Numerical Aperture of Optical Fiber & Its Derivation - numerical aperture formula
Metric hex keys are measured in millimeters (mm), while SAE hex keys are measured in fractional inches. The most significant difference between the two systems lies in the increments between sizes. Metric hex keys tend to have smaller increments, allowing for a more precise fit with fasteners.
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When deciding between metric and SAE hex keys, it's essential first to determine the specific requirements of your project. Consider the origin of the products and materials you'll be working with, as this will often dictate whether you'll need metric or SAE tools.
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Many flat-pack furniture pieces use hex bolts and screws for assembly. Products designed for the American market may use SAE fasteners, while those made elsewhere will likely use metric fasteners. It's crucial to have the correct hex key size to avoid damaging the fasteners and ensure a secure fit.
The choice between SAE and metric hex keys often depends on the origin of the products and materials you are working with. SAE hex keys are compatible with American-made products, while metric hex keys are widely used in products from Europe, Asia, and other parts of the world. To improve torque and grip, it's crucial to select the appropriate hex key system for your specific needs. Metric hex keys, with their smaller size increments, offer greater precision, while SAE hex keys provide familiarity for those accustomed to the imperial system.
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Manschwetus, B. et al. Two-photon double ionization of neon using an intense attosecond pulse train. Phys. Rev. A 93, 061402 (2016).
Barillot, T. R. et al. Towards XUV pump-probe experiments in the femtosecond to sub-femtosecond regime: new measurement of the helium two-photon ionization cross-section. Chem. Phys. Lett. 683, 38–42 (2017).
Neidel, C. et al. Probing time-dependent molecular dipoles on the attosecond time scale. Phys. Rev. Lett. 111, 033001 (2013).
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Snigirev, A., Kohn, V., Snigireva, I. & Lengeler, B. A compound refractive lens for focusing high-energy X-rays. Nature 384, 49–51 (1996).
Santoro, G. et al. Use of intermediate focus for grazing incidence small and wide angle X-ray scattering experiments at the beamline P03 of PETRA III, DESY. Rev. Sci. Instrum. 85, 043901 (2014).
Choosing the right hex key system based on the origin of materials enhances torque and grip during use. Whether metric or SAE, selecting the appropriate system ensures a proper fit and minimizes the risk of damage to both the tool and the fastener.
The art of optimizing torque and grip revolves around the deliberate choice of the appropriate hex key system based on the origin of materials. Whether opting for metric precision or relying on the familiarity of SAE, aligning the hex key system with the task at hand ensures a snug fit and mitigates the risk of damage to both the tool and the fastener. This thoughtful selection process underscores the importance of precision and adaptability in achieving successful outcomes across a spectrum of projects.
Chollet, M. et al. The X-ray pump–probe instrument at the Linac Coherent Light Source. J. Synchrotron Radiat. 22, 503–507 (2015).
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Hex keys are versatile tools used in various applications, including assembling furniture, repairing bicycles, and working on automobiles. They provide increased torque and control compared to traditional screwdrivers, making them ideal for tightening and loosening fasteners in tight spaces.
Gademann, G., Ple, F., Paul, P.-M. & Vrakking, M. J. J. Carrier-envelope phase stabilization of a terawatt level chirped pulse amplifier for generation of intense isolated attosecond pulses. Opt. Express 19, 24922 (2011).
Schafer, K. J. & Kulander, K. C. High harmonic generation from ultrafast pump lasers. Phys. Rev. Lett. 78, 638–641 (1997).
Mauritsson, J. et al. Measurement and control of the frequency chirp rate of high-order harmonic pulses. Phys. Rev. A 70, 021801 (2004).
The dynamic choice between long and short arm hex keys is a pivotal consideration in optimizing your toolkit for diverse project requirements. Long arm hex keys offer a distinct advantage by providing increased leverage and torque, making them indispensable for tasks demanding greater force.
Refraction is a well-known optical phenomenon that alters the direction of light waves propagating through matter. Microscopes, lenses and prisms based on refraction are indispensable tools for controlling light beams at visible, infrared, ultraviolet and X-ray wavelengths1. In the past few decades, a range of extreme-ultraviolet and soft-X-ray sources has been developed in laboratory environments2,3,4 and at large-scale facilities5,6. But the strong absorption of extreme-ultraviolet radiation in matter hinders the development of refractive lenses and prisms in this spectral region, for which reflective mirrors and diffractive Fresnel zone plates7 are instead used for focusing. Here we demonstrate control over the refraction of extreme-ultraviolet radiation by using a gas jet with a density gradient across the profile of the extreme-ultraviolet beam. We produce a gas-phase prism that leads to a frequency-dependent deflection of the beam. The strong deflection near to atomic resonances is further used to develop a deformable refractive lens for extreme-ultraviolet radiation, with low absorption and a focal length that can be tuned by varying the gas pressure. Our results open up a route towards the transfer of refraction-based techniques, which are well established in other spectral regions, to the extreme-ultraviolet domain.
The terms "hex key" and "Allen wrench" are often used interchangeably, but understanding their origins and nuances can provide valuable context for professionals who use these tools. Both refer to a tool used to drive bolts and screws with a hexagonal socket, but their history and application contexts vary slightly, reflecting on the tool's versatility and global adoption.
Takahashi, E. J., Lan, P., Mücke, O. D., Nabekawa, Y. & Midorikawa, K. Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses. Nat. Commun. 4, 2691 (2013).
Allaria, E. et al. Highly coherent and stable pulses from the Fermi seeded free-electron laser in the extreme ultraviolet. Nat. Photon. 6, 699–704 (2012).
Nature thanks J. Cryan, M. Gaarde and the other anonymous reviewer(s) for their contribution to the peer review of this work.
ExtremeUV wavelength
Schroer, C. G. et al. Coherent X-ray diffraction imaging with nanofocused illumination. Phys. Rev. Lett. 101, 090801 (2008).
Having a mix of long and short arm hex keys in your toolkit provides versatility, enabling you to handle various tasks with the right balance of leverage and reach.
Proper technique, careful inspection, and timely replacement of worn hex keys are essential steps to prevent rounding off screws and bolts, ensuring the longevity of both the tool and the fastener.
To ensure the longevity of your hex keys, it's essential to use them correctly and store them properly. When using a hex key, make sure it's fully inserted into the fastener to prevent stripping or damage. Additionally, avoid using excessive force or leveraging the tool in a way that could cause it to bend or break.
Galbraith, M. C. E. et al. Few-femtosecond passage of conical intersections in the benzene cation. Nat. Commun. 8, 1018 (2017).
Drescher, L. et al. Communication: XUV transient absorption spectroscopy of iodomethane and iodobenzene photodissociation. J. Chem. Phys. 145, 011101 (2016).
Schütte, B., Arbeiter, M., Fennel, T., Vrakking, M. J. J. & Rouzée, A. Rare-gas clusters in intense extreme-ultraviolet pulses from a high-order harmonic source. Phys. Rev. Lett. 112, 073003 (2014).
Drescher, L., Kornilov, O., Witting, T. et al. Extreme-ultraviolet refractive optics. Nature 564, 91–94 (2018). https://doi.org/10.1038/s41586-018-0737-3
Automotive repairs typically require a mix of metric and SAE tools, as different manufacturers use varying fastener types. American-made vehicles often use SAE fasteners, while European and Asian vehicles generally use metric fasteners. Having both sets of hex keys on hand will allow you to tackle any repair job with ease.
Valentin, C. et al. Spectral selection of high harmonics via spatial filtering. In High-Brightness Sources and Light-driven Interactions HW3A.3 (Optical Society of America, 2018).
Heimann, P. et al. Compound refractive lenses as prefocusing optics for X-ray FEL radiation. J. Synchrotron Radiat. 23, 425–429 (2016).
Wiese, W. L. Smith, M. W. & Miles, B. M. Atomic Transition Probabilities: Sodium through Calcium. Technical report, National Standard Reference Data System (NBS, 1969).
Conversely, short arm hex keys excel in navigating confined spaces where the use of a longer tool might be impractical. Striking the right balance between these options is achievable through a comprehensive hex key set that includes both long and short arm variants, offering versatility for a wide spectrum of projects.
Bengtsson, S. et al. Space–time control of free induction decay in the extreme ultraviolet. Nat. Photon. 11, 252–258 (2017).
The nuanced decision between SAE and metric hex keys is a pivotal consideration dictated by the geographical origin of products and materials. SAE hex keys find compatibility with American-made products, while metric hex keys are the go-to choice for items from Europe, Asia, and various global regions. Elevating torque and grip during usage hinges on the judicious selection of the hex key system tailored to your specific needs. Metric hex keys, with their smaller size increments, provide heightened precision, catering to meticulous applications. Conversely, SAE hex keys offer a sense of familiarity for individuals accustomed to the imperial system.
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When storing your hex keys, keep them organized in a case or holder that prevents them from becoming lost or damaged. Avoid exposing them to moisture or corrosive substances, as this can lead to rust and degradation.
The distinction, while subtle, highlights the evolution of tool nomenclature and the importance of specificity in professional settings.
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Meijer, J.-M. et al. Observation of solid–solid transitions in 3D crystals of colloidal superballs. Nat. Commun. 8, 14352 (2017).
Tzallas, P., Charalambidis, D., Papadogiannis, N. A., Witte, K. & Tsakiris, G. D. Direct observation of attosecond light bunching. Nature 426, 267 (2003).
Marr, G. V. Handbook on Synchrotron Radiation: Vacuum Ultraviolet and Soft X-ray Processes Vol. 2 (Elsevier, Amsterdam, 2013).
Liao, C.-T., Sandhu, A., Camp, S., Schafer, K. J. & Gaarde, M. B. Beyond the single-atom response in absorption line shapes: probing a dense, laser-dressed helium gas with attosecond pulse trains. Phys. Rev. Lett. 114, 143002 (2015).
ExtremeUV meaning
Baez, A. V. A self-supporting metal Fresnel zone-plate to focus extreme ultra-violet and soft X-rays. Nature 186, 958 (1960).
One common issue when using hex keys is the risk of rounding off screws and bolts, which can lead to damage to both the tool and the fastener. To avoid this, ensure the hex key is fully inserted into the fastener before applying force. Using excessive force or applying pressure at an angle can result in slippage and rounding. Regularly inspect your hex keys for signs of wear, and replace them promptly if you notice any damage to maintain precise and effective use.
While the standard L-shaped hex key is the most common type, there are several other variations that offer unique benefits for specific applications. These include:
Hex keys, also known as Allen keys, come in various materials, but the choice of material significantly impacts their durability. High-quality steel options, such as chrome-vanadium or alloy steel, are preferred for their toughness and longevity. These materials provide resistance against wear and deformation, ensuring that the hex keys maintain their shape and effectiveness over time.
We thank A. A. Ünal and R. Schumann for their support with the laser systems. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Sklodowska-Curie grant agreement no. 641789 MEDEA.
Extreme ultravioletlithography
Opting for hex keys made from robust materials like chrome-vanadium or alloy steel ensures durability and longevity in your tools. Investing in quality materials enhances the overall performance and reliability of your hex key set.
Equipped with the right tools, you'll be prepared to tackle any DIY project with confidence and ease, ensuring successful outcomes and a sense of accomplishment in your endeavors.
Pan, H. et al. Low chromatic Fresnel lens for broadband attosecond XUV pulse applications. Opt. Express 24, 16788–16798 (2016).
Bicycle components often use a mix of metric and SAE fasteners, depending on the manufacturer. For example, American-made bicycles may use SAE fasteners for some components, while European or Asian manufacturers may use metric fasteners. Owning both sets of hex keys ensures you're prepared for any maintenance task.
Understanding the subtleties between hex keys and Allen wrenches, alongside adhering to best practices for their use, can significantly impact the efficiency, safety, and outcome of your work. Whether you're a seasoned professional or a dedicated hobbyist, investing time in organizing, maintaining, and correctly utilizing your hex keys will pay dividends in the quality of your projects and the longevity of your tools.
Wiese, W. L. Smith, M. W. & Glennon, B. M. Atomic Transition Probabilities: Hydrogen through Neon. Technical report, National Standard Reference Data System. (NBS, 1966).
The preventive measures extend beyond technique to include regular inspections of hex keys for signs of wear. Timely identification of any damage allows for prompt replacement, ensuring that the tools remain in optimal condition for precise and effective use. In conclusion, the trifecta of proper technique, vigilant inspection, and timely replacement serves as a proactive approach to safeguarding both hex keys and fasteners, ensuring their longevity and sustained functionality.
Both metric and SAE unit systems are used in various DIY and home improvement projects. Typically, products made in the United States or designed for the American market utilize SAE fasteners, while those made in Europe, Asia, and other parts of the world use metric fasteners.
The strategic inclusion of both long and short arm hex keys in your toolkit is a testament to adaptability. This thoughtful selection empowers you to seamlessly transition between tasks, ensuring that you always have the optimal tool for the job, whether it involves applying substantial force or navigating tight spaces with precision and ease.
Semushin, S. & Malka, V. High density gas jet nozzle design for laser target production. Rev. Sci. Instrum. 72, 2961–2965 (2001).
Hex keys, also known as Allen keys or Allen wrenches, are small, L-shaped tools with a hexagonal cross-section used to drive bolts and screws with a hexagonal socket. These tools are available in various sizes and can be found in both metric and SAE (Society of Automotive Engineers) measurements.
Avoiding the common pitfall of rounding off screws and bolts when using hex keys is paramount for preserving the integrity of both the tool and the fastener. Successful navigation of this challenge involves adopting a set of best practices. First and foremost, ensuring the hex key is fully inserted into the fastener before applying force is a fundamental technique that minimizes the risk of slippage and subsequent rounding. Moreover, exercising caution against using excessive force or applying pressure at an angle is crucial to maintaining precision during operation.
Hex keys, crucial tools in various applications, are best understood by examining the materials they are made of. The durability of hex keys significantly relies on the choice of material. Among the top-notch options are chrome-vanadium and alloy steel, known for their toughness and extended lifespan. These materials offer resistance to wear and deformation, ensuring that hex keys maintain their structural integrity and efficiency over prolonged usage.
Rupp, D. et al. Coherent diffractive imaging of single helium nanodroplets with a high harmonic generation source. Nat. Commun. 8, 493 (2017).
Wu, M., Chen, S., Camp, S., Schafer, K. J. & Gaarde, M. B. Theory of strong-field attosecond transient absorption. J. Phys. B 49, 062003 (2016).
Hex keys are simple tools, but like any tool, improper use can lead to injuries or damage to the workpiece. The compact size and force required to operate hex keys can pose particular risks, such as the tool slipping or breaking. Ensuring safe usage is paramount to prevent accidents and maintain a high standard of work.
Lengeler, B. et al. A microscope for hard X-rays based on parabolic compound refractive lenses. Appl. Phys. Lett. 74, 3924–3926 (1999).
Proper usage of hex keys not only ensures the safety of the user but also the longevity of the tool and the integrity of the workpiece. Here are some professional tips to maximize the effectiveness and lifespan of your hex keys.
When it comes to choosing between SAE and metric hex keys, the decision ultimately depends on your specific needs and the types of projects you'll be undertaking. By considering the origin of the products and materials you're working with, assessing your project requirements, and understanding the pros and cons of each system, you can make an informed decision on which hex key set is best suited for your toolbox.
Wang, Y., Yun, W. & Jacobsen, C. Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging. Nature 424, 50 (2003).
Regularly inspect your hex keys for signs of wear, such as rounded edges or bent arms. If you notice any damage, replace the tool immediately to avoid further issues. Additionally, consider investing in a set of hex keys with a ball-end design, which allows for better contact with fasteners and reduces the risk of wear and tear.
L.D. and B.S. performed the prism experiments. B.S. performed the lens experiments. O.K. carried out the simulations. All authors discussed the results and contributed to writing the manuscript.
The choice between long and short arm hex keys depends on the specific requirements of your projects. Long arm hex keys offer increased leverage and torque, making them ideal for tasks that require more force. On the other hand, short arm hex keys are advantageous in tight spaces where a longer tool might be impractical. A comprehensive hex key set that includes both long and short arm options provides versatility, allowing you to tackle a wide range of projects effectively.
The metric system, also known as the International System of Units (SI), was developed in the late 18th century and is now the most commonly used system of measurement worldwide. It uses base units such as meters for length, kilograms for mass, and seconds for time.
SAE units, on the other hand, are part of the United States customary system, which has its roots in the British Imperial System. SAE measurements typically use inches, feet, and pounds as their base units.
Effective storage solutions are key to mitigating these issues, ensuring that hex keys are both accessible and protected. By investing in the right type of organization system, users can significantly improve their workflow and extend the life of their tools.
Understanding the mechanics of hex keys and adopting best practices for their use can significantly reduce the risk of injury and damage. This section will delve into the essential safety measures and techniques that should be employed whenever using hex keys.
Selecting hex keys crafted from robust materials, such as chrome-vanadium or alloy steel, is an investment in both durability and longevity. This choice not only safeguards the tools against premature wear but also enhances their overall performance and reliability. As with any quality tools, the careful consideration of materials underscores the importance of precision and longevity in achieving successful outcomes across a range of projects.
However, there are also drawbacks to each system. For example, using an SAE hex key on a metric fastener can result in damage to both the tool and the fastener. Similarly, using a metric hex key on an SAE fastener can lead to an improper fit, causing the tool to slip and potentially cause injury.
Hex keys, also known as Allen keys or wrenches, are indispensable tools in both professional and hobbyist settings. Their unique design allows for the application of torque to hexagonal socket screws, making them crucial for a wide range of assembly, maintenance, and repair tasks. However, despite their utility, hex keys can easily become a source of frustration if not properly organized. A disorganized collection can lead to wasted time, decreased productivity, and the risk of using the wrong size, which could damage both the tool and the workpiece.
He, X. et al. Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications. Phys. Rev. A 79, 063829 (2009).