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Improved theoretical model for differential wavefront sensing based on complex Gaussian decomposition with hard-edge

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    We developed a new model for differential wavefront sensing (DWS) that improves accuracy for larger quadrant photodiodes (QPDs). This enhanced model reduces errors from approximations, leading to more precise angular measurements in optical systems.

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    Area of Science:

    • Optical Engineering
    • Metrology
    • Instrumentation

    Background:

    • Differential wavefront sensing (DWS) utilizes quadrant photodiodes (QPDs) for angular measurements.
    • Larger QPDs offer enhanced sensitivity and accuracy in DWS.
    • Existing models based on error function (erf) approximations introduce significant deviations for larger QPDs.

    Purpose of the Study:

    • To develop an improved theoretical model for DWS that minimizes approximation errors.
    • To enhance the accuracy of angular measurements, particularly for larger QPDs.
    • To provide a more precise model for the design and optimization of DWS systems.

    Main Methods:

    • Proposed a novel model based on complex Gaussian decomposition of hard-edge apertures.
    • Replaced erf-based integration with a window function constructed from complex Gaussian functions.
    • Optimized complex Gaussian function parameters to improve integration accuracy and phase calculation.

    Main Results:

    • The new model significantly reduces theoretical deviations associated with integral approximations.
    • Achieved a two-order-of-magnitude improvement in phase accuracy through simulations and experiments.
    • Demonstrated enhanced performance and precision for larger QPD sizes.

    Conclusions:

    • The complex Gaussian decomposition model offers superior accuracy for DWS with larger QPDs.
    • This improved model provides more reliable guidance for designing high-precision DWS systems.
    • The findings are crucial for advancing optical sensing technologies requiring accurate angular measurements.