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 (); 10, analyser; 11, polariser; 12, ring light; 13, optical axis () |
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 |