High-precision Interferometer Research Articles

A vertical inertial sensor with interferometric readout

High precision interferometers such as gravitational-wave detectors require complex seismic isolation systems in order to decouple the experiment from unwanted ground motion. Improved inertial sensors for active isolation potentially enhance the sensitivity of existing and future gravitational-wave detectors, especially below 30 Hz, and thereby increase the range of detectable astrophysical signals. This paper presents a vertical inertial sensor which senses the relative motion between an inertial test mass suspended by a blade spring and a seismically isolated platform. An interferometric readout was used which introduces low sensing noise, and preserves a large dynamic range due to fringe-counting. The expected sensitivity is comparable to other state-of-the-art interferometric inertial sensors and reaches values of at 100 mHz and at 1 Hz. The potential sensitivity improvement compared to commercial L-4C geophones is shown to be about two orders of magnitude at 10 mHz and 100 mHz and one order of magnitude at 1 Hz. The noise performance is expected to be limited by thermal noise of the inertial test mass suspension below 10 Hz. Further performance limitations of the sensor, such as tilt-to-vertical coupling from a non-perfect levelling of the test mass and nonlinearities in the interferometric readout, are also quantified and discussed.

Interferometric measurements of refractive index and dispersion at high pressure

We describe a high precision interferometer system to measure the pressure dependence of the refractive index and its dispersion in the diamond anvil cell (DAC). The reflective Fabry–Perot fringe patterns created by both a white light and a monochromatic beam are recorded to determine both the sample thickness and its index at the laser wavelength and to characterize the dispersion in the visible range. Advances in sample preparation, optical setup, and data analysis enable us to achieve 10^{-4} random uncertainty, demonstrated with an air sample, a factor of five improvement over the best previous DAC measurement. New data on {text{H}}_{2}text{O} liquid water and ice VI up to 2.21 GPa at room temperature illustrate how higher precision measurements of the index and its optical dispersion open up new opportunities to reveal subtle changes in the electronic structure of water at high pressure.

Exploration of the coupling between thrust and interference in Taiji-1

As the first technology verification satellite of the space-based gravitational wave detection in China, Taiji-1 has tested the high-precision space laser interferometer, the inertial sensor, the micro thruster and the hyperstatic satellite platform in orbit. The micro thruster plays an important role in the micro propulsion system. The purposes of the research are to investigate the relationship between the thrust and the interference, and then get a comprehensive understanding about the maximum effect of the thrust in Taiji-1. The transfer function between the thrust and the optical path difference fluctuations is established through the modeling, the simulation and the data postprocessing of Taiji-1. In addition, the maximum effect of the thrust in Taiji-1 is about 32 pm/[Formula: see text] with an integration time of 100 s. It can be neglected compared to the requirement of 100 pm/[Formula: see text] for the interferometer stability in Taiji-1.

Structure and morphology of low mechanical loss TiO2-doped Ta2O5

The exceptional stability required from high finesse optical cavities and high precision interferometers is fundamentally limited by Brownian motion noise in the interference coatings of the cavity mirrors. In amorphous oxide coatings these thermally driven fluctuations are dominant in the high index layer compared to those in the low index SiO2 layer in the stack. We present a systematic study of the evolution of the structural and optical properties of ion beam sputtered TiO2-doped Ta2O5 films with annealing temperature. We show that low mechanical loss in TiO2-doped Ta2O5 with a Ti cation ratio = 0.27 is associated with a material that consists of a homogeneous titanium-tantalum-oxygen mixture containing a low density of nanometer sized Ar-filled voids. When the Ti cation ratio is 0.53, phase separation occurs leading to increased mechanical loss. These results suggest that amorphous mixed oxides with low mechanical loss could be identified by considering the thermodynamics of ternary phase formation.

Structure and morphology of low mechanical loss TiO2-doped Ta2O5

The exceptional stability required from high finesse optical cavities and high precision interferometers is fundamentally limited by Brownian motion noise in the interference coatings of the cavity mirrors. In amorphous oxide coatings these thermally driven fluctuations are dominant in the high index layer compared to those in the low index SiO2 layer in the stack. We present a systematic study of the evolution of the structural and optical properties of ion beam sputtered TiO2-doped Ta2O5 films with annealing temperature. We show that low mechanical loss in TiO2-doped Ta2O5 with a Ti cation ratio = 0.27 is associated with a material that consists of a homogeneous titanium-tantalum-oxygen mixture containing a low density of nanometer sized Ar-filled voids. When the Ti cation ratio is 0.53, phase separation occurs leading to increased mechanical loss. These results suggest that amorphous mixed oxides with low mechanical loss could be identified by considering the thermodynamics of ternary phase formation.

A Noncontact Method for Calibrating the Angle and Position of the Composite Module Array

Freeform surface is one of the research focuses in the measurement field. A composite module is composed of a plane and rotating paraboloid. The composite module array can identify 21 geometric errors of the machine tool in a wide range, which is composed of several composite modules. Eliminating the error of the array itself is of great significance for improving measurement accuracy. For this reason, this paper proposed a noncontact method for calibrating the angle and position of the composite module array. This paper used a self-developed angle sensor to access corresponding information and established the mathematical model according to the freeform surface’s geometric characteristics to achieve calibration. In addition, the influence of array placement error on calibration was analyzed. The experimental results showed that the angle repeatability was within 0.4″ around the X-axis and within 0.3″ around the Y-axis, and the position repeatability was within 0.4 µm in the X direction and within 0.7 µm in the Y direction. The measurement comparison experiments with high-precision laser interferometer and uncalibrated array verified the correctness of the experimental results. This method provides an important reference for practical application and freeform surface array calibration, and creates conditions for the implementation of machine tool error detection.

Quantum Interferometer Combining Squeezing and Parametric Amplification.

High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24 dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.

Method to Remove Tilt-to-Length Coupling Caused by Interference of Flat-Top Beam and Gaussian Beam

We discuss the tilt-to-length (TTL) coupling noise caused by interference between a flat-top beam and a Gaussian beam. Several physical models are presented to research the effects of non-diffracted and diffracted beams on TTL noise. A special case that can remove TTL coupling noise is discovered and is verified via both theoretical analysis and numerical simulations. The proposed case could provide desirable suggestions for the construction of high-precision interferometers such as the Laser Interferometer Space Antenna (LISA), Taiji program, or other interferometry systems.

Generating Controllable Laguerre-Gaussian Laser Modes Through Intracavity Spin-Orbital Angular Momentum Conversion of Light

The rapid developments in orbital-angular-momentum-carrying Laguerre-Gaussian (LG0 l) modes in recent years have facilitated progresses in optical communication, micromanipulation and quantum information. However, it is still challenging to efficiently generate bright, pure and selectable LG0 l laser modes in compact devices. Here, we demonstrate a low-threshold solid-state laser that can directly output selected high-purity LG0 l modes with high efficiency and controllability. Spin-orbital angular momentum conversion of light is used to reversibly convert the transverse modes inside cavity and determine the output mode index. The generated LG0 1 and LG0 2 laser modes have purities of ~97% and ~93% and slope efficiencies of ~11% and ~5.1%, respectively. Moreover, our cavity design can be easily extended to produce higher-order Laguerre-Gaussian modes and cylindrical vector beams. Such compact laser configuration features flexible control, low threshold, and robustness, making it a practical tool for applications in super-resolution imaging, high-precision interferometer and quantum correlations.

线性位移台直线度高精密外差干涉测量装置

线性位移台直线度高精密外差干涉测量装置

Masses of the components of SB2 binaries observed with Gaia – IV. Accurate SB2 orbits for 14 binaries and masses of three binaries*

The orbital motion of non-contact double-lined spectroscopic binaries (SB2), with periods of a few tens of days to several years, holds unique accurate informations on individual stellar masses, that only long-term monitoring can unlock. The combination of radial velocity measurements from high-resolution spectrographs and astrometric measurements from high-precision interferometers allows the derivation of SB2 components masses down to the percent precision. Since 2010, we observed a large sample of SB2 with the SOPHIE spectrograph at the Observatoire de Haute-Provence, aiming at the derivation of orbital elements with sufficient accuracy to obtain masses of components with relative errors as low as 1$\%$ when the astrometric measurements of the Gaia satellite will be taken into account. In this paper we present the results from six years of observations of 14 SB2 systems with periods ranging from 33 to 4185 days. Using the TODMOR algorithm we computed radial velocities from the spectra, and then derived the orbital elements of these binary systems. The minimum masses of the 28 stellar components are then obtained with a sample average accuracy of 1.0$\pm$0.2$\,\%$. Combining the radial velocities with existing interferometric measurements, we derived the masses of the primary and secondary components of HIP 61100, HIP 95995 and HIP 101382 with relative errors for components (A,B) of respectively (2.0, 1.7)$\,\%$, (3.7, 3.7)$\,\%$, and (0.2, 0.1)$\,\%$. Using the Cesam2k stellar evolution code, we could constrain the initial He-abundance, age and metallicity for HIP 61100 and HIP 95995.

Experimental research on spectrum and imaging of continuous-wave terahertz radiation based on interferometry**Project supported by the National Natural Science Foundation of China (Grant Nos. 61377109 and 11374007).

A system for measuring terahertz spectrum is proposed based on optical interferometer theory, and is experimentally demonstrated by using a backward-wave oscillator as the terahertz source. A high-resolution, high-precision interferometer is constructed by using a pyroelectric detector and a chopper. The results show that the spectral resolution is better than 1 GHz and the relative error of frequency is less than 3%. The terahertz energy density distribution is calculated by an inverse Fourier transform and tested to verify the feasibility of the interferometric approach. Two kinds of carbon-fiber composites are imaged. The results confirm that the interferometer is useful for transmission imaging of materials with different thickness values.

Analysis and Optimization of Dynamic Measurement Precision of Fiber Optic Gyroscope

In order to improve the dynamic performance of high precision interferometer fiber optic gyroscope (IFOG), the influencing factors of the fast response characteristics are analyzed based on a proposed assistant design setup, and a high dynamic detection method is proposed to suppress the adverse effects of the key influencing factors. The assistant design platform is built by using the virtual instrument technology for IFOG, which can monitor the closed-loop state variables in real time for analyzing the influence of both the optical components and detection circuit on the dynamic performance of IFOG. The analysis results indicate that nonlinearity of optical Sagnac effect, optical parameter uncertainty, dynamic characteristics of internal modules and time delay of signal detection circuit are the major causes of dynamic performance deterioration, which can induce potential system instability in practical control systems. By taking all these factors into consideration, we design a robust control algorithm to realize the high dynamic closed-loop detection of IFOG. Finally, experiments show that the improved 0.01 deg/h high precision IFOG with the proposed control algorithm can achieve fast tracking and good dynamic measurement precision.

Laboratory demonstration of accurate and efficient nanometer-level wavefront control for extreme adaptive optics

A 32 x 32 microelectricalmechanical systems mirror is controlled in a closed-loop adaptive optics test bed with a spatially filtered wavefront sensor (WFS), Fourier transform wavefront reconstruction, and calibration of references with a high-precision interferometer. When correcting the inherent aberration of the mirror, 0.7 nm rms phase error in the controllable band is achieved. When correcting an etched phase plate with atmospheric statistics, a dark hole 10(3) deeper than the uncontrollable phase is produced in the phase power spectral density. Compensation of the mirror's influence function is done with a Fourier filter, which results in improved loop convergence. Use of the spatial filter is shown to reduce the gain variability of the WFS in a quadcell configuration.

Secure Identification of Free‐floating Planets

Among the methods proposed to detect extrasolar planets, microlensing is the only technique that can detect free-floating planets. Free-floating planets are detected through the channel of short-duration isolated lensing events. However, if a seemingly isolated planetary event is detected, it is difficult to firmly conclude that the event is caused by a free-floating planet, because a wide-separation planet can also produce an isolated event. There were several methods proposed to break the degeneracy between the isolated planetary events produced by the free-floating and wide-separation planets, but they are incomplete. In this paper, we show that free-floating planets can be securely identified by conducting astrometric follow-up observations of isolated events to be detected in future photometric lensing surveys by using high-precision interferometers to be operated contemporarily with the photometric surveys. The method is based on the fact that the astrometric lensing effect covers a much longer range of the lens-source separation than the photometric effect. We demonstrate that several astrometric follow-up observations of isolated planetary events associated with source stars brighter than V ~ 19 using the Space Interferometry Mission with an exposure time of 10 minutes for each observation will make it possible to measure the centroid shift induced by primaries with projected separations up to ~100 AU. Therefore, the proposed method is far more complete than previously proposed methods, which are flawed by limited applicability only to planets with projected separations 20 AU or planets accompanied by bright primaries.

Thermoelastic-Damping Noise from Sapphire Mirrors in a Fundamental-Noise-Limited Interferometer

We report the first high-precision interferometer using large sapphire mirrors, and we present the first direct, broadband measurements of the fundamental thermal noise in these mirrors. Our results agree well with the thermoelastic-damping noise predictions of Braginsky, et al. and Cerdonio et al., which have been used to predict the astrophysical reach of advanced interferometric gravitational wave detectors.

Rubidium-stabilized diode laser for high-precision interferometer

An Rb-stabilized diode laser has been developed for use in a high-precision interferometer. The light source is a commercially available external-cavity tunable diode laser. The laser frequency is stabilized to a Doppler-free absorption line of Rb by the third-harmonic technique. The laser emits an output beam with a high power (more than 7 mW) and fast frequency modulation (10 kHz). The relative optical frequency uncertainty of 4.3×10 –10 is achieved for a 0.01-s averaging time.

Astrometric microlensing: a channel to detect multiple lens systems

If a source star is gravitationally microlensed by a multiple lens system, the resulting light curve can have significant deviations from the standard form of a single lens event. The chance of producing significant deviations becomes important when the separations between the component lenses are equivalent to the combined angular Einstein ring radius of the system. For multiple lens systems composed of more than two lenses, however, this condition is difficult to meet because the orbits of such systems are unstable. Even if events are caused by a multiple lens system with stable orbits where a pair of lenses are closely located and the other component (a third body) has a wide separation from the pair, identifying the lens multiplicity photometrically will be difficult because the event will be identified by either a binary lens event caused by the close pair of lenses or a single lens event caused by the third body. In this paper, we show that if a seemingly binary lens event is followed up astrometrically using future high-precision interferometers, the existence of an additional third body can be identified via a repeating event. We show that the signatures of third bodies can be unambiguously identified from the characteristic distortions they make in the centroid shift trajectories. We also show that owing to the long-range astrometric effect of third bodies, the detection efficiency will be considerable even for third bodies with large separations from their close lens pairs.

Astrometric Method for Breaking the Photometric Degeneracy between Binary‐Source and Planetary Microlensing Perturbations

An extrasolar planet can be detected by microlensing because the planet can perturb the smooth lensing light curve created by the primary lens. However, it was shown by Gaudi that a subset of binary-source events can produce light curves that closely resemble those produced by a significant fraction of planet/star lens systems, causing serious contamination of samples of suspected planetary systems detected via microlensing. In this paper, we show that if a lensing event is observed astrometrically, one can unambiguously break the photometric degeneracy between the binary-source and the planetary lensing perturbations. This is possible because while the planet-induced perturbation in the trajectory of the lensed source image centroid shifts points away from the opening of the unperturbed elliptical trajectory, the perturbation induced by the binary-source companion always points toward the opening. Therefore, astrometric microlensing observations using future high-precision interferometers will be important for solid confirmation of microlensing planet detections.

Phase measurement accuracy of feedback interferometers

Feedback interferometers are described with specific reference to potential applications in micro-machines. A theoretical analysis is developed to determine the linearity, stability, and noise performance of this type of interferometer. The theoretical analysis was tested using a prototype high-precision feedback interferometer which showed that, at a feedback loop gain which enabled the system to track 6 fringes, the linearity of the interferometer was better than λ/100 and single phase measurements could be made with an accuracy of λ/80.