Aberration coefficient

The simulations were carried out on a Silicon Graphics Iris Indigo workstation using the CERIUS molecular modeling and the associated HRTEM module. The multislice simulation technique was applied using the following parameters electron energy 400 kV (lambda = 0.016 A) (aberration coefficient) = 2.7 mm focus value delta/ = 66 nm beam spread = 0.30 mrad. 

Figure. 4a is a [110] projected high-resolution image taken with a JEM-2010FEG electron microscope with a spherical aberration coefficient 0.5 mm. A dislocation can be seen in the framed area, of which a magnified photo is shown in Fig. 4b. It can be seen that two extra half 111 planes mnning from the top left to the bottom right and from the top right to the bottom left, respectively. Both of them end in the center of the picture.

Fig. 1. CTF and E function simulation. EM imaging parameters electron energy = 300 keV spherical aberration coefficient Q = 1.6 mm ()= 7%. No envelope decay B = 0) was used for the dotted (underfocus = 0.5 pm) and dashed (underfocus =...

Figure 14.5. Representative plots of the contrast transfer function (CTF) as a function of spatial frequency, for two different defocus settings (0.7 and 4.0 fxm underfocus) and for a field emission (light curve) or tungsten (dark curve) electron source. AH plots correspond to electron images formed in an electron microscope operated at 200 kV and with objective lens aberration coefficients, Cg =...

Cs is the spherical aberration coefficient. This phase shift by spherical aberration can be significant for short wavelength waves such as electrons. Fortunately, this phase shift can be offset by phase shift caused by defocusing the image. We can defocus the image and make the focal point at the distance further from the focal plane (i.e. weaken the lens power). The phase shift from defocusing the image is a function of the defocus distance (D) from the focal plane. 

K is a constant close to unity, Cs is the spherical aberration coefficient and A. is the wavelength of the electrons. Equation 4.3 simply tells us that we should decrease wavelength and spherical aberration and increase brightness of electron illumination to obtain the minimal probe size. The importance of electron gun type in determining SEM resolution becomes obvious because there are significant differences in their brightnesses. Figure 4.5 shows the difference... 

Fig. 1. The imaginary part of the phase contrast transfer function, sinX, plotted as a function in reciprocal space for a microscope operating at 200 kV with a spherical aberration coefficient of 1.2 mm a) Gaussian focus b) 325A underfocus c) 65OA underfocus.

The complete diffraction diagram, which appears at the back focal plane of an electronic objective lens, is actually a mapping of the Fourier transform of the specimen [1, 2]. An object point usually is displaced from its true conjugate point by an amount due to defocus (Az) and the spherical aberration coefficient (Cs) giving rise to a total displacement on the TEM image of ... 

The spherical aberration coefficients C and Cjj are referred to the object side and to the image side, respectively, and the beam semiangles and a, are referred to in a similar manner. The chromatic aberration caustic is given by... 

The chromatic aberration coefficients and are referred to the object side and to the image side respectively and iSV, is the variation about the beam voltage Vq- The focal spot size df found by adding the components dj, and d in quadrature according to... 

The aberration characteristics of the objective lens are determined by the polepiece geometry and magnetic field strength. The diameters of the discs of confusion associated with these aberrations, i.e. the magnitude of the aberration and the associated image resolution limitation, are directly proportional to two lens parameters called the spherical aberration coefficient (Cg) and the chromatic aberration coefficient (C ). 

Aberration A perfect lens would produce an image that was a scaled representation of the object real lenses suffer from defects known as aberrations and measured by aberration coefficients. 

Although accurate values of the optical properties of magnetic lenses can be obtained only by numerical methods, in which the field distribution is first calculated by one of the various techniques available—finite differences, finite elements, and boundary elements in particular—their variation can be studied with the aid of field models. The most useful (though not the most accurate) of these is Glaser s bell-shaped model, which has the merits of simplicity, reasonable accuracy, and, above all, the possibility of expressing all the optical quantities such as focal length, focal distance, the spherical and chromatic aberration coefficients Cg and Q, and indeed all the third-order aberration coefficients, in closed form, in terms of circular functions. In this model, 5(z) is represented by... 

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