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Completeness condition for unambiguous profile reconstruction by sub-aperture stitching.

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    Accurate mirror profile reconstruction is possible by carefully selecting sub-aperture measurement spacing. This method removes systematic errors and ensures precise surface metrology without needing a reference surface.

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    Area of Science:

    • Optical Engineering
    • Metrology
    • Surface Science

    Background:

    • Stitching interferometry is a common technique for measuring large optical surfaces.
    • Systematic errors from measuring instruments and stage imperfections can compromise accuracy.
    • Existing methods often rely on reference surfaces or are susceptible to translation errors.

    Purpose of the Study:

    • To define conditions for reconstructing stitched mirror profiles free of systematic errors.
    • To eliminate dependence on reference surfaces and translation stage guidance errors.
    • To identify and mitigate sources of periodic and curvature errors in reconstructed profiles.

    Main Methods:

    • Analysis of information content in displaced sub-aperture measurements.
    • Theoretical modeling of error propagation during stitching.
    • Computer simulations and experimental validation using two distinct metrology instruments.

    Main Results:

    • Sufficient information for error-free profile reconstruction exists within displaced sub-aperture measurements.
    • Evenly spaced stitching must be avoided; pitch error or reference curvature must be measured.
    • Successful reconstruction of 1D profiles free of additive systematic errors was demonstrated.

    Conclusions:

    • The proposed method enables accurate mirror profile reconstruction by addressing specific measurement conditions.
    • Understanding and compensating for linear stage pitch errors or reference curvature is crucial.
    • This approach offers a robust solution for high-accuracy surface metrology in optical manufacturing.