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Stitching method based on dual quaternion for cylindrical mirrors.

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    A novel dual quaternion stitching method enhances sub-aperture stitching interferometry accuracy. This high-efficiency technique is ideal for metrology and manufacturing of long cylindrical optics.

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    Area of Science:

    • Optical Engineering
    • Metrology
    • Computational Geometry

    Background:

    • Sub-aperture stitching interferometry is crucial for measuring large optical components.
    • Existing stitching methods can face challenges in accuracy and efficiency.
    • Dual quaternions offer a robust mathematical framework for 3D transformations.

    Purpose of the Study:

    • To propose and analyze a novel sub-aperture stitching method utilizing dual quaternions.
    • To develop a calculation method for stitching based on dual quaternion algebra.
    • To validate the accuracy and efficiency of the proposed stitching technique.

    Main Methods:

    • Detailed analysis of dual quaternion application in sub-aperture stitching interferometry.
    • Deduction of a specific calculation method for stitching using dual quaternions.
    • Experimental validation using a stitching by parts algorithm and a long trace profiler.

    Main Results:

    • The proposed dual quaternion stitching method achieved high accuracy with residuals of approximately 0.22 nm RMS in overlapping areas.
    • Residual differences of 0.79 nm RMS were obtained between figure errors using the dual quaternion method and a long trace profiler.
    • Demonstrated accuracy and efficiency of the novel stitching approach.

    Conclusions:

    • The dual quaternion-based stitching method provides a significant advancement in sub-aperture stitching interferometry.
    • The method shows high accuracy and efficiency, suitable for precise optical metrology.
    • This technique has potential applications in the metrology and manufacturing of long cylindrical mirrors.