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Related Concept Videos

Range00:59

Range

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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
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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

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.
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    Laser pointing error significantly impacts photon-counting lidar ranging performance for low Earth orbit targets. Constraining pointing error below 20% of the laser divergence angle is crucial for accurate measurements.

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    Area of Science:

    • Space technology
    • Optical engineering
    • Laser physics

    Background:

    • Photon-counting lidar systems are vital for tracking low Earth orbit (LEO) targets.
    • Ranging performance is a critical metric for laser ranging systems.
    • Laser pointing error is a significant factor affecting ranging accuracy.

    Purpose of the Study:

    • To develop a theoretical model for laser pointing error in lidar systems.
    • To derive an improved lidar equation accounting for pointing error.
    • To analyze the impact of pointing error on ranging performance for LEO targets.

    Main Methods:

    • Derived the joint probability distribution function of laser pointing error.
    • Developed an improved lidar equation incorporating pointing error.
    • Calculated and analyzed the energy expectation value of laser illumination.
    • Utilized Monte Carlo simulations for verification.
    • Developed a range performance model including range walk error and ranging precision.

    Main Results:

    • The derived analytical expression for energy expectation value was validated by Monte Carlo simulations.
    • Average signal photon numbers matched experimental data from the Shanghai Astronomical Observatory.
    • Pointing error increased range walk error to 31.75 cm and ranging precision to 2.5 cm with a powerful laser (2 J) and ~1'' pointing error.
    • A pointing error less than 20% of the laser divergence angle is recommended.

    Conclusions:

    • The theoretical model accurately predicts lidar ranging performance under pointing error.
    • Pointing error has a substantial impact on ranging accuracy, especially with high-power lasers.
    • Systematic design should constrain laser pointing error to maintain optimal ranging performance.