Nanometer Displacement Research Articles

A novel peak positioning method for nanometer displacement measurement by optical linear encoder

In the field of precision measurement, subdividing displacement within the grating period to achieve high precision and high resolution remains a significant challenge. For subdivision, traditional optical linear encoders need complex coding and complicated optical systems, which struggle to meet the demands of nanometer measurement. In this paper, based on the fundamental principles of grating displacement measurement, a high-precision peak positioning method from grating images is proposed for linear displacement measurements with nanometer resolution and submicron accuracy. By utilizing a local gradient interpolation algorithm to optimize curves, it could further improve the accuracy of displacement measurement. Experiments demonstrate that this method achieves a resolution of 2 nm and an accuracy of ± 0.1 μm in a range of 50 mm using a grating with a 20 μm period. This sets the groundwork for subdividing optical linear encoders further, the resolution and accuracy could be further improved by optimizing the subdivision method.

Piezoceramic Stick–Slip Actuator with Nanometer Displacement Resolution for Liquid Bridge Stretching

Piezoceramic Stick–Slip Actuator with Nanometer Displacement Resolution for Liquid Bridge Stretching

Design and experiment of multidimensional and subnanometer stage driven by spatially distributed piezoelectric ceramics.

Multidimensional microdriving stage is one of the key components to realize precision driving and high-precision positioning. To meet nanometer displacement and positioning in the fields of micro-/nano-machining and precision testing, a new six-degree-of-freedom microdriving stage (6-DOF-MDS) of multilayer spatially distributed piezoelectric ceramic actuators (PZTs) is proposed and designed. The interior of the 6-DOF-MDS is a hollow design. The flexure hinge is used as the transmission mechanism, and the series-parallel hybrid driving of the corresponding PZTs achieves the microtranslation in the X, Y, and Z directions and the microrotation around the three axes of the microdriving stage, forming a microdisplacement mechanism with high rigidity and simple structure, which can realize the microfeed of 6-DOF. The force-displacement theory and lug boss structure optimization of the 6-DOF-MDS are analyzed, while the strength checking and natural frequency of the 6-DOF-MDS are also simulated by the finite element method. In addition, the real-time motion control system of the 6-DOF-MDS is designed based on Advanced RISC Machines. Through a series of verification experiments, the stroke and resolution results of the 6-DOF-MDS are obtained, where the displacements in the X, Y, and Z directions are 20.72, 20.02, and 37.60μm, respectively. The resolution is better than 0.68nm. The rotation angles around X, Y, and Z are 38.96″, 33.80″, and 27.87″, respectively, with an angular resolution of 0.063″. Relevant coupling experiments were also performed in this paper; in the full stroke linear running of X-axis, the maximum coupling displacements of the Y- and Z-axes are 1.04 and 0.17μm, respectively, with the corresponding coupling rates of ∼5.0% and 0.8%. The maximum coupling angles for the X-, Y-, and Z-axes are 0.33″, 0.14″, and 2.30″, respectively. Considering the coupling of the 6-DOF-MDS, decoupling measures and specific mathematical models have also been proposed. The proposed multidimensional microdriving stage achieves subnanometer resolution and can be used for the precise positioning and attitude control of precision instruments at the nano-/subnanometer level.

A simplified version of rapid susceptibility testing of bacteria and yeasts using optical nanomotion detection.

We present a novel optical nanomotion-based rapid antibiotic and antifungal susceptibility test. The technique consisted of studying the effects of antibiotics or antifungals on the nanometric scale displacements of bacteria or yeasts to assess their sensitivity or resistance to drugs. The technique relies on a traditional optical microscope, a video camera, and custom-made image analysis software. It provides reliable results in a time frame of 2-4 h and can be applied to motile, non-motile, fast, and slowly growing microorganisms. Due to its extreme simplicity and low cost, the technique can be easily implemented in laboratories and medical centers in developing countries.

Characterization of flexural acoustic waves in optical fibers using a fiber-tip interferometer

An experimental study using a fiber-tip interferometer (FTI) to characterize traveling flexural acoustic waves (TFAWs) along an optical fiber is reported. The measurements carried out with the FTI are performed following two different procedures: one of them relies on adjusting the interferometer at the quadrature condition and the other extracts the information from the amplitudes of the fundamental and second harmonic of the interference signal. From our measurements, the detection limit of the FTI is 0.5 nm and the upper limit of the linear regime is 30 nm. These results validate the use of the FTI to detect nanometric displacements associated to the amplitude of acoustic waves along an optical fiber. Parameters such as the acoustic wavelength, attenuation coefficient, and phase velocity are measured for a range of acoustic frequencies around the 2 MHz region. Furthermore, and supported by the in-fiber acousto-optic (AO) effect produced by TFAWs, parameters associated to an acoustic wave packet such as the group velocity and the group attenuation coefficient are also determined. This set of experimental results provide useful information of the mechanisms underlying the propagation of TFAWs along an optical fiber and its corresponding AO effect.

From atomic attrition to mild wear at multi-asperity interfaces: The wear of hard Si3N4 repeatedly contacted against soft Si

Wear causes surfaces to be irreversibly damaged, thereby incurring significant economic cost, for instance in the semiconductor industry. Much progress has been made in describing wear at single asperity interfaces between silicon based materials (Si, SiOx, Si3N4), translating the fundamental understanding of wear into wear predictions and control over wear. Yet, predicting and controlling wear at industrially relevant multi-asperity interfaces remains a challenge, especially when considering the wear of the harder material subjected to repeated, nanometric scale displacement. We studied pre-sliding Si3N4-on-Si wear using the atomic force microscopy topography difference method and showed that the harder Si3N4 wears through either atomic attrition or ductile removal enhanced by subsurface damage, depending on the magnitude of the local Si3N4-on-Si contact pressure. Our methods and results bridge fundamental insight into wear based on nanoscale studies to industrial applications.

Absolute distance measurement using frequency sweeping interferometry with large swept range and target drift compensation

Frequency sweeping interferometry (FSI) is an attractive absolute distance measurement (ADM) method because of the advantages of large unambiguity range, simple structure and excellent flexibility. By using a reference interferometer (RI), the calibration of the frequency sweeping range in FSI can be avoided, and the complexity and cost of the system can be further reduced. Then, the measurement accuracy is associated with the accuracy of phase demodulation, the range of frequency sweeping and the compensation of target drift. In this paper, ADM using FSI with large swept range and target drift compensation is presented. A frequency stabilized HeNe laser that travels along the same optical path with the swept source laser was employed to monitor the target drifts of the measurement interferometer and RI. Interference phases of the corresponding interferometers were extracted simultaneously using phase generated carrier demodulation technique, and an accuracy better than 1° was verified by nanometer displacement measurement. Comparative experiments of ADM at a distance of ∼4.5 m with different swept ranges before and after target drift compensation were carried out, and the results demonstrated that larger swept range and target drift compensation could greatly improve the stability and accuracy of measurement.

Ultrasensitive and long-range transverse displacement metrology with polarization-encoded metasurface.

A long-range, high-precision, and compact transverse displacement metrology method is of crucial importance in many research areas. Recent schemes using optical antennas are limited in efficiency and the range of measurement due to the small size of the antenna. Here, we demonstrated the first prototype polarization-encoded metasurface for ultrasensitive long-range transverse displacement metrology. The transverse displacement of the metasurface is encoded into the polarization direction of the outgoing light via the Pancharatnam-Berry phase, which can be read out directly according to the Malus law. We experimentally demonstrate nanometer displacement resolution with the uncertainty on the order of 100 picometers for a large measurement range of 200 micrometers with the total area of the metasurface being within 900 micrometers by 900 micrometers. The measurement range can be extended further using a larger metasurface. Our work opens new avenues of applying metasurfaces in the field of ultrasensitive optical transverse displacement metrology.

Absolute distance measurement using sinusoidal phase modulating frequency sweeping interferometry with a reference interferometer.

Frequency sweeping interferometry with reference interferometer based on sinusoidal phase modulating technique is proposed in this paper for absolute distance measurement. With the frequency of the external cavity diode laser (ECDL) swept continuously in sinusoidal, a HeNe laser was employed to monitor the drifts of the target and the reference length, and influences caused by drifts during the measurement were compensated in real time. Sinusoidal phase modulation with non-overlapping frequencies were applied to the two laser lights individually by two electro-optic modulators (EOM), and the interference phases corresponding to the two laser lights were extracted simultaneously using the phase generated carrier (PGC) demodulation based on frequency-division multiplex technique. Performance of the phase detection method has been verified by nanometer displacement measurements. Experimental results show that the measurement uncertainty can be considerably reduced by compensating the influences of drifts and by applying linear regression to get the ratio of interference phase changes between the measurement interferometer and the reference interferometer. Comparison of the absolute distance measurement with an incremental interferometer yields a measurement uncertainty of 10-5, which is in good agreement with the estimation of the measurement uncertainty.

Multimode fiber ruler for detecting nanometric displacements

Light is a perfect tool for numerous metrology applications. To deliver light to hard-to-reach places, fiber probes are widely used. Hair-thin endoscopes based on multimode fibers offer exceptional performance in terms of information density and instrument footprint. Here, we integrate optical metrology into a flexible fiber probe and present a multimode fiber ruler for detecting nanometric displacements. A fast single-shot measurement demonstrates two-dimensional resolving power of 1.8 nm, which is 670 times smaller than the diffraction limit of the optical system and 24 times smaller than the demagnified image pixel size. The multimode fiber ruler does not require detailed field mapping; therefore, low-magnification optical systems can be used to increase the light intensity on a sensor. Moreover, the proposed approach does not rely on any special structures, such as optical grating or metasurfaces. A high-resolution two-dimensional fingerprint is naturally “printed” on the multimode fiber output facet. Our results enable fiber-based displacement measurements with nanometer precision, establishing a new benchmark for fiber-based optical alignment sensors and metrology.

Simultaneous Phase Detection of Multi-Wavelength Interferometry Based on Frequency Division Multiplexing

Simultaneous phases detection in multi-wavelength interferometry (MWLI) is essential for high-accuracy dynamic absolute distance measurement in high-end equipment manufacturing. To address this problem, a simultaneous phase detection scheme based on frequency-division multiplexing (FDM) technique is proposed in this paper. High-frequency sinusoidal phase modulation with non-overlapping frequencies were applied to multiple lasers individually using electro-optic modulators (EOMs), and interference phases of multiple wavelengths were extracted in parallel using phase generated carrier (PGC) demodulation technique from the FDM interference signal. Principles of FDM multi-wavelength interferometry and simultaneous phase detection scheme were illustrated. A FDM dual-wavelength interferometer was constructed to verify the performance of the proposed phase detection scheme by simulation analysis and experiments. Results of simulations show that the resolution, accuracy and nonlinear error of the two demodulated phases are all better than 0.01°. Experiments of nanometer displacement measurement further verified the good performance of the phase detection scheme and its feasibility in dynamic measurement.

Self-referenced nanometric displacement sensing assisted by optical anapole mode

Long range optical rulers measuring distance greater than 10 nm have important applications in monitoring biological processes, nanolithography, and nanometrology. In this work, we show that lateral displacement over 120 nm can be determined by measuring two reflection peaks of the proposed nanostructure. The optical anapole in the nanostructure is excited, resulting from interactions of plasmonic resonance modes of nanoholes perforated in metal films and an array of nanoblocks. Results show that a 120 nm relative displacement between the nanoblocks and nanoholes induces a negative correlated 90% variation of reflection spectrum which can be used for self-referenced measurement. The proposed design could find applications in nanometrology, biosensing, and nanofabrication.

Optically computed phase microscopy for quantitative dynamic imaging of label-free cells and nanoparticles.

Numerous drug delivery systems based on nanoparticles have been developed, such as those used in BioNTech/Pfizer's and Moderna's Covid vaccines. Knowledge on mechanical interactions between cells and nanoparticles is critical to advance the efficiency and safety of these drug delivery systems. To quantitatively track the motion of cell (transparent) and nanoparticles (nontransparent) with nanometer displacement sensitivity, we investigate a novel imaging technology, optically computed phase microscopy (OCPM) that processes 3D spatial-spectral data through optical computation. We demonstrate that OCPM has the capability to image the motion of cells and magnetic nanoparticles that are mechanically excited by an external magnetic field, quantitatively and in the en face plane.

Single-cell all-optical coherence elastography with optical tweezers.

The elastic properties of cells are important for many of their functions, however the development of label free noninvasive cellular elastography method is a challenging topic. We present a novel single-cell all-optical coherence elastography method that combines optical tweezers producing mechanical excitation on the cell membrane or organelle and phase-sensitive optical coherence microscopy measuring sample response and determining its mechanical properties. The method allows living cells imaging with a lateral resolution of 0.5 μm and an axial resolution up to 10 nm, making it possible to detect nanometer displacements of the cell organelles and to record the propagation of mechanical wave along the cell membrane in response to optical tweezers excitation. We also demonstrate applicability of the method on single living red blood cells, yeast and cancer cells. The all-optical nature of the method developed makes it a promising and easily applicable tool for studying cellular and subcellular mechanics in vivo.

A Nanometer Resolution Wearable Wireless Medical Device for Non Invasive Intracranial Pressure Monitoring

The non-invasive intracranial pressure (NIICP) method based on a skull deformation has been proven to be a significant tool for an assessment of the intracranial pressure (ICP) and compliance. Herein, we present the development and characterization of a novel wireless sensor that uses this method as its working principle and was designed to be easy to use, to have a high resolution, and to achieve a good accessibility. Initially, a brief review of the physiology fundamentals of the ICP and the historic evolution of the NIICP method are mentioned. The sensor architecture and the rationale for the chosen components are then presented, aiming to ensure nanometer displacement measurements, the conversion of analog resolution to digital at a high speed, the fewest amount of distortion, wireless communication, and signal calibration. The NIICP signal has a typical amplitude of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5~\mu \text{m}$ </tex-math></inline-formula> , and thus a resolution of at least 1% of this amplitude is required for an NIICP waveform analysis. We also demonstrate a 40-nm resolution of the sensor using a nanometric displacement test system that can also respond dynamically for NIICP signals from 50 to 180 bpm without any significant distortion (maximum deviation of P2/P1 ratio of 2.6%). The future applications for this device are broad and can enhance a clinical assessment of the intracranial dynamics.

Self-correction of air refractive index in distance measurement using two-color sinusoidal phase modulating interferometry

A two-color sinusoidal phase modulating (SPM) interferometer based on electro-optic modulator (EOM) is devised for self-correction of air refractive index in distance measurement. Two laser sources with high frequency stability and close wavelengths (633 nm and 782 nm) are used in this scheme. High-accuracy phase demodulation was realized using phase generated carrier (PGC) demodulation techniques with an FPGA-based signal processing board. Experimental results of nanometer displacement measurements show that the resolution and accuracy of PGC demodulation is better than 1°, and the nonlinear error is less than 0.2°. Performance tests of two-color SPM interferometer compared with one-color interferometers under dynamic environment were implemented with an arm length difference of 4 m. The results show that, the measured distance of one-color interferometer drifts 4.8 μm in 600 s, which is caused by the deviation between the measured value of air refractive index and the actual value along the laser propagation path, and this drift reduces to ±1.5 μm using two-color interferometer without environmental sensing.

High-speed laser speckle imaging to unravel picoliter drop-on-demand to substrate interaction.

Understanding phenomena such as evaporation and imbibition of picoliter droplets into porous substrates is crucial in printing industry to achieve a higher printing quality and print speed. After printing, the residual pigment must remain fixed at the desired location on a substrate and be of a desired volume to yield a high resolution and vibrantly printed page that has become the expectation of modern printing technology. Current research entails not only chemical composition of the ink but also how this links to the dynamics and interactions that occur between the ink and the substrate at every stage of the printed spot formation, including evaporation, wetting, and imbibition. In this paper, we present an instrument that can print on-demand picoliter volume droplets of ink onto substrates and then immediately record on evolution of the resulting dynamics when these two materials interact. This high-speed laser speckle imaging (HS-LSI) technique has been developed to monitor nanometer displacement of the drying and imbibing ink droplet at a high frame rate, up to 20000Hz, given the short timescales of these interactions. We present the design of the instrument, discuss the related challenges and the theory underlying the LSI technique, specifically how photons non-evasively probe opaque objects in a multiple scattering regime, and show how this technique can unravel the dynamics of drying and imbibition. We will finish giving a validation on the instrument and an example of its usage.

Nanometric displacement sensor with a switchable measuring range using a cylindrical vector beam excited silicon nanoantenna.

We demonstrate a nanometric displacement sensor with a switchable measuring range by using a single silicon nanoantenna. It is revealed that the interference between the longitudinal and transverse dipolar scattering can be well tuned by moving the nanoantenna in the focal field of the cylindrical vector beam. As a result, a position related scattering directivity is found and is used as a displacement sensor with a 4.5 nm lateral resolution. Interestingly, the measuring range of this displacement sensor can be extended by twice through simply changing the excitation from the azimuthally polarized beam to the radially polarized beam. Our results provide a facile way to tune the measuring range of the nanometric displacement sensor and may open up an avenue to super-resolution microscopy and optical nanometrology.

Absolute distance measurement using laser interferometric wavelength leverage with a dynamic-sideband-locked synthetic wavelength generation.

Absolute distance measurement with laser interferometry has the advantages of high precision and traceability to the definition of meter but its accuracy is primarily limited by the phase demodulation. Among kinds of absolute distance interferometric measurements, the multi-wavelength interferometry is widely used but seriously limited by the generation of suitable synthetic wavelength and the stability of adopted synthetic wavelength. Inspired by the mechanical lever, we hereby establish a principle of laser interferometric wavelength leverage (LIWL) for absolute distance measurement. By keeping the phase difference in two single wavelengths constant, LIWL achieves the measurement of large distance with respect to synthetic wavelengths by detecting nanometer displacement with respect to a single wavelength. The merit of LIWL is eliminating the influence of phase demodulation error. And a dynamic-sideband locking method based on a high-frequency electro-optic modulator is proposed, which can flexibly and quickly generate variable synthetic wavelengths from tens of kilometer to millimeter with high stability. Experimental setup was constructed and absolute distance measurements were performed. Experimental results show that a measurement range of 100 m with residual error of less than 15 µm has been achieved by comparing the LIWL system and an incremental laser interferometer.

Experimental and numerical investigation of difference in diameter enlargement and circularity of micro-holes drilled by flexural spindle head

The flexural bearing or the flexural cartridge allows very nano-meter axial displacement movement, which is frictionless and noiseless. The repeatability of the mechanism obtained is achieved by bending of the load element. The bearing can operate under stringent conditions such as vacuum, elevated temperatures (0–40 °C), and moist conditions. Hence, due to these indigenous properties, these bearings are observed in applications such as linear bearing of linear compressor, flexural bearing electromagnetic linear actuator, and parasitic error-free mechanism. The endorsed capability of obtaining high-level positional accuracy along with repeatability leads to design and development of low-cost flexural cartridge for micro-drilling spindle head. This flexural cartridge provides a linear guideway while feeding inside the test specimen (in micro-drilling operation). The designed head dampens and nullifies the force, acting on the shaft carrying the micro-tool. The designed spindle head carrying the three-leg spiral flexural stack is assembled on the designed machine tool. The run out measured on the spindle shaft is 50 µm. Four test specimens, namely aluminum, brass, acrylic and mild steel, are drilled by three drills of diameter 1 mm, 0.8 mm, and 0.5 mm each. The main objective of the article is to understand the differential analysis of diameter enlargement and circularity between the experimental method and the numerical method. The answers predicted by the experimental method may have second possible value as it depends upon judgment of inscribing the circle/points in the computer-aided design (CAD) environment. This ambiguity is excluded by the MATLAB code, which gives one specific answer. The maximum difference in diameter enlargement for aluminum, brass, acrylic, and mild steel specimens are 3.8 µm, 11 µm, 24.6 µm, and 16.1 µm, respectively, whereas the maximum difference in circularity for the same specimens is 11.8 µm, 1.3 µm, 8.2 µm, and 16.8 µm, respectively. This difference is termed as the |error|.