|
1 X-ray wave-fields in free space |
|
|
1 | (63) |
|
1.1 Vacuum wave equations for electromagnetic fields |
|
|
2 | (3) |
|
1.2 Spectral decomposition and the analytic signal |
|
|
5 | (1) |
|
1.3 Angular spectrum of plane waves |
|
|
6 | (4) |
|
|
10 | (6) |
|
1.4.1 Operator formulation |
|
|
11 | (1) |
|
1.4.2 Convolution formulation |
|
|
12 | (4) |
|
1.5 Fraunhofer diffraction |
|
|
16 | (2) |
|
1.6 Kirchhoff and Rayleigh--Sommerfeld diffraction theory |
|
|
18 | (8) |
|
1.6.1 Kirchhoff diffraction integral |
|
|
18 | (5) |
|
1.6.2 Rayleigh--Sommerfeld diffraction integrals |
|
|
23 | (3) |
|
1.7 Partially coherent fields |
|
|
26 | (11) |
|
1.7.1 Random variables and random processes |
|
|
26 | (3) |
|
1.7.2 Intermediate states of coherence |
|
|
29 | (1) |
|
|
30 | (6) |
|
|
36 | (1) |
|
1.8 The mutual coherence function |
|
|
37 | (9) |
|
1.9 Propagation of two-point correlation functions |
|
|
46 | (13) |
|
1.9.1 Vacuum wave equations |
|
|
47 | (3) |
|
1.9.2 Operator formulation |
|
|
50 | (3) |
|
1.9.3 Green function formulation |
|
|
53 | (5) |
|
1.9.4 Van Cittert--Zernike theorem |
|
|
58 | (1) |
|
1.10 Higher-order correlation functions |
|
|
59 | (1) |
|
|
60 | (4) |
|
2 X-ray interactions with matter |
|
|
64 | (72) |
|
2.1 Wave equations in the presence of scatterers |
|
|
65 | (6) |
|
2.2 The projection approximation |
|
|
71 | (6) |
|
2.3 Point scatterers and the outgoing Green function |
|
|
77 | (6) |
|
2.3.1 First method for obtaining Green function |
|
|
79 | (1) |
|
2.3.2 Second method for obtaining Green function |
|
|
80 | (3) |
|
2.4 Integral-equation formulation of scattering |
|
|
83 | (2) |
|
2.5 First Born approximation for kinematical scattering |
|
|
85 | (12) |
|
2.5.1 Fraunhofer and first Born approximation |
|
|
86 | (3) |
|
2.5.2 Angular spectrum and first Born approximation |
|
|
89 | (1) |
|
|
90 | (7) |
|
2.6 Born series and dynamical scattering |
|
|
97 | (2) |
|
2.7 Multislice approximation |
|
|
99 | (2) |
|
2.8 Eikonal approximation and geometrical optics |
|
|
101 | (7) |
|
2.9 Scattering, refractive index, and electron density |
|
|
108 | (7) |
|
2.10 Inelastic scattering and absorption |
|
|
115 | (7) |
|
2.10.1 Compton scattering |
|
|
115 | (4) |
|
2.10.2 Photoelectric absorption and fluorescence |
|
|
119 | (3) |
|
2.11 Information content of scattered fields |
|
|
122 | (8) |
|
2.11.1 Scattered monochromatic fields |
|
|
122 | (5) |
|
2.11.2 Scattered polychromatic fields |
|
|
127 | (3) |
|
|
130 | (6) |
|
3 X-ray sources, optical elements, and detectors |
|
|
136 | (92) |
|
|
137 | (15) |
|
3.1.1 Brightness and emittance |
|
|
137 | (1) |
|
3.1.2 Fixed-anode and rotating-anode sources |
|
|
138 | (1) |
|
3.1.3 Synchrotron sources |
|
|
139 | (6) |
|
3.1.4 Free-electron lasers |
|
|
145 | (4) |
|
3.1.5 Energy-recovering linear accelerators |
|
|
149 | (2) |
|
|
151 | (1) |
|
3.2 Diffractive optical elements |
|
|
152 | (34) |
|
3.2.1 Diffraction gratings |
|
|
152 | (8) |
|
3.2.2 Fresnel zone plates |
|
|
160 | (9) |
|
|
169 | (7) |
|
3.2.4 Crystal monochromators |
|
|
176 | (2) |
|
3.2.5 Crystal beam-splitters and interferometers |
|
|
178 | (5) |
|
3.2.6 Bragg--Fresnel crystal optics |
|
|
183 | (2) |
|
|
185 | (1) |
|
3.3 Reflective optical elements |
|
|
186 | (9) |
|
3.3.1 X-ray reflection from surfaces |
|
|
186 | (5) |
|
|
191 | (1) |
|
3.3.3 Square-channel arrays |
|
|
192 | (1) |
|
|
193 | (2) |
|
3.4 Refractive optical elements |
|
|
195 | (8) |
|
|
195 | (3) |
|
3.4.2 Compound refractive lenses |
|
|
198 | (5) |
|
3.5 Virtual optical elements |
|
|
203 | (2) |
|
|
205 | (11) |
|
3.6.1 Critical detector parameters |
|
|
205 | (3) |
|
3.6.2 Types of X-ray detector |
|
|
208 | (4) |
|
3.6.3 Detectors and coherence |
|
|
212 | (4) |
|
|
216 | (12) |
|
|
228 | (113) |
|
4.1 Operator theory of imaging |
|
|
230 | (10) |
|
4.1.1 Imaging using coherent fields |
|
|
230 | (7) |
|
4.1.2 Imaging using partially coherent fields |
|
|
237 | (1) |
|
|
238 | (2) |
|
|
240 | (14) |
|
4.2.1 Talbot effect for monochromatic fields |
|
|
242 | (4) |
|
4.2.2 Talbot effect for polychromatic fields |
|
|
246 | (3) |
|
4.2.3 Montgomery effect for monochromatic fields |
|
|
249 | (4) |
|
4.2.4 Montgomery effect for polychromatic fields |
|
|
253 | (1) |
|
|
254 | (7) |
|
|
254 | (4) |
|
4.3.2 Off-axis holography |
|
|
258 | (1) |
|
|
258 | (3) |
|
|
261 | (28) |
|
4.4.1 Zernike phase contrast |
|
|
263 | (5) |
|
4.4.2 Differential interference contrast |
|
|
268 | (2) |
|
4.4.3 Analyser-based phase contrast |
|
|
270 | (8) |
|
4.4.4 Propagation-based phase contrast |
|
|
278 | (6) |
|
4.4.5 Hybrid phase contrast |
|
|
284 | (5) |
|
|
289 | (21) |
|
4.5.1 Gerchberg--Saxton algorithm and extensions |
|
|
291 | (4) |
|
4.5.2 The transport-of-intensity equation |
|
|
295 | (6) |
|
4.5.3 One-dimensional phase retrieval |
|
|
301 | (9) |
|
|
310 | (12) |
|
4.6.1 Bonse--Hart interferometer |
|
|
311 | (4) |
|
4.6.2 Young interferometer |
|
|
315 | (3) |
|
4.6.3 Intensity interferometer |
|
|
318 | (3) |
|
4.6.4 Other means for coherence measurement |
|
|
321 | (1) |
|
4.7 Virtual optics for coherent X-ray imaging |
|
|
322 | (5) |
|
4.7.1 General remarks on virtual optics |
|
|
322 | (2) |
|
4.7.2 Example of virtual optics |
|
|
324 | (3) |
|
|
327 | (14) |
|
|
341 | (52) |
|
5.1 Vortices in complex scalar fields |
|
|
342 | (1) |
|
|
342 | (4) |
|
5.3 Nodal lines are vortex cores |
|
|
346 | (1) |
|
5.4 Polynomial vortex solutions to d'Alembert equation |
|
|
347 | (4) |
|
|
351 | (6) |
|
5.5.1 Vortex nucleation and annihilation |
|
|
351 | (2) |
|
5.5.2 Stability with respect to perturbations |
|
|
353 | (1) |
|
5.5.3 Vortex interaction with a background field |
|
|
354 | (3) |
|
5.6 Means of generating wave-field vortices |
|
|
357 | (23) |
|
5.6.1 Interference of three coherent plane waves |
|
|
357 | (6) |
|
5.6.2 Synthetic holograms |
|
|
363 | (7) |
|
|
370 | (3) |
|
5.6.4 Spontaneous vortex formation |
|
|
373 | (7) |
|
5.7 Domain walls and other topological phase defects |
|
|
380 | (2) |
|
5.8 Caustics and the singularity hierarchy |
|
|
382 | (5) |
|
|
387 | (6) |
|
A Review of Fourier analysis |
|
|
393 | (4) |
|
A.1 Fourier transforms in one and two dimensions |
|
|
393 | (1) |
|
|
394 | (1) |
|
A.3 Fourier shift theorem |
|
|
395 | (1) |
|
A.4 Fourier derivative theorem |
|
|
395 | (1) |
|
A.5 Sifting property of Dirac delta |
|
|
396 | (1) |
|
B Fresnel scaling theorem |
|
|
397 | (4) |
|
C Reciprocity theorem for monochromatic scalar fields |
|
|
401 | (4) |
Index |
|
405 | |