Image formation in cellular X-ray microscopy

Abstract

Soft X-ray Tomographic (TomoX) microscopy has become a reality in the last years. The resolution range of this technique nicely fits between confocal and electron microscopies and will play a key role in the elucidation of the organization between the molecular and the organelle levels. In fact, it offers the possibility of imaging three-dimensional structures of hydrated biological specimens near their native state without chemical pre-treatment. Ideally, TomoX reconstructs the specimen absorption coefficients from projections of this specimen, but, unfortunately, X-ray micrographs are only an approximation to projections of the specimen, resulting in inaccuracies if a tomographic reconstruction is performed without explicitly incorporating these approximations. In an attempt to mitigate some of these inaccuracies, we develop in this work an image formation model within the approximation of assuming incoherent illumination.

Introduction

Structural biology aims at the visualization of microscopic biological structures with the ultimate goal of understanding the molecular mechanisms taking place in the healthy as well as in the pathological cell. In the last decade a new microscopy technique has emerged, a technique able to visualize whole cells in cryo conditions with a resolution between 50 and 15 nm. This is the field of Cellular Soft X-ray Tomography (TomoX) (Schneider, 1998). Many studies so far have presented 3D reconstructions generated by X-ray microscopy (Weiss et al., 2000a, Thieme et al., 2003, Larabell and Le Gros, 2004, Le Gros et al., 2005, Gu et al., 2007, Parkinson et al., 2008, Uchida et al., 2009, Carrascosa et al., 2009, Hanssen et al., 2011). In most cases, the data have been processed using software developed for electron microscopy (EM) data (as can be SPIDER (Frank et al., 1996) or IMOD (Kremer et al., 1996)) without considering the particularities of the new microscope. Obviously, this is a suboptimum situation, and still better results would be obtained should an accurate TomoX image formation model were embedded within the 3D reconstruction process. The main purpose of this article is to start investigating this issue, presenting a first development in which we describe the image formation process within the simplification of assuming incoherent illumination. However, and still within its approximation, this modeling work opens the door to the design of new 3D reconstruction algorithms that explicitly incorporate the image model within the reconstruction algorithm.

Clearly, image processing for TomoX data should be rather different from the EM case, since TomoX images have larger contrast and are less noisy than EM ones. Moreover, the data collection geometry (usually single-tilt axis) helps to reduce the space of possible solutions. Unfortunately, TomoX images are, in general, a poorer approximation to ideal projection images than EM ones. Therefore, in this field the image processing challenge is not the one of fighting the poor signal-to-noise ratio as in EM, but that of the characterization of the microscope PSF and its appropriate incorporation into 3D reconstruction methods. As in any other microscopy, the objective in the X-ray microscope acts as a low-pass spatial frequency filter. Therefore, the PSF of the zone plate objective has to be taken into account. Weiss et al. (2000b) presented PSF calculations for realistic X-ray objectives assuming that the whole specimen is in focus.