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    Area of Science:

    • Spectroscopy
    • Data Analysis
    • Instrumental Science

    Background:

    • Recovering original spectral line shapes from instrumental data is crucial in spectroscopy.
    • Extended transmission profiles in instruments complicate accurate spectral recovery.

    Purpose of the Study:

    • To develop a method for recovering spectral line shapes from data with extended transmission profiles.
    • To establish ultimate bounds on the precision of spectral moment estimation.

    Main Methods:

    • Utilizing moments of measured spectral lines as variables for linear inversion.
    • Employing a semiparametric model to account for nuisance parameters.
    • Experimental validation using ghost spectroscopy.

    Main Results:

    • The problem of spectral line shape recovery was transformed into a linear inversion problem.
    • A semiparametric model was developed to determine precision limits.
    • Experimental results confirmed the theoretically established precision bounds.

    Conclusions:

    • The proposed method enables accurate recovery of spectral line shapes.
    • The semiparametric model provides a framework for understanding precision limitations in spectral analysis.
    • Experimental validation confirms the robustness of the method and its theoretical underpinnings.