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Optimum plane selection for transport-of-intensity-equation-based solvers.

J Martinez-Carranza, K Falaggis, T Kozacki

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    Summary
    This summary is machine-generated.

    Minimizing axial intensity derivative error in transport of intensity equation (TIE) phase retrieval is not optimal. This study reveals an optimal plane separation to reduce phase retrieval errors and noise sensitivity in TIE systems.

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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Wavefront Sensing

    Background:

    • Transport of Intensity Equation (TIE) is a key technique for phase retrieval in optics.
    • Current TIE methods often focus on minimizing errors in the axial intensity derivative.
    • This approach can lead to suboptimal plane separation and increased noise sensitivity.

    Purpose of the Study:

    • To challenge the assumption that minimizing axial intensity derivative error directly minimizes phase retrieval error.
    • To identify and analyze an optimal plane separation for TIE-based phase retrieval.
    • To develop a model for determining optimal plane separation based on noise levels and measurement parameters.

    Main Methods:

    • Detailed theoretical analysis of TIE-based phase retrieval error propagation.
    • Development of a model to identify optimal plane separation.
    • Derivation of analytical expressions for optimal equidistant plane separation.
    • Validation of the model for Fourier-transform-based and multigrid TIE solvers.

    Main Results:

    • The common practice of minimizing axial intensity derivative error leads to underestimation of optimal plane separation.
    • An optimal plane separation exists that minimizes phase retrieval errors and noise sensitivity.
    • Analytical expressions for optimal plane separation are derived considering noise and number of planes.
    • The findings are applicable to various TIE solvers, including Fourier-transform and multigrid methods.

    Conclusions:

    • Optimizing measurement conditions for TIE phase retrieval requires considering an optimal plane separation, not just derivative error minimization.
    • The derived analytical expressions provide a practical method for improving TIE system performance.
    • This work enhances the robustness and accuracy of TIE-based phase retrieval techniques, particularly in noisy conditions.