Iterative phase retrieval for digital holography: tutorial.

Area of Science:

• Digital holography
• Wavefront reconstruction
• Phase retrieval algorithms

Background:

• Iterative phase retrieval algorithms, particularly Gerchberg-Saxton (GS), are crucial for digital holography.
• Previous GS-based algorithms were limited to reconstructing 2D samples.
• Realistic objects are often 3D, necessitating methods for 3D reconstruction.

Purpose of the Study:

• To provide a tutorial on GS-based iterative phase retrieval for digital holography.
• To demonstrate a novel GS-based algorithm for reconstructing 3D samples.
• To establish criteria for the number of holograms required for 2D and 3D object reconstruction.

Main Methods:

• Utilizing Gerchberg-Saxton (GS) algorithm for iterative phase retrieval.
• Employing back-and-forth propagation between two planes with superimposed constraints.
• Applying iterative phase retrieval between intensity measurement planes for 3D reconstruction.

Main Results:

• Single-shot in-line holograms are sufficient for reconstructing 2D sample amplitude and phase.
• A novel GS-based algorithm successfully reconstructs 3D samples, including phase objects, from two or more holograms.
• Two holograms are theoretically sufficient to recover the entire wavefront diffracted by a 3D sample.

Conclusions:

• GS-based iterative phase retrieval enables quantitatively correct and twin-image-free reconstructions.
• The developed method extends phase retrieval to complex 3D objects, including thick biological samples and particle distributions.
• The study provides a foundation for advanced holographic imaging of 3D structures.