A gyro is a device that can measure the angular velocity with respect to an inertial frame. A fiber optic gyro (FOG), specifically, detects the rotation by measuring the Sagnac effect induced phase difference between the clockwise (CW) and counter clockwise (CCW) lightwaves that propagate inside a closed-loop formed with an optical fiber. FOGs have been under intense research and development since the 1970s, due to the fast development in low-loss optical fiber, solid-state semiconductor light source, and other optical components for telecommunication applications. FOGs show significant advantages over traditional spinning gyros with gimbals, bearings, and torque motors, especially in the aspects of short warm-up time, reliable operation, wide dynamic range, low power consumption, and etc. As a result, the FOG has paved its way for many successful commercial applications, such as aircraft navigation, rocket control, ship navigation, and etc. However, the applications are limited to the industrial grade (>10 o/h) and the inertial navigation grade (0.01~10 o/h). To produce superior grade models with sensitivity better than 0.01 o/h, further research about the FOG is needed.

There are three major types of FOGs: the interferometer fiber optic gyro (I-FOG), the resonator fiber optic gyro (R-FOG), and the Brillouin fiber optic gyro (B-FOG). The I-FOG measures the rotation by detecting the intensity of the interference signal between the two counter propagating lightwaves. The R-FOG, which utilizes a high finesse resonator as the sensing component, gauges the rotation by measuring the resonant frequency difference between the CW and the CCW lightwaves. The B-FOG extracts the rotation information by determining the lasing frequencies of two essentially independent counter propagating Brillouin lasers.

Although the I-FOG has achieved the highest performance among the three types of FOGs up to now, it suffers an inherent problem resulted from its use of a long fiber (~ km). Performance degradation due to the time-variant temperature distribution along the long fiber, called as the Shupe effect, becomes a bottleneck for the I-FOG's further upgrade. Besides, the wavelength stability and light intensity of semiconductor superluminescent diodes and fiber type broad-band light sources, which are used as I-FOGs' light sources, are inferior to laser sources. The R-FOG and the B-FOG, on the other hand, may have the capability to solve the inherent problems in the I-FOG. For example, theoretical analyses estimate that a 5 to 10 m long fiber is enough for the R-FOG to satisfy aircraft navigation requirement.

In practice, however, the performances achieved up to now for both the R-FOG and the B-FOG are still below expectation. For the R-FOG, countermeasures against performance degradation factors, such as the polarization-fluctuation induced drift caused by the existence of dual eigen-states of polarization (ESOP) in the resonator and by temperature-sensitive birefringence of the fiber, the backscattering, the optical Kerr effect caused by the nonlinearity of the fiber, the Shupe effect caused by temporally variant temperature distribution along the fiber coil, the Faraday effect, and other external fluctuation induced drifts, have to be further studied. For the B-FOG, the "lock-in" phenomenon, which indicates a zero output when the rotation rate is very small, and the instability of the lasing frequency are pointed out as major drawback that limit the performance of the B-FOG.

For the R-FOG, the recent advent of air-core photonic-bandgap fibers (PBFs) offers a radically new means for further reducing all of the above performance degradation factors simultaneously, as in a PBF the optical mode is mostly confined to the air core, whereas in a conventional fiber, the lightwave travels entirely through silica. Thus, by replacing the solid-core fiber with the PBF in the R-FOG, the R-FOG is still a promising candidate for high grade rotation sensing. Yet, before the PBF-based optical components are available, there still exist constant drives for further investigation and invention of engineering solutions for the remaining performance degradation factors.

As a countermeasure against multiple performance degradation factors in the R-FOG, a bipolar digital serrodyne phase modulation scheme has been invented. In this scheme, the laser frequency is locked to the resonant frequency of one of the CW or CCW sides by synchronously detecting the frequency component that the bipolar digital serrodyne waveform changes its slope with. Determined by the absolute value of the slope of the bipolar digital serrodyne waveform, the laser frequencies of the CW and the CCW sides can be shifted to different frequency bands such that the intensity contribution by the backscattered lightwave goes out of the detection band. Moreover, by precisely adjusting the amplitude of the bipolar digital serrodyne waveform to exact 2π, the interference signal between the CW and the CCW lightwaves is removed due to the suppressed carrier lightwave. Additionally, by modifying the slope of the bipolar digital serrodyne waveform, the intensity of the injected lightwaves can be adjusted; thus, the optical Kerr effect induced performance degradation is alleviated. Finally, the closed-loop operation can be achieved by using the bipolar digital serrodyne waveform adding an additional digital serrodyne waveform with smaller slopes to the original one to shift the laser frequency.

Most of above functions of performance degradation suppression realizable by the bipolar digital serrodyne phase modulation scheme call for the precise control of the waveform and careful designing of peripheral signal processing circuits. Up to now, they are realized by analogue or partially analogue circuits, which lack in accuracy, processing speed and convenience. Meanwhile, during the past decades, digital signal processing techniques have undergone tremendous developments, especially the field-programmable gated array (FPGA) technologies have exhibited higher precision, faster handling speed, and easier transforming to other platforms than the analogue circuits. Thus, in this thesis, to improve the performance of the R-FOG, the performance degradation factors in the R-FOG are studied, with countermeasures proposed and experimentally demonstrated by implementing an FPGA-based digital signal processor.

The structure of the thesis is stated below.

At first, the history of fiber optic gyros is reviewed in Chapter 1. Two important classes of gyros, the optical gyro and the MEMS gyro, are introduced. By studying the working principles, investigating the performance-limiting factors, and exploring the up-to-date applications, comparisons are drawn between several types of gyros. The study indicates that gyros are driven for technological breakthroughs towards improved stability, lower cost, smaller size and lighter weight. Besides, the purpose and the constitution of the thesis are also stated.

Next, the performance degradation factors in the R-FOG are summarized in Chapter 2, including the polarization fluctuation, the backscattering, the optical Kerr effect, the thermal fluctuation, the Faraday effect, and other external fluctuations. The corresponding engineering countermeasures are also presented. However, these elegant engineering solutions are not perfect. The performance achieved is still not satisfying. Thus, there is a trend to study the PBF-based R-FOG.

In Chapter 3, a passive method to suppress the polarization-fluctuation induced performance degradation using twin 90o polarization-axis rotated splicing scheme is analyzed, with the effect demonstrated experimentally. To begin with, the physical image of the eigen-state of polarization (ESOP) in R-FOG is introduced. Then, the principle of selective excitation of single ESOP in R-FOG with twin 90o polarization-axis rotated splicing is shown mathematically. Next, the polarization-fluctuation induced bias drift is estimated, especially for the case when polarization dependent loss (PDL) exists inside the resonator. Simulation results indicate that the twin 90o polarization-axis rotated splicing method can effectively suppress the polarization-fluctuation induced bias drift in the R-FOG, when the length difference of the fiber segments between the two splicing points (Δl) is set around a half of the beat-length of PMF (B/2). It is also shown that such an R-FOG is tolerant to PDL if the polarization crosstalk in the resonator is low. Then, experiments to demonstrate the effectiveness of the twin 90o polarization-axis rotated splicing method in suppressing the polarization-fluctuation induced performance degradation are carried out. A single ESOP is selectively excited for the first time using this method. Besides, significantly suppressed bias drift is observed with selective excitation of a single ESOP.

Then in Chapter 4, a method to automatically suppress the polarization-fluctuation in the R-FOG is proposed by adopting a resonator with twin 90o polarization-axis rotated splicing. Both theoretical analysis and experimental results demonstrate the effectiveness of the method. As shown in Chapter 3, to effectively suppress the polarization-fluctuation induced bias drift in the R-FOG, the length difference of the fiber segments between the two splicing points of an R-FOG with twin 90o polarization-axis rotated splicing should be set around a half of the beat-length of PMF. Although this ideal condition can be realized at the startup of the system, long term preservation cannot be guaranteed due to varied temperature around the fiber coil and the temperature sensitivity of the birefringence in PMF. To achieve high long-term bias stability, a scheme that can monitor the variation of Δl and hence suppress the polarization-fluctuation induced performance degradation is proposed, in which a feedback scheme is built up to fix Δl to B/2 to excite the wanted ESOP only (linear and polarized along the x-axis of PMF) with the error signal generated by inserting a y-axis polarizer in one output branch of the resonator. After demonstrating the effectiveness of the proposal numerically with a mathematical model based on Jones transfer matrix, experiments are carried out to compare the gyro bias drifts with the control loop on and off. Experimental results indicate that the bias stability is increased with polarization-fluctuation induced drift suppressed significantly.

In Chapter 5, the implementation of digital signal processing based on FPGA is introduced. At first, an overview of the multiple functions realized by the digital processor is presented. Then, as one of the functions, suppression of R-FOG performance degradation due to backscattering using the digital processor is discussed in detail. The digital processor is designed to automatically adjust the amplitude of the bipolar digital serrodyne phase modulation waveform applied to the CW and CCW lightwaves to exact 2π. Experimental results indicate significant suppression of bias drift resulted from the backscattering. Moreover, improved bias stability is realized experimentally by incorporating oversampling technique into the digital signal processing system. Further improvement is achieved with a newly proposed lock-in detection scheme using 90o out-of-phase reference signal.

Next, suppression of other external fluctuations induced performance degradation using the self-developed digital signal processor is shown in Chapter 6. The difference between the laser frequency and the resonator's resonant frequency fluctuates in two ways: the fast drift with small amplitude and the slow drift with large amplitude due to the thermal fluctuation and/or the mechanical vibration. The digital processor serves to suppress the fast-drift by a proportional controller with oversampling technique to reduce the quantization error and to track the slow drift using an up/down counter. Experimental results demonstrate the effectiveness of the digital processor in stabilizing both kinds of fluctuations. Improved laser frequency tracking precision by removing higher harmonic frequency noises is also realized experimentally.

As a final demonstration, a closed-loop R-FOG with all digital signal processing is presented in Chapter 7. The system adopts the bipolar digital serrodyne phase modulation scheme as a countermeasure against multiple performance degradation factors in the R-FOG. The FPGA based digital processor realizes not only the full operation of the bipolar digital serrodyne waveform but also other signal processing functions. The closed-loop operation is realized by adding an additional bipolar digital serrodyne waveform to the original waveform to maintain the laser frequencies of both the CW and the CCW sides operating at the resonator's resonant frequency.

Finally, the conclusions and the future prospects of the R-FOG are stated in Chapter 8.

本論文は、"Studies toward the Realization of Resonator Fiber Optic Gyro with All Digital Signal Processing (全ディジタル信号処理を指向した共振型光ファイバジャイロの実装法と性能向上)" と題し、英文で書かれていて、8章よりなる。光ファイバジャイロは慣性空間に対する回転センサであり、航空機や人口衛星の姿勢制御および航法、あるいは望遠テレビカメラのぶれ防止装置やヒューマノイドロボットの制御など、航空・宇宙応用から民生応用まで広範囲に活用できる可動部分のない光センサである。長尺光ファイバを比較的小半径のコイルにしたセンシング部を左右逆回りに伝搬する光波間には、サニャック効果によって、回転に比例した位相差が生じる。干渉計を構成してこの位相差を測定する「干渉型光ファイバジャイロ」は既に実用化が進んでいる。しかし、長尺となる光ファイバに沿う温度分布が時間的に変動すると大きな出力ドリフトが生じ、また各種雑音を低減するためにスペクトル線幅の広い光源を使用する必要があって中心波長の温度変動が大きく出力強度も不十分となり、これらが本ジャイロの高性能化を阻んでいる。そこで本論文では、干渉方式におけるこれらの問題を解決する可能性を有する「共振型光ファイバジャイロ」に関して、主要な雑音要因への対策を提案・実証するとともに、種々の雑音を低減して出力信号の高機能な処理をも実現するために全ディジタル信号処理の実装を指向したジャイロシステムの構成法を提案・研究している。

第1章は"Introduction"であり、本研究の背景や、光ファイバジャイロの研究の歴史とその方式分類を述べ、機械式ジャイロとの比較も行って、本技術領域における「共振型光ファイバジャイロ」の位置づけを明確化している。つづいて、本研究において基盤とするバイポーラディジタルセロダイン方式共振型光ファイバジャイロのコンセプトを述べて、本論文の構成を示している。

第2章は"Performance Degradation Factors and Countermeasures in the R-FOG"である。光ファイバ中での偏波状態変動、後方散乱、光カー効果、温度分布の時間変動、地磁気によるファラデー効果等、主要な性能制限要因について、これまでの研究成果を説明するとともに、これらへの対策として考案された方法とその問題点を述べている。また、最近開発が進んでいるフォトニックバンドギャップ光ファイバでは、光波は中空部分を伝搬するので、本質的に上記の雑音要因そのものの発生を低減できることも述べて、共振型光ファイバジャイロの研究を展開することの価値を説明している。

第3章は"Twin 90° Polarization-axis Rotated Splicing as a Countermeasure against Polarization-fluctuation Induced Performance Degradation"と題し、偏波維持光ファイバを用いた光ファイバリング共振器構成として、優れた安定性を示す方法を具体的に提案し、シミュレーションにより性能限界を明らかにするとともに、実験系を構成して機能実証にも成功している。偏波維持光ファイバの偏波軸を2箇所で90度捩って接続することにより、共振器を構成する。ここで、2分された光ファイバの長さの差を偏波維持光ファイバの複屈折長の半分とすることで安定な共振器特性が得られ、さらに偏波依存損失がジャイロ性能に大きく影響することも明らかにして、好ましい共振器構成を提案している。シミュレーションによって、本提案構成によれば、航空機の慣性航法用の性能(0.01度/時の感度)も達成できることが示された。

第4章では、"Automated Suppression of Polarization-Fluctuation Induced Performance Degradation in R-FOG with Twin 90° Polarization-axis Rotated Splicing"について、研究成果を述べている。第3章で述べたように、本共振器構成では、2分された光ファイバの長さの差を偏波維持光ファイバの複屈折長の半分に設定する必要がある。この長さは数mmであり、自動的に本条件を設定する手法の開発が必須である。本研究では、共振器からの出力光のある直線偏波成分を抽出することで、この長さの差を制御するための誤差信号が得られることを見い出した。この手法に関して、まずシミュレーションを行い、自動的に光ファイバ長の差を制御できることを示した。つづいて実験系を構成し、提案手法によって自動制御が可能であることを実証し、制御が稼働しているときに安定な偏波状態が維持され、またジャイロ性能も向上することを示している。

第5章は"Implementation of Digital Signal Processing and Suppression of R-FOG Performance Degradation due to Backscattering"である。本研究の基盤となっている「バイポーラディジタルセロダイン方式」は、光位相を階段状鋸歯状波によって変調することにり、光波周波数を等価的に変化させ、共振型光ファイバジャイロの性能制限要因を抑圧するとともに、ジャイロ出力の処理をも行う技術である。本論文では、この方式の機能向上を図る具体的な手法を提案して、それをFPGA (Field Programmable Gate Array) によって実装した。本章では、本FPGAによるディジタル信号処理によって、光ファイバ共振器中で生じる後方散乱による性能制限を回避する手法も、提案・実証された。光周波数を精緻に制御するためには、バイポーラディジタルセロダイン波形の振幅は2πでなければならない。この条件を自動的に実現するために、FPGAによるオーバサンプリング手法と利得可変アンプを用いた独自システムを提案して、その機能も実証した。また、本制御のための誤差信号の取得手法も新たに提案して、ジャイロ性能の向上に成功している。

第6章は"Suppression of Other External Fluctuations Induced Performance Degradation Using Digital Signal Processing"と題している。光源であるレーザの発振周波数を、光ファイバ共振器中を伝搬する一方の光の共振周波数に追尾させる必要がある。両周波数のずれは、バイポーラディジタルセロダイン波形による位相変調によって生じるジャイロ出力の変化から捉えられる。こ誤差信号をFPGAで処理して、レーザの発振周波数を制御した。振幅は大きいがゆっくりと変化する変動成分と、振幅は小さいが比較的早く変化する成分に対する自動制御ループを、それぞれFPGAに実装し、レーザ周波数を制御する技術を実現した。

第7章は"Demonstration of Closed-loop R-FOG with All Digital Signal Processing"である。第6章までに提案・実現したディジタルセロダイン方式共振型光ファイバジャイロの性能制限要因への対策と信号処理技術を全て含むジャイロ系に、さらにクローズドループ方式を導入した。航空機の慣性航法用などの高級用途には、6桁にも及ぶダイナミックレンジが要求される。これを実現するためには、左右両周り光を、ともに光ファイバ共振器の共振周波数に追尾させて、両光の共振周波数の差を測定する必要がある。これを実現する手法をクローズドループ方式と呼ぶ。本研究では、一方の光波はレーザの発振周波数を追尾させ、他方の光波はディジタルセロダイン波形を変形させることで中心周波数を等価的に変化させて、共振周波数を追尾させる。本研究ではこのための手法を提案し、やはりFPGA中に実装した。光ファイバ共振器を実際に回転させて、回転角速度の検出に成功している。

第8章は"Conclusions"であり、本論文の総括を述べ、残された課題と今後の展望についてまとめている。

以上、本論文は、共振型光ファイバジャイロの性能制限要因への対策とジャイロ出力信号の形成を全てディジタル信号処理によって実現することを指向しつつ、偏波変動による性能制限への対策の提案とその理論検討ならびに実証実験を行い、本対策の最適条件を自動的に実現する手法を提案・実証し、そのためのディジタル信号処理をFPGAによって実装して、後方散乱誘起雑音の低減法ならびに光源レーザを共振器の共振周波数に自動追尾させるためのディジタル信号処理も、それぞれ提案・実装した。さらに、これらの提案技術を全て含むジャイロ系において、高性能ジャイロにとって必須なクローズドループ方式の実現手法も提案して、やはりFPGAによってこれを実装し、回転角速度の検出にも成功したものであって、電子工学への貢献が少なくない。

よって本論文は博士(工学)の学位請求論文として合格と認められる。