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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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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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Updated: May 8, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
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Improved digital holographic reconstruction algorithm by zeroth-order term elimination based on the Riesz transform.

Mingguang Shan, Qiqiang Jin, Wanting Zhao

    Optics Letters
    |December 24, 2024
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    Summary

    This study introduces a new digital holography algorithm that eliminates the zeroth-order term using the Riesz transform. This method enhances effective bandwidth ratio for high-resolution holographic reconstruction.

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    Area of Science:

    • Optics and Photonics
    • Digital Imaging
    • Signal Processing

    Background:

    • Off-axis digital holography often suffers from a low effective bandwidth ratio.
    • This limitation is primarily caused by interference from zeroth- and first-order terms impacting the desired first-order term.
    • Efficiently retrieving high-resolution amplitude and phase information remains a challenge.

    Purpose of the Study:

    • To propose an improved digital holographic reconstruction algorithm.
    • To effectively eliminate the zeroth-order term in off-axis holography.
    • To enhance the effective bandwidth ratio and improve reconstruction quality.

    Main Methods:

    • The proposed algorithm utilizes the Riesz transform for zeroth-order term elimination.
    • Off-axis holograms are convolved with Riesz kernels.
    • A singularity at the origin of the Riesz kernels is exploited to remove the zeroth-order term in the spectrum.

    Main Results:

    • The Riesz transform-based method effectively eliminates the zeroth-order term.
    • The effective bandwidth ratio is significantly improved, optimizing bandwidth utilization.
    • High-resolution amplitude and phase information retrieval is achieved.
    • Simulated and experimental results validate the algorithm's effectiveness.

    Conclusions:

    • The developed algorithm offers superior performance compared to traditional methods.
    • It enables high-resolution holographic reconstruction by effectively addressing bandwidth limitations.
    • This technique provides a robust solution for improving digital holographic imaging.