.4 Temporal coherence	p. 36
1.8 The mutual coherence function	p. 37
1.9 Propagation of two-point correlation functions	p. 46
1.9.1 Vacuum wave equations	p. 47
1.9.2 Operator formulation	p. 50
1.9.3 Green function formulation	p. 53
1.9.4 Van Cittert-Zernike theorem	p. 58
1.10 Higher-order correlation functions	p. 59
1.11 Summary	p. 60
2 X-ray interactions with matter	p. 64
2.1 Wave equations in the presence of scatterers	p. 65
2.2 The projection approximation	p. 71
2.3 Point scatterers and the outgoing Green function	p. 77
2.3.1 First method for obtaining Green function	p. 79
2.3.2 Second method for obtaining Green function	p. 80
2.4 Integral-equation formulation of scattering	p. 83
2.5 First Born approximation for kinematical scattering	p. 84
2.5.1 Fraunhofer and first Born approximations	p. 86
2.5.2 Angular spectrum and first Born approximation	p. 89
2.5.3 The Ewald sphere	p. 90
2.6 Born series and dynamical scattering	p. 97
2.7 Multislice approximation	p. 99
2.8 Eikonal approximation and geometrical optics	p. 101
2.9 Scattering, refractive index, and electron density	p. 108
2.10 Inelastic scattering and absorption	p. 115
2.10.1 Compton scattering	p. 115
2.10.2 Photoelectric absorption and fluorescence	p. 119
2.11 Information content of scattered fields	p. 122
2.11.1 Scattered monochromatic fields	p. 122
2.11.2 Scattered polychromatic fields	p. 127
2.12 Summary	p. 130
3 X-ray sources, optical elements, and detectors	p. 136
3.1 Sources	p. 137
3.1.1 Brightness and emittance	p. 137
3.1.2 Fixed-anode and rotating-anode sources	p. 138
3.1.3 Synchrotron sources	p. 139
3.1.4 Free-electron lasers	p. 145
3.1.5 Energy-recovering linear accelerators	p. 149
3.1.6 Soft X-ray lasers	p. 151
3.2 Diffractive optical elements	p. 152
3.2.1 Diffraction gratings	p. 152
3.2.2 Fresnel zone plates	p. 160
3.2.3 Analyser crystals	p. 169
3.2.4 Crystal monochromators	p. 176
3.2.5 Crystal beam-splitters and interferometers	p. 178
3.2.6 Bragg-Fresnel crystal optics	p. 183
3.2.7 Free space	p. 185
3.3 Reflective optical elements	p. 186
3.3.1 X-ray reflection from surfaces	p. 186
3.3.2 Capillary optics	p. 191
3.3.3 Square-channel arrays	p. 192
3.3.4 X-ray mirrors	p. 193
3.4 Refractive optical elements	p. 195
3.4.1 Prisms	p. 195
3.4.2 Compound refractive lenses	p. 198
3.5 Virtual optical elements	p. 203
3.6 X-ray detectors	p. 205
3.6.1 Critical detector parameters	p. 205
3.6.2 Types of X-ray detector	p. 208
3.6.3 Detectors and coherence	p. 212
3.7 Summary	p. 216
4 Coherent X-ray imaging	p. 228
4.1 Operator theory of imaging	p. 230
4.1.1 Imaging using coherent fields	p. 230
4.1.2 Imaging using partially coherent fields	p. 237
4.1.3 Cascaded systems	p. 238
4.2 Self imaging	p. 240
4.2.1 Talbot effect for monochromatic fields	p. 242
4.2.2 Talbot effect for polychromatic fields	p. 246
4.2.3 Montgomery effect for monochromatic fields	p. 249
4.2.4 Montgomery effect for polychromatic fields	p. 253
4.3 Holography	p. 254
4.3.1 In-line holography	p. 254
4.3.2 Off-axis holography	p. 258
4.3.3 Fourier holography	p. 258
4.4 Phase contrast	p. 261
4.4.1 Zernike phase contrast	p. 263
4.4.2 Differential interference contrast	p. 268
4.4.3 Analyser-based phase contrast	p. 270
4.4.4 Propagation-based phase contrast	p. 278
4.4.5 Hybrid phase contrast	p. 284
4.5 Phase retrieval	p. 289
4.5.1 Gerchberg-Saxton algorithm and extensions	p. 291
4.5.2 The transport-of-intensity equation	p. 295
4.5.3 One-dimensional phase retrieval	p. 301
4.6 Interferometry	p. 310
4.6.1 Bonse-Hart interferometer	p. 311
4.6.2 Young interferometer	p. 315
4.6.3 Intensity interferometer	p. 318
4.6.4 Other means for coherence measurement	p. 321
4.7 Virtual optics for coherent X-ray imaging	p. 322
4.7.1 General remarks on virtual optics	p. 322
4.7.2 Example of virtual optics	p. 324
4.8 Summary	p. 327
5 Singular X-ray optics	p. 341
5.1 Vortices in complex scalar fields	p. 342
5.2 Nodal lines	p. 342
5.3 Nodal lines are vortex cores	p. 346
5.4 Polynomial vortex solutions to d'Alembert equation	p. 347
5.5 Vortex dynamics	p. 351
5.5.1 Vortex nucleation and annihilation	p. 351
5.5.2 Stability with respect to perturbations	p. 353
5.5.3 Vortex interaction with a background field	p. 354
5.6 Means of generating wave-field vortices	p. 357
5.6.1 Interference of three coherent plane waves	p. 357
5.6.2 Synthetic holograms	p. 363
5.6.3 Spiral phase masks	p. 370
5.6.4 Spontaneous vortex formation	p. 373
5.7 Domain walls and other topological phase defects	p. 380
5.8 Caustics and the singularity hierarchy	p. 382
5.9 Summary	p. 387
A Review of Fourier analysis	p. 393
A.1 Fourier transforms in one and two dimensions	p. 393
A.2 Convolution theorem	p. 394
A.3 Fourier shift theorem	p. 395
A.4 Fourier derivative theorem	p. 395
A.5 Sifting property of Dirac delta	p. 396
B Fresnel scaling theorem	p. 397
C Reciprocity theorem for monochromatic scalar fields	p. 401
Index	p. 405

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