Image formation in cellular X-ray microscopy Joaquin Oton a , C.O.S. Sorzano a , Eva Pereiro b , Jesús Cuenca-Alba a , Rafael Navarro c , Jose M. Carazo a , Roberto Marabini d,⇑ a Centro Nacional de Biotecnología, Ciudad Universitaria de Cantoblanco, Calle Darwin, 3, 28049 Madrid, Spain b MISTRAL Beamline – Experiments Division, ALBA Synchrotron Light Source, BP 1413, Km. 3.3 Carretera de Cerdanyola del Vallés a Sant Cugat del Vallés, 08290 Cerdanyola del Vallés, Barcelona, Spain c ICMA, CSIC-Universidad de Zaragoza, Facultad de Ciencias-c, Pedro Cerbuna 12, 50009 Zaragoza, Spain d Escuela Politécnica Superior, Ciudad Universitaria de Cantoblanco, Calle Francisco Tomás y Valiente, 11, 28049 Madrid, Spain article info Article history: Received 4 October 2011 Received in revised form 4 January 2012 Accepted 5 January 2012 Available online 15 February 2012 Keywords: X-ray microscopy 3D reconstruction Point spread function Image formation model 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 elu- cidation of the organization between the molecular and the organelle levels. In fact, it offers the possibil- ity 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 projec- tions 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. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Structural biology aims at the visualization of microscopic bio- logical 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 tech- nique 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 gen- erated 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 micro- scope. Obviously, this is a suboptimum situation, and still better results would be obtained should an accurate TomoX image forma- tion 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 for- mation 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 reconstruc- tion algorithms that explicitly incorporate the image model within the reconstruction algorithm. Clearly, image processing for TomoX data should be rather dif- ferent 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 pos- sible 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) pre- sented PSF calculations for realistic X-ray objectives assuming that the whole specimen is in focus. 2. Theoretical background In this section we discuss the physical principles in which X-ray microscopy is based. First, the interaction of X-ray and matter is introduced and then the image formation process for an ideal microscope is presented for the incoherent case. 1047-8477/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jsb.2012.01.006 ⇑ Corresponding author. Fax: +34 91 497 2235. E-mail address: roberto@cnb.uam.es (R. Marabini). Journal of Structural Biology 178 (2012) 29–37 Contents lists available at SciVerse ScienceDirect Journal of Structural Biology journal homepage: www.elsevier.com/locate/yjsbi