WIEN Software for Design of Columns Containing Wien Filters and Multipole Lenses

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Joseph Bryan
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WIEN Software for Design of Columns Containing Wien Filters and Multipole Lenses An integrated workplace for analysing and optimising the column optics Base Package (WIEN) Handles round lenses,

1 WIEN Software for Design of Columns Containing Wien Filters and Multipole Lenses An integrated workplace for analysing and optimising the column optics Base Package (WIEN) Handles round lenses, quadrupoles, hexapoles, octapoles, Wien filters Imaging and paraxial focusing properties Primary geometrical and chromatic aberrations Graphical output of fields, trajectories and aberration spot diagrams, etc. Optional Upgrade Modules: WIEN-5 To simulate aberrations up to fifth order WIEN-REFINE Column optimization to minimize aberrations WIEN-REFINE-5 Optimization to minimize aberrations up to 5 th order Graphical User Interface Features: GUI provides high interactivity during the design process Intuitive control of system variables Seamless integration of package features System Requirements: Runs under Microsoft Operating System (Windows 7, Vista or XP)

2 WIEN FAMILY OVERVIEW The Wien filter family handles the analysis and optimization of the optics of straight-axis systems that contain a Wien filter plus any combinations of electrostatic and magnetic round lenses, quadrupole lenses, hexapole lenses and octopole lenses. If a Wien filter is not present, then a deflection system consisting of a magnetic or electrostatic dipole element can also be included. The program can handle both Gaussian round-beam and shaped-beam systems. The magnetic field of the Wien filter is automatically adjusted to give the Wien condition. The output includes: the optical element settings after focusing and filter adjustment (e.g. the lens excitations, the filter deflector strengths); the first-order optical properties (e.g. column magnifications and dispersions); and the coefficients. These coefficients are used to display the aberration spot diagrams and to compute the aberration values for the given initial conditions. WIEN (base package) The Wien filter program, WIEN, will handle the primary beam optics of straight-axis systems, as shown schematically in Figure 1. Return Beam Object Primary Beam Electrostatic Quadrupole Wien Filter Magnetic Quadrupole Magnetic Round Lens Electrostatic Round Lens Image Figure 1: Schematic of system handled by WIEN

The system can contain a Wien filter plus any combinations of the following optical elements: (1) Electrostatic and Magnetic Round Lenses, (2) Electrostatic & Magnetic Quadrupole lenses, (3)

3 The system can contain a Wien filter plus any combinations of the following optical elements: (1) Electrostatic and Magnetic Round Lenses, (2) Electrostatic & Magnetic Quadrupole lenses, (3) Electrostatic & Magnetic Hexapole lenses, and (4) Electrostatic & Magnetic Octopole lenses. If a Wien filter is not present, then a deflection system consisting of a magnetic or electrostatic dipole element can also be included. WIEN has a Graphic User Interface (GUI), which affords a better understanding and control of the system and its parameters during the analytical and design procedures. A typical screen-shot of the WIEN GUI is shown in Figure 2. Figure 2: WIEN Control Panel The input data of WIEN includes the imaging condition data (e.g. the positions of object and image planes) and the optical element parameters (e.g. the positions and strengths of the elements). The field functions of the round lenses, quadrupole lenses and Wien filters are computed with our software packages SOFEM and 3D (available separately). The axial field functions are fitted with Hermite series to enable their high-order derivatives to be computed accurately. The program can handle both Gaussian round-beam and shaped-beam systems. The program will compute the first-order optical properties for any setting of the electric and magnetic deflection parts of the Wien filter. This enables the required strength of the deflectors to be chosen to give the desired deflection of the return beam. For the primary beam, the user can set the strength of the electrostatic dipole field and the program will adjust the strength of magnetic dipole field in the filter in order to satisfy the Wien condition to allow the beam to pass through the filter with zero net deflection. The first-order optical properties are computed by numerical solution of the paraxial ray equation. The aberrations are computed by evaluating a differential algebra ray-trace. The computed optical properties include: the optical element settings after focusing and filter adjustment (e.g. the lens excitations, the filter deflector strengths); the first-order optical properties (e.g. column magnifications and dispersions) and tables of the second and third-order geometric and 1 st order chromatic aberration coefficients. This numerical output can subsequently be displayed graphically as aberration spot diagrams and is used to compute the aberration values for the given initial conditions.

4 If the Wien filter is replaced by a single-channel deflection system, the program can operate the deflectors in two modes: scanning or rocking. In scanning mode, the deflectors move the beam linearly over the target. In rocking mode, the beam does not move linearly over the image plane but is fixed on the optical axis: instead, the deflector can be used to tilt the beam. WIEN-5 Module (Optional) WIEN-5 is an extension of WIEN which computes the second, third, fourth and fifth-order geometrical aberrations and chromatic aberrations up to fourth-rank. Intermediate images do not need to be stigmatic, however the computed aberration coefficients are meaningful only if the beam is stigmatically focused in both x and y directions at the final image plane. WIEN-5 also has an integrated aberration spot generator to visually show the aberration effects using the computed aberration coefficients and given initial image conditions, such as beam half angle, beam size, deflection parameter at either object or image plane. The spot plots can include only the primary aberrations or a combination of all aberrations up to 5 th -order. Layout of Hexapole Cs Corrector Paraxial Rays in quadrupole/octopole Cs corrector Spot for Cs Corrector 3 rd -order aberrations Spot for Cs Corrector 3 rd & 5 th -order aberrations

5 WIEN-REFINE and WIEN-REFINE-5 Modules (Optional) WIEN-REFINE and WIEN-REFINE-5 are extensions to WIEN and WIEN-5, respectively. They compute and optimise the optical properties and aberrations of the system. WIEN-REFINE computes and optimises the third -order geometrical aberrations and chromatic aberrations up to second-rank.wien-refine-5 computes and optimises the third and fifth-order geometrical aberrations and chromatic aberrations up to fourth-rank. After defining the imaging conditions data, optical element settings and parameter values and the focus constraints for the autofocus scheme, as in WIEN or WIEN-5, you can specify and the weighting factors for the optimization scheme via the Weighting Factors Window control screen. WIEN-REFINE-5 Weighting Factors Control Screen The weighting factors assigned on this form are used in the refining process to target certain aberrations for special consideration when minimizing the overall spot size. In general terms, each aberration will contribute a certain fraction to the overall size of the final spot. During the refine cycle, the chosen positions, sizes, strengths and rotations of the elements are adjusted so as to minimise a weighted sum of squares of the individual contributions to the overall spot size from each aberration. The user can choose the weighting factor to assign to each contributing aberration. When the appropriate weighting factors have been selected, the optimization control screen allows the user to interactively refine the system to minimize the selected aberrations, subject to the constraints and weighting factors chosen. After the system has been optimized to the user s satisfaction, the column data can then be updated and the final aberration values computed. After this, a diagram of the final, optimized spot shape can be plotted, for any desired initial imaging data.

WIEN-REFINE-5 Optimisation Control Screen Aberration Correction using WIEN-5 and WIEN-REFINE-5 Use of additional optical elements can reduce the aberrations introduced in the original system.

6 WIEN-REFINE-5 Optimisation Control Screen Aberration Correction using WIEN-5 and WIEN-REFINE-5 Use of additional optical elements can reduce the aberrations introduced in the original system. Examples of using hexapoles or a combination of quadrupoles and octopoles to reduce primary spherical aberration have been shown above. In addition, if we have a deflection system to scan or rock the beam, the deflection aberrations will, in general, scale with deflection field strength: we call these aberrations the dynamic deflection aberrations. We can use additional optical elements whose strength varies with deflection field strength to correct some aberrations introduced by the deflection system: we call these additional optical elements the dynamic correction elements. Common dynamic correction elements include a round lens to correct for normal deflection field curvature, a quadrupole element to correct for normal deflection astigmatism. Both WIEN-5 and WIEN-REFINE-5 can handle round lenses and multipole lenses that can be used to compensate the dynamic deflection aberrations. In addition, the optimization function in WIEN-REFINE-5 can be used to compute the required settings (strength and/or rotation angle) for the dynamic correction elements to compensate the deflection aberrations. In the software, the dynamic correction elements are not energized during the autofocus procedure, but they are switched on when the beam is in focus and the deflection system is energized. The settings of the dynamic correction elements are then optimized to reduce or eliminate the chosen set of deflection aberrations.

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