Computational Surface and Roundness Metrology

Cover -- Copyright -- Dedication -- Preface -- Acknowledgment -- TOC$Contents -- Notation -- Part I: Filtering -- CH$1 Introduction -- 1.1 Surface and Roundness Metrology -- 1.2 Scope and Objectives -- 1.3 Organization -- References -- CH$2 A Brief History of Filtering -- 2.1 Introduction -- 2.2 Electrical Filters -- 2.3 Digital Filters -- 2.4 The Envelope Method -- 2.5 The Gaussian Filter -- 2.6 Overlap of Measurement Techniques -- 2.7 Recent Advances in Filtering -- 2.8 Summary -- References -- CH$3 Filtering in the Frequency Domain -- 3.1 Surface Wavelengths -- 3.2 Fourier Transform, Discrete Fourier Transform, and Fast Fourier Transform -- 3.3 Filtering in the Frequency Domain -- 3.4 Wrap-Around Effect -- 3.5 Amplitude Transmission and Phase Characteristics -- 3.6 Summary -- Exercises -- References -- CH$4 Filtering in the Time Domain -- 4.1 Filtering as an Averaging Process -- 4.2 Relationship Between Frequency-Domain and Time-Domain Filtering -- 4.3 Filtering Profiles: Putting It All Together -- 4.4 Summary -- Exercises -- References -- CH$5 Gaussian Filter -- 5.1 Introduction -- 5.2 High-Pass and Low-Pass Filters -- 5.3 Roughness, Waviness, and Form Using the Gaussian Filter -- 5.4 Effect of Cutoff -- 5.5 Phase Characteristics -- 5.6 Summary -- Exercises -- References -- CH$6 The 2RC Filter -- 6.1 Introduction -- 6.2 The 2RC High-Pass Filter -- 6.3 More on the 2RC Filter -- 6.4 Comparison of the 2RC and Gaussian Filters -- 6.5 Summary -- Exercises -- References -- CH$7 Filtering Roundness Profiles -- 7.1 Introduction -- 7.2 Gaussian Filter for Roundness -- 7.3 Amplitude Transmission Characteristics -- 7.4 Filtering Roundness Profiles in the Time Domain -- 7.5 Circular Convolution in the Frequency Domain -- 7.6 Summary -- Exercises -- References -- CH$8 Filtering 3D Surfaces -- 8.1 Areal Surface Texture Analysis -- 8.2 2D Convolution -- 8.3 Gaussian Filter in 3D -- 8.4 A Note on Indices -- 8.5 Frequency-Domain Filtering in 3D -- 8.6 Summary -- Exercises -- References -- Part II: Advanced Filtering -- CH$9 Gaussian Regression Filters -- 9.1 Introduction -- 9.2 Zero-Order Gaussian Regression Filter -- 9.3 Second-Order Gaussian Regression Filter -- 9.4 3D Zero-Order Gaussian Regression Filter -- 9.5 3D Second-Order Gaussian Regression Filter -- 9.6 Summary -- Exercises -- References -- CH$10 Spline Filter -- 10.1 Introduction -- 10.2 Amplitude Transmission Characteristics -- 10.3 Implementation of the Non-periodic Spline Filter -- 10.4 Implementation of the Periodic Spline Filter -- 10.5 Summary -- Exercises -- References -- CH$11 Robust Filters -- 11.1 Rk Filter -- 11.2 Robust Gaussian Regression Filter -- 11.3 Summary -- Exercises -- References -- CH$12 Envelope and Morphological Filters -- 12.1 Envelope Filters -- 12.2 Stylus Tip Convolution -- 12.3 Morphological Filters -- 12.4 A Word on the Fundamentals -- 12.5 3D Morphological Filtering -- 12.6 Summary -- Exercises -- References -- CH$13 Multi-scale Filtering -- 13.1 Introduction -- 13.2 Alternate Sequence Filters or Scale Space Analysis -- 13.3 Wavelet-Based Filters -- 13.4 Summary