Phase retrieval for arbitrary Fresnel-like linear shift-invariant imaging systems suitable for tomography

Area of Science:

• Optics and Imaging
• X-ray Microscopy
• Phase Contrast Imaging

Background:

• X-ray phase contrast imaging (XPCI) is crucial for visualizing unstained biological samples.
• Existing phase retrieval methods often require iterative algorithms or specific system constraints.
• Linear shift-invariant (LSI) systems with Fresnel-like propagation present unique challenges for phase retrieval.

Purpose of the Study:

• To develop a generalized non-iterative phase retrieval method for X-ray imaging systems.
• To overcome limitations of propagation distance and system requirements in phase retrieval.
• To provide a robust initial guess for iterative phase retrieval algorithms.

Main Methods:

• A novel non-iterative phase retrieval algorithm is proposed for arbitrary linear shift-invariant (LSI) imaging systems.
• The method requires the optical element's transfer function to be approximated by second-order Taylor polynomials.
• The approach is validated using synthetic data and experimental holograms from a Bragg magnifier microscope.

Main Results:

• The generalized method successfully performs phase retrieval without restrictions on propagation distance.
• The approach significantly accelerates convergence when used as an initial guess for iterative methods.
• High-resolution (300 nm) morphological details of a tardigrade were revealed through micro-tomography.

Conclusions:

• The developed non-iterative phase retrieval technique offers a versatile solution for X-ray phase contrast imaging in LSI systems.
• This method enhances the efficiency and applicability of phase retrieval in microscopy.
• The successful application to biological micro-tomography demonstrates its practical utility for high-resolution imaging.