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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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A Multimodal Wide-Field Fourier-Transform Raman Microscope
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Enhancing frequency accuracy of linear frequency-modulated BOTDR using Richardson-Lucy deconvolution.

LiHuang Li, Jiageng Chen, Yang Zhang

    Optics Letters
    |December 1, 2025
    PubMed
    Summary

    This study introduces a novel algorithm for Brillouin optical time-domain reflectometry (BOTDR) that enhances measurement accuracy and extends the detectable event zone length. The method significantly reduces spectral bandwidth, improving Brillouin frequency shift (BFS) extraction.

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    Area of Science:

    • Optics and Photonics
    • Signal Processing

    Background:

    • Brillouin optical time-domain reflectometry (BOTDR) uses linear frequency-modulated (LFM) pump pulses for rapid measurements.
    • A key limitation of LFM pulses in BOTDR is the constrained detectable event zone length due to linear frequency-time mapping validity within the pulse width.

    Purpose of the Study:

    • To overcome the limitations of LFM pulses in BOTDR for extended event zone lengths.
    • To develop a novel algorithm for accurate Brillouin frequency shift (BFS) extraction in BOTDR.

    Main Methods:

    • A two-step Richardson-Lucy (RL) deconvolution algorithm operating in the frequency domain was proposed.
    • The algorithm aims to compress spectral bandwidth and accurately extract BFS for event zones exceeding detection constraints.

    Main Results:

    • Experimental results showed a 13.5-times reduction in spectral bandwidth (from ~540 MHz to ~40 MHz).
    • Achieved a Brillouin frequency shift (BFS) measurement accuracy of 0.34 MHz.
    • Demonstrated a 4.2-times improvement in accuracy compared to conventional peak-search methods.

    Conclusions:

    • The proposed RL deconvolution algorithm effectively enhances BFS measurement accuracy in BOTDR.
    • The method successfully extends the detectable event zone length by compressing spectral bandwidth.
    • This advancement offers improved performance for temperature and strain variation detection in BOTDR systems.