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

Directional Sensitivity

Homodyne Laser Encoder

Heterodyne Interferometry Systems

Basic Heterodyne Interferometer

Heterodyne Directional Sensitivity

Homodyne and Heterodyne Comparison

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

Beam Fly Height

Grid Alignment

Normal Mirror Alignment

45-deg Mirror Alignment

Mirror Steering

Beamsplitter Alignment

Polarizer Alignment

45-deg HWP Alignment

45-deg QWP Alignment

Polarization Flipping

In-line Beam Steering

Cosine Error

Cosine Mirror Alignment

Mixing and Periodic Error

Lissajous Figure

Source Mixing

Beam Leakage

Periodic Error

Assessing Periodic Error

Quantifying Periodic Error

Spatial Fourier Analysis

Measurement Errors and Uncertainty

Measurement Uncertainty

Probability Distributions

Combined Uncertainty

Uncertainty Sources

DMI Measurement Model

Source Vacuum Wavelength

Refractive Index Uncertainty

Cosine Error: Retroreflector Target

Cosine Error: Plane Mirror Target

Phase Change Uncertainty

Abbé Uncertainty

Measurement Axis Location

Interferometer Thermal Drift

Deadpath Uncertainty

Periodic Error Uncertainty

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

Equation Summary

Bibliography

Index

This Field Guide to Displacement Measuring Interferometry delves into a subfield of optical metrology that is prevalent in many precision systems. Precision systems that require accurate positioning knowledge use displacement measuring interferometry either through direct measurement or calibration of alternative metrology systems. Displacement measuring interferometry offers high-accuracy measurements with a wide bandwidth and direct traceability to international length standards.

The aim of this Field Guide is to provide a practical treatment of the fundamental theory of displacement interferometry along with examples of interferometry systems and uses, to outline alignment techniques for optical components, and to discuss measurement uncertainty with a practical example.

For practicing engineers, this will serve as a refresher manual for error sources and uncertainty budgets. For researchers, this will hopefully bring new insight to ways in which this technology can be useful in their field. For new engineers, researchers, and students, this Field Guide will serve as an introduction to basic alignment techniques for breadboard-based optical systems.

I would like to thank Vivek Badami for his helpful insight and for being a great mentor and friend. I am grateful for a thorough review of this manuscript by Steven Gillmer. I am indebted to many professors for training me in precision engineering and metrology, especially Stuart T. Smith, Robert J. Hocken, and the other faculty members of the Center for Precision Metrology at UNC Charlotte.

This Field Guide is dedicated to Kate Medicus for reducing my uncertainty budget in life.

Jonathan D. Ellis
Institute of Optics
University of Rochester