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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 sampling...
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Related Experiment Video

Updated: Jun 12, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

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Published on: January 28, 2019

Two-dimensional phase retrieval by exponential filtering.

N Nakajima

    Applied Optics
    |June 16, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Two novel phase retrieval methods reconstruct 2-D objects from Fourier moduli. These techniques enhance reconstruction range using entire functions of the exponential type, validated by simulations.

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    Area of Science:

    • Optics and Photonics
    • Image Reconstruction
    • Fourier Optics

    Background:

    • Phase retrieval is crucial for reconstructing objects from limited diffraction data.
    • Traditional methods face limitations in extending the range of successful object reconstructions.

    Purpose of the Study:

    • To introduce and evaluate two advanced phase retrieval methods for 2-D object reconstruction.
    • To improve the success range of reconstructions using properties of entire functions of the exponential type.

    Main Methods:

    • Phase retrieval using Fourier series expansion.
    • Phase retrieval utilizing logarithmic Hilbert transform and Fourier series expansion.
    • Application of an exponential filter at the object plane.

    Main Results:

    • Successful reconstruction of 2-D objects from Fourier moduli using both proposed methods.
    • Demonstrated extension of the reconstruction range compared to conventional techniques.
    • Validation through computer simulations for real and phase objects.

    Conclusions:

    • The developed phase retrieval methods effectively reconstruct 2-D objects.
    • Utilizing entire functions of the exponential type significantly broadens the scope of successful phase retrieval.
    • The methods show promise for applications requiring accurate object reconstruction from Fourier modulus data.