A Python framework for the online reconstruction of X-ray near-field holography data

The phase problem is a well known ill-posed reconstruction problem of coherent lens-less microscopic imaging, where only the squared magnitude of a complex wavefront is measured by a detector while the phase information from the wave field is lost. To retrieve the lost information, common algorithms rely either on multiple data acquisitions under varying measurement conditions or on the application of strong constraints such as a spatial support. In X-ray near-field holography however, these methods are rendered impractical in the setting of time sensitive in situ and in operando measurements. In this framework, we forego the spatial support constraint and propose a projected gradient descent (PGD) based reconstruction scheme in combination with proper preprocessing that significantly reduces artifacts for refractive reconstructions from only a single acquired hologram without a spatial support constraint.

For the reconstruction of sharp images from experimental holograms in the near-field regime, it is crucial to precisely estimate the Fresnel number of the forward model. Otherwise, blurred out-of focus images that also can contain artifacts are the result. In general, a simple distance measurement at the experimental setup is not sufficiently accurate, thus the fine-tuning of the Fresnel number has to be done prior to the actual phase retrieval. This can be done manually or automatically by an estimation algorithm. In this framework, we propose a novel criterion, based on a model matching approach with respect to the underlying reconstruction of the projected refractive index of an object. With respect to this criterion, we provide a downhill-simplex method for the automatic optimization of the Fresnel number. This approach provides  a solutIon for automatic focusing for the phase retrieval of near-field holograms.

This repository contains the implementation and examples shown in the papers:

• "Artifact-suppressing reconstruction of strongly interacting objects in X-ray near-field holography without a spatial support constraint". https://doi.org/10.1364/OE.514641
• "Model-based autofocus for near-field phase retrieval". https://doi.org/10.1364/OE.544573