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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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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.
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Variation: Normal Distribution, Range, and Standard Deviation02:32

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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

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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

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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.
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Cube-corner autocollimator with expanded measurement range.

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    This study introduces a cube-corner reflector for photoelectric autocollimators, significantly extending the angle measurement range to 12° without optical changes. The enhanced system maintains high accuracy, proving effective for precise angular measurements.

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    Area of Science:

    • Optical Engineering
    • Metrology
    • Instrumentation

    Background:

    • Traditional photoelectric autocollimators have limited angle measurement ranges.
    • Expanding measurement range often requires larger, more complex optical systems.
    • Need for compact, high-accuracy angle measurement solutions persists.

    Purpose of the Study:

    • To enhance the angle measurement range of photoelectric autocollimators.
    • To develop and validate algorithms for a cube-corner reflector based system.
    • To assess the accuracy and performance of the extended range system.

    Main Methods:

    • Employed a cube-corner reflector as the primary reflective element.
    • Deduced and implemented novel algorithms for angle calculation.
    • Conducted experimental investigations to validate performance.

    Main Results:

    • Successfully extended the angle measurement range from 1.2° to 12°.
    • Achieved this extension without increasing the objective lens aperture.
    • Demonstrated accuracy better than 35 arcseconds for deflections under 8°.

    Conclusions:

    • The cube-corner reflector effectively broadens the angular measurement capability of photoelectric autocollimators.
    • The developed algorithms enable precise measurements within the extended range.
    • This approach offers a compact and accurate solution for angular metrology.