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Optical Gyroscopes: Sensing Rotation Without Moving Parts Abstract Abstract The desire for accurate navigation has been one of the great technology drivers since ancient times. Astronomy, timekeeping, magnetic sensors, the GPS system, MEMs, and spinning- mass gyroscopes are all familiar methods to measure position. The sensing of rotation by Optical Gyroscopes: optical means was first demonstrated by Sagnac in 1913, and in 1925 Michelson and Gale measured the rotation of the Earth with a 2km loop interferometer. The Sagnac effect was relegated to being a physics curiosity, until the 1960s and the advent of the laser and optical Sensing Rotation fiber. One of the great achievements of navigation engineering was the harnessing of the Sagnac effect, to make practical and extremely sensitive yet rugged optical rotation sensors. Without Moving Parts The Sagnac effect is very small, and it is necessary to measure on the order of one part out of 1020 to reach high-accuracy requirements. The design and manufacturing of practical optical gyroscopes is a tour-de-force of physics and engineering. Basic concepts such as symmetry, relativity, and reciprocity, and considerable interdisciplinary effort are needed in order to create a design such that every perturbation cancels out except rotation. Optical gyroscopes, Robert Dahlgren and their research and production contracts, were an early driver for many ultra-high- performance optical technologies. Such commonplace items as low-scatter mirrors, ultrasonic Silicon Valley Photonics, Ltd. machining of glass, lithium niobate integrated optics, polarization-maintaining fiber, superluminescent and narrow-linewidth lasers found their first major applications and customers in these sensors. Presented to the IEEE SCV Preceding Image: Monolithic Ring Laser Gyro (MRLG). Copyright © 2000 LEOS & IMS 5/27/2003. Kearfott Guidance and Navigation Corporation. Reproduced with permission. Outline Gyroscope Basics • Gyroscope Basics and Applications • Gyroscope Specifications • Introduction to the Sagnac effect Input Axis (IA) • The Ring Laser Gyroscope • Rate Gyro: Measures angular velocity ? about IA T • Interferometric Fiber Optic Gyroscope • Rate-Integrating Gyro: Measures ??t • Accelerometer ?0 • Resonant Fiber Optic Gyroscope • Inertial Measurement Unit • Waveguide Laser Gyroscope – Three or more Gyros • Micro Optic Gyroscope – Three or more Accelerometers – Signal processing, navigation computer Types of Gyroscopes Gyro Application Space STRATEGIC NAV TACTICALTACTICAL LOW • Spinning-Mass gyroscope 10,000 Robotics, Flight control, – Exquisite single and dual-axis versions Tactical munitions 1000 missile torpedo, midcourse – Generally not a “strapdown” IMU AHRS guidane MEMS 100 • Vibratory gyroscope (Coriolis force) RLG FOG – Hemispherical, cylindrical, tuning-fork strategic air/land/sea 10 missile navigation, – MEMS gyroscope cruise missile MECH Submarine • Nuclear Magnetic Resonance 1 navigation • Optical Gyroscope 0.1 15 1.5 150 0.15 After John Elwell, 1500 0.015 Draper Lab. 0.0015 0.00015 0.000015 1 nautical MPH ?E 0.0000015 1 Important Concepts Optical Interferometer • Intertial Frame – Absolute reference system • Classic example of two precisely-aligned mirrors • Reciprocity having ideally 100% reflection, separated by L – Replace (t) with (-t) and (x,y,z) with (-x,-y,-z) • Under certain conditions, constructive interference • Symmetry of multiple reflections permits light to pass through • Transmission only for certain wavelengths ? – Exploited whenever possible ?/2 = L, ? = L, 3?/2 = L, 2? = L, ... • Special Theory of Relativity • Generally: m?/2 = L where m is an integer, and 8 – Light in vacuum travels at 3?10 meters/second propagation vector perpendicular to mirror coatings – Light speed is independent of velocity of source • There will be m “Standing Waves” of size ?/2 Circulation in Interferometers Stationary Inertial Frame = Null 2 Mirrors ? 3 Mirrors Re-circulating Waveguide CW photon CCW photon Light Two Independent • Both photons experience exactly the same time-of-flight, Two Independent Back Beams Circulating -and- Clockwise & Beams Circulating resulting in destructive interference at the starting point CW and CCW Forth Counterclockwise • Tcw = Tccw = 2?R/c where R is the radius CW and CCW light occupy same physical space • For optical fiber n ~ 1.5 and T ~ 5 microsecond/kilometer Rotating Inertial Frame Rotating Inertial Frame • Consider rotation rate to be ? – Units of radians/second, ? > 0 for clockwise CW photon • Rigorous approach requires use of General ? Relativity, beyond the scope of this talk CCW photon • Use a simplified approach – Calculate ?L and ?T – Refractive index = 1 • Both photons start at splice – Number of loops = 1 2 Rotating Inertial Frame ?11? 4? R2 4A ?T?2? R ??? ?2??2 ? ?c?R?c?R? ? cc CCW photon • Path Length: ?L = c?T = 4A?/c • Phase shift: ??? = (2?/?)?L = 8?A?/?c • Phase shift is measured in rotating frame CW photon – ? can be deduced by measuring ?? via fringe shift, without knowledge of the absolute reference frame • Example ? = 633nm, A = 100 cm2 (L ~ 35 cm) • Both photons start at splice -5 • Earth’s rate ?e = 7.3?10 radians/second • Splice point rotated ?T radians, at tangential velocity R? – ?L ~ 9.7 ?10-15 meters - a very small amount • Lcw = 2?R + R?Tcw cTcw – ?? ~ 9.6 ?10-8 radians - just to measure Earth! • Lccw = 2?R – R?Tccw cTccw – Need 1000? better than this for navigation. Ring Laser Gyroscope Ideally mirrors Zero- Expansion Ring Laser Gyroscope Material He-Ne mixture • 3 or more mirrors in a stable alignment • Sealed and filled with e.g. Helium and Neon • Electrical discharge excites Helium and Neon ions, producing a population inversion of excited states • These excited ions provide the gain medium • With feedback, lasing commences when gain > loss Ring Laser Gyro Block Ring Laser Gyro Schematic Readout Dither Mirror Motor Anode Anode PLC Mirror Concave Mirror Image courtesy SVP PZT Cathode 3 Lasing in a Ring Cavity Lock-In Effect in Optical Gyros • Two lasing beams of light Gyro Output vs. Rotation Rate – CW and CCW Slope = Scale factor K – Occupy the same physical space • Use readout optics to interfere CW and CCW • If stationary, beams have same wavelength ? (= c/ƒ) ????? ????? – Cavity length is the same for both directions – Null output when CW and CCW interfere ƒcw = ƒccw Lock-in Range • For negligible rotation, beams also have same ? – Lock-in effect, due to backscatter (coupled oscillator) • For rotation above a lock-in rate ? ƒ ? ƒ L cw ccw Gyroscope Output (Arbitrary Units) Maximum Dynamic Range – Beat frequency is observed ?ƒ = 4A?/?L Beat Frequencies RLG Readout Optics Detectors Corner • Several approaches to avoid lock-in Detectors Detectors Cube Beam- – Dither motor Prism splitter – Magnetic Mirror • Beat frequency ?ƒ = 4A?/?L Readout • In terms of phase shift Mirror • Unlike other mirrors, the readout mirror is designed to have < 100% – ?? = 2?(?ƒ)t = 8?A?t/?L reflectivity, along with a slight transmission factor • Example ? = 633nm, A = 100 cm2 (L ~ 35 cm) – This allows a small fraction of the circulating light to emit • Attempt to overlay CW and CCW beams – Optical frequency approximately ƒ = c/??? 4.74?1014 – Several approaches to achieve stable and robust implementation -5 • Earth’s rate ?e = 7.3?10 radians/second • Often uses 2 or more silicon photodetectors – ?ƒ ~ 13 Hertz • Followed by low-noise and low-drift electronic preamplification – ?? ~ 83t radians • Several signal processing approaches to extract ? from ?? Signal Processing Path Length Control Laser output power vs. PZT drive voltage Fringe Motion Split Detector VFSR • Fringe counting (1 fringe corresponds to ?? = 2?) • Laser power fluctuates as a function of cavity length – Since ? ? ??/t, fringe is ??? ???L/4A (5.5 ?-radians for 35cm) • Free Spectral Range FSR = c/nL ~ 860 MHz for 35 cm • Fringe counting + sub-fringe interpolation • One mirror pistons in and out several microns • Inverse tangent algorithm • Piezoelectric transducer precisely controls mirror position • Numerous digital techniques • Servo electronics stabilized cavity length 4 Miniature Ring Laser Gyroscope Miniature Ring Laser Gyroscope Temp & Concave Power Mirror Monitor Cathode Block Readout Cathode Mirror PLC Mirror Detector PZT Readout Optics Fill Tube (pinched off) Image courtesy SVP ~ 1 inch Anode Optical Contact Bonding Honeywell GG1342 RLG OCB Zero-order Fringe Newton’s Rings • Bonding mirrors to block without adhesive • Demanding flatness, roughness specifications • Ultra-clean assembly brings surfaces into contact – Newton’s rings observed, zero-order fringe is grey • If conditions are met, a slight pressure initiates bond – Van Der Waals force draws surfaces together if d is << 1 micron Image courtesy Honeywell • Ageing produces strong, permanent, hermetic seal Multiple Ring Laser Gyroscope Multiple RLG Block • Possible reduction from nine to six mirrors for 3- axis RLG Kearfott • Common block, gas reservoir, and cathode • Complex machining, but overall parts savings • Multiple scattering can cause interactions Image courtesy Springer-Verlag © 1993 Monolithic Ring Laser Gyro (MRLG). Copyright © 2000 Guidance and Navigation Corporation. Reproduced with permission. 5 Multiple RLG in Action Components • RLG block – Low-expansion material: ULE, Zerodur, or Cervit Kearfott – Filled with proprietary cocktail of He2 and Ne2 isotopes • Mirrors – Low scatter is important – May have path-length control • Readout Optics • Photodetectors • Dither motor • Anode/Cathode/Fill tube/Getters Monolithic Ring Laser Gyro (MRLG). Copyright © 2000 Guidance and
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