Inverse diffraction in phase space

Area of Science:

• Computational Optics
• Wave Propagation Physics

Background:

• Inverse diffraction is crucial for computational optics, enabling simulations of round-trip wave propagation.
• Existing ambiguities in inverse diffraction necessitate a re-examination of the problem.

Purpose of the Study:

• To provide an exhaustive analysis of inverse diffraction using a phase space perspective.
• To clarify ambiguities related to diffraction kernels and negative propagation distances.

Main Methods:

• Phase space analysis utilizing the Wigner distribution function.
• Geometric interpretation of forward and inverse diffraction as phase space diagram (PSD) transformations.

Main Results:

• Forward and inverse diffraction are shown to be equivalent to the deformation and recovery of the PSD.
• Symmetries in PSD transformations for different inverse diffraction forms are identified.
• Ambiguities concerning diffraction kernel conjugation and negative diffraction distance are resolved.

Conclusions:

• Phase space analysis offers an intuitive framework for understanding inverse diffraction.
• This approach simplifies the study of 3D wave field propagation, including holographic phase conjugation.