Quadrupole-Octopole and Foil Lens Corrector Systems

1971 ◽  
Vol 29 ◽  
pp. 16-17 ◽  
Author(s):  
M. G. R. Thomson ◽  
E. H. Jacobsen
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Order Effect ◽  
Objective Lens ◽  
Axially Symmetric ◽  
Third Order ◽  
First Order ◽  
Short Focal Length ◽  
Strong Focusing

The theorem due to Scherzer which states, in essence, that a conventional axially symmetric, magnetic or electrostatic lens can never be free from third order spherical aberration is well known. Attempts to circumvent this limitation have been carried out over the past thirty years with little result, but meanwhile the ill effects have been minimized by using magnetic lenses of very short focal length.The most studied alternative is the use of doubly symmetric strong focusing lenses. The first order imaging is performed with three or more quadrupoles, and the third order aberrations corrected with three octopoles. The design by Deltrap for example has no first order effect other than to invert the image, and has a third order spherical aberration coefficient which exactly cancels out that of the magnetic objective lens with which it us used. To avoid chromatic aberration this magnetic objective lens must have a very short focal length (2 mm for 100 kv operation with a resolution of 1 Å), and the overall system then has so much coma that the field of view is limited to 50 Å diameter.

A Spherical-Aberration Corrector Using Electrontransparent Conducting Foils

1973 ◽  
Vol 31 ◽  
pp. 262-263
Author(s):  
M. G. R. Thomson
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Field Of View ◽  
Objective Lens ◽  
Electric Field Gradients ◽  
Field Gradients ◽  
Short Focal Length ◽  
Successful Approach ◽  
Fifth Order

One of the problems associated with building any aberration-corrected electron microscope objective lens lies in the difficulty of obtaining a sufficiently short focal length. A number of systems have focal lengths in the 1cm. range, and these are more suitable for microprobe work. If the focal length can be made short enough, the chromatic aberration probably does not need to be corrected, and the design is much simplified. A corrector device which can be used with a conventional magnetic objective lens of short focal length (Fig. 1) must either have dimensions comparable to the bore and gap of that lens, or have very large magnetic or electric field gradients. A successful approach theoretically has been to use quadrupoleoctopole corrector units, although these suffer from very large fifth order aberrations and a limited field of view.

The Reduction of Chromatic Aberrations Due to Instrumental Instabilities

1971 ◽  
Vol 29 ◽  
pp. 14-15
Author(s):  
J. S. Lally ◽  
R. Evans
Keyword(s):  
Electron Microscope ◽  
High Voltage ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Usual Practice ◽  
Voltage Electron ◽  
Short Focal Length ◽  
Chromatic Aberrations ◽  
Electron Microscopes

One of the instrumental factors often limiting the resolution of the electron microscope is image defocussing due to changes in accelerating voltage or objective lens current. This factor is particularly important in high voltage electron microscopes both because of the higher voltages and lens currents required but also because of the inherently longer focal lengths, i.e. 6 mm in contrast to 1.5-2.2 mm for modern short focal length objectives.The usual practice in commercial electron microscopes is to design separately stabilized accelerating voltage and lens supplies. In this case chromatic aberration in the image is caused by the random and independent fluctuations of both the high voltage and objective lens current.

Comparison of Deterministic and Linear Cosine Spatial Filtering of Transmission Electron Micrographs

1972 ◽  
Vol 30 ◽  
pp. 596-597
Author(s):  
David A. Ansley
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Spatial Filter ◽  
Operating Conditions ◽  
Objective Lens ◽  
List Type ◽  
Spatial Filters ◽  
Transmission Electron ◽  
Wide Range

The coherence of the electron flux of a transmission electron microscope (TEM) limits the direct application of deconvolution techniques which have been used successfully on unmanned spacecraft programs. The theory assumes noncoherent illumination. Deconvolution of a TEM micrograph will, therefore, in general produce spurious detail rather than improved resolution.A primary goal of our research is to study the performance of several types of linear spatial filters as a function of specimen contrast, phase, and coherence. We have, therefore, developed a one-dimensional analysis and plotting program to simulate a wide 'range of operating conditions of the TEM, including adjustment of the:(1) Specimen amplitude, phase, and separation(2) Illumination wavelength, half-angle, and tilt(3) Objective lens focal length and aperture width(4) Spherical aberration, defocus, and chromatic aberration focus shift(5) Detector gamma, additive, and multiplicative noise constants(6) Type of spatial filter: linear cosine, linear sine, or deterministic

Observation of Electron Energy Losses in Dark Field Images

1967 ◽  
Vol 25 ◽  
pp. 246-247
Author(s):  
J. S. Lally ◽  
R. M. Fisher ◽  
A. Szirmae ◽  
H. Hashimoto
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Dark Field ◽  
Bragg Angle ◽  
Energy Losses ◽  
Objective Lens ◽  
Characteristic Energy ◽  
Crystalline Materials ◽  
Dark Field Electron

It is commonly assumed that the poor resolution of axially illuminated dark field electron micrographs of crystalline materials is due to the spherical aberration of the objective lens. Actually in many cases the lack of sharpness of the image results from the displacement by chromatic aberration of additional images formed by the electrons which have suffered large energy losses as a result of single or multiple plasmon scattering. In the case of very small diffracting particles, grains or other fine structures in the specimen it is possible to observe multiple images corresponding to these characteristic energy losses. The displacement (Δx) of the image is given by Δx = C f α ΔE/E where C is the chromatic aberration coefficient, f the focal length, α is twice the Bragg angle, E the accelerating potential, and ΔE the energy loss. For a typical plasmon loss of 20 ev the displacement at 100 kv is about 100 Å.

Development of a Computer-Controlled 120kV High-Performance Tem

1996 ◽  
Vol 54 ◽  
pp. 446-447
Author(s):  
H. Kobayashi ◽  
I. Nagaoki ◽  
E. Nakazawa ◽  
T. Kamino
Keyword(s):  
High Resolution ◽  
High Performance ◽  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Wide Field ◽  
High Contrast ◽  
Computer Controlled ◽  
The Magnetic Field

A new computer controlled 120kV high performance TEM has been developed(Fig. 1). The image formation system of the microscope enables us to observe high resolution, wide field,and high contrast without replacing the objective lens pole-piece. The objective lens is designed for high- contrast (HC) and high-resolution(HR) modes, and consists of a double gap and two coils. A schematic drawing of the objective lens and the strength of the magnetic field of the lens is described in Fig.2. When the objective lens is used in HC mode, upper and lower coils are operated at a lens current of same polarity to form the long focal length. The focal length(fo), spherical aberration coefficient(Cs) and chromatic aberration coefficient (Cc) in HC mode at 100kV are 6.5, 3.4 and 3.1mm, respectively. Magnification range at HC mode is × 700 to × 200,000. The viewing area with an objective aperture of a diameter of 10μm is 160mm in diameter. In HR mode, the polarity of lower coil current is reversed to form a shorter focal length for high resolution image observation. The fo, Cs and Cc of the objective lens in HR mode at lOOkV are 3.1, 2.8 and 2.3mm, respectively. The highest magnification in HR mode is × 600,000.

Beyond One Angstrom

1990 ◽  
Vol 48 (1) ◽  
pp. 204-205
Author(s):  
Albert. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Low Energy ◽  
Objective Lens ◽  
Squeeze Out ◽  
Electron Microscopes

I believe everyone would agree we have just about reached the limit of performance of today's electron microscopes. This is not to say that additional advances will not take place, because there is always one more drop of blood to squeeze out. But it is certainly becoming increasingly apparent that we can not expect more out of the magnetic lenses that we now have. I am sure that everyone who has ever been concerned with this problem has arrived at the same set of conclusions but it may help to set them down one more time.The available resolution in electron microscopy is distressingly poor compared to the wavelength of the electrons. The culprit is always the objective lens. For low energy, say less than 5,000 volts, chromatic aberration is the offending element whereas at high voltages it is the spherical aberration coefficient which we must be concerned with. In both cases, there are some basic restrictions which apply. In the case of chromatic aberration it is always very closely equal with the focal length of the lens and for the spherical aberration coefficient the best we can do is about 1/4 or 1/2 the focal length.

Chromatic Aberration Correction of a Low-Voltage SEM using a Wien Filter: Adjusting the Correction Strength

2001 ◽  
Vol 7 (S2) ◽  
pp. 874-875
Author(s):  
T. Steffen ◽  
P.C. Tiemeijer ◽  
M.P.C.M. Krijn ◽  
S.A.M. Mentink
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Aberration Correction ◽  
Wien Filter ◽  
Electron Microscopes ◽  
Working Distance ◽  
Scanning Electron Microscopes

The resolution of state-of-the-art low-voltage scanning electron microscopes (LV SEM), which is currently limited by the chromatic and spherical aberrations of the objective lens, can be improved by incorporating an aberration correcting device. At present four different concepts are discussed in literature: Zach and Haider demonstrated that a quadrupole/octupole corrector can correct both chromatic and spherical aberration. Rose proposed a Wien filter for chromatic aberration correction, which has relaxed stability requirements. Recently, we reported a simplified version of this corrector and showed that a spherical aberration corrector can be integrated in a Wien filter. Henstra and co-workers suggested a purely electrostatic corrector that can correct both chromatic and spherical aberration.For all these concepts problems may arise when the lens-to-sample (working) distance for an aligned corrector is to be changed. in general, the corrector settings depend on the ratio Cc/f2, where Cc and f denote the coefficient of the chromatic aberration and the focal length of the objective lens, respectively. When the working distance is changed, this ratio is no longer perfectly matched to the corrector settings. The tedious realignments and readjustments, which then seem necessary, can be avoided by using a doublet objective lens as illustrated schematically in Figure 1.

Improvements in the electron probe forming capabilities and x-ray hole counts in the Philips TEM

1983 ◽  
Vol 41 ◽  
pp. 376-377
Author(s):  
Richard L. McConville
Keyword(s):  
Field Strength ◽  
Electron Probe ◽  
Spherical Aberration ◽  
Focal Length ◽  
Objective Lens ◽  
Parallel Beam ◽  
Tilt Axis ◽  
X Ray ◽  
Small Probe ◽  
Specimen Height

A second generation twin lens has been developed. This symmetrical lens with a wider bore, yet superior values of chromatic and spherical aberration for a given focal length, retains both eucentric ± 60° tilt movement and 20°x ray detector take-off angle at 90° to the tilt axis. Adjust able tilt axis height, as well as specimen height, now ensures almost invariant objective lens strengths for both TEM (parallel beam conditions) and STEM or nano probe (focused small probe) modes.These modes are selected through use of an auxiliary lens situ ated above the objective. When this lens is on the specimen is illuminated with a parallel beam of electrons, and when it is off the specimen is illuminated with a focused probe of dimensions governed by the excitation of the condenser 1 lens. Thus TEM/STEM operation is controlled by a lens which is independent of the objective lens field strength.

Ultra-high resolution SEMI-in-lens type FE-SEM, JSM-6320F, with strong magnetic-field lens with built-in secondary-electron detector

1994 ◽  
Vol 52 ◽  
pp. 484-485
Author(s):  
T. Miyokawa ◽  
H. Kazumori ◽  
S. Nakagawa ◽  
C. Nielsen
Keyword(s):  
High Resolution ◽  
Secondary Electron ◽  
Spherical Aberration ◽  
Incident Beam ◽  
Chromatic Aberration ◽  
Magnetic Flux Density ◽  
Objective Lens ◽  
Electron Detector ◽  
High Resolution Images ◽  
Working Distance

We have developed a strongly excited objective lens with a built-in secondary electron detector to provide ultra-high resolution images with high quality at low to medium accelerating voltages. The JSM-6320F is a scanning electron microscope (FE-SEM) equipped with this lens and an incident beam divergence angle control lens (ACL).The objective lens is so strongly excited as to have peak axial Magnetic flux density near the specimen surface (Fig. 1). Since the speciien is located below the objective lens, a large speciien can be accomodated. The working distance (WD) with respect to the accelerating voltage is limited due to the magnetic saturation of the lens (Fig.2). The aberrations of this lens are much smaller than those of a conventional one. The spherical aberration coefficient (Cs) is approximately 1/20 and the chromatic aberration coefficient (Cc) is 1/10. for accelerating voltages below 5kV. At the medium range of accelerating voltages (5∼15kV). Cs is 1/10 and Cc is 1/7. Typical values are Cs-1.lmm. Cc=l. 5mm at WD=2mm. and Cs=3.lmm. Cc=2.9 mm at WD=5mm. This makes the lens ideal for taking ultra-high resolution images at low to medium accelerating voltages.

Electron Holography Improving Transmission Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 208-209
Author(s):  
Hannes Lichte
Keyword(s):  
Electron Microscopy ◽  
Transfer Functions ◽  
Imaging System ◽  
Spherical Aberration ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
Wave Aberration

Generally, the electron object wave o(r) is modulated both in amplitude and phase. In the image plane of an ideal imaging system we would expect to find an image wave b(r) that is modulated in exactly the same way, i. e. b(r) =o(r). If, however, there are aberrations, the image wave instead reads as b(r) =o(r) * FT(WTF) i. e. the convolution of the object wave with the Fourier transform of the wave transfer function WTF . Taking into account chromatic aberration, illumination divergence and the wave aberration of the objective lens, one finds WTF(R) = Echrom(R)Ediv(R).exp(iX(R)) . The envelope functions Echrom(R) and Ediv(R) damp the image wave, whereas the effect of the wave aberration X(R) is to disorder amplitude and phase according to real and imaginary part of exp(iX(R)) , as is schematically sketched in fig. 1.Since in ordinary electron microscopy only the amplitude of the image wave can be recorded by the intensity of the image, the wave aberration has to be chosen such that the object component of interest (phase or amplitude) is directed into the image amplitude. Using an aberration free objective lens, for X=0 one sees the object amplitude, for X= π/2 (“Zernike phase contrast”) the object phase. For a real objective lens, however, the wave aberration is given by X(R) = 2π (.25 Csλ3R4 + 0.5ΔzλR2), Cs meaning the coefficient of spherical aberration and Δz defocusing. Consequently, the transfer functions sin X(R) and cos(X(R)) strongly depend on R such that amplitude and phase of the image wave represent only fragments of the object which, fortunately, supplement each other. However, recording only the amplitude gives rise to the fundamental problems, restricting resolution and interpretability of ordinary electron images:

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