Phase Recovery Guarantees from Designed Coded Diffraction Patterns in Optical Imaging.

Area of Science:

• Optical Imaging
• Computational Imaging
• Inverse Problems

Background:

• Phase retrieval (PR) is crucial for reconstructing images from diffraction intensity measurements.
• Existing methods primarily address PR in the far-field diffraction zone.
• Current approaches often use random coded apertures, leading to suboptimal and sometimes unfeasible reconstructions.

Purpose of the Study:

• To theoretically address the phase retrieval problem using coded diffraction patterns (CDP) in near, middle, and far diffraction zones.
• To develop a strategy for designing coded apertures to improve reconstruction quality.
• To provide theoretical guarantees for scene recovery with admissible modulations.

Main Methods:

• Developed a theoretical framework for phase retrieval from CDP across all three diffraction zones.
• Proposed a coded aperture design strategy based on scene properties (e.g., sparsity).
• Validated the approach through experimental results.

Main Results:

• Established theoretical guarantees for scene recovery from CDP in all diffraction zones.
• Demonstrated that coded aperture structure critically impacts image reconstruction quality.
• Showcased successful scene recovery using designed coded apertures with up to 40% fewer measurements.

Conclusions:

• The proposed method enables robust phase retrieval in optical imaging across all diffraction zones.
• Optimized coded aperture design is essential for efficient and accurate phase retrieval.
• This work advances computational imaging by providing a theoretically grounded and experimentally validated approach to phase retrieval.