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FIBER-OPTIC-BASED SENSING SYSTEMS FIBER-OPTIC-BASED SENSING SYSTEMS Lazo M. Manojlović, PhD First edition published 2022 Apple Academic Press Inc. CRC Press 1265 Goldenrod Circle, NE, 6000 Broken Sound Parkway NW, Palm Bay, FL 32905 USA Suite 300, Boca Raton, FL 33487-2742 USA 4164 Lakeshore Road, Burlington, 2 Park Square, Milton Park, ON, L7L 1A4 Canada Abingdon, Oxon, OX14 4RN UK © 2022 Apple Academic Press, Inc. Apple Academic Press exclusively co-publishes with CRC Press, an imprint of Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the authors, editors, and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors, editors, and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Library and Archives Canada Cataloguing in Publication Title: Fiber-optic-based sensing systems / Lazo M. Manojlović, PhD. Names: Manojlović, Lazo M., author. Description: First edition. | Includes bibliographical references and index. Identifiers: Canadiana (print) 20210376783 | Canadiana (ebook) 20210376813 | ISBN 9781774637241 (hardcover) | ISBN 9781774637364 (softcover) | ISBN 9781003277293 (ebook) Subjects: LCSH: Optical fiber detectors. | LCSH: Fiber optics. Classification: LCC TA1815 .M36 2022 | DDC 681/.25—dc23 Library of Congress Cataloging‑in‑Publication Data CIP data on file with US Library of C ongress ISBN: 978-1-77463-724-1 (hbk) ISBN: 978-1-77463-736-4 (pbk) ISBN: 978-1-00327-729-3 (ebk) Contents Synopsis................................................................................................................ ix Abbreviations ....................................................................................................... xi Preface ...............................................................................................................xiii 1. The Properties and the Nature of Light ..................................................... 1 1.1 The Brief History of Light Phenomena Perception ...........................................1 1.2 The Wave Nature of Light .................................................................................3 1.3 The Corpuscular Nature of Light ....................................................................14 References ..................................................................................................................23 2. Radiometric and Photometric Measurements ........................................ 25 2.1 Introduction to Radiometry and Photometry ...................................................25 2.2 Optical Radiometry .........................................................................................28 2.2.1 The Radiative Transfer ....................................................................................29 2.2.2 The Lambertian Emitters .................................................................................30 2.2.3 Radiometric Measurements .............................................................................31 2.2.4 Reflection, Absorption, and Transmission.......................................................34 2.2.5 Kirchhoff's Law ...............................................................................................36 2.3 Measurement Techniques in Radiometry ........................................................38 2.3.1 Absolute Radiometer .......................................................................................38 2.3.2 Radiant Flux Measurement .............................................................................40 2.3.3 Integrating Sphere ...........................................................................................45 2.4 Photometry ......................................................................................................47 2.4.1 Spectral Response of a Human Eye ................................................................47 2.4.2 Standard Photometer and the Realization of the Candela ...............................51 References ..................................................................................................................52 3. Optical Detection ....................................................................................... 55 3.1 Photon Counting ..............................................................................................56 3.2 Photodetection Modeling ................................................................................60 3.3 Photodetectors .................................................................................................63 3.3.1 Photomultiplier ................................................................................................64 3.3.2 Photoconductors ..............................................................................................65 3.3.3 Photodiodes .....................................................................................................67 vi Contents 3.3.4 Avalanche Photodiodes ...................................................................................71 3.3.5 Position Sensing Photodiodes .........................................................................72 3.3.6 Quadrant Photodiode .......................................................................................75 3.3.7 Equivalent Circuit Model of the Photodiode ...................................................92 3.3.8 Photodiode Amplifier Circuit ..........................................................................95 References ................................................................................................................103 4. Coherence and Interference of Light ..................................................... 105 4.1 Two-Beam Interference .................................................................................105 4.1.1 Wavefront Division Method ..........................................................................108 4.1.2 Amplitude Division Method ..........................................................................111 4.1.3 The Michelson Interferometer .......................................................................114 4.1.4 The Mach–Zehnder Interferometer ...............................................................115 4.1.5 The Sagnac Interferometer ............................................................................117 4.2 COHERENCE ...............................................................................................118 4.2.1 The Mutual Coherence Function ...................................................................119 4.2.2 Spatial Coherence ..........................................................................................122 4.2.3 Coherence Time and Coherence Length .......................................................124 4.3 White-Light Interferometry ...........................................................................127 4.4 Multiple-Beam Interference ..........................................................................135 4.5 Multilayer Thin Films ...................................................................................140 4.6 Interferometric Sensors .................................................................................146 4.6.1 The Rayleigh Refractometer .........................................................................146 4.6.2 Laser-Doppler Interferometry .......................................................................147 4.6.3 Vibration Amplitudes Measurements ............................................................148 4.6.4 Michelson’s Stellar Interferometer ................................................................148 References ................................................................................................................151 5. Fiber Optics ..............................................................................................153 5.1 Optical Fibers ................................................................................................155 5.1.1 Geometrical Optics and the Optical Fibers ...................................................157 5.1.2 Wave Optics and the Optical Fibers ..............................................................163 5.1.3 Chromatic Dispersion ....................................................................................174 5.1.4 Polarization Mode Dispersion .......................................................................180 5.1.5 Fiber Losses. ..................................................................................................181 5.2 Fiber-Optic Communication Systems ...........................................................183 5.2.1 Point-to-Point Links ......................................................................................183 5.2.2 Distribution Networks ...................................................................................185 5.2.3 Local Area Networks .....................................................................................186 5.2.4 Fiber-Optic Network Design Consideration..................................................188 5.2.5 Coherent Fiber-Optic Communication Systems............................................191 Contents vii 5.3 Basic Concepts of Fiber-Optic Sensing Systems ..........................................195 5.3.1 Fiber-Optic Sensor Basic Topologies ............................................................195 5.3.2 Basic Concepts of Interferometric Fiber-Optic Sensors................................197 References ................................................................................................................202 6. Low‑Coherence Fiber‑Optic Sensor Principle of Operation ............... 205 6.1 Algorithms for Signal Processing of Low-Coherence Interferograms ..........209 6.1.1 Threshold Comparison Method .....................................................................210 6.1.2 Envelope Coherence Function Method .........................................................212 6.1.3 Centroid Algorithm .......................................................................................213 6.1.4 Algorithm with Phase-Shifted Interferograms ..............................................214 6.1.5 Wavelet Transform Algorithm .......................................................................215 6.2 A Modified Centroid Algorithm ....................................................................217 6.2.1 Sensitivity of the Modified Centroid Algorithm with Linear Scanning ........220 6.2.2 Optical Path Difference Measurement Error of Linear Scanning .................228 References ................................................................................................................242 7. Fiber‑Optic Sensor Case Studies ............................................................ 245 7.1 Absolute Position Measurement with Low-Coherence Fiber-Optic Interferometry ............................................................................245 7.2 Rough Surface Height Distribution Measurement with Low-Coherence Interferometry .....................................................................258 7.3 Wide-Dynamic Range Low-Coherence Interferometry ................................289 7.4 Optical Coherence Tomography Technique with Enhanced Resolution .......299 References ................................................................................................................315 Author Biography ............................................................................................ 321 Index ................................................................................................................. 323 Synopsis Since the revival of human civilization, there was an inevitable need for some sort of simple measurements of basic physical quantities such as length, time, and mass. In order to be able to exchange goods, the first traders established some primordial measurement standards. The earliest recorded systems of weights and measures originated in the 3rd or 4th millennium BC. Therefore, one can estimate that the history of measurements and consequently the history of measurement instruments is 5 to 6 millennia old. Early measurement standard units probably have been used only in a single community or small region, where every region developed its own standards for the physical quantity of interests, such as length, area, volume, and mass. Starting from the first industrial revolution and subsequent development of manufacturing technologies, and consequently the growing importance of trade across the globe, standardized weights and measures became critical. Hence, since the 18th century, modernized, simplified, and uniform systems of weights and measures were developed. During the last three centuries, the fundamental units were defined by ever more precise methods in the science of metrology. Today’s state-of-the-art measurement systems and instruments are capable of measuring different physical quantities with the resolution and speed that was unthinkable several decades ago. Although optical fibers are almost exclusively used in the telecommunica tion networks for the high capacity data transfer, there is also another specific use of the optical fibers. Namely, having in mind that optical interferometry is one of the most sensitive measuring techniques that are capable of high- precision and high-speed measurements of different physical quantities, a large number of different sensors have been developed that are based on the optical fibers. —Dr. Lazo M. Manojlović