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Complex division as a common basis for calculating phase differences in electronic speckle pattern interferometry in

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    This study reveals a unified mathematical approach for analyzing object deformations. A single complex division formalism simplifies phase map calculations for deformation analysis.

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    Area of Science:

    • Optics and Photonics
    • Materials Science
    • Computational Mechanics

    Background:

    • Phase map calculation is crucial for understanding object deformations.
    • Existing methods for deformation analysis often involve complex, multi-step calculations.
    • A unified approach could streamline deformation analysis and improve accuracy.

    Purpose of the Study:

    • To introduce a simplified, unified formalism for calculating phase maps of object deformations.
    • To demonstrate that diverse phase map calculation formulas can be unified under a single mathematical framework.
    • To enhance the efficiency and accessibility of deformation analysis techniques.

    Main Methods:

    • Development of a novel mathematical formalism based on complex division.
    • Application of the formalism to various object deformation scenarios.
    • Comparative analysis of the proposed method against existing techniques.

    Main Results:

    • All tested formulas for one-step phase map calculation of object deformations can be expressed using a single complex division formalism.
    • The proposed formalism offers a simplified and unified approach to deformation analysis.
    • This unification reduces computational complexity and potential for error.

    Conclusions:

    • A single complex division formalism provides a universal method for calculating phase maps of object deformations.
    • This unified approach has the potential to significantly advance the field of deformation analysis.
    • The findings pave the way for more efficient and robust optical metrology and material characterization techniques.