X-ray ptychography with extended depth of field

Abstract

Ptychographic X-ray computed tomography is a coherent diffractive imaging method that offers nanometer-scale resolution with quantitative contrast. It offers the possibility to study relatively thick samples by using high energy X-ray photons and exploiting the phase contrast. However, the limited depth of field forces a compromise between resolution and sample thickness. Multi-slice techniques have been used to account for propagation effects within the sample, enabling imaging beyond the depth-of-field limit. Here we introduce and experimentally demonstrate our multi-slice algorithms that allow for the reconstruction of multiple object slices and the incident illumination, as well as the retrieval of unknown object thickness. Additionally, through numerical studies, we show that smaller scanning steps surprisingly increase the depth of field, which can be further extended by the use of multi-slice methods under conditions stated by theoretical expressions. The results presented here will be instrumental for the routine implementation of the technique for X-ray nanotomography.

3D x-ray imaging of continuous objects beyond the depth of focus limit

“…When combined with the Rayleigh resolution of Eq. 2, the DOF can be written as $$\text{DOF}=2{\delta }_z=\frac{2}{{0.61}^2}\frac{{\delta }_r^2}{\text{λ}}\simeq 5.4{\delta }_r\frac{{\delta }_r}{\text{λ}},$$ which agrees well with experimental observations for absorption contrast imaging in a scanning transmission x-ray microscope [19] as well as with multiple-plane x-ray ptychography observations [20]. That is, as the transverse resolution approaches the x-ray wavelength, the DOF approaches the transverse resolution.…”

“…When using a circular lens, the depth of focus (DOF) of an image is given by [19] $$\text{DOF}=\frac{2}{{0.61}^2}\frac{{\delta }_r^2}{\text{λ}}\simeq 5.4{\delta }_r\frac{{\delta }_r}{\text{λ}},$$ while $\text{DOF}=5.2{\delta }_r^2/\text{λ}$ has been found to describe the depth of focus of x-ray ptychographic images [20]. For samples with an overall dimension less than the equivalent depth of focus of the imaging approach used, each view as the object is rotated can be treated as representing a pure projection for use in a standard tomographic reconstruction algorithm.…”

“…In the reconstruction process, the probe and object functions are updated at each plane, since the ptychographic update steps work to maximize the separability of object and probe. Using this multislice approach, images have been obtained of a few discrete, separated planes by using a single viewing direction [20, 25–28] or a limited range of tilt angles [29]. …”

Three-Dimensional Imaging of Biological Tissue by Cryo X-Ray Ptychography

“…This assumption gives rise to the limited depth of field, which poses a compromise between the object size and image resolution. For the current sample thickness and the energy used in this experiment, the resolution and image quality become suboptimal at resolutions below 50 nm due to this effect 49 . The multi-slice methods 49–52 , in which the object is represented by multiple axial slices in the reconstruction to account for multiple scattering effects, provide a promising means to image even larger volumes with nanometer resolution, opening up new possibilities for thick biological tissue nanotomography.…”

Optical ptychography with extended depth of field

“…Instead of pursuing the 3D imaging performance of multislice ptychography, here we demonstrate its ability to extend the depth of field via an optical experiment. This has been demonstrated in x-ray regime [6], although in this case the breakdown of the multiplicative approximation is nowhere near as severe as that in the visible light regime, due to the strong penetration power of x-rays. …”