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Updated: Oct 17, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Universal approach for local higher-order wavefront tracing equations for complex optical systems.

W Becken, S Trumm, P Kerner

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
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    Summary
    This summary is machine-generated.

    This study introduces an efficient method for wave tracing in complex optical systems. It enables rapid analysis of multiple wavefronts by calculating derivatives, overcoming limitations of traditional step-by-step approaches.

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    Area of Science:

    • Optics and Photonics
    • Computational Physics

    Background:

    • Analytical wave tracing is state-of-the-art but limited to single propagation/refraction.
    • Complex optical systems require time-consuming successive application of elementary wave-tracing steps.

    Purpose of the Study:

    • To develop an efficient method for wave tracing in complex optical systems.
    • To enable tracing of multiple wavefronts through a fixed system.

    Main Methods:

    • Utilizing ray transfer properties summarized as a nonlinear function f.
    • Deriving wave-tracing equations for wavefront local derivatives of any order using multiple derivatives.
    • Expressing outgoing wavefront derivatives as weighted sums of incoming wavefront derivatives.

    Main Results:

    • The new approach is significantly more efficient than stepwise wave tracing for multiple wavefronts.
    • Wavefront derivatives are calculated based on system-dependent coefficients and aberration factors.
    • The method handles complex optical systems with numerous refractive surfaces.

    Conclusions:

    • This derivative-based method offers a computationally efficient alternative for wave tracing in complex optical systems.
    • It overcomes the limitations of traditional methods for analyzing multiple wavefronts.