Minimum Aberrations Research Articles

Microguns with 100-V electron beams

The microgun is a combination of a nanotip and a microlens which is composed of two planar micron-size bore electrodes and a coplanar four-pole deflector microfabricated on the same Si chip. The focusing and deflection characteristics of the microgun, working as an immersion lens at 100 V, have been studied both experimentally and by numerical simulations. Results show unique electron optics properties due mainly to the coherence of the electron beam emitted from the nanotip and to the noninteraction of the incident electrons with the different microelectrodes. The focus spot can reach nanometric dimensions with minimum aberrations and a deflection amplitude of ∼2.5 mrad/V.

Optimized superstationary anastigmatic mounts of concave gratings

Two subfamilies of concave grating superstationary anastigmatic mounts that provide minimum chromatic aberrations are described. The obtained approximate formulas can be used to design flat-field spectrographs and multi/demultiplexers for optical communication networks. Two specific mounts and their performance are presented.

Conical geometry for sagittal focusing as applied to x rays from synchrotrons

We describe a method for simultaneously focusing and monochromatizing x rays from a fan of radiation having as high as 15-mrad divergence in one dimension. This geometry is well suited to synchrotron radiation sources at magnifications of 1/5 to 2 and is efficient for x-ray energies between 3 and 40 keV (0.48 and 6.4 fJ). The method uses crystals bent to part of a cone for sagittal focusing and permits the collection of a larger divergence with less mixing of the horizontal into the vertical divergence than is possible with x-ray mirrors. We describe the geometry required for achieving the highest efficiency when a conical crystal follows a flat crystal in a nondispersive two-crystal monochromator. At a magnification of 1/3, the geometry is identical to that of a cylindrical focusing design described previously [ Nucl. Instrum. Methods172, 237 ( 1980)]. A simple theoretical calculation is shown to agree well with ray-tracing results. Minimum aberrations are observed at magnifications near 1. Applications of the conical focusing geometry to existing and future synchrotron radiation facilities is discussed.

Analytic optimization of Dyson optics

A prototype of a 248-nm optical projection printer based on the unit magnification Dyson configuration was designed and built [J. Vac. Sci. Technol. 9, 3108 (1991)]. Iterative computer methods were used to optimize the geometry of the system to provide minimum aberrations over a given field. Here we present an alternative optimization procedure and use it to design a 193-nm system. This new procedure yields useful insights into the design process and allows us to see why modifications in geometry are required for optimum performance. An understanding of the trade-offs involved in the optimization allows us to suggest and evaluate future design changes.

Effects of Methyl Parathion and Tri-miltox on the Mitosis of Allium cepa.

Treatment of Alium cepa seeds with different concentrations of Methyl parathion (insecticide) and Tri-miltox (fugicide) induced different types of chromosomal aberrations, such as micronuclei, chromosomal fragments, laggard chromosomes, single and multiple bridge formation. Maximum number of cells were observed with micronuclei, then with bridges and the minimum with laggard chromosomes. Methyl parathion produced comparatively more chromosomosomal aberrations than Tri-miltox. Comparing the three treatments applied, seed treatment produced maximum chromosomal aberrations, and the root treatment with recovery period produced the minimum chromosomal aberrations with the root treatment occupying the intermediate position.

Numerical analysis of trajectories and aberrations of a Wien filter including the effect of fringing fields

Trajectory equations of a stigmatic Wien filter including the effects of unmatched fringing fields are formulated, and an optimum shape with minimum geometrical aberrations is described. A low-aberration Wien filter is realized under the following conditions: (1) electric and magnetic fields satisfy the orthogonal relation even in the off-axial region, and (2) gap lengths between electrodes and magnetic poles are the same for achieving the balancing condition of electric and magnetic forces in fringing regions. The former condition can be realized by both fields with finite but the same hexapole components; this fact enables us to design a filter with simplified geometry that fulfills the latter condition simultaneously. It is shown that a large deflection of trajectories and resultant aberrations appear if the gap lengths are set to be different.

Synthesis of electrostatic lenses by simulated annealing

The use of simulated annealing is proposed for automatic design of electrostatic lenses with given first-order properties and minimum aberrations. The synthesis of a high-quality lens for focusing an ion beam produced by a liquid-metal source is shown as an example.

Holographic optical scanning elements with minimum aberrations

An analytical method to design holographic optical elements for focusing laser scanners, especially disk scanners, with minimum aberrations and optimum scan line definition is reported. The results reveal that the focused spot constraint to a straight line is always astigmatic. However, by accepting small deviations from the straight line, the astigmatism can be eliminated. The second-order analytical solutions are examined with the help of geometrical ray tracing and compared with experimental results. By extending the method to higher-order approximations, it was found that the correction of the aberrations is essentially limited to the direction perpendicular to the scan line.

A novel approach to the synthesis of electrostatic lenses with minimized aberrations

A novel approach to the synthesis of axially symmetric electrostatic lenses with minimum aberrations is presented. The method uses computer optimization to determine the electrode potentials of a multielectrode lens. The method can be used for designing lenses for many different applications. As a preliminary result, an example of a lens with very small spherical aberration is given. The synthesis of electrostatic lenses can be accomplished automatically with an experimental setup controlled by an online computer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimum design of electrostatic lenses

A method of design for electrostatic lenses with given source parameters, first-order properties, and minimum aberrations is presented. It is based on constrained nonlinear optimization techniques. The variables in these procedures are spline coefficients of the axial potential distribution, or the electrode potentials of a given multielectrode lens. The optimization constraints are the minimum object- and image-side working distances, maximum possible electrode potentials, and maximum allowed electrostatic fields. The parameters of the source and the final beam voltage are fixed. The goal of the design is to find an electrode configuration that would minimize the beam spot size and maximize the current density at the target. Three examples of the method’s application are presented. Keeping the given source parameters and working distances constant, essential improvements of the optical properties of three well-known designs could be achieved by replacing the lenses with those designed by our procedures. In these examples for field ionization sources the current density at the target is increased by more than an order of magnitude.

New mounting for X-ray and extreme ultraviolet concave holographic grating

An entirely new mounting for concave holographic gratings for X-ray and the extreme ultraviolet (EUV) has been proposed and its properties have been investigated theoretically. Design parameters for recording a holographic concave grating for minimum spectral image aberrations have been calculated. It is found that this mounting is very suitable.

Procedure for electron and ion lens optimization

This letter describes a computational technique for optimal control problems arising in the synthesis of electron and ion lenses. The method provides an effective search algorithm for electrostatic and/or magnetic imaging fields with minimum aberrations. An optimized electrostatic field distribution is given as an example of application.

General theory of the magnetic einzel lens based on the axial field distribution model H(z)=H0C∣ z/a ∣m-1/(1+∣ z/a ∣2m)

Investigations are described which show that the magnetic einzel lens given by the axial field distribution H(z)=H0C mod z/a mod m-1/(1+ mod z/a mod 2m), where m is the parameter depending on the double-gap pole-piece geometry and the magnetic flux concentration, is the simple magnetic einzel lens whose solutions of paraxial ray paths can be obtained in the form of hypergeometric functions. Based on these solutions, the important focal quantities and third-order aberrations are expressed analytically in terms of the maximum width amax of the field and the lens strength k, mostly depending on the ampere-turns for various magnetic einzel lenses specified by m. The important parameters m and amax and their dependence upon double-gap pole-piece geometry are derived approximately in accordance with the potential theory for a cylindrical magnetic einzel lens. The optimum lenses with the minimum focal length and aberrations, and satisfying the anastigmatic conditions, are described and discussed in terms of practical design.

Anastigmatic catadioptric telescopes

A conic mirror and an afocal achromatic refractive corrector located at the proximate geometrical focus of the conic define a family of anastigmatic telescopes of which the Schmidt telescope is a special member. In general, the corrector must consist of at least two elements whose surfaces can be spherical. Equations are given for the third-order design of thin two-element correctors. A solution that satisfies the condition of minimum higher-order aberrations is given for a corrector for a paraboloidal mirror. An example is given of a trigonometrically corrected paraboloidal-mirror anastigmat, and its aberrations are discussed. Conic-mirror anastigmats with mirrors of eccentricity e ~ 1 are a potentially valuable class of telescopes that merit consideration by the astronomical community.

Compensation of Aberrations due to a Wavelength Shift in Holography

A shift in wavelength between the recording and reconstruction beams of a hologram introduces aberrations in the image wavefront and decreases the diffraction efficiency. The holograms investigated in this paper are recorded on dichromate gelatin film with either plane waves or point sources and are designed to image to a point source when illuminated with a plane wave. A computer program is employed to calculate the aberrations present in the image wavefront and to determine an optimized recording geometry necessary for minimum aberrations. It is shown that the computer program, which was designed for surface-type holograms, has some application in thick transmission-type phase holograms. The experimental results are in close agreement with the computed results indicating that compensation for the wavelength shift may be obtained by using a computer program to calculate the proper recording geometry.

Minimum Chromatic Aberrations of Magnetic Quadrupole Objective Lenses

Orthogonal magnetic quadrupole lens systems that could serve as electron microscope objectives are treated theoretically. After certain constraints are placed on the quadrupole field strength, the calculus of variations is applied to obtain systems with minimum chromatic aberrations. A digital computer was used to calculate optimum orthomorphic and anamorphotic objective type systems. The resulting orthomorphic systems have four lenses while the corresponding anamorphotic systems have three. The chromatic aberration only varies by a factor of 2 in this study indicating its relative insensitivity to choice of lens systems. It is found that the optimum quadrupoles have about 3.6 times as much chromatic aberration as round lenses with comparable fields and dimensions.

Computer-Based Analysis of Hologram Imagery and Aberrations II: Aberrations Induced by a Wavelength Shift

Numerical values are shown for the aberrations that are induced by a wavelength shift from construction to reconstruction. The holograms discussed in this paper may be constructed and reconstructed from a plane wave or point source. Four types of hologram geometries have been studied: in-line, off-axis, near-image plane, and lensless-fourier transform. The aberrations are first considered where the reconstruction beam geometry is the same as that needed to reconstruct an ideal image if no wavelength shift is present. The change in wavelength, however, causes aberrations and these are discussed as a function of the various hologram geometries and parameters. A considerable reduction in the aberrations can be realized in off-axis holograms by a technique of aberration balancing. In one example the total aberrations were reduced to approximately a Rayleigh limit of lambda/4 in a hologram that was recorded at 4880 A and reconstructed at 6328 A. The minimum aberrations possible using the balancing process are discussed with respect to various hologram parameters.

Minimum Aperture Aberrations of Quadrupole Lens Systems

A focusing system for monochromatic beams of charged particles, with magnetic quadrupole fields having common planes of optical symmetry, is treated theoretically. After specifying certain linear focusing properties for such systems, the calculus of variations is applied to obtain systems with minimum aperture aberrations. First order variational theory is applied to obtain the Euler equations that define extremal systems. This derivation gives four second order, coupled, ordinary differential equations. An iterative technique is presented for solving these Euler equations. Second order variational theory shows that the extrema of the aperture aberrations are local minima with respect to other systems having the same specified linear focusing properties. A digital computer was used to calculate a variety of systems with minimum aperture aberrations. Sample calculations are given for systems with magnifications of −1 and −2. General studies are presented for high magnification systems where the lenses are confined to a region near the object. The best orthomorphic systems have four lenses while the best anamorphotic systems have three. Several methods for regulating the quadrupole gradient strength are studied. It is found that optimum systems have aberration coefficients about one fifth as large as the best systems previously studied. It appears that quadrupoles alone are not as good as round lenses unless the quadrupole bore radius is less than 1/14 of the length of the shortest quadrupole.

A 4-m Asymmetric Czerny-Turner Grating Spectrograph

The design and construction of a high resolution asymmetric Czerny-Turner grating vacuum spectrograph are described. The two spherical mirrors are of equal radii but not concentric; the grating can be translated sideways so that various configurations, calculated by ray tracing to give minimum aberrations for different angles, can be established. The focal length is 4 m, and simple tests suggest that resolving powers of at least 700,000 in the green are attainable over the whole of a 50-cm plate.

Production and analysis of one-dimensional magnetic deflection fields

An experimental yoke consisting of four sets of independently excited coils has been made. The field distribution of the experimental yoke can be controlled to approximate the theoretically calculated ideal fields, which produce minimum aberrations for certain specified working distances, field coverage, and beam convergence angle. The aberrations that would be produced by the experimental yoke are calculated and compared with those of the ideal field.