TOLERANCE: Simulation of Machining Errors
Tolerance is a supplement to OPTICS, and is used for computing the effects of machining errors in electron and ion beam columns. The software can handle complete columns, containing any combination of electrostatic and magnetic lenses and deflectors, and computes the asymmetry aberrations caused by small mechanical imperfections in the construction and alignment of the individual optical components of the column. This software can be used to assign tolerances for the construction and alignment of complete electron and ion optical columns, to ensure that they will perform in accordance with their design specifications.
The software handles the effects of misalignments and tilts of complete lenses and deflectors, relative to the optical axis of the column. The software also computes the effects of axial and radial misalignments, tilts and ellipticities of any individual polepiece, coil winding or electrode of any lens or deflector in the column. In the case of deflectors, the software also handles the effects of azimuthal misalignments of individual coil windings or electrodes.
The effects of the asymmetry errors in the individual lenses and deflectors are computed using a perturbation method, based on Sturrock’s principle. The displacements of individual polepieces, coil windings or electrodes are replaced by equivalent perturbations in the boundary potentials. The perturbation fields are then computed by finite element and integral equation methods. The asymmetry fields are expressed in terms of a set of axial perturbation field functions. These fields form the input to an optical properties program, which computes all the asymmetry aberrations, using a set of aberration integrals. The asymmetry aberration coefficients, and their effects at the corners of the deflection field, are output in tabular form.
The software can also handle static deflectors and stigmators. Static deflectors are used to correct the first-order image shifts due to misalignment and tilt of lens electrodes or polepieces; and static stigmators are used to correct the astigmatism due to ellipticity of lens electrodes or polepieces. In this case, the static deflection and stigmation field functions are computed, using the field programs of the OPTICS and DYNAMIC packages, respectively. The software computes the additional aberrations due to the static deflectors and stigmators. The software also calculates the required signals for correcting the first-order image shifts due to the specified misalignments and tilts of the lens polepieces and electrodes, and the astigmatism due to the specified ellipticities of the lens polepieces and electrodes.
The software includes a graphical post-processor, which plots the effects of the aberrations graphically in the form of spot diagrams, with and without the asymmetry errors.
The diagrams on the following page show a typical example of the output, for a shaped-beam column containing the magnetic and electrostatic focusing and deflection elements, with small misalignment and ellipticity in one polepiece of the magnetic lens.
If you are interested in the TOLERANCE package, please contact us at info@electronoptica.com.