Applied Charged Particle Optics
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Parallel trajectories continue being parallel Fig. In case the particles emitted from a planar surface are accelerated through a slotted electrode Fig. This is done with an emission lens for electrons also called cathode lens. The simplest emission lens is obtained by adding a second apertured electrode to the acceleration electrode Fig. The two electrodes with their apertures constitute an immersion lens. The value eV2 is the energy of the beam after passing through the lens. An important case for beam sources is telescopic imaging Fig.
In particular, particle trajectories starting parallel to the axis are also parallel to the axis after the lens. The angular spread is then entirely due to the initial energy. Telescopic imaging through emission lens by converging—diverging apertures 1. There are the two solutions, shown in Figs.
In the second solution Fig. This is called an accel—decel arrangement because the particles are accelerated in L1 and decelerated in L2. This can be important when space charge limitations play a role at the emitting surface. On the other hand, for a given beam energy eV2 , the voltage V1 required in case Fig. With the above relations the properties of the emission lens with telescopic imaging are completely described. Again, as in telescopic imaging, the second solution represents a large accel—decel voltage ratio, and the same applies as above.
In the backfocal plane all beamlets starting from the individual points on the surface cross the axis. When an aperture stop is placed in the backfocal plane eliminating a peripheral part of the beam waist, particles with higher initial energies are discriminated against, viz. This is generally applied in emission microscopy to improve the lateral resolution, which depends on V0.
The system can be treated as the one above with a transfer matrix. This is obtained by forming the product of the matrix for the lens of Fig. Again, there are in general two solutions, as 1. Emission lens with three apertures, two operating modes indicated in Fig. In practice this is frequently not the case: The electrodes may have to be conical in order to accommodate some primary radiation see Fig.
This would correspond to a transition from Fig. The axial potential distribution which in Fig. Thus, the lens actions are not sharply localized at the apertures but more widely distributed along the curvatures of the potential curve. Axial potential distributions of two emission lenses with similar optical properties comp. A great advantage of particle optics compared to light optics is the possibility of continuous variation of optical properties by simple potential variations. In a triode system such as sketched in Fig.
In the general case there is no 1. Thus, it is not possible to operate such a lens with telescopic imaging as the emission lens shown in Fig. Since in electrostatic optics particle trajectories are reversible, the optical parameters on the entrance side, f1 , g1 and h1 can be found simply by applying 1.
For f1 follows from 1. In practice, immersion lenses are frequently constructed with tubular electrodes Fig. This has the advantage that in comparison with an immersion lens as described above, the lens diameter is smaller for a given beam diameter. Furthermore, as a consequence of the smoother axial potential distribution, the spherical image aberration aperture aberration is smaller.
The lens properties are determined experimentally or by computation. As is shown in Fig. Frequently, particularly with tubular lenses such as shown in Fig. Immersion lens with tubular electrodes Fig. This inserted in 1. Einzel lens built of three planar apertured electrodes This is another form of the imaging equation. It is equivalent to 1. The number of electrodes is arbitrary. Very frequently three-electrode immersion lenses are used.
They are constructed like einzel lenses see Fig. Just as immersion lenses, einzel lenses are always focusing lenses. The potential distribution resembles a saddle surface when the equipotential lines are considered as topographic level lines. Typical dependency of refractive power of einzel lens on the potential of the middle electrode VL for a beam energy eVB has two branches for the two modes.
Applied Charged Particle Optics - Helmut Liebl - Google книги
In the accel—decel mode, a separate voltage supply with the opposite polarity as the source voltage supply is required, and much higher voltages are required for the same refractive power. In spite of this, the accel—decel mode is advantageous when the focal length required is not too short. The reason is that in this mode both the spherical and the chromatic image aberrations are smaller than in the decel—accel mode.
The former is smaller because the trajectories are closer to the axis. If this mode is chosen, the bore of the center electrode can be made smaller than that of the outer electrodes Fig. This reduces the voltage required for a given focal length. Einzel lens geometry advantageous for accel—decel mode Fig.
For some applications this is advantageous because then both the source and the lens can be supplied by the same voltage. Figures 1.
In the construction of lenses the most important feature is good concentricity of the lens elements in connection with the necessary electrical insulation to guarantee voltage stability. Distances and contours are less critical as long as everything is rotationally symmetric. Example of einzel lens with decel—accel mode Fig. Example of einzel lens with accel—decel mode Fig.
Example of einzel lens where the middle electrode is centered and insulated by six precision ceramic balls 1. The lens is self-centering during assembly and the voltage stability is very good because the center electrode touches the centering insulation spheres at six points only. Depending on the application, the electrode contours can be chosen arbitrarily. In both cases the beam energy is not altered by the passage through the device. We can replace t in E x, 2V0 2.
Above the trajectories for singly charged particles are calculated. A more popular energy spectrometer is the cylindrical condenser Fig. Potential distribution in a cylindrical condenser. The potential in between the plates can be written to be Fig. As a test, the Laplace equation 1. Inserting these into 2. The mass m drops out, only the energy eV of the particles matters. In the exit principal plane P2 the center of energy dispersion is located. From 2. For intensity reasons the exit slit should be made as wide as the image of the entrance slit.
If it is wider, one loses energy resolution, if it is narrower, one loses intensity without gaining energy resolution. Energy resolution of cylindrical condenser energy distribution. When the energy distribution is to be surveyed, the pass energy is scanned over the energy distribution. Also the radius re does not appear in 2. In designing such an energy analyzer care must be taken that the image is formed outside the condenser, where the exit slit can be placed.
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This is the well-known case of the Cylindrical condenser with Minimum gap width of cylindrical condenser Fig. In the z -direction there is no focusing in a cylindrical condenser. Stigmatic focusing by spherical condenser Fig. Potential distribution in a spherical condenser. Therefore, spherical condensers are frequently used as energy spectrometers because they focus stigmatically like a round lens, but with a curved optic axis Fig. Here the potential between the plates can be written to be Fig.
The principal planes cross each other at the intersection of the entrance and exit axes Fig. For the spherical condenser the image distance according to 2.
The theoretical energy resolution according to 2. It is better by a factor 2 than with the cylindrical condenser. The energy resolution is for symmetric imaging, with 2. Lens action of spherical condenser, radially and axially. A fairer comparison would be on the basis of equal path length between object and image slit. A toroidal condenser Fig. This, however, goes at the expense of object to image distance along the optic axis. Further, the axial focusing has to be taken into account, so that the intensity is not lost by axial divergence of the beam. Stigmatically imaging toroidal condenser with axial intermediate image.
Note that the axial lens parameters are the same as the radial ones for the cylindrical condenser 2. Remembering the hyperbolic functions Fig. The strong axial focusing, however may be a hindrance. Toroidal condenser with Re Fig. The hyperbolic functions Another class of toroidal condensers, which is also covered by 2. In this case the radius Re is counted negative, so that c is negative. Therefore, 1 3. If they are equal but opposite, no dispersion occurs. This is also true for virtual objects and images Figs.
The mass dispersion in the image plane is, from 3. This would be due to ions with the energy eV0. Because of the unavoidable energy spread of the ions, the energy dispersion in the image plane has to be added, which 3. Figure 3. The following are the focusing parameters for the general case Fig. The mass resolution is obtained see. When the pole piece surfaces of the sector magnet are not parallel but conical Fig. In this case the radius of curvature of a particle trajectory equals the distance from the z-origin, there is no radial focusing, only axial focusing Fig.
kendrabrekke.com/how-to-location-mobile-phone-calls-galaxy-a3.php In view of the rising characteristic of the sinh function see Fig. When used as a mass spectrometer, a radially focusing lens has to be provided. Pages are clean and intact. Seller Inventory mon Condition: Used: Good. Very well kept complete copy, light wear, unmarked with well kept jacket if issued , may have exowner iniscription. Satisfaction Guaranteed! Book is in Used-Good condition. Pages and cover are clean and intact. Used items may not include supplementary materials such as CDs or access codes. May show signs of minor shelf wear and contain limited notes and highlighting.
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