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Obtaining the Transfer Function of optical instruments using large calibrated reference objects.

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    This summary is machine-generated.

    This study presents analytical solutions for measuring the Transfer Function (TF) of Coherence Scanning Interferometers using spherical artefacts. It reveals limitations in current methods, showing the TF is unmeasurable at certain spatial frequencies, and proposes solutions.

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    Area of Science:

    • Optical metrology
    • Interferometry
    • Image processing

    Background:

    • Coherence Scanning Interferometers (CSIs) are crucial for precise surface measurements.
    • Measuring the Transfer Function (TF) of instruments like CSIs is essential for understanding their performance.
    • A recent method proposed measuring CSI TF using a single spherical artefact.

    Purpose of the Study:

    • To provide analytical solutions for the Fourier transform of the 'foil' model used in spherical artefact-based TF measurement.
    • To identify limitations of the single spherical artefact method for TF measurement.
    • To propose extensions to overcome these limitations.

    Main Methods:

    • Derivation of analytical solutions for the Fourier transform of a partial spherical shell model.
    • Analysis of the resulting Fourier transform for points of zero amplitude.
    • Identification of spatial frequencies where the Transfer Function becomes unmeasurable.

    Main Results:

    • Analytical solutions reveal points of zero amplitude in the Fourier transform of the spherical shell model.
    • These zero-amplitude points correspond to spatial frequencies within the instrument's Transfer Function.
    • The Transfer Function is unmeasurable at these specific spatial frequencies when using a single spherical artefact.

    Conclusions:

    • The 'foil' model, when applied to a single spherical artefact, has inherent limitations for complete Transfer Function measurement.
    • Analytical solutions offer a deeper understanding of these limitations compared to numerical approaches.
    • Proposed extensions to the method are necessary to achieve comprehensive Transfer Function characterization.