Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Beam Optics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Wavefront preserving X-ray optics for Synchrotron and Free Electron Laser photon beam transport systems

We report in the last two decades, after the first light from the new Free Electron Lasers, either in the UV (FLASH and FERMI@Elettra) or X-ray (LCLS and SACLA), more and more new diffraction limited sources have been either constructed or planned. Third generation storage rings are upgraded to provide a more collimated, brighter, and coherent light for the next generation experimental techniques. X-ray optics are the bridge between the light sources and the experimental stations. They are the key to the success of advanced experiments but also the potential bottleneck preventing the exploitation of the full characteristics of the source. The beam degradation originated by any mirror defect (either from mirror polishing or from contamination) is amplified with a coherent source. Delivering diffraction-limited spots, including the option for variable spot sizes in and out of focus, requires the control of the surface of the optics at the 1 nm rms level, if not better. At LCLS, only very recently an almost perfectly uniform beam out of focus has been obtained in the hard X-rays. It has been obtained after two 1-m long mirrors with 0.5 nm rms shape precision (after installation). Those mirrors were not readily available just a decade ago. But, thanks to the pioneering work performed at the Osaka University, those optics are now commercially available with arbitrary tangential profiles. This new generation of mirrors permits achieving unprecedented results. However, they do not remove all road blocks to a perfect photon transport system. Instead, they highlighted the critical importance of mirror mounting, handling of the thermal deformation, and the need of advanced diagnostics to properly exploit all the new potentiality of these optics. Besides the need of “perfect” mirrors, other aspects of the beamline design and elements may impact the quality of the beam in the experimental station, from the lack of blaze gratings to the need of advanced simulation tools, just to cite two. In this article, after a brief historical excursus, we will present the current state of the art of mirrors, gratings, crystals, lenses, diagnostics, and simulation tools. The main problems yet to solve and a look ahead at what would be achievable in the next decade will give the reader an idea on the search for an almost ideal photon transport system and how the path toward experiments, not conceivable today, will unfold.

47 OTHER INSTRUMENTATION↗
NASA NTRS2004

Compact Instrument for Measuring Profile of a Light Beam

The beamviewer is an optical device designed to be attached to a charge-coupled-device (CCD) image detector for measuring the spatial distribution of intensity of a beam of light (the beam profile ) at a designated plane intersecting the beam. The beamviewer-and-CCD combination is particularly well suited for measuring the radiant- power profile (for a steady beam) or the radiant-energy profile (for a pulsed beam) impinging on the input face or emerging from the output face of a bundle of optical fibers. The beamviewer and-CCD combination could also be used as a general laboratory instrument for profiling light beams, including beams emerging through small holes and laser beams in free space.

Papanyan, Valeri↗
NASA NTRS2001

Sun and Sky Radiance Measurements and Data Analysis Protocols

This chapter is concerned with two types of radiometric measurements essential to verify atmospheric correction algorithms and to calibrate vicariously satellite ocean color sensors. The first type is a photometric measurement of the direct solar beam to determine the optical thickness of the atmosphere. The intensity of the solar beam can be measured directly, or obtained indirectly from measurements of diffuse global upper hemispheric irradiance. The second type is a measurement of the solar aureole and sky radiance distribution using a CCD camera, or a scanning radiometer viewing in and perpendicular to the solar principal plane. From the two types of measurements, the optical properties of aerosols, highly variable in space and time, can be derived. Because of the high variability, the aerosol properties should be known at the time of satellite overpass. Atmospheric optics measurements, however, are not easy to perform at sea, from a ship or any platform. This complicates the measurement protocols and data analysis. Some instrumentation cannot be deployed at sea, and is limited to island and coastal sites. In the following, measurement protocols are described for radiometers commonly used to measure direct atmospheric transmittance and sky radiance, namely standard sun photometers, fast-rotating shadow-band radiometers, automated sky scanning systems, and CCD cameras. Methods and procedures to analyze and quality control the data are discussed, as well as proper measurement strategies for evaluation of atmospheric correction algorithms and satellite-derived ocean color.

Frouin, Robert↗
NASA NTRS1986

Recent developments in materials and detectors for the infrared; Proceedings of the Meeting, Cannes, France, November 25, 26, 1985

The present conference on advancements in IR-sensitive materials and detector technologies employing them gives attention to thermal detectors, focal plane array processing detectors, novel detector designs, general properties of IR optics materials, and preparation methods for such materials. Specific topics encompass the fabrication of InSb MIS structures prepared by photochemical vapor deposition, IR heterodyne detectors employing cadmium mercury telluride, low microphony pyroelectric arrays, IR detection based on minority carrier extrusion, longwave reststrahl in IR crystals, and molecular beam techniques for optical thin film fabrication.

Morten, F. D.↗
DOE OSTI2020

Plasma Photonics for the Control of Kilojoule Lasers

The main goal of this project was to develop plasma photonic devices (plasma lenses or ellipsoidal plasma mirrors (EPMs)) for controlling the focus of high-energy (kJ-class) laser systems. In order to defocus a kJclass laser beam, a plasma optic must produce a very specific plasma density profile. For a plasma lens, this profile must be peaked on axis and fall off parabolicly with radius. We developed four plasma-lens target designs that were predicted to yield the ideal plasma profile required for defocusing kJ-class laser beams. Particle-in-cell (PIC) simulations using the code OSIRIS were used to explore the design. The resulting plasma lens must also be underdense, which sets an upper limit on the solid density of the plasma-lens targets to ~ 1 mg/cm 3 or less. This low of a density is highly challenging to fabricate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1984

Optical and interfacial electronic properties of diamond-like carbon films

Hard, semitransparent carbon films were prepared on oriented polished crystal wafers of silicon, indium phosphide and gallium arsenide, as well as on KBr and quartz. Properties of the films were determined using IR and visible absorption spectrocopy, ellipsometry, conductance-capacitance spectroscopy and alpha particle-proton recoil spectroscopy. Preparation techniques include RF plasma decomposition of methane (and other hydrocarbons), ion beam sputtering, and dual-ion-beam sputter deposition. Optical energy band gaps as large as 2.7 eV and extinction coefficients lower than 0.1 at long wavelengths are found. Electronic state densities at the interface with silicon as low as 10 to the 10th states/eV sq cm per were found.

Woollam, J. A.↗
NASA NTRS2009

Critical Coupling Between Optical Fibers and WGM Resonators

Two recipes for ensuring critical coupling between a single-mode optical fiber and a whispering-gallery-mode (WGM) optical resonator have been devised. The recipes provide for phase matching and aperture matching, both of which are necessary for efficient coupling. There is also a provision for suppressing intermodal coupling, which is detrimental because it drains energy from desired modes into undesired ones. According to one recipe, the tip of the single-mode optical fiber is either tapered in diameter or tapered in effective diameter by virtue of being cleaved at an oblique angle. The effective index of refraction and the phase velocity at a given position along the taper depend on the diameter (or effective diameter) and the index of refraction of the bulk fiber material. As the diameter (or effective diameter) decreases with decreasing distance from the tip, the effective index of refraction also decreases. Critical coupling and phase matching can be achieved by placing the optical fiber and the resonator in contact at the proper point along the taper. This recipe is subject to the limitation that the attainable effective index of refraction lies between the indices of refraction of the bulk fiber material and the atmosphere or vacuum to which the resonator and fiber are exposed. The other recipe involves a refinement of the previously developed technique of prism coupling, in which the light beam from the optical fiber is collimated and focused onto one surface of a prism that has an index of refraction greater than that of the resonator. Another surface of the prism is placed in contact with the resonator. The various components are arranged so that the collimated beam is focused at the prism/resonator contact spot. The recipe includes the following additional provisions:

Matsko, Andrey↗
DOE OSTI2026

Towards robust laser beam propagation in atmospheric turbulence

High-fidelity optical propagation through the atmosphere is essential for free-space optical technologies, including laser-based remote sensing and optical communication. However, atmospheric turbulence severely distorts beams and compromises system performance. In this work, we employ hypergeometric-Gaussian (HyGG) vortex beams as probes to characterize and mitigate atmospheric turbulence. Using over 250,000 experimental and simulated frames, we show that refining the power spectrum density (PSD) can reduce numerical prediction errors by up to 79.8%. Concurrently, experimental observations supported by numerical simulations demonstrate that HyGG beams exhibit superior turbulence resilience across multiple metrics compared to conventional Gaussian beams, particularly in their ability to withstand over 5 times stronger turbulence while maintaining similar intensity fluctuations. These dual investigations, on both turbulence mitigation and robust beam solutions, converge to form a unified strategy for enhancing free-space optical system performance. Collectively, our findings provide new insights into light–turbulence interactions and highlight the practical utility of vortex beams under atmospheric conditions.

Zhang, Boyu↗
DOE OSTI2026

A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II

Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Hard x-ray – optical four-wave mixing using a split-and-delay line

New, hard x-ray free electron lasers (FEL) produce intense femtosecond-to-attosecond pulses at angstrom wavelengths, giving access to the fundamental spatial and temporal scales of matter. These revolutionary light sources open the door to applying the suite of nonlinear, optical spectroscopy methods at hard x-ray photon energies. Nonlinear spectroscopy with hard x-rays can allow for measuring the coherence properties of short wavelength excitations with atomic specificity and for understanding how high energy excitations couple to other degrees of freedom in atomic, molecular or condensed-phase systems. As a step in this direction, here we present hard x-ray, optical four-wave mixing (4WM) measurements done at 9.8 keV at the split-and-delay line at the x-ray correlation spectroscopy (XCS) hutch of the Linac Coherent Light Source (LCLS). In this work, we create an x-ray transient grating (TG) from a pair of crossing x-ray beams and diffract optical laser pulses at 400 nm from the TG. The key technical advance here is being able to independently vary the delays of the x-ray pulses. Measurements were made in 3 different solid samples: bismuth germinate (BGO), zinc oxide (ZnO) and yttrium aluminum garnet (YAG). The resulting phase-matched, 4WM signal is measured in two different ways: by varying the x-ray, x-ray pulse delay which can reveal both material and light source coherence properties and also by varying the optical laser delay with respect to the x-ray TG to study how the x-ray excitation couples to the optical properties. Although no coherent 4WM signal was seen in these measurements, the absence of this signal gives important information on experimental requirements for detecting this in future work. Also, our laser-delay scans, although not a new measurement, were applied to different materials than in past work and reveal new examples x-ray induced lattice dynamics in solids. This work represents a key step towards extending nonlinear optics and time-resolved spectroscopy into the hard x-ray regime.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Development of an Ultrahigh-bandwidth Phase Contrast Imaging System for detection of electron scale turbulence and Gigahertz Radio-Frequency Waves

The study of waves and turbulence is vital to the development of future reactor-grade plasma devices developed in the quest for fusion energy. These fluctuations are responsible for moving heat and particles across the magnetic field, and a predictive understanding of them is needed to achieve the density and temperature required to sustain a plasma fusion reaction. While many techniques have been developed for measuring waves and fluctuations, every measurement method has limitations. There are relatively few techniques for measuring very high frequency fluctuations, such as radio frequency waves injected to heat the plasma, unstable waves driven by suprathermal particles, or short wavelength electrostatic waves driven by electron temperature or density gradients. The present project builds upon the proven phase contrast imaging (PCI) technique to extend the response of the diagnostic by orders of magnitude in frequency and almost a factor of ten in spatial resolution. PCI provides a measurement of electron density based on small angle scattering of a CO-2 laser beam by using optical techniques to render a phase shift as an intensity change on a detector. Due to the telecommunications revolution, technological development by manufacturers has focused on components in the near -infrared, so that high- quality lasers and detectors at 1.55 µm are readily available. Shifting PCI design to a new, shorter wavelength has numerous advantages and challenges. Similar detector performance is available with room-temperature arrays with GHz bandwidth, while the detector arrays for 10.6 µm required liquid nitrogen cooling and were therefore limited to a bandwidth of about 1 MHz. Shifting to a shorter wavelength reduces the angle at which the laser beam scatters off of plasma waves, allowing more such scattered components to pass through the aperture of the vacuum vessel port and be collected by the PCI, which increases the spatial resolution. Concomitant with these benefits, various questions of performance arise. At shorter laser wave- length, the sensitivity to mirror and lens quality is increased, the contribution of the laser to the overall system noise is increased, and the sensitivity to vibrations is increased. The custom optical components at the heart of the PCI technique were required to be properly scaled for the shorter wavelength, so fabrication technologies needed to be explored. This project was designed to show that a low noise, high response PCI system at 1.55 µm could be constructed and operated, and then to quantify potential issues to allow extrapolation to a full-size production system providing physics measurements on a large plasma device. The first stage, producing the custom optical component called a Phase Plate, was successfully achieved using two methods. First, an easily reproduced masking and coating technique was able to produce good phase plates with the required parameters. Second, a nanofabrication technique was found to produce extremely high quality phase plates at a competitive price. The PCI constructed with the new phase plates and 1.55 µm laser was found to provide excellent wavelength measurements with the theoretically expected response. The sensitivity to optical surface quality was found to be in line with previous measurements at 10.6 µm. The observed signal-to-noise ratio was similar to the theoretically expected value. The effect of vibrations on PCI was studied with the first measurement of the effect of beam motion on PCI response and comparison to theory, allowing for a quantitative prediction of the effect of vibrations on a production PCI system and the requirements for improved beam stabilization. PCI is an extremely cost-effective method to provide a low noise, absolutely calibrated measurement of plasma fluctuations across a wide spatial scale. This project has shown that a 1.55 µm PCI using modern techniques and components is less expensive than the 10.6 µm PCI of a few years ago, with the largest savings in phase plate fabrication and the infrared detector array.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Molecular beam epitaxy engineered III-V semiconductor structures for low-power optically addressed spatial light modulators

Device approaches are investigated for optically addressed SLMs based on molecular-beam epitaxy (MBE) engineered III-V materials and structures. Strong photooptic effects can be achieved in periodically delta-doped multiple-quantum-well structures, but are still insufficient for high-contrast modulation with only single- or double-pass absorption through active layers of practical thickness. The asymmetric Fabry-Perot cavity approach is employed to permit extinction of light due to interference of light reflected from the front and back surfaces of the cavity. This approach is realized with an all-MBE-grown structure consisting of GaAs/AlAs quarter-wave stack reflector grown over the GaAs substrate as the high reflectance mirror and the GaAs surface as the low reflectance mirror. High-contrast modulation is achieved using a low-power InGaAs/GaAs quantum well laser for the control signal.

Larsson, Anders G.↗
NASA NTRS2002

Interferometer Control of Optical Tweezers

This paper discusses progress in using spatial light modulators and interferometry to control the beam profile of an optical tweezers. The approach being developed is to use a spatial light modulator (SLM) to control the phase profile of the tweezers beam and to use a combination of the SLM and interferometry to control the intensity profile. The objective is to perform fine and calculable control of the moments and forces on a tip or tool to be used to manipulate and interrogate nanostructures. The performance of the SLM in generating multiple and independently controllable tweezers beams is also reported. Concurrent supporting research projects are mentioned and include tweezers beam scattering and neural-net processing of the interference patterns for control of the tweezers beams.

Decker, Arthur J.↗
DOE OSTI2024

Quantum enhanced magneto-optical microscopy and spectroscopy

A system comprising a nonlinear medium (NLM), an optical transduction module, a dual homodyne detector and a processor is provided. The NLM receives at least a pump beam and issues the pump, probe and conjugate beams, where the beams are linearly polarized. Optics route the probe, the conjugate or both beams to the sample. The sample imparts polarization rotation to light that interacts therewith. The optical transduction module imparts to the interacted light an optical phase shift that is a 1:1 transduction of the polarization rotation, where at least one of the probe light or the conjugate light carries the imparted optical phase shift. The processor obtains the optical-phase shift based on respective detection signals from the dual homodyne detector and determines, based on the obtained optical-phase shift, at least one of a Faraday polarization rotation, a Kerr polarization rotation or a spin noise spectrum.

Lawrie, Benjamin J.↗
NASA NTRS1983

Experimental investigations of elastohydrodynamic lubrication

Various experimental studies of elastohydrodynamic lubrication have been reviewed. The various types of machines used in these investigations, such as the disc, two and four ball, crossed-cylinders, and crossed-axes rolling disc machine, are described. The measurement of the most important parameters, such as film shape, film thickness, pressure, temperature, and traction, is considered. Determination of the film thickness is generally the most important of these effects since it dictates the extent to which the asperities on opposing surfaces can come into contact and thus has a direct bearing on wear and fatigue failure of the contacting surfaces. Several different techniques for measuring film thickness have been described, including electrical resistance, capacitance, X-ray, optical interferometry, laser beam diffraction, strain gage, and spring dynamometer methods. An attempt has been made to describe the basic concepts and limitations of each of these techniques. These various methods have been used by individual researchers, but there is no universally acceptable technique for measuring elastohydrodynamic film thickness. Capacitance methods have provided most of the reliable data for nominal line or rectangular conjunctions, but optical interferometry has proved to be the most effective procedure for elliptical contacts. Optical interferometry has the great advantage that it reveals not only the film thickness, but also details of the film shape over the complete area of the conjunction.

Hamrock, B. J.↗
NASA NTRS1993

Use of particle beams for lunar prospecting

A key issue in choosing the appropriate site for a manned lunar base is the availability of resources, particularly oxygen and hydrogen for the production of water, and ores for the production of fuels and building materials. NASA has proposed two Lunar Scout missions that would orbit the Moon and use, among other instruments, a hard X-ray spectrometer, a neutron spectrometer, and a Ge gamma ray spectrometer to map the lunar surface. This passive instrumentation will have low resolution (tens of kilometers) due to the low signal levels produced by natural radioactivity and the interaction of cosmic rays and the solar wind with the lunar surface. This paper presents the results of a concept definition effort for a neutral particle beam lunar mapper probe. The idea of using particle beam probes to survey asteroids was first proposed by Sagdeev et al., and an ion beam device was fielded on the 1988 Soviet probe to the Mars moon Phobos. During the past five years, significant advances in the technology of neutral particle beams (NPB) have led to a suborbital flight of a neutral hydrogen beam device in the SDIO-sponsored BEAR experiment. An orbital experiment, the Neutral Particle Beam Far Field Optics Experiment (NPB-FOX) is presently in the preliminary design phase. The development of NPB accelerators that are space-operable leads one to consider the utility of these devices for probing the surface of the Moon using gamma ray, X-ray, and optical/UV spectroscopy to locate various elements and compounds. We consider the utility of the NPB-FOX satellite containing a 5-MeV particle beam accelerator as a probe in lunar orbit. Irradiation of the lunar surface by the particle beam will induce secondary and back scattered radiation from the lunar surface to be detected by a sensor that may be co-orbital with or on the particle beam satellite platform, or may be in a separate orbit. The secondary radiation is characteristic of the make-up of the lunar surface. The size of the spot irradiated by the beam is less than 1 km wide along the ground track of the satellite, resulting in the potential for high resolution. The fact that the probe could be placed in polar orbit would result in global coverage of the lunar surface. The orbital particle beam probe could provide the basis for selection of sites for more detailed prospecting by surface rovers.

Toepfer, A. J.↗
NASA NTRS2005

NASA Tech Briefs, April 2005

Gas-Tolerant Device Senses Electrical Conductivity of Liquid Nanoactuators Based on Electrostatic Forces on Dielectrics Replaceable Microfluidic Cartridges for a PCR Biosensor CdZnTe Image Detectors for Hard-X-Ray Telescopes High-Aperture-Efficiency Horn Antenna Full-Circle Resolver-to-Linear-Analog Converter Continuous, Full-Circle Arctangent Circuit Advanced Three-Dimensional Display System Automatic Focus Adjustment of a Microscope Topics covered include: FastScript3D - A Companion to Java 3D; Generating Mosaics of Astronomical Images; Simulating Descent and Landing of a Spacecraft; Simulating Vibrations in a Complex Loaded Structure; Rover Sequencing and Visualization Program; Software Template for Instruction in Mathematics; Support for User Interfaces for Distributed Systems; Nanostructured MnO2-Based Cathodes for Li-Ion/Polymer Cells; Multi-Layer Laminated Thin Films for Inflatable Structures; Two-Step Laser Ranging for Precise Tracking of a Spacecraft; Growing Aligned Carbon Nanotubes for Interconnections in ICs; Multilayer Composite Pressure Vessels; Texturing Blood-Glucose-Monitoring Optics Using Oxygen Beams; Fault-Tolerant Heat Exchanger; Atomic Clock Based on Opto-Electronic Oscillator; Microfocus/Polycapillary-Optic Crystallographic X-Ray Sys; Depth-Penetrating Luminescence Thermography of Thermal- Barrier Coatings; One-Dimensional Photonic Crystal Superprisms; Measuring Low-Order Aberrations in a Segmented Telescope; Mapping From an Instrumented Glove to a Robot Hand; Application of the Hilbert-Huang Transform to Financial Data; Optimizing Parameters for Deep-Space Optical Communication; and Low-Shear Microencapsulation and Electrostatic Coating.

Source record↗
NASA NTRS2001

Shortwave Radiative Fluxes, Solar-Beam Transmissions, and Aerosol Properties: TARFOX and ACE-2 Find More Absorption from Flux Radiometry than from Other Measurements

The Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX) and the Second Aerosol Characterization Experiment (ACE-2) made simultaneous measurements of shortwave radiative fluxes, solar-beam transmissions, and the aerosols affecting those fluxes and transmissions. Besides the measured fluxes and transmissions, other obtained properties include aerosol scattering and absorption measured in situ at the surface and aloft; aerosol single scattering albedo retrieved from skylight radiances; and aerosol complex refractive index derived by combining profiles of backscatter, extinction, and size distribution. These measurements of North Atlantic boundary layer aerosols impacted by anthropogenic pollution revealed the following characteristic results: (1) Better agreement among different types of remote measurements of aerosols (e.g., optical depth, extinction, and backscattering from sunphotometers, satellites, and lidars) than between remote and in situ measurements; 2) More extinction derived from transmission measurements than from in situ measurements; (3) Larger aerosol absorption inferred from flux radiometry than from other measurements. When the measured relationships between downwelling flux and optical depth (or beam transmission) are used to derive best-fit single scattering albedos for the polluted boundary layer aerosol, both TARFOX and ACE-2 yield midvisible values of 0.90 +/- 0.04. The other techniques give larger single scattering albedos (i.e. less absorption) for the polluted boundary layer, with a typical result of 0.95 +/- 0.04. Although the flux-based results have the virtue of describing the column aerosol unperturbed by sampling, they are subject to questions about representativeness and other uncertainties (e.g., unknown gas absorption). Current uncertainties in aerosol single scattering albedo are large in terms of climate effects. They also have an important influence on aerosol optical depths retrieved from satellite radiances. More tests are needed of the consistency among different methods and of the effects of changing humidity on aerosol.

Russell, Philip B.↗