Estimating contrast transfer function and associated parameters by constrained non-linear optimization

J Microsc. 2009 Mar;233(3):391-403. doi: 10.1111/j.1365-2818.2009.03137.x.


The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Publication types

  • Evaluation Study
  • Research Support, N.I.H., Extramural

MeSH terms

  • Algorithms*
  • Bacteriophage P22 / ultrastructure*
  • Carbon / chemistry*
  • Computational Biology / methods
  • Cryoelectron Microscopy* / methods
  • Cryoelectron Microscopy* / standards
  • Ice
  • Models, Biological*
  • Motion Pictures
  • Tissue Embedding / methods
  • Virion / ultrastructure*


  • Ice
  • Carbon