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    Area of Science:

    • Optical Physics
    • Image Processing
    • Spectroscopy

    Background:

    • Hyperspectral imaging requires accurate phase information for detailed analysis.
    • Existing phase retrieval methods struggle with noisy intensity observations.
    • Fellgett's disadvantage in Fourier transform spectroscopy amplifies noise, complicating phase reconstruction.

    Purpose of the Study:

    • To develop a novel phase retrieval algorithm for broadband hyperspectral phase imaging.
    • To overcome limitations of existing methods in handling noisy data.
    • To reconstruct both the phase and depth profile of objects.

    Main Methods:

    • Utilizing Fourier transform spectroscopy in a self-referencing optical setup.
    • Implementing a sparse wavefront noise filtering technique within the algorithm.
    • Validating the algorithm through simulations and physical experiments with transparent objects.

    Main Results:

    • The algorithm successfully reconstructs the phase distribution of investigated objects.
    • Noise amplification, a known issue (Fellgett's disadvantage), is significantly mitigated.
    • Precise phase imaging and accurate object depth (profile) reconstruction were demonstrated.

    Conclusions:

    • The proposed algorithm offers a robust solution for hyperspectral phase imaging from noisy data.
    • It enhances phase reconstruction accuracy and enables detailed object profiling.
    • The method shows promise for applications requiring high-resolution imaging of transparent materials.