The Fiber-Optic Gyroscope Third Edition 77002211__LLeeffeevvrree__BBooookk..iinnddbb 11 1122//88//2211 1100::3377 AAMM For a listing of recent titles in the Artech House Applied Photonics Series, turn to the back of this book. 77002211__LLeeffeevvrree__BBooookk..iinnddbb 22 1122//88//2211 1100::3377 AAMM The Fiber-Optic Gyroscope Third Edition Hervé C. Lefèvre artechhouse.com 77002211__LLeeffeevvrree__BBooookk..iinnddbb 33 1122//88//2211 1100::3377 AAMM Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress British Library Cataloguing in Publication Data A catalog record for this book is available from the British Library. ISBN-13: 978-1-63081-862-3 Cover design by Charlene Stevens © 2022 Artech House 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. 10 9 8 7 6 5 4 3 2 1 77002211__LLeeffeevvrree__BBooookk..iinnddbb 44 1122//88//2211 1100::3377 AAMM To Sophie, Charlotte, Elliot, and Orphée 77002211__LLeeffeevvrree__BBooookk..iinnddbb 55 1122//88//2211 1100::3377 AAMM 77002211__LLeeffeevvrree__BBooookk..iinnddbb 66 1122//88//2211 1100::3377 AAMM “C’est un gyroscope, c’est la clef de l’Absolu.” (It is a gyroscope, it is the key to the Absolute.) Michel Tournier Le Roi des Aulnes (The Erl-King) 77002211__LLeeffeevvrree__BBooookk..iinnddbb 77 1122//88//2211 1100::3377 AAMM “Eppur si muove!”–Galileo Galilei (Although it does move!) Chambre Mentale #79 Photograph by Marc Le Mené, 2000. 77002211__LLeeffeevvrree__BBooookk..iinnddbb 88 1122//88//2211 1100::3377 AAMM Contents Foreword xvii Preface to the First Edition xix Preface to the Second Edition xxi Preface to the Third Edition xxiiii CHAPTER 1 Introduction 1 References 5 CHAPTER 2 Principle of the Fiber-Optic Gyroscope 7 2.1 Sagnac-Laue Effect 7 2.1.1 A History of Optics from Aether to Relativity 7 2.1.2 Sagnac-Laue Effect in a Vacuum 8 2.1.3 Sagnac-Laue Effect in a Medium 13 2.2 Active and Passive Ring Resonators 16 2.2.1 Ring-Laser Gyroscope 16 2.2.2 Resonant Fiber-Optic Gyroscope 20 2.3 Passive Fiber-Ring Interferometer 21 2.3.1 Principle of the Interferometric Fiber-Optic Gyroscope 21 2.3.2 Theoretical Sensitivity of the I-FOG 23 2.3.3 Noise, Drift, and Scale Factor 27 2.3.4 ARW Versus Root PSD 29 2.3.5 Evaluation of Noise and Drift by Allan Variance (or Allan Deviation) 36 2.3.6 Allan Variance/Deviation Versus Standard Variance/Deviation 41 2.3.7 Bandwidth 45 2.3.8 Various Functions of a Gyro: Attitude Measurement, Gyro Compassing, and Inertial Navigation 45 References 48 CHAPTER 3 Reciprocity of a Fiber Ring Interferometer 51 3.1 Principle of Reciprocity 51 3.1.1 Single-Mode Reciprocity of Wave Propagation 51 3.1.2 Reciprocal Behavior of a Beam Splitter 52 ix 77002211__LLeeffeevvrree__BBooookk..iinnddbb 99 1122//88//2211 1100::3377 AAMM