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Ellipse fitting for interferometry. Part 1: static methods.

M J Collett, G J Tee

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    This study compares ellipse fitting methods for interferometry. An algebraic fit with data-dependent normalization offers the best accuracy and robustness for phase and amplitude estimation.

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    Area of Science:

    • Optical metrology
    • Image analysis

    Background:

    • Accurate ellipse fitting is crucial for analyzing interferometric data.
    • Existing methods may suffer from bias and lack robustness with uneven data distributions.

    Purpose of the Study:

    • To evaluate various ellipse fitting techniques for interferometric applications.
    • To propose improvements for geometric and algebraic fitting methods.

    Main Methods:

    • Comparison of least-square geometric fitting with an improved distance approximation.
    • Evaluation of alternative normalizations for linear algebraic fitting.
    • Assessment of fitting methods using static data points.

    Main Results:

    • An algebraic fit with data-dependent normalization demonstrates minimal bias in phase and amplitude estimation.
    • This method exhibits superior robustness against unevenly distributed data.
    • An improved distance approximation is suggested for geometric fitting.

    Conclusions:

    • Algebraic ellipse fitting with data-dependent normalization is recommended for interferometric applications.
    • The proposed method enhances accuracy and reliability in data analysis.
    • Further research can explore these methods in dynamic interferometric systems.