Optimization of a field-widened Michelson interferometer

This paper considers the optical design of a wide-angle fixed-path Michelson interferometer consisting of two arm glasses and an air gap. It is shown that this configuration can be optimized to give (a) extra large fringes (over 50 degrees in diameter) over a range of wavelength, (b) a path difference nearly independent of wavelength, or (c) a path difference specified differently at two different wavelengths for observing a pair of doublets. Specific examples refer to the airglow wavelengths of 557.7, 630.0, 732.0 nm and others, and to a path difference of 4.5 cm. The properties of different glass combinations are discussed.     

Analysis of light noise sources in a recycled Michelson interferometer with Fabry-Perot arms

We present a method by which the effect of laser field variations on the signal output of an interferometric gravitational wave detector is rigorously determined. Using the Laser Interferometer Gravitational Wave Observatory (LIGO) optical configuration of a power recycled Michelson interferometer with Fabry-Perot arm cavities as an example, we calculate the excess noise after the input filter cavity (mode cleaner) and the dependence of the detector strain sensitivity on laser frequency and amplitude noise, radio frequency oscillator noise, and scattered-light phase noise. We find that noise on the radio frequency sidebands generally limits the detector's sensitivity.     

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.     

Direct-detection Doppler wind measurements with a Cabannes-Mie lidar: a. Comparison between iodine vapor filter and Fabry-Perot interferometer methods

Atmospheric line-of-sight (LOS) wind measurement by means of incoherent Cabannes-Mie lidar with three frequency analyzers with nearly the same maximum transmission of ~80% that could be fielded at different wavelengths is analytically considered. These frequency analyzers are (a) a double-edge Fabry-Perot interferometer (FPI) at 1064 nm (IR-FPI), (b) a double-edge Fabry-Perot interferometer at 355 nm (UV-FPI), and (c) an iodine vapor filter (IVF) at 532 nm with two different methods, using either one absorption edge, single edge (se-IVF), or both absorption edges, double edge (de-IVF). The effect of the backscattered aerosol mixing ratio, R(b), defined as the ratio of the aerosol volume backscatter coefficient to molecular volume backscatter coefficient, on LOS wind uncertainty is discussed. Assuming a known aerosol mixing ratio, R(b), and 100,000 photons owing to Cabannes scattering to the receiver, in shot-noise-limited detection without sky background, the LOS wind uncertainty of the UV-FPI in the aerosol-free air (R(b)=0), is lower by ~16% than that of de-IVF, which has the lowest uncertainty for R(b) between 0.02 and 0.08; for R(b)>0.08, the IR-FPI yielded the lowest wind uncertainty. The wind uncertainty for se-IVF is always higher than that of de-IVF, but by less than a factor of 2 under all aerosol conditions, if the split between the reference and measurement channels is optimized. The design flexibility, which allows the desensitization of either aerosol or molecular scattering, exists only with the FPI system, leading to the common practice of using IR-FPI for the planetary boundary layer and using UV-FPI for higher altitudes. Without this design flexibility, there is little choice but to use a single wavelength IVF system at 532 nm for all atmospheric altitudes.     

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.     

Active feedback regulation of a Michelson interferometer to achieve zero-background absorption measurements

An active phase-controlling scheme based on a proportional-integral-derivative-controlled piezoelectric transducer is presented with the purpose of stabilizing a quasi-zero-background absorption spectrometer. A fiber-based balanced Michelson interferometer is used, and absorption due to a gas sample in one of its arms results in an increased light signal to a detector, which otherwise, thanks to destructive interference, experiences a very low light level. With the presented approach, the sensitivity of already potent absorption measurement techniques, e.g., based on modulation, could be improved even further.     

Distance and velocity measurements by the use of an orthogonal Michelson interferometer

A novel signal processing scheme for detecting distance and velocity signals simultaneously is demonstrated. In this method, a frequency-modulated diode laser is used to illuminate a dual-channel Michelson interferometer with two orthogonal output signals. The distance and the velocity signals then exist on the beat frequencies of the output interferometric signal. Two interferometric output signals with a quadrature phase shift are used to adjust the gating time period of frequency counters for beat-frequency measurement. The distance and velocity signals can thus be obtained from the counting number within the gated-in time period.     

Modulation depth of Michelson interferometer with Gaussian beam

Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

Refractive-index measurements of zinc germanium diphosphide at 300 and 77 K by use of a modified Michelson interferometer

A method to determine the absolute refractive index of materials available in the shape of flat wafers with parallel sides by using interferometric techniques is presented. With this method, nondestructive, sample-specific measurements can be made. The method is tested by using silicon, germanium and zinc selenide, and measurements for both the ordinary and extraordinary axes of ZnGeP2 for temperatures of 300 and 77 K are reported.     

Influence of the form of the illuminating beam upon the error of length measurements made with a laser-type Michelson interferometer

Conclusions By solving the problem of the interference of Gaussian beams, we obtained formulas for the calculation of the systematic error which is made when a laser-type Michelson interferometer is used to measure length. We gave recommendations on the geometrical dimensions of the Michelson interferometer and its matching to the laser radiation so that the above error is reduced. We have described the experimental verification of our formulas.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 40–42, February, 1976.     

Dual Fabry-Perot spectrometer measurements of daytime thermospheric temperature and wind velocity: data analysis procedures

Daytime thermospheric temperatures and wind velocities have been inferred from dual Fabry-Perot spectrometer observations of the atomic oxygen emission line at lambda630 nm, and this paper details the analysis procedures applied to the recorded spectra. Numerical simulation of the recorded spectra was used to examine the limitations imposed by analysis assumptions and by the influence of atmospheric molecular oxygen and water vapor absorption lines near lambda630 nm. The observational and analysis procedures provide a reliable ground-based means of monitoring the thermal and dynamical state of the neutral thermosphere during the daytime.     

Multiplexing of Michelson interferometer sensors in a matrix array topology

We report on the operation and performance of a matrix array topology for multiplexing reflective interferometric sensors that uses (a) frequency-division multiplexing (FDM) and (b) a combination of frequency-division and time-division multiplexing. The use of reflective sensors in this FDM topology illuminated by a cw source imposes a power limitation not encountered with the use of transmissive sensors. Combining FDM with time-division multiplexing improves the multiplexing gain of the network and improves the level of isolation of the lasers from the signal of the reflective sensors.     

Performance of a circle-to-line optical system for a Fabry-Perot interferometer: a laboratory study

We describe the characterization and laboratory study of a new optical device, a circle-to-line interferometer optical (CLIO) system, for a Fabry-Perot interferometer. The CLIO system converts a circular Fabry-Perot interferometer fringe pattern into a linear fringe pattern that can be analyzed by a linear array detector or a charge-coupled device. One can achieve the circle-to-line conversion by the use of a mirrored kaleidoscope and a 90-deg segment of a 45-deg half-angle internally reflecting cone. Our laboratory results are in good agreement with theoretical predictions. The aberrations associated with this optical system are minor for large F-number optical systems, especially for the cone segment. The finesse degradation caused by this CLIO system is relatively small, which agrees with the results of a ray-trace study.     

Spatiospectral transmission of a plane-mirror Fabry-Perot interferometer with nonuniform finite-size diffraction beam illuminations

The transmission of a plane-mirror Fabry-Perot (PFP) interferometer is theoretically modeled and investigated by treating the spatial and spectral features in a unified manner. A spatiospectral transfer function is formulated and utilized to describe the beam propagation and the multiple-beam interference occurring in an ideal one-dimensional strip PFP interferometer with no diffraction loss. The spatial-frequency filtration of a finite-size beam input not only determines the transmitted spatial beam profile but also plays a crucial role in affecting the overall spectral transmittance. The inherent deviations of the spectral transmittance from what we know as the standard Airy's formula are revealed in diverse aspects, including the less-than-unity peak transmittance, the displacement of a resonance peak frequency, and the asymmetric detuning profile. Our theoretical analysis extends to the misaligned PFP interferometers, such as the cases in which non-normal-incidence beams or wedge-aligned mirrors are used that could severely degrade the effective interferometer finesse.     

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.