Richard Leach - Fundamental prinsiples of engineering nanometrology, страница 4

27Magnetic splitting of neon – g is the Landé g factor,m the Bohr magneton .............................................................. 29Calibration scheme for Zeeman-stabilised laser.................... 30(a) A Type I Kelvin clamp, (b) a Type II Kelvin clamp ............ 38A single degree of freedom motion device.............................. 39Effects of Abbe error on an optical length measurement ...... 40Mutual compression of a sphere on a plane .......................... 42Kevin Lindsey with the Tetraform grinding machine ............ 47Measured vertical amplitude spectrum on a ‘noisy’(continuous line) and a ‘quiet’ (dotted line) site [29] .............

48Damped transmissibility, T, as a function of frequencyratio (u/u0)............................................................................... 50Definition of the length of a gauge block ............................... 57A typical gauge block wrung to a platen ................................. 58Amplitude division in a Michelson/Twyman-Greeninterferometer..........................................................................

60Intensity as a function of phase for different visibility .......... 61Intensity distribution for a real light source .......................... 62Illustration of the effect of a limited coherence lengthfor different sources ................................................................ 63Schema of the original Michelson interferometer ................. 64xviixviiiFiguresFigure 4.8 Schema of a Twyman-Green interferometer .......................... 65Figure 4.9 The Fizeau interferometer ...................................................... 66Figure 4.10 Typical interference pattern of a flat surface in aFizeau interferometer .............................................................. 67Figure 4.11 Schema of a Jamin interferometer.......................................... 69Figure 4.12 Schema of a Mach-Zehnder interferometer ...........................

69Figure 4.13 Schematic of the Fabry-Pérot interferometer ......................... 70Figure 4.14 Transmittance as a function of distance, L, for variousreflectances .............................................................................. 71Figure 4.15 Possible definition of a mechanical gauge block length ........ 72Figure 4.16 Schema of a gauge block interferometer containinga gauge block ........................................................................... 73Figure 4.17 Theoretical interference pattern of a gauge blockon a platen ............................................................................... 74Figure 4.18 Method for determining a surface and phase changecorrection.................................................................................

79Figure 5.1 Homodyne interferometer configuration ............................... 87Figure 5.2 Heterodyne interferometer configuration............................... 88Figure 5.3 Optical arrangement to double pass aMichelson interferometer ....................................................... 90Figure 5.4 Schema of a differential plane mirror interferometer ............ 91Figure 5.5 Cosine error with an interferometer ...................................... 94Figure 5.6 Schema of an angular interferometer ..................................... 98Figure 5.7 A typical capacitance sensor set-up ........................................

99Figure 5.8 Schematic of an LVDT probe ............................................... 101Figure 5.9 Error characteristic of an LVDT probe ................................. 102Figure 5.10 Schema of an optical encoder ............................................... 103Figure 5.11 Total internal reflectance in an optical fibre ........................ 104Figure 5.12 End view of bifurcated optical fibre sensors,(a) hemispherical, (b) random and (c) fibre pair ................... 105Figure 5.13 Bifurcated fibre optic sensor components ............................ 106Figure 5.14 Bifurcated fibre optic sensor response curve ........................ 106Figure 5.15 Schema of an X-ray interferometer ......................................

109Figure 5.16 Schema of a combined optical and X-ray interferometer .... 110Figure 6.1 Amplitude-wavelength space depicting the operatingregimes for common instruments ........................................ 117Figure 6.2 The original Talysurf instrument (courtesy ofTaylor Hobson) ...................................................................... 119Figure 6.3 Example of the result of a profile measurement .................. 120Figure 6.4 Profiles showing the same Ra with differingheight distributions ...............................................................

122FiguresFigure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.12Figure 6.13Figure 6.14Figure 6.15Figure 6.16Figure 6.17Figure 6.18Figure 6.19Figure 6.20Figure 6.21Figure 6.22Figure 6.23Figure 6.24Figure 6.25Figure 6.26Figure 6.27Figure 6.28A profile taken from a 3D measurement shows thepossible ambiguity of 2D measurement andcharacterisation ..................................................................... 122Schema of a typical stylus instrument ................................. 123Damage to a brass surface due to a high stylus force .......... 124Numerical aperture of a microscope objective lens ............. 128Example of the batwing effect when measuringa step using a coherence scanning interferometer ............... 131Over-estimation of surface roughness due tomultiple scattering in vee-grooves ........................................

132Principle of a laser triangulation sensor ............................... 133Confocal set-up with (a) object in focus and (b) objectout of focus ............................................................................ 135Demonstration of the confocal effect on a piece of paper:(a) microscopic bright field image (b) confocal image.The contrast of both images has been enhanced fora better visualisation .............................................................

136Schematic representation of a confocal curve.If the surface is in focus (position 0) the intensityhas a maximum .................................................................... 136Schema of a Nipkow disk. The pinholes rotate throughthe intermediate image and sample the whole area withinone revolution .......................................................................

137Schema of a confocal microscope using a Nipkow disk ...... 137Chromatic confocal depth discrimination ........................... 139Schema of a point autofocus instrument ............................. 140Principle of point autofocus operation ................................. 141Schema of a focus variation instrument .............................. 142Schema of a phase-shifting interferometer .......................... 144Schematic diagram of a Mirau objective .............................. 145Schematic diagram of a Linnik objective ............................. 146Schematic diagram of DHM with beam-splitter (BS),mirrors (M), condenser (C), microscope objective (MO) andlens in the reference arm (RL) used to perform a referencewave curvature similar to the object wave curvature (someDHM use the same MO in the object wave) ........................

148Schema of a coherence scanning interferometer ................. 150Schematic of how to build up an interferogramon a surface using CSI .......................................................... 151Integrating sphere for measuring TIS .................................. 154Analysis of a type A1 calibration artefact ............................ 158xixxxFiguresFigure 6.29Figure 6.30Figure 6.31Figure 6.32Figure 6.33Figure 6.34Figure 6.35Figure 6.36Figure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 7.6Figure 7.7Figure 7.8Figure 7.9Type ER1 – two parallel groove standard ............................. 160Type ER2 – rectangular groove standard ..............................

160Type ER3 – circular groove standard .................................... 161Type ES – sphere/plane measurement standard ................... 162Type CS – contour standard.................................................. 163Type CG1 – X/Y crossed grating ........................................... 163Type CG2 – X/Y/Z grating standard ..................................... 164Results of a comparison of different instrumentsused to measure a sinusoidal sample ...................................

166Schematic image of a typical scanning probe system,in this case an AFM .............................................................. 179Block diagram of a typical SPM ............................................ 182Noise results from an AFM. The upper image shows anexample of a static noise investigation on a bare siliconwafer. The noise-equivalent roughness is Rq ¼ 0.013 nm.For comparison, the lower image shows the wafer surface:scan size 1 mm by 1 mm, Rq ¼ 0.081 nm ............................ 184Schematic of the imaging mechanism of spherical particleimaging by AFM. The geometry of the AFM tip prevents‘true’ imaging of the particle as the apex of the tip is not incontact with the particle all the time and the final image isa combination of the tip and particle shape.