Introduction to Optical Metrology

Introduction to Optical Metrology

by Rajpal S. Sirohi
Released July 2017
Publisher(s): CRC Press
ISBN: 9781351831116

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Book description

This book examines the theory and practice of various measurement methodologies utilizing the wave nature of light. It discusses interferometry, speckle metrology, moiré phenomenon, photoelasticity, and microscopy. It describes the principles used to measure refractive indices of solids, liquids, and gases. It presents methods for measuring curvature, focal length, angle, thickness, velocity, pressure, and length. It details techniques for optical testing as well as for making fiber optic- and MEMS-based measurements. It also features exercise problems at the end of each chapter for applied learning.

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents
  7. Series Preface
  8. Preface
  9. Acknowledgments
  10. Author
  11. Chapter 1 Introduction to Optics
    1. 1.1 Introduction
    2. 1.2 Law of Reflection
    3. 1.3 Law of Refraction
    4. 1.4 Interference
    5. 1.5 Diffraction
      1. 1.5.1 Propagation of a Monochromatic Wave
      2. 1.5.2 Kirchhoff Theory of Diffraction
      3. 1.5.3 Small Angle Approximation
      4. 1.5.4 Fresnel Approximation
      5. 1.5.5 Fraunhofer Approximation
    6. 1.6 Polarization
      1. 1.6.1 Polarization Ellipse
      2. 1.6.2 Representation of Polarization
        1. 1.6.2.1 Jones Vector
        2. 1.6.2.2 Stokes Vector
    7. 1.7 Fresnel Equations
    8. 1.8 Thin Film Optics
    9. 1.9 Optical Components
      1. 1.9.1 Reflective Components
        1. 1.9.1.1 Mirror
      2. 1.9.2 Refractive Components
        1. 1.9.2.1 Refraction at Dielectric Interface
      3. 1.9.3 Diffractive Components
    10. 1.10 Refraction at Curved Interface
      1. 1.10.1 Lenses
    11. 1.11 Paraxial Optics
      1. 1.11.1 Translation Matrix
      2. 1.11.2 Refraction Matrix
        1. 1.11.2.1 Plane Dielectric Interface
        2. 1.11.2.2 Spherical Dielectric Interface
      3. 1.11.3 Matrix for a Thin Lens
    12. Problems
  12. Chapter 2 Laser Beams
    1. 2.1 Gaussian Beams
    2. 2.2 The ABCD Law for Gaussian Beams
      1. 2.2.1 Free Space Propagation
      2. 2.2.2 Propagation through a Lens
        1. 2.2.2.1 Beam Waist Lies at Plane 1 at the Lens
        2. 2.2.2.2 Beam Waist Lies in Front of the Lens
        3. 2.2.2.3 Beam Focusing
    3. 2.3 Laser Collimator
    4. 2.4 Vortex Beams
    5. 2.5 Bessel Beams
    6. Problems
  13. Chapter 3 Sources, Detectors, and Recording Media
    1. 3.1 Introduction
    2. 3.2 Radiometric Units
    3. 3.3 Blackbody
    4. 3.4 Light Sources
      1. 3.4.1 Incandescent Tungsten Lamps
        1. 3.4.2 Tungsten-Halogen Lamps
        2. 3.4.3 Discharge Lamps
        3. 3.4.4 Coherent Sources
        4. 3.4.4.1 Helium-Neon Laser
        5. 3.4.4.2 Argon Ion Laser
        6. 3.4.4.3 Nd:YAG/Nd:Glass Laser
        7. 3.4.4.4 Semiconductor Lasers
    5. 3.5 Detectors
      1. 3.5.1 Eye
      2. 3.5.2 Photoelectric Detectors
        1. 3.5.2.1 Photoemissive Detectors
        2. 3.5.2.2 Photomultipliers
        3. 3.5.2.3 Photoconductive Detectors
        4. 3.5.2.4 Photovoltaic Detectors
        5. 3.5.2.5 Avalanche Photodiode
      3. 3.5.3 Thermal Detectors
    6. 3.6 Recording Media
      1. 3.6.1 Photographic/Holographic Plates and Films
      2. 3.6.2 Dichromated Gelatin
      3. 3.6.3 Photoresists
      4. 3.6.4 Photopolymers
      5. 3.6.5 Thermoplastics
      6. 3.6.6 Photochromics
      7. 3.6.7 Ferroelectric Crystals
    7. 3.7 Image Detectors
      1. 3.7.1 Time Delay and Integration Mode of Operation
    8. 3.8 Spatial Light Modulators
    9. Problems
  14. Chapter 4 Interferometry
    1. 4.1 Introduction
    2. 4.2 Early History
      1. 4.2.1 Arrival of Laser
    3. 4.3 Generation of Coherent Waves/Sources
      1. 4.3.1 Wave Front Division: Double-Slit Experiment
      2. 4.3.2 Amplitude Division: Plane Parallel Plate
    4. 4.4 Fringe Patterns
      1. 4.4.1 Interference between Two Plane Waves
      2. 4.4.2 Interference between Two Plane Waves of Slightly Different Frequencies
    5. 4.5 Some More Interferometers
      1. 4.5.1 Two-Frequency Interferometer
      2. 4.5.2 Doppler Interferometer
      3. 4.5.3 Cyclic Interferometer
      4. 4.5.4 Shear Interferometer
    6. 4.6 Phase Shifting
      1. 4.6.1 Temporal Phase Shifting
      2. 4.6.2 Spatial Phase Shifting
    7. Problems
  15. Chapter 5 Techniques
    1. 5.1 Holography and Hologram Interferometry
      1. 5.1.1 Hologram Recording
      2. 5.1.2 Reconstruction
      3. 5.1.3 In-Line Holography
      4. 5.1.4 Off-Axis Holography
        1. 5.1.4.1 Choice of Angle of the Reference Wave
        2. 5.1.4.2 Choice of Intensity of the Reference Wave
      5. 5.1.5 Types of Holograms
        1. 5.1.5.1 Diffraction Efficiency
      6. 5.1.6 Experimental Arrangement
        1. 5.1.6.1 Lasers
        2. 5.1.6.2 Beam Splitters
        3. 5.1.6.3 Beam Expanders
        4. 5.1.6.4 Object Illumination Beam
        5. 5.1.6.5 Reference Beam
        6. 5.1.6.6 Angle between Object and Reference Beams
      7. 5.1.7 Holographic Recording Materials
      8. 5.1.8 Holographic Interferometry
        1. 5.1.8.1 Real-Time HI
        2. 5.1.8.2 Double-Exposure HI
        3. 5.1.8.3 Time-Average HI
        4. 5.1.8.4 Real-Time, Time-Average HI
        5. 5.1.8.5 Stroboscopic Illumination/ Stroboscopic HI
      9. 5.1.9 Special Techniques in Holographic Interferometry
        1. 5.1.9.1 Two-Reference Beam HI
        2. 5.1.9.2 Sandwich HI
        3. 5.1.9.3 Reflection HI
        4. 5.1.9.4 Heterodyne HI
      10. 5.1.10 Holographic Contouring/Shape Measurement
        1. 5.1.10.1 Dual-Wavelength Method
        2. 5.1.10.2 Dual-Refractive Index Method
        3. 5.1.10.3 Dual-Illumination Method
      11. 5.1.11 Digital Holography
        1. 5.1.11.1 Recording of Digital Holograms
        2. 5.1.11.2 Reconstruction of Digital Holograms
      12. 5.1.12 Digital Holographic Interferometry
      13. 5.1.13 Fringe Formation and Measurement of Displacement Vector
      14. 5.1.14 Loading of the Object
    2. 5.2 Speckle Phenomenon, Speckle Photography, and Speckle Interferometry
      1. 5.2.1 Speckle Phenomenon
      2. 5.2.2 Average Speckle Size
        1. 5.2.2.1 Objective Speckle Pattern
        2. 5.2.2.2 Subjective Speckle Pattern
      3. 5.2.3 Relation between Object Displacement and Speckle Shift
        1. 5.2.3.1 In-Plane Displacement
        2. 5.2.3.2 Out-of-Plane Displacement
        3. 5.2.3.3 Tilt of the Object
      4. 5.2.4 Speckle Photography
      5. 5.2.5 Methods of Evaluation
        1. 5.2.5.1 Point-Wise Filtering Method
        2. 5.2.5.2 Whole-Field Filtering
        3. 5.2.5.3 Fourier Filtering Method: Measurement of Out-of-Plane Displacement
      6. 5.2.6 Speckle Photography with Vibrating Objects: In-Plane Vibration
      7. 5.2.7 Sensitivity of Speckle Photography
      8. 5.2.8 Particle Image Velocimetry
      9. 5.2.9 White Light Speckle Photography
      10. 5.2.10 Shear Speckle Photography
      11. 5.2.11 Speckle Interferometry
      12. 5.2.12 Correlation Coefficient in Speckle Interferometry
      13. 5.2.13 Out-of-Plane Speckle Interferometer
      14. 5.2.14 In-Plane Measurement: Duffy’s Method
        1. 5.2.14.1 Filtering
        2. 5.2.14.2 Fringe Formation
        3. 5.2.14.3 Duffy’s Arrangement: Enhanced Sensitivity
      15. 5.2.15 Speckle Shear Interferometry
        1. 5.2.15.1 Meaning of Shear
        2. 5.2.15.2 Methods of Shearing
        3. 5.2.15.3 Theory of Speckle Shear Interferometry
        4. 5.2.15.4 Fringe Formation
        5. 5.2.15.5 Shear Interferometry without the Influence of In-Plane Component
      16. 5.2.16 Electronic Speckle Pattern Interferometry
        1. 5.2.16.1 Out-of-Plane Displacement Measurement
        2. 5.2.16.2 In-Plane Displacement Measurement
        3. 5.2.16.3 Vibration Analysis
        4. 5.2.16.4 Measurement on Small Objects
      17. 5.2.17 Shear ESPI Measurement
        1. 5.2.18 Contouring in ESPI—Shape Measurement
        2. 5.2.18.1 Change of Direction of Illumination
        3. 5.2.18.2 Change of Wavelength
        4. 5.2.18.3 Change of Medium Surrounding the Object
        5. 5.2.18.4 Tilt of the Object
    3. 5.3 Moiré Phenomena
      1. 5.3.1 Formation of Moiré Pattern
        1. 5.3.1.1 Moiré Fringe Pattern between Two Linear Gratings
      2. 5.3.2 Moiré between Reference and Deformed Gratings
        1. 5.3.2.1 Reference and Deformed Gratings Oriented along Y-Axis
        2. 5.3.2.2 Reference Grating Inclined
        3. 5.3.2.3 Gratings with Different Periods
      3. 5.3.3 Derivative of Distortion Function
      4. 5.3.4 Moiré Pattern with Deformed Sinusoidal Grating
        1. 5.3.4.1 Multiplicative Moiré Pattern
        2. 5.3.4.2 Additive Moiré Pattern
      5. 5.3.5 Talbot Phenomenon
        1. 5.3.5.1 Talbot Effect in Collimated Illumination
        2. 5.3.5.2 Cut-Off Distance
        3. 5.3.5.3 Talbot Effect in Noncollimated Illumination
    4. 5.4 Photoelasticity
      1. 5.4.1 Superposition of Two Plane Polarized Waves
        1. 5.4.1.1 Linear Polarization
        2. 5.4.1.2 Circular Polarization
      2. 5.4.2 Production of Polarized Light
        1. 5.4.2.1 Reflection
        2. 5.4.2.2 Refraction
        3. 5.4.2.3 Double Refraction
      3. 5.4.3 Optical Elements from Crystals
        1. 5.4.3.1 Polarizers
        2. 5.4.3.2 Phase Plates
      4. 5.4.4 Dichroism
      5. 5.4.5 Scattering
      6. 5.4.6 Malus Law
      7. 5.4.7 Stress-Optic Law
      8. 5.4.8 Strain-Optic Law
      9. 5.4.9 Methods of Analysis
        1. 5.4.9.1 Plane Polariscope
        2. 5.4.9.2 Circular Polariscope
        3. 5.4.9.3 Evaluation Procedure
      10. 5.4.10 Measurement of Fractional Fringe Order
        1. 5.4.10.1 Tardy’s Method
      11. 5.4.11 Phase Shifting
        1. 5.4.11.1 Isoclinics Computation
        2. 5.4.11.2 Computation of Isochromatics
      12. 5.4.12 Birefringent Coating Method—Reflection Polariscope
      13. 5.4.13 Holophotoelasticity
        1. 5.4.13.1 Single-Exposure Holophotoelasticity
        2. 5.4.13.2 Double-Exposure Holophotoelasticity
      14. 5.4.14 Three-Dimensional Photoelasticity
        1. 5.4.14.1 Frozen Stress Method
        2. 5.4.14.2 Scattered Light Photoelasticity
    5. 5.5 Microscopy
      1. 5.5.1 Simple Magnifier
      2. 5.5.2 Compound Microscope
      3. 5.5.3 Köhler Illumination
      4. 5.5.4 Empty Magnification
      5. 5.5.5 Depth of Field
      6. 5.5.6 Depth of Focus
      7. 5.5.7 Contrast-Enhancing Techniques
        1. 5.5.7.1 Dark Field Microscopy
        2. 5.5.7.2 Rheinburg Illumination
        3. 5.5.7.3 Phase Contrast Microscopy
        4. 5.5.7.4 Interference Microscopy
        5. 5.5.7.5 Polarization Microscopy
        6. 5.5.7.6 Hoffman Modulation Contrast
        7. 5.5.7.7 Differential Interference Contrast Microscopy
      8. 5.5.8 Metrological Microscope
      9. 5.5.9 Confocal Scanning Optical Microscope
    6. Problems
  16. Chapter 6 Measurement of Refractive Index
    1. 6.1 Introduction
    2. 6.2 Spectrometer
    3. 6.3 Goniometer
      1. 6.3.1 Measurement of Refractive Index of a Liquid
      2. 6.3.2 Hilger–Chance Refractometer
    4. 6.4 Methods Based on the Measurement of Critical Angle
      1. 6.4.1 Pulfrich Refractometer
      2. 6.4.2 Abbe Refractometer
    5. 6.5 Measurement of Brewster Angle
    6. 6.6 Ellipsometry
      1. 6.6.1 Null Ellipsometry
      2. 6.6.2 Photometric Ellipsometry
      3. 6.6.3 Optical Constants of a Sample
      4. 6.6.4 Optical Constant of a Thin Film
    7. 6.7 Spectral Transmission Measurement
      1. 6.7.1 Refractive Index of the Substrate
    8. 6.8 Interferometry
    9. Problems
  17. Chapter 7 Measurement of Radius of Curvature and Focal Length
    1. 7.1 Introduction
    2. 7.2 Measurement of Radius of Curvature
      1. 7.2.1 Indirect Method: Measurement of the Sagitta
        1. 7.2.1.1 Mechanical Spherometer
      2. 7.2.2 Direct Methods
        1. 7.2.2.1 Image Formation
        2. 7.2.2.2 Differences in Conjugate Positions
        3. 7.2.2.3 Optical Spherometer
        4. 7.2.2.4 Measurement of Long Radius of Curvature
        5. 7.2.2.5 Cavity Method—Measurement of Long Radius of Curvature of a Concave Surface
        6. 7.2.2.6 Measurement of Very Long Radii of Curvature
        7. 7.2.2.7 Radius of Curvature with a Test Plate
        8. 7.2.2.8 Newton’s Rings Method
    3. 7.3 Scanning Profilometry
    4. 7.4 Radius of Curvature Measurement by Talbot Interferometry
    5. 7.5 Measurement of Focal Length
      1. 7.5.1 Focal Length of a Thin Lens
        1. 7.5.1.1 Focal Length by Imaging
        2. 7.5.1.2 Y’/tan θ’ Method
        3. 7.5.1.3 Magnification Method
        4. 7.5.1.4 Focal Length of a Negative/Diverging Lens
        5. 7.5.1.5 Nodal Slide Method
        6. 7.5.1.6 Focal Length Measurement from the Difference between Conjugate Positions
    6. 7.6 Moiré Deflectometry
    7. Problems
  18. Chapter 8 Optical Testing
    1. 8.1 Testing of a Flat Surface
      1. 8.1.1 Liquid Surface as a Reference
      2. 8.1.2 Calibration by Three-Flat Method
    2. 8.2 Testing of Spherical Surfaces
      1. 8.2.1 Scatter-Plate Interferometer
      2. 8.2.2 Point Diffraction Interferometer
      3. 8.2.3 Laser Unequal Path Interferometer
      4. 8.2.4 Fizeau Interferometer
      5. 8.2.5 Shack Cube Interferometer
    3. 8.3 Testing of Aspherical Surfaces
      1. 8.3.1 Null Test with a Computer-Generated Hologram
    4. 8.4 Oblique Incidence Interferometer
    5. 8.5 Shear Interferometry
    6. 8.6 Long Wavelength Interferometry
    7. Problems
  19. Chapter 9 Angle Measurement
    1. 9.1 Definition of an Angle
    2. 9.2 Autocollimator
      1. 9.2.1 Measurement of Angle of a Glass Wedge
      2. 9.2.2 Angle of a Prism
      3. 9.2.3 Measurement of Error in 90° Angle of a Right-Angle Prism
      4. 9.2.4 Measurement of Error in 45° Angle of a Right-Angle Prism
      5. 9.2.5 Testing of a Pentaprism
    3. 9.3 Goniometer
      1. 9.3.1 Measurement of Absolute Angle
    4. 9.4 Interferometry
      1. 9.4.1 Angle of a Wedge Plate
      2. 9.4.2 Angle between the Surfaces of an Opaque Plate or a Long Cylinder/Bar
      3. 9.4.3 Interferometric Testing of Prisms
        1. 9.4.3.1 Testing of a Right-Angle Prism
    5. Problems
  20. Chapter 10 Thickness Measurement
    1. 10.1 Triangulation-Based Probe
    2. 10.2 Spectral Reflectometry
    3. 10.3 Ellipsometry
    4. 10.4 Interferometry
      1. 10.4.1 Fringes of Equal Chromatic Order
      2. 10.4.2 Fizeau Fringes
      3. 10.4.3 Michelson Interferometer
      4. 10.4.4 Haidinger Fringes
    5. 10.5 Low Coherence Interferometry
    6. 10.6 Confocal Microscopy
    7. 10.7 Light Section Microscopy
    8. Problems
  21. Chapter 11 Measurement of Velocity
    1. 11.1 Introduction
    2. 11.2 Scattering from a Moving Particle-Doppler Shift
      1. 11.2.1 Reference Beam Mode
      2. 11.2.2 Fringe Mode
    3. 11.3 Scatter Light Beams Anemometry
    4. 11.4 Multichannel LDA Systems
    5. 11.5 Signal Processing
    6. 11.6 Particle Image Velocimetry
    7. 11.7 Measurement of Very High Velocity
    8. Problems
  22. Chapter 12 Pressure Measurement
    1. 12.1 Pressure Sensitive Paint
    2. 12.2 Measurement of Pressure with Photoelastic Material
    3. 12.3 Ruby Pressure Standard
    4. 12.4 Fabry–Perot Etalon as Pressure Sensor
      1. 12.4.1 FP Etalon with Flexible Mirrors
      2. 12.4.2 Change of Refractive Index
    5. Problems
  23. Chapter 13 Fiber Optic- and MEM-Based Measurements
    1. 13.1 Introduction
    2. 13.2 Intensity Modulation
      1. 13.2.1 Displacement Measurement: Lateral Shift between the Fibers
      2. 13.2.2 Displacement Sensor: Beam Attenuation
      3. 13.2.3 Proximity Probe
      4. 13.2.4 Microbend Displacement or Pressure Sensor
      5. 13.2.5 Measurement of the Refractive Index of Liquids: Fiber Optic Refractometer
    3. 13.3 Phase Modulation
      1. 13.3.1 Interferometric Sensors
        1. 13.3.1.1 Temperature Measurement
        2. 13.3.1.2 Fiber Optic Pressure Sensor
        3. 13.3.1.3 Fiber Optic Strain Sensor
        4. 13.3.1.4 Fiber Optic Accelerometers
        5. 13.3.1.5 Fiber Optic Gyroscope or Rotation Rate Sensors
        6. 13.3.1.6 Fiber Optic Fabry–Perot Interferometer
    4. 13.4 Pressure Sensor: Membrane Type
      1. 13.4.1 Pressure Sensor: Capillary Tip
    5. 13.5 Bragg Grating Sensors
    6. 13.6 Polarization Maintaining Single-Mode Fibers
      1. 13.6.1 Current Measurement: Faraday Rotation
    7. 13.7 Fiber Optic Biosensors
      1. 13.7.1 Direct Fiber Optic Sensors
      2. 13.7.1.1 Direct Physical Sensors
      3. 13.7.1.2 Direct Chemical Sensors
    8. 13.7.2 Indirect Fiber Optic Sensors
      1. 13.7.2.1 Indirect Physical Sensors
      2. 13.7.2.2 Indirect Chemical Sensors
    9. Problems
  24. Chapter 14 Length Measurement
    1. 14.1 Introduction
    2. 14.2 Measurement of Gauge Blocks and Slip Gauges
      1. 14.2.1 Method of Exact Fractions
    3. 14.3 Gauge Block Interferometry: Comparison with a Standard
      1. 14.3.1 Single Wavelength Interferometry for Gauge Blocks
    4. 14.4 Comb Generation and Gauge Block Calibration
      1. 14.4.1 Measurement of Gauge Block with Optical Comb
      2. 14.4.2 Distance Measurement with Frequency Comb
    5. 14.5 Modulated Frequency-Displacement Sensor
      1. 14.5.1 Frequency-Modulated Continuous Wave Laser Radar
    6. 14.6 Displacement Measurement with Interferometry
      1. 14.6.1 Two-Frequency Laser Interferometer for Displacement Measurement
    7. 14.7 Angle Interferometer
    8. 14.8 Moiré Technique for Displacement Measurement
    9. 14.9 Displacement Distribution Measurement
      1. 14.9.1 Hologram Interferometry
      2. 14.9.2 Measurement of Amplitude of Vibration
      3. 14.9.3 Electronic Detection: Electronic Speckle Pattern Interferometry/Digital Speckle Pattern Interferometry and Speckle Photography
    10. 14.10 Moiré Techniques
      1. 14.10.1 Measurement of In-Plane Displacement/ Deformation
      2. 14.10.2 Two-Dimensional In-Plane Displacement Measurement
      3. 14.10.3 High Sensitivity In-Plane Displacement Measurement
      4. 14.10.4 Measurement of Out-of-Plane Component
        1. 14.10.4.1 Shadow Moiré Method
        2. 14.10.4.2 Projection Moiré
      5. 14.10.5 Measurement of Amplitudes of Vibration
      6. 14.10.6 Reflection Moiré Method
      7. 14.10.7 Slope Determination for Dynamic Events
    11. 14.11 Digital Image Correlation
    12. Problems
  25. Bibliography
  26. Index

Product information

  • Title: Introduction to Optical Metrology
  • Author(s): Rajpal S. Sirohi
  • Release date: July 2017
  • Publisher(s): CRC Press
  • ISBN: 9781351831116