Welcome to the CPO Programs

The CPO programs have an unrivalled accuracy, an unrivalled help system and a very wide range of options.  They have been called the 'gold standard' of electrostatic electron optics.


For a recent description see the paper: Achieving the highest accuracy with the BEM, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 182-187 (2015).

The CPO programs use the Boundary Element Method (BEM), instead of the traditional Finite Difference Method, which is conceptually simple and relatively easy to program, or the related Finite Element Method.  The published comparisons show that because of this the CPO programs are typically 2 orders of magnitude more accurate or 2 orders of magnitude faster for the same accuracy than those using the traditional methods.  To underline this the CPO package includes a very large number of 'benchmark tests' that demonstrate this high accuracy and speed. 

The regular versions of the CPO programs are CPO2D and CPO3D for 2 and 3 dimensional simulations respectively.  The versions that deal with space-charge and cathodes are CPO2DS and CPO3DS.  More advanced versions are also available.

Some other features of the programs and package:


  • Developed over many years by the group that was the first to use the BEM to obtain accurate and systematic lens data and that produced the standard data book 'Electrostatic Lenses', by E Harting and F H Read (available as part of the package).
  • Deals easily with electrodes of any shape and size, including sharp tips and unbounded systems.
  • The Boundary Element Method is ideally suited for space-charge and cathodes, allowing all shapes and many types of cathodes.
  • Fully and automatically relativistic.
  • Easy to calculate lens properties and spectrometer coefficients.
  • Easy-to-use option for automatic focusing.
  • Users can use their own equations to define electrode shapes.
  • The Help system has a great deal of information, for example on formulas used in electron optics.


Also, welcome to Help


The new Help system is very comprehensive (over 2000 pages) and is fully linked to the programs.  We hope that you will enjoy using it.  As well as explainations of how the program should be used, it also contains a great deal of information on electron optics.

(You might notice an apparent surplus of keywords (for example the 'notes') and some near-repetitions, which are essentially relics of historic links to the Help buttons that appear on many screens, and we apologise for not having changed them yet.)

We very much welcome suggestions for improvements on the program and the Help system, and are also happy to offer free advice to new users on their first simulation.