Redundancy of phase-space distribution functions in complex field recovery problems

Area of Science:

• Optics and Photonics
• Quantum Information Science

Background:

• Phase-space distributions are crucial for characterizing optical fields.
• Complete reconstruction often requires extensive data acquisition.

Purpose of the Study:

• To demonstrate that optical field amplitude and phase can be recovered from partial phase-space data.
• To identify and explain the redundancy of information in certain phase-space sections.

Main Methods:

• Analysis of phase-space distribution functions.
• Theoretical investigation of information redundancy.
• Exploration of implications for optical field reconstruction.

Main Results:

• Amplitude and phase of an optical field are recoverable from a limited section of its phase-space distribution.
• Significant information redundancy exists in other sections of the phase-space distribution.
• The sampling problem in optical tomography is resolved for arbitrary field distributions.

Conclusions:

• Partial phase-space measurements are sufficient for complete optical field reconstruction.
• This finding simplifies experimental requirements and data processing.
• The study provides a physical interpretation and resolves long-standing sampling challenges in tomography.