Additional approaches to solving the phase problem in optics

Area of Science:

• Optics and Photonics
• Image Processing
• Wave Phenomena

Background:

• Complex optical fields contain intricate structures crucial for various applications.
• Diagnosing these structures, particularly the phase information, presents a significant challenge.
• Existing methods for localizing special points in speckle fields are often limited by discretization and resolution.

Purpose of the Study:

• To develop and validate an optimal approach for diagnosing the structure-forming skeleton of complex optical fields.
• To address the phase problem in localizing special points within speckle fields.
• To propose a robust method for phase reconstruction and skeleton element identification.

Main Methods:

• Analysis of optical field singularity algorithms considering intensity discretization and image resolution.
• Application of a "window" 2D Hilbert transform for phase distribution reconstruction.
• Development of an additional algorithm for solving the phase problem in random 2D intensity distributions.

Main Results:

• An optimal approach was identified, significantly improving the localization of special points in speckle fields.
• The proposed 2D Hilbert transform method enables reconstruction of phase distribution and identification of structure-forming elements, including singular and saddle points.
• Equi-phase lines were reconstructed within a narrow confidence interval, demonstrating the method's accuracy.

Conclusions:

• The "window" 2D Hilbert transform offers an effective solution for reconstructing the phase of speckle fields.
• This method provides invariance to transformation kernel position and accurately identifies key structural elements of optical fields.
• The developed approach advances the ability to solve the phase problem for complex optical intensity distributions.