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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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NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Theoretical ranging performance model and range walk error correction for photon-counting lidars with multiple

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    This study introduces a new theoretical model and correction method to reduce range walk error in photon-counting lidar systems. The method uses multiple detectors to achieve centimeter-level ranging accuracy, improving lidar performance.

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    Area of Science:

    • Photon-counting lidar technology
    • Optical remote sensing systems

    Background:

    • Ranging performance is critical for lidar systems.
    • Signal photon number fluctuations cause range walk error in photon-counting lidars, impacting accuracy.

    Purpose of the Study:

    • To develop a theoretical ranging performance model for photon-counting lidars with multiple detectors.
    • To propose and verify a method for correcting range walk error.

    Main Methods:

    • Derivation of a theoretical ranging performance model using the lidar equation and photon-counting detector statistics.
    • Experimental verification using a Geiger-mode avalanche photodiode (Gm-APD) lidar system.
    • Implementation of a correction method utilizing multiple detectors and repetitive measurements.

    Main Results:

    • Multiple detectors enhance ranging precision stability with variable received signal photons.
    • The new method achieved centimeter-level ranging accuracy (mean residual error 1.14 cm, std dev 1.23 cm) over 1600 measurements.
    • The technique demonstrated effectiveness in mitigating range walk error.

    Conclusions:

    • The proposed theoretical model and correction method effectively address range walk error in photon-counting lidars.
    • Multiple detectors are crucial for maintaining consistent ranging precision.
    • The method is suitable for satellite lidar systems like ICESat-2, requiring only repetitive measurements and triggered detectors.