title: Error analysis in the determination of the electron microscopical contrast transfer function parameters from experimental power Spectra.
abstract: BACKGROUND
  The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.
  
  
  RESULTS
  In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.
  
  
  CONCLUSIONS
  We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.
authors.affiliation: Escuela Politécnica Superior, Universidad San Pablo-CEU, Campus Urb, Montepríncipe s/n, E-28668 Boadilla del Monte, Madrid, Spain. coss@cnb.csic.es
authors.forename: Carlos Oscar S
authors.initials: CO
authors.lastname: Sorzano
authors.forename: Abraham
authors.initials: A
authors.lastname: Otero
authors.forename: Estefanía M
authors.initials: EM
authors.lastname: Olmos
authors.forename: José María
authors.initials: JM
authors.lastname: Carazo