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Fiber Optic Gyroscopes

Fiber Optic Gyroscopes. by Sean Moultrie. Gyroscopes. Heart of Guidance, Control, and Navigation Systems Desired Properties low cost high precision high reliability low maintenance long life spans. Gyroscopes. Mechanical Ring Laser assumed active Fiber Optic assumed passive.

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Fiber Optic Gyroscopes

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  1. Fiber Optic Gyroscopes by Sean Moultrie

  2. Gyroscopes • Heart of Guidance, Control, and Navigation Systems • Desired Properties • low cost • high precision • high reliability • low maintenance • long life spans

  3. Gyroscopes • Mechanical • Ring Laser • assumed active • Fiber Optic • assumed passive

  4. Active vs Passive Laser Laser Active Passive

  5. Mechanical Gyroscopes • Discovered 1817 • Earth’s Rotation 1852 • electric motors 1860’s • Gyroscopic Inertia • conversation of angular momentum • Newton’s first law

  6. Mechanical Gyroscopes • Measurements • rotating disk provides reference plane

  7. Mechanical Gyroscope Drawbacks • Precision Moving Parts • friction • limited life span • cost • environment restrictions • Mature Technology

  8. Physical Optics • TEM Wave • Interference • In Phase Out of Phase

  9. Ring Laser Gyroscopes • Square or Triangle Cavity • Standing Wave Laser • Doppler Effect • (due to active construction)

  10. Ring Laser • Unique λ • multiple of OPL • Standing Wave Produced

  11. Ring Laser Gyroscope • Doppler Effect • red & blue shift • Output is Interfered

  12. Ring Laser Gyroscope • Interference • beating – chrono (not spatial) interference pattern • Period α Angular Velocity

  13. Beating • example #1 • 110Hz Magenta • 104Hz Cyan • chrono Interference

  14. Ring Laser Gyroscope Drawbacks • Lock In • desire to be monochromatic • Dither

  15. Fiber Optic Gyroscopes • History • Sagnac Interferometry • Sagnac Effect • Optical Fiber Waveguide • fiber optic theory • Sources of Error • Biasing

  16. History • Sagnac – 1913 • Michelson & Gale – 1925 • Laser – 1961 • mode locking • cavity • Macek & Davis - 1962 • Ring Laser • Vali & Shorhill – FOG - 1976

  17. Sagnac Interferometer

  18. Sagnac Interferometry • High Resolution • Phase Difference • Rotation

  19. Sagnac Effect • Horses on Rotating Track Race Track Race Track

  20. Sagnac Effect • Birds Flying Over Rotating Track Race Track Race Track

  21. Sagnac Interferometer

  22. Sagnac Effect • Assume Circular Cavity • τ = 2πR/c • τ = propagation time & R = cavity radius • Δτ = (2π+Ωτ)(R/c) - (2π-Ωτ)(R/c) • Ωτ = rotation per τ • Δτ = 4πR2Ω/c2 • for ω, Δφ = ωΔτ = 4πR2ωΩ/c2 • Fresnel-Fizeau Drag Effect

  23. Fiber Optics • Cylindrical Dielectric Waveguide

  24. Fiber Optics

  25. Snell’s Law • n1sin(θ1) = n2sin(θ2)

  26. Critical Angle • n1sin(θ1) = n2sin(θ2) • set θ2 = 90o • divide by n1 • sin(θ1) = n2/n1 • θ1 = arcsin(n2/n1) = θc

  27. Total Internal Reflection • For θ1 ≥ θc • θc = arcsin(n2/n1) • there can be no refraction • all light is reflected • n2 < n1 • θc increases as n2/n1 decreases

  28. Fiber Optics

  29. Optical Fiber as Medium • Closed Cavity Defined by Optical Fiber

  30. Optical Fiber as Medium • Stable Alignment • Coiling • increased sensitivity • smaller dimensions

  31. Advantages of Coiling Fiber • Δφ = 2πLDΩ/λc • L = length of fiber • D = diameter of coil • Ω = angular rotation • λ = vacuum wavelength • c = speed of light • Δφ = 8πANΩ/λc • A = are enclosed by coil • N = number of coils

  32. Sources of Error • Polarization • Backscattering • Faraday Effect

  33. Polarization • Two Degenerate Modes • Not Ideal • random birefringence • Stress • additional birefringence • Unequal Propagation Constants

  34. Polarization • 100’s of Radians Error • Polarizer • input • output

  35. Backscattering • Rayleigh • αλ-4 • Interfaces • normal: (n1-n2)2/(n1+n2)2 • Crosstalk • Short Coherence Source

  36. Faraday Effect • Magnetic Interference • rotation of polarization state • Untwisted Polarization-Maintaining Fiber

  37. Nonlinear Kerr Effect • Optical Induced Electric Field • n α local irradiance • Source • broad-band • low-coherence • unpolarized

  38. Biasing • Calibrated for Maximum Change in Intensity vs Rotation Rate

  39. Conclusion • Easy to Fabricate • Stable • No Moving Parts • Small Dimensions • High Sensitivity

  40. References • Sabina Merlo, Michele Norgia, and Silvano Donati, “Fiber Gyroscope Principles”, Handbook of Fibre Optic Sensing Technology, 2000 John Wiley & Sons Ltd. • Ralph A. Bergh, H. C. Lefevre, and Herbert J. Shaw, “An Overview of Fiber-Optic Gyroscopes”, Journal of Lightwave Technology, Vol. Lt-2, No. 2, April 1984. • E. J. Post, “Sagnac Effect”, Reviews of Modern Physics, Volume 39, Number 2, April 1967. • Jia-Ming Liu. Photonic Devices. Cambridge University Press, New York 2005. • Bahaa E. A. Saleh & Malvin Carl Teich, Fundamentals of Photonics. John Wiley & Sons, Inc. New York, 1991. • Wikipedia, http://en.wikipedia.org/wiki/Main_Page

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