Basics of Interferometry

P. Hariharan

• Publisher: Academic Press
• Year: 2012
• Print ISBN: 9780123252180
• eBook ISBN: 9780080918617
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

This book is for those who have some knowledge of optics, but little or no previous experience in interferometry. Accordingly, the carefully designed presentation helps readers easily find and assimilate the interferometric techniques they need for precision measurements. Mathematics is held to a minimum, and the topics covered are also summarized in capsule overviews at the beginning and end of each chapter. Each chapter also contains a set of worked problems that give a feel for numbers.The first five chapters present a clear tutorial review of fundamentals. Chapters six and seven discuss the types of lasers and photodetectors used in interferometry. The next eight chapters describe key applications of interferometry: measurements of length, optical testing, studies of refractive index fields, interference microscopy, holographic and speckle interferometry, interferometric sensors, interference spectroscopy, and Fourier-transform spectroscopy. The final chapter offers suggestions on choosing and setting up an interferometer.

Chapter 1

Introduction

Publisher Summary

Phenomena caused by the interference of light waves can be seen all around us. Some of the current applications of optical interferometry are the accurate measurements of distances, displacements, and vibrations; the tests of optical systems; the studies of gas flows and plasmas; the measurements of temperature, pressure, electrical, and magnetic fields; rotation sensing; and high-resolution spectroscopy. Several new developments have extended the scope and accuracy of optical interferometry and they make the use of optical interferometry practical for a very wide range of measurements. The most important of these new developments has been the invention of laser. Lasers have removed many of the limitations imposed by conventional sources and have made possible many new interferometric techniques.

Phenomena caused by the interference of light waves can be seen all around us: typical examples are the colors of an oil slick or a thin soap film.

Only a few colored fringes can be seen with white light. As the thickness of the film increases, the optical path difference between the interfering waves increases, and the changes of color become less noticeable and finally disappear. However, if monochromatic light is used, interference fringes can be seen with quite large optical path differences.

Since the wavelength of visible light is quite small (approximately half a micrometre for green light), optical interferometry permits extremely accurate measurements and has been used as a laboratory technique for almost a hundred years. Several new developments have extended its scope and accuracy and have made the use of optical interferometry practical for a very wide range of measurements.

The most important of these new developments was the invention of the laser. Lasers have removed many of the limitations imposed by conventional sources and have made possible many new interferometric techniques. New applications have also been opened up by the use of single-mode optical fibers to build analogs of conventional interferometers. Yet another development that has revolutionized interferometry has been the increasing use of photodetectors and digital electronics for signal processing.

Some of the current applications of optical interferometry are accurate measurements of distances, displacements and vibrations, tests of optical systems, studies of gas flows and plasmas, microscopy, measurements of temperature, pressure, electrical and magnetic fields, rotation sensing, and high resolution spectroscopy. There is little doubt that in the near future many more will be found.

Chapter 2

Interference: A Primer

Publisher Summary

This chapter discusses light waves. Light can be thought of as a transverse electromagnetic wave propagating through space. As the electric and magnetic fields are linked to each other and propagate together, it is usually sufficient to consider only the electric field at any point; this field can be treated as a time-varying vector perpendicular to the direction of propagation of the wave. If the field vector always lies in the same plane, the light wave is said to be linearly polarized in that plane. The chapter describes intensity in an interference pattern. When two light waves are superposed, the resultant intensity at any point depends on whether they reinforce or cancel each other. This is the well-known phenomenon of interference. This chapter discusses the localization of fringes. When an extended quasi-monochromatic source, such as a mercury vapor lamp with a monochromatic filter, is used instead of a monochromatic point source, interference fringes are often observed with good contrast only in a particular region. This phenomenon is known as the localization of fringes and is related to the lack of coherence of illumination.

This chapter discusses some basic concepts.

• Light waves

• Intensity in an interference pattern

• Visibility of interference fringes

• Interference with a point source

• Localization of interference fringes

2.1 Light Waves

Light can be thought of as a transverse electromagnetic wave propagating through space. Because the electric and magnetic fields are linked to each other and propagate together, it is usually sufficient to consider only the electric field at any point; this field can be treated as a time-varying vector perpendicular to the direction of propagation of the wave. If the field vector always lies in the same plane, the light wave is said to be linearly polarized in that plane. We can then describe the electric field at any point due to a light wave propagating in a vacuum along the z direction by the scalar equation

(2.1)

where a is the amplitude of the light wave, v is its frequency, and λ is its wavelength. Visible light comprises wavelengths from 0.4 μm (violet) to 0.75 μm (red), corresponding to frequencies of around 7.5 × 10¹⁴ Hz and 4.0 × 10¹⁴ Hz, respectively. Shorter wavelengths lie in the ultra violet (UV) region, while longer wavelengths lie in the infrared (IR) region.

Th...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Acknowledgments
• Chapter 1: Introduction
• Chapter 2: Interference: A Primer
• Chapter 3: Two-Beam Interferometers
• Chapter 4: Light Sources
• Chapter 5: Multiple-Beam Interference
• Chapter 6: The Laser as a Light Source
• Chapter 7: Detectors
• Chapter 8: Measurements of Length
• Chapter 9: Optical Testing
• Chapter 10: Digital Techniques
• Chapter 11: Macro- and Micro-Interferometry
• Chapter 12: Holographic and Speckle Interferometry
• Chapter 13: Interferometric Sensors
• Chapter 14: Interference Spectroscopy
• Chapter 15: Fourier-Transform Spectroscopy
• Chapter 16: Choosing an Interferometer
• Appendix A: Monochromatic Light Waves
• Appendix B: Phase Shifts on Reflection
• Appendix C: Diffraction
• Appendix D: Polarized Light
• Appendix E: The Twyman–Green Interferometer
• Appendix F: Adjustment of the Mach–Zehnder Interferometer
• Appendix G: Fourier Transforms and Correlation
• Appendix H: Coherence
• Appendix I: Heterodyne Interferometry
• Appendix J: Laser Frequency Shifting
• Appendix K: Evaluation of Shearing Interferograms
• Appendix L: Phase-Stepping Interferometry
• Appendix M: Holographic Imaging
• Appendix N: Laser Speckle
• Appendix O: Laser Frequency Modulation
• Index