Mirror Surface Research Articles

Automated interferometric stand for determination of amplitude-frequency characteristics of acoustic emitters

An automated interferometric stand (AIS) was created to determine the amplitude-frequency characteristics of acoustic emitters in the range from 0.5 to 200 kHz. The created AIS contains a unit for generating acoustic sinusoidal excitation pulse packets and a recording unit. The unit for generating acoustic pulse packets includes a generator of sinusoidal signals, a microprocessor unit for pulse packets generation and the AIS synchronization, a power amplifier of a sinusoidal signal to create a sufficient power of the acoustic emitter excitation signal. The recording unit includes a Michelson interferometer with a sound-conducting rod in one of the arms. One of the ends of the rod has a mirror surface. The other end is connected to the acoustic emitter through an acoustic contact. The length of the sound-conducting rod is 50 cm, which is enough to ensure measurements at the lower limit of the frequency range of the acoustic emitter radiation. The propagation time of the acoustic wave in the rod is of the order of 75 microseconds. As the end of the rod vibrates due to acoustic excitation, the initial path difference of the optical beams in the interferometer will change, causing a change in the intensity of the illumination produced by the interfering beams. These changes are recorded by photodiode in the other arm of the interferometer. After the photodiode signal is amplified in the amplifier, it is fed to the analog-to-digital converter, the output of which is transferred to the buffer memory, where the discretized values of the response signal amplitude during the time of the measuring pulse are accumulated. The control algorithm of the AIS is carried out with the help of developed software. The results of measuring the amplitude-frequency characteristics of mass-produced broadband acoustic emitters using AIS proved the satisfactory convergence of the obtained frequency responses with the passport data of these serial devices frequency responses. The amplitude-frequency characteristic of experimental sample of a piezoelectric acoustic emitter, made for research on the detection and identification of internal defects in laminated composite structures and "composite-concrete" adhesive joints, was obtained.

Unveiling the origin of XMM-Newton soft proton flares

Context. Low-energy (<300 keV) protons entering the field of view of XMM-Newton can scatter with the X-ray mirror surface and reach the focal plane. They are observed in the form of a sudden increase in the background level, the so-called soft proton flares, affecting up to 40% of the mission observing time. Soft protons can hardly be disentangled from true X-ray events and cannot be rejected on board. Aims. All future high throughput grazing incidence X-ray telescopes operating outside the radiation belts are potentially affected by soft proton-induced contamination that must be foreseen and limited since the design phase. In-flight XMM-Newton’s observations of soft protons represent a unique laboratory to validate and improve our understanding of their interaction with the mirror, optical filters, and X-ray instruments. At the same time, such models would link the observed background flares to the primary proton population encountered by the telescope, converting XMM-Newton into a monitor for soft protons. Methods. We built a Geant4 simulation of XMM-Newton, including a verified mass model of the X-ray mirror, the focal plane assembly, and the EPIC MOS and pn-CCDs. Analytical computations and, when available, laboratory measurements collected from literature were used to verify the correct modelling of the proton scattering and transmission to the detection plane. Similarly to the instrument X-ray response, we encoded the energy redistribution and proton transmission efficiency into a redistribution matrix file (RMF), mapping the probability that a proton from 2 to 300 keV is detected in a certain detector channel, and an auxiliary response file (ARF), storing the grasp towards protons. Both files were formatted according to the standard NASA calibration database and any compliant X-ray data analysis tool can be used to simulate or analyse soft proton-induced background spectra. An overall systematic uncertainty of 30% was assumed on the basis of the estimated accuracy of the mirror geometry and transmission models. Results. For the validation, three averaged soft proton spectra, one for each filter configuration, were extracted from a collection of 13 years of MOS observations of the focused non X-ray background and analysed with Xspec. A similar power-law distribution is found for the three filter configurations, plus black-body-like emission below tens of keV used as a correction factor, based on the dedicated spectral analysis of 55 in-flight proton flares presented in Paper II. The best-fit model is in agreement with the power-law distribution predicted from independent measurements for the XMM-Newton orbit, spent mostly in the magnetosheath and nearby regions. For the first time we are able to link detected soft proton flares with the proton radiation environment in the Earth’s magnetosphere, while proving the validity of the simulation chain in predicting the background of future missions. Benefiting from this work and contributions from the Athena instrument consortia, we also present the response files for the Athena mission and updated estimates for its focused charged background.

Unveiling the origin of XMM-Newton soft proton flares

Context. Low-energy (< 300 keV) protons entering the field of view of the XMM-Newton telescope scatter with the X-ray mirror surface and might reach the X-ray detectors on the focal plane. They manifest in the form of a sudden increase in the rates, usually referred to as soft proton flares. By knowing the conversion factor between the soft proton energy and the deposited charge on the detector, it is possible to derive the incoming flux and to study the environment of the Earth magnetosphere at different distances, given the wide and elliptical XMM-Newton orbit. Thanks to detailed Geant4 simulations, we were able to build specific soft proton response matrices for MOS and PN. Aims. In this second paper, we present the results of testing these matrices with real data for the first time, while also exploring the seasonal and solar activity effect on the proton environment. The selected spectra are relative to 55 simultaneous MOS and PN observations with flares raised in four different temporal windows: December-January and July-August of 2001-2002 (solar maximum) and 2019-2020 (solar minimum). Methods. We selected and extracted the flare mean spectra and count rates in the 2–11.5 keV energy range for the four epochs. After investigating the rate variations among the MOS1, MOS2, and PN instruments, we fit the X-ray spectra using XSPEC and the proton response matrices. The best-fitting parameters derived for the three instruments were compared in order to obtain the systematic errors. Results. There is no seasonal or solar activity effect on the soft proton mean count rates, but we find large discrepancies in the instrument cross-correlations across the 20 years of satellite operations. In 2001-2002, after a few years of operation, the MOS1 and MOS2 rates are similar, and about 20% with regard to the PN ones. After 20 years, PN does not present any variation in its response, while MOS1 suffers a reduction of ∼30%, in addition to the 30% loss due to the damage of two CCDs, and MOS2 is affected by an even worse degradation (70%). The main result of the spectral analysis is that the physical model representative of the proton spectra at the input of the telescope is a power law. However, a second and phenomenological component is necessary to take into account imprecision in the generation of the matrices at softer (< 5 keV) energies. This component contributes for 21% for the MOS and 5% for the PN to the total flux in the 2–5 keV energy range. Conclusions. This study, which is the first application of the soft proton response matrices to real data, shows coherent results between detectors and allows us to estimate systematic uncertainties in the measured spectra of 3% between the two MOS detectors and of 24% between MOS and PN, together with a systematic in the input flux of about a factor of two. They are all likely due to uncertainties in the proton transmission models, with the presence of additional passive material in front of the front-illuminated MOS, and element deposition on its electrode structure across the mission life. Dedicated studies and laboratory measurements are required for improving the accuracy of the proton response files.

MULTI-SENSOR CAMERA MODEL FOR CONTROLLING COORDINATES OF POINTS ON THE SURFACE OF TELESCOPES

A new optoelectronic system for measuring the reflective mirror surface distortion of large telescopes is discussed in this study. This system comprises a multi-matrix structure of CMOS sensors, each sensor responsible for capturing an image of a control point on the mirror surface through a common objective. Simulation and calculation studies show that during operation, the position of the multi-sensor camera on the supporting ring is determined by control points on the telescope surface. The more control points, the higher the accuracy of the calculations. Simulation results indicate that the camera position error falls within acceptable limits when using 5 or more control points. Experimental results show that when calculating simultaneously with 3 control points, the error in determining the angular position of the camera reaches a value of  = 0.302 arc minutes, which is 2 - 2.5 times smaller than when calculating with only one control point.

Hybrid Refractive and Diffractive Testing Method for Free-Form Convex Mirror in High-Resolution Remote-Sensing Cameras

The development of high-resolution and large field of view remote-sensing cameras is inextricably linked to the application of free-form mirrors. The free-form mirror offers higher design of freedom and is more effective at correcting aberrations in optical systems. The surface shape error of a free-form mirror directly affects the imaging quality of remote-sensing cameras. Consequently, a high-precision free-form mirror detection method is of paramount importance. For the convex free-form surface mirror with a large aperture, a hybrid refractive and diffractive testing method combining computer-generated holography (CGH) and spherical mirrors for high-precision null test is proposed in this paper. When comparing the effect of error and the detection sensitivity of different designs, the results showed that the influence of the system error is reduced by about 42% and the sensitivity is increased by more than 2.6 times. The proposed method can achieve higher testing accuracy and represents an effective and feasible approach for the surface shape detection method.

Research on the position of the neutral surface of the space lightweight mirror with a two-axis bipod flexible mount.

This study offers a theoretical solution for the neutral surface position of a space lightweight mirror employing two-axis bipod flexible mounts (TABFM) evenly distributed at three locations along the circumference. To maximize the surface shape accuracy of the mirror (SSAM) under the influence of radial gravity, it is typically necessary that the center of rotation of the TABFM coincides with the position of the neutral surface of the mirror (PNSM). Departing from the PNSM, the SSAM will be substantially deteriorated. In this paper, the compliance matrix of the TABFM utilized for space lightweight mirrors is initially solved. Subsequently, based on the compliance matrix, the analytical formulas and solution approaches for the PNSM under the action of 1g gravity are derived when the support structure of the mirror is symmetrically arranged horizontally and vertically. Additionally, a sensitivity analysis of the PNSM is also conducted. Finally, it is verified through the finite element simulation method. The results indicate that when the support structure of the mirror is uniformly distributed along the circumference and symmetrically arranged horizontally, the PNSM is solely related to the flexibility of the support structure, and the error between the theoretical calculation results and the finite element simulation results is merely 3.2‰; when the mirror support structure is uniformly distributed along the circumference and symmetrically arranged vertically, the PNSM is determined by the flexibility of the support structure and the mass characteristics of the mirror, and the error between the theoretical calculation results and the finite element simulation results is 2.1%. The proposed solution method of PNSM has been implemented in practical engineering projects. The method proposed in this paper can rapidly solve the PNSM and significantly enhance the efficiency and accuracy of integrated simulation optimization. Additionally, the method applies not only to the TABFM investigated in this paper but also to tripod mounts or other symmetric side support structures.

Single-channel high-precision laser rangefinder

The article deals with the construction of a single-channel light rangefinder. At the same time, one of the main difficulties is the presence of depolarization of light, which forms residual light at the output of the analyzer, which greatly affects the measurement accuracy. It is shown that in order to exclude residual light by compensating for depolarization, a KDP crystal plate with the possibility of rotation in a plane parallel to the optical axis is installed at the input of the demodulator.The possibility of using an optical delay line on a single mirror with the possibility of moving along the axis of the radiation source is also considered. The normal to the mirror surface and the optical axes of the KDP crystals are located to the axis of the light source at an angle of 0.7–0.9∘.

Mid-spatial frequency reduction via zero-depth of cut rapid-feed passes in face-turning

The single point diamond turning process (SPDT) is used widely in creating optical grade mirror surfaces on several engineering materials ranging from polymers, and metals, to brittle materials such as silicon and germanium. In visual optic mirror applications, mid-spatial frequency (MSF) errors generated during the SPDT process interfere with the visible spectrum of light thereby affecting the image quality. To overcome these errors, a post-processing operation of polishing the optical mirrors is required. The post-processing step not only increases the complexity of the manufacturing process but also leads to minor geometrical form changes in the mirror which affects performance. To avoid post-processing and minimize MSFs formed during turning- a novel method to modify the toolpath during the machining process has been proposed in this paper. The suggested toolpath strategy comprises two consecutive operations: i) employing variable low feed rates with the specified depth of cut (DoC) and ii) executing rapid traverse rates with zero depth of cut for a predetermined number of passes. The effectiveness of the proposed strategy is tested by carrying out facing experiments in a micro-precision CNC lathe. The power spectral density (PSD) content of the machined surface is then analyzed to check for any improvement in the frequency characteristics. The results show that the frequency errors generated by the toolpath in normal turning operations can be minimized, distributing the resulting PSD peak over a wide range of spatial frequencies. From the PSD plots, it is observed that there is a decrease of 77% and 85.82% in the peak intensity values when compared with surfaces machined at constant feedrates of 150 μm/rev and 200 μm/rev respectively. This method can be applied to nanoprecision SPDT machines to improve the surface quality and to eliminate the MSF errors of the visual optical grade mirrors without the need for post-processing.

CGH calculation algorithm for expressing reflection on a curved mirror surface.

Rendering techniques are important in computer-generated holograms (CGHs) for expressing various types of holo-realistic 3D images. Rendering techniques such as hidden surface removal and reflection by a planar mirror have been proposed thus far, but reflection on a curved mirror surface has yet to be achieved. In this study, we propose a calculation algorithm that can express the reflection of the surrounding environment on a mirror surface defined as a Bézier surface. The results of optical experiments demonstrate that the proposed algorithm enables reflection on such a mirror surface and that the calculation can be accelerated by using a graphics processing unit (GPU).

Interactive CAD Layout of Reflection-Based Mirror Metrology Systems

Concentrating solar mirrors need to accurately focus sunlight onto a receiver. Since mirror surface normal determines reflected light direction, reflection-based metrology methods that measure surface normal have the advantage of directly measuring the mirror’s intended functional performance characteristic. Several methods have been reported that produce high-resolution measurements of mirror surface normal of concentrating solar mirrors [1-8]; these systems typically employ an optical target, a camera, and sometimes an external light source. These elements must be placed in a configuration that satisfies multiple feasibility constraints, including mechanical and optical visibility and reflection constraints. For complex problems or installations in cluttered environments, it can be difficult to analyze all of these constraints manually. We have created a computer automated design (CAD) tool that aids in visualization of reflection-based metrology systems, making it possible to determine layouts for complex metrology design problems. The tool is implemented SolidWorks, a commercial CAD system [9]. By exploiting the SoidWorks constraint satisfaction mechanism, the tool is able to present interactive visualization of reflection and field of view constraints in real time without any additional code or macros. The tool supports ease of use and multiple design configurations through an ordinary spreadsheet interface. The tool can be used to address a variety of reflection-based metrology design problems, and is available to the public as open source.

Greenhouse Gas Mitigation Potential Through Clean Energy for Cement Production in India

Abstract A preliminary approach has been made to assess the concentrated solar energy applications in cement production as well as greenhouse gas mitigation potential. The work starts with identification of processes that utilize thermal energy in cement production. Then, a cluster of cement plants located at different locations in the country has been made. Also, the availability of solar radiation and wind speed at each plant location have been identified. Subsequently, the solar industrial process heating systems have been developed for different locations in the country. Further, solar reactor output, number of heliostats, total land area and mirror surface have been estimated. All these estimations are done by considering three types of thermal losses in solar reactors, i.e., 15, 30 and 45%, respectively. Solar energy can provide a total of 738.11 PJ of thermal energy, which is needed to fulfill the process heating requirement of the calcination process for the manufacturing of cement in India. Solar industrial process heating systems for cement production in India can reduce yearly CO2 emissions by 2457–7648 thousand tons.

Surface quality enhancement in ultrasonic vibration-assisted electrochemical machining

The aviation industry's evolution has introduced electrochemical machining (ECM) as a promising non-traditional technology for aero-engine blades. However, the surface quality of challenging-to-cut materials is compromised due to insoluble electrolytic products on the machined surface. To enhance ECM's surface quality, ultrasonic-assisted ECM (UA-ECM) was introduced for effective electrolytic product removal. This study conducted numerical simulations involving coupled flow field and cavitation models. It also performed observation experiments and a series of UA-ECM trials with varying inlet pressures (0.1 MPa, 0.2 MPa, 0.3 MPa, 0.4 MPa, and 0.5 MPa), vibration amplitudes (21 µm, 17 µm, 13 µm, 8 µm, 4 µm, and 0 µm), and current densities (31.9 A/cm2, 42.1 A/cm2, 61.1 A/cm2, 76 A/cm2, and 100.9 A/cm2). These aimed to elucidate the mechanism of tool ultrasonic vibration's influence on surface quality and corroborate the simulation findings. Notably, under conditions of low inlet pressure (0.1 MPa), high vibration amplitude (21 µm), and high current density (100.9 A/cm2), complete removal of electrolytic products, inhibition of pitting defects, and attainment of a mirror surface with a surface roughness of Ra = 0.14 µm were achieved, with no change in hardness. This clearly demonstrates that the surface quality of ECM on complex surfaces can be significantly enhanced by ultrasonic assistance.

Heliostat geometrical characterization by UAV-assisted, close-range photogrammetry

An innovative approach for the characterization of the mirror geometry of Concentrating Solar Thermal (CST) plants is presented in this article. The approach takes advantage of the current advances in the commercial unmanned aerial vehicle (UAV) technology to perform airborne, close-range photogrammetry for accurate characterization of the mirror’s geometry. To improve spatial resolution and, thus, reconstruction performance, the approach involves a projector for projecting a feature-rich image on the surface of the mirror to be characterized. A UAV flying on a predetermined flight path is used to capture overlapping snapshots of the projected image using its on-board high definition digital camera. By the use of photogrammetry tools, the snapshots are stitched together and processed accordingly to reconstruct the surface of the reflector. Although the approach was tested and validated experimentally by characterizing the mirror surface of a single-facet heliostat, the developed method can also be applied for the characterization of any type of solar concentrating mirror geometry.

Lightwave-controlled relativistic plasma mirrors.

We report on attosecond-scale control of high-harmonic and fast electron emission from plasma mirrors driven by relativistic-intensity near-single-cycle light waves at a kHz repetition rate. By controlling the waveform of the intense light transient, we reproducibly form a sub-cycle temporal intensity gate at the plasma mirror surface, leading to the observation of extreme ultraviolet spectral continua, characteristic of isolated attosecond pulse (IAP) generation. We also observe the correlated emission of a waveform-dependent relativistic electron beam, paving the way toward fully lightwave-controlled dynamics of relativistic plasma mirrors.

Reflectivity measurement of a silicon carbide mirror sample for ITER divertor vacuum ultraviolet spectrometer.

The first mirror is the front-end optic component that reflects light emitted from the plasma to the diagnostic system in fusion plasmas. Silicon carbide (SiC), known for its relatively high mechanical strength and radiation tolerance, has been selected as the substrate material for the first mirror in the ITER divertor vacuum ultraviolet (VUV) spectrometer. To measure the reflectivity of the ellipse cylindrical SiC mirror to be manufactured, a device for reflectivity measurement in the VUV wavelength range was developed. First, the reflectivity of a sample SiC mirror (15mm diameter × 10mm thick) was measured across the ITER-required incidence angles, and the results are reported in this study. A hollow cathode lamp with helium gas was used as the VUV light source in the wavelength range of 23-60nm, and a dedicated VUV spectrometer to select specific wavelengths was developed. The spectrometer utilized laminar-type replica diffraction gratings (Shimadzu 30-006) and two back-illuminated charge-coupled devices (BI-CCD, Andor DO 940P-BEN) for the grating and detector, respectively. A cropping technique with aperture was employed to precisely localize the VUV light's reflection onto the SiC mirror surface. The experimentally measured reflectivity values of SiC at the required incidence angles of VUV light were compared with theoretically calculated reflectivity curves. The oxidation layer (SiO2) formed on the SiC surface and the incidence angle of VUV light to the BI-CCD chip (E2V) would be the factors affecting the accuracy of the reflectivity.

Self-Cleaning Solar Mirror Coatings: From the Laboratory Scale to Prototype Field Tests

In this study, a low-cost, scalable and robust process is proposed as an innovative method for coating solar mirrors with a self-cleaning, transparent in the full solar range and versatile material based on auxetic aluminum nitrides, previously obtained at the laboratory scale. This work presents the scaling-up of the fabrication process from the laboratory to prototypal scale and the preliminary results of outdoor self-cleaning solar mirror field tests in the demonstrative concentrating solar power (CSP) plant ENEASHIP located in Casaccia (Rome) ENEA Research Center. Prototypes with a size of 50 × 40 cm have shown stability in external conditions: no coating degradation occurred during the test campaign. Their washing restores the initial reflectance affected by soiling and the self-cleaning performance allows for the utilization of a reduced quantity of water for cleaning operations with respect to the uncoated glass of back surface mirrors. A similar self-cleaning AlN coating could be utilized on other solar components affected by soiling, such as the glass envelopes in heat-collecting elements, PV panels and other parts where a self-cleaning performance combined with an optical one is required.

Liquid drop interferometry on reflective surfaces.

We resolve the main bottleneck of achieving optimal fringe contrast on highly reflective surfaces through the innovative application of rear surface mirrors, unveiling a pioneering approach to precision measurements exemplified by the modified liquid drop interferometry (LDI) technique. By utilizing a liquid drop on a highly reflective surface, the need for a reference lens with a specific coating is eliminated, showcasing the technique's versatility. Furthermore, we first validate a novel, to our knowledge, expression for p-polarization-dependent radiation pressure, addressing a century-old problem reported in the literature. Beyond advancing measurement techniques, this study broadens the scope of applications requiring high precision, particularly in nanotechnology and surface characterization of metallic-coated surfaces.

Soiling, Adhesion, and Surface Characterization of Concentrated Solar Power Reflectors: Insights and Challenges in the MENA Region

Desert environments are prime locations for concentrated solar power (CSP) applications due to abundant direct normal irradiance. Despite this advantage, the accumulation and adhesion of dust on CSP mirror surfaces present significant challenges to plant efficiency. This paper comprehensively explores soiling phenomena and dust adhesion mechanisms, complemented by advanced measurement techniques tailored for CSP reflector mirrors. By elucidating the factors influencing dust accumulation and delving into the thermodynamics of self-cleaning coatings, alongside an analysis of various mirror materials, this study aims to enrich our understanding of soiling in CSP systems. This study aims to provide valuable insights that will help develop strategies to reduce dust-related efficiency losses in CSP plants, ultimately supporting the development of more reliable and sustainable solar energy solutions for the MENA region.

Optical performance of a solar dish concentrator formed by the same size mirror located on parabolic frame

Solar dish concentrator with low cost and meeting the flux distribution is always pursued for the efficient utilization of concentrated solar energy. This paper investigates the optical performance of a solar dish concentrator formed by using a number of identical square mirror units arranged on a parabolic surface frame. The manufacturing of the mirror surface of this concentrator requires only one kind of mold, which has the significant advantage of low-cost manufacturing. Three common types of mirror units including the parabolic mirror (focal length fm), spherical mirror (radius Rm) and plane mirror are considered. The influence of key geometric parameters including the mirror width d (250–750 mm) and dimensionless parameters such as f1/D, fm/f1 and Rm/f1 (f1 is the focal length of parabolic frame) on its optical performance indexes such as the focused spot size (i.e., intercept width w), average local concentrator ratio (LCR), peak LCR and flux uniformity is analyzed using ray-tracing method, and the correctness of optical model and concentrator optical function is verified by outdoor concentrating experiments. The results show that the concentrator composed of parabolic or spherical mirrors can easily obtain a small circular focusing spot with high LCR and the intercept width can be easily controlled within 200 mm, the peak LCR can reach 34457 (average LCR is 12898), and average LCR reaches 14794 (peak LCR is 29497) at the smallest spot with w = 38.4 mm, which can be a low-cost alternative to parabolic dish concentrator. The concentrator with plane mirrors are easier to obtain square focusing spots with excellent flux uniformity, w can be controlled from 180 to 380 mm and uniform LCR is between 100 and 1400, which is very suitable for concentrating photovoltaic field.

Dual First and Second Surface Solar Mirrors of Polished WS2 and Silver by Dynamical Chemical Plating Technique on Polycarbonate.

This work proposes for the first time protecting-reflecting on both sides of plated mirrors and a solution to polycarbonate surface vulnerability to weathering and scratching using tungsten disulfide (WS2) by mechanical polishing. The ability of the dynamic chemical plating (DCP) technique to deposit Ag films at the nanometer scale on a polycarbonate (PC) substrate and its characteristics to be metallized is also shown. These deposits hold significant promise for concentrated solar power (CSP) applications. Complementarily, the application of WS2 as a reflective film for CSP by mechanical polishing on smooth polycarbonate surfaces is both novel and practical. This technique is innovative and scalable without needing reactants or electrical potential, making it highly applicable in real-world scenarios, including, potentially, on-site maintenance. The effects of surface morphology and adhesion, and the reflectivity parameters of the silver metallic surfaces were investigated. Wettability was investigated because it is important for polymeric surfaces in the activation and metal deposition immediately after redox reactions. The flame technique improved wettability by modifying the surface with carbonyl and carboxyl functional groups, with PC among the few industrial polymers that resisted such a part of the process. The change in the chemical composition, roughness, and wettability of the surfaces effectively improved the adhesion between the Ag film and the PC substrate. However, it did not significantly affect the adhesion between PC and WS2 and showed its possible implementation as a first surface mirror. Overall, this work provides a scalable, innovative method for improving the durability and reflectivity of polycarbonate-based mirrors, with significant implications for CSP applications.