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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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Separation and compensation of nonlinear errors in sub-nanometer grating interferometers.

Qilin Zeng, Zhengyi Zhao, Hao Du

    Optics Express
    |December 23, 2022
    PubMed
    Summary
    This summary is machine-generated.

    This study addresses nonlinear errors in grating interferometers. A new method using cross-correlation coefficients successfully reduced these errors from 17.40 nm to 7.05 nm.

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    Area of Science:

    • Metrology
    • Optical Engineering
    • Instrumentation

    Background:

    • Grating interferometers are crucial for precise measurements.
    • Nonlinear errors, arising from factors like ghost reflections and angular deviations, limit measurement accuracy.
    • Existing methods struggle to fully compensate for these complex errors.

    Purpose of the Study:

    • To analyze the source and mechanism of nonlinear errors in grating interferometers.
    • To establish a nonlinear error model for measured and phase signals.
    • To propose and validate a novel method for separating and compensating these errors.

    Main Methods:

    • Analysis of nonlinear error sources and generation mechanisms.
    • Deduction of nonlinear error models for measured and phase signals.
    • Development of a nonlinear error separation and compensation method utilizing cross-correlation coefficients.

    Main Results:

    • The non-integer frequency multiplier relationship of higher-order nonlinear errors is explained.
    • Experimental validation shows the frequency multiplier is close to, but not equal to, 3-fold.
    • The proposed method significantly reduced peak-to-peak nonlinear error from 17.40 nm to 7.05 nm.

    Conclusions:

    • The established nonlinear error model accurately characterizes the behavior of these errors.
    • The cross-correlation coefficient-based method is effective in separating and compensating nonlinear errors.
    • This research enhances the precision and reliability of grating interferometer measurements.