Reference Mirror Research Articles

Geometry of plastic deformation in metals as piecewise isometric transformations

Deformation mechanisms of crystalline solids has been the subject of research for more than two centuries. The theory of dislocations dominates modern views but still has significant gaps demanding the introduction of additional concepts for the coherent quantitative description of physical phenomena. In this work, we propose a coherent geometric description of motion and deformation in crystalline solids as piecewise isometric transformations (PWIT). The latter only includes operations that, similar to interatomic spacing in crystalline lattice, do not alter distances between reference points, i.e. translations, rotations and mirror reflections. The difference between solid-body translations and plastic deformations is that the isometric transformations have discontinuities that in real-life materials realise through dislocations (termination of shifts), disclinations (termination of rotations), and twins (mirror reflections). The conceptual description of plastic deformations as PWIT can be useful for the better description of physical phenomena, proposing new hypothesis, and for developing predictive analytical models. In this paper, the use of this conceptual description enables proposing new hypothesis about the nature of such interesting phenomena in severe plastic deformation as (i) stationary ‘solid state turbulence’ stage in high pressure torsion, and (ii) rate of mass transfer (mechanically assisted diffusion) in simple-shear deformation.

Large-range high-precision macroscopic common phase detection of segmented mirrors based on white light dynamic Twyman-Green interferometer

Segmented mirrors (SMs) provide a solution for the construction of the next generation of extremely large telescopes. The large-range, high-precision detection of piston error between mirror segments is a must-be solved problem in the application of SMs. This paper proposes a large-range high-precision macroscopic co-phase detection method of SMs based on white light dynamic Twyman-Green interferometer. By adopting a white light interferometry in the macroscopic co-phase detection, the probability of the occurring of the 2π ambiguity anomalies can be reduced. A piston error calculation model for SMs was established through Zernike fitting analysis, which improved the detection accuracy. A white light Twyman-Green interferometer with Kohler illumination was experimentally constructed. Based on the scanning of the reference mirror, an efficient detection of the piston error was achieved simultaneously with large range and high precision. Through the new method, the piston error of two planar mirrors was compensated from 38.9344 μm in coarse co-phase stage to 3.6 nm in fine co-phase stage. The method shows great potential for efficient co-phase adjustment of large primary segmented mirrors.

Atom interferometry at arbitrary orientations and rotation rates

The exquisite precision of atom interferometers has sparked the interest of a large community for uses ranging from fundamental physics to geodesy and inertial navigation. However, their implementation for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. We present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. A model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using fiber-optic gyroscopes and a rotating reference mirror to maintain the full contrast of the interferometer. We demonstrate a single-shot sensitivity to acceleration of 24 μg for rotation rates reaching 14° s−1.

High-temperature setup for infrared reflection spectroscopy

We have designed an oven for optical reflection measurements at temperatures as high as 1000 K. The compact setup can be attached to any Fourier-transform infrared spectrometer using a microscope. The details of the layout, operation, and performance are discussed as well as ways for reference measurements and data correction. Finally, the high-temperature setup is utilized to determine the infrared reflectivity of tungsten up to T = 1000 K, which can serve as a reference mirror for future experiments.

An on-machine measurement technique with sub-micron accuracy on a low-precision grinding machine tool

The on-machine measurement system can effectively improve the machining efficiency and accuracy of the optics in the grinding stage, but the common grinding machine has large geometric errors and ambient temperature errors, which are the key factors restricting the accuracy of on-machine measurement. In this paper, a high-precision error separation technique including geometric error separation and temperature error separation is proposed to achieve sub-micron level measurement accuracy in the grinding stage. The on-machine measurement system is built based on the color confocal sensor. A sensitive error model is established based on Abbe's principle and multi-body dynamics, and the geometric error separation with zero Abbe's error is achieved by a high-precision reference mirror. Then the temperature error influence model is established based on the scanning path, and the temperature error separation method based on the auxiliary profile line is proposed according to the temperature error model. Finally, it is verified through experiments that after error separation, the measurement accuracy of the on-machine measurement system is improved from tens of micron to sub-micron, which exceeds the measurement accuracy of ordinary coordinate measurement machines (CMMs), and can effectively improve the machining accuracy and efficiency in the grinding stage.

LISA and LISA-like mission test-mass charging for gamma-ray burst detection

Cubic gold-platinum test-masses (TMs) play the role of free-falling geodesic reference and interferometer end mirrors of the future Laser Interferometer Space Antenna (LISA) observatory for low-frequency gravitational wave detection in space. A similar arrangement has been proposed for the Chinese missions Taiji and TianQin and for the LISA follow-on missions such as ALIA and BBO. The TMs are charged by high-energy particles and photons. The deposited charge couples with stray electric fields surrounding the TMs thus inducing spurious forces that limit the sensitivity of the mission mainly at low frequencies. The TM charging was measured in space in 2016-2017 with LISA Pathfinder (LPF), meant for the testing of the LISA instrumentation. Unfortunately, during the time LPF remained in orbit, no solar energetic particle events or major astrophysical phenomena were observed. We aim at estimating the LISA TM charging attributable to long, short gamma-ray bursts (GRBs) and magnetar flares in comparison to that of charged particles of galactic and solar origin. The contribution of these major astrophysical phenomena to the LISA TM charging is discussed here for the first time. The results found here can be extended to LISA-like missions. The response of the radiation monitors hosted on the three LISA S/C is also evaluated. We show that long, intense extragalactic GRBs and galactic magnetar flares at kpc distances can be detected and monitored through a sudden change from positive to negative charging of the TMs and an increase of the TM charging noise. This is a unique signature since both galactic and solar particles charge positively the LISA TMs. This peculiar behavior of the TM charging would allow monitoring the whole dynamics of GRBs. The suggestion reported in the literature, about the detection of long GRBs and gravitational waves from the same sources, in principle, may apply to LISA and other LISA-like missions since the increase of the TM charging noise during these extreme transient phenomena is estimated to remain below the mission sensitivity while particle detectors are expected to saturate.

A dual-stage correction approach for high-precision phase-shifter in Fizeau interferometers

This paper proposes a dual-stage correction approach for a high-accuracy phase-shifter in Fizeau laser interferometers, effectively reducing the phase shift errors in PSI (Phase-Shifting interferometry) and improving the precision of surface profile measurements. The precision of PSI depends on the displacement accuracy of the reference mirror, and the function of the phase shifter is to drive the reference mirror to generate wavelength-level displacements with nanometer-level accuracy. The first-stage correction aims to reduce the nonlinearity error of the reference mirror by ULPS (Ultra-High Linearity Phase Shifter). The second-stage correction aims to reduce the average velocity error and plane velocity uniformity error of the reference mirror by AVIC (Auto Velocity Iterative Correction). The experimental results indicate that, after the first-stage correction, ULPS exhibits a 0.05 % nonlinearity, a 2.5 nm repeatability, and a 0.2 nm resolution under a load of 20 kg, and its nonlinearity surpassing all phase-shifters documented in the literature. After the second-stage correction, the average velocity error and plane velocity uniformity error of the reference mirror are reduced to 0.07 %.

Stitching interferometry for long X-ray mirrors with lateral multi-shift-based absolute calibration.

To eliminate the reference mirror (REF) error of the Fizeau interferometer for measuring X-ray mirrors, the reference calibration method of lateral multi-shift measurements at the hundreds-micrometer pixel level is presented. Because of the high aspect ratio of long X-ray mirrors, by shifting the surface under test (SUT) along the tangential direction with integer multiple pixels, we extend the calibration method by using the difference between multiple shifted measurements to build an augmented multi-matrix for extracting the two-dimensional (2D) absolute surface. The method can be applied to arbitrary measurement regions of the test optics, and the measurement for both the benchmark sub-aperture and calibration of the REF is accomplished in a single measuring process. Furthermore, by adjusting the shift to the millimeter scale, reference-subtracted sub-apertures can be stitched to obtain the absolute 2D map of the X-ray mirror. Experimental results show that all the 2D discrepancies reach sub-nanometer repeatability, and comparison results between the long trace profiler (LTP) and the proposed method have been performed. Therefore, the results demonstrated that the proposed method meets the requirements of X-ray mirror measurements.

Length measurement based on multi-wavelength interferometry using numerous stabilized frequency modes of an optical comb

Abstract The electro-optic comb (EO comb) with a relatively wide mode spacing of 25 GHz can be resolved into individual frequency modes with a commercially available high-resolution spectrometer. The EO comb has numerous discrete frequency modes, which can serve as a light source for a monochromatic laser interferometer to realize the meter. In this study, a method for measuring the absolute distances based on the multi-wavelength interferometer principle is proposed and demonstrated by simultaneously implementing 102 monochromatic laser interferometers using an EO comb. A phase shifting technique was used to determine the phase for each frequency mode by precisely translating a reference mirror with a constant interval. The phases of the interference signals for 102 stabilized individual frequency modes were measured by applying the model-based analysis on the phase-shifted interference signals. The absolute distance can be determined using phase values of a wavelength set corresponding to five to seven randomly selected frequency modes. In this study, the absolute distances for round-trip distances of 166 mm and 1316 mm were measured and the measurement uncertainty of each distance was evaluated. Through the uncertainty analysis of the distance measurement, the combined uncertainties of the measured distances in a short and long ranges were evaluated to be 30.1 nm and 211.1 nm, respectively. In addition, for each distance, the consistent measurement results of absolute distances were obtained through four different wavelength sets, which show the flexibility of wavelength selection in this work.

High-precision phase-shift method for heavy-load reference mirror based on capacitance sensor monitoring

To address the problems associated with the high-precision phase shift of heavily loaded reference mirrors in large-aperture interferometry, this study proposes a high-precision phase-shifting method based on capacitance sensor monitoring. This method achieves spatial nanoscale phase shifting for a heavy-load reference mirror via spatial three-point synchronous driving of piezoelectric ceramics combined with flexible hinges. The highly sensitive spatial translation of a heavy-load reference mirror is achieved through the gravitational loading of air-floating support and the spatial translation motion modeling of the reference mirror. Nano precision phase-shifting feeds are achieved through spatial in-situ monitoring by combining capacitive sensors and piezoelectric ceramics with a proportion integration differentiation closed-loop drive. Finally, high-precision and high-stability mechanical phase shifting in large-aperture interferometry circumvent the principal shortcomings of existing large-aperture wavelength-tuned phase shifting. The experimental results reveal that the established heavy-load reference mirror mechanical phase shift system has a resolving power of 1.1 nm, frequency response of 120 Hz, and synchronization accuracy of 2° for three-phase shift quantities. This method provides a novel phase-shifting technique for constructing large-aperture phase-shifting interferometers.

High-precision phase shift method for heavy-load reference mirrors based on nano-precision grating sensor monitoring

In large-aperture interferometry, achieving high-precision phase shifting for heavy-load reference mirrors is challenging. This study introduces a method based on nano-precision grating sensor monitoring. The technique utilizes spatial three-point synchronous driving by piezoelectric ceramics, combined with flexible hinges, to enable nanoscale phase shifting of heavy-load reference mirrors. Additionally, it integrates in-situ PID closed-loop drive monitoring at these three points, using nano-precision grating sensors and piezoelectric ceramics. To ensure nanoscale resolved spatial translation, the mirrors are supported by air-bearings that counteract gravity, coupled with a phase shift error calibration model. The final realization of high-precision and high-stability mechanical phase shifting in large-aperture interferometry circumvents the principle defects of existing large-aperture wavelength-tuned phase shifting. The experiments show that the established mechanical phase shifting system with heavy-load reference mirror has a resolution of 1.5 nm, a frequency response of 116 Hz, and a synchronization accuracy of 2° for the three phase shifting quantities, and the method provides a new method and means of phase shifting for the construction of large-aperture phase shifting interferometer.

Low-coherence optical profilometry with multi-reflection reference mirrors for large-depth object measurement.

A new, to the best of our knowledge, optical configuration for digital holographic profilometry for surface profile measurement of large-depth objects is proposed. Two multi-reflection mirrors were employed to extend the maximum axial measurable range by a factor of 2 without any degradation of the spatial resolution. By adjusting the distance and the position of the two multi-reflection reference mirrors, the system can be made more flexible for measuring different parts of the object. In addition to the axial extension, the two-mirror system also increases the visibility of the interference fringes so that the object profile can be measured with high accuracy.

Liquid crystal on silicon-based real time phase stepping interferometry by spatial multiplexing.

In this paper, we present a method to perform phase-shifting interferometry in real time. The technique is based on the use of a parallel aligned liquid crystal on a silicon display as a customized reference mirror. In order to implement the four-step algorithm, a set of macropixels is programmed onto the display, and these are divided into four zones with the appropriate phase shifts. This way, by spatial multiplexing, it is possible to obtain the phase of the wavefront at a rate limited only by the integration time of the employed detector. The customized mirror is able to both compensate the initial curvature of the object under study and introduce the necessary phase shifts to perform phase calculation. Examples of the phase reconstruction of static and dynamic objects are shown.

Bottom-Up Generated Height Gauges for Silicon-Based Nanometrology.

Steady progress in integrated circuit design has forced basic metrology to adopt silicon lattice parameter as a secondary realization of the SI meter that lacks convenient physical gauges for precise surface measurements at a nanoscale. To employ this fundamental shift in nanoscience and nanotechnology, we propose a set of self-organized silicon surface morphologies as a gauge for height measurements within the whole nanoscale (0.3-100 nm) range. Using 2 nm sharp atomic force microscopy (AFM) probes, we have measured the roughness of wide (up to 230 μm in diameter) singular terraces and the height of monatomic steps on the step-bunched and amphitheater-like Si(111) surfaces. For both types of self-organized surface morphology, the root-mean-square terrace roughness exceeds 70 pm but has a little effect on step height measurements having 10 pm accuracy for AFM technique in air. We implement a step-free 230-μm-wide singular terrace as a reference mirror in an optical interferometer to reduce the systematic error of height measurements from >5 nm to about 0.12 nm, which allows visualizing 136-pm-high monatomic steps on the Si(001) surface. Then, using a "pit-patterned" extremely wide terrace with dense but counted monatomic steps in a pit wall, we have optically measured mean Si(111) interplanar spacing (313.8 ± 0.4 pm) that agrees well with the most precise metrological data (313.56 pm). This opens up avenues for the creation of silicon-based height gauges using bottom-up approaches and advances optical interferometry among techniques for metrology-grade nanoscale height measurements.

Optical coherence tomography – basic optical principles

AbstractOptical Coherence Tomography (OCT) is an optical analogue to ultrasound imaging. The much higher speed of light compared with sound allows for finer cross‐sectional views of the retina and anterior segment. Since it is extremely difficult to directly detect the shorter “echo” times it takes light to travel from different structures at axial distances within the eye, interferometry is used. Incident light is thus split into two beams, and the beam backscattered from the ocular tissue is then compared (“interfered”) with the beam that has travelled a known time from the reference mirror. Broadband (i.e., low “coherence”) light sources are used, because they produce a wider band of wavelengths, and thereby enable greater sensitivity in comparing the travel time differences of the two beams. In time‐domain OCT, the reference mirror position is altered, so that interference patterns are generated whenever the two beams have travelled almost the same amount of time. In spectral‐domain OCT, the reference mirror position is fixed and the mixed interference patterns are separated via spectral wavelength analysis. This lecture will explain underlying concepts of OCT with a discussion of cutting‐edge technological developments.

Hybrid Electrostatic–Atomic Accelerometer for Future Space Gravity Missions

Long-term observation of Earth’s temporal gravity field with enhanced temporal and spatial resolution is a major objective for future satellite gravity missions. Improving the performance of the accelerometers present in such missions is one of the main paths to explore. In this context, we propose to study an original concept of a hybrid accelerometer associating a state-of-the-art electrostatic accelerometer (EA) and a promising quantum sensor based on cold atom interferometry. To assess the performance potential of such an instrument, numerical simulations were performed to determine its impact in terms of gravity field retrieval. Taking advantage of the long-term stability of the cold atom interferometer (CAI), it is shown that the reduced drift of the hybrid sensor could lead to improved gravity field retrieval. Nevertheless, this gain vanishes once temporal variations of the gravity field and related aliasing effects are taken into account. Improved de-aliasing models or some specific satellite constellations are then required to maximize the impact of the accelerometer performance gain. To evaluate the achievable acceleration performance in-orbit, a numerical simulator of the hybrid accelerometer was developed and preliminary results are given. The instrument simulator was in part validated by reproducing the performance achieved with a hybrid lab prototype operating on the ground. The problem of satellite rotation impact on the CAI was also investigated both with instrument performance simulations and experimental demonstrations. It is shown that the proposed configuration, where the EA’s proof-mass acts as the reference mirror for the CAI, seems a promising approach to allow the mitigation of satellite rotation. To evaluate the feasibility of such an instrument for space applications, a preliminary design is elaborated along with a preliminary error, mass, volume, and electrical power consumption budget.

A coefficient searching based vibration correction method

Absolute gravimeter has played an important role in geophysics, metrology, geological exploration, etc. It is an instrument applying laser interferometry or atom interferometry to the measurement of gravitational acceleration <i>g</i> (approximately 9.8 m/s<sup>2</sup>). To achieve a high accuracy, a vibration correction method is often employed to reduce the influence of the vibration of the reference object (a retro-reflector or a mirror) on the measurement result of absolute gravimeter. Specifically, in an atomic-interferometry absolute gravimeter, the phase noise caused by the vibration of the reference mirror, namely the vibration phase, can be calculated from the output signal of a sensor, either a seismometer or an accelerometer, placed below or next to the mirror. Considering this vibration phase, the fringe signal of the atomic interferometer as a function of the phase shift set by the control system of the gravimeter can be corrected to approach to an ideal sinusoidal curve, thus reducing the fitting residual. Currently, the parameters in the algorithm of most vibration correction methods used in atomic-interferometry absolute gravimeters are set to be constant. As a result, the performances of these methods may be limited when the practical transfer function between the real vibration of the reference mirror and the signal of the sensor has a variation due to the change of measurement environments. In this paper, based on a simplified model of the practical transfer function previously proposed in an algorithm used in laser-interferometry absolute gravimeter, a new vibration correction method for atomic-interferometry absolute gravimeter is presented. Firstly, a detailed description of its principle is introduced. With a searching algorithm, the time delay and the proportional element in the simplified model can be obtained from the fringe signal of the atomic interferometer and the output of the vibration sensor. In this way, the parameters used to calculate the vibration phase can be adjusted to approach to their true values in different environments, causing the fitting residual of the corrected fringe to decrease as much as possible. Then the measurement results of the homemade NIM-AGRb-1 atomic-interferometry absolute gravimeters using this method is analyzed. It is indicated that with the vibration correction algorithm, the standard deviation of the fitting residual of the measured fringe signal can be reduced by 58% at the best level in a quiet environment. In the future, the performance of this vibration correction algorithm will be further improved in other atomic-interferometry absolute gravimeters during their measurements in hostile environments.

Optimal compensation methods of wedge angle of reference mirror in equal optical path interferometers

在测量多表面平行样品时，多面干涉会影响测量结果。为了能改善多面干涉问题，介绍了等光程干涉仪，并研究了参考镜楔角的最佳补偿方式。在等光程干涉仪中，由于参考镜和分光镜的楔角和倾角的存在，测量结果中会带有回程误差。根据参考镜楔角的不同情况采用了不同的补偿，理论分析并确定了各种补偿的放置方式和补偿量，同时研究了倾角和楔角的大小对于要被遮拦光束高度和像方数值孔径NA的影响。再利用Zemax进行不同补偿方式下的干涉仪仿真，并根据仿真得到的干涉图PV值分析回程误差的大小。分析表明：选用最佳补偿方式，参考镜楔角为1′，回程误差优于0.003个波长。

Measurement Range Enhancement of a Scanning Probe by the Real Time Adjustment of the Interferometer Reference Mirror

Scanning probes on the micro/nano-coordinate measuring machines (micro/nano-CMMs) can produce on/off signals and achieve 3D measurement ability within a specific range. The authors have developed several scanning probes based on a 2D angle sensor and a miniature Michelson interferometer that can work within ± $10~\mu \text{m}$ . When the probe’s lateral displacement is greater than $10~\mu \text{m}$ , the interferometer signal is easy to break, limiting the measurement range of these probes. A 2D angle fine-tuning stage using piezoelectric stack actuators is designed to adjust the reference mirror in real-time to solve signal separation between the reference beam and the measuring beam of the miniature Michelson interferometer. The coupling of the 2D angle fine-tuning stage in the x and y directions is analyzed, and the coupling model is established for a relatively precise compensation. Experimental results show that through the proposed 2D angle fine-tuning stage, the measurement range of the probe can be extended to ± $30~\mu \text{m}$ , and the interference signal can still remain stable and uninterrupted.

Mirau-Based CSI with Oscillating Reference Mirror for Vibration Compensation in In-Process Applications

We present a Mirau-type coherence scanning interferometer (CSI) with an oscillating reference mirror and an integrated interferometric distance sensor (IDS) sharing the optical path with the CSI. The IDS works simultaneously with the CSI and measures the distance changes during the depth scanning process with high temporal resolution. The additional information acquired by the IDS is used to correct the CSI data disturbed by unwanted distance changes due to environmental vibrations subsequent to the measurement. Due to the fixed reference mirror in commercial Mirau objectives, a Mirau attachment (MA) comprising an oscillating reference mirror is designed and built. Compared to our previous systems based on the Michelson and the Linnik interferometer, the MA represents a novel solution that completes the range of possible applications. Due to its advantages, the Mirau setup is the preferred and most frequently used interferometer type in industry. Therefore, the industrial use is ensured by this development. We investigate the functioning of the system and the capability of the vibration compensation by several measurements on various surface topographies.