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Superresolved swept-wavelength interferometry using frequency estimation methods.

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    Swept-wavelength interferometry (SWI) superresolution methods like Nonlinear Least Squares (NLS) and Local Linear Regression (LLR) achieve high precision distance measurements. NLS excels at short distances, while LLR is faster for longer ranges.

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    Area of Science:

    • Optical Metrology
    • Precision Measurement Science

    Background:

    • High signal-to-noise ratios in swept-wavelength interferometry (SWI) enable superresolution of distance measurements.
    • Achieving uncertainties as low as 10-4-10-5 of Fourier transform-limited resolution is possible with SWI.

    Purpose of the Study:

    • To compare three superresolution techniques for SWI distance measurements: Local Linear Regression (LLR), Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), and Nonlinear Least Squares (NLS).
    • To determine how superresolution methods and SWI hardware influence measurement precision, uncertainty, and the range of superresolvable distances.

    Main Methods:

    • Comparison of LLR, ESPRIT, and NLS for superresolving SWI distance measurements.
    • Analysis of measurement uncertainty and precision as a function of superresolution method and SWI hardware.

    Main Results:

    • The choice of superresolution method impacts both measurement precision and the minimum superresolvable distance.
    • NLS offers the least uncertainty for short distances (2-20 times Fourier transform-limited resolution), while LLR provides faster unbiased estimates for longer distances.
    • LLR and NLS demonstrate greater noise tolerance than ESPRIT and approach the Cramér-Rao bound, achieving 1σ precision of 10-4 of the transform limit with sufficient signal-to-noise ratio (SNR).

    Conclusions:

    • Superresolution method selection is critical for optimizing SWI distance measurements based on the desired range and precision.
    • NLS and LLR are robust and high-precision methods for SWI superresolution, particularly in noisy conditions.
    • SWI hardware limitations primarily dictate the maximum superresolvable distance, independent of the superresolution technique used.