TheDesignof HighPerformance
3rd revisededition
RobertMunnigSchmidt
GeorgSchitter
AdrianRankers
JanvanEijk
DelftUniversityPress
©2020TheauthorsandIOSPress.Allrightsreserved.
ISBN978-1-64368-050-7(print)
ISBN978-1-64368-051-4(online)
doi:10.3233/STAL9781643680514
3rd revisededition,2020
PublishedbyIOSPressundertheimprintDelftUniversityPress
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1.1HistoricalBackground
1.1.1VideoLong-PlayDisk(VLP)
1.1.1.1SignalEncodingandRead-OutPrinciple ...4
1.1.1.2CompactDiscandDigitalOpticalRecording .6
1.1.2SiliconRepeater ........................9
1.1.2.1ICManufacturingProcess
1.1.2.2HighlyAccurateWaferstage
1.1.3ImpactofMechatronics ....................16
1.2DefinitionandInternationalPositioning .............17
1.2.1DifferentViewsonMechatronics ..............18
1.2.1.1MainTargetedApplication
1.2.1.2FocusonPrecision-ControlledMotion .....21
1.3SystemsEngineeringandDesign
1.3.1SystemsEngineeringMethodology
1.3.1.1ProductCreationProcess
1.3.1.2RequirementBudgeting ..............29
1.3.1.3Roadmapping ....................30
1.3.2DesignMethodology ......................32
1.3.2.1ConcurrentEngineering
1.3.2.2ModularDesignandPlatforms
1.3.2.3AgileandScrum
2.1.1CoordinateSystems
2.1.1.1CartesianCoordinateSystem
2.1.1.2GeneralisedCoordinateSystem
2.1.1.3ModalCoordinateSystem
2.1.2ForceandMotion ........................43
2.1.2.1GalileiandNewton’sLawsofMotion
2.1.2.2Hooke’sLawofElasticity
2.1.2.3LagrangeEquationsofMotion
2.2ElectricityandMagnetism ......................50
2.2.1ElectricField ..........................50
2.2.1.1PotentialDifferenceandCapacitance .....52
2.2.1.2ElectricCurrentinConductiveMaterial
2.2.2MagnetismandtheMaxwellEquations
2.2.3ElectricSourcesandElements
2.2.3.1VoltageSource
2.2.3.2SummaryonVoltageandCurrent ..
2.2.3.3ElectricPower ....................62
2.2.3.4Ohm’sLaw
2.2.3.5PracticalValuesandSummary
2.3SignalTheoryandWavePropagation ...............66
2.3.1TheConceptofFrequency ..................66
2.3.1.1RandomSignalsorNoise
2.3.1.2PowerofAlternatingSignals ..........70
2.3.2UseofComplexNumbers ..................72
2.3.2.1DynamicImpedanceandOhm’sLaw .....73
2.3.2.2PowerinDynamicImpedance ..........73
2.3.2.3CapacitiveImpedance ...............75
2.3.2.4InductiveImpedance ...............78
2.3.3EnergyPropagationinWaves ................80
2.3.3.1MechanicalWaves .................82
2.3.3.2WaveEquation ...................83
2.3.3.3ElectromagneticWaves ..............87
2.3.3.4ReflectionofWaves .................88
2.3.3.5StandingWaves ...................90
2.3.4FourierDecompositionofAlternatingSignals ......93
2.3.4.1Fourierinthefrequency-domain ... .....95
2.3.4.2TriangleWaveform .................95
2.3.4.3SawtoothWaveform ................97
2.3.4.4SquareWaveform ..................98
2.3.4.5Non-ContinuousAlternatingSignals .....99
2.4DynamicSystemAnalysisandModelling .............105
2.4.0.1Laplace-Transform .................105
2.4.0.2PolesandZeros ...................106
2.4.0.3OrderofaDynamicSystem
2.4.1DynamicResponsesinthetime-domain .........108
2.4.1.1StepResponse ....................109
2.4.1.2ImpulseResponse .................110
2.4.1.3ImpulseResponseandPoleLocation ......112
2.4.2DynamicResponsesinthefrequency-domain . .....113
2.4.2.1FrequencyorFourier-DomainResponses ...113
2.4.2.2DomainNotationofDynamicFunctions ...114
2.4.2.3FrequencyResponsePlots ............115
2.4.2.4BodePlot .......................116
2.4.2.5NyquistPlot .....................120
2.4.2.6LimitationtoLTISystems ............122
3DynamicsofMotionSystems
3.1Stiffness
3.1.1ImportanceofStiffnessforPrecision
3.1.2ActiveStiffness .........................130
3.2Mass-SpringSystemswithDamping ................134
3.2.1DynamicCompliance .....................134
3.2.1.1ComplianceofaSpring ..............135
3.2.1.2ComplianceofaDamper
3.2.1.3ComplianceofaBody ...............136
3.2.1.4DynamicStiffness .................137
3.2.1.5LumpingtheDynamicElements ........137
3.2.2TransferFunctionofCompliance ..............141
3.2.2.1DampedMass-SpringSystem. ..........142
3.2.2.2Magnitude ......................144
3.2.2.3Phase .........................144
3.2.2.4BodePlot .......................146
3.2.3EffectsofDamping .......................147
3.2.3.1DampedResonanceandAperiodicDamping .148
3.2.3.2PolesandCriticalDamping ...........149
3.2.3.3Quality-Factor Q andEnergyinResonance .155
3.2.4Transmissibility ........................160
3.2.5Fourth-OrderDynamicSystem ...............164
3.2.5.1AnalyticalDescription ...............165
3.2.5.2MultiplicativeExpression ............166
3.2.5.3EffectofDifferentMassRatios .........167
3.3ModalDecomposition .........................172
3.3.1EigenmodesofTwo-BodyMass-SpringSystem .....173
3.3.2TheoryofModalDecomposition ..............179
3.3.2.1MultiDegreeofFreedomEquationofMotion 180
3.3.2.2EigenvaluesandEigenvectors ..........180
3.3.2.3ModalCoordinates .................182
3.3.2.4ResultingTransferFunction ...........183
3.3.3GraphicalRepresentationofMode-Shapes ........185
3.3.3.1TraditionalRepresentation ...........185
3.3.3.2LeverRepresentation ...............186
3.3.3.3GeneralSystem ...................188
3.3.3.4User-DefinedPhysicalDOF ...........190
3.3.4PhysicalMeaningofModalParameters ..........193
3.3.4.1Two-BodyMass-SpringSystem .........194
3.3.4.2PlanarFlexiblyGuidedSystem .........198
3.3.5APragmaticViewonSensitivityAnalysis ........201
3.3.5.1ExampleofTwoBodyMass-SpringSystem .203
3.3.5.2ExampleofSlightlyDampedResonance ...205
3.3.6SuspensionandRigid-BodyModes .............207
3.3.6.1QuasiRigid-BodySuspensionmode .....210
3.4MechanicalFrequencyResponse ..................211
3.4.1Multipleeigenmodes .....................211
3.4.2CharacteristicFrequencyResponses ...........213
3.4.2.1FrequencyResponseTypeI ...........217
3.4.2.2FrequencyResponseTypeII ...........218
3.4.2.3FrequencyResponseTypeIII ..........220
3.4.2.4FrequencyResponseTypeIV ..........221
3.4.3ExampleSystemswithTypeI/II/IVResponse ......223
3.4.3.1PlanarMovingBodyonCompliantSpring ..223
3.4.3.2H-driveWaferstage .................229
3.5SummaryonDynamics ........................231
4.1AWalkaroundtheControlLoop
4.1.1PolesandZerosinMotionControl
4.1.2OverviewFeedforwardControl
4.1.2.1SummaryofFeedforwardControl
4.1.3OverviewFeedbackControl
4.1.3.1SummaryofFeedbackControl
4.2FeedforwardControl ..........................244
4.2.1Model-BasedFeedforwardControl
4.2.2Input-Shaping .........................248
4.2.3AdaptiveFeedforwardControl
4.2.4TrajectoryProfileGeneration ................251
4.3FeedbackControl ............................253
4.3.1SensitivitytoInputSignals .................253
4.3.1.1SensitivityFunctions ...............254
4.3.1.2RealFeedbackErrorSensitivity ........258
4.3.2StabilityandRobustnessinFeedbackControl
4.3.2.1Stabilitymargins ..................260
4.4PIDFeedbackControl .........................265
4.4.1PID-ControlofaCompact-DiscPlayer ..........267
4.4.1.1RelevantSensitivityFunctions .........269
4.4.1.2ProportionalFeedback ..............270
4.4.1.3Proportional-DifferentialFeedback .......273
4.4.1.4LimitingtheDifferentiatingAction ......275
4.4.1.5AddingI-Control ..................279
4.4.2PID-ControlofaSpringSupportedMass .........281
4.4.2.1P-Control .......................283
4.4.2.2D-Control .......................284
4.4.2.3I-Control .......................285
4.4.2.4SensitivityFunctionGraphs ...........288
4.4.3LimitationsandSideEffectsofPID-FeedbackControl 290
4.4.3.1IncreasedSensitivity,theWaterbedEffect ..290
4.4.3.2IntegratorWind-UpandDelays .........291
4.4.4PID-ControlofaFourth-OrderDynamicSystem ....297
4.4.4.1ControllingaTypeIIIDynamicSystem ....298
4.4.4.2PassiveDamping ..................299
4.4.4.3ShiftingthePhase .................301
4.4.5PID-ControlofaPiezoelectricActuator ..........304
4.4.5.1CreatingaFourth-OrderSystem ........305
4.4.6PID-ControlofaMagneticBearing
4.4.6.1FrequencyResponse ................306
4.4.6.2PositiveStiffnessbyP-Control .........308
4.4.6.3D-ControlandPolePlacement ..........308
4.4.6.4I-controlforReducedSensitivity ... .....311
4.4.7OptimisationbyLoop-ShapingDesign ..........313
4.4.7.1OptimalValueofAlpha ..............314
4.4.7.2AdditionalLow-PassFiltering ..........315
4.4.7.3NotchingFilters ...................316
4.4.7.4PeakingandShelvingFilters ..........318
4.4.8DesignStepsforPID-control ................319
4.5DigitalSignalProcessing-TheZ-Domain
4.5.1ContinuousTimeversusDiscreteTime ..........320
4.5.2SamplingofContinuousSignals ..............323
4.5.3DigitalNumberRepresentation ..............324
4.5.3.1FixedPointArithmetic ..............324
4.5.3.2FloatingPointArithmetic ............325
4.5.4DigitalFilterTheory .....................326
4.5.4.1Z-TransformandDifferenceEquations ....326
4.5.5FiniteImpulseResponse(FIR)Filter ...........328
4.5.6InfiniteImpulseResponse(IIR)Filter ..........331
4.5.7ConvertingContinuoustoDiscrete-TimeFilters
4.6State-SpaceFeedbackControl
4.6.1State-SpaceinRelationtoMotionControl
4.6.1.1MechanicalDynamicSysteminState-Space .338
4.6.1.2PID-ControlFeedbackinState-Space .....342
4.6.2StateFeedback .........................344
4.6.2.1SystemIdentification
4.6.2.2StateEstimation
4.6.2.3AdditionalRemarksonState-SpaceControl
4.7ConclusiononMotionControl
5.1.1Hopkinson’sLaw
5.1.1.1PracticalAspectsofHopkinson’sLaw .....362
5.1.1.2MagneticEnergy ..................362
5.1.2FerromagneticMaterials
5.1.2.1CoilwithFerromagneticYoke
5.1.2.2MagnetisationCurve ...............366
5.1.2.3PermanentMagnets ................367
5.1.3CreatingaMagneticFieldinanAir-Gap .........371
5.1.3.1OptimalUseofPermanentMagnetMaterial 375
5.1.3.2FlatMagnetsReduceFringingFlux ......376
5.1.3.3LowCostLoudspeakerMagnet .........377
5.2LorentzActuator ............................378
5.2.1LorentzForce ..........................378
5.2.1.1ForcefromFlux-Linkage .............381
5.2.2TheLorentzactuatorasaGenerator ...........382
5.2.3ImprovingtheForceofaLorentzActuator .....384
5.2.3.1TheMoving-CoilLoudspeakerActuator ....385
5.2.4PositionDependencyoftheLorentzForce ... .....386
5.2.4.1Over-HungandUnder-HungCoil ........386
5.2.5ElectronicCommutation ...................388
5.2.5.1Three-PhaseElectronicControl .........390
5.2.6FiguresofMeritofaLorentzActuator ..........392
5.3VariableReluctanceActuation ....................395
5.3.1ReluctanceForceinLorentzActuator ...........395
5.3.1.1Eddy-CurrentRing .................396
5.3.1.2IronlessStator ...................397
5.3.2AnalyticalDerivationofReluctanceForce ... .....398
5.3.3VariableReluctanceActuator. ................402
5.3.3.1ElectromagneticRelay ...............404
5.3.3.2MagneticAttractionForce ............405
5.3.4PermanentMagnetBiasedReluctanceActuator ....407
5.3.4.1DoubleVariableReluctanceActuator .....407
5.3.4.2ConstantCommonFlux ..............409
5.3.4.3CombiningtwoSourcesofMagneticFlux ...410
5.3.4.4HybridForceCalculation .............413
5.3.4.5MagneticBearings .................415
5.3.5ActiveLinearisationoftheReluctanceForce . .....416
5.4ApplicationofElectromagneticActuators .............418
5.4.1ElectricalInterfaceProperties ...............418
5.4.1.1DynamicEffectsofSelf-Inductance ......418
5.4.1.2Limitationofthe“Jerk” ..............421
5.4.1.3ElectromagneticDamping ............422
5.4.2ComparisonofthreeElectromagneticActuators ....425
5.4.2.1Force-Constants ...................426
5.4.2.2FiguresofMeritIncludingMass ........428
5.4.2.3Stiffness .......................429
5.4.2.4RepeatabilityandPredictability ... .....429
5.4.2.5DynamicEffectsontheControlLoop .....430
5.5PiezoelectricActuators ........................431
5.5.1Piezoelectricity .........................431
5.5.1.1Poling .........................432
5.5.1.2TappingtheBoundChargebyElectrodes ...434
5.5.2TransducerModels ......................435
5.5.3NonlinearityofPiezoelectricActuators ..........438
5.5.3.1Creep .........................438
5.5.3.2Hysteresis ......................439
5.5.3.3Aging .........................441
5.5.4MechanicalConsiderations .................441
5.5.4.1PiezoelectricActuatorStiffness .........442
5.5.4.2ActuatorTypes ...................442
5.5.4.3LongRangeActuationbyFriction .....445
5.5.4.4ActuatorIntegration ................446
5.5.4.5MechanicalAmplification .............447
5.5.4.6MultipleMotionDirectionsbyStacking ....448
5.5.5ElectricalConsiderations ..................450
5.5.5.1Chargevs.VoltageControl ............450
5.5.5.2Self-SensingActuation ..............451
5.6ChoosingtherightActuatorType
6.1.1NetworkTheoryandLaws
6.1.1.1VoltageSource
6.1.1.2CurrentSource ...................460
6.1.1.3TheoremofNortonandThevenin ...
6.1.1.4Kirchhoff’sLaws
6.1.1.5ImpedancesinSeriesorParallel ........463
6.1.1.6VoltageDivider ...................464
6.1.1.7MaximumPowerofaRealVoltageSource ..466
6.1.2ImpedancesinElectronicCircuits
6.1.2.1Resistors .......................468
6.1.2.2Capacitors ......................470
6.1.2.3Inductors
6.1.3PassiveFilters
6.1.3.1PassiveFirst-OrderRC-Filters .........474
6.1.3.2PassiveHigher-OrderRC-Filters ........477
6.1.3.3PassiveLCR-Filters ................479
6.1.4Mechanical-ElectricalDynamicAnalogy .........485 6.2SemiconductorsandActiveElectronics ..............489
6.2.1BasicDiscreteSemiconductors ...............490
6.2.1.1SemiconductorDiode ...............493
6.2.1.2BipolarTransistors ................496
6.2.1.3MOSFET .......................499
6.2.1.4OtherDiscreteSemiconductors .........501
6.2.2SingleTransistorLinearAmplifiers ............504
6.2.2.1EmitterFollower ..................504
6.2.2.2VoltageAmplifier ..................507
6.2.2.3DifferentialAmplifier ...............509
6.2.3OperationalAmplifier .....................512
6.2.3.1BasicOperationalAmplifierDesign ......512
6.2.3.2OperationalAmplifierwithFeedback .....514
6.2.4LinearAmplifierswithOperationalAmplifiers .....515
6.2.4.1DesignRules .....................516
6.2.4.2Non-InvertingAmplifier .............516
6.2.4.3InvertingAmplifier .................518
6.2.4.4AddingandSubtractingSignals ........519
6.2.4.5TransimpedanceAmplifier ............522
6.2.4.6TransconductanceAmplifier ...........523
6.2.5ActiveElectronicFilters ...................527
6.2.5.1IntegratorandFirst-OrderLow-Pass .....527
6.2.5.2DifferentiatorandFirst-OrderHigh-Pass ...529
6.2.6AnaloguePID-Controller ...................531
6.2.6.1PIDTransferFunction ..............532
6.2.6.2PIDControlGains .................534
6.2.6.3High-SpeedPID-Control .............535
6.2.7Higher-orderElectronicFilters ...............535
6.2.7.1Second-OrderLow-PassFilter ..........537
6.2.7.2DifferentTypesofActiveFilters ........538
6.2.8IdealandRealOperationalAmplifiers ..........539
6.2.8.1Open-LoopVoltageGain .............541
6.2.8.2DynamicLimitations ...............541
6.2.8.3InputRelatedLimitations ............546
6.2.8.4PowerSupplyandOutputLimitations ....549
6.2.9ClosingRemarksonLow-PowerElectronics ....550
6.3PowerAmplifiersforMotionControl ................552
6.3.1RequiredPropertiesforActuatorDrive ..........553
6.3.1.1PowerDeliveryCapability ............554
6.3.1.2DynamicProperties ................554
6.3.1.3Linearity,FreedomofDistortion ... .....555
6.3.1.4VoltageorCurrentDrive .............555
6.3.1.5Efficiency .......................556
6.3.1.6Four-QuadrantOperation ............557
6.3.1.7PreferredPowerAmplifierPrinciple .. ....557
6.3.2Switched-ModePowerAmplifiers ..............560
6.3.2.1PowerMOSFET,aFastHigh-PowerSwitch .561
6.3.2.2SwitchingSequenceGeneration .........564
6.3.2.3VoltageDriveAmplifier ..............566
6.3.2.4EnergyFlowinthePowerOutputStage ...570
6.3.2.5IntermediateConclusionsandOtherIssues .574
6.3.2.6DrivingthePowerMOSFETs ..........575
6.3.2.7ChargePumping ..................577
6.3.2.8H-BridgeConfiguration ..............578
6.3.2.9OutputFilter ....................580
6.3.3Resonant-ModePowerAmplifiers .............581
6.3.3.1SwitchingSequenceoftheOutputStage ...582
6.3.3.2LosslessCurrentSensing .............586
6.3.4Three-PhaseAmplifiers ....................587
6.3.4.1ConceptofThree-PhaseAmplifier ... ....588
6.3.4.2Three-PhaseSwitchingPowerStages .....589
6.3.5SomeLastRemarksonPowerElectronics ........590
7.1PropertiesofLightandLightSources
7.1.1LightGenerationbyThermalRadiation .........596
7.1.2PhotonsbyElectronEnergyStateVariation .......597
7.1.2.1LightEmittingDiodes ...............599
7.1.2.2LaserasanIdealLightSource .........600
7.1.3UsefulPowerfromaLightSource .............604
7.1.3.1RadiantEmittanceandIrradiance .. .....605
7.1.3.2Radiance .......................605
7.1.3.3Etendue ........................608
7.2ReflectionandRefraction .......................609
7.2.1ReflectionandRefractionaccordingtotheLeastTime 610
7.2.1.1PartialReflectionandRefraction ........613
7.2.2ConceptofWavefront .....................614
7.2.2.1AWavefrontisNotReal ..............615
7.3GeometricOptics ............................617
7.3.1ImagingwithRefractiveLensElements .........617
7.3.1.1SignConventions ..................619
7.3.1.2RealLensElements ................620
7.3.1.3Magnification ....................623
7.3.2Aberrations ...........................625
7.3.2.1SphericalAberration ...............625
7.3.2.2Astigmatism .....................627
7.3.2.3Coma .........................629
7.3.2.4GeometricandChromaticAberrations ....629
7.3.3CombiningMultipleOpticalElements ..........631
7.3.3.1CombiningTwoPositiveLenses .........632
7.3.4ApertureStopandPupil ...................635
7.3.5Telecentricity ..........................636
7.3.5.1Pupil,ApertureandLensDimensions .....638
7.3.5.2PracticalApplicationsandConstraints ....638
7.4PhysicalOptics .............................640
7.4.1Polarisation ...........................640
7.4.1.1Birefringence
7.4.2Interference ...........................644
7.4.2.1Fabry-PerotInterferometer
7.4.3Diffraction ............................648
7.4.3.1Amplitudegratings ................649
7.4.3.2PhaseGratings ...................651
7.4.3.3DirectionoftheIncomingLight .........658
7.4.4ImagingQualitybasedonDiffraction ...........658
7.4.4.1NumericalApertureandf-Number .......662
7.4.4.2DepthofFocus ...................665
7.5AdaptiveOptics .............................668
7.5.1ThermalEffectsinOpticalImagingSystems . .....668
7.5.2CorrectingtheWavefront ..................670
7.5.2.1ZernikePolynomials ................671
7.5.2.2CorrectingZernikesbyAdaptiveOptics ....675
7.5.3AdaptiveOpticsPrincipleofOperation ..........676
7.5.3.1ActiveMirrors ....................678
8MeasurementinMechatronicSystems 683 Introduction ..................................683
8.0.1MeasurementSystems ....................684
8.0.2ErrorsinMeasurementSystems,Uncertainty .....685
8.0.2.1UncertaintyinTraceableMeasurements ...687
8.0.3FunctionalModelofaMeasurementSystemElement 689
8.1DynamicErrorBudgeting
8.1.1ErrorStatisticsinRepeatedMeasurements
8.1.2TheNormalDistribution
8.1.3CombiningDifferentErrorSources ............694
8.1.4PowerSpectralDensityandCumulativePower .....695
8.1.5DonotusetheCumulativeAmplitudeSpectrum! ...698
8.1.6VariationsinDynamicErrorBudgeting .........698
8.1.7SourcesofNoiseandDisturbances
8.1.7.1MechanicalNoise ..................699
8.1.7.2ElectronicNoise ...................700
8.2SensorSignalSensitivity .......................703
8.2.1SensingElement ........................704
8.2.2ConvertinganImpedanceintoanElectricSignal ...705
8.2.2.1WheatstoneBridge .................706
8.2.3ElectronicInterconnectionofSensitiveSignals .....712
8.2.3.1MagneticDisturbances ..............712
8.2.3.2CapacitiveDisturbances .............714
8.2.3.3GroundLoops ....................716
8.3SignalConditioning ..........................718
8.3.1InstrumentationAmplifier
8.3.2FilteringandModulation
8.3.2.1AMwithSquareWaveCarrier
8.3.2.2AMwithSinusoidalCarrier ...........723
8.4SignalProcessing ............................726
8.4.1SchmittTrigger ........................726
8.4.2DigitalRepresentationofMeasurementData
8.4.2.1GrayCode ......................728
8.4.2.2SamplingofAnalogueValues ..........730
8.4.2.3Nyquist-ShannonTheorem
8.4.2.4FilteringtoPreventAliasing ...........734
8.4.3Analogue-to-DigitalConverters ...............735
8.4.3.1Dual-SlopeADC ..................735
8.4.3.2Successive-ApproximationADC
8.4.3.3Sigma-DeltaADC
8.4.3.4ADCLatencyinaFeedbackLoop ........743
8.4.4ConnectingtheLessSensitiveElements .........744
8.4.4.1CharacteristicImpedance ............744
8.4.4.2Non-GalvanicConnection .............747
8.5Short-RangeMotionSensors .....................748
8.5.1OpticalSensors .........................748
8.5.1.1PositionSensitiveDetectors ...........749
8.5.1.2OpticalDeflectometer ...............752
8.5.2CapacitivePositionSensors .................754
8.5.2.1LinearisingbyDifferentialMeasurement ...755
8.5.2.2AccuracyLimitsandImprovements ......756
8.5.2.3SensingtoConductiveMovingPlate ......759
8.5.3InductivePositionSensors ..................760
8.5.3.1LinearVariableDifferentialTransformer ...762
8.5.3.2Eddy-CurrentSensors ...............764
8.5.4PneumaticProximitySensororAir-Gage .....765
8.6MeasurementofMechanicalDynamics ..............766
8.6.1MeasurementofForceandStrain .............766
8.6.1.1StrainGages .....................766
8.6.1.2FibreBraggGratingStrainMeasurement ..769
8.6.2VelocityMeasurement ....................771
8.6.2.1Geophone .......................772
8.6.3Accelerometers .........................776
8.6.3.1Closed-LoopFeedbackAccelerometer .....776
8.6.3.2PiezoelectricAccelerometer ...........778
8.6.3.3MEMSAccelerometer ...............787
8.7OpticalLong-RangeIncrementalPositionSensors .. .....789
8.7.1LinearOpticalEncoders ...................790
8.7.1.1Interpolation .....................794
8.7.1.2VernierResolutionEnhancement ........796
8.7.1.3InterferometricOpticalEncoder ........798
8.7.1.4ConcludingRemarksonLinearEncoders ...803
8.7.2LaserInterferometerMeasurementSystems . .....804
8.7.2.1HomodyneDistanceInterferometry ......805
8.7.2.2HeterodyneDistanceInterferometry ......812
8.7.2.3MeasurementUncertainty ............821
8.7.2.4Configurations ...................828
8.7.2.5Multi-AxisLaserInterferometers ........833
8.7.3MechanicalAspects ......................834
8.7.3.1AbbeError ......................835
9PrecisionPositioninginWaferScanners 839 Introduction ..................................839
9.1TheWaferscanner ............................841
9.1.1RequirementsonPrecision .................843
9.2DynamicArchitecture .........................847
9.2.1BalanceMasses ........................848
9.2.2VibrationIsolation .......................850
9.2.2.1EigendynamicsoftheSensitiveParts .....853
9.3Zero-StiffnessStageActuation ....................857
9.3.1WaferstageActuationConcept ...............858
9.3.1.1WaferstepperLong-RangeLorentzActuator .858
9.3.1.2Multi-AxisPositioning ...............861
9.3.1.3Long-andShort-StrokeActuation .. .....862
9.3.2FullMagneticLevitation ...................865
9.3.3AccelerationLimitsofReticleStage ............866
9.4PositionMeasurement .........................868
9.4.1AlignmentSensor .......................870
9.4.2KeepingtheWaferinFocus .................872
9.4.3Dual-StageMeasurementandExposure .........875
9.4.4Long-RangeIncrementalMeasurementSystem ....876
9.4.4.1Real-TimeMetrologyLoop ............877
9.5MotionControl .............................880
9.5.1FeedforwardandFeedbackControl
9.5.1.1Thermal,TheFinalFrontier
9.5.2TheMassDilemma ......................884
9.6FutureDevelopmentsinICLithography
Wrong Numbers
IHAVE invented a new telephone game. It is a thoroughly discreditable, anti-social game, and I am not proud of it, but it has been forced upon me by circumstances. It is now clear that my telephone number is the only one the operators know, and my game follows the lines of all the best modern movements, the principle of which is that, if you cannot hit the man you are annoyed with, you hit somebody else instead. Nowadays, when some perfect stranger is introduced to me in error on the telephone, I no longer murmur, “Wrong number, I’m afraid,” in my usual accents of sweet sympathy, cool resignation, irritation, hatred or black despair; I pretend that it is the right number. I lead my fellow-victim on into a morass of mystification; I worm out his precious secrets; I waste his precious time. If you can square your conscience you will find it is a glorious game, though I ought to add that considerable skill is required. It is best, perhaps, to make a general rule of answering the call in the first instance in a high feminine voice, as much like a housemaid, or a charwoman, or a Government typist as possible; then you are prepared for any development.
The following are some of the best matches I have played:——
IMe. Hullo!
A Voice. Is that the Midland Railway?
Me. Yes, Madam. Which department do you require?
A V. It’s about some eggs. An egg-box was despatched from Hitchin——
Me (obsequious). I will put you through to the Goods and Transit Department, Madam.
A V. (fervent). Oh, thank you!
Me (after a short stroll round the garden—in a gruff railwayvoice). Hullo! Motor-vans and Haulage Department——
A V. Oh, it’s about some eggs. An egg-box——
Me (more in sorrow than in anger). You require the Goods and Transit Department. I will put you through.
A V. Oh, thank you!
Me (after planting a few more of those confounded cuttings— very suddenly). The 4.45 to Bunby Major is suspended, Sir.
A V. (apologetic). I want to speak about some eggs——
Me (horrified). Some legs!
A V. (patient). No, some eggs:— —double — , eggs. An egg-box was despatched from Hitchin by a friend of mine on the 21st——
Me (sharply). What name, Madam?
A V. Major Bludyer. It was despatched on——
Me. Is he one of the Buckinghamshire Bludyers?
A V. What? Hullo!... Hullo! It was despatched on——
Me. I mean, is he the Major Bludyer—that well-grown old boy? From what I know of his eggs——
A V. (growing fainter). I can’t hear you very well. It’s about some eggs——
Me. Well, I’m very glad to have had this little talk. Remember me to old Bludyer. Good-bye. II
Me (squeaky). Hullo!
A Voice (business-like, in a great hurry). Hullo! Is that you, Mortimer?
Me (very deliberate). Mr. Mortimer is in the next room. If you will hold the line I will fetch him. Who is it speaking, please?
A V Oh, never mind that.
Me (firm). Who is it speaking, please?
A V. Oh, da——! Say it’s George. And be quick, please.
Me (after a good deal of unavoidable delay). Hullo, George!
A V. Hullo, Mortimer! You have been a time! Look here— about this meeting: have you got your minutes ready yet?
Me. Not quite. Practically. I was just doing them——
A V. Oh! Well, it’s like this: I’ve had a talk with Sir Donald and he thinks you’d better leave out that scene about Atkins and the Debentures. He thinks we might have trouble with the Manchester lot if you read that out, but if you don’t say anything about it they’ll never know——
Me. You dirty dog!
A V. What’s that?
Me (innocent). I didn’t say anything. I think there’s someone on the line—(in a brand-new voice) Cuckoo!
A V. (indignant). I say, Sir, do you mind getting off the line? Hullo! Hullo!... He’s gone now. Well, don’t forget that. So long, old man. Sorry you couldn’t come round the other night; I wanted you to meet my fiancée—you haven’t, have you?
Me. Which one.
A V (skittishly). You old ass—Miss Tickle, of course.
Me.. Oh, I know her As a matter of fact I was engaged to her myself once—but that’s many years ago.
A V. What’s that? You sound as if you’d got a cold.
Me. I rather think I have. You always make such a draught down the telephone. Good-bye, old man.
A Voice. Is that the Box-Office?
Me. Which Box-Office?
A V. Is that the Paragon Theatre?
Me. Yes, Madam.
A V. Oh, have you two seats for next Thursday?
Me. Yes, Madam. There is a stall in row D, and I have one seat left in the back row in the dress-circle—a very good view of the stage, Madam.
A V. Oh, but I want them together.
Me. I’m afraid we never sell seats together, Madam. The Lord Chamberlain——
A V. Oh, but——
Me. May I ask why you want to see this play, Madam?
A V. I can’t hear you.... Hullo!
Me. I mean, between ourselves, it’s a thoroughly bad adaptation of a thoroughly bad foreign play thoroughly badly acted by a rotten lot of actors. Letty Loo is perfectly awful, and there’s no room for your legs, unless you would care for a box, and there isn’t one if you would; so if I were you I should stay quietly at home with Henry. Au revoir!
A Voice (most important). Hullo! Is that the Treasury?
Me (sweetly feminine). Treasury speaking.
A V. (as if the end of the world was in sight). I want to speak to the Prime Minister’s Private Secretary.
Me. The Prime Minister’s Private Secretary is engaged. I can put you through to the Whips’ Office.
A V. (angrily). I don’t want the Whips’ Office. I want——
Me. One moment, please.
[A good many moments pass.]
A V. (menacing). Hullo! Hullo! Hullo!
Me (sweetly, as if conferring some priceless boon). Put three pennies in the slot and turn the handle, please.
A V. (spluttering). Look here, put me through to the supervisor at once.
Me (very far off). Supervisor speaking.
A V. (with suppressed passion, yet pompous withal). Look here—I’m a Member of Parliament. I’ve been——
Me (gently). Do not shout into the receiver, please.
A V. Hullo! I’m a——
Me. Do not say “Hullo!”
A V. (maddened). What’s that? Hullo! Look here—I’m a Member of Parliament, and I’ve been trying for half an hour to get through to the Prime Minister’s——
Me. I am sorry you have been trrrr-roubled. You are thrrrrough now.
A V. Hullo! Is that the Prime Minister’s Private Secretary?
Me (quiet, weary and competent). Which one do you want?
A V. Hullo! Sir Thingummy Jig speaking. I want to speak to the Prime Minister’s——
Me. Yes, I heard that. But do you want the Principal Private Secretary, or the Assistant Principal Private Secretary, or one of the Personal Private Secretaries? I mean there are fortyseven of us altogether and it makes a lot of difference——
A V (weakening). I can’t quite hear Perhaps you can help me. It’s about——
Me. One moment, please. Here is the Prime Minister himself. Would you mind speaking to him? I’m rather busy.
A V. (awestruck). Of course.... Hullo!
Me. Hullo!... The Prime Minister speaking.... Look here, Jig, I want to have a word with you. Would you mind holding the line a moment while I speak to my secretary?
A V (fawning). By all means.... There’s no hurry—no hurry at all. · · · · ·
As far as I know the poor fellow is holding still.
