Index

Note: Page numbers followed by “f” and “t” refers to figures and tables respectively.

A

Abbe criterion, 155
Abbe error, 48, 48, 48f, 49, 106, 109–110, 305, 319
Abbe offset, 48, 123, 319
Abbe Principle, 48–49, 90, 305–306
Absorption index, 150
Accuracy, 19, 20–21
Acoustic noise, 59
Acousto-optic frequency shifter, 100
Active vibration isolation, 58
Added-mass method, 220
Adhesion force, 217–219, 225–226
Amplitude distribution curve, 254, 258
Amplitude parameters, 252–255
Amplitude profile parameters, 249–251
Amplitude–wavelength space, 135–136
Analogue probe, 298
Analogue-to-digital converter, 100–101
Angle, 16–18
Angle-resolved scatter, 174–175
Angular distribution of scatter, 174–175
Angular interferometer, 112–113
Angular power spectrum, 274–275
Aperture correction, 87, 90, 148
Area-integrating, 142–143
Areal filtering, 262–264
Areal height parameters, 268–269
Areal hybrid parameters, 270–271
Areal material ratio, 271, 271, 272f, 273
Areal optical techniques, 162–172
Areal parameter, 186–187, 267–268, 271–272
Areal spacing parameters, 269–270
Areal specification standards, 264–267
Areal surface texture, 134, 140–142, 180, 261–282
Areal topography measuring, 142–143, 180
Area-scale fractal complexity, 288
Arithmetic mean of the absolute height, 268
Arithmetic mean peak curvature, 281
Arithmetical mean deviation of the assessed profile, 252–253
Articulated-arm CMMs, 300
Associated features, 297
Atomic force microscope, 15–16, 209–226, 215–216, 216–217
Atomic lattice parameter, 125
Atomic resolution, 206–207, 209–210
Autocollimator, 17–18, 64–65, 300, 319
Auto-correlation function, 269
Auto-correlation length, 269–270
Avogadro constant, 14–15, 333
Avogadro method, 14–15
Avogadro project, 333
Axial resolution, 21, 158, 167

B

Backscattered electrons, 228
Balanced interferometers, 109
Band-pass filter, 244, 247
Base quantities, 9–10
Batwings, 150–151
Beam waist, 149–150
Bearing length ratio, 256
Bearing ratio curve, 256–257, 257–258
Bi-directional fringe counting, 97–98
Bidirectional scatter distribution function, 172–173
Bifurcated sensor, 121
Birefringent, 99
Bragg angle, 125
Brewster’s angle, 120–121
Buoyancy effect, 329–330
Bureau International des Poids et Mesures, 14, 330

C

Calibration of a laser’s frequency, 34–35
Cantilever, 121–123, 219
Capacitive displacement sensors, 115–116
Capacitive instruments, 175
Capacitive sensor, 115
Capillary force, 222, 347
Carbon nanotube, 3, 223–224, 225
Cartesian coordinates, 43, 296
Central limit theorem, 25, 26
Change tree, 276–279, 278
Charge on an electron, 14–15
Chemical force microscopy, 223
Chemical vapour deposition, 223–224
Closed dale area, 282
Closed dale volume, 282
Closed hill area, 282
Closed hill volume, 282
Coblentz sphere, 173
Coefficient of friction, 222
Coefficient of linear thermal expansion, 104
Coefficient of thermal expansion, 85–86
Coherence length, 30, 70–72
Coherence scanning interferometer, 151, 169–172, 170f
Combined Optical and X-ray Interferometer, 126
Commercial interferometers, 109
Comparator, 65, 302–303, 328, 334
Computer-aided accuracy correction field, 320
Computer-aided design, 297
Co-nanomet, 2
Conférence Générale des Poids et Mesures, 9
Confocal chromatic, 151, 159–160
Confocal curve, 156, 159
Confocal instruments, 155–160
Constraint, 43, 43, 44–46, 46–47, 100
Contact mode, 208, 220–221
Contrast, 69–70
Coordinate measuring machine, 5, 13, 47, 295–296, 295–300, 296, 296, 296, 302–303
Coordinate metrology, 5, 295–296
Core material volume, 273
Core void volume, 273
Correlation length, 269–270, 270
Cosine error, 90, 105–106
Course line, 276, 276
Coverage factor, 26
Coverage interval, 23, 23
CSI, See Coherence scanning interferometer; Coherence scanning interferometry
Cumulative error, 104
Current balance, 333
Curves and related parameters, 256–259
Cut-off filter, 187
Cut-off length, 289
Cylindrical capacitor, 116

D

Dale change tree, 278
Dale volume, 273
Damping, 47, 58
Deadpath length, 104–105
Deadweight, 16, 340
Deep reactive ion etched structures, 303
Degrees of freedom, 23–24, 25
Density of peaks, 281
Developed interfacial area ratio, 271
Differential interferometry, 102–103
Differential plane mirror interferometer, 102–103, 125–126
Diffuse reflection, 172
Digital hologram, 168–169
Digital holographic microscope, 168–169, 168–169
Dimensionless quantity, 16–17
Displacement interferometry, 34, 97–113, 104–110
Displacement measurement, 36
Displacement sensor, 5, 96, 123–126
Displacement, 96
Distance, 96
Doppler broadening, 29
Doppler shift, 98, 99–100
Double-pass interferometry, 101–102
Dynamic noise, 212

E

Eddy current displacement sensors, 116–118
Elastic averaging, 44
Elastic compression, 49–50
Elastic element, 341–343
Electrical Nanobalance, 343–344, 343–344, 344f
Electrical resistivity measurement, 226–227
Electromagnetic waves, 12–13, 67
Electron backscattered diffraction, 229
Electron gun, 230
Electron microscope, 135, 228–235
Electronic balance, 335
Electrostatic force balance, 339
Elliptical polarisation, 68
End standard, 10–11, 65
Energy level, 28, 28f
Engineering nanometrology, 4, 64
Equivalent viscous damping, 58
Error mapping, 301
Error, 5, 19–20, 21–22
European nanotechnology, 2
Evaluation length, 244
Expanded uncertainty, 26, 104
Extreme-value parameter, 249–250

F

Fabry-Pérot interferometer, 28, 30, 78–80, 124
Feature attribute statistics, 281
Feature parameter, 176, 261, 267, 275
Feedback, 32–33, 47
Field of view, 146
Field parameter, 177, 193, 267, 268–275
Field programmable gate array, 100–101
Film thickness, 88
Finesse, 79
Five point peak height, 282
Five point pit height, 282
Fizeau interferometer, 74–77
Focal length, 87, 149–150
Focal shift error, 160–161
Focus variation instrument, 162–164
Focused ion beam, 207, 235
F-operator, 261, 263f
Force curve, 217–219, 218f
Force loops, 51–52
Force, 5, 15–16
Force–distance curve, 217–219, 218f
Fractal dimension, 284, 285
Fractal geometry, 283, 284
Fractal methods, 283–289
Fractal parameter, 267, 283
Free spectral range, 80, 103
Free-form component, 300
Frequency comb, 35–36, 36, 36
Frequency-stabilised laser, 28
Fresnel equations, 172–173
Frictional force, 222
Fringe counting, 98–99, 100–101
Fringe fraction, 83–84, 88–89
Full change tree, 278
Full width at half maximum, 156
Fundamental physical constants, 14–15

G

Gauge block interferometer, 80–91, 89
Gauge block, 11, 65–67, 87–88
Gauge factor, 114
Gaussian distribution, 25, 26
Gaussian filter, 246, 260, 262
Gaussian probability function, 245–246
Geometric element, 299
Geometric error, 300
Geometrical Product Specification, 259–260, 264–265, 267
Geometry, 42
Ghost steps, 151
Goniophotometer, 174–175
Gradient density function, 274
Gravitational wave detector, 55
Guide to the Expression of Uncertainty in Measurement, 22–23

H

Hardware fringe counting, 100
Height discrimination, 250–251
Heisenberg’s Uncertainty Principle, 19–20
Helium ion microscope, 235
Helium–neon laser, 12, 13f, 28–29
Heterodyne interferometer, 97–98, 99–100, 110–111
Heydemann correction, 107–109
High-pass filter, 245
Hill change tree, 278
Homodyne interferometer, 35, 98, 98–99, 110–111

I

Inductive sensor, 116, 116–118
Integrating sphere, 173
Interfacial surface roughness, 172
Interference microscopy, 148
Interference, 21–22, 70–72
Interferometer, 17–18, 72–80
Interferometry, 5, 67–72
Intermittent mode, 208
Inter-molecular forces, 207
Internal resonances, 58
International Organization for Standardization, 3
International Prototype Kilogram, 328–329, 329–330
International Prototype of the Kilogram, 14
Intra-molecular forces, 220–224
Inverse areal material ratio, 271
Iodine-stabilised He-Ne laser, 31, 31f
Ion accumulation approach, 334
Isara 400, 305, 305–306

J

Jamin beam splitter, 102–103
Jamin interferometer, 77, 77, 77f
Josephson junction, 333, 334

K

Kelvin clamp, 44–46, 45f
Kinematic design, 43–47
Kinematics, 43
Knife-edge balance, 328
Knife-edge, 123, 335
Korea Research Institute of Standards and Science, 339
Kurtosis of the assessed profile, 255
Kurtosis of topography height distribution, 269

L

Lamb dip, 30
Laser frequency stabilisation, 30–33
Laser frequency standards, 35–36
Laser interferometer-based micro-CMMs, 305–306
Laser interferometer-based nano-CMM, 306–307
Laser tracker, 64–65, 300
Lateral Electrical Nanobalance, 343–344
Lateral resolution, 21, 76
Lau pattern, 118–119
Law of propagation of uncertainty, 25
Length, 5, 8, 10–14, 64–65, 96
Length-scale plot, 285, 285, 286
Lennard-Jones potential, 221
Levitated superconductor approach, 334
L-filter, 261, 261–262
Line profiling, 142–143
Line standard, 10–11, 65
Linear calibration, 231
Linear filter, 263
Linear fractal complexity parameter, 284–285
Linear interpolation, 284, 288
Linear variable differential transformer, 117
Linescale-based micro-CMMs, 304–305
Linnik objective, 165–167
Low-force balance, 339
Low-force measurement, 336–347, 346t
Low-mass measurement, 335–336
Low-pass filter, 149–150, 245

M

Mach-Zehnder interferometer, 77–78
Magnification, 137–138, 138
Mass comparator, 328, 328, 334–335
Mass measurement, 328–335
Mass standards, 330
Mass, 4, 14–15
Material ratio curve, 256–257, 257f
Material ratio of the profile, 256
Material volume, 273
Maximum height of the profile, 250
Maximum height of the surface, 269
Maximum pit height of the surface, 269
Maximum profile peak height, 249–250
Maximum profile valley depth, 250
Maximum surface peak height, 269
Mean height of the profile elements, 250–251
Mean line, 246, 249
Mean width of the profile elements, 255–256
Measurand, 21, 23, 23, 41–42
Measurements in the nanometre, 2
Measurements, 7–9
Mechanical comparators, 65
Mechanical micro-CMM probes, 308–310
Meniscus, 222, 337t
Method of exact fractions, 84
Metre, 8, 10, 10–11
Metrological AFM, 216
Metrology frame, thermal expansion of, 104
Metrology loop, 51, 51–52
Michelson interferometer, 55, 72
Micro- and nanotechnology, 1
Micro-CMMs, 303–307, 316–321
Microelectromechanical systems, 15–16, 303
Microscope objective, 147, 158
Miniature CMM, 295–296
Mirau objective, 165–167
Modulation depth, 70
Moiré pattern, 118–119
Monte Carlo method, 23, 23, 26–27
Morphological filters, 263
Motif, 261, 264
Multiple scattering, 152
Multi-wavelength interferometry uncertainty, 89

N

Nanoguitar, 344–345
Nanomaterials, 3
Nanomeasuring Machine, 306, 307f
Nanoparticle, 214f, 227–228, 232–235
Nanotechnology markets, 2
National Institute of Standards and Technology, 9
National Measurement Institute, 8
National Metrology Institute of Japan, 9
National Nanotechnology Initiative, 2
National Physical Laboratory, 9
Natural frequency, 53–54, 57
Nesting index, 261
Nettoyage-lavage, 330, 330–331, 331–332
Newton, 15–16
Nipkow disk, 157, 158
Non-contact mode, 208
Non-cumulative error, 104
Non-linearity, 99, 114
Numerical aperture, 21, 120–121, 156
Numerical wavefront propagation algorithm, 169

O

Objective lens, 147–148
Obliquity correction, 87
Obliquity factor, 173
Optical beam deflection, 210
Optical cavity, 28, 29
Optical encoder, 118–120
Optical fibre sensor, 120–123, 121
Optical instrument, 21, 51–52, 146–175
Optical interferometry, 123–125
Optical lever sensitivity, 219
Optical resolution, 147–148, 148–149
Optical transfer function, 191
Optomechanical micro-CMM probes, 312–314

P

‘Parameter rash’, 242
Passive vibration isolation, 56–58
Pattern recognition, 275
Peak extreme height, 273
Peak material volume, 273
Pendulum, 18, 56–57
Performance verification, 301
Periodic error, 106–107
Permittivity, 115, 116
Phase change correction, 88f, 90
Phase change on reflection, 150
Phase quadrature, 97–98, 102–103
Phase sensitive detection, 173
Phase-shifting interferometer, 164–167, 169–170
Phase-unwrapping algorithm, 164–165
Physical quantity, 9–10
Physikalisch-Technische Bundesanhalt, 9
Pickup, 143
Piezoelectric actuator, 125
Piezoelectric scanner, 206–207
Piezoresistive cantilever, 342
Piezoresistive strain element, 341–342
Piezoresistive strain sensors, 114
Pinhole aperture, 155
Planck’s constant, 14–15, 333
Platen, 65
Pneumatic gauging, 175
Pneumatic instruments, 175
Point autofocus instrument, 160
Point autofocus profiling, 160–161
Point spread function, 191
Poisson’s ratio, 49–50
Population inversion, 29
Position, 97
Position-sensitive detector, 319–320
Power spectral density, 174–175
Precision, 5, 20–21, 41–42
Primary profile, 244, 246–247
Principle of superposition, 68
Prismatic component, 299–300
Prismatic slideway, 46–47
Probability density function, 258
Probability distribution, 23–25
Probing force, 135–136
Probing system, 180–181, 298
Profile and areal characterisation, 289–290
Profile calibration artefact, 178
Profile characterization, 247–248, 248–249
Profile element, 248–249, 250–251, 255–256
Profile filtering, 245–247
Profile height amplitude curve, 258–259
Profile measuring instruments, 178–179
Profile peak, 249, 249–250
Profile section height difference, 257
Profile specification standards, 259–261
Profile valley, 249, 250
PSD
See Position-sensitive detector; Power spectral density
PSI
See Phase-shifting interferometer; Phase-shifting interferometry

Q

Quality factor, 72, 72t, 345–346
Quantity of dimension one, 16–17
Quantum mechanical effects, 14–15, 123

R

Radian, 16–17
Random error sources, 109
Random errors, 21–22, 109
Random variable, 26
Rayleigh criterion, 148–149
Reference AFM, 216
Reference data files, 193
Reference graticule, 232
Reference software, 193
Reference surface, 74
Refractive index, 33, 86–87, 90
Refractometer, 86
Relative length parameter, 286
Relative material ratio, 257–258
Resolution, 21–22
Resonant frequency, 56–57, 57
Ridge line, 276
Ringlight, 164
Robust filters, 263
Robust Gaussian filter, 262
Root mean square deviation of the assessed profile, 253–254
Root mean square gradient, 270
Root mean square value of the ordinates, 268
Roughness profile, 247

S

Saddle point, 276
Sampling length, 179, 244
Scale-limited surface, 261–262
Scanning electron microscope, 228–230
Scanning near-field optical microscope, 207
Scanning optical techniques, 152–161
Scanning probe microscope, 3, 207–208, 227–228
Scanning probe, 3, 206–207
Scanning spreading resistance microsocopy, 226–227
Scanning thermal microscopy, 226
Scanning tunnelling microscope, 206–207, 208–209
Scattering instruments, 172–175
Scattering, 152, 172–175
Secondary electrons, 228
Segmentation filters, 264
Segmentation, 261, 275–279
Seismic vibration spectrum, 55
Self-affine, 284
Sensitivity coefficients, 26
Sexagesimal, 17
SF surface, 261–262
S-filter, 261
Sharpness, 163
Shearing interferometry, 77
Silicon-based micro-CMM probes, 310–312
Single-mode laser wavelength stabilisation schemes, 30
Skewness of the assessed profile, 254–255
Skewness of topography height distribution, 268
Skid, 144
SL surface, 261–262
Smooth–rough crossover, 284
Softgauge, 193
Software fringe counting, 100–101
Software measurement standard, 192–193
Solid angle, 16–17
Solid-state laser, 28
Sound pressure attenuation, 59
Spacing discrimination, 250–251
Sparrow criterion, 148–149
Spatial frequency response, 191–192
Spatial wavelength ranges, 135–136
Specular reflection, 162–163
Speed of light, 11–12, 67–68
Spot size, 149–150
Spring constant, 16, 219
Stand-alone micro-CMMs, 304–307
Standard deviation, 23–24, 24–25
Standard uncertainty, 16, 23
Static noise, 211
‘Stedman’ space, See Amplitude–wavelength space
Steradian, 16–17
Stiffness, 42, 47
Stimulated emission, 29
Stitching, 152
Strain sensors, 113–115
Stratified functional properties, 260–261
Stray capacitance, 115–116
Stray reflection, 110
Structural loop, 51
Structured light projection, 155
Stylus force, 143–144
Stylus instruments, 18, 143–146
Stylus qualification, 296
Stylus tip, 143–144, 145
Subdivision calibration process, 336
Sub-pixel resolution, 152–154
Surface damage, 143–144
Surface datum, 144
Surface form, 134
Surface integrity, 134
Surface profile measurement, 139–140
Surface profile, 13, 137–138, 243–261
Surface texture parameters, 139–140
Surface texture, 3, 137–139, 139
Surface topography, 41–42, 134, 176–180, 189–191
SURFSTAND, 243
Swept-frequency interferometry, 103–104
Symmetry, 47, 54
Systematic errors, 21–22, 110
Système International d’Unitès, 9–10

T

Talysurf instrument, 138
Tapping mode, 208
T-distribution, 25, 26, 26
Temperature measurement, 89
Ten point height, 282
Texture aspect ratio, 270
Texture direction, 274–275
Texture feature selection, 275
Thermal conductivity, 52–53
Thermal diffusivity, 53
Thermal distortion, 52–53
Thermal expansion coefficient, 51
Thermal expansion, 52–53, 85–86, 104
Thermal loop, 51
Thermal mass, 53
Thermal measurement, 226
Total height of the surface, 251
Total integrated scatter, 173
Total internal reflectance, 120–121
Total profile, 243–244
Total traverse length, 244
Touch trigger probe, 298
Traceability in length, 64–65
Traceability, 9, 18–19
Traceable measurements, 36
Traced profile, 243–244
Transmissibility, 56–57
Transmission characteristic, 59, 245–246
Transmission electron microscope, 230, 230, 230–232
Triangulation instruments, 152–155
Triangulation sensors, 154
True value, 19–20
Tunnelling effect, 207
Two-pan balance, 328, 334–335
Twyman-Green interferometer, 72–74
Type A evaluation, 23–24
Type B evaluation, 24–25

U

Uncertainty, 5, 19–20, 21–22, 186–187
Unified coordinate system, 267
Unit, 3–4, 9–10

V

Vacuum wavelength uncertainty, 89
van der Waals forces, 222
Vertical scanning white light interferometry, 169–170
Vibrating micro-CMM probes, 314–316
Vibration isolation system, 54–59, 56–57, 58
VIM, 19–20
Virtual CMM, 303
Viscous damping, 58
Visibility, 69–70
Visible light, 67
Vision system, 298
Void volume, 273
Volumetric error compensation, 300

W

Watt balance, 14–15, 333
Wavelength at 50% depth modulation, 150
Waviness profile, 244, 247
Weight, 14
Weighting function, 245–246
Welch-Satterthwaite formula, 26
White light interference, 70–72
White light scanning interferometry, 169–170
Wolf pruning, 278–279
Work function, 208–209
Wringing, 65, 67

X

X-ray interferometer, 125, 125–126

Y

Young’s modulus, 49–50, 220

Z

Zeeman-stabilised laser, 33–34
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