Sinusoidal phase-modulating interferometer insensitive to intensity modulation of a laser diode for displacement measurement

In sinusoidal phase-modulating laser diode interferometers, an injection current of a laser diode is sinusoidally modulated to scan the laser wavelength. However, the modulation of the injection current also involves an intensity modulation of the light, which increases the measurement error if a conventional signal processing is used. A novel signal processing for displacement measurement is proposed to eliminate the influence of the intensity modulation. Numerical simulation results and experimental results make it clear that an optimal depth of the sinusoidal phase modulation exists that can reduce the measurement error to a few nanometers.     

Sinusoidal wavelength-scanning interferometric reflectometry

We propose interferometric reflectometry in which a sinusoidal wavelength-scanning tunable laser diode is used to detect positions and profiles of multiple reflecting surfaces. An objective signal extracted from an interference signal contains modulation amplitude Z and phase alpha, which are related to the positions and profiles, respectively, of multiple reflecting surfaces. By using values of the objective signal at special times, we can produce an image intensity that shows where the reflecting surfaces exist. To obtain exact values of Z or values of alpha, we estimated the objective signal by using a conjugate gradient method. Experimental results show that a resolution of two-optical-path difference (OPD) in the image intensity is ~60 mum, and the final OPD precisions are 2 and 8 mum for two and three reflecting surfaces, respectively, for a wavelength-scanning width of 7 nm. Profiles of the front and rear surfaces of a silica glass plate with a thickness of 20 mum have been measured with a precision of ~10 nm.     

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     

Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets

Phase-shifting interferometry based on the integrating-bucket technique with sinusoidal phase modulation is studied theoretically and demonstrated experimentally to obtain phase maps from double-beam interferometers. The method uses four frames obtained by integration of the time-varying intensity in an interference pattern during the four quarters of the modulation period. An optimum sinusoidal phase modulation is found to minimize the effect of the additive noise. The absolute accuracy of the phase measurements is discussed. Possible applications of the method are demonstrated with two interference microscopes with which the phase modulation is achieved by sinusoidal oscillation of a mirror attached to a piezoelectric transducer and by sinusoidal birefringence modulation with a photoelastic modulator. In both experimental arrangements, phase images can be produced in real time at a rate of several hertz. Noise measurements are reported and compared with theory.     

Simplified intracavity phase plates for increasing laser-mode discrimination

Recently, a new class of laser resonators was introduced that utilizes diffractive mirrors and an additional intracavity diffractive phase element. High modal discrimination and low fundamental-mode loss were achieved simultaneously by use of sinusoidal and pseudorandom diffractive phase elements. An intracavity phase element consisting of a simple single-step phase modulation is approximated by a Gaussian with a small radius. Explicit expressions are obtained for the modal-discrimination factor as a function of resonator parameters with a Gaussian output mirror. Numerical simulations are performed for a phase element with a step singularity in the phase function, the fundamental mode of this cavity being super-Gaussian. The modal discrimination of the cavity is studied for different radii of the single-step phase modulation, the position of the phase plate, and the cavity Fresnel number. Optimum solutions are found for a plane output mirror with either a striped or a circular shape.     

光热调制半导体激光波长降低干涉测量误差

本文首次将光源波长的光热调制技术用于正弦相位调制干涉仪中,消除了因直接调制激光波长引起的光强度变化对测量的影响,降低了测量误差。     

基于CCD探测器的全视场层析成像方法研究

由正弦信号驱动PZT调制参考镜以实现参考光相位调制,CCD光探测器的曝光时间为正弦驱动信号的四分之一周期,利用频率-同步探测技术,在一个参考光调制周期共提取四帧全视场参考光与样品反射和散射光干涉图像.为了获得最优的参考光信号调制参数,一种基于PID控制器的闭环控制技术与数字移相相结合的方法用于调制系统,采用50Hz的理想正弦曲线的数字离散量来控制PZT的调制幅度,数字移相电路调整PZT的振动相位来保证最优调制参数的获得.CCD(频率f=200Hz)由软件驱动,采用积分算法,实现了由CCD探测器提取微弱全视场层析信号的方法.     

Extending the continuous tuning range of an external-cavity diode laser

The continuous tuning range of an external-cavity diode laser can be extended by making small corrections to the external-cavity length through an electronic feedback loop so that the cavity resonance condition is maintained as the laser wavelength is tuned. By maintaining the cavity resonance condition as the laser is tuned, the mode hops that typically limit the continuous tuning range of the external-cavity diode laser are eliminated. We present the design of a simple external-cavity diode laser based on the Littman-Metcalf external-cavity configuration that has a measured continuous tuning range of 1 GHz without an electronic feedback loop. To include the electronic feedback loop, a small sinusoidal signal is added to the drive current of the laser diode creating a small oscillation of the laser power. By comparing the phase of the modulated optical power with the phase of the sinusoidal drive signal using a lock-in amplifier, an error signal is created and used in an electronic feedback loop to control the external-cavity length. With electronic feedback, we find that the continuous tuning range can be extended to over 65 GHz. This occurs because the electronic feedback maintains the cavity resonance condition as the laser is tuned. An experimental demonstration of this extended tuning range is presented in which the external-cavity diode laser is tuned through an absorption feature of diatomic oxygen near 760 nm.     

采用DBR LD的正弦相位调制激光干涉仪

分析影响正弦相位调制半导体激光干涉仪测量精度和系统分辨力的因素,提出了用分布布拉格反射半导体激光器DBR LD实现高分辨力亚纳米精度测量的方案。理论计算表明,DBR LD的波长连续调制深度比F-P腔LD高一个量级。指出邮于DBR LD的特殊结构可通过简单的反馈回路稳定输出光功率,有效地避免了光强波动对测量精度提高的限制。     

Optical time-domain reflectometry in optical fiber with reflection delay time matched to the period of the optical frequency modulation

A method of optical time-domain reflectrometry in optical fiber is described that uses a single distributed feedback diode laser and a reference reflector. When the period of the frequency modulation of the laser matches the time difference between the reference reflection and the reflection of interest an increase in the noise at the detector occurs. The locations of reflections within the fiber are then mapped to frequencies at which the noise at the detector increases. A sinusoidal frequency modulation is analyzed, and an experiment is described in which the system is used to measure the location and the wavelength of two Bragg gratings located 10 cm apart in an optical fiber. Wavelength measurement is accomplished by temperature tuning the diode laser.     

Measurement of AM to PM conversion in medium wave AM transmitter

A method for measuring AM (amplitude modulation) signal distortion caused by AM to PM (phase modulation) conversion at the output of an AM radio transmitter is presented. A novel type of measuring instrument is also presented for testing the phase distortion which may occur in an AM radio transmitter when an AM modulation signal is applied. The down-converted AM signal is first divided into the inphase and orthogonal-phase components, and these signals are processed by an operational circuit to obtain phase distortion, which is the angle between the orthogonal-phase and inphase components. A phase angle of 10° or more is detected in the prototype version     

捷变正弦信号源波形建立时间的精确测量

针对正弦信号源捷变状态切换后的建立时间、开机后波形建立时间以及过载恢复时间等的精确测量问题,提出了一种基于局域波形四参数拟合的测量分析方法,然后将拟合模型参数拓展到全局,进而获得拟合回归波形与过渡过程波形的回归残差波形。该波形的收敛过程反映了正弦波建立过程中的残差收敛变化过程。以它为目标对象,加上主观设定的建立时间的条件判据,可以获得正弦建立时间的起始和终止两个时刻点,最终获得完整的正弦信号建立时间。在两组不同条件下的状态切换实验结果,验证了该方法的有效性和可行性。该方法也可以推广应用到脉冲调频、脉冲调幅、脉冲调相、捷变频信号的建立时间测量评价中。     

Ultimate linewidth reduction of a semiconductor laser frequency-stabilized to a Fabry-Pérot interferometer

We report a theoretical dynamical analysis on effect of semiconductor laser phase noise on the achievable linewidth when locked to a Fabry-Perot cavity fringe using a modulation-demodulation frequency stabilization technique such as the commonly used Pound-Drever-Hall frequency locking scheme. We show that, in the optical domain, the modulation-demodulation operation produces, in the presence of semiconductor laser phase noise, two kinds of excess noise, which could be much above the shot noise limit, namely, conversion noise (PM-to-AM) and intermodulation noise. We show that, in typical stabilization conditions, the ultimate semiconductor laser linewidth reduction can be severely limited by the intermodulation excess noise. The modulation-demodulation operation produces the undesirable nonlinear intermodulation effect through which the phase noise spectral components of the semiconductor laser, in the vicinity of even multiples of the modulation frequency, are downconverted into the bandpass of the frequency control loop. This adds a spurious signal, at the modulation frequency, to the error signal and limits the performance of the locked semiconductor laser. This effect, reported initially in the microwave domain using the quasistatic approximation, can be considerably reduced by a convenient choice of the modulation frequency.     

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 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.     

A Novel Method of Distance Measurement Based on Pulse Position Modulation and Synchronization of Chaotic Signals Using Ultrasonic Radar Systems

This paper deals with a novel method of transmission and receipt of a signal based on both the property of two chaotic systems generating the same chaotic signal when they are synchronized and the property of pulse position modulation (PPM) to be insensitive to the distortions of the transmission channel. The method is discussed in the context of ultrasonic radar systems, in which the transmitter and receiver, which consist of ultrasonic sensors, are near each other, and the received signal consists of the transmitted signal reflected by an obstacle. A reference sinusoidal signal is superimposed to a chaotic signal generated by a master chaotic system, and the whole signal is modulated according to the PPM method and transmitted by the sensor. The received signal is demodulated, and the demodulated signal forces a slave chaotic system to generate the chaotic signal embedded in it, which allows recovery of the sinusoidal signal by subtracting this chaotic signal from the demodulated echo. The difference of the phases of the reference sinusoidal signal and the recovered sinusoidal signal allows computation of the time of flight of the signal and, consequently, the distance of the radar system from the obstacle. The novel method is illustrated and tested by both simulation and experiments. The interference problem between the considered radar system and other radar systems ( crosstalk) is also addressed, and a solution is proposed to avoid it.     

Absolute linearity measurement of photodetectors using sinusoidal modulated radiation

A method is presented for characterizing the linearity of photodetectors based on time-domain analysis of response to sinusoidal excitation. Nonlinearity is quantified solely from the output distortion. Relative response is converted to absolute response by including two calibration points. For low signal level, one calibration point is required, while using dark current as the second point. The response is mapped over a wider range using a series of overlapping sinusoids for calibration transfer. The method is demonstrated with a relatively linear photodiode and a nonlinear phototransistor. A Michelson interferometer is used to generate sinusoidal modulation of a laser source. Results demonstrate the potential of the proposed technique.     

Least-squares algorithm for phase-stepping interferometry with an unknown relative step

A pointwise least-squares phase-stepping algorithm with an unknown relative phase step is proposed. In phase-stepping interferometry the recorded temporal intensity sequence is a discrete sinusoidal signal biased by a direct-current component. Its value at a certain time can be predicted from its three past samples by use of a recursive formula. Based on this linear prediction property, an unbiased least-squares estimator is deduced to determine the relative phase step from a sequence of intensity values, and the result is used to evaluate the phase value. The validity and performance of this algorithm are verified by computer simulations.     

Wavelength modulation spectroscopy: combined frequency and intensity laser modulation

A theoretical model of wavelength modulation spectroscopy that uses a laser diode on a Lorentzian absorption line is presented. This theory describes the general case of a current-modulated semiconductor laser, for which a combined intensity and frequency modulation with an arbitrary phase shift occurs. On the basis of this model, the effect of several modulation parameters on the detected signals is evaluated. Experimental signals measured on an absorption line of CO2 by use of a 2-microm distributed-feedback laser are also presented and validate this analysis. These experimental results agree with the calculated signals, confirming the relevance of the model.     

Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases

Tunable diode laser absorption measurements at high pressures by use of wavelength-modulation spectroscopy (WMS) require large modulation depths for optimum detection of molecular absorption spectra blended by collisional broadening or dense spacing of the rovibrational transitions. Diode lasers have a large and nonlinear intensity modulation when the wavelength is modulated over a large range by injection-current tuning. In addition to this intensity modulation, other laser performance parameters are measured, including the phase shift between the frequency modulation and the intensity modulation. Following published theory, these parameters are incorporated into an improved model of the WMS signal. The influence of these nonideal laser effects is investigated by means of wavelength-scanned WMS measurements as a function of bath gas pressure on rovibrational transitions of water vapor near 1388 nm. Lock-in detection of the magnitude of the 2f signal is performed to remove the dependence on detection phase. We find good agreement between measurements and the improved model developed for the 2f component of the WMS signal. The effects of the nonideal performance parameters of commercial diode lasers are especially important away from the line center of discrete spectra, and these contributions become more pronounced for 2f signals with the large modulation depths needed for WMS at elevated pressures.