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Phase-shifting interferometry and maximum-likelihood estimation theory.

E W Rogala, H H Barrett

    Applied Optics
    |February 12, 2008
    PubMed
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    A new method using maximum-likelihood estimation validates the traditional four-step algorithm for phase-shifting interferometry. This statistically sound approach provides unbiased and efficient surface-height profile estimation.

    Area of Science:

    • Optical Metrology
    • Interferometry
    • Surface Profilometry

    Background:

    • Phase-shifting interferometry (PSI) is a key technique for quantitative surface measurement.
    • Traditional PSI algorithms lack a rigorous statistical foundation.
    • Accurate surface-height estimation is crucial in various scientific and engineering fields.

    Purpose of the Study:

    • To introduce a novel, statistically grounded method for assessing PSI performance.
    • To validate the classical four-step PSI algorithm using maximum-likelihood estimation (MLE).
    • To analyze the impact of irradiance ratio on PSI accuracy.

    Main Methods:

    • Application of maximum-likelihood estimation theory to noisy phase-shifted measurements.
    • Derivation of the analytical expression for the MLE surface-height profile.

    Related Experiment Videos

  • Monte Carlo simulations to evaluate estimator performance (bias, variance).

    • Main Results:

    • The MLE analytical expression is identical to the classical four-step algorithm.
    • The MLE is proven to be unbiased and efficient, meeting the Cramer-Rao lower bound.
    • Optimal PSI performance is achieved when irradiances from both interferometer arms are equal.

    Conclusions:

    • Maximum-likelihood estimation provides a statistically rigorous foundation for the four-step PSI algorithm.
    • The derived method offers an unbiased and efficient approach to surface-height profiling.
    • Controlling the irradiance ratio is critical for optimizing interferometric measurement accuracy.