Transient response of a resonator fiber optic gyro with triangular wave phase modulation

We present an in-depth analysis of the transient response of a resonator fiber optic gyro based on triangular wave phase modulation. Unusual effects have been observed in the process of tracking the resonant frequency of an optical fiber ring resonator (OFRR). There is a distortion phenomenon, unlike the ideally square wave or a pure DC output of the OFRR, but signal overshoot or undershoot occurs. A deep analysis of the influence of the nonideal square wave or pure DC output on gyro performance is fully developed for the first time, to the best of our knowledge. Further analysis shows that this is the transient response process after modulation by the triangular wave, and the process is related both to the parameters of the OFRR and the modulation frequency of the triangular wave. By sampling the steady-state signal of the distortion square wave, or by oversampling the distortion signal to get a number of data, and then accumulating and averaging these data to be demodulated, the distortion's effect can be considerably decreased.     

基于锁相环的解调技术研究

介绍了调相信号的锁相解调技术基本原理以及利用集成锁相环NE564实现对信号的锁相解调。为了解调出不失真的波形,利用集成锁相环NE564和LM725CN芯片设计PM调制解调系统,可以直接实现信号的调制解调功能,利用相位能稳定跟踪的特点避免了频率失锁的缺陷,提高了测量精度。该系统具有操作简单、稳定性强的优点,并在激光外差干涉信号的解调中具有较强的实用性。     

Resonance asymmetry induced bias errors in waveguide type optical passive resonator gyro

We present an in-depth analysis of the resonance asymmetry in a silica waveguide ring resonator (WRR) and its influence on the waveguide-type optical passive resonator gyro (OPRG). A big bias error appears at the output of the OPRG. This big error is caused not only by the resonance asymmetry in the WRR, but also by the modulation parameters in the phase modulation spectroscopy technique (PMST). It has been proved that the bias error is proportional to the modulation frequency difference between the clockwise (CW) and counterclockwise (CCW) lightwaves. Three types of resonance asymmetries are thoroughly introduced and discussed. Methods to overcome the big bias error are demonstrated. A high reciprocal resonator is crucial to reduce the bias error. For a certain resonator, a proper temperature needs to be set to minimize the resonance asymmetry. A proper modulation frequency difference between the CW and CCW lightwaves is also helpful to reduce the bias error.     

Expansion of linear range of Pound-Drever-Hall signal

We propose new solutions for expanding the linear signal range between the laser frequency deviation (or mirror position) and the voltage signal derived by the Pound-Drever-Hall (PDH) method for optical Fabry-Perot cavity resonance control. One solution is to perform not in-phase demodulation but near-Q-phase demodulation. Another solution is to take a suitable combination of signals demodulated by odd-harmonic modulation frequencies in the in phase. Although the PDH signal sensitivity will be diminished, the PDH signal linear range can be extended. From a practical standpoint, it is desirable that a sideband frequency for the PDH method is near the FP cavity resonance.     

Y波导残余强度调制对IFOG性能的影响

本文首先通过正弦波调制下干涉信号光强分析解调出光纤陀螺的输出信号,进而得出残余强度调制存在的情况下陀螺输出信号的变化情况,同时,通过分析陀螺信号的变化说明残余强度调制对光纤陀螺性能的影响与陀螺精度要求有关,精度越高,其影响越明显.其次,具体分析了数字闭环光纤陀螺受残余强度调制影响的情况下,其解调输出电压变化引起的数字阶梯高度变化,并通过残余强度调制系数与数字阶梯高度的关系式,说明了残余强度调制对光纤陀螺零偏和标度因数的影响.最后,对所得出的残余强度调制系数与光纤陀螺标度因数稳定性的关系进行了Matlab仿真,通过仿真结果,更进一步说明残余强度调制对数字闭环光纤陀螺标度因数稳定性的影响.     

调相信号的数字化解调

通过单周期正弦波曲线模型的滑动拟合法,获得正弦序列的瞬时频率信息,使用对瞬时频率的积分运算,实现了正弦载波相位调制信号波形的精确解调.在调制信号是方波的情况下,给出了相位解调的仿真结果和其它参数的波动情况;在1个实测调相曲线波形上进行的解调分析,给出了相位调制波形的解调结果;在调制信号也是正弦波的情况下,给出了解调失真的计算方法和结果.本方法用于评价载波为正弦波的调相信号时,具有准确度高、分辨力高的特点,可用于调相信号源及其解调设备的指标评价和计量测试.     

Single actuator alignment control for improved frequency stability of a cavity-based optical frequency reference

We demonstrate a method of controlling the alignment of a laser beam to a Fabry-Perot resonator through synchronous detection of the misalignment arising from modulating the orientation of a single beam-steering mirror. The horizontal and vertical tilt of the mirror are modulated in quadrature to drive a circular motion of the beam orientation. A corresponding modulation of the intensity of the optical field circulating in the cavity is measured at either the reflected or transmitted port and demodulated synchronously to derive two error signals to indicate the vertical and horizontal misalignment. These signals are fed back to the beam-steering mirror to suppress fluctuations below 30 Hz. This method avoids the complexity of monitoring off-axis cavity modes and is particularly effective in the case where unwanted pointing fluctuations are introduced by one or two elements in the optical setup. We have applied the technique to two Fabry-Perot resonators in use as precision frequency references, delivering a result of 10 dB suppression of alignment fluctuations at 1 Hz and an improvement in frequency stability by up to a factor of 4.     

Characterization technique of optical whispering gallery mode resonators in the microwave frequency domain for optoelectronic oscillators

Optical Q factor measurements are performed on a whispering gallery mode (WGM) disk resonator using a microwave frequency domain approach instead of using an optical domain approach. An absence of hysteretic behavior and a better linearity are obtained when performing linewidth measurements by using a microwave modulation for scanning the resonances instead of the piezoelectric-based frequency tuning capability of the laser. The WGM resonator is then used to stabilize a microwave optoelectronic oscillator. The microwave output of this system generates a 12.48 GHz signal with -94 dBc/Hz phase noise at 10 kHz offset.     

Optical modulation techniques for length sensing and control of optical cavities

We present a discussion of the use of amplitude modulation techniques with regard to the length sensing and control of optical cavities for laser interferometric gravitational-wave detectors. Traditional radio-frequency amplitude modulation techniques automatically include phase modulation as a product of the modulation process, which can contaminate the signal after demodulation. In particular, with many length-sensing and control schemes the detected signals are demodulated in quadrature, which, in the case of a traditional amplitude modulation scheme, will result in offsets due to the additional phase modulation. We demonstrate this effect using a simple optical cavity configuration and show that minor adjustments to the modulator system can be used to compensate for the extra modulation components and provide additional flexibility.     

谐振式光纤陀螺的数字检测方案及其优化设计

提出了一种基于 DSP 芯片实现的双频率数字调制谐振式光纤陀螺系统的闭环检测方案。在此方案中,利用带通滤波器从探测器的输出光强信号中提取其基波频率的正弦信号,通过相关检测原理去掉干扰的噪声,并利用低通滤波器提取与探测器输出光强幅度直接成正比的直流信号,将其转换成相应的谐振频差,利用此频差即可求得陀螺的旋转角速度。此方案检测线路简单,操作方便,基于 DSP 芯片的实现则大大提高了系统处理速度。同时,还利用 Matlab 软件对检测系统中的滤波器参数进行了优化设计,提高了系统的检测精度。     

基于FPGA的硅微机械谐振式陀螺仪数据采集系统设计

介绍了一种硅微机械谐振式陀螺仪的结构,给出了调制系数或最大频偏与输入角速度成正比的关系.通过对陀螺仪敏感质量块静电驱动力和双端音叉谐振器输出信号的分析,得出了双端音叉谐振器输出信号的相位差与调制系数之间的关系.提出了一种调频信号最大频偏的检测方法,通过此相位差的计算得出调制系数或最大频差,进而计算出输入角速度的值.设计了一种基于FPGA的数字化解调方案,给出了基于FPGA的数字化最大频差测量电路的测试结果.结果表明测量电路对最大频偏有很好的测量效果.     

Measurement of static and vibration-induced phase noise in UHF thin-film resonator (TFR) filters

Measurements of the static phase noise and vibration sensitivity of thin-film resonator (TFR) filters operating at 640 and 2110 MHz have been made. They show that the short-term frequency instability of the filters is small compared with that induced in the oscillator signal by the sustaining stage amplifier PM (phase modulation) noise. In-oscillator measurement of filter performance under vibration indicates that fractional frequency vibration sensitivities (δf ₀/f₀) are on the order of several parts in 10^-9/g. Because the percentage bandwidth and order (number of poles) of the filters was fairly constant, so was the product of the center frequency and group delay. Thus, the fractional frequency vibration sensitivity of the filters can be expressed alternatively as carrier signal phase sensitivity to vibration. The τ-ω₀ product for the filters that were tested was on the order of 300 rad, so that the equivalent phase sensitivity to vibration was approximately 1 grad/g     

High-sensitivity laser absorption measurements of broadband absorbers in the near-infrared spectral region

We describe the development and characterization of a near-infrared diode-laser-based sensor to measure the vapor from trace gases having unstructured absorption spectra. The technique uses two equal amplitude-modulated laser beams, with the modulation of the two lasers differing in phase by 180 deg. One of the laser beams is at a wavelength absorbed by the gas [for these experiments, vapor is from pyridine (C(5)H(5)N)], and the second laser beam is at a wavelength at which no absorption occurs. The two laser beams are launched onto near-coincident paths by graded-index lens-tipped optical fibers. The mixed laser beam signal is detected by use of a single photodiode and is demodulated with standard phase-sensitive detection. Data are presented for the detection and measurement of vapor from pyridine (C(5)H(5)N) by use of the mixed laser technique. The discussion focuses on experimental determination of whether a compound exhibits unstructured absorption spectra (referred to here as a broadband absorber) and methods used to maximize sensitivity.     

Optical signal processing in dual-wavelength optoelectronic drop analyzer

Dual-wavelength optical signals are injected into the liquid drop through optical fibers in order to study the light intensity variation during the drop growth. Modulation and demodulation are used to reduce the influence of ambient light on the valuable optical signals. HA17555 chip composes the oscillating circuit for light modulation, with different high oscillating frequency for different light source. The light signal collected by a fiber detector after propagation inside the drop is changed into electric signal through the OPA2111 photoelectric circuit. The second-order band-pass filter composed of MAX275 chip is used for signal-separation. The high-pass filter is used to prevent the low frequency signal of ambient light. The valuable signal related to the drop is demodulated by a linear demodulation circuit including a half-wave rectifier, full-wave composition and low-pass filter.     

Limitation of the frequency stability by local oscillator phase noise: new investigations and natural improvements

In frequency standards in which the atoms have a continuous interaction with the probe signal, local oscillator phase noise may limit medium term frequency stability. This spurious effect cannot be suppressed whenever there Is any truncation in the spectrum of the resonator response. Nevertheless, a simultaneous processing of the probe signal, similar to that of the NIST, and of the resonator response (by means of an appropriate demodulation) makes it possible to reduce this limiting effect. Previously achieved with a square wave frequency modulation, this result is now extended to various frequency modulations. An uncontrolled distortion in the demodulation waveform may significantly degrade the performance. For the case of a square wave phase modulation, the limiting effect also exists, but it is smaller than for a frequency modulation. When the phase noise of the local oscillator is naturally "not flat", it is possible to easily reduce the spurious effect: using the quasi-static approximation, one can calculate various optimized demodulation waveforms and the corresponding improvements. For the simplest optimized demodulation (f (M), 3f(M)), theoretical predictions are experimentally confirmed for flicker phase noise and flicker frequency noise.     

New interferometric fiber-optic gyroscope with amplified optical feedback

A novel interferometric fiber-optic gyroscope with amplified optical feedback by an Er-doped fiber amplifier (EDFA) is proposed and theoretically investigated (the proposed gyroscope is named the feedback EDFA-FOG, FE-FOG in what follows). The FE-FOG functions like a resonant fiber-optic gyro (R-FOG) because of its multiple utilization of the Sagnac loop; however, it is completely different because a low-coherence light source is used. In addition, the gyro output signal is pulsed because the modulation frequency of the phase modulator placed in the Sagnac loop is selected to match the total round-trip time delay of the light, which includes the Sagnac-loop delay plus that of the feedback loop of the fiber amplifier. The sharpness of the output pulse can be adjusted by both the gain of an EDFA and the modulation depth of the phase modulator. When rotation occurs the peak position of the output pulse is shifted as a result of the Sagnac effect. The resolution of the rotation measurement depends on the sharpness of the output pulse. The techniques of both the open-loop and closed-loop methods are described in detail, which shows the great advantage of the proposed gyroscope over the to the conventional interferometric fiber-optical gyroscope (I-FOG).     

A novel technique to measure the dynamic response of an opticalphase modulator

This paper describes a novel technique that can be used to measure the frequency response of an optical phase modulator. An interesting feature of this technique is that it does not require the use of an interferometer for phase-to-amplitude conversion, thus alleviating stability and alignment problems. Instead, the electro-optically induced birefringence of the modulator and a simple polarizer are used to transform phase modulation into intensity modulation. The latter is detected with a high-speed photodiode and, for a sinusoidal modulating signal, the resulting output power spectrum is shown to be related to the actual phase modulation index by simple mathematical expressions involving Bessel functions. Using only a spectrum analyzer, the magnitude and the variations of the modulation index are measured over a broad frequency range     

Direct bidirectional angle-insensitive imaging of the flow signal intensity in Doppler optical coherence tomography

We introduce a new method, to our knowledge, for direct detection of flow signal intensity by stationary target rejection. In our system, two delay lines are constructed with identical scanning speed and ranging depth. One delay line is used for depth ranging as well as phase modulation, and the other one acts as a full-range retroreflector (FRRR). The signal from this FRRR carries the overall features of local phase modulation, and it is used as the local oscillator for coherent demodulation. With this setup, stationary targets can be rejected at a 4-kHz high-pass cutoff frequency of the filter that follows the demodulator, compared with 20 kHz for conventional fixed-frequency demodulation. This technique features angle insensitivity and provides flow direction as well by implementing standard in-phase and quadrature detection. Besides the direct directional detection of flow signal intensity, flow speed information can be acquired with postprocessing.     

Secondary-phase-modulation method for open-loop fiber-optic gyroscopes

A proposed method of secondary phase modulation for open-loop fiber-optic gyroscopes is examined in general terms. To detect the rotation rate of a system through a beat-frequency channel, we employ linearly combined signals with different frequencies for the optical phase modulation. We find that the proper combinations of the modulation frequencies can optimize the sensitivity of gyroscopes. With this method we can employ a high-frequency band for optical phase modulations while keeping relative a lower-frequency band of the detection channel. The theoretically derived result is experimentally confirmed by using a lithium-niobate (LiNbO(3)) optical phase modulator. We also discuss the combination setup with an optical integrated-circuit device and digital signal processing.     

A model for phase noise generation in amplifiers

In this paper, a model is presented for predicting the phase modulation (PM) and amplitude modulation (AM) noise in bipolar junction transistor (BJT) amplifiers. The model correctly predicts the dependence of phase noise on the signal frequency (at a particular carrier offset frequency), explains the noise shaping of the phase noise about the signal frequency, and shows the functional dependence on the transistor parameters and the circuit parameters. Experimental studies on common emitter (CE) amplifiers have been used to validate the PM noise model at carrier frequencies between 10 and 100 MHz