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    Area of Science:

    • Optics and photonics
    • Beam physics
    • Mathematical modeling

    Background:

    • Vortex beams are essential in physics, imaging, and communications.
    • Topological charge (TC) quantifies orbital angular momentum and is critical for applications.
    • Diffraction through a triangular aperture is a common TC measurement method, but lacks dimensional constraints.

    Purpose of the Study:

    • To address the gap in literature regarding dimensional constraints for vortex beam TC measurement.
    • To develop a mathematical model for determining the precise limits of vortex beams and triangular apertures.
    • To provide a rigorous framework for optimizing TC measurement setups.

    Main Methods:

    • Development of a concise mathematical model based on geometric considerations.
    • Validation of the model through numerical simulations.
    • Analysis of the interplay between vortex beam properties and triangular aperture dimensions.

    Main Results:

    • The study defines specific dimensional limits for vortex beams and triangular apertures.
    • The mathematical model provides accurate predictions for optimal measurement configurations.
    • Numerical simulations confirm the model's validity across various parameters.

    Conclusions:

    • The established dimensional constraints are crucial for accurate topological charge measurement.
    • This work provides a foundational tool for researchers and engineers working with vortex beams.
    • The findings will enhance the reliability and precision of optical communication and imaging systems.