Picometer Level Research Articles

A 2-DOF drag-free control ground simulation system based on Stewart platform

Space-based gravitational wave detection missions use multiple satellites to form a very large scale Michelson laser interferometer in space. This requires extremely high precision displacement measurements at the picometer level between test masses even millions of kilometers apart. Drag-free control is a key technology to ensure the ultra-static and ultra-stable space experiment platform for space-based gravitational wave detection. This paper proposes an innovative ground simulation scheme for drag-free control principle based on the Stewart platform. The kinematics and dynamics modeling of the Stewart platform used in the experiment is presented. A drag-free ground simulation experimental equipment is designed and built. A two-degree-of-freedom (2-DOF) drag-free controller is designed based on the H∞ loop shaping algorithm which outperforms a PID controller in Simulink simulation. A semi-physical simulation experiment is conducted to verify the controller designed using rapid control prototyping technology. The experimental results show that the control performance reaches the limit accuracy of the hardware device, thus verifying the effectiveness of the drag-free control algorithm.

Experimental demonstration of sub-100 picometer level signal extraction with time-delay interferometry technique

In this work, we have built an experimental setup to simulate the clock noise transmission between two spacecrafts, and further demonstrated the extraction of picometer level signal drowned by the large laser frequency noise and clock noise with the data post-processing method. Laser frequency noise is almost eliminated by using the idea of time-delay interferometry (TDI) to construct an equal arm interferometer. Clock asynchronism and clock jitter noise are significantly suppressed by laser sideband transmitting the clock noise with an electro-optic modulator (EOM). Experimental results show a reduction in laser frequency noise by approximately 105 and clock noise by 102, recovering a weak displacement signal with an average amplitude about 60 picometer and period 1 s. This work has achieved the principle verification of the noise reduction function of TDI technique to some extent, serving the data processing research of space-borne gravitational wave detection.

A nano-radian precision absolute local slope measurement method for X-ray reflectors.

Ultra-precise reflectors in the advanced light source facilities urgently call for local slope error measurements with nano-radian precision. However, the existing methods currently utilized in the long trace profiler systems struggle to meet the requirements. In this paper, we present a weak-value amplification enhanced absolute local slope measurement scheme, in which the surface height difference between two adjacent points can be measured directly with precision on the pico-meter level. As a result, the absolute local slope measurement reaches a record precision level of 9.7 nrad (RMS) with a small lateral separation of 0.5 mm. Comparing to the existing methods, our scheme is more disturbance-resistant, more compact and cost-effective. The local curvature measuring capability is also validated with two synchronously parallel local slope measurement paths, between which the separation is set as 2mm. A local curvature measurement is obtained with precision of 3.4 × 10-6m-1 (RMS) and its corresponding slope variation is 6.8 nrad. Our method exhibits important application prospects in the field of ultra-precise surface fabrication inspection.

Random vibration testing of microelectromechanical deformable mirrors for space-based high-contrast imaging

Space-based stellar coronagraph instruments aim to directly image exoplanets that are a fraction of an arcsecond separated from and 10 billion times fainter than their host star. To achieve this, one or more deformable mirrors (DMs) are used in concert with coronagraph masks to control the wavefront and minimize diffracted starlight in a region of the image known as the “dark zone” or “dark hole (DH).” The DMs must have a high number of actuators (50 to 96 across) to allow for DHs that are large enough to image a range of desired exoplanet separations. In addition, the surfaces of the DMs must be controlled at the picometer level to enable the required contrast. Any defect in the mechanical structure of the DMs or electronic system could significantly impact the scientific potential of the mission. Thus NASA’s Exoplanet Exploration Program procured two 50 × 50 microelectromechanical DMs manufactured by Boston Micromachines Corporation to test their robustness to the vibrational environment that the DMs will be exposed to during launch. The DMs were subjected to a battery of functional and high-contrast imaging tests before and after exposure to flight-like random vibrations. The DMs did not show any significant functional nor performance degradation at 10 − 8 contrast levels.

Intramolecular Force Mapping at Room Temperature.

Acquisition of dense, three-dimensional, force fields with intramolecular resolution via noncontact atomic force microscopy (NC-AFM) has yielded enormous progress in our ability to characterize molecular and two-dimensional materials at the atomic scale. To date, intramolecular force mapping has been performed exclusively at cryogenic temperatures, due to the stability afforded by low temperature operation, and as the carbon monoxide functionalization of the metallic scanning probe tip, normally required for submolecular resolution, is only stable at low temperature. In this paper we show that high-resolution, three-dimensional force mapping of a single organic molecule is possible even at room temperature. The physical limitations of room temperature operation are overcome using semiconducting materials to inhibit molecular diffusion and create robust tip apexes, while challenges due to thermal drift are overcome with atom tracking based feedforward correction. Three-dimensional force maps comparable in spatial and force resolution to those acquired at low temperature are demonstrated, permitting a quantitative analysis of the adsorption induced changes in the geometry of the molecule at the picometer level.

Frequency Division Control of Line-of-Sight Tracking for Space Gravitational Wave Detector

The space gravitational wave detector uses the inter-satellite laser interferometer to measure a change in distance with ultra-high precision at the picometer level. Its special differential wavefront sensing technology based on laser interference is used to obtain the ultra-high-precision relative attitude between spacecrafts. In order to acquire the measurement, it is necessary to maintain high-precision attitude pointing and alignment for the optical path line-of-sight of the detector. This paper proposes a frequency division control method. More specifically, we chose the telescope attitude control loop frequency division as it is the faster response part, mainly relative to the high-frequency band within the measurement bandwidth. The spacecraft attitude frequency division is mainly in the low-frequency band within the measurement bandwidth. Finally, a high-precision simulation analysis is carried out. The results show that compared with traditional methods, the use of frequency division control design can significantly improve the attitude and pointing stability of the system and provide control support for systems requiring high pointing coordination accuracy, such as space gravity wave detectors.

Quantifying the Structure and Chemistry of Semiconductor Devices with the Latest Advancements in Scanning Transmission Electron Microscopy

Electron microscopy has been revolutionized by the advent of the aberration corrector and advances in detector both for imaging and spectroscopy. Aberration correction dramatically improved spatial resolution into the sub-ångstrom regime, while new detectors have unlocked information about materials that was previously only imaginable.While these recent advances have proven essential to the atomic scale characterization of materials, many measurements have remained largely semi-quantitative. In particular, accuracy and precision for scanning transmission electron microscopy (STEM) was significantly hampered by the presence of sample drift and scan distortion. Until recently, this limitation has obscured the capabilities to characterize minute changes to the atomic structure that can ultimately define material properties.In this talk, we will introduce revolving scanning transmission electron microscopy (RevSTEM) for the characterization of semiconductors. The method uses a series of fast-acquisition STEM images, but with the scan coordinates rotated between successive frames. This scan rotation introduces a concomitant change in image distortion that is then used to analyze the sample drift rate and direction. Multiple case studies will be presented to demonstrate the power of this technique to characterize electronic materials. For example, we will show how picometer level precision and accuracy enabled the capability to directly quantify ferroelectric HfO2 thin films. We will also show how RevSTEM images can be used to accurately determine crystallographic parameters in real-space, and to determine the structural origins of polarization.When combined with modern spectroscopy tools, the technique can directly inform growth mechanisms in AlN based materials for fabrication of quantum well structures. Specifically, We will show the interface quality between various AlGaN/AlN quantum wells using a combination of high-angle annular dark-field (HAADF) imaging and energy dispersive X-ray spectroscopy (EDS). We will show that we can directly measure the lattice parameters for each layer and how they vary across each AlN/AlGaN interface. Using EDS, we correlate the lattice parameters and lattice parameter values to the chemical composition in each layer. We show that throughout multiple quantum well structures, there is an asymmetrical interface with a diffusion of Ga on one side of the AlGaN layer. Further, we will discuss fluctuation in the composition present throughout each layer and the role on the local strain distribution.

Dual-comb ranging yields reliable surface acoustic wave amplitude measurements

Quantitative evaluation of mechanical movement at the picometer level found to be precise and accurate.

Automatic digital optical heterodyne phase locking loop in the milliradian domain for spaceborne laser interferometry.

We developed a digital optical phase locking loop (OPLL) with three advantages, including high precision of phase locking, high control bandwidth up to 2.8 MHz, and automatic laser locking strategy. Spaceborne laser interferometers will be used to measure tiny displacements caused by gravitational waves in millions of kilometers range. A slave laser will be heterodyne phase locked to the incoming weak light at the end of an arm, emitting a higher power light back to the other satellite to measure pathlength variations at the picometer level. Such accuracy requires extremely precise OPLL. We report an experiment to demonstrate a digital OPLL that can automatically lock two independent free-running Nd:YAG lasers with residual phase error below 1mrad/Hz above 0.01 Hz, which is the best performance recorded for digital servos, to our knowledge. Such performance tested under a normal laboratory environment will be highly improved in a vacuum environment with temperature and vibration well controlled. Both the digital OPLL and the automatic strategy were implemented on a field programmable gate array that could be potentially used for future gravitational-wave detection. Our experiment might change the thinking of scientists who study phasemeters of gravitational-wave detection because we are aware that the digital phase locking loop used for "optical phase tracking" is differently designed from "optical phase locking."

Hydrogen Bond Engineering Visualized by Picometer-Level Distortion of Planar Porphyrin Isomers.

Directly investigating hydrogen bond (HB) dynamics in molecular materials is a challenging task. Here, we report a set of porphyrin isomers, porphycenes, that visualize slight changes on the order of picometers in the intramolecular HB dynamics. Intramolecular HBs of porphycenes were regulated by the systematic modification at meso positions with methyl (Me), cyclopentyl (Cy5), and cyclohexyl (Cy6) moieties. Notably, the quantum yields varied from 35 to 0.04% in chloroform, depending on a slight distortion in the porphycene framework. SC-XRD, XPS, and NMR clearly revealed that the Me and Cy6 moieties increased the nonradiative deactivation by strengthening the intramolecular NH···N HBs whereas Cy5 retained their photoluminescence properties. This is the first example of how the distortion of planar porphyrinoids at the picometer level along with the strength of the intramolecular NH···N HBs can drastically affect their optical properties. The results revealed new avenues of HB engineering based on porphyrinoids.

A low-noise analog frontend design for the Taiji phasemeter prototype.

The Taiji program plans to utilize the laser interferometer to measure the movement at the picometer level between free-floating test masses. As the phase readout equipment, the phasemeter needs to obtain the beat note with an accuracy of μrad/Hz. The main source of noise in the phasemeter is the analog frontend of the analog to digital converter. A self-designed phasemeter prototype with a low-noise analog frontend, which includes the theme of the pilot tone correction, has been developed and tested for the Taiji program in this Note. The experimental results show that the performance of the developed phasemeter can satisfy the Taiji sensitivity requirement in the whole frequency range. The sensitivity of the board can reach 0.5 μrad/Hz in the frequency range of 0.1-1Hz. Therefore, the prototype gives us a good model for the fully functional Taiji phasemeter.

The Calibration of Displacement Sensors.

Displacement measuring sensors play an essential role in all aspects of dimensional metrology. They can be used for direct displacement measurements but more often they are part of a measurement system, such as an atomic force microscope, roughness tester or a coordinate measuring machine (CMM). In order to achieve traceable measurements that can be related to the meter, these sensors must be calibrated against a reference standard that is more noise- and error-free than the sensor under test. A description of the various methods to achieve the ultimate traceability, repeatability and accuracy of such a calibration system is the main part of this paper. Various interferometric methods will be reviewed including several methods that use directly a primary standard as a reference: either an iodine-stabilized laser or a frequency comb. It is shown that various methods exist to quantify or mitigate the periodic errors that are inherent to interferometric methods. Also it is shown that knowledge of this periodicity may lead to a separation of periodic and non-periodic non-linearity errors of both the calibration instrument as the sensor under test. This review is limited to small-range sensors, typically with a range <100 μm. It is concluded that today’s technology enables sound and traceable sensor calibration up to the sub-nano and even picometer level of uncertainties

Measurement Error of Interferometers with Diffraction Reference Wave

An experimental setup and results on aberration of sources of a reference spherical wave (SRSW) based on a single-mode optical fiber with a subwavelength output aperture obtained with the aid of an optical part of recording system (OPRS) are presented. SRSW and OPRS are developed for referenceless interferometer with diffraction reference wave. Methods for minimization of the measurement error are proposed. The SRSW and OPRS provide subnanometer measurement accuracy for optics. An increase in the measurement accuracy of the interferometer to a picometer level is discussed.

The LISA interferometer: impact of stray light on the phase of the heterodyne signal

The Laser Interferometer Space Antenna is a foreseen gravitational wave detector, which aims to detect 10−20 strains in the frequency range from 0.1 mHz to 0.1 Hz. It is a triangular constellation, with equal sides of m, of three spacecraft, where heterodyne interferometry measures the spacecraft distances. The stray light from the powerful transmitted beam can overlap with the received one and interfere with the heterodyne signal. We investigated the contribution of random phase variations of the stray photons to the noise of the heterodyne signal. A balanced detection scheme more effectively mitigates this adverse effect than a separation of the frequencies of the transmitted and local radiation. In the balanced scheme, in order to limit the phase noise to picometer level, the incoherent power of the stray light must be kept below about 10 nW W−1 for an asymmetry of the recombination beam splitter of 1%.

Ошибки измерений интерферометров с дифракционной волной сравнения

The paper describes the experimental stand and the results of studies of aberrations of the sources of a reference spherical wave (SRSW) based on a single-mode optical fiber with a sub-wave output aperture using the optical part of the recording system (OPRS). SRSW and OPRS are being developed for a referenceless interferometer with a diffraction reference wave. The technique to minimize measurement errors is described. Developed SRSW and OPRS provide subnanometer optics measurement accuracy. The possibilities of improving the accuracy of interferometer measurements to the picometer level are discussed.

Tuning LaAlO3 lattice structure by growth rate at the picometer scale in LaAlO3/SrTiO3 heterostructures

Here, we report an abnormal lattice reconstruction of LaAlO3 in the LaAlO3/SrTiO3 two-dimensional electron liquid heterostructure using the layer-by-layer pulsed laser deposition. We found that the lattice structure change of the top LaAlO3 layer is at the picometer level and is mainly controlled by the oxygen vacancies with an abnormal dependence on the oxygen background pressure. The lattice of the LaAlO3 film expands with more oxygen vacancies grown with high oxygen pressure and collapses with less oxygen vacancies grown with low oxygen pressure. The in situ monitoring of reflective high energy electron diffraction shows the lattice change coincident to the layer-by-layer deposition period change, revealing a non-equilibrium correlation between the lattice and the deposition environment, instead of the commonly assumed equilibrium correlation.

Nonlinear Errors Resulting from Ghost Reflection and Its Coupling with Optical Mixing in Heterodyne Laser Interferometers.

Even after the Heydemann correction, residual nonlinear errors, ranging from hundreds of picometers to several nanometers, are still found in heterodyne laser interferometers. This is a crucial factor impeding the realization of picometer level metrology, but its source and mechanism have barely been investigated. To study this problem, a novel nonlinear model based on optical mixing and coupling with ghost reflection is proposed and then verified by experiments. After intense investigation of this new model’s influence, results indicate that new additional high-order and negative-order nonlinear harmonics, arising from ghost reflection and its coupling with optical mixing, have only a negligible contribution to the overall nonlinear error. In real applications, any effect on the Lissajous trajectory might be invisible due to the small ghost reflectance. However, even a tiny ghost reflection can significantly worsen the effectiveness of the Heydemann correction, or even make this correction completely ineffective, i.e., compensation makes the error larger rather than smaller. Moreover, the residual nonlinear error after correction is dominated only by ghost reflectance.

Electron microscopy with high accuracy and precision at atomic resolution: In-situ observation of a dielectric crystal under electric field

Measuring atomic positions in-situ under an external electric field can provide important insights into the structure-property relationship of electronic materials. In this paper, we demonstrate picometer level accuracy and precision of atomic positions in single-crystalline SrTiO3 under an electric field through annular dark-field scanning transmission electron microscopy. By carrying out electrical biasing in-situ electron microscopy at the atomic scale, the lattice constant was measured with a precision of 9.0 pm under an electric field of ±0.57 kV/cm. In addition, the Ti position in the SrTiO3 unit cell was measured with an accuracy of 20.0 pm at a confidence level of greater than 93%. This opens up a possibility of characterizing functional electronic devices at atomic resolution under operative conditions.

Laser-Frequency Stabilization via a Quasimonolithic Mach-Zehnder Interferometer with Arms of Unequal Length and Balanced dc Readout

Low frequency high precision laser interferometry is subject to excess laser-frequency-noise coupling via arm-length differences which is commonly mitigated by locking the frequency to a stable reference system. This approach is crucial to achieve picometer level sensitivities in the 0.1 mHz to 1 Hz regime, where laser frequency noise is usually high and couples into the measurement phase via arm-length mismatches in the interferometers. Here we describe the results achieved by frequency stabilising an external cavity diode laser to a quasi-monolithic unequal arm-length Mach-Zehnder interferometer read out at mid-fringe via balanced detection. We find this stabilization scheme to be an elegant solution combining a minimal number of optical components, no additional laser modulations and relatively low frequency noise levels. The Mach-Zehnder interferometer has been designed and constructed to minimize the influence of thermal couplings and to reduce undesired stray light using the optical simulation tool ifocad. We achieve frequency-noise levels below 100 Hz/$\sqrt{\textrm{Hz}}$ at 1 Hz and are able to demonstrate the LISA frequency prestabilization requirement of 300 Hz/$\sqrt{\textrm{Hz}}$ down to frequencies of 100 mHz by beating the stabilized laser with an iodine-locked reference.

Improved KLT Algorithm for High-Precision Wavelength Tracking of Optical Fiber Bragg Grating Sensors

Fiber Bragg Gratings (FBGs) are among the most popular optical fiber sensors. FBGs are well suited for direct detection of temperature and strain and can be functionalized for pressure, humidity, and refractive index sensing. Commercial setups for FBG interrogation are based on white-light sources and spectrometer detectors, which are capable of decoding the spectrum of an FBG array. Low-cost spectrometers record the spectrum on a coarse wavelength grid (typically 78–156 pm), whereas wavelength shifts of 1 pm or lower are required by most of the applications. Several algorithms have been presented for detection of small wavelength shift, even with coarse wavelength sampling; most notably, the Karhunen-Loeve Transform (KLT) was demonstrated. In this paper, an improved algorithm based on KLT is proposed, which is capable of further expanding the performances. Simulations show that, reproducing a commercial spectrometer with 156 pm grid, the algorithm estimates wavelength shift with accuracy well below 1 pm. In typical signal-to-noise ratio (SNR) conditions, the root mean square error is 22–220 fm, while the accuracy is 0.22 pm, despite the coarse sampling. Results have been also validated through experimental characterization. The proposed method allows achieving exceptional accuracy in wavelength tracking, beating the picometer level resolution proposed in most commercial and research software, and, due to fast operation (&gt;5 kHz), is compatible also with structural health monitoring and acoustics.