Tomographic reconstruction in soft x-ray microscopy using focus-stack back-projection

Tomographic reconstruction in soft x-ray microscopy is a powerful technique for obtaining high-resolution 3D images of biological samples. However, the depth of focus of such zone-plate-based microscopes is typically shorter than the thickness of many relevant biological objects, challenging the validity of the projection assumption used in conventional reconstruction algorithms. In order to make full use of the soft x-ray microscopes' high resolution, the tomographic reconstruction needs to take the depth of focus into account. Here we present a method to achieve high resolution in the full sample when the depth of focus is short compared to the sample thickness. The method relies on the back-projection of focus-stacked image data from x-ray microscopy. We demonstrate the method on theoretical and experimental data.