From Fienup's phase retrieval techniques to regularized inversion for in-line holography: tutorial.

Area of Science:

• Optics and Photonics
• Computational Imaging
• Applied Mathematics

Background:

• In-line holography is a powerful technique for 3D imaging of micro-objects.
• Traditional reconstruction methods like Fienup's phase retrieval algorithm have limitations.
• An inverse problems approach offers a flexible framework for addressing these limitations.

Purpose of the Study:

• To provide a tutorial on reconstructing in-line holograms using an inverse problems approach.
• To explore the connections between alternating projections and the inverse problems framework.
• To demonstrate the advantages of the inverse problems formulation for hologram reconstruction.

Main Methods:

• Modeling holographic observations.
• Selecting appropriate regularizations and constraints for inverse problems.
• Designing a reconstruction algorithm based on proximal gradient descent.
• Interpreting Fienup's algorithm within the inverse problems framework.

Main Results:

• A clear connection is established between alternating projections strategies and the inverse problems framework.
• Fienup's algorithm is interpreted as a proximal gradient descent for a specific cost function.
• Successful reconstructions of micrometric beads from simulated and experimental holograms are achieved.

Conclusions:

• The transition from alternating projections to an inverse problems formulation for in-line hologram reconstruction is straightforward.
• The inverse problems approach provides advantageous results compared to traditional methods.
• This work facilitates improved 3D imaging in various scientific applications.