Simple method for measuring frequency chirps with a Fabry-Perot interferometer

A simple method for measuring the frequency-chirped response of lasers is presented. This method relates the deviation from the Lorentzian line shape of the transmission of a Fabry-Perot interferometer to the frequency chirp of the laser and allows a direct measurement of the frequency chirp. Two chirps produced by an external-cavity laser diode with an intracavity electro-optic crystal were measured. The first measurement was of a linear chirp of 800 MHz occurring in a time of 12.3 mus, and the second measurement was of eight repeated 800-MHz linear chirps each occurring in 337 mus. Agreement between the measured and the expected frequency-chirped response of the laser is shown.     

Amplitude response of Fabry-Perot frequency discriminators

The amplitude noise responses of optical-frequency-discriminating systems, based on Fabry-Perot cavities with intensity noise compensation, are analyzed considering also the effect of the resonator transient. From the point of view of amplitude noise immunity, systems based on transmission or reflection alone behave in a quite similar way within the discriminator bandwidth, whereas a proper combination of both these signals not only increases the sensitivity to frequency noise but also allows for higher rejection to amplitude noise.     

Modeling and analysis of an extrinsic Fabry-Perot interferometer cavity

A schematic representation of optical feedback between two resonator mirrors undergoing a phase shift each round trip as a function of the separation of the mirrors is studied. A transfer function modeling of the extrinsic Fabry-Perot interferometer (EFPI) is presented. Nyquist analysis has been used to forecast the operational stability and possibility of interference in an EFPI. The analysis with two perfectly parallel surfaces of the cavity shows efficient interference. The performance when there is some tilt between the two mirrors in the cavity is also studied and is presented. In this case some restricted interference is found.     

Spatial and spectral response of a Fabry-Perot interferometer illuminated by a Gaussian beam

A generalized study has been done of the transmission characteristics of a Fabry-Perot interferometer (FPI) illuminated by a Gaussian light beam impinging on it at normal and non-normal incidence. The theoretical approach is based on a plane-wave, angular-spectrum representation of both the incident Gaussian beam and the transmitted beam. Expressions are obtained for the FPI instrumental function and for the spatial distribution of the transmitted beam. Numerical results are presented for the FPI maximum transmission, effective finesse, and spectral displacement of the interference maximum.     

Automated stabilization of a single-pass plane Fabry-Perot interferometer

We describe a home-built data-acquisition and stabilization system designed for small-angle Brillouin experiments. The stabilization system exhibits good performance, as supported by the obtained experimental spectra. Collected data for the sound velocity of benzene and isopropyl alcohol against sample temperature are compatible with existing results.     

Transmission of a Gaussian beam through a Fabry-Perot interferometer

The transmission of a Gaussian beam through a Fabry-Perot interferometer (FPI) has been investigated. The equation for the electric field of the transmitted beam was derived and then the transmitted irradiance I(t) was numerically calculated for different selected parameters of both the FPI and the beam. The results show that the energy profile of the transmitted beam has been distorted to different degrees depending on the various parameters of the Gaussian beam and the FPI. Moreover the results show that the positions of the peaks of the transmitted beam are shifted, especially for intermediate waists for which the arctan term is nonlinear. The results also show that for nonnormal incidence successive transmitted beams are spatially separated and are not interfering appreciably with each other.     

Wind-velocity lidar measurements by use of a Mach-Zehnder interferometer, comparison with a Fabry-Perot interferometer

We present the first wind-velocity profiles obtained with a direct-detection Doppler lidar that uses a Mach-Zehnder interferometer (MZI) as spectral discriminator. The measurements were performed in the lower stratosphere, between 10 and 40 km in altitude, at the Observatoire de Haute Provence (OHP), France, during nighttime. They are in excellent agreement with those obtained simultaneously and independently with the already validated double Fabry-Perot interferometer (FPI) of the OHP Doppler lidar (mean difference lower than the combined standard deviation). A statistical analysis shows that the random error obtained with this experimental MZI is 1.94 times the Cramer-Rao lower bound and is approximately half of that given by the FPI (both operating in photometric mode). Nevertheless, the present MZI measurements are sensitive to the presence of atmospheric particles and need an additional correction, whereas the OHP FPI is designed to be insensitive to particulate scattering.     

轮胎激光散斑干涉相位图多方向频域滤波方法

为解决激光数字剪切散斑干涉技术应用于轮胎缺陷检测中轮胎缺陷相位条纹图噪声对包裹相位图解包和轮胎缺陷尺寸测量产生严重影响问题,通过对散斑干涉相位图的形成与条纹特征分析,研究一种根据不同方向的条纹密度来设置不同截止频率的多方向频域低通滤波方法。该方法只需进行一次滤波就能有效滤除噪声,还能更好地保留图像的边缘信息。实验结果表明:在两组滤波实验中,与中值滤波方法相比,多方向频域低通滤波的边缘保持指数分别是其4.257倍、2.869倍;与正余弦滤波方法相比,多方向频域低通滤波方法的残差点数分别是正余弦滤波方法的16.456%、36.555%,体现出较好的滤波特性。     

Errors in measuring the displacement of a Fabry-Perot interferometer mirror

Translated from Izmeritel'naya Tekhnika, No. 1, pp. 23–24, January, 1989.     

Electronically swept millimeter-wave interferometer for spatially resolved measurement of plasma electron density

We report the development and initial implementation of what we believe to be a new rapid- spatial-scan millimeter-wave interferometer for plasma density measurements. The fast scan is effected by electronic frequency sweeping of a wideband (180-280 GHz) backward-wave oscillator whose output is focused onto a fixed blazed diffraction grating. The system, which augments the rotating-grating scanned multiview H-1 heliac interferometer, can sweep the plasma cross section in a period of less than 1 ms with a beam diameter in the plasma of 20 mm and phase noise of the order of 0.01 rad.     

Development of an optically pumped Cs frequency standard at theNRLM

Describes development of an optically pumped Cs frequency standard aiming at a primary frequency standard. Using this laboratory-type standard, a Ramsey resonance spectrum was observed. It has been shown that a laser power of about 1 mW is almost sufficient for two-frequency optical pumping. It has also been shown that the C-field strength can be measured using Zeeman coils by establishing a population difference among the Zeeman sublevel with σ⁺ polarized laser light     

Light shifts in an optically pumped Cs beam frequency standard

Frequency shifts caused by light, which are called light shifts in an optically pumped Cs beam frequency standard, were estimated. Frequency shifts due to monolithic light were measured by introducing laser light along the Cs beam. The relative dependence of the shift on the laser frequency agreed very well with the theory, but the absolute shift was between one and two times that of the theory. The light shifts due to the optical pumping and optical detection in the standard are estimated to be less than 2×10^-15 and 1×10^-16, respectively, and both are negligible at the present state of development     

Signals of an intermodal fiber interferometer induced by laser frequency modulation

Signals of an intermodal fiber interferometer induced by laser optical frequency modulation are studied. Dependences of signal amplitudes and spectra on the laser frequency deviation are examined theoretically and experimentally for various optical fibers. It is established that the sensitivity of the intermodal fiber interferometer to the laser frequency variation essentially depends on the fiber refractive index profile. The minimal sensitivity corresponds to graded-index (α ≈ 2) multimode optical fibers. Step-index optical fibers (α = ∞) are more sensitive to the laser frequency variation by more than a factor of 100.     

Optical zooming interferometer for subnanometer positioning using an optical frequency comb

A high-precision positioning stage based on an optical zooming interferometer is proposed. Two external-cavity diode lasers, stabilized to a femtosecond optical frequency comb, are used as optical sources. The zooming principle is demonstrated, and the positioning resolution of 0.2 nm is achieved. The positioning accuracy was partly evaluated.     

Extrinsic fiber-optic Fabry-Perot interferometer sensor for refractive index measurement of optical glass

A simple fiber-optic sensor based on Fabry-Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry-Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.     

High-gain power recycling of a Fabry-Perot Michelson interferometer for a gravitational-wave antenna

Power recycling was implemented on a fully suspended prototype interferometer with arm lengths of 20 m. A wave-front-sensing technique for alignment control of the suspended mirrors was also implemented, which allowed for several hours of stable operation. A power-recycling gain of greater than 12 was achieved, a significant increase over the highest gain in a suspended mirror Fabry-Perot Michelson interferometer reported to date.     

Time domain automatic focusing of an applebaum array

The effect of a finite-distance signal source on the performance of an Applebaum array has been removed by applying the automatic focusing technique (AFT). However, this technique requires a considerable amount of data acquisition and processing. It is shown in this article that the performance of the AFT is maintained when the scanned frequencies are simultaneously sent in one signal. As a result, this novel procedure provides the AFT with additional capabilities while removing its drawbacks. © 1996 John Wiley & Sons, Inc.     

Locking bandwidth of optically injected Fabry-Perot semiconductor lasers for high injection strengths

The authors compare simulated results using a commercial software program with solutions of the rate equation (RE) and Fabry?Perot (FP) models of an optically injected FP semiconductor laser for high injection strengths (with injection ratios between the master and slave lasers above 0 dB). For linewidth enhancement factors (-factors) of 0 and 3, the locking bandwidth is compared with the RE model and in the case of an -factor of 0, the results are also compared with the FP model. It is found that the RE model for high injection strengths does not describe the locking bandwidth very well, whereas the FP model gives good agreement with our simulated results. Additionally, the longitudinal variation of optical power and electron concentration are shown for different injection strengths and different detuning values. For an a-factor of 3, the spatial variations of these properties become asymmetrical for higher injection strengths and with an increase in detuning, they are found to exhibit decreased fluctuations when the lower locking boundary is approached through the locking region. Therefore it is important to take spatial variation into account for high injection strengths.     

Polar cap mesosphere wind observations: comparisons of simultaneous measurements with a Fabry-Perot interferometer and a field-widened Michelson interferometer

Polar cap mesospheric winds observed with a Fabry-Perot interferometer with a circle-to-line interferometer optical (FPI/CLIO) system have been compared with measurements from a field-widened Michelson interferometer optimized for E-region winds (ERWIN). Both instruments observed the Meinel OH emission emanating from the mesopause region (~86 km) at Resolute Bay, Canada (74.9 degrees N, 94.9 degrees W). This is the first time, to our knowledge, that winds measured simultaneously from a ground-based Fabry-Perot interferometer and a ground-based Michelson interferometer have been compared at the same location. The FPI/CLIO and ERWIN instruments both have a capability for high temporal resolution (less than 10 min for a full scan in the four cardinal directions and the zenith). Statistical comparisons of hourly mean winds for both instruments by scatterplots show excellent agreement, indicating that the two optical techniques provide equivalent observations of mesopause winds. Small deviations in the measured wind can be ascribed to the different zenith angles used by the two instruments. The combined measurements illustrate the dominance of the 12-h wave in the mesopause winds at Resolute Bay, with additional evidence for strong gravity wave activity with much shorter periods (tens of minutes). Future operations of the two instruments will focus on observation of complementary emissions, providing a unique passive optical capability for the determination of neutral winds in the geomagnetic polar cap at various altitudes near the mesopause.