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Topography restoration in white-light interferometry using an instrument transfer function evaluated with binary

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    Accurate white-light interferometry (WLI) topography measurements require knowing the instrument transfer function (ITF). This study derives an ITF using a binary pseudo-random array (BPRA) to enhance measurement accuracy and WLI performance.

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    Area of Science:

    • Surface metrology
    • Optical instrumentation
    • Signal processing

    Background:

    • Accurate topography measurements are crucial in various scientific and engineering fields.
    • White-light interferometry (WLI) is a common technique for surface characterization.
    • The instrument transfer function (ITF) significantly impacts WLI measurement accuracy.

    Purpose of the Study:

    • To develop a robust method for determining the instrument transfer function (ITF) for white-light interferometry (WLI).
    • To enhance the accuracy of WLI topography measurements through improved ITF characterization and data processing.
    • To establish a theoretical benchmark for ITF analysis using a binary pseudo-random array (BPRA).

    Main Methods:

    • Derivation of analytical expressions for the power spectral density (PSD) of a discretely sampled binary pseudo-random array (BPRA).
    • Determination of the ITF by comparing the theoretical PSD of the BPRA with its measured PSD.
    • Integration of the determined ITF (or nominal modulation transfer function - MTF) into Fourier-domain restoration filters.
    • Application of filters to WLI topography data and comparison with atomic force microscopy (AFM) measurements.

    Main Results:

    • A complete set of analytical expressions for the PSD of a BPRA was derived.
    • The determined ITF for a specific WLI system closely matched its nominal modulation transfer function (MTF).
    • Restored WLI topography data showed improved agreement with atomic force microscopy (AFM) measurements after applying ITF-based filters.

    Conclusions:

    • The proposed BPRA-based method provides a robust and practical approach for measuring the ITF of WLI systems.
    • Integrating the ITF into filtering significantly enhances the accuracy of WLI surface topography measurements.
    • This methodology offers a valuable tool for characterizing WLI performance and improving surface metrology.