HoToPy: A toolbox for X-ray holo-tomography in Python

TL;DR

The toolbox comprises a collection of phase retrieval algorithms for the deeply holographic and direct contrast imaging regimes, including non‐linear approaches and extended choices of regularization, constraint sets and optimizers, all implemented with a unified and intuitive interface.

Abstract

We present a Python toolbox for holographic and tomographic X-ray imaging. It comprises a collection of phase retrieval algorithms for the deeply holographic and direct contrast imaging regimes, including non-linear approaches and extended choices of regularization, constraint sets, and optimizers, all implemented with a unified and intuitive interface. Moreover, it features auxiliary functions for (tomographic) alignment, image processing, and simulation of imaging experiments. The capability of the toolbox is illustrated by the example of a catalytic nanoparticle, imaged in the deeply holographic regime at the 'GINIX' instrument of the P10 beamline at the PETRA III storage ring (DESY, Hamburg). Due to its modular design, the toolbox can be used for algorithmic development and benchmarking in a lean and flexible manner, or be interfaced and integrated in the reconstruction pipeline of other synchrotron or XFEL instruments for phase imaging based on propagation.

Figures (3)

• Figure 1: Schematic for propagation-based imaging (PBI) in cone-beam geometry. A diverging X-ray beam illuminates a sample with weak absorption, which is placed at a defocus distance $z_{01}$. The sample imprints phase shifts onto the X-ray wavefront, which render into a measurable self-interference pattern on a detector, placed at distance $z_{12}$ downstream the sample, after sufficient free-space propagation. For tomography the sample is rotated and imaged at multiple angles.
• Figure 2: Hologram and phase reconstructions of a catalytic particle. a Exemplary shows one of the two normalized holographic intensity interference patterns $I/I_0$ (hologram) of a catalytic particle at one tomographic angle. b-d Comparison of different phase retrieval methods and constraints. The reconstruction in b uses an unconstrained linear contrast transfer function (CTF). The reconstructions c and d are obtained using the HoToPy--Tikhonov algorithm. For these, a pixel-wise non-positivity constraint is used and for d additionally a finite disk-shaped support, indicated by the dashed circle. Scale bars: $\qty{5}{\um}$. Effective pixel size: $\qty{17.2}{\nm}$. Images have $2160\times2560$ pixels.
• Figure 3: Tomographic reconstruction by the FDK algorithm. a shows a zoom into the center of a reconstructed horizontal slice. Concentric ring artifacts (top left) are mitigated (bottom right) after applying wavelet-based ring removal ($l=4$, $\sigma=1$) to the sinogram. b displays a vertical slice through a volume reconstruction assuming an idealized acquisition trajectory. c shows the shifts of the projection images estimated by registration of opposite projections and reprojection registration ($8\times8$ pixel binning, high-pass filter with $\sigma=5$, 100 iterations). d shows a virtual slice through the volume reconstruction after applying the shift correction. The effective voxel size is $\qty{17.2}{nm}$.