Phase front retrieval by means of an iterative shadowgraphic method

Area of Science:

• Optics and Photonics
• Wavefront Sensing
• Image Processing

Background:

• Optical phase retrieval is crucial for characterizing optical elements and systems.
• Existing methods for self-referencing phase retrieval have limitations in accuracy and convergence speed.
• Shadowgraphic methods offer a simpler approach but often suffer from diffraction artifacts.

Purpose of the Study:

• To propose and validate an Iterative Shadowgraphic Method (ISM) for self-referencing optical phase retrieval.
• To develop an algorithm that corrects for diffraction effects in phase retrieval.
• To demonstrate the superiority of ISM over existing methods in terms of accuracy, resolution, and convergence.

Main Methods:

• Acquiring two defocused intensity images of a weakly absorbing phase object.
• Developing an iterative algorithm to retrieve the transverse phase distribution.
• Mathematically proving the convergence of the algorithm.
• Conducting numerical simulations to test the algorithm's performance.

Main Results:

• The ISM successfully retrieves the transverse phase distribution of a distorted illuminating beam.
• The developed algorithm corrects for diffraction effects, improving phase map accuracy.
• Numerical tests show the ISM recovers full phase details with increased resolution compared to simple shadowgraphy.
• ISM demonstrates faster convergence and avoids stagnation issues compared to a Gerchberg-Saxton-type algorithm.

Conclusions:

• The Iterative Shadowgraphic Method (ISM) provides an effective and robust solution for optical phase retrieval.
• ISM offers significant advantages in speed, accuracy, and resolution over conventional techniques.
• The method is mathematically validated and numerically proven for practical applications in optics.