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    This study presents a fast method for arbitrary focusing through scattering media by considering cross-term effects. An optimized input mode significantly improves focusing quality and signal-to-noise ratio.

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    Area of Science:

    • Wave optics
    • Photonics
    • Scattering media

    Background:

    • Focusing light through scattering media is challenging due to complex wave interactions.
    • Traditional methods for wavefront shaping are often slow and susceptible to noise.
    • Cross-term effects in transmission matrices significantly impact multi-point focusing accuracy.

    Purpose of the Study:

    • To develop a fast compensation scheme for arbitrary focusing after light propagation through scattering samples.
    • To theoretically analyze and mitigate the influence of cross terms on focusing performance.
    • To enhance the signal-to-noise ratio (SNR) of the focused output.

    Main Methods:

    • Theoretical analysis using transmission matrix theory to understand cross-term effects.
    • Application of the Multi-Population Genetic Algorithm to retrieve optimal input modes for cross-term suppression.
    • Utilizing the off-axis holographic method for efficient measurement of large transmission matrices, reducing experimental time and noise.

    Main Results:

    • Demonstrated that cross-term influence is significant and must be accounted for in focusing schemes.
    • Successfully retrieved input modes that suppress cross-term effects, enabling arbitrary focusing.
    • Achieved a high-quality focal output with a significant increase in signal-to-noise ratio by 13.6 dB.

    Conclusions:

    • The proposed fast compensation scheme effectively enables arbitrary focusing through scattering media.
    • The integration of transmission matrix theory, genetic algorithms, and holographic methods provides a robust approach for wavefront shaping.
    • The method offers a significant improvement in focusing quality and SNR, with potential applications in imaging and optical manipulation.