Field Guide to Displacement Measuring I nterferometry Jonathan D. Ellis SPIE Field Guides Volume FG30 John E. Greivenkamp, Series Editor SPIE PRESS Bellingham, Washington USA
Vll Glossary of Terms and Acronyms Fundamentals of Light and Interference Basic Assumptions Degrees of Freedom The Meter Electromagnetic Radiation Electric Field Polarization States Complex Polarization Superposition Interference Irradiance Polarization Overlap Fringe Contrast Interferometer Components and Notation More Interferometer Components Polarization-Based Components Waveplates Ghosts, Absorption, and Scatter Michelson's Interferometer Temporal Coherence Displacement from Phase Change Unwrapping and Folding Basic Interferometry Systems Interferometry Systems Homodyne Interferometer Retroreflector Homodyne Interferometer Homodyne Optical Power Efficiency Polarization-Sensitive Homodyne Interferometer Directional Sensitivity Direction-Sensitive Homodyne Interferometer Homodyne Laser Encoder Heterodyne Interferometry Systems Basic Heterodyne Interferometer Heterodyne Directional Sensitivity Homodyne and Heterodyne Comparison xi 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 22 23 24 25 26 27 28 29 30 31 32 33
Vlll Interferometry System Characteristics Unequal Plane Mirror Interferometer Plane Mirror Interferometer (PMI) PMI Variants Beam Walkoff Doppler Velocity Dynamic Range and Acceleration Limitations Laser Sources Optical Power and Laser Modes Zeeman-Stabilized Laser Two-Mode Intensity-Balanced Laser Heterodyne Frequency Generation Phase Measurements Interference Detection Detection Bandwidth Phase Quadrature Measurements Time Interval Analysis Lock-In Detection Discrete Fourier Transform Special Interferometer Configurations Special Interferometer Configurations Quad-Pass Interferometer Differential Interferometer Coaxial Differential Interferometer Angle Interferometer Straightness Interferometer Refractometry Wavelength Tracking Refractive Index Tracker Multiaxis Systems Multi-DOF Interferometers X-Y-Theta System Tip-Tilt-Z System Interferometer Alignment Setup and Alignment Techniques Commercial Interferometer Alignment Vector Alignment and Breadboard Alignment 35 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 53 54 55 56 57 58 59 60 61 62 63 64 65 66 66 67 68
Beam Fly Height 69 Grid Alignment 70 Normal Mirror Alignment 71 45-deg Mirror Alignment 72 Mirror Steering 73 Beamsplitter Alignment 74 Polarizer Alignment 75 45-deg HWP Alignment 76 45-deg QWP Alignment 77 Polarization Flipping 78 In-line Beam Steering 79 Cosine Error 80 Cosine Mirror Alignment 81 Mixing and Periodic Error 82 Lissajous Figure 82 Source Mixing 83 Beam Leakage 84 Periodic Error 85 Assessing Periodic Error 86 Quantifying Periodic Error 87 Spatial Fourier Analysis 88 Measurement Errors and Uncertainty 89 Measurement Uncertainty 89 Probability Distributions 90 Combined Uncertainty 91 Uncertainty Sources 92 DMI Measurement Model 93 Source Vacuum Wavelength 94 Refractive Index Uncertainty 95 Cosine Error: Retroreflector Target 96 Cosine Error: Plane Mirror Target 97 Phase Change Uncertainty 98 Abbe Uncertainty 99 Measurement Axis Location 100 Interferometer Thermal Drift 101 Deadpath Uncertainty 102 Periodic Error Uncertainty 103
X Surface Figure Error Data Age Uncertainty Error Corrections Air Refractive Index Compensation Error Budget Measurement Uncertainty Example Stage Measurement Uncertainty Example Example Uncertainty Parameters Example Uncertainty Propagation Example Combined Uncertainty 104 105 106 107 108 109 109 110 111 115 Equation Summary Bibliography Index 116 125 129