Optical System Components for Navigation Grade Fiber Optic Gyroscopes

Transcription

1 Optical System Components for Navigation Grade Fiber Optic Gyroscopes Marcus Heimann 1, Maximilian Liesegang², Norbert Arndt-Staufenbiel 1, Henning Schröder 2, Klaus-Dieter Lang 1 1 Technical University of Berlin, Gustav-Meyer-Allee 25, Berlin, Germany 2 Fraunhofer IZM, Gustav-Meyer-Allee 25, Berlin, Germany ABSTRACT Interferometric fiber optic gyroscopes belong to the class of inertial sensors. Due to their high accuracy they are used for absolute position and rotation measurement in manned/unmanned vehicles, e.g. submarines, ground vehicles, aircraft or satellites. The important system components are the light source, the electro optical phase modulator, the optical fiber coil and the photodetector. This paper is focused on approaches to realize a stable light source and fiber coil. Superluminescent diode and erbium doped fiber laser were studied to realize an accurate and stable light source. Therefor the influence of the polarization grade of the source and the effects due to back reflections to the source were studied. During operation thermal working conditions severely affect accuracy and stability of the optical fiber coil, which is the sensor element. Thermal gradients that are applied to the fiber coil have large negative effects on the achievable system accuracy of the optic gyroscope. Therefore a way of calculating and compensating the rotation rate error of a fiber coil due to thermal change is introduced. A simplified 3 dimensional FEM of a quadrupole wound fiber coil is used to determine the build-up of thermal fields in the polarization maintaining fiber due to outside heating sources. The rotation rate error due to these sources is then calculated and compared to measurement data. A simple regression model is used to compensate the rotation rate error with temperature measurement at the outside of the fiber coil. To realize a compact and robust optical package for some of the relevant optical system components an approach based on ion exchanged waveguides in thin glass was developed. This waveguides are used to realize 1x2 and 1x4 splitter with fiber coupling interface or direct photodiode coupling. Keywords: fiber-optic gyroscope, inertial sensor, sagnac effect, rotation rate error, Superluminescent diode, erbium doped fiber laser, fiber-coil, quadrupole winding, FEM, thermal gradient, bias drift, linear regression, ion exchanged waveguide, waveguide splitter 1. INTRODUCTION For Inertial Measurement Units (IMU) the rotation rate and acceleration are most important measurement values for orientation in a multi-dimensional environment. These values allow the IMU to determine its six geographical degrees of freedom (x, y, z, χ, ψ, ω), the velocity in each dimensions (v x, v y, v z, v χ, v ψ, v ω ) and as well gravitational forces. The most important sensor component of an IMU is the gyroscope which measures the rotation rate. These gyroscopes are used as standalone sensor or combined with additional sensors in IMUs in the field of automotive, aviation and aerospace in manned and unmanned system. They can be used as backup system if primary navigation systems, like GPS or star camera (used in satellites), are inoperative. In the field of robotics and in picosatellites the gyroscopes are also used as primary navigation system. 1.1 Types of Gyroscopes The sensor principles of gyroscopes for rotation rate measurement base on different physical effects. These are the Gyroscopic Effect (mechanical) derived from the Newton s Second Law of Motion e.g. in Dry Tuned Gyros or Levitated Gyros, the Coriolis Effect (mechanical) e.g. in MEMS Gyros and the Sagnac Effect (optical) e.g. in fiber-optic gyroscopes [1]. These different types of gyroscopes offer a variety of measurement ranges and bias stability. Emerging Technologies in Security and Defence; and Quantum Security II; and Unmanned Sensor Systems X, edited by K. L. Lewis, R. C. Hollins, T. J. Merlet, M. T. Gruneisen, M. Dusek, J. G. Rarity, E. M. Carapezza, Proc. of SPIE Vol. 8899, 88991A 2013 SPIE CCC code: X/13/$18 doi: / Proc. of SPIE Vol A-1

2 High Bias Stability Gyroscope Bias Stability 100 /h 5 /h 1 /h 0.5 /h 0.1 /h 0.05 /h 0.01 /h /h Corresponding Grade Industrial Tactical Short Term Navigation High-End Navigation & Strategic Figure 1: application grades of gyroscopes Fiber-optic gyroscopes offer a high bias stability and low noise in combination with large measurement range. Due to their performance they are used for short term navigation and high-end navigation. 1.2 Sagnac Effect The Sagnac Effect is describe as a relativistic effect that occurs if two light signals travel counter-clockwise through an optical path e.g. fiber-coil. Case 1: describes a static system without any rotation, shown in Figure Input Signals CW CCW Start End Output Signal resulting interference signal Figure 2: Behavior of the interference signal if no rotation occurs (CW: clock wise, CCW: counter clock wise) Case 2: shows a system in rotation, Figure 3. Due to rotation of the optical path the light signal that is propagating in the same direction as the rotation (CW: clock wise) undergoes an extension of the path length. While in opposite direction (CCW: counter clock wise) a reduction of the path length occurs. - Input Signals CW Start Ω End 1 0,9 Output Signal resulting interference signal - CCW -0,9-1 Φ Figure 3: Behavior of the interference signal if a rotation occurs (CW: clock wise, CCW: counter clock wise) This leads to a phase shift between the counter propagation light signals and is described as [2]: Proc. of SPIE Vol A-2

3 Where is the length of the fiber, is the radius of the fiber-coil, is speed of light, wavelength of the system and the change in rotation angle. 1.3 Interferometric fiber-optic gyroscope Fiber-optic gyroscopes are divided into three groups. The resonant fiber-optic gyroscope (RFOG) has a fiber-ring as optical path which acts as a passive resonator. The Brillouin fiber-optic gyroscope (BFOG) has also a fiber-ring as optical path but with doped fiber in its center, that acts as active resonator. The third type is the interferometric fiberoptic gyroscope (IFOG) which has a fiber-coil with a length of a few hundred up to some thousand meters. The standard configuration for an IFOG is shown in Figure 4. When using a micro integrated optic chip (MIOC) the 1x2 and both modulators are integrated to one component. (1) source detector 2x1 1x2 modulator modulator fiber-coil Figure 4: standard configuration of an interferometric fiber-optic gyroscope 1.4 Requirements and constraints for gyroscopes in microsatellites at low Earth orbit Gyroscopes for applications in microsatellites at low Earth orbit have to work under harsh environmental conditions: temperature range between -40 C to +80 C and radiation dose up to 50 krad. Their life must reach more than 7 years. If the Gyroscope is used as secondary navigation system respectively backup solution there are high requirements to it specifications: measurement range of ±10 /s, angular random walk (ARW) less than / h per channel, bias drift less than 0.01 /h per channel and a scale factor less than 10 ppm per axis. Due to the compact dimension of microsatellites and their limited electrical power, the volume of a three-axis gyroscope is restricted to 700 cm³, a total mass of 1 kg and a maximum electrical power consumption of 8 W. 2. COMPARISON OF THE LIGHT SOURCES For an interferometric fiber-optic gyroscope a light source with a small coherence length is required to avoid noise effects due to optical nonlinearities. Super luminescence diode (SLD) or erbium-doped fiber sources (EDFS) are taken into account. Compared to a laser they have a broadband spectrum. EDFS have many advantages in stability of wavelength and optical power output compared to SLD [6]. For space applications radiation hard components are required for the gyroscope. EDFS have a mayor disadvantage under radiation due to their dopants. A degradation of the EDFS properties will occur over. SLDs show wavelength drift and power drift over temperature as well as a high degree of polarization. Also an inherent reinforcement of SLD due to back reflection of optical signals from optical path occurs. The measurements and components were done for the SLD DL-CS5403A from DenseLight Semiconductors. 2.1 Wavelength drift and power drift over temperature Due to a temperature gradient a change in optical power output as well as change in wavelength appears. The peak wavelength drift over a temperature range from 10 C to 35 C for DL-CS5403A is shown in Figure 5. A linear correlation is shown in this measurement range with a slope of nm/ C. Proc. of SPIE Vol A-3

4 i i Peak Wavelength in nm Temperature in C Figure 5: Peak Wavelength vs. Temperature of DL-CS5403A A wavelength drift and a power drift goes hand in hand. That is shown for three temperatures in Figure at 30 C at 25 C at 20 C Relative Intensity in % r. 1. i r. i i II r I r I ' 1580 rill' r Wavelength in nm i I 1620 Figure 6: Wavelength and power drift due to temperature of DL-CS5403A To compensate the influence of these drifts to the measured rotation rate of a gyroscope, the laser current controller and fiber Bragg grating are required. The optical power output of a SLD can be stabilized by using a monitor photodiode that is used as input value for a laser current controller. Also an arrangement with two fiber Bragg grating (FBG) coupled to two additional monitor photodiodes is required to determine the wavelength drift (Figure 7). eo C Relative Intensity in % FBG 1 FBG 2 Relative Intensity in % FBG 1 FBG J, 1050 Wavelength in nm Wavelength in nm Figure 7: Wavelength monitoring with fiber Bragg grating, optical signal for monitor photodiodes at 20 C (left), at 30 C (reight) Proc. of SPIE Vol A-4

5 The differential measured intensity at the FBGs and the controlling value of the laser current controller can be used to determine a wavelength and power drift of a characterized SLD. 2.2 Degree of polarization A SLD has a high degree of polarization (DOP) of around 95 %. To avoid any negative effects due to polarizationinduced dependencies of the measured rotation rate an all polarization maintaining fiber approach is suitable. In this approach all optic components are coupled with polarization maintaining fiber. Another approach is using a fiber depolarizer, also known as Lyot Depolarizator, to reduce the DOP of the SLD [7]. This allows using of single mode fiber s instead of significantly more expensive polarization maintaining fiber s for the 2x1. A normal Panda fiber with 125 µm cladding diameter is used. The fiber depolarizer consists of two pieces of this fiber, one part twice as long as the other. The tension zones of both fibers are turned 45 C in respect to each other (Figure 8). 45 Degree of Polarization (DOP) 2 % to 5 IDegree of Polarization (DOP) 95 % to 99 Figure 8: fiber depolarizer for SLD Table 1 shows that the DOP of the SLD is significantly reduced when using a total fiber length of 2.1 meter. Table 1: achieved DOP with fiber depolarizer 1/3 length in mm 2/3 length in mm DOP in % Inherent reinforcement The inherent reinforcement that leads to an intensity drift of the SLD occurs due to back reflection of optical signals from optical path. To avoid back reflection an optic isolator is used. In Figure 9 the customized design of the optical path of a gyroscope is shown with source monitoring and MIOC as integrated component. source isolator 1x2 detector 1x2 2x1 FBG with monitor photodiode FBG with monitor photodiode MIOC 1x2 modulator modulator fiber-coil Figure 9: customized design for source monitoring Proc. of SPIE Vol A-5

6 3. CALCULATION AND REGRESSION OF THERMALLY INDUCED ROTATION RATE ERRORS IN FIBER OPTIC GYROSCOPES Working conditions of gyroscopes often include high thermal gradients. These gradients severely affect accuracy and stability of the fiber-coil, which is the sensor element [4]. To eliminate measurement instability, the propagation of thermal gradients through the fiber-coil must be simulated and estimated with live measurable data. As the split optical waves propagate in both directions of the fiber, each wave experiences an alternating refractive index. Their difference in propagation results in a phase shift which can t be separated from the phase shift due to the Sagnac Effect. This has been addressed by a number of works since the mid-1960s. An approach by F. Mohr in 1996s Journal of Lightwave Technology [3] established a calculation of the measured rotation due to thermal gradients to be derived from the thermal gradient each layer of fiber experiences as the light wave propagates around the coil in the winding scheme of. ( ) { ( ) ( )} (2) With The approach states a variation of the error signal correlating to the position of the layer, the term ( ) can be replaced with a two-dimensional matrix of winding-correction factors ranging from -1 to 1 depending on the distance of layer from the fiber center. The calculation shall divide the fiber in pieces, hence. As both layers and turns of the fiber contribute in this order, has both x- and y-coordinates. Due to the fact that a fiber coil is designed to have very low thermal conductivity, a scalar correction factor for the fiber coil section of interest must be added. ( ) ( ) { ( ) } (3) 3.1 Verification of the model The thermal gradients can be extracted from a finite element simulation. To verify the method with actual measurement, the 1996 experiment of [3] is reconstructed. The experiment uses a fiber with 52 turns and layers, potted and laid flat on a styrofoam surface. A heating foil is brought to the inside of the fiber coil (Figure 10). o opos ODOM 0) Figure 10: reconstructed fiber coil from experiment [3] in two models: full (left) and slice (right) The thermal data from the slice model is extracted and used to calculate ( ). The correction factor for thermal conductivity is estimated to be 0.53 as slightly more than half the fiber coil actually undergoes thermal change. The thermal Matrix is now combined with the two-dimensional winding scheme of the coil. Proc. of SPIE Vol A-6

7 With the modified approach, the rotation rate error simulated compares to the one measured as in Figure o rotation rate error in /h J20 J00 20 quadrupole dnsquilme micrinu0 winding inuquacpe Adyciinu0 cylindric winding rotation rate error in /h C 13 quadrupole winding.200 JO J J in s in s Figure 11: simulated (solid) and measured (red marks) rotation rate error due to thermal change in a fiber coil with cylindrical (left) and quadrupole (right) winding As seen in Figure 11, peak value and variation over of the experimental data are consistent with the calculations. 3.2 Prediction and regression A scenario for a satellite-application of a test coil is used to estimate accuracy grade for the coil. The coil has 116 turns on its base layer with 20 layers total. The fiber is potted with a thermally low conductive epoxy and mounted on an aluminum L-shape support spool. Its worst case scenario is depicted as a rise in temperature of 5 K/min between 233 and 333 Kelvin. A multiple linear regression model using 4 measurement points at each side of the coil shall provide a regression for the simulated case. Each thermal probe is located in the middle of the surface with an approximated measurement speed of 8 sample/sec and an accuracy of 0.01 K (Figure 12). T 1 support spole winded fiber-coil T 4 T 2 T 3 Figure 12: section of wound fiber-coil with temperature sensors Regression parameters include only differences of thermal gradients of each side. Proc. of SPIE Vol A-7

8 ( ) (4) With rotation rate error in /h 7,00 5,00 3,00 1,00-1,00 in s Figure 13: rotation rate error of the fiber-coil: simulated (blue), multiple linear regression (red) and difference (green) As seen in Figure 13, a multiple linear regression can be used to eliminate the rotation rate error of a fiber-coil due to thermal change to about 20 % of its original value. 4. ION EXCHANGE WAVEGUIDES FOR INTEGRATED COUPLER The limited electrical power for a gyroscope that is available in a microsatellite leads to the necessity of saving energy especially if the rotation rate is measured for three dimensions. Therefor a smart approach is using one light source for three to four gyroscopes that are arranged in a rectangular or tetrahedron setup (Figure 14). Figure 14: rectangular (left) and tetrahedron (right) setup with gyroscopes for three dimensional rotation rate measurement To couple one light source to three or four optic paths of a gyro, shown in Figure 4, a 1x3 respectively a 1x4 couple is required. These can be manufactured with ion exchanged waveguide in thin display glass like D 263 T eco by Schott [5]. A 1x4 integrated waveguide based on two cascades of Y-bench with straight waveguides followed by two s-bends (Figure 15). Proc. of SPIE Vol A-8

9 Figure 15: 1x4 based on two cascades of Y-bench with straight waveguides followed by two s-bends The angular A between the straight waveguides is 1 deg. The radius R of the s-bends is 40 mm. Straight waveguides and s-bends have a length L of 13.2 mm. That results in a final pitch of 250 µm between each of the four outputs. An extinction loss of less than 1.7 db and a propagation loss of less than 0.5 db/cm were achieved at 1550 nm wavelength. 5. CONCLUSION An all PM-Fiber gyroscope was developed. Optic isolators and fiber Bragg gratings are used to achieve a higher stability of the SLD. A simulation standard to calculate the rotation rate error caused by thermal gradients in a fiber optic gyroscope coil was derived. The method and models used to simulate the propagation of thermal waves in a fiber optic coil comply with measured data, verifying the approach. Predictions about a fiber-coil in use are made. A simple regression model based on live measurable data is used to compensate the rotation rate error. An energy efficient approach with integrated waveguide s for gyroscopes in microsatellites was shown. REFERENCES [1] Bosgiraud, T., Two Degrees of Freedom Miniaturized Gyroscope based on Active Magnetic Bearings, Thesis No at École Polytechnique Fédérale de Lausanne (2008) [2] Sagnac, G., Sur la preuve de la réalité de l éther lumineux par l expérience de l interférographe tournant, Comptes rendus de l'academie des Sciences, Vol. 95, pp (1913) [3] Mohr, F., "Thermooptically induced Bias Drift" Journal of Lightwave Technology 14(1), p27-41 (1996) [4] Shupe, D., Thermally induced nonreciprocity in the fiber-optic interferometer, Journal of Applied Optics Vol. 19(5), p.654 (1980) [5] Schott AG, Germany Product Information D 263 T eco Thin Glass (25 August 2013) [6] Seidel, C., Optimierungsstrategie für faseroptische Rotationssensoren: Einfluss der spektralen Eigenschaften der Lichtquelle Dissertation at University Fridericiana Karlsruhe, Germany (2004) [7] Nayak, J., Design, fabrication and testing of high performance fiber optic depolarizer (2004) Proc. of SPIE Vol A-9