the FIBER-OPTIC GYROSCOPE.

The Fiber-Optic Gyroscope,
Third Edition
	Contents
	Foreword
	Preface to the First Edition
	Preface to the Second Edition
	Preface to the Third Edition
	Chapter 1 Introduction
		References
	Chapter 2
Principle of the Fiber-Optic Gyroscope
		2.1 Sagnac-Laue Effect
			2.1.1 A History of Optics from Aether to Relativity
			2.1.2 Sagnac-Laue Effect in a Vacuum
			2.1.3 Sagnac-Laue Effect in a Medium
			2.2 Active and Passive Ring Resonators
				2.2.1 Ring-Laser Gyroscope
				2.2.2 Resonant Fiber-Optic Gyroscope
		2.3 Passive Fiber-Ring Interferometer
			2.3.1 Principle of the Interferometric Fiber-Optic Gyroscope
			2.3.2 Theoretical Sensitivity of the I-FOG
			2.3.3 Noise, Drift, and Scale Factor
			2.3.4 ARW Versus Root PSD
			2.3.5 Evaluation of Noise and Drift by Allan Variance (or Allan Deviation)
			2.3.6 Allan Variance/Deviation Versus Standard Variance/Deviation
			2.3.7 Bandwidth
			2.3.8 Various Functions of a Gyro: Attitude Measurement, Gyro Compassing,and Inertial Navigation
		References
	Chapter 3
Reciprocity of a Fiber Ring Interferometer
		3.1 Principle of Reciprocity
			3.1.1 Single-Mode Reciprocity of Wave Propagation
			3.1.2 Reciprocal Behavior of a Beam Splitter
		3.2 Minimum Configuration of a Ring Fiber Interfero
			3.2.1 Reciprocal Configuration
			3.2.2 Reciprocal Biasing Modulation-Demodulation
			3.2.3 Proper (or Eigen) Frequency
		3.3 Reciprocity with All-Guided Schemes
			3.3.1 Evanescent-Field Coupler (or X-Coupler or Four-Port Coupler)
			3.3.2 Y-Junction
			3.3.3 All-Fiber Approach
			3.3.4 Hybrid Architectures with Integrated Optics:Y-Coupler Configuration
		3.4 Problem of Polarization Reciprocity
			3.4.1 Rejection Requirement with Ordinary Single-Mode Fiber
			3.4.2 Use of Polarization-Maintaining (PM) Fiber
			3.4.3 Use of Depolarizer
			3.4.4 Use of an Unpolarized Source
		References
	Chapter 4
Backreflection and Backscattering
		4.1 Problem of Backreflection
			4.1.1 Reduction of Backreflection with Slant Interfaces
			4.1.2 Influence of Source Coherence
		4.2 Problem of Backscattering
			4.2.1 Coherent Backscattering
			4.2.2 Use of a Broadband Source
			4.2.3 Evaluation of the Residual Rayleigh Backscattering Noise
		References
	Chapter 5
Analysis of PolarizationNonreciprocities with BroadbandSource and High-BirefringencePolarization-Maintaining Fiber
		5.1 Depolarization Effect in High-BirefringencePolarization-Maintaining Fibers
		5.2 Analysis of Polarization Nonreciprocities in a Fiber GyroscopeUsing an All-Polarization-Maintaining Waveguide Configuration
			5.2.1 Intensity-Type Effects
			5.2.2 Comment About Length of Depolarization Ld Versus Length ofPolarization Correlation Lpc
			5.2.3 Amplitude-Type Effects
		5.3 Use of a Depolarizer
		5.4 Testing with Optical Coherence Domain Polarimetry (OCDP), orToday, Distributed Polarization Crosstalk Analysis (DPXA)
			5.4.1 OCDP, or DPXA, Based on Path-Matched White-Light Interferometry
			5.4.2 OCDP/DPXA Using Optical Spectrum Analysis
		References
	Chapter 6
 Time-Transience Related Nonreciprocal Effects
		6.1 Effect of Temperature Transience: The Shupe Effect
		6.2 Symmetrical Windings
		6.3 Strain-Induced T-Dot Effect
		6.4 Basics of Heat Diffusion and Temporal Signature of the Shupe and
T-Dot Effects
		6.5 Case of a Sinusoidal Temperature Variation
		6.6 Simple Model of Thermally-Induced Differential Strainsin a Self-Standing Coil
			6.6.1 Reminders About the Theory of Elasticity
			6.6.2 Effect of the Fiber Coating
			6.6.3 Simple Model of a Free-Standing Coil
		6.7 Simple Viewing of Symmetrical Windings with the Thermally-Induced Differential Strains
		6.8 Orthocyclic Winding for Hexagonal Close Packing
		6.9 Effect of Acoustic Noise and Vibration
		References
	Chapter 7
Truly Nonreciprocal Effects
		7.1 Magneto-Optic Faraday Effect
		7.2 Axial Magneto-Optic Effect
		7.3 Nonlinear Kerr Effect
		References
	Chapter 8
Scale Factor Linearity and Accuracy
		8.1 Problem of Scale Factor Linearity and Accuracy
		8.2 Closed-Loop Operation Methods to Linearize Scale Factor
			8.2.1 Use of a Frequency Shift
			8.2.2 Use of an Analog Phase Ramp (or Serrodyne Modulation)
			8.2.3 Use of a Digital Phase Ramp
			8.2.4 All-Digital Closed-Loop Processing Method
			8.2.5 Control of the Gain of the Modulation Chain with “Four-State”Modulation
			8.2.6 Potential Spurious Lock-In (or Deadband) Effect
		8.3 Scale Factor Accuracy
			8.3.1 Problem of Scale Factor Accuracy
			8.3.2 Wavelength Dependence of an Interferometer Response with a
Broadband Source
			8.3.3 Effect of Phase Modulation
			8.3.4 Wavelength Control Schemes
			8.3.5 Mean Wavelength Change with a Parasitic Interferometeror Polarimeter
		References
	Chapter 9 Recapitulation of the Optimal Operating Conditions and Technologies of the I-FOG
		9.1 Optimal Operating Conditions
		9.2 Broadband Source
			9.2.1 Superluminescent Diode
			9.2.2 Rare-Earth Doped Fiber ASE Sources
			9.2.3 Excess RIN Compensation Techniques
		9.3 Sensing Coil
		9.4 “Heart” of the Interferometer
		9.5 Detector and Processing Electronics
		9.6 Summary of the Various Noises
		9.7 Thermal Phase Noise (Optical Nyquist Noise)
		References
	Chapter 10
Alternative Approaches for the I-FOG
		10.1 Alternative Optical Configurations
			10.1.1 Use of a [3 × 3] Coupler
			10.1.2 Use of a Quarter-Wave Plate
			10.1.3 Use of a Laser Diode
		10.2 Alternative Signal Processing Schemes
			10.2.1 Open-Loop Scheme with Use of Multiple Harmonics
			10.2.2 Second Harmonic Feedback
			10.2.3 Gated Phase Modulation Feedback
			10.2.4 Heterodyne and Pseudo-Heterodyne Schemes
			10.2.5 Beat Detection with Phase Ramp Feedback
			10.2.6 Dual Phase Ramp Feedback
		10.3 Extended Dynamic Range with Multiple Wavelength Source
		References
	Chapter 11
Resonant Fiber-Optic Gyroscope
		11.1 Principle of Operation of an All-Fiber Ring Cavity
		11.2 Signal Processing Method
		11.3 Reciprocity of a Ring Fiber Cavity
			11.3.1 Introduction
			11.3.2 Basic Reciprocity Within the Ring Resonator
			11.3.3 Excitation and Detection of Resonances in a Ring Resonator
		11.4 Other Parasitic Effects in the R-FOG
		Acknowledgment
		References
	Chapter 12
Conclusions
		12.1 The State of Development and Expectations in 1993
		12.2 The State of the Art, Two Decades Later, in 2014, for the
Second Edition
			12.2.1 FOG Versus RLG
			12.2.2 FOG Manufacturers, in 2014
		12.3 The State of the Art, Today, in 2021
		12.4 Trends for the Future and Concluding Remarks
		References
	Appendix A
Fundamentals of Opticsfor the Fiber Gyroscope
		A.1 Basic Parameters of an Optical Wave: Wavelength,Frequency, and Power
		A.2 Spontaneous Emission, Stimulated Emission, and Related Noises
			A.2.1 Fundamental Photon Noise
			A.2.2 Spontaneous Emission and Excess Relative Intensity Noise
			A.2.3 Resonant Stimulated Emission in a Laser Source
			A.2.4 Amplified Spontaneous Emission
		A.3 Propagation Equation in a Vacuum
		A.4 State of Polarization of an Optical Wave
		A.5 Propagation in a Dielectric Medium
			A.5.1 Index of Refraction
			A.5.2 Chromatic Dispersion, Group Velocity, and Group Velocity Dispersion
			A.5.3 E and B, or E and H?
		A.6 Dielectric Interface
			A.6.1 Refraction, Partial Reflection, and Total Internal Reflection
			A.6.2 Dielectric Planar Waveguidance
		A.7 Geometrical Optics
			A.7.1 Rays and Phase Front
			A.7.2 Plane Mirror and Beam Splitte
			A.7.3 Lenses
		A.8 Interferences
			A.8.1 Principle of Two-Wave Interferometry
			A.8.2 Most Common Two-Wave Interferometers:Michelson and Mach-Zehnder Interferometers, Young Double-Slit
			A.8.3 Channeled Spectral Response of a Two-Wave Interferometer
		A.9 Multiple-Wave Interferences
			A.9.1 Fabry-Perot Interferometer
			A.9.2 Ring Resonant Cavi
			A.9.3 Multilayer Dielectric Mirror and Bragg Reflector
			A.9.4 Bulk-Optic Diffraction Grating
		A.10 Diffraction
			A.10.1 Fresnel Diffraction and Fraunhofer Diffraction
			A.10.2 Knife-Edge Fresnel Diffraction
		A.11 Gaussian Beam
		A.12 Coherence
			A.12.1 Basics of Coherence
			A.12.2 Mathematical Derivation of Temporal Coherence
			A.12.3 Concept of Wave Train
			A.12.4 Case of an Asymmetrical Spectrum
			A.12.5 Case of Propagation in a Dispersive Medium
		A.13 Birefringence
			A.13.1 Birefringence Index Difference
			A.13.2 Change of Polarization with Birefringence
			A.13.3 Interference with Birefringence
		A.14 Optical Spectrum Analysis
		Bibliography
	Appendix B Fundamentals of Fiber-Optics for the Fiber-Gyroscope
		B.1 Main Characteristics of a Single-Mode Optical Fiber
			B.1.1 Attenuation of a Silica Fiber
			B.1.2 Gaussian Profile of the Fundamental Mode
			B.1.3 Beat Length and h Parameter of a PM Fiber
			B.1.4 Protective Coating
			B.1.5 Temperature Dependence of Propagation in a PM Fiber
		B.2 Discrete Modal Guidance in a Step-Index Fiber
		B.3 Guidance in a Single-Mode Fiber
			B.3.1 Amplitude Distribution of the Fundamental LP01 Mode
			B.3.2 Effective Index neff and Phase Velocity vϕ of the Fundamental LP01 Mode
			B.3.3 Group Index ng of the Fundamental LP01 Mode
			B.3.4 Case of a Parabolic Index Profile
			B.3.5 Modes of a Few-Mode Fiber
		B.4 Coupling in a Single-Mode Fiber and Its Loss Mechanisms
			B.4.1 Free-Space Coupling
			B.4.2 Misalignment Coupling Losses
			B.4.3 Mode-Diameter Mismatch Loss of LP01 Mode
			B.4.4 Mode Size Mismatch Loss of LP11 and LP21 Modes
		B.5 Birefringence in a Single-Mode Fiber
			B.5.1 Shape-Induced Linear Birefringence
			B.5.2 Stress-Induced Linear and Circular Birefringence
			B.5.3 Combination of Linear and Circular Birefringence Effects
		B.6 Polarization-Maintaining Fibers
			B.6.1 Principle of Conservation of Polarization
			B.6.2 Residual Polarization Crossed-Coupling
			B.6.3 Depolarization of Crossed-Coupling with a Broadband Source
			B.6.4 Polarization Mode Dispersion
			B.6.5 Polarizing Fiber
		B.7 All-Fiber Components
			B.7.1 Evanescent-Field Coupler and Wavelength Multiplexer
			B.7.2 Piezoelectric Phase Modulator
			B.7.3 Polarization Controller
			B.7.4 Lyot Depolarizer
			B.7.5 Fiber Bragg Grating
		B.8 Pigtailed Bulk-Optic Components
			B.8.1 General Principle
			B.8.2 Optical Isolator
			B.8.3 Optical Circulator
		B.9 Rare-Earth–Doped Amplifying Fiber
		B.10 Microstructured Optical Fiber
		B.11 Nonlinear Effects in Optical Fibers
		Bibliography
	Appendix C
Fundamentals of Integrated Opticsfor the Fiber-Gyroscope
		C.1 Principle and Basic Functions of LiNbO3 Integrated Optics
			C.1.1 Channel Waveguide
			C.1.2 Coupling Between an Optical Fiber and an Integrated-Optic Waveguide
			C.1.3 Fundamental Mode Profile and Equivalence with an LP11 Fiber Mode
			C.1.4 Mismatch Coupling Attenuation Between a Fiber and a Waveguide
			C.1.5 Low-Driving–Voltage Phase Modulator
			C.1.6 Beam Splitting
			C.1.7 Polarization Rejection and Birefringence-Induced Depolarization
		C.2 Ti-Indiffused LiNbO3 Integrated Optics
			C.2.1 Ti-Indiffused Channel Waveguide
			C.2.2 Phase Modulation and Metallic-Overlay Polarizer with
Ti-Indiffused Waveguide
		C.3 Proton-Exchanged LiNbO3 Integrated Optics
			C.3.1 Single-Polarization Propagation
			C.3.2 Phase Modulation in Proton-Exchanged Waveguide
			C.3.3 Theoretical Polarization Rejection of a Proton-ExchangedLiNbO3 Circuit
			C.3.4 Practical Polarization Rejection of Proton-Exchanged LiNbO3 Circuit
			C.3.5 Improved Polarization Rejection with Absorbing Grooves
		Bibliography
	Appendix D
Electromagnetic Theory of the Relativistic Sagnac Effect
		D.1 Special Relativity and Electromagnetism
		D.2 Electromagnetism in a Rotating Frame
		D.3 Case of a Rotating Toroidal Dielectric Waveguide
		Bibliography
	Appendix E
Basics of Inertial Navigation
		E.1 Introduction
		E.2 Inertial Sensors
			E.2.1 Accelerometers (Acceleration Sensors)
			E.2.2 Gyroscopes (Rotation-Rate Sensors)
			E.2.3 Classification of Inertial Sensor Performance
		E.3 Navigation Computation
			E.3.1 A Bit of Geodesy
			E.3.2 Reference Frame
			E.3.3 Orientation, Velocity, and Position Computation
			E.3.4 Altitude Computation
		E.4 Attitude and Heading Initialization
			E.4.1 Attitude Initialization
			E.4.2 Heading Initialization
		E.5 Velocity and Position Initialization
		E.6 Orders of Magnitude to Remember
		Bibliography
	List of Abbreviations
	List of Symbols
	About the Author
	Index