book

Introduction to Optical Metrology

by Rajpal S. Sirohi

July 2017

Intermediate to advanced

449 pages

12h 40m

English

CRC Press

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1.1 Introduction1.2 Law of Reflection1.3 Law of Refraction1.4 Interference1.5 Diffraction1.5.1 Propagation of a Monochromatic Wave1.5.2 Kirchhoff Theory of Diffraction1.5.3 Small Angle Approximation1.5.4 Fresnel Approximation1.5.5 Fraunhofer Approximation1.6 Polarization1.6.1 Polarization Ellipse1.6.2 Representation of Polarization1.6.2.1 Jones Vector1.6.2.2 Stokes Vector1.7 Fresnel Equations1.8 Thin Film Optics1.9 Optical Components1.9.1 Reflective Components1.9.1.1 Mirror1.9.2 Refractive Components1.9.2.1 Refraction at Dielectric Interface1.9.3 Diffractive Components1.10 Refraction at Curved Interface1.10.1 Lenses1.11 Paraxial Optics1.11.1 Translation Matrix1.11.2 Refraction Matrix1.11.2.1 Plane Dielectric Interface1.11.2.2 Spherical Dielectric Interface1.11.3 Matrix for a Thin LensProblems
2.1 Gaussian Beams2.2 The ABCD Law for Gaussian Beams2.2.1 Free Space Propagation2.2.2 Propagation through a Lens2.2.2.1 Beam Waist Lies at Plane 1 at the Lens2.2.2.2 Beam Waist Lies in Front of the Lens2.2.2.3 Beam Focusing2.3 Laser Collimator2.4 Vortex Beams2.5 Bessel BeamsProblems
3.1 Introduction3.2 Radiometric Units3.3 Blackbody3.4 Light Sources3.4.1 Incandescent Tungsten Lamps3.4.2 Tungsten-Halogen Lamps3.4.3 Discharge Lamps3.4.4 Coherent Sources3.4.4.1 Helium-Neon Laser3.4.4.2 Argon Ion Laser3.4.4.3 Nd:YAG/Nd:Glass Laser3.4.4.4 Semiconductor Lasers3.5 Detectors3.5.1 Eye3.5.2 Photoelectric Detectors3.5.2.1 Photoemissive Detectors3.5.2.2 Photomultipliers3.5.2.3 Photoconductive Detectors3.5.2.4 Photovoltaic Detectors3.5.2.5 Avalanche Photodiode3.5.3 Thermal Detectors3.6 Recording Media3.6.1 Photographic/Holographic Plates and Films3.6.2 Dichromated Gelatin3.6.3 Photoresists3.6.4 Photopolymers3.6.5 Thermoplastics3.6.6 Photochromics3.6.7 Ferroelectric Crystals3.7 Image Detectors3.7.1 Time Delay and Integration Mode of Operation3.8 Spatial Light ModulatorsProblems
4.1 Introduction4.2 Early History4.2.1 Arrival of Laser4.3 Generation of Coherent Waves/Sources4.3.1 Wave Front Division: Double-Slit Experiment4.3.2 Amplitude Division: Plane Parallel Plate4.4 Fringe Patterns4.4.1 Interference between Two Plane Waves4.4.2 Interference between Two Plane Waves of Slightly Different Frequencies4.5 Some More Interferometers4.5.1 Two-Frequency Interferometer4.5.2 Doppler Interferometer4.5.3 Cyclic Interferometer4.5.4 Shear Interferometer4.6 Phase Shifting4.6.1 Temporal Phase Shifting4.6.2 Spatial Phase ShiftingProblems
5.1 Holography and Hologram Interferometry5.1.1 Hologram Recording5.1.2 Reconstruction5.1.3 In-Line Holography5.1.4 Off-Axis Holography5.1.4.1 Choice of Angle of the Reference Wave5.1.4.2 Choice of Intensity of the Reference Wave5.1.5 Types of Holograms5.1.5.1 Diffraction Efficiency5.1.6 Experimental Arrangement5.1.6.1 Lasers5.1.6.2 Beam Splitters5.1.6.3 Beam Expanders5.1.6.4 Object Illumination Beam5.1.6.5 Reference Beam5.1.6.6 Angle between Object and Reference Beams5.1.7 Holographic Recording Materials5.1.8 Holographic Interferometry5.1.8.1 Real-Time HI5.1.8.2 Double-Exposure HI5.1.8.3 Time-Average HI5.1.8.4 Real-Time, Time-Average HI5.1.8.5 Stroboscopic Illumination/ Stroboscopic HI5.1.9 Special Techniques in Holographic Interferometry5.1.9.1 Two-Reference Beam HI5.1.9.2 Sandwich HI5.1.9.3 Reflection HI5.1.9.4 Heterodyne HI5.1.10 Holographic Contouring/Shape Measurement5.1.10.1 Dual-Wavelength Method5.1.10.2 Dual-Refractive Index Method5.1.10.3 Dual-Illumination Method5.1.11 Digital Holography5.1.11.1 Recording of Digital Holograms5.1.11.2 Reconstruction of Digital Holograms5.1.12 Digital Holographic Interferometry5.1.13 Fringe Formation and Measurement of Displacement Vector5.1.14 Loading of the Object5.2 Speckle Phenomenon, Speckle Photography, and Speckle Interferometry5.2.1 Speckle Phenomenon5.2.2 Average Speckle Size5.2.2.1 Objective Speckle Pattern5.2.2.2 Subjective Speckle Pattern5.2.3 Relation between Object Displacement and Speckle Shift5.2.3.1 In-Plane Displacement5.2.3.2 Out-of-Plane Displacement5.2.3.3 Tilt of the Object5.2.4 Speckle Photography5.2.5 Methods of Evaluation5.2.5.1 Point-Wise Filtering Method5.2.5.2 Whole-Field Filtering5.2.5.3 Fourier Filtering Method: Measurement of Out-of-Plane Displacement5.2.6 Speckle Photography with Vibrating Objects: In-Plane Vibration5.2.7 Sensitivity of Speckle Photography5.2.8 Particle Image Velocimetry5.2.9 White Light Speckle Photography5.2.10 Shear Speckle Photography5.2.11 Speckle Interferometry5.2.12 Correlation Coefficient in Speckle Interferometry5.2.13 Out-of-Plane Speckle Interferometer5.2.14 In-Plane Measurement: Duffy’s Method5.2.14.1 Filtering5.2.14.2 Fringe Formation5.2.14.3 Duffy’s Arrangement: Enhanced Sensitivity5.2.15 Speckle Shear Interferometry5.2.15.1 Meaning of Shear5.2.15.2 Methods of Shearing5.2.15.3 Theory of Speckle Shear Interferometry5.2.15.4 Fringe Formation5.2.15.5 Shear Interferometry without the Influence of In-Plane Component
5.2.16.1 Out-of-Plane Displacement Measurement5.2.16.2 In-Plane Displacement Measurement5.2.16.3 Vibration Analysis5.2.16.4 Measurement on Small Objects5.2.17 Shear ESPI Measurement5.2.18 Contouring in ESPI—Shape Measurement5.2.18.1 Change of Direction of Illumination5.2.18.2 Change of Wavelength5.2.18.3 Change of Medium Surrounding the Object5.2.18.4 Tilt of the Object5.3 Moiré Phenomena5.3.1 Formation of Moiré Pattern5.3.1.1 Moiré Fringe Pattern between Two Linear Gratings5.3.2 Moiré between Reference and Deformed Gratings5.3.2.1 Reference and Deformed Gratings Oriented along Y-Axis5.3.2.2 Reference Grating Inclined5.3.2.3 Gratings with Different Periods5.3.3 Derivative of Distortion Function5.3.4 Moiré Pattern with Deformed Sinusoidal Grating5.3.4.1 Multiplicative Moiré Pattern5.3.4.2 Additive Moiré Pattern5.3.5 Talbot Phenomenon5.3.5.1 Talbot Effect in Collimated Illumination5.3.5.2 Cut-Off Distance5.3.5.3 Talbot Effect in Noncollimated Illumination
5.4.1 Superposition of Two Plane Polarized Waves5.4.1.1 Linear Polarization5.4.1.2 Circular Polarization5.4.2 Production of Polarized Light5.4.2.1 Reflection5.4.2.2 Refraction5.4.2.3 Double Refraction5.4.3 Optical Elements from Crystals5.4.3.1 Polarizers5.4.3.2 Phase Plates5.4.4 Dichroism5.4.5 Scattering5.4.6 Malus Law5.4.7 Stress-Optic Law5.4.8 Strain-Optic Law5.4.9 Methods of Analysis5.4.9.1 Plane Polariscope5.4.9.2 Circular Polariscope5.4.9.3 Evaluation Procedure5.4.10 Measurement of Fractional Fringe Order5.4.10.1 Tardy’s Method5.4.11 Phase Shifting5.4.11.1 Isoclinics Computation5.4.11.2 Computation of Isochromatics5.4.12 Birefringent Coating Method—Reflection Polariscope5.4.13 Holophotoelasticity5.4.13.1 Single-Exposure Holophotoelasticity5.4.13.2 Double-Exposure Holophotoelasticity5.4.14 Three-Dimensional Photoelasticity5.4.14.1 Frozen Stress Method5.4.14.2 Scattered Light Photoelasticity5.5 Microscopy5.5.1 Simple Magnifier5.5.2 Compound Microscope5.5.3 Köhler Illumination5.5.4 Empty Magnification5.5.5 Depth of Field5.5.6 Depth of Focus5.5.7 Contrast-Enhancing Techniques5.5.7.1 Dark Field Microscopy5.5.7.2 Rheinburg Illumination5.5.7.3 Phase Contrast Microscopy5.5.7.4 Interference Microscopy5.5.7.5 Polarization Microscopy5.5.7.6 Hoffman Modulation Contrast5.5.7.7 Differential Interference Contrast Microscopy5.5.8 Metrological Microscope5.5.9 Confocal Scanning Optical MicroscopeProblems
6.1 Introduction6.2 Spectrometer6.3 Goniometer6.3.1 Measurement of Refractive Index of a Liquid6.3.2 Hilger–Chance Refractometer6.4 Methods Based on the Measurement of Critical Angle6.4.1 Pulfrich Refractometer6.4.2 Abbe Refractometer6.5 Measurement of Brewster Angle6.6 Ellipsometry6.6.1 Null Ellipsometry6.6.2 Photometric Ellipsometry6.6.3 Optical Constants of a Sample6.6.4 Optical Constant of a Thin Film6.7 Spectral Transmission Measurement6.7.1 Refractive Index of the Substrate6.8 InterferometryProblems
7.1 Introduction7.2 Measurement of Radius of Curvature7.2.1 Indirect Method: Measurement of the Sagitta7.2.1.1 Mechanical Spherometer7.2.2 Direct Methods7.2.2.1 Image Formation7.2.2.2 Differences in Conjugate Positions7.2.2.3 Optical Spherometer7.2.2.4 Measurement of Long Radius of Curvature7.2.2.5 Cavity Method—Measurement of Long Radius of Curvature of a Concave Surface7.2.2.6 Measurement of Very Long Radii of Curvature7.2.2.7 Radius of Curvature with a Test Plate7.2.2.8 Newton’s Rings Method7.3 Scanning Profilometry7.4 Radius of Curvature Measurement by Talbot Interferometry7.5 Measurement of Focal Length7.5.1 Focal Length of a Thin Lens7.5.1.1 Focal Length by Imaging7.5.1.2 Y’/tan θ’ Method7.5.1.3 Magnification Method7.5.1.4 Focal Length of a Negative/Diverging Lens7.5.1.5 Nodal Slide Method7.5.1.6 Focal Length Measurement from the Difference between Conjugate Positions7.6 Moiré DeflectometryProblems
8.1 Testing of a Flat Surface8.1.1 Liquid Surface as a Reference8.1.2 Calibration by Three-Flat Method8.2 Testing of Spherical Surfaces8.2.1 Scatter-Plate Interferometer8.2.2 Point Diffraction Interferometer8.2.3 Laser Unequal Path Interferometer8.2.4 Fizeau Interferometer8.2.5 Shack Cube Interferometer8.3 Testing of Aspherical Surfaces8.3.1 Null Test with a Computer-Generated Hologram8.4 Oblique Incidence Interferometer8.5 Shear Interferometry8.6 Long Wavelength InterferometryProblems
9.1 Definition of an Angle9.2 Autocollimator9.2.1 Measurement of Angle of a Glass Wedge9.2.2 Angle of a Prism9.2.3 Measurement of Error in 90° Angle of a Right-Angle Prism9.2.4 Measurement of Error in 45° Angle of a Right-Angle Prism9.2.5 Testing of a Pentaprism9.3 Goniometer9.3.1 Measurement of Absolute Angle9.4 Interferometry9.4.1 Angle of a Wedge Plate9.4.2 Angle between the Surfaces of an Opaque Plate or a Long Cylinder/Bar9.4.3 Interferometric Testing of Prisms9.4.3.1 Testing of a Right-Angle PrismProblems
10.1 Triangulation-Based Probe10.2 Spectral Reflectometry10.3 Ellipsometry10.4 Interferometry10.4.1 Fringes of Equal Chromatic Order10.4.2 Fizeau Fringes10.4.3 Michelson Interferometer10.4.4 Haidinger Fringes10.5 Low Coherence Interferometry10.6 Confocal Microscopy10.7 Light Section MicroscopyProblems
11.1 Introduction11.2 Scattering from a Moving Particle-Doppler Shift11.2.1 Reference Beam Mode11.2.2 Fringe Mode11.3 Scatter Light Beams Anemometry11.4 Multichannel LDA Systems11.5 Signal Processing11.6 Particle Image Velocimetry11.7 Measurement of Very High VelocityProblems
12.1 Pressure Sensitive Paint12.2 Measurement of Pressure with Photoelastic Material12.3 Ruby Pressure Standard12.4 Fabry–Perot Etalon as Pressure Sensor12.4.1 FP Etalon with Flexible Mirrors12.4.2 Change of Refractive IndexProblems
13.1 Introduction13.2 Intensity Modulation13.2.1 Displacement Measurement: Lateral Shift between the Fibers13.2.2 Displacement Sensor: Beam Attenuation13.2.3 Proximity Probe13.2.4 Microbend Displacement or Pressure Sensor13.2.5 Measurement of the Refractive Index of Liquids: Fiber Optic Refractometer13.3 Phase Modulation13.3.1 Interferometric Sensors13.3.1.1 Temperature Measurement13.3.1.2 Fiber Optic Pressure Sensor13.3.1.3 Fiber Optic Strain Sensor13.3.1.4 Fiber Optic Accelerometers13.3.1.5 Fiber Optic Gyroscope or Rotation Rate Sensors13.3.1.6 Fiber Optic Fabry–Perot Interferometer13.4 Pressure Sensor: Membrane Type13.4.1 Pressure Sensor: Capillary Tip13.5 Bragg Grating Sensors13.6 Polarization Maintaining Single-Mode Fibers13.6.1 Current Measurement: Faraday Rotation13.7 Fiber Optic Biosensors13.7.1 Direct Fiber Optic Sensors13.7.1.1 Direct Physical Sensors13.7.1.2 Direct Chemical Sensors13.7.2 Indirect Fiber Optic Sensors13.7.2.1 Indirect Physical Sensors13.7.2.2 Indirect Chemical SensorsProblems
14.1 Introduction14.2 Measurement of Gauge Blocks and Slip Gauges14.2.1 Method of Exact Fractions14.3 Gauge Block Interferometry: Comparison with a Standard14.3.1 Single Wavelength Interferometry for Gauge Blocks14.4 Comb Generation and Gauge Block Calibration14.4.1 Measurement of Gauge Block with Optical Comb14.4.2 Distance Measurement with Frequency Comb14.5 Modulated Frequency-Displacement Sensor14.5.1 Frequency-Modulated Continuous Wave Laser Radar14.6 Displacement Measurement with Interferometry14.6.1 Two-Frequency Laser Interferometer for Displacement Measurement14.7 Angle Interferometer14.8 Moiré Technique for Displacement Measurement14.9 Displacement Distribution Measurement14.9.1 Hologram Interferometry14.9.2 Measurement of Amplitude of Vibration14.9.3 Electronic Detection: Electronic Speckle Pattern Interferometry/Digital Speckle Pattern Interferometry and Speckle Photography14.10 Moiré Techniques14.10.1 Measurement of In-Plane Displacement/ Deformation14.10.2 Two-Dimensional In-Plane Displacement Measurement14.10.3 High Sensitivity In-Plane Displacement Measurement14.10.4 Measurement of Out-of-Plane Component14.10.4.1 Shadow Moiré Method14.10.4.2 Projection Moiré14.10.5 Measurement of Amplitudes of Vibration14.10.6 Reflection Moiré Method14.10.7 Slope Determination for Dynamic Events14.11 Digital Image CorrelationProblems

Content preview from Introduction to Optical Metrology

10	Thickness Measurement

Measurements of thickness of a thin film, while being deposited or after being deposited, and of surface undulation are required in many applications. A number of techniques to cover a large range of thickness have been developed. These techniques are based on triangulation principle, interference, polarization, and so on. Some of these techniques are described in this chapter.

10.1 TRIANGULATION-BASED PROBE

This makes use of laser radiation as it can be focused to a tight spot on the surface of an object that is diffuse. A well-corrected lens images the spot on a linear array detector, which is aligned perpendicular to the optical axis of the imaging lens. Figure 10.1 shows the schematic of the instrument.

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ISBN: 9781482236118

Introduction to Optical Metrology

by Rajpal S. Sirohi

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