List of Figures

Figure 2.1 An ancient Egyptian cubit (a standard of mass is also shown) 8
Figure 2.2 Metal bar length standards (gauge blocks and length bars) 11
Figure 2.3 The UK’s official copy of the prototype X-section metre bar (Photo courtesy Andrew Lewis) 12
Figure 2.4 An iodine-stabilised helium–neon laser based at NPL, UK 13
Figure 2.5 Kilogram 18 held at NPL, UK 15
Figure 2.6 An autocollimator being used to check the angular capability of a machine tool (Courtesy of Taylor Hobson) 17
Figure 2.7 Traceability 18
Figure 2.8 The difference between accuracy and precision. The reference value may be the true value or a calibrated value, abscissa is the value of the measurand and the ordinate is the probability density of the measured values 20
Figure 2.9 Illustration of an imperfect measurement. The average of the indication values (shown as crosses) is offset from the true quantity value. The offset relates to a systematic error, and the dispersion of the indication values about the average relates to random errors 22
Figure 2.10 Illustration of the propagation of distributions. Three input quantities, characterised by different distributions, including a rectangular distribution, a Gaussian distributions and an asymmetric distribution, are related to the measurand Y for which the probability distribution is to be determined 24
Figure 2.11 Energy levels in the He–Ne gas laser for 632.8 nm radiation 28
Figure 2.12 Schema of an iodine-stabilised He–Ne laser 31
Figure 2.13 Frequency and intensity profiles in a two-mode He–Ne laser 32
Figure 2.14 Magnetic splitting of neon – g is the Landé g factor, µ is the Bohr magneton 33
Figure 2.15 Calibration scheme for Zeeman-stabilised laser 35
Figure 3.1 Representation of a rigid constraint with force applied 43
Figure 3.2 (a) A Type I Kelvin clamp and (b) a Type II Kelvin clamp 45
Figure 3.3 (a) A vee-groove made from three spheres and (b) a vee-groove made using a milling cutter 45
Figure 3.4 A single degree of freedom motion device 46
Figure 3.5 Effects of Abbe error on an optical length measurement 48
Figure 3.6 Mutual compression of a sphere on a plane 50
Figure 3.7 Kevin Lindsey with the Tetraform grinding machine 55
Figure 3.8 An overlay of seismic vibration spectra measured at 75 seismograph stations worldwide (Adapted from Ref. [32]) 56
Figure 3.9 Damped transmissibility, T, as a function of frequency ratio (ω/ω0) 57
Figure 4.1 Definition of the length of a gauge block 66
Figure 4.2 A typical gauge block wrung to a platen 66
Figure 4.3 Amplitude division in a Michelson/Twyman–Green interferometer where S is the source, A and B are lenses to collimate and focus the light, respectively, C is a beam splitter, D is a detector and M1 and M2 are plane mirrors 69
Figure 4.4 Intensity as a function of phase for different visibility 70
Figure 4.5 Intensity distribution for a real light source 71
Figure 4.6 Illustration of the effect of a limited coherence length for different sources 71
Figure 4.7 Schema of the original Michelson interferometer 73
Figure 4.8 Schema of a Twyman–Green interferometer 74
Figure 4.9 The Fizeau interferometer 75
Figure 4.10 Typical interference pattern of a flat surface in a Fizeau interferometer 75
Figure 4.11 Schema of a Jamin interferometer 77
Figure 4.12 Schema of a Mach–Zehnder interferometer 78
Figure 4.13 Schematic of the Fabry–Pérot interferometer 79
Figure 4.14 Transmittance as a function of distance, L, for various reflectances 80
Figure 4.15 Possible definition of a mechanical gauge block length 81
Figure 4.16 Schema of a gauge block interferometer containing a gauge block 82
Figure 4.17 Theoretical interference pattern of a gauge block on a platen 83
Figure 4.18 Method for determining a surface and phase change correction 88
Figure 4.19 Double-sided gauge block interferometer [28]. HM1-3, half-reflecting mirrors; RM1-2, reference mirrors; GB, gauge block 91
Figure 5.1 Homodyne interferometer configuration 98
Figure 5.2 Heterodyne interferometer configuration 99
Figure 5.3 Optical arrangement to double pass a Michelson interferometer 101
Figure 5.4 Schema of a differential plane mirror interferometer 102
Figure 5.5 Cosine error with an interferometer 105
Figure 5.6 Cosine error of a plane mirror target 106
Figure 5.7 Fibre-delivered homodyne plane mirror interferometer system 111
Figure 5.8 (a) Wu interferometer configuration adapted from Ref. [61] and (b) modified Joo interferometer configuration adapted from Ref. [25] 112
Figure 5.9 Schema of differential wavefront sensing. Tilted wavefronts are individually measured on each quadrant of a quad photodiode. The scaled difference of matched pairs can be used to measure tip and tilt 113
Figure 5.10 Schema of an angular interferometer 114
Figure 5.11 A typical capacitance sensor set-up 115
Figure 5.12 Schematic of an LVDT probe 118
Figure 5.13 Error characteristic of an LVDT probe 119
Figure 5.14 Schema of an optical encoder 120
Figure 5.15 Total internal reflectance in an optical fibre 121
Figure 5.16 End view of bifurcated optical fibre sensors, (a) hemispherical, (b) random and (c) fibre pair 122
Figure 5.17 Bifurcated fibre optic sensor components 122
Figure 5.18 Bifurcated fibre optic sensor response curve 122
Figure 5.19 Schema of an X-ray interferometer 126
Figure 5.20 Schema of a combined optical and X-ray interferometer 127
Figure 6.1 Typical constraints in traditional AW space plots (Adapted from Ref. [16]) 136
Figure 6.2 AW space depicting the operating regimes for common instruments 136
Figure 6.3 The original Talysurf instrument 138
Figure 6.4 Example of the result of a profile measurement 139
Figure 6.5 Lay on a machined surface. The direction of the lay is represented by the arrow (Courtesy of François Blateyron) 140
Figure 6.6 SEM image of focussed ion beam (FIB) fabricated 2×2 array of moth-eye lenses, (10×10×2) µm. The insert: SEM zoom-in image of the patterned bottom of the micro-lenses with nano-lenses, Ø150 nm×50 nm, in hexagonal arrangement (From Ref. [41]) 141
Figure 6.7 A profile taken from a 3D measurement shows the possible ambiguity of 2D measurement and characterisation 142
Figure 6.8 Schema of a typical stylus instrument 143
Figure 6.9 Damage to a brass surface due to a high stylus force 144
Figure 6.10 Numerical aperture of a microscope objective lens 147
Figure 6.11 Light that is reflected diffusely can travel back into the aperture to be detected (From Ref. [14]) 148
Figure 6.12 Example of the batwing effect when measuring a step using a coherence scanning interferometer. Note that the batwing effect is less evident when the data processing incorporates the interference phase 151
Figure 6.13 Comparison of stylus and coherence scanning interferometry profiles at 50× for a type D material measure 153
Figure 6.14 Correlation study comparing coherence scanning interferometry and stylus results on eight sinusoidal material measures 153
Figure 6.15 Principle of a laser triangulation sensor 154
Figure 6.16 Confocal set-up with (a) object in focus and (b) object out of focus 156
Figure 6.17 Demonstration of the confocal effect on a piece of paper: (a) microscopic bright-field image and (b) confocal image. The contrast of both images has been enhanced for better visualisation 157
Figure 6.18 Schematic representation of a confocal curve. If the surface is in focus (position 0), the intensity has a maximum 157
Figure 6.19 Schema of a Nipkow disk. The pinholes rotate through the intermediate image and sample the whole area within one revolution 158
Figure 6.20 Chromatic confocal depth discrimination 159
Figure 6.21 Schema of a point autofocus instrument 161
Figure 6.22 Principle of point autofocus operation 162
Figure 6.23 Schema of a focus variation instrument. 1, sensor; 2, optical components; 3, white light source; 4, beam-splitting mirror; 5, objective; 6, specimen; 7, vertical scanning; 8, focus information curve with maximum position; 9, light beam (image); 10, analyser; 11, polariser; 12, ring light; 13, optical axis (image) 163
Figure 6.24 Schema of a phase-shifting interferometer 165
Figure 6.25 Schematic diagram of a Mirau objective 166
Figure 6.26 Schematic diagram of a Linnik objective 166
Figure 6.27 Schematic diagram of DHM with beam splitter (BS), mirrors (M), condenser (C), microscope objective (MO) and lens in the reference arm (RL) used to perform a reference wave curvature similar to the object wave curvature (some DHM use the same MO in the object wave) 168
Figure 6.28 Schema of a coherence scanning interferometer 170
Figure 6.29 Schematic of how to build up an interferogram on a surface using CSI 171
Figure 6.30 Integrating sphere for measuring TIS 174
Figure 6.31 An approach to traceability for surface topography measurement employing transfer artefacts certified by a primary stylus instrument 177
Figure 6.32 Analysis of a type A1 calibration material measure 179
Figure 6.33 Type APS material measure 181
Figure 6.34 Type AGP material measure 182
Figure 6.35 Type AGC material measure 182
Figure 6.36 Type APS material measure 183
Figure 6.37 Type PRI material measure 184
Figure 6.38 Type ACG material measure 184
Figure 6.39 Type ACG material measure 185
Figure 6.40 Type ADT material measure 185
Figure 6.41 Type ASG material measure, where dark areas are raised in comparison to light areas 186
Figure 6.42 Publicity material for the NPL areal calibration material measures 188
Figure 6.43 Results of a comparison of different instruments used to measure a sinusoidal sample 190
Figure 7.1 Schematic image of a typical scanning probe system, in this case an AFM 208
Figure 7.2 Block diagram of a typical SPM 210
Figure 7.3 Noise results from an AFM. The upper image shows an example of a static noise investigation on a bare silicon wafer. The noise-equivalent roughness is Rq=0.013 nm. For comparison, the lower image shows the wafer surface: scan size 1 μm×1 μm, Rq=0.081 nm 212
Figure 7.4 Schematic of the imaging mechanism of spherical particle imaging by AFM. The geometry of the AFM tip prevents ‘true’ imaging of the particle as the apex of the tip is not in contact with the particle all the time and the final image is a combination of the tip and particle shape. Accurate sizing of the nanoparticle can only be obtained from the height measurement 214
Figure 7.5 Definition of the pitch of lateral artefacts: (a) 1D and (b) 2D 215
Figure 7.6 Schematic of (a) a force curve and (b) force–distance curve 218
Figure 7.7 Schematic illustration of the strong capillary force that tends to drive the tip and sample together during imaging in air 222
Figure 7.8 (a) TEM image of nominal 30 nm diameter gold nanoparticles; (b) using threshold to identify the individual particles and (c) histogram of the measured diameters 233
Figure 7.9 TEM image of 150-nm-diameter latex particles. This image highlights the drawback to TEM size measurement using TEM or SEM. The first is that a white ‘halo’ surrounds the particle. Should the halo area be included in the size measurement? If so there will be a difficulty in determining the threshold level. The second is that the particles are aggregated, again making sizing difficult 234
Figure 8.1 The various lengths used for profile analysis 245
Figure 8.2 Separation of surface texture into roughness, waviness and profile 246
Figure 8.3 Primary (top), waviness (middle) and roughness (bottom) profiles 247
Figure 8.4 Maximum profile peak height, example of roughness profile 250
Figure 8.5 Maximum profile valley depth, example of roughness profile 251
Figure 8.6 Height of profile elements, example of roughness profile 251
Figure 8.7 The derivation of Ra 252
Figure 8.8 Profiles showing the same Ra with differing height distributions 253
Figure 8.9 Profiles with positive (top), zero (middle) and negative (bottom) values of Rsk 254
Figure 8.10 Profiles with low (top) and high (bottom) values of Rku 255
Figure 8.11 Width of profile elements 256
Figure 8.12 Material ratio curve 257
Figure 8.13 Profile section-level separation 258
Figure 8.14 Profile height amplitude distribution curve 259
Figure 8.15 Amplitude distribution curve 259
Figure 8.16 Epitaxial wafer surface topographies in different transmission bands: (a) the raw measured surface; (b) roughness surface (short-scale SL surface) S-filter=0.36 μm (sampling space), L-filter=8 μm; (c) wavy surface (middle-scale SF surface) S-filter=8 μm, F-operator and (d) form error surface (long-scale form surface), F-operator 263
Figure 8.17 Areal material ratio curve 272
Figure 8.18 Inverse areal material ratio curve 272
Figure 8.19 Void volume and material volume parameters 274
Figure 8.20 Example simulated surface 277
Figure 8.21 Contour map of Figure 8.20 showing critical lines and points 277
Figure 8.22 Full change tree for Figure 8.21 278
Figure 8.23 Dale change tree for Figure 8.21 279
Figure 8.24 Hill change tree for Figure 8.21 279
Figure 8.25 Line segment tiling on a profile 285
Figure 8.26 Inclination on a profile 286
Figure 8.27 Tiling exercises for area-scale analysis 287
Figure 9.1 A typical moving bridge CMM 296
Figure 9.2 CMM configurations 297
Figure 9.3 Illustration of the effect of different measurement strategies on the diameter and location of a circle. The measurement points are indicated in red; the calculated circles from the three sets are in black and the centres are indicated in blue. 302
Figure 9.4 Schema of the kinematic design of the Zeiss F25 CMM 304
Figure 9.5 Schema of the kinematic design of the Isara 400 from IBSPE 306
Figure 9.6 Schema of the NMM 307
Figure 9.7 The METAS TouchProbe 308
Figure 9.8 Schema of the NPL small-CMM probe 309
Figure 9.9 DVD pickup head micro-CMM probe [43] 310
Figure 9.10 Schema of the boss-probe developed at PTB 311
Figure 9.11 The fibre probe developed by PTB. Notice the second micro-sphere on the shaft of the fibre; this gives accurate measurement of variations in sample ‘height’ (z-axis) 313
Figure 9.12 The concept of ‘buckling’ measurement, used to increase the capability of the fibre deflection probe to 3D 313
Figure 9.13 A vibrating fibre probe. The vibrating end forms a ‘virtual’ tip that will detect contact with the measurement surface while imparting very little force 315
Figure 9.14 Schema of the NPL vibrating micro-CMM probe 316
Figure 9.15 A suggested physical set-up for testing a length, L, along any face diagonal, including z-axis travel or any space diagonal of a micro-CMM 317
Figure 9.16 Micro-CMM performance verification artefacts. (a) METAS miniature ball bars, (b) PTB ball plate, (c) METAS ball plate, (d) A*STAR mini-sphere beam and (e) Zeiss half-sphere plate 318
Figure 9.17 Straightness (xTx) measurement of the F25 with the CAA correction enabled 320
Figure 10.1 Two-pan balance used by Poynting to determine the Universal Gravitational Constant (G) in the nineteenth century, currently at NPL 329
Figure 10.2 Comparative plot of described surface interaction forces, based on the following values: R=2 μm; U=0.5 V; γ=72 mJ·m−2; H=10−18 J and e=r=100 nm. Physical constants take their standard values: e0=8.854×10−12 C2·N−1·m−2; h=1.055×10−34 m2·kg·s−1 and c=3×108 m·s−1 337
Figure 10.3 Traceability of the newton to fundamental constants of nature, in terms of practical realisations in which base units may be dependent on derived units (Courtesy of Dr Christopher Jones, NPL) 338
Figure 10.4 Schema of the NPL low-force balance (LFB) 340
Figure 10.5 Experimental prototype reference cantilever array – plan view 342
Figure 10.6 Images of the NPL C-MARS device, with detail of its fiducial markings; the 10 μm oxide squares form a binary numbering system along the axis of symmetry 343
Figure 10.7 Computer model of the NPL Electrical Nanobalance device. The area shown is 980 μm×560 μm. Dimensions perpendicular to the plane have been expanded by a factor of 20 for clarity 344
Figure 10.8 Schema of a resonant force sensor – the nanoguitar 345
..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset