Optical Scattering. Analysis. Measurement and SPIE PRESS. John C. Stover THIRD EDITION. Bellingham, Washington USA

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1 Optical Scattering Measurement and Analysis THIRD EDITION John C. Stover SPIE PRESS Bellingham, Washington USA

2 Contents Preface to the First Edition xiii Preface to the Second Edition xv Acknowledgments for the Second Edition xvii Preface to the Third Edition xix Acknowledgments for the Third Edition xxi List of Acronyms xxiii Chapter 1 Quantifying Light Scatter The Scattering of Light Scatter from a Smooth Sinusoidal Surface Scatter from Other Surfaces Scatter from Windows and Particulates Bidirectional Scatter Distribution Functions Total Integrated Scatter Differential Scattering Cross Section Summary 21 Chapter 2 Quantifying Surface Roughness Profile Characterization Deterministic profiles Random profiles Sampled profiles Two-dimensional (area) profiles The Surface Power Spectral Density and Autocovariance Functions The power spectral density function from the profile Extension to two-dimensional spectra The autocorrelation function The Effects of Profile Measurement Error Summary 44 vii

3 Contents Chapter 3 Scatter Calculations and Diffraction Theory Overview Kirchhoff Diffraction Theory The Rayleigh Approach Comparison of Scalar and Vector Results Calculating Scatter from Optically Rough Surfaces The Beckmann rough-surface result Other rough-surface calculations Summary 68 Chapter 4 Using Rayleigh-Rice to Calculate Smooth-Surface Statis tics from the BRDF Practical Application of the Rayleigh-Rice Perturbation Theory Roughness Statistics of Isotropic Surfaces Roughness Statistics of One-Dimensional Surfaces Roughness Statistics for the General Case The ABC or if-correlation Surface Power Spectrum Models The Lorentzian power spectrum Fractal surfaces The TIS Derivation from the Rayleigh-Rice Perturbation Theory Summary 89 Chapter 5 Polarization of Scattered Light A Review of Polarization Concepts The Polarization Factor Q Scattering Vectors and Matrices Summary 108 Chapter 6 Scattering Models for Discrete Surface Features Particle Scatter Modeling Techniques and Accomplishments Model Availability Summary 114 Chapter 7 Instrumentation and Measurement Issues Scatterometer Components Instrument Signature Aperture Effects on the Measured BSDF Signature Reduction and Near-Specular Measurements Reflective versus refractive focusing optics 124

4 Contents x Minimizing the near-angle/far-angle boundary 6# Scatter measurement inside QN Scatter Screens The Noise-Equivalent BSDF Measurement of Scatter from Discrete Surface Features in DSC Units Measurement of />, and Instrument Calibration Measurement of Curved Optics Coordinate Systems and Out-of-Plane Measurements Camera-based Systems Raster Scans Measurement of Retroreflection Alternative TIS Devices Error Analysis of the Measured BSDF Obtaining Appropriate PSD Measurements Summary 155 Chapter 8 Predicting Scatter from Roughness Optical Surfaces: Using the Rayleigh-Rice Equation The general case Isotropic samples One-dimensional samples Optically Rough Front-Surface Reflectors Stretching the Rayleigh smooth-surface limit Predicting rough-surface scatter from the PSD TIS measurements and rough surfaces Partial Data Sets Fractal surfaces Curve fitting Scatter from Diffuse Samples Lambertian samples Non-Lambertian samples and material signatures BRDF Standard Surfaces Software for Prediction of Stray Light in Optical Systems Summary 183 Chapter 9 Detection of Discrete Defects Polarization Effects Associated with Defect Scatter Bulk Defects in Transparent Optics Near-Point-Scatter Sources Nontopographic Defects in Opaque Materials Summary 200

5 X Contents Chapter 10 Appearance and Scattered Light Beauty is in The Eye of the Beholder And What We See is Scattered Light Practical Appearance Monitoring Other Examples Summary 207 Chapter 11 Industrial Applications Semiconductor Applications Finding small particulates and point defects on polished surfaces Scattering and roughness characterization of silicon Particle scanner inspection of wafers Computer Disks Measurement of Retinal Scatter Induced by Intraocular Lenses Contamination Measurement by Wavelength Discrimination Solar Energy Applications Photovoltaic collectors General Manufacturing Examples Detection of paper flaws Noncontact monitoring of emissivity and temperature Ballbearings Summary 228 Chapter 12 Published Scatter Standards Integrated Scatter Standards Angle-Resolved Scatter Standards The PSD Standard Standards for Semiconductor Particle Scanners : SEMI M52 Scanner specifications SEMI M50 Capture rate SEMI M53 Scanner calibration SEMI M58 Particle deposition confirmation Summary 237 Chapter 13 Scatter Specifications Generic Specifications Application-Specific Specifications Example 1: Scatterometer-focusing mirrors Example 2: Imaging optics Example 3: Laser resonator losses 246

6 Contents xi Example 4: Diffraction from precision-machined turning mirrors Example 5: Scatter in a laser rangefinder Example 6: Roughness specifications for semiconduc tor components Empirical Scatter Specifications Summary 255 Appendix A Review of Electromagnetic Wave Propagation 257 A. 1 The Wave Equation 257 A.2 Electromagnetic Plane Waves in Free Space 258 A.3 Plane Waves in a Dielectric 261 A.4 Plane Waves in a Conducting Medium 263 Appendix B Kirchhoff Diffraction from Sinusoidal Gratings 265 Appendix C BSDF Data 273 Appendix D Units 281 References 283 Works Consulted 297 Index 303

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