Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design.

Area of Science:

• Coherent diffractive imaging
• Computational imaging
• Phase retrieval

Background:

• Ptychographic reconstruction traditionally relies on iterative algorithms.
• The Wigner Distribution Deconvolution Method (WDDM), a closed-form solution, has been largely overlooked for two decades.
• WDDM generates a high-dimensional data cube of relative phases.

Purpose of the Study:

• To re-evaluate and enhance the Wigner Distribution Deconvolution Method (WDDM) for ptychographic phase retrieval.
• To develop novel strategies for utilizing the full information content of WDDM.
• To improve the robustness and performance of WDDM against noise.

Main Methods:

• A new method to leverage the complete 4D data cube generated by WDDM, surpassing the limitations of the original 'stepping out' procedure.
• Development of an optimized probe design to mitigate noise during deconvolution.
• Implementation of an iterative deconvolution process to circumvent numerical instability issues (division by small numbers).

Main Results:

• Significant noise suppression achieved by utilizing the full WDDM data.
• Demonstrated effectiveness of the improved probe design in reducing noise artifacts.
• Model calculations show WDDM, when enhanced, performs comparably to state-of-the-art iterative methods like extended Ptychographical Iterative Engine (ePIE).

Conclusions:

• The revisited WDDM, with noise-reduction and probe-optimization strategies, offers a viable alternative to conventional iterative ptychographic reconstruction methods.
• This work revives a powerful closed-form solution, potentially offering new avenues for ptychographic imaging.
• Enhanced WDDM demonstrates competitive performance, particularly in noise-sensitive scenarios.