Modern Developments in X-Ray and Neutron Optics Episode 14 pps

520 V. ´ Aˇcetal. 30.3.4 Cooling Temperature Decreasing the cooling temperature is the best way to reduce mechanical deformations caused by absorption of radiation heat. The increase of the thermal conductivity of silicon (Fig. 30.1) together with the decreasing ther- mal expansion coefficient as the cooling temperature is decreased makes it possible to significantly reduce the surface deformations. These results are documented in Fig. 30.4c, d. The cooling by liquid nitrogen (LN2) (78 K) can reduce the surface overheating and surface deformation by more than one order of magnitude in comparison to these effects using room temperature cooling. 30.3.5 Cooling Channels Variations In this section, we will show how it is possible to reduce variations of the sur- face temperature and deformation due to the reproduction of the channel arrangement by optimization of cooling channels geometry. Two possible locations of rectangular cooling channels are seen in Fig. 30.5. The cooling channels are built in the silicon target (a) or in a cooler block (b), respectively. Usually, the cooler block is made from a high thermally conductive mate- rial (copper). Simulations in Fig. 30.5 show higher effectivity of the cooling channels made in copper block. This fact is caused by the higher thermal conductivity in the bulk of the copper cooler together with its larger surface of the cooling channels in comparison to that in the silicon target. In addition, “print-through” of the channel geometry to the optical surface is reduced. Fig. 30.5. Cooling channels variations and corresponding simulations of surface deformation (at photon energy, E p = 100 eV) for cooling channels in the silicon target (a) and cooling channels in the copper cooler block (b) 30 Thermal Effects under Synchrotron Radiation Power Absorption 521 30.3.6 Cooling Block Arrangement The next example is devoted to the revision of cooling block efficiency. Two variations of the cooling block arrangement shown in Fig. 30.6 have been inves- tigated. From mechanical point of view, the lateral side coolers are optimal for a higher target body thickness. Back side cooling is optimal for a smaller target body thickness. The simulation results for block Si target (220×120×40 mm 3 ) and rectangular beam spot (5 ×35 mm 2 ,E p = 100 eV, 0.43 W mm −2 )shown in Fig. 30.6c, d confirm the comparable effectiveness of lateral side coolers compared to back side coolers if the target body thickness is comparable with lateral target size. The benefit of back side cooling is seen at smaller target Fig. 30.6. The cooling block arrangement with (a) lateral side coolers, (b)back side cooler and simulations of surface deformations (c), and surface temperature (e) for lateral side cooling and (d, f) for back side cooling. The silicon target body thickness h = 40 mm. The indium foil thermally connects the silicon target to the copper cooling block 522 V. ´ Aˇcetal. Fig. 30.7. Temperature and size dependence of the heat dissipation time constant τ d for monocrystalline silicon (a), and (b) shows the time dependence of the Si surface temperature under the load of a sequence of six pulses for a target body thickness h =3mm body thickness. The significant effect is seen in a reduction of the surface deformation, which is the aim of the cooling system optimization. The min- imum size of the target body thickness is given by the penetration depth of the X-ray beam, which depends upon its photon energy and the surface incident angle. 30.3.7 Dynamic Thermal Properties of Silicon The dynamic thermal properties are significant in case of pulsed irradiation of the surface. The transient heat properties of the material are characterized by the heat dissipation time constant, τ d , defined by the thermal diffusivity, α T , and the target size. The typical temperature and target size dependences of τ d for monocrystalline silicon are shown in Fig. 30.7a. The time constant resulting from the solution of (30.3) with respect to (30.4) characterizes the dynamics of heat dissipation in the material after a pulsed heat load. The typical time dependence of the temperature at the start of the pulse load process (six pulses) is shown in Fig. 30.7b. The swing of surface temperature is dependent on the heat pulse frequency. The maximum of temperature under a long time periodic load goes to saturation. It is possible to minimize the temperature swing for Si target with the thickness in the millimeter range for pulse frequencies higher than 100 Hz. 30.4 X-Ray Diffraction Spot Deformation In synchrotron beamlines, a crystal used as the first monochromator is subject to a white radiation. Monochromatization by Bragg reflection leads to a high heat load on the surface of the crystal. Heat conduction in the bulk and cooling at the bottom leads to a stationary distribution of crystal parameters. This is mainly the case for a Bragg reflecting crystal. The heated crystal 30 Thermal Effects under Synchrotron Radiation Power Absorption 523 exhibits deformations as shown in previous sections. Limiting ourselves to cooled monochromators, we will further focus only on diffraction in Bragg (reflection) geometry for semi-infinite crystals. Let us first make a qualitative discussion about the expected diffrac- tion image. It will be similar to X-ray topography images. This leads to the following: 1. Surface waviness follows the height profile. Surface roughness does not play a role in X-ray diffraction. Ray-tracing the scattered rays are inco- herent. A surface elevation would shift the diffracted spot on the detec- tor, which is negligible for micrometer pixel sizes and sub-micrometer elevations. 2. Crystal lattice waviness is equivalent to lattice misorientation. The angle of incidence of the Bragg maximum is shifted by the surface slope angle pro- jection, α x , which is given by the tangent to the crystal lattice plane (or the diffraction vector angle) as projected into the scattering plane. The direction of the diffracted beam (angle of α f ) will slightly change as well. 3. Crystal lattice deformation. This locally changes the Bragg angle θ B .From the differential form of the Bragg law Δθ B = −(Δa/a)tanθ B , (30.10) where a is the crystal lattice constant. In summary, the angle of incidence (α i ) of the Bragg peak maximum changes locally by Δα i = α x − (Δa/a)tanθ B . (30.11) Qualitatively, this value influences the diffracted intensity via rocking curve shift. As an example, let us take a cooled Si (111) monochromator at 8 keV. The Bragg angle is 14.2 ◦ , the Bragg extinction length is 1.5 μm, and the Darwin curve fwhm is 7 arcsec (σ-polarization). The latter corresponds to 34 μrad or Δa/a =10 −4 , which are smaller than values calculated in the previous section. Thus, for a temperature change of a few degrees Kelvin, the diffraction image is kept almost unchanged. For lower energy and higher Bragg angles, the requirements are less strict. Furthermore, real beam homogeneity is driven by its (a) divergence and (b) its wavelength spread. These are the effects that smooth the diffracted image. For example, a divergence of 10 arcsec is higher than the Bragg curve fwhm. The diffraction image from a monochromator is simulated by usual ray- tracing methods. In brief, for perfect crystals, the usual dynamical diffraction is used, while for deformed crystals the Takagi-Taupin or (semi) kinematic approximation are adequate. For heated monochromators, there is a deforma- tion gradient from the surface to the bulk. Qualitatively, the limit between dynamical theory for perfect and deformed crystals is the angular shift of the Bragg peak on the surface within a Borrmann fan. For a perfect crystal, it 524 V. ´ Aˇcetal. should be smaller than the Bragg peak width. Otherwise, for a large deforma- tion on a micrometer scale, the use of the Takagi-Taupin approach for reflected wave intensity would be required. Diffraction spot simulations by ray-tracing verify these qualitative conclu- sions. For a temperature field with a variation of several degrees, the diffracted image is homogeneous. The acceptable surface deformation limit in terms of the diffraction spot damage follows from (30.11) and depends not only on target surface deformation but also on beam divergence. Acknowledgement The authors acknowledge the support by the Slovak Ministry of Education (grants VEGA 1/4134/07 and APVV -0459-06) and by the Czech Ministry of Education (grants MSM 0021622410 and 1P04OCP07.004). References 1. D. Koryt´ar, P. Mikul´ık,C.Ferrari,J.Hrd´y, T. Baumbach, A. Freund, A. Kubˇena, Phys. D Appl. Phys. 36, A65 (2003) 2. L. Zhang, J. Hoszowska, J.S. Migliore, V. Mocella, C. Ferrero, A.K. Freund, Nucl. Instrum. Methods Phys. Res. A 467–468, 409 (2001) 3. V. Mocella, W.K. Lee, G. Tajiri, D. Mills, C. Ferrero, Y. Epelboin, J. Appl. Crystallogr. 36, 129 (2003) 4. A. Thompson, D. Vaughan et al., X-ray Data Booklet (Lawrence Berkeley National Laboratory, Berkeley, CA 2001), http://xdb.lbl.gov/xdb.pdf 5. D.W. Nicholson, Finite Element Analysis: Thermomechanics of Solids,(CRC Press, West Palm Beach, FL, 2003) ISBN 0- 8493-0749-X 6. T. Ruf, R.W. Henn, M. Asen-Palmer, E. Gmelin, M. Cardona, H J. Pohl, G.G. Devyatych, P.G. Sennikov, Solid State Commun. 115(5), 243 (2000) 7. J. Kim, D. Cho, R.S. Muller, in Proceedings of the 11th International Conference on Solid State Sensors and Actuators, Munich, 10–14 June 2001, pp. 662–665 8. J.J. Wortman, R.A. Evans, J. Appl. Phys. 36(1), 153 (1965) 9. J.E. Graebner, J. Thermophys. 19(2), 511 (1998) Index Absorption coefficient, 391, 505 Anti-stress layer, 386 Aperiodic multilayer, 411 Asymmetric Laue crystal, 455 Atomic force microscope, 376 Atomic layer epitaxy, 390 Autocollimating telescope (ACT), 193 Ballistic guide, principle of, 126 Beam intensity distribution, methods for measuring, 43 Beam knife-edge measurements, 231 Beam transport system, 86 Bent perfect crystal, 118 Bi-concave lens, 336 focal length, 337 refraction angle, 336 transmission function, 337 Bias voltage, stress dependence on, 380 Bragg diffraction, 440 asymmetric, DuMond diagram of, 441 inclined, 442 on longitudinal groove crystal surface, 447 on transverse groove, 443, 444 refraction effect, 451 symmetric, 440, 442 symmetric and asymmetric difference, 449, 450 Bragg reflector, 473 in sagittal grating, 473 monochromatization by, 522 Bragg–Fresnel grating, 472, 473, 476 meridional grating, 477 sagittal grating, 473 Braggs law, 235 Brewster angle, 413 Broadband polarizers, 2 Calibrated reference mirror, 185 Capillary optics, 4, 128 on multiple reflections, 289 on single reflections, 288 radiation transport principle, 290 for synchrotron radiation, 302 micro-XRF applications, 296 optical profile measurements, 299 physical basics of, 288 two-dimensional distributions, 297 Channel-cut crystal monochromator, 445 harmonics-free, 446 with circular grooves, 450 Chemical vapor deposition (CVD), 516, 518 Chromatic optics, 132 Circular polarization, definition of, 30 Clessidra lens, 342 diffractive and the refractive images, 344 focal length of, 341 geometric aperture, 342 Coating design, 432 Coherent radiation, phase space volume for, 93 526 Index Coherent synchrotron radiation (CSR), 69 Cold source metal canister, 114 Common correlation functions, 399 Compound refractive lenses (CRLs), 119, 335 advantages and drawbacks of, 120 MgF 2 biconcave lenses, 119, 120 parabolic, 260, 274 Computer controlled polishing (CCP), 201 Concave beam, 446 Coplanar 1D crystal optics, 509 Critical angle, for total reflection, 95, Crystal focusing, 117 Crystal monochromator, 93, 100 bandwidth of, 100 in synchrotron radiation beamline, 93 Crystal optics, 33 Crystal slabs, 461 cuts of, 461 diffraction of, 461 MBR-effect with, 467 reflections of, 460 Curvature measurement, techniques for, 374 Darwin–Prins (DP), 33, 445 curves, 445 formalism, 33 Debye–Waller model, 310 Distributed electron cyclotron resonance (DECR), 393 DECR sputtering, 399 Depth-graded multilayers, 410 flat reflectivity, 413 layer thickness distribution, 412 Detector gas absorption efficiency, 45 Diffraction gratings, 26 error estimation, 209 structure and use of, 207 variable line spacing (VLS) grating, 208 Diffractive optics, 62 Diffuse scattering, 120, 121 at interfaces, 121 polish finish, 120 Direct front coupling diffraction phenomena, 104 from dielectric corner, 105 in dielectric FC waveguide, 106 Double focusing monochromator, 117 Downhill annealing, 241 Dynamical theory, 504 Effective aperture, 95 defined as, 95 exponentially decaying transmission function, 96 Effective footprint size (l eff ), 96 Elastic emission machining (EEM), 263 Electromagnetic modes, 93 Electromagnetic spectrum, 407, 417 Electron diffraction, 399, 401 Electron storage rings, 157 Electron-beam, 392 lithography, 474 UHV evaporation, 392 Elliptical toroid, construction of, 23 Elliptically shaped mirrors reflection, 416 Energy Recovery Linac Prototype (ERLP), 70, 86, 201 Epithermal neutrons, 53 Etched gratings, 472 efficiency of, 476 groove profile, 475 Extreme ultraviolet (EUV) lithography, 320, 371 field of view, 320 gas-puff laser plasma, 320 in microprocessor industry, 335 intensity distribution, 326 ray-tracing simulation of, 322 stress mitigation, 383 TEFLON dry etching with, 328 use of plexiglass, 339 X-ray lenses production, 335 Ewald sphere concept, 503 Figure of merit (FOM), 240 description, 240 parameters, 241 Film roughness, 384 Film stress, 372 Index 527 Finite element analysis, 313, 513, 514 heat transfer and temperature field, 514 mechanical deformations, analyses, 513, 515 monocrystalline silicon, simulation of, 513 radiation heat absorption, in matter, 514 Flat response mirrors, applications of, 408 Focal spot profile estimation, 327 Focal spot, EUV beam, 319 by Wolter X-ray optics, 326 characterization in EUV region, 325 Focusing honeycomb collimators, 116 Focusing monochromators, 117 applications, 132 focal spot, 117 Focusing neutron optics, 113, 122, 131, 132 applications of, 132 collimating focusing, 115 crystal focusing, 117 diffractive optics, 129 figure of merit for, 131 modeling programs, 131 principles, 113 refractive optics, 118 Focusing techniques, 133, see also Focusing neutron optics Fourier coefficient, of crystal polarization, 476 Fourier optics technique, 39, 76 Fourier transform lens, 182 focal position of, 184 interference pattern, 182 laser beam pairs, tilt induced in, 183 Fourier transform spectrometer, 87 Free electron laser (FEL), 69, 201, 404 Frequency-domain electric field, 73, 118 Fresnel diffraction, 10 Fresnel equations, recursive application of, 31 Fresnel Kirchoff equation, for propagating the field, 70 Fresnel lens, 342 Fresnel reflection coefficient, 419 Fresnel zone plates, 4, 129, 472 vs. KB mirror systems, 269 capillaries in, 265 consists of, 266 coupled-wave theory for, 141 diameter limitation, 130, 268 diffraction efficiency ηm(t), 140 diffraction properties, 157 fabrication process, 170 first-order diffraction of, 141 focusing efficiency, 270 for hard X-ray applications, 267 for soft and hard X-rays, 259 high-order diffraction of, 154 interdiffusion and roughness line-to-space ratio influence on, 15 lithographic techniques, 268 micro-electro-mechanical systems (MEMS) technology, 268 micromechanical motion system, 271 nickel zone structures, 155 of m-th diffraction order, 140 phase zone plates, 129 resolving power of, 154, 164, 168 Rayleigh resolution of, 267 spatial resolution of, 137, 267 stacking technique, 270 tilted zone and layers, 168 FTL, see Fourier transform lens Gamma-ray telescopes, 389 Genetic algorithms (GA), 241 Geometric aperture (A geo ), 96 Geometrical optics approximation, 64 Glancing angle, 408 Goebel mirror, 131 Grain boundary diffusion, 396 Grain size in FeCo layers, 378 Graphitization, 398 Gray Cancer Institute microprobe, 314 Grazing incidence X-ray optics, 320 Grid point distribution, 76 Halo effect, 294 Hartmann wavefront measurement, 226 ALS beamline, 226 normalized beam intensity profiles, 227 528 Index High-gain harmonic generation (HGHG), 71 Huygens–Fresnel principle, 74 Imaging systems, method for determining focus position, 28 In-line X-ray optics, 508 Inclined diffraction, wave vectors in reciprocal space for, 442 Induction-hardened S45C steel, diffraction profiles, 467, 468 Ion beam finishing (IBF), 201 Isothermal annealings, 399 K correlation function, 394 Kinematical theory, 503 Kirchhoff integral theorem, 73 Kirkpatrick–Baez (KB) systems, reflective optics, 255 elliptical surfaces, 263 geometrical characteristics, 262 grazing incidence optic, 262 refractive index, 260 Kirz formula, 476 Langasite (LGS), 494 as piezoelectric crystal, 495 Laue diffraction, 301 image of, 456 sagittal deviation, 454 with profiled surfaces, 457 Lens-based X-ray microscopy, 256 classification, 256 optical schematic of, 257 Levenberg–Marquardt method, 60, 65 Lift-off technology, 474 Line for ultimate characterizations by imaging and absorption (LUCIA), 229 Line-to-space ratio, 151 influence on diffraction efficiencies, 151 of laminar zone structures, 141 of transmission grating, 144 Lobster Eye (LE), 127 in Schmidt arrangement, 321 optics, 127 Long Trace Profiler (LTP), 3, 193, 208 calibrated reference mirror, 185 design modifications, 185 digital CCD camera, 187 environmental control enclosure, 186 Wollaston prism arrangement, 188 calibration setup, 189 optical setup of, 189 source and detector, 188 split retro reflector, 190 features, 181 optics head, 182 source of error, 183 misalignment of optics head, 184 refractive index changes, 183 systematic errors, 184 thermal instability, 183 Magnetron sputtering, 384 Maxwell–Boltzmann distribution, 54 Maxwellian distribution, 62 MBE, see Molecular beam epitaxy MBR, see Multiple Bragg reflections MBR-monochromator, diffraction profiles of, 466, 467 Media-Lario technologies, 237, 239, 240, 245 Metrology, 3 “footprint” measurement, 204 computer controlled scanning, 203 demonstration components, 202 ion source parameters, 204 van Citter deconvolution, 204 Michelson interferometer, for measuring wave front, 375 Microcrystalline layers, 395 Microdiffractometry, 300 Microphotonics, elements of, 472 Microstructured optical array (MOA), 312 finite element analysis (FEA), 313 manufacture of, 315 ray tracing method, 314 Mirrors surface roughness of, 31 Molecular beam epitaxy, 390 Monochromatic waves, propagation of, 81 Index 529 Monochromator designs, simulation of, 516 block arrangement, 521 channels variations, 520 cooling temperature effects, 520 mechanical deformation, dependence of, 518 silicon properties, 522 silicon target, 516 temperature field and mechanical deformation, 518 Monochromator FeCo-Si, 377 stress values for, 378, 379 Monocrystalline silicon, 513 finite element (FE) simulations of, 513 thermomechanical parameters of, 517 Monolithic system, of diffractors, 507 Multichannel supermirror, 59 Multifoil optical (MFO) condenser, 319 design and testing for, 319 in EUV region, 325 in visible and X-ray region, 324 EUV bifacial Kirkpatrick–Baez condenser, 321, 327 focal spot size determination, 328 glass mirror, thermal shaping of, 323 reflecting mirror parameter of, 323 solid angle, 323 source imaging by, 328 Multilayer Laue lens (MLL), 270 Multilayer systems, 234, 372, 389 as-deposited, XRR and GIXDS simulation parameters, 396, 398, 399, 401 bandwidth of, 410 biaxial elastic modulus, 373 coatings, depositon, 237, 385, 422 energy dispersion of, 415 laterally graded, 409 layer thickness distribution, 412 layer thicknesses for FeCo, 377 layer-by-layer design methods, 426 with barrier layers, 430 nonperiodic, 415 optimization algorithm, 427 optimization method with fixed thickness layers, 431 partially polarized radiation, 434 polarization analysis, 414 reciprocal space maps of Sc/Cr, 402 reflectivities measurement, 414 reflectivity and inreflectance for comparison of, 429 reflectivity of broad angular range, 412 reflectivity spectrum, 411 stress developing in FeCo/Si, 376 stress measurement, 374 stress mitigation, 383, 387 stress variation vs. argon pressure in, 373 sub-quarter-wave, 417 thermal stability, 401 with continuous refractive index variation, 432 with strongly absorbing materials, 417 with ultra-short periods, 389 Multiple Bragg reflections, 460 effects of, 463 in elastically bent perfect crystals, 460 investigation methods for, 461 reflection with primary reflection, 462 schematic diagram of, 460 Nanometer beams, 91 Nanometer optical component measur- ing machine (NOM), 3, 176, 193, 213 45 ◦ -pentaprism design, 194 autocollimator, 193 improved measurement techniques, 193 thermal stability, 195 Nanometer radiation, 202, 471 wavelength of, 472 Nested mirror systems, 308 computer simulations, 309, 310 laboratory-scale microfocus and bending magnet sources, 309 mirror fabrication process, 310–312 surface roughness, 310 Neutron beam, 43, 49, 51 beam divergence, 114, 123 focusing guides, 123 extraction guide system, 51 [...]...530 Index extraction system, 49 focusing parameters affecting, 115 optical index for, 118 phase-space mapping, 43 polarization of, 356 scattering, 115 Neutron focusing optics, see Focusing neutron optics Neutron optical components, quality assessment of, 43 Neutron radiography experimental test, 467 Neutron spectrometers, 113 focal lengths of, 113 refractive lens on, 119 Neutron supermirrors,... see Small angle neutron scattering spectrometers SAW, see Surface acoustic wave Scalar wave equation, 142 complex amplitudes Am (z), 145 in two-dimensional inhomogeneous medium, 142 matrix solution of, 148 solution of modulated, 148 Scanning microscopes, 257, 259 Scanning pentaprism, 184 Scanning transmission X-ray microscopes (STXRM), 259 Scattering length density (SLD), 365 Scattering vector, 502... horizontal interfaces, 96 in guiding layer, 94, 95 with lateral waves, 108 with nonuniform plane waves, 108 in three layer WG, 92 limiting case for, 95 RESTRAX Code, 58 sampling strategy for, 59 531 Round-Robin mirrors consistency in results, 218 description and use, 214 measurement procedures, 214 residual error concordance, 217 Sagittal deviation, 449 Sagittal focusing, 447 Sagittally focusing monochromator... 331 Transmission X-ray microscope (TXRM), full-field, 256 vs scanning microscope, 258 phase contrast in, 259 Transverse grooves, 454 Ultra-high vacuum (UHV), electron beam evaporation in, 392 Ultrasonic super-lattice, use in X-ray wavelength, 484 Vacuum furnace annealing, 392 Varied line spacing (VLS) gratings, 12, 27 Volume gratings, 472 characteristics of, 480 types of, 472 Water window, 391 Wave vector... transfer, 502 Index Waveguide Front coupling intensity distribution, 107 interference, 108 normalized integrated power, 108 spatial spectral amplitude, 106 wave field, 106, 107 incoming radiation, 92 with prereflection, 92 absorption losses, 103 plane wave incoming radiation, 101 spatially coherent illumination, 102, 103 spatially incoherent radiation, 102 Wavefront propagation, 10 codes for, 10 principle... Sirenko, N.P Yashina, and S Str¨ m, 2007, 110 figs., XIV, 353 pages o 123 Wavelength Filters in Fibre Optics By H Venghaus (Ed.), 2006, 210 figs., XXIV, 454 pages 124 Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs By A Doicu, T Wriedt, and Y.A Eremin, 2006, 123 figs., XIII, 324 pages Springer Series in optical sciences 125 Electromagnetic and Optical Pulse... Surface Nanophotonics Principles and Applications By D.L Andrews and Z Gaburro (Eds.) 2007, 89 figs., X, 176 pages 134 Strong Field Laser Physics By T Brabec, 2007, approx 150 figs., XV, 500 pages 135 Optical Nonlinearities in Chalcogenide Glasses and their Applications By A Zakery and S.R Elliott, 2007, 92 figs., IX, 199 pages 136 Optical Measurement Techniques Innovations for Industry and the Life Sciences... for Industry and the Life Sciences By K.E Peiponen, R Myllyl¨ and A.V Priezzhev, 2008, approx 65 figs., IX, 300 pages a 137 Modern Developments in X-Ray and Neutron Optics By A Erko, M Idir, T Krist and A.G Michette, 2008, approx 150 figs., XV, 400 pages 138 Optical Micro-Resonators Theory, Fabrication, and Applications By R Grover, J Heebner and T Ibrahim, 2008, approx 100 figs., XXII, 330 pages ... as coherence filter, 93 for X-ray microbeam production, 91 front coupling (FC), 92 resonance beam coupling, 93 X-ray absorption fine structure (XAFS), classification of, 287 XUV polarimetry, 408 YAG:Ce crystal scintillator plate, use of, 327 Youngs modulus, 373 ZEMAX c , 313 Springer Series in optical sciences Volume 1 1 Solid-State Laser Engineering By W Koechner, 5th revised and updated ed 1999, 472 figs.,... capillary optics, 287 critical angle, 288 Transmission electron microscopy (TEM), 389, 391, 394 Transmission grating material distribution of, 144 modulated region of, 145 periodically changing permittivity of, 143 Transmission lenses, 333 cross-sectional view of, 332 historical development of X-ray, 333 main parameters for, 331 numerical aperture, 333 spatial resolution, 332, 333 surface errors in X-ray, . 71 Huygens–Fresnel principle, 74 Imaging systems, method for determining focus position, 28 In- line X-ray optics, 508 Inclined diffraction, wave vectors in reciprocal space for, 442 Induction-hardened. 51 530 Index extraction system, 49 focusing parameters affecting, 115 optical index for, 118 phase-space mapping, 43 polarization of, 356 scattering, 115 Neutron focusing optics, see Focusing neutron. A m (z), 145 in two-dimensional inhomogeneous medium, 142 matrix solution of, 148 solution of modulated, 148 Scanning microscopes, 257, 259 Scanning pentaprism, 184 Scanning transmission X-ray microscopes