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Related Concept Videos

Range00:59

Range

14.1K
The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount - 16 ounces of liquid, was not...
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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Variation: Normal Distribution, Range, and Standard Deviation02:32

Variation: Normal Distribution, Range, and Standard Deviation

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In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
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Angle of Twist - Elastic Range01:13

Angle of Twist - Elastic Range

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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Range Rule of Thumb to Interpret Standard Deviation01:13

Range Rule of Thumb to Interpret Standard Deviation

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The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height...
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Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

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Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
732

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A Contusive Model of Unilateral Cervical Spinal Cord Injury Using the Infinite Horizon Impactor
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Infinite deflectometry enabling 2π-steradian measurement range.

L R Graves, H Quach, H Choi

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    Summary
    This summary is machine-generated.

    Infinite Deflectometry enables full aperture surface reconstruction for challenging optics, including highly convex surfaces. This novel technique offers precise metrology for freeform optics where traditional methods fail.

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    Area of Science:

    • Optical Metrology
    • Surface Characterization
    • Freeform Optics

    Background:

    • Measuring freeform optical surfaces, especially highly convex ones, presents significant challenges for traditional metrology techniques.
    • Existing methods often struggle with dynamic range limitations and full aperture coverage for complex optical designs.

    Purpose of the Study:

    • To introduce and validate a novel deflectometry technique, Infinite Deflectometry, for comprehensive surface reconstruction of freeform optics.
    • To demonstrate the capability of Infinite Deflectometry in measuring challenging optical components, including highly convex surfaces and freeform Alvarez lenses.

    Main Methods:

    • Infinite Deflectometry utilizes a virtual source enclosure to achieve a 2π-steradian measurement range.
    • The technique reconstructs a full aperture surface sag map of the tested optic.
    • Performance is validated by measuring a fast f/1.26 convex surface and a freeform Alvarez lens.

    Main Results:

    • Infinite Deflectometry achieved an absolute RMS surface accuracy of 16.26 nm for a convex surface, outperforming a commercial interferometer (18.48 nm RMS).
    • A freeform Alvarez lens was measured with 22.34 𝜇m surface sag RMS, showing good agreement with a profilometer (488 nm RMS deviation).
    • Standard interferometry failed to measure the Alvarez lens due to its non-nulled wavefront dynamic range limitation.

    Conclusions:

    • Infinite Deflectometry provides a robust and accurate solution for metrology of challenging freeform and convex optical surfaces.
    • The technique overcomes limitations of conventional interferometry, enabling precise characterization of complex optical systems.