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

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.