Focal Spot Research Articles

The Microchip Laser and Its Drive Control System for Planetary Mass Spectrometry Measurements

To fulfill the requisites of planetary mass spectrometry applications, this paper introduces the creation of a miniaturized, low-power passive Q-switched microchip laser system. The entire system, inclusive of the laser and all electronic components, weighs 106 g, with power consumption below 3 W. The laser output exhibits a pulse duration of 410 ps, accompanied by a single pulse energy of 16.8 μJ. Augmented by the optical focusing system, the system attains a focal spot size of approximately 15 μm and laser irradiance of up to 22 GW/cm2. The driving control system facilitates versatile regulation of parameters such as output current amplitude, pulse duration, and frequency, thereby modulating the laser output frequency and duty cycle. The microchip laser fully meets the power requirements for exciting plasma from planetary rocks and soil.

Characterisation of coherent ultrasonic nonlinear imaging

Nonlinear ultrasonic imaging methods for non-destructive testing have shown sensitivity to early damage formation. Among those, the Fundamental wave Amplitude Difference (FAD) technique has been proposed in the literature as a nonlinearity mapping method for defect visualisation. It does so by calculating the residual between a low and high nonlinearity image, which is achieved by some modulation of the focal spot amplitude. This is realised either through different input voltages or alternating the element-wise firing scheme. This paper assesses the sensitivity of FAD through different techniques used for the generation of the low nonlinearity images, using both theoretical and experimental approaches. These techniques include (1) Different-Voltage FAD (DV-FAD); (2) Odd-Even FAD (OE-FAD) and; (3) Parallel–Sequential FAD (PS-FAD). Formulae are derived that allow the different firing sequences and image corrections to be compared. The FAD techniques are then experimentally evaluated against the theory, showing a 50% amplitude gain at the crack tip when comparing PS-FAD to OE-FAD and DV-FAD. Additionally, the instrument behaviour is assessed by considering the image correction required to improve the image contrast for the visualisation of the crack tip. Finally, it is shown that all FAD techniques are equivalent in terms of nonlinear detection but additional work is required in comparing the performance of other array controllers when using FAD.

Fiber end integrated surface plasma lens for circular airy beam shaping

This paper presents a circular Airy beam generator based on a fiber end integrated surface plasma lens. The surface plasma lens consists of a nano-annular slot and an array of series concentric circular grooves etched on the gold film coated on the fiber end. When the fiber light field illuminates the nano-annular slot, surface plasmon polaritons (SPPs) will be excited, then the SPPs propagates along the surface of the gold film, and will finally be decoupled into free space to generate circular Airy beam by the array of concentric circular grooves. The effect of the parameters of the plasma lens on the properties of the output circular Airy beam, such as self-focusing, focal spot size, is studied in detail via FDTD simulations. In addition, we found that the proposed plasma lens has a high tolerance to manufacturing errors. The case that instead of the nano-annular slit with a circular wheat-spike shaped structure is also investigated. In this case, due to the different photon spin response of the circular wheat-spike shaped structure, the device can generate circular Airy beam when the input fiber light field is right-handed circularly polarized (RHCP) light, and subwavelength Bessel-like nondiffracting beam when the input fiber light field is left-handed circularly polarized (LHCP) light. These results provide a highly integrated all-fiber circular Airy beam and subwavelength Bessel-like nondiffracting beam generation scheme, which may be useful in the areas of fiber end structured light beam shaping and fiber-integrated photonic devices.

Large-volume focus control at 10 MHz refresh rate via fast line-scanning amplitude-encoded scattering-assisted holography

The capability of focus control has been central to optical technologies that require both high temporal and spatial resolutions. However, existing varifocal lens schemes are commonly limited to the response time on the microsecond timescale and share the fundamental trade-off between the response time and the tuning power. Here, we propose an ultrafast holographic focusing method enabled by translating the speed of a fast 1D beam scanner into the speed of the complex wavefront modulation of a relatively slow 2D spatial light modulator. Using a pair of a digital micromirror device and a resonant scanner, we demonstrate an unprecedented refresh rate of focus control of 31 MHz, which is more than 1,000 times faster than the switching rate of a digital micromirror device. We also show that multiple micrometer-sized focal spots can be independently addressed in a range of over 1 MHz within a large volume of 5 mm × 5 mm × 5.5 mm, validating the superior spatiotemporal characteristics of the proposed technique – high temporal and spatial precision, high tuning power, and random accessibility in a three-dimensional space. The demonstrated scheme offers a new route towards three-dimensional light manipulation in the 100 MHz regime.

Effect of beam and gate offset size on x-ray focal spot resolution of a cold cathode electron beam

In x-ray imaging, high resolution is essential, particularly in sectors such as medical and industries where the need for nondestructive defect detection is required. Previous research has shown that altering beam design and the number of gates offset holes has an impact on focal spot size (FSS). However, the specific effects of beam size and offset size were not thoroughly assessed. In the present study, the influence of beam size and gate offset size was evaluated by utilizing a cold cathode electron beam. Various beam sizes were employed to achieve a small FSS, and subsequently, the smallest beam was utilized to examine the impact of gate offset size. In doing so, the smallest FSS of 0.25 mm vertical and 0.33 mm horizontal was attained without the utilization of any additional focusing lens. This illustrates that by adjusting the beam size and gate offset size, it is possible to attain a small FSS, facilitating the development of an economically viable x-ray imaging beam.

Dual‐beam lasers meet challenges of the automotive industry

AbstractThe challenges of transport electrification require the adoption of new manufacturing techniques. Lasers excel in most difficult tasks due to their ability to deliver energy with great precision, and their temporal and spatial control. Dual‐beam, adjustable mode beam (AMB) technology enables the versatile spatial control of laser energy deposition, providing wide process windows for defect‐free welding and focal spot positioning. The AMB technology improves process quality and speed in dissimilar material welding, copper welding and in structural aluminum welding across many applications in the automotive industry – from the production of batteries and drivetrains to structural body parts.

Multi‐focal channel attention for medical image segmentation

AbstractMedical image segmentation through the use of deep learning is becoming a trend targeting to automate disease detection and provide effective treatment. Traditionally huge manual efforts are associated with medical image processing by medical staff. The wide use of neural networks driven by the progressive advancement in computing power and the availability of training data provides instrumental means to automate medical image processing. A polyp refers to an abnormal growth that can occur in various parts of the body. While the majority of polyps are noncancerous or benign, there are instances where certain types can develop into cancer. Detecting and segmenting polyps is highly valuable for identifying early signs and potentially enabling more effective treatment of colon cancer. In this paper, we introduce a novel method for segmenting polyp images. The proposed method utilizes convolutional neural networks (CNNs) and employs an enhanced attention mechanism. To cater to a more granular attention view, this paper enhances the Convolutional Block Attention Module by introducing the multi‐focal channel attention (MFCA) concept, which we call MFCA. In the proposed MFCA channel attention, focal attention spots allow us to consider scattered areas of interest more effectively. To evaluate the effectiveness of the proposed method, multiple experiments are conducted on five well‐known benchmark datasets for polyp image segmentation: Kvasir, CVC‐Clinic DB, CVC‐Colon DB, CVC‐T, and ETIS‐Larib. Various testing scenarios are examined, including the impact of two focal attention spots and four focal attention spots. The experimental results demonstrated that the proposed method achieved superior performance compared to previous state‐of‐the‐art techniques on two of the benchmark datasets, and ranked second on a third dataset.

Geant4 Simulation of Scatter Radiation Removal: Comparison and Validation of Anti-scatter Grid and Air Gap for X-ray Mammography

Abstract: X-ray mammography modality provides excellent low-contrast resolution images with low scatter radiation, making it the gold standard in diagnosing breast cancer. Anti-scatter grid and air gap techniques are typically used to further minimize the scatter radiation and improve image quality. Thus, Geant4 simulation was used to investigate the effectiveness of these techniques in removing scatter radiation in X-ray mammography. The effectiveness of an anti-scatter grid was evaluated using the Bucky factor, where it linearly increased with increasing the anti-scatter grid ratio. It was found that increasing the grid frequency affects the Bucky factor depending on the design of the grid ratio. This research proved that designing an anti-scatter grid with high grid frequency (80 lp/mm), low grid ratio (2:1), and proper orientation minimized common anti-scatter grid artifacts. The effectiveness of the air gap technique was also evaluated using the air gap dose factor. It increased non-linearly with increasing magnification. This research validated that using smaller pixel sizes and small focal spot sizes improved spatial resolution with magnification. Our simulation validated that the anti-scatter grid and air gap were effective techniques in removing scatter radiation. By comparing these techniques, the anti-scatter grid was more effective in removing scatter radiation at the expense of increasing the radiation absorbed dose with the exception of 2.0 magnification. It’s recommended to be extremely cautious when using 2.0 magnification or a grid ratio higher or equal to 8:1. These parameters may cause the radiation absorbed dose to be increased by several folds. Keywords: Geant4, Gate, X-ray mammography, Scatter removal, Anti-scatter grid, Air gap.

Multilayer Kirkpatrick-Baez focusing mirrors with phase compensation for sub-20 nm focusing at the hard X-ray nanoprobe beamline of SSRF

The hard X-ray nanoprobe beamline is the first beamline to take advantage of the full coherent beam to attain the nanoscale focusing at the Shanghai Synchrotron Radiation Facility (SSRF). Here we introduce the beamline and specially go over the features of the multilayer Kirkpatrick-Baez focusing system and its supporting phase compensator system. The performance and stability of the phase compensator are also put to the test. By using the speckle scanning metrology, the wavefront of a focused beam was characterized and intensity distribution near the focus was reconstructed. The focusing performance was greatly enhanced by two phase compensations based on a global optimization technique, and a two-dimensional focal spot of 26 nm × 17 nm was achieved and maintained with good stability.

A carbon nanotube x-ray source array designed for a new multisource cone beam computed tomography scanner

Cone beam computed tomography (CBCT) is known to suffer from strong scatter and cone beam artifacts. The purpose of this study is to develop and characterize a rapidly scanning carbon nanotube (CNT) field emission x-ray source array to enable a multisource CBCT (ms-CBCT) image acquisition scheme which has been demonstrated to overcome these limitations. A CNT x-ray source array with eight evenly spaced focal spots was designed and fabricated for a medium field of view ms-CBCT for maxillofacial imaging. An external multisource collimator was used to confine the radiation from each focal spot to a narrow cone angle. For ms-CBCT imaging, the array was placed in the axial direction and rapidly scanned while rotating continuously around the object with a flat panel detector. The x-ray beam profile, temporal and spatial resolutions, energy and dose rate were characterized and evaluated for maxillofacial imaging. The CNT x-ray source array achieved a consistent focal spot size of 1.10 ± 0.04 mm × 0.84 ± 0.03 mm and individual beam cone angle of 2.4° ± 0.08 after collimation. The x-ray beams were rapidly switched with a rising and damping times of 0.21 ms and 0.19 ms, respectively. Under the designed operating condition of 110 kVp and 15 mA, a dose rate of 8245 μGy s−1 was obtained at the detector surface with the inherent Al filtration and 2312 μGy s−1 with an additional 0.3 mm Cu filter. There was negligible change of the x-ray dose rate over many operating cycles. A ms-CBCT scan of an adult head phantom was completed in 14.4 s total exposure time for the imaging dose in the range of that of a clinical CBCT scanner. A spatially distributed CNT x-ray source array was designed and fabricated. It has enabled a new multisource CBCT to overcome some of the main inherent limitations of the conventional CBCT.

High-Density Polyethylene Custom Focusing Lenses for High-Resolution Transient Terahertz Biomedical Imaging Sensors.

Transient terahertz time-domain spectroscopy (THz-TDS) imaging has emerged as a novel non-ionizing and noninvasive biomedical imaging modality, designed for the detection and characterization of a variety of tissue malignancies due to their high signal-to-noise ratio and submillimeter resolution. We report our design of a pair of aspheric focusing lenses using a commercially available lens-design software that resulted in about 200 × 200-μm2 focal spot size corresponding to the 1-THz frequency. The lenses are made of high-density polyethylene (HDPE) obtained using a lathe fabrication and are integrated into a THz-TDS system that includes low-temperature GaAs photoconductive antennae as both a THz emitter and detector. The system is used to generate high-resolution, two-dimensional (2D) images of formalin-fixed, paraffin-embedded murine pancreas tissue blocks. The performance of these focusing lenses is compared to the older system based on a pair of short-focal-length, hemispherical polytetrafluoroethylene (TeflonTM) lenses and is characterized using THz-domain measurements, resulting in 2D maps of the tissue refractive index and absorption coefficient as imaging markers. For a quantitative evaluation of the lens effect on the image resolution, we formulated a lateral resolution parameter, R2080, defined as the distance required for a 20-80% transition of the imaging marker from the bare paraffin region to the tissue region in the same image frame. The R2080 parameter clearly demonstrates the advantage of the HDPE lenses over TeflonTM lenses. The lens-design approach presented here can be successfully implemented in other THz-TDS setups with known THz emitter and detector specifications.

Ultrafast random polarization beam smoothing driven by counter-rotating wavefronts via the optical Kerr effect

We propose an ultrafast random polarization smoothing scheme to achieve ultrafast speckle movement and polarization randomization of the focal spot. In the scheme, each beamlet in a laser quad is driven by a rotating petal-like wavefront, giving rise to the ultrafast redistribution of the speckles within the focal spot. The rotating wavefront is induced by an optical Kerr medium pumped by a laser beam with rotating intensity distribution that is generated by the superposition of two Laguerre–Gaussian beams carrying conjugate vortex phase and frequency shift. In addition, by properly selecting the topological charges of the pump beams and polarization states of the beamlets, the beamlets in a quad can be divided into two sets with counter-rotating wavefronts and orthogonal polarizations, which further randomizes the polarization of the focal spot. Results indicate that the proposed scheme can reduce the contrast by more than 70% and the degree of polarization by more than 75% within several picoseconds, by utilizing the rotating phase pumped by two Laguerre-Gaussian beams with a peak intensity of 0.18GW/cm2 and a frequency shift of 1 THz. The ultrafast random polarization smoothing scheme is expected to suppress the growth of Laser Plasma Instabilities (LPIs) including the filamentation and backscatter in indirect-drive inertial confinement fusion (ICF) facilities.

Terahertz multi-foci metalens enabling high-accuracy intensity distributions and polarization-dependent images based on inverse design

A multi-foci metalens can realize unprecedented functions (i.e., the large field of view and fully reconfigurable imaging) that are extremely challenging to achieve by conventional lenses. However, a traditional multi-foci metalens shows inhomogeneous/chaotical intensity distributions between multiple focal spots, which is a key challenge in metasurface design and limited for further applications. Herein, an inverse design method is proposed to automatically optimize the in-plane orientation (rather than the shape) of each meta-atom in terahertz multi-foci metalenses that can generate a plethora of focal spots with high-accuracy intensity distributions. The inverse design of multi-foci metalenses for generating circularly polarized and linearly polarized images (rather than holograms) with nearly homogeneous intensity distributions is proposed and experimentally demonstrated. The robust approach for simultaneously and accurately modulating the amplitude, phase, polarization, and intensity distributions of terahertz waves to generate polarization-dependent images with high-accuracy intensity of each focal spot will open an avenue in developing compact imaging, face unlock, and motion sensing.

Three-dimensional wall-thickness distributions of unruptured intracranial aneurysms characterized by micro-computed tomography

Aneurysmal rupture is associated with wall thinning, but the mechanism is poorly understood. This study aimed to characterize the three-dimensional wall-thickness distributions of unruptured intracranial aneurysms. Five aneurysmal tissues were investigated using micro-computed tomography. First, the wall thickness was related to the aneurysmal wall appearances during surgery. The median wall thicknesses of the translucent and non-translucent walls were 50.56 and 155.93 µm, respectively (p < 0.05) with significant variation in the non-translucent wall thicknesses (p < 0.05). The three-dimensional observations characterized the spatial variation of wall thicknesses. Thin walls showed a uniform thickness profile ranging from 10 to 40 µm, whereas thick walls presented a peaked thickness profile ranging from 300 to 500 µm. In transition walls, the profile undulated due to the formation of focal thin/thick spots. Overall, the aneurysmal wall thicknesses were strongly site-dependent and spatially varied by 10 to 40 times within individual cases. Aneurysmal walls are exposed to wall stress driven by blood pressure. In theory, the magnitude of wall stress is inversely proportional to wall thickness. Thus, the observed spatial variation of wall thickness may increase the spatial variation of wall stress to a similar extent. The irregular wall thickness may yield stress concentration. The observed thin walls and focal thin spots may be caused by excessive wall stresses at the range of mechanical failure inducing wall injuries, such as microscopic tears, during aneurysmal enlargement. The present results suggested that blood pressure (wall stress) may have a potential of acting as a trigger of aneurysmal wall injury.

Dependence of spectral purity of Gd plasma emission around 6.7 nm on laser irradiation conditions

Gadolinium is a compelling candidate for the next-generation 6.x nanolithography light source. We present a systematically study on the spectral purity at 6.7 nm in the gadolinium laser produced plasma. Variations in extreme ultraviolet spectra are observed over a wide range of laser focal spot sizes and laser pulse energies due to the combined effect of plasma temperature and opacity. When varying laser focal spot size, ionic populations of Gd ions at different electron temperatures were estimated by the collisional-radiative model for the explanation of changes in the spectral profile. When adjusting the laser pulse energy, modifications in the electron density profile were measured through Nomarski interferometry, and the related optical depth was quantified assisted with a one-dimensional radiation transfer model. Results show that, appropriate laser energy and focal spot size are necessary to achieve the high spectral purity, and with a lens with focal length of f = 175 mm and a laser pulse energy of 100 mJ, a spectral purity of Gd plasma up to 3.7% over range of 5.5–10 nm is achieved.

Design and Analysis of the Dual-Band Far-Field Super-Resolution Metalens with Large Aperture.

The resolving power of metalens telescopes rely on their aperture size. Flat telescopes are advancing with the research on super-resolution confocal metalenses with large aperture. However, the aperture sizes of metalenses are usually bound within hundreds of micrometers due to computational and fabrication challenges, limiting their usage on practical optical devices like telescopes. In this work, we demonstrated a two-step designing method for the design of dual-band far-field super-resolution metalens with aperture sizes from the micro-scale to macro-scale. By utilizing two types of inserted unit cells, the phase profile of a dual-wavelength metalens with a small aperture of 100 μm was constructed. Through numerical simulation, the measured FWHM values of the focal spots of 5.81 μm and 6.81 μm at working wavelengths of 632.8 nm and 1265.6 nm were found to all be slightly smaller than the values of 0.61 λ/NA, demonstrating the super-resolution imaging of the designed metalens. By measuring the optical power ratio of the focal plane and the incident plane, the focusing efficiencies were 76% at 632.8 nm and 64% at 1265.6 nm. Based on the design method for small-aperture metalens, far-field imaging properties through the macro metalens with an aperture of 40 mm were simulated by using the Huygens-Fresnel principle. The simulation results demonstrate confocal far-field imaging behavior at the target wavelengths of 632.8 nm and 1265.6 nm, with a focal length of 200 mm. The design method for dual-band far-field super-resolution metalens with a large aperture opens a door towards the practical applications in the dual-band space telescope system.

Magneto-optical-like effect in tight focusing of azimuthally polarized sine-Gaussian beams.

Magneto-optical effects, which have been known for over a century, are among the most fundamental phenomena in physics and describe changes in the polarization state of light when it interacts with magnetic materials. When a polarized plane wave propagates in or through a homogeneous and isotropic transparent medium, it is generally accepted that its transverse polarization structure remains unchanged. However, we show that a strong radial polarization component can be generated when an azimuthally polarized sine-Gaussian plane wave is tightly focused by a high numerical aperture lens, resulting in a magneto-optical-like effect that does not require external magnetic field or magnetic medium. Calculations show that the intensity structure and polarization distribution of the highly confined electric field strongly depend on the parameters m and φ0 in the sinusoidal term, where m can be used to control the number of the multifocal spots and φ0 can be used to control the position of each focal spot. Finally, we show that this peculiar electric field distribution can be used to realize multiple particles trapping with controllable numbers and locations.

An RGB‐Achromatic Aplanatic Metalens

AbstractOptical metalenses offer a compact approach for the development of nanoscale optical devices with various imaging functionalities. Realizing high‐quality images using metalenses with large numerical aperture (NA) requires eliminating unwanted optical aberrations. Existing strategies have largely focused only on correcting chromatic aberrations, and a metalens capable of simultaneously correcting chromatic and spherical aberrations has not yet been developed. Here, this issue is addresed by realizing an aplanatic phase profile for a red–green–blue (RGB) achromatic metalens, thereby demonstrating an RGB‐achromatic aplanatic metalens. This device consists of crystalline silicon nanostructures and it enables RGB‐achromatic aplanatic focusing with an NA of 0.635. The focal length of metalens remains unchanged at the three RGB wavelengths, whereas the associated focal spots are significantly smaller than those of an RGB‐achromatic metalens with spherical aberrations. An enhanced RGB imaging resolution is demonstrated, offering exciting opportunities to power up various imaging and display applications using flat metalenses.

Off-axis bifocal metalens for displacement measurement

Metasurface is a new type of micro-optical element developed in recent years. It can intelligently modulate electromagnetic waves by adjusting the geometrical parameters and arrangement of dielectric structures. In this paper, a bifocal metalens based on modulation of propagation phase was designed for the potential application in displacement measurement. The phase of the bifocal lens is designed by the optical holography-like method, which is verified by the scalar diffraction theory. We designed a square aperture lens with a side length of 200 μm to realize two focal spots with focal lengths of 900 and 1100 μm. The two focal spots aren’t on one optical axis. The polarization insensitive TiO2 cylinders are chosen as structure units. Four structures with different radius were selected to achieve the four phase steps. We fabricated the designed bifocal metalens using electron beam lithography and atomic layer deposition techniques, and measured the light intensity in the areas near the two foci in the direction of the longitudinal axis. The differential signal was calculated, from which we obtained a linear interval. It demonstrates the ability of bifocal differential measurement to be applied to displacement measurement. Because the metasurfaces production process is semiconductor compatible, the bifocal lens is easy to integrate and can be used for miniaturized displacement measurements, micro-resonators, acceleration measurements, and so on.

Refocusing beams of a satellite mirror antenna with moderate deformations of its reflector

Multibeam hybrid reflector antenna (MBHRA) is part of high-performance satellite communication systems. It provides high gain thanks to its large mirror and the use of antenna array to form enough beams covering the working area. Therefore, it is crucial to maintain the needed beams configuration to provide clients with high quality signal. The location of the beams may change because the reflector profile changes under the changeable thermal flux from the Sun, which is not stationary due to orbital motion of the satellite. Although the appearing distortions of the reflector profile are a priori small, but they cause beams to displace from their assigned positions in up to their width of tenth of a degree. Consequently, the level of the signal in coverage areas goes down. Modern MBHRA form their beams with clusters, i.e. groups of elements of the antenna array. Typically, cluster consists out of seven elements: one in the center and others at the vertices of a perfect hexagon. The fact that several antenna elements form a beam opens up the possibility of electronically controlling the beams by adjusting the amplitudes and phases of the exciting distribution, or more precisely, the weighting coefficients of the clusters. To determine which amplitudes and phases to apply, it is necessary to know the current state of the reflector, characterized by either its geometry or its electrodynamic equivalent, such as the best-fit paraboloid (BFP). Laser measurement and photogrammetry are popular solutions for that. A useful alternative to them is reconstruction of the BFP from the signals received by the MBHRA antenna array from a ground-based radio beacon. Emphasizing the dependence of these signals on the state of the reflector, we call them the “signal imprint” of the reflector. The possibility to implement a single ground beacon is due approximation the reflector profile as an equivalent best-fit paraboloid. BFP is uniquely defined by six parameters: change of the focal length, turns in two orthogonal planes and shift of the apex in space {ΔF; αz; αy; Δx; Δy; Δz}. Since some of the parameters are highly correlated in terms of their influence on the signal imprint, the re-construction problem becomes more complicated. So a question whether the set of parameters is overloaded arises reasonably. Maybe it is possible to get rid of some parameters. We considered two options to reduce the number of parameters: focal displacement + turns {ΔF; αz; αy} and apex shift {Δx; Δy; Δz}. Statistical modelling confirms the possibility to reduce the number of sought-for BFP parameters down to the mentioned three instead of six. If the maximum of the focal spot does not shift outside the cluster, then reducing the number of the sought-for BFP parameters to three causes a very small decrease in the gain of beams compared to using the full set of parameters. For the above options, the decrease in gain is 0.03 dB or 0.25 dB. It is interesting to note that in the turns option {ΔF; αz; αy} there is a better correspondence to the reflector surface compared to the displacement option {Δx; Δy; Δz}, but worse matching of the signal imprint, and as a consequence a greater loss in gain. This is due to the higher sensitivity of the beam orientation to the mirror rotations than to the vertex displacement.