REFINE: Optimization of Electron and Ion Beam Columns

This package is supplied as an upgrade to the OPTICS package.  Its purpose is to take an initial design of electron or ion beam column, and interactively refine the design to optimize the performance by minimizing the aberrations.

The program uses the damped least squares method, a standard numerical technique for minimizing a weighted sum of squares of functions of several variables.  The variable parameters are the axial position, size and relative strength of each lens and deflector, and the rotation angle of each deflector.  The quantity to be minimized is a weighted sum of squares of all the individual aberrations.  For this purpose, all the aberrations are expressed in microns, so they all have the same dimensionality, so the function to be minimized has dimensions of μm2.  Starting from an initial design, the program alters each variable parameter by a small amount, and recomputes the aberrations.  This yields the partial derivative of each aberration with respect to each variable parameter.  A least squares equation is then solved, to find the change in each variable that would minimize the weighted sum of squares of the aberrations in the "least squares" sense, if the partial derivatives were to remain constant.  To ensure stability, a positive damping factor is introduced into the principal diagonal elements of the least squares matrix.  The calculation is repeated for several values of the damping factor, and the damping factor which minimizes the target function is selected using a one-dimensional binary search.  This constitutes one optimization cycle.  The entire cycle is repeated several times, until a local minimum is reached.

Each variable parameter is defined by three values -- its current value, and its minimum and maximum permitted values.  These two latter values define the constraints on the range of the variable.  All three values can be changed interactively by the user before the start of any optimization cycle.  If the minimum and maximum are set equal, the corresponding variable is held fixed, i.e. removed from the optimization.  If the optimization tries to change the variable beyond its permitted range, its value is reset to its minimum or maximum value as appropriate.

The user can also interactively modify the weighting factors assigned to each aberration.  For example, if the designer's primary aim is to minimize field curvature and distortion, the weighting factors for these aberrations would be set to one and all the others to zero.

Since the software finds a local minimum, which is not necessarily the global one, the user can try running the optimization process several times, starting from different initial conditions, and with different constraints and weighting factors, to try to find the best design.

The software is a comprehensive package and has recently been enhanced to incorporate a graphical user interface (GUI) that operates under the latest Microsoft Windows Operating systems. 

If you are interested in the REFINE package, please contact us at info@electronoptica.com.