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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Approximations for the arctangent function in efficient fringe pattern analysis.

Hongwei Guo, Guoqing Liu

    Optics Express
    |June 18, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel method to approximate the arctangent function, significantly speeding up real-time fringe pattern analysis by reducing computational load in phase measurements.

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    Area of Science:

    • Optical Metrology
    • Computational Mathematics

    Background:

    • Fringe pattern analysis is crucial for real-time measurements but computationally intensive.
    • The arctangent function's implementation poses a significant computational burden.

    Purpose of the Study:

    • To develop a general method for approximating the arctangent function.
    • To enhance the efficiency of phase evaluations in fringe pattern analyses for real-time applications.

    Main Methods:

    • Approximating the arctangent function by splitting its domain into intervals.
    • Determining approximation polynomials in the maximum-norm sense for each interval.
    • Applying these polynomials to fringe analyses instead of the standard arctangent function.

    Main Results:

    • Significant improvements in the efficiency of phase evaluations were achieved.
    • Numerical analysis confirmed the accuracy and simplicity of the proposed approximations.
    • Experimental results validated the practical applicability of the method.

    Conclusions:

    • The proposed arctangent approximation method effectively reduces computational burden.
    • This method enables faster and more efficient real-time fringe pattern analysis.
    • The validated technique offers a practical solution for real-time optical metrology.