Handbook of Surface Metrology

Cover
Half Title
Title Page
Copyright Page
Dedication
Foreword
Table of Contents
Preface
Acknowledgments
1: General Philosophy of Measurement
1.1 Where Does Surface Metrology Fit in Engineering Metrology?
1.2 Importance of Surface Metrology
2: Surface Characterization the Nature of Surfaces and the Signals Obtained from Them
2.1 Surface Roughness Characterization
2.1.1 Profile Parameters
2.1.1.1 Amplitude Parameters
2.1.1.2 Spacing Parameters
2.1.1.3 Hybrid Parameters
2.1.2 Reference Lines
2.1.2.1 Straight Lines
2.1.2.2 Polynomial Fitting
2.1.2.3 Spline Functions
2.1.2.4 Filtering Methods
2.1.2.5 Envelope Methods
2.1.2.6 Summary
2.1.3 Statistical Parameters of Surface Roughness
2.1.3.1 Amplitude Probability Density Function (APDF) or p(z)
2.1.3.2 Material Ratio
2.1.3.3 Autocorrelation Function (ACF) and Power Spectral Density (PSD)
2.1.3.4 Power Spectrum
2.1.3.5 Hybrid Statistical Parameters—Peak and Valley Characteristics
2.1.4 Areal Texture Parameters, Isotropy and Lay (Continuous Signal)
2.1.4.1 Direct Methods of Statistical Assessment over an Area
2.1.5 Discrete Characterization
2.1.5.1 General
2.1.5.2 Alternative Discrete Methods
2.1.6 Assessment of Isotropy and Lay
2.1.7 Potential Methods of Characterization
2.1.7.1 Amplitude and Hybrid Parameters
2.1.7.2 Skew and Kurtosis
2.1.7.3 Beta Function
2.1.7.4 Chebychev Function and Log Normal Function
2.1.7.5 Variations on Material Ratio Curve
2.1.7.6 Time Series Analysis Methods of Characterization—The Characterization of Spatial Information
2.1.7.7 Possible Methods of Classification Based on a Fourier Approach
2.1.7.8 Space-Frequency Functions
2.1.8 Fractals
2.1.9 Surface Texture and Non-Linear Dynamics in Machines
2.2 Waviness
2.3 Errors of Form
2.3.1 Introduction
2.3.2 Straightness and Related Topics
2.3.3 Generalized Probe Configurations for Variable Errors
2.3.4 Assessments and Classification
2.3.5 Flatness
2.3.6 Roundness
2.3.6.1 Nature of Departures from Roundness
2.3.6.2 Chordal Methods
2.3.6.3 Radial Methods
2.3.6.4 Nature of the Signal Produced by a Radial Departure Instrument
2.3.6.5 Relation Between the Centred Workpiece Profile and the Radius-Suppressed Polar Plot
2.3.6.6 Effect of Imperfect Centring
2.3.6.7 Assessment of Radial, Diametral and Angular Variations
2.3.6.8 Roundness Assessment
2.3.6.9 Effect of Imperfect Centring on the Minimum Zone Method
2.3.6.10 Effect of Angular Distortion
2.3.6.11 Equation of a Reference Line to Fit a Partial Circular Arc as Seen by a Roundness Instrument
2.3.6.12 Lobing Coefficients
2.3.6.13 Roundness Assessment Without a Formal Datum
2.3.6.14 Eccentricity, Concentricity
2.3.6.15 Squareness
2.3.6.16 Curvature Measurement from Roundness Data
2.3.6.17 Estimation of Curvature in the Presence of Noise
2.3.6.18 Estimation of Radial Slope
2.3.6.19 Assessment of Ovality and Other Shapes
2.3.6.20 Two-dimensional Measurement—Sphericity
2.3.6.21 Interpretation of Results of Equations (2.354)—(2.362)
2.3.7 Cylindricity
2.3.7.1 Methods of Specifying Cylindricity
2.3.7.2 Assessment of Cylindrical Form
2.3.7.3 Reference Figures for Cylinder Measurement
2.3.7.4 Practical Considerations of Cylindroid References
2.3.7.5 Limaçon Cylindrical References
2.3.7.6 Conicity
2.4 Comparison of Definitions for Surface Metrology and Coordinate-Measuring Machines
2.4.1 Other Differences
2.5 Characterization of Defect Shapes on the Surface
2.5.1 General
2.5.2 Dimensional Characteristics of Defects
2.5.3 Types of Defect
2.6 Summary
References
3: Processing
3.1 Digital Methods
3.1.1 Sampling
3.1.2 Quantization
3.1.3 Numerical Analysis—The Digital Model
3.1.3.1 Differentiation
3.1.3.2 Integration
3.1.3.3 Interpolation, Extrapolation
3.2 Digital Properties of Random Surfaces
3.2.1 Some Numerical Problems Encountered in Surface Metrology
3.2.2 Definitions of a Peak and Density of Peaks
3.2.3 Effect of Quantization
3.2.4 Effect of Numerical Model
3.2.5 Effect of Distance Between Samples on Peak Density Value
3.2.6 Digital Evaluation of Other Important Peak Parameters
3.2.6.1 Peak Height Measurement
3.2.6.2 Peak Curvature
3.2.6.3 Profile Slopes
3.2.6.4 Summary
3.2.7 Areal (Two-Dimensional) Digital Measurement of Surface Roughness Parameters
3.2.7.1 General
3.2.7.2 The Expected Summit Density and the Distributions of Summit Height and Curvature
3.2.7.3 The Effect of the Sampling Interval and Limiting Results for the Discrete Surface
3.2.8 Patterns of Sampling and Their Effects on Discrete Properties
3.2.8.1 Comparison of Three-, Four-, Five- and Seven-Point Analysis of Surfaces
3.2.8.2 Four-point Sampling Scheme in a Plane
3.2.8.3 the Effect of Sampling Interval and Limiting Results on Sample Patterns
3.2.8.4 Discussion
3.3 Fourier Transform and the Fast Fourier Transform
3.3.1 General Properties of the Fourier Transform
3.3.2 Fast Fourier Transform Routine
3.3.2.1 Fast Fourier Transform Analytic Form
3.3.3 A Practical Realization of the Fast Fourier Transform
3.3.4 General Considerations
3.3.4.1 The Fourier Series of Real Data
3.3.5 Applications of Fourier Transforms with Particular Reference to the FFT
3.3.5.1 Use of Fourier Transform for Non-recursive Filtering
3.3.5.2 Power Spectral Analysis
3.3.5.3 Correlation
3.3.5.4 Other Convolutions
3.3.5.5 Interpolation
3.3.5.6 Other Analysis
3.3.5.7 Roundness Analysis
3.4 Statistical Parameters in Digital Form
3.4.1 Amplitude Probability Density Function
3.4.2 Statistical Moments of the APDF
3.4.3 Autocorrelation Function (ACF)
3.4.4 Autocorrelation Measurement Using FFT
3.4.5 Measurement of Power Spectral Density (PSD)
3.5 Properties and Implementation of the Ambiguity Function and Wigner Distribution Function
3.5.1 General
3.5.2 Ambiguity Function
3.5.2.1 Spatial Shift
3.5.2.2 Frequency Shift
3.5.2.3 Spatial-Limited Signals
3.5.2.4 Frequency-Limited Signals
3.5.2.5 Concentration of Energy
3.5.2.6 Total Energy
3.5.2.7 Convolution
3.5.2.8 Modulation
3.5.2.9 Discrete Ambiguity Function
3.5.2.10 Computation of DAF
3.5.3 the Wigner Distribution Function
3.5.3.1 Properties
3.5.3.2 Symmetry
3.5.3.3 Realness
3.5.3.4 Spatial Shifting
3.5.3.5 Frequency Shifting
3.5.3.6 Spatial-Limited Signal
3.5.3.7 Frequency Limiting
3.5.3.8 Spatial Energy
3.5.3.9 Frequency Energy
3.5.3.10 Total Energy
3.5.3.11 Convolution
3.5.3.12 Modulation
3.5.3.13 Analytic Signals
3.5.3.14 Moments
3.5.4. Some Examples of Wigner Distribution: Application to Signals—Waviness
3.5.5 Comparison of the Fourier Transform, the Ambiguity Function and the Wigner Distribution Function
3.6 Digital Estimation of Reference Lines for Surface Metrology
3.6.1 Numerical Filtering Methods for Establishing Mean Lines for Roughness and Waviness Profiles
3.6.2 Convolution Filtering
3.6.3 Standard Filter
3.6.4 Phase-Corrected (Linear Phase) Filters, Other Filters and Filtering Issues
3.6.5 Gaussian Filter
3.6.6 Box Functions
3.6.7 Truncation
3.6.8 Alternative Methods of Computation
3.6.9 Equal-Weight Techniques
3.6.10 Recursive Filters
3.6.11 The Discrete Transfer Function
3.6.12 The 2CR Filter
3.6.13 Use of the Fft in Surface Metrology Filtering—Areal Case
3.6.14 Examples of Numerical Problems in Straightness and Flatness
3.6.15 Effect of Computer Word Format
3.7 Algorithms
3.7.1 Differences Between Surface and Dimensional Metrology Algorithms: Least-squares Evaluation of Geometric Elements
3.7.1.1 Optimization
3.7.1.2 Linear Least Squares
3.7.1.3 Eigenvectors and Singular Value Decomposition
3.7.2 Best-Fit Shapes
3.7.2.1 Best-Fit Plane
3.7.2.2 Circles, Spheres, etc
3.7.2.3 Cylinders and Cones
3.7.3 Other Methods
3.7.3.1 Minimum Zone Method
3.7.4 Minimax Methods—Constrained Optimization
3.7.5 Simplex Methods
3.7.6 Basic Concepts in Linear Programming
3.7.6.1 General
3.7.6.2 Dual Linear Programmes in Surface Metrology
3.7.6.3 Minimum Radius Circumscribing Limaçon
3.7.6.4 Minimum Zone, Straight Lines and Planes
3.7.6.5 Minimax Problems
3.8 Transformations in Surface Metrology
3.8.1 General
3.8.2 Hartley Transform
3.8.3 Square Wave Functions—Walsh Functions
3.8.4 Space–Frequency Functions
3.8.5 Gabor Transforms
3.9 Graphical Methods
3.9.1 The Planimeter and Its Uses in Surface Metrology
3.9.2 Graphical Ways of Estimating Random Process Parameters
3.9.2.1 Autocorrelation Function
3.9.2.2 Harmonic Analysis
3.10 Other Methods of Processing
3.10.1 Correlation
3.10.1.1 Real-Time Magnetic Tape Correlator
3.10.1.2 Optical Analogue Method (Simultaneous Method)
3.10.1.3 Optical Analogue Method (Sequential Method)
3.10.1.4 Stylus Method—Sequential Operation
3.10.2 Quantization Correlators
3.10.2.1 Sampled and Clipped Signals Involving Digital Time Compression
3.10.2.2 Power Spectra
3.11 Surface Generation
3.11.1 Profile Generation
3.11.2 Two-Dimensional Surface Generation
3.12 Summary
References
4: Instrumentation
4.1 Introduction and Historical
4.1.1 Historical Details
4.1.2 Some Early Dates of Importance in the Metrology and Production of Surfaces
4.1.3 Specification
4.1.4 Design Criteria for Instrumentation
4.1.5 Kinematics
4.1.6 Pseudo-Kinematic Design
4.1.7 Mobility
4.1.8 Linear Hinge Mechanisms
4.1.9 Angular Motion Flexures
4.1.10 Measurement and Force Loops
4.1.11 Alignment Errors
4.1.11.1 Abbé Offset
4.1.12 Other Mechanical Considerations—Balance of Forces
4.1.13 Systematic Errors and Non-Linearities
4.1.14 Material Selection
4.1.15 Drive Systems
4.2 Measurement Systems
4.2.1 General Stylus Systems
4.2.2 Stylus Characteristics
4.1.2.1 Tactile Considerations
4.2.2.2 Pick-Up Dynamics
4.2.2.3 Conclusions About Mechanical Pick-Ups of Instruments Using the Conventional Approach
4.2.2.4 Relationship Between Static and Dynamic Forces
4.2.2.5 Alternative Stylus Systems and Effect on Reaction/Random Surface
4.2.2.6 Criteria for Scanning Surface Instruments
4.2.2.7 Forms of the Pick-Up Equation
4.2.2.8 Measurement Systems
4.2.2.9 Spatial Domain Instruments
4.2.2.10 Open- and Closed-loop Considerations
4.2.3 Scanning Microscopes
4.2.3.1 Scanning Tunnelling Microscope (STM)
4.2.3.2 Other Scanning Microscopes
4.2.3.3 Operation and Theory of the STM
4.2.3.4 Spectroscopy
4.2.3.5 Some Simple Scanning Systems
4.2.3.6 The Atomic Force Microscope
4.2.4 Aspects of Stylus Instruments
4.2.4.1 Pick-Up Configuration
4.2.4.2 Generation of the Skid Datum
4.2.4.3 Stylus Instruments Where the Stylus Integrates
4.2.4.4 Alignment of the Stylus System
4.2.4.5 Limitations of References' Used in Roundness Measurement
4.2.4.6 Other Stylus Methods
4.2.4.7 Replication
4.2.5 Areal (3D) Mapping of Surfaces Using Stylus Methods
4.2.5.1 General Problem
4.2.5.2 Mapping
4.2.5.3 Criteria for Areal Mapping
4.2.5.4 Movement Positions on Surface and Sampling Patterns
4.2.5.5 Contour and Other Maps of Surfaces
4.3 Optical Techniques for the Measurement of Surfaces
4.3.1 General
4.3.2 Properties of the Focused Spot
4.3.3 Optical Followers
4.3.4 Hybrid Microscopes
4.3.5 Oblique Angle Methods
4.3.6 Phase Detection Systems
4.3.6.1 Spatial and Temporal Coherence
4.3.6.2 Interferometry and Surface Metrology
4.3.7 Heterodyne Methods
4.3.7.1 Frequency-Splitting Method
4.3.7.2 Other Methods in Interferometry Comparable with Heterodyne Methods
4.3.7.3 Relative Merits of Different Nanometre Instruments
4.3.7.4 High-precision Non-Contacting Metrology Using Short Coherence Interferometry
4.3.8 Moiré Methods
4.3.8.1 General
4.3.8.2 Strain Measurement
4.3.8.3 Moiré Contouring
4.3.8.4 Shadow Moiré
4.3.8.5 Projection Moiré
4.3.8.6 Summary
4.3.9 Holographic Techniques
5.3.9.1 Introduction
4.3.10 Speckle Methods
4.3.11 Diffraction Methods
4.3.12 Scatterometers (Glossmeters)
4.3.13 Flaw Detection
4.3.13.1 General
4.3.13.2 Transform Plane Methods
4.3.13.3 Image Plane Detection
4.3.13.4 'Whole-Field' Measurement—Plane Detection
4.3.13.5 Comment
4.3.14 Comparison of Optical Techniques
4.3.14.1 General Optical Comparison
4.4 Capacitance Techniques for Measuring Surfaces
4.4.1 General
4.4.2 Scanning Capacitative Microscopes
4.4.3 Capacitance as a Proximity Gauge
4.5 Inductance Technique for Measuring Surfaces
4.6 Impedance Technique—Skin Effect
4.7 Other Non-Standard Techniques
4.7.1 General
4.7.2 Friction Devices
4.7.2.1 the Friction Dynamometer
4.7.3 Rolling-Ball Device
4.7.4 Liquid Methods—Water
4.7.5 Liquid Methods—Oils
4.7.6 Pneumatic Methods
4.7.7 Thermal Method
4.7.8 Ultrasonics
4.7.9 Summary
4.8 Electron Microscopy
4.8.1 General
4.8.2 Reaction of Electrons with Solids
4.8.3 Scanning Electron Microscope
4.8.4 Transmission Electron Microscope
4.9 Merit of Transducers
4.9.1 Comparison of Transducer Systems
4.9.2 Types of Conversion and Transducer Noise
4.9.2.1 Limitations
4.9.2.2 Random Noise Limitation
4.9.3 Types of Conversion and Types of Transducer
4.9.3.1 General
4.9.3.2 Variable Resistance
4.9.3.3 Variable Inductance
4.9.3.4 Variable Reluctance
4.9.3.5 Voltage or Current Generators
4.9.3.6 Variable Capacitance
4.9.3.7 Self-Generation Voltage or Circuit
4.9.3.8 Photodetectors
4.9.4 Merit and Cost
4.9.5 Examples of Transducer Properties
4.9.5.1 Inductive
4.9.5.2 Capacitative Transducer
4.9.5.3 Optical Lateral Positional Sensor
4.9.5.4 Optical Area Pattern Photodiodes, Transducer for Lateral Displacement
4.9.6 Talystep
4.9.7 Comparison of Techniques—General Summary
References
5: Traceability—Standardization—Variability
5.1 Introduction
5.2 Nature of Errors
5.2.1 Systematic Errors
5.2.2 Random Errors
5.3 Deterministic or Systematic Error Model
5.4 Basic Components of Accuracy Evaluation
5.5 Basic Error Theory for a System
5.6 Propagation of Errors
5.6.1 Deterministic Errors
5.6.2 Random Errors
5.7 Some Useful Statistical Tests for Surface Metrology
5.7.1 Confidence Intervals for Any Parameter
5.7.2 Tests for the Mean Value of a Surface—The Student t Test
5.7.3 Tests for the Standard Deviation—The X2 Test
5.7.4 Goodness of Fit
5.7.5 Tests for Variance—the F Test
5.7.6 Measurement of Relevance—Factorial Design
5.7.6.1 The Interactions
5.7.7 Lines of Regression
5.7.8 Methods of Discrimination
5.8 Uncertainty in Instruments—Calibration in General
5.9 the Calibration of Stylus Instruments
5.9.1 Stylus Calibration
5.9.2 Calibration of Amplification
5.9.3 X-Ray Methods
5.9.4 Practical Standards
5.9.5 Calibration of Transmission Characteristics
5.9.6 Filter Calibration Standards
5.10 Calibration of Form Instruments
5.10.1 Magnitude
5.10.1.1 Magnitude of Diametral Change
5.10.2 Separation of Errors—Calibration of Roundness and Form
5.10.3 General Errors Due to Motion
5.10.3.1 Radial Motion
5.10.3.2 Face Motion
5.10.3.3 Error Motion—General Case
5.10.3.4 Fundamental and Residual Error Motion
5.10.3.5 Error Motion Versus Run-Out (or TIR)
5.10.3.6 Fixed Sensitive Direction Measurements
5.10.3.7 Considerations on the Use of the Two-gaugehead System for a Fixed Sensitive Direction
5.10.3.8 Other Radial Error Methods
5.11 Variability of Surface Parameters
5.12 National and International Standards
5.12.1 Selected List of Standards Applicable to Surface Roughness Measurement
5.13 Specification on Drawings
5.13.1 Surface Roughness
5.13.1.1 Indications Generally—Multiple Symbols
5.13.1.2 Reading the Symbols
5.13.1.3 General Points
5.13.1.4 Other Points
5.14 Summary
References
6: Surface Metrology in Manufacture
6.1 Introduction
6.2 Manufacturing Processes
6.2.1 General
6.3 Cutting
6.3.1 Turning
6.3.1.1 General
6.3.1.2 Finish Machining
6.3.1.3 Effect of Tool Geometry—Theoretical Surface Finish—Secondary Cutting Edge
6.3.1.4 Primary Cutting Edge Finish
6.3.1.5 Fracture Roughness
6.3.1.6 Built-Up Edge
6.3.1.7 Other Surface Roughness Effects in Finish Machining
6.3.1.8 Tool Wear
6.3.2 Diamond Turning
6.3.3 Milling and Broaching
6.3.3.1 General
6.3.3.2 Roughness on the Surface
6.3.3.3 Theoretical Milling Finish
6.4 Abrasive Processes
6.4.1 General
6.4.2 Types of Grinding
6.4.3 Comments on Grinding
6.4.4 Nature of the Guiding Process
6.4.4.1 General
6.4.4.2 Factorial Experiment
6.4.5 Centreless Grinding
6.4.5.1 General
6.4.5.2 Important Parameters for Roughness and Roundness
6.4.5.3 Roundness Considerations
6.4.6 Cylindrical Grinding
6.4.6.1 Spark-Out
6.4.6.2 Elastic Effects
6.4.6.3 Texture Generated in Grinding
6.4.6.4 Chatter
6.4.6.5 Other Types of Grinding
6.4.7 General Comments on Grinding
6.4.8 Nanogrinding
6.4.9 General Comments on Roughness
6.4.10 Honing
6.4.11 Polishing (Lapping)
6.5 Unconventional Machining
6.5.1 Ultrasonic Machining
6.5.2 Magnetic Float Polishing
6.5.3 Physical and Chemical Machining
6.5.3.1 Electrochemical Machining (ECM)
6.5.3.2 Electrolytic Grinding
6.5.3.3 Electrodischarge Machining (EDM)
6.5.4 Forming Processes
6.5.4.1 General
6.5.4.2 Ballizing
6.5.5 Micro- and Nanomachining
6.5.5.1 General
6.5.5.2 Micropolishing
6.5.6 Atomic-scale Machining
6.5.6.1 General
6.5.6.2 Electron Beam Machining
6.5.6.3 Ion Beam Machining
6.5.6.4 General Comment on Atomic-Type Processes
6.6 Surface Roughness Produced by Machining Difficult Materials
6.7 Surface Effects Other Than Geometry
6.7.1 Surface Effects Resulting from the Machining Process
6.7.2 Surface Alterations
6.7.3 Residual Stress
6.7.3.1 General
6.7.3.2 Grinding
6.7.3.3 Turning
6.7.3.4 M Illing
6.7.3.5 Shaping
6.7.3.6 General Comment
6.7.4 Measurement of Stresses
6.7.4.1 General
6.7.4.2 Indirect Methods
6.7.4.3 Direct Methods
6.7.5 Subsurface Properties Influencing Function
6.7.5.1 General
6.7.5.2 Influences of Residual Stress
6.8 Surface Geometry—A Fingerprint of Manufacture
6.8.1 General
6.8.2 Use of Random Process Analysis
6.8.2.1 on Turned Parts—Single-Point Machining
6.8.2.2 Abrasive Machining
6.8.3 Space—Frequency Functions (The Wigner Function)
6.8.4 Non-Linear Dynamics
6.9 Summary
References
7: Surface Geometry and Its Importance in Function
7.1 Introduction
7.2 Two-body Interaction—The Static Situation
7.2.1 Contact
7.2.1.1 Point Contact
7.2.2 Macroscopic Behaviour
7.2.2.1 Two Spheres in Contact
7.2.2.2 Two Cylinders in Contact
7.2.2.3 Crossed Cylinders at Any Angle
7.2.2.4 Sphere on a Cylinder
7.2.2.5 Sphere Inside a Cylinder
7.2.3 Microscopic Behaviour—Number of Asperity Contacts and Behaviour Under Load
7.2.3.1 General
7.2.3.2 Microcontact Under Load
7.2.3.3 Elastic/plastic Balance—Plasticity Index
7.2.3.4 Contacts and Areas, Profiles and Maps
7.2.4 Effect of Waviness on Contact
7.3 Functional Properties of Contact
7.3.1 General
7.3.2 Stiffness
7.3.3 Mechanical Seals
7.3.4 Adhesion
7.3.5 Thermal Conductivity
7.3.6 Relationship Between Electrical and Thermal Conductivity
7.3.7 Summary
7.4 Two-body Interactions—Dynamic Effect
7.4.1 General
7.4.2 Friction
7.4.2.1 Mechanisms—General
7.4.2.2 Friction—Wear, Dry Conditions
7.4.3 Wear Classification
7.4.4 Lubrication
7.4.4.1 General
7.4.4.2 Hydrodynamic Lubrication and Surface Geometry
7.4.5 Contact Between Two Surfaces Via a Third Body
7.4.5.1 General
7.4.5.2 EHD Lubrication and the Influence of Roughness
7.4.6 Boundary Lubrication
7.4.6.1 General
7.4.6.2 Mechanical Properties of Thin Boundary Layer Films
7.6.4.3 Breakdown of Boundary Lubrication
7.5 Surface Roughness and Mechanical System Life
7.5.1 Weibull and Dual-frequency—Space Functions
7.5.2 Running-in Process
7.5.3 Surface Roughness 'One-Number Specification and Running-in
7.5.4 Influence of Roughness on Scuffing Failure
7.5.5 Rolling Fatigue Failure (Pitting, Spalling)
7.5.5.1 Rolling Failure
7.5.52 Roughness Effects on 3D Body Motion
7.5.5.3 Rough Surfaces and Rolling
7.5.5.4 Pitting Due to Debris and Subsequent Surface Effects
7.5.6 Vibrating Effects
7.5.6.1 Dynamic Effects
7.5.6.2 Squeeze Films and Roughness
7.5.6.3 Fretting and Fretting Fatigue
7.6 One-body Interactions
7.6.1 General
7.6.2 Fatigue
7.6.3 Corrosion and Corrosion Fatigue on the Effect of Roughness
7.6.3.1 Corrosion Fatigue—General
7.6.4 Corrosion
7.6.4.1 General
7.6.4.2 Localized Attack—Electromechanical
7.6.4.3 Heterogeneities
7.6.4.4 Localized Attack—Electrochemical
7.7 One Body with Radiation (Optical). The Effect of Roughness on the Scattering of Electromagnetic and Other Radiation
7.7.1 Optical Scatter—General
7.7.1.1 Models
7.7.2 General Optical
7.7.3 Smooth Random Surface
7.7.4 Geometric Ray-Tracing Criterion—Rough Random Surfaces
7.7.4.1 Effect of Surface Curvature
7.7.4.2 Estimation of l, the Facet Length
7.7.5 Scatter from Deterministic Surfaces
7.7.6 Smooth Deterministic Signal
7.7.7 Geometric Ray Condition, Rough Deterministic Surfaces
7.7.8 Summary of Results, Scalar and Geometrical
7.7.9 M Ixture of Two Random Components
7.7.10 Other Considerations on Light Scatter
7.7.10.1 Angle Effects
7.7.10.2 Multiple Reflections
7.7.10.3 Shadowing
7.7.11 Scattering from Non-Gaussian Surfaces
7.7.11.1 Fresnel Scattering
7.7.11.2 Caustics
7.7.11.3 Fractal Surfaces
7.7.11.4 Fractal Slopes: Subfractal Model
7.8 Scattering by Different Worts of Waves
7.8.1 General
7.8.1.1 Em Waves
7.8.1.2 Elastic, Ultrasonic and Acoustic Scattering
7.8.2 Scattering from Particles and Influence of Surface Roughness
7.8.2.1 Rayleigh Scattering
7.8.3 Bragg Scattering
7.8.3.1 Non-Elastic Scattering
7.8.3.2 Influence of Roughness—Thin-Film Measurement
7.9 System Function
7.9.1 Surface Geometry and Tolerances and Fits
7.9.2 Tolerances
7.10 Summary and Conclusions
References
8: Summary and Conclusions
8.1 General
8.2 Characterization and Nature of Signals
8.3 Data Processing
8.4 Measurement Trends
8.5 Calibration
8.6 Manufacture
8.7 Function
8.8 Overview
Glossary
Index