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

Abstract

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.

Laboratory cryo x-ray microscopy for 3D cell imaging

“…Naturally, smaller cells like algae and/or cell types that accept capillary sample stages 8 avoid this problem. As for the DOF problem Selin 31 has proposed a method, focus-stack back-projection, which would be helpful. The missing wedge is in practice determined by the shadowing of highly absorbing features, neighboring cells, and the ice layer thickness.…”

XTEND: Extending the depth of field in cryo soft X-ray tomography

“…A recently proposed method in X-ray microscopy reconstructs the 3D information using a multi-focus approach that requires specific algorithms as well as precise measurement of the relative position of the best focusing plane over specimen thickness26. However, in all these cases, the algorithms only qualitatively enhance information contrast in projections and 3D volumes without quantitatively recovering the linear absorption coefficients.…”

PSF correction in soft x-ray tomography

“…In this fashion, though a sample is not fully in focus at one rotation angle, the sampling at a 180 • shift provides additional information, as a different part of the sample will be in focus. Such acquisition can be seen as a modification to the method suggested by Selin et al [32], where a depth-dependent weight was introduced in the reconstruction scheme to account for projections acquired at different foci. In our case, the projection matrix A h servers a similar function.…”

“…In SXT the problem of limited DOF has only recently been addressed, and thus far only experimentally. This has been done by acquiring multiple images at different focus and using a depth-dependent weight on their backprojection to account for their different foci [32], by using through-focus imaging to then computationally extract the ideal projection [22] or by a wavelet based fusion of reconstructions with different foci [19].…”