透镜系统

1. einzel lens

An electrostatic lens that has the same potential at the entrance and exit of the lens. Normally, the "einzel lens" consists of three electrodes. Two electrodes at both ends are set at the ground potential, and a positive or negative potential is given to the central electrode. The lens with a positive potential at the central electrode is called the acceleration-type einzel lens, whereas the lens with a negative potential is called the deceleration-type einzel lens. Both are convex lenses. The electrons passing through the einzel lens undergo lens action without acceleration and deceleration at the exit of the lens. This lens is used for ion-beam instruments, for example, an ion mass analyzer.

Related term
immersion lens

2. anastigmat

A lens that corrects all of five Seidel aberrations. Almost all the commercial cameras, which have been recently developed, are fitted with an anastigmat lens.

Related term
Five Seidel aberrations

3. anaplat

A lens that corrects spherical and coma aberrations. A telescope and an optical microscope are equipped with an achromatic (chromatic aberration corrected) "anaplat." The anaplat is accomplished in the following way. The surface at the object side of the lens is finished in a spherical shape to eliminate the spherical aberration. The surface at the image side of the lens is fabricated to suppress the occurrence of the coma aberration (surface satisfying the sine condition).

Related term
spherical aberration, (off-axial) coma aberration

4. underfocus

"Underfocus" means that the excitation of the objective lens in a TEM is slightly decreased from that at the in-focus (focused on a specimen). At this excitation, the image produced on the selector aperture is the specimen image when the objective lens is focused on a position above the specimen. To enhance contrast in a bright (or dark) field image (to make the outline of the image clear), the image is often taken at a slight underfocus, instead of at the in-focus.

Related term
overfocus

5. phase plate

A plate that causes a change in the phase of an electron wave. The phase plate placed at the back focal plane of an electron microscope creates a relative phase change between the transmitted wave and scattered waves from a specimen. By the interference between the transmitted wave and the scattered waves, a phase change due to an object, which is originally difficult to view, can be visualized as an intensity change. Since the phase plate produces the relative phase change effectively at a small spatial-frequency region (corresponding to a long-distance region in the real space), it is effectively used in obtaining high contrast for biological specimen. There are two practically-used phase plates: Phase plate made of a carbon thin film with a controlled thickness having a hole at the center (Zernike phase plate) (Fig. (a)) and Hole-free phase plate (Fig. (b)).

(a) Zernike phase plate, (b) Hole-free phase plate

A Zernike phase plate has a hole where the transmitted wave passes and causes a phase shift of π/2 of scattered waves with respect to the transmitted wave. A hole-free phase plate does not have any hole, but produces a relative phase change between the transmitted wave and scattered waves. This phase change may be interpreted as follows: The part of the thin film plate which receives the electron beam is electrically charged and suffered by a change in electrostatic potential, and then the phase of the transmitted wave is changed relative to the scattered waves.

Related term
Zernike phase contrast

6. immersion lens

An electrostatic lens that has different potentials at the entrance and exit of the lens. The term of "immersion lens" originates from the immersion lens of light optical lenses, where the refraction index is different at the entrance and exit of the lens. The extraction electrode of the electron gun is an acceleration-type immersion lens. The Wien filter is normally a deceleration-type immersion lens. It is noted that lens action arises when electrons are accelerated or decelerated.

Related term
einzel lens

7. image wobbler

A function to perform focusing of the illumination beam by the use of deflection coils below the condenser lens. The electron beam is repeatedly tilted at slightly positive and negative directions with respect to the optical axis. The excitation of the objective lens or the specimen position is adjusted so that the image does not move while the "image wobbler" is operated. The image wobbler is useful for rough focusing at magnifications up to ～50,000×.

8. chromatic aberration

If there is energy (wavelength) spread of the incident electron beam or the electron beam passing through a specimen, the refraction angles of these electron beams are different depending on wavelength. Thus, a blurred image is produced on the image plane. This phenomenon is called "chromatic aberration." The energy spread of the electron beam arises from instability of the accelerating voltage, the spread of the initial speed of electrons emitted from the electron gun, the Boersch effect and change of the focal length caused by fluctuations of the excitation current of the lens coils. In addition, as a specimen is thicker (～10 nm or more), energy loss of electrons (change of wavelength) due to inelastic scattering gives rise to the chromatic aberration.

Related term
Boersch effect, inelastically scattered electron

9. airy disk

Related term
diffraction limit

10. S-shaped distortion

"S-shaped distortion" means the distortion characteristic of the electromagnetic lens for the electron beam. Unlike the light beam in the optical lens, the electron beam suffers rotation in the electromagnetic lens. The rotation magnitude increases as the electron beam deviates from the optical axis, and then an image that should be observed as a line on the image plane (fluorescent screen) is viewed as an s-shaped image. The distortion becomes a problem for the projector lens because there exist electron beams which pass largely apart from the optical axis. Combination of lenses with opposite polarity can cancel the distortion, but this technique has not been used yet.

11. overfocus

"Overfocus" means that the excitation of the objective lens in a TEM is slightly increased from that at the in-focus (focused on a specimen). At this excitation, the image produced on the selector aperture is the specimen image when the objective lens is focused below the specimen.

Related term
underfocus

12. objective mini lens

The "objective mini lens" is a weakly excited lens placed below the objective lens. This lens does not have a polepiece to strengthen a magnetic field as the objective lens does. This lens is used to form an image on the selector aperture in Low MAG mode (～50× to 3,000×) by stopping the excitation of the objective lens. The magnification at the objective mini lens is 1× to 2×. This lens is also used to obtain a high quality low magnification image of about 1,000× in the MAG mode. That is, the excitation of the objective lens is kept strong to maintain image quality of the objective-lens, and the image is demagnified (to ～0.5×) by the objective mini lens, thus a wide view image is formed on the object plane of the intermediate lens.

Related term
objective lens, condenser mini lens

13. diffraction limit

The diffraction limit is the resolution limit due to diffraction of an electron wave for the optical system with no aberrations. Even in the aberration-free optical system, electron waves exiting from one point on the object do not form an infinitesimal point on the image plane but these electron waves are focused into a finite size spot (airy disk) due to their diffraction phenomenon. The radius r of the airy disk is given by the equation r = 0.6λ/sinα, where λ is the wavelength of the electron and α is the divergence angle of the electron. From the equation, it is seen that the size of the airy disk is small for a large divergence angle of the electron beam. This limitation makes it impossible to produce an infinitesimal point resolution even for ideal lenses.

Figure shows the diffraction limit (vertical axis) r ＝ 0.6λ/sinα for each accelerating voltage as a function of divergence semi-angle α. Since the wavelength of an electron beam is longer for the lower accelerating voltage, the diffraction limit r becomes larger for the lower accelerating voltage even for the same semi-angle α. In the case of an accelerating voltage of 200 kV, a resolution of 0.1 nm expected from the diffraction limit is achieved with a divergence semi-angle of approximately 15 mrad. In the case of 80 kV, however, a larger divergence semi-angle of an approximately 25 mrad is required because of a longer wavelength of the electron beam.

14. rotationally symmetric lens

A lens whose symmetry does not change even when rotated with respect to the lens axis. Conventionally-used lenses (objective lens, condenser lens, etc.) are "rotationally symmetric lenses." On the other hand, recently-developed lenses for analytical purposes, such as the Wien filter, the omega filter, the alfa filter and the Cs corrector, are non-rotationally symmetric lenses.

Related term
objective lens, Wien filter, omega filter, alfa filter, Cs corrector

15. Gaussian focus

A focus (imaging) condition for an ideal lens without aberrations. The image plane formed by the ideal lens is called the Gaussian plane.

Related term
Five Seidel aberrations, parasitic aberration

16. caustic surface

In the ideal (aberration-free) lens, all the electrons that exit from a point on the object plane converge at a point on the image plane, and trajectories of adjacent electron beams do not intersect each other. However, in an actual lens with aberration, the adjacent trajectories intersect and the trace of intersections forms a bright envelope surface. The bright surface is called the "caustic surface."

17. movable aperture

An aperture that allows selection of its hole diameter and adjustment of its position from the outside of vacuum. The "movable aperture" includes the condenser aperture, the objective aperture and the selector aperture.

elated term
fixed aperture

18. camera constant

The product of the camera length and the wavelength of the incident electron is called "camera constant." The camera constant is equal to the product of the distance from the central spot produced by a transmitted wave to a certain diffraction spot and the lattice spacing corresponding to the diffraction spot. Thus, if the camera constant is calculated using a standard specimen whose lattice spacing is known, measuring the distance from the transmission spot to a certain diffraction spot makes it possible to calculate the lattice spacing of the corresponding diffraction spot.

Related term 
camera length

19. camera length

An effective distance from a specimen to a plane where an observed diffraction pattern is formed.

Related term
camera constant

20. geometrical aberration

20-1. axial geometrical aberration

The axial geometrical aberrations are aberrations depending only on α, angle between the beam and the optical axis. The axial geometrical aberrations are defocus, two-fold astigmatism, three-fold astigmatism, axial coma aberration, spherical aberration, four-fold astigmatism, star aberration, etc. On the other hand, aberrations that depend on α and r, distance of an electron beam from the optical axis, are called “off-axial (geometrical) aberrations.” As an example of the off-axial aberrations, the coma aberration of Five Seidel aberrations is mentioned. In the case of high-resolution electron microscopy (HREM), the field of view is very narrow because its magnification is very high. Thus, the off-axial geometrical aberrations can be ignored, enabling us to account for only the axial geometrical aberrations. In the case of scanning transmission electron microscopy (STEM), a converged electron probe on the optical axis scans a specimen area. Only the axial geometrical aberrations are accounted for in STEM image formation as in the case of HREM.

Related term
geometrical aberration

20-2．geometrical aberration

In geometrical optics where electron trajectories are described as motions of charged particles in an electromagnetic field, the deviation of the real imaging point of an electron from the ideal imaging point with no aberrations is called “geometrical aberration.” Optical properties are expressed by a power-series polynomial of r (distance of an electron beam from the optical axis) and α (angle between the beam and the optical axis), in which a beam emitted from one point on the object plane is mapped to a point on the image plane. If only the first order terms of the expression is taken, the polynomial expresses ideal imaging with no aberrations (Gauss imaging). If the higher order terms than the second order are taken into account, the deviation of the real imaging point from the ideal imaging point appears. The order of the geometrical aberration is determined by the sum of the order of α (angle between the beam and the optical axis) and that of r (distance of an electron beam from the optical axis). It is conviniently used for describing the order of the aberration. On the other hand, the wave aberration is useful because the order of the wave aberration is closely related to the symmetry of the aberration. The order of the wave aberration is expressed by adding 1 (one) to the order of the geometrical aberration. For examples, the two-fold astigmatism is a first-order aberration in terms of the geometrical aberration but is the second-order aberration in terms of the wave aberration, and that the three-fold astigmatism is a second order in the geometrical aberration but a third order in the wave aberration.

elated term
wave aberration, Five Seidel aberrations

21. parasitic aberration

"Parasitic aberrations" are not inherent aberrations like five Seidel aberrations, but residual aberrations which arise from magnetic non-uniformity of the polepiece material, inaccuracy of machining the polepiece and disagreement of the optical axes between lenses. The parasitic aberrations include axial coma aberration, star aberration, three lobes and axial two-, three-, four-, five- and six-fold astigmatisms.

Related term
Five Seidel aberrations, axial astigmatism, (off-axial) coma aberration

22. spherical aberration

22-1. fifth-order spherical aberration

Among the aberrations of rotationally symmetric magnetic and electrostatic lenses, the aberration proportional to α5 (α: an angle between an electron beam and the optical axis) is called "fifth-order spherical aberration." Not only the third-order spherical aberration, but also the fifth-order spherical aberration inevitably exists in an electron lens. The term, "spherical aberration," normally indicates the third-order aberration proportional to α3, and a symbol Cs is used as the spherical aberration coefficient. On the other hand, a symbol C5 is normaly used as the fifth-order spherical aberration coefficient. In recent years, the third-order spherical aberration has been corrected, thus the fifth-order spherical aberration has been needed to be considered. Fortunately, the use of a Cs corrector with the two-stage hexapoles and transfer lenses between them makes possible the value of C5 variable, thus C5 = 0 being available.

Related term
spherical aberration, Five Seidel aberrations, combination aberration

22-2. spherical aberration

When an electron beam exiting obliquely from the point at the optical axis on the object plane passes through the objective lens, it does not come to the optical axis on the ideal Gaussian image plane, but intersects the optical axis at a point slightly shifted from the image plane (in the TEM , slightly before the image plane (lens side)). As a result, a circular blurred image is produced on the image plane. This defect is called "spherical aberration." The amount of blur is given by Csα3 on the object plane, where Cs is a spherical aberration coefficient and α is an angle between the electron beam and the optical axis. The spherical aberration is the most important aberration of the objective lens among the aberrations. For a rotationally symmetric lens with respect to the optical axis, the value of Cs is always positive. In TEM, the third-order spherical aberration has nowadays been successfully corrected. Cs correctors using combination of hexapoles and transfer lenses have become main stream.

Related term
Five Seidel aberrations, fifth-order spherical aberration, combination aberration

23．Cs corrector

The "Cs corrector" produces a negative spherical aberration coefficient (Cs) to cancel positive Cs of the objective and condenser lenses, which are axially-symmetric magnetic field lenses. The following Cs correctors are now in practical use. 1) One consists of two hexapoles with opposite polarity and transfer lenses that connect the hexapoles. The first hexapole produces a negative Cs. The unnecessary three-fold distortion produced by the first hexapole is compensated by the second hexapole. The value of negative Cs is doubled by the second hexapole. 2) The other consists of three pairs of elements combining octupoles and quadrupoles. Negative Cs is produced in the X direction by the first element, in the Y direction by the second element and the intermediate direction by the third element, respectively. Cs correction of the objective lens achieves a higher resolution TEM image. Cs correction of the condenser lens leads to a smaller, higher-intensity electron probe, thus, enabling us to obtain a higher-resolution HAADF image and to perform elemental analysis of one atomic column. Figure shows the schematic of a Cs corrector and its basic action. The corrector, which consists of two hexapoles with opposite polarity and transfer lenses connecting the hexapoles, produces a negative Cs and cancels a triangle shape of the beam caused by the first-stage hexapole field using the second-stage hexapole field.

• 

Fig.Two-stage hexapole Cs corrector Electron trajectory in hexapoles or dodecapoles (upper left) and schematic of lens configuration (lower tight) In a two-stage hexapole Cs corrector, the thick hexapole field produces a negative Cs, and this action is used to correct the positive Cs of the objective lens. Upper left figure shows the cross section of the electron trajectory in the hexpoles for every 10 mrad angle (from inside blue line to outside red line). The first-stage hexapole field creates a negative Cs but an unwanted triangle shape trajectory. The second-stage hexapole field with the opposite polarity again creates the same amount of negative Cs and the opposite sense of triangle to cancel the triangle shape trajectory caused by the first hexapole, As a result, the amount of negative Cs is doubled and a cylindrical symmetric trajectory is retrieved. Owing to the negative Cs, the cross section of the trajectory expands outwards (shown in red), compared to the trajectory for the case of no hexapole field (in green). With the use of this negative Cs, the positive Cs of the objective lens is canceled. It should be noted that, the transfer lens (lower right figure) is used to transfer an electron beam emerged from the first-stage hexapole into the second-stage hexapole while preserving the beam shape. In the upper left figure, the action of the transfer lens is omitted.

Related term
point resolution, probe diameter, hexapole (sextupole), octupole (octopole)

24．paraxial approximation

"Paraxial approximation" is an approximation used in ray tracing of an electron beam where the angle between the electron beam and the optical axis is small. In other words, trigonometric functions of the angles appearing in ray optics are approximated by linear functions (ex. sin α → α) and optical surfaces are replaced by portions of a sphere. In the paraxial approximation, five Seidel aberrations do not appear.

Related term
Five Seidel aberrations

25．crossover point

A point where the cross section of the electron beam becomes minimum when the beam is converged with the electron lens.

26. Koehler illumination

A beam illumination method, which illuminates the specimen with a parallel electron beam by increasing the excitation of the condenser mini lens so that the incident electron beam is focused onto the pre-focal point of the pre-magnetic field of the objective lens. This illumination is used for the observation of bright-field image, dark-field image and HREM image. If the parallel illumination onto the specimen is failed, the diffraction condition becomes different depending on the specimen position. This may mislead interpretation of the image.

27. imaging lens system

The "imaging lens system" consists of the objective-, intermediate-, and projector lenses. By adjusting the excitation currents of the respective lenses, various aberrations are suppressed and image rotations are eliminated. Then, images can be taken at a wide range of magnifications, from low magnifications (～50×) to high magnifications (～1,500,000×). In addition, by changing the focal point of the first intermediate lens, a diffraction pattern is obtained.

Related term
objective lens, intermediate lens, projector (projection) lens

28. high-tension wobbler

A function to align the optical axis to the acceleration voltage center by adding slight voltage fluctuations (～±250 V) to the accelerating voltage of the electron beam.

Related term
accelerating (acceleration) voltage center

29. optical-axis alignment

"Optical-axis alignment" is to align the axes of the illumination and imaging systems, ranging from the electron gun to the projector lens, with the optical axis. This alignment enables the electron beam to travel in a straight path.

30. back focal plane

A focal plane located in the opposite side of the object (plane) with respect to a lens is called the back focal plane. A diffraction pattern is formed on the "back focal plane," thus the plane corresponds to the reciprocal space of the specimen.

Related term
reciprocal space

31. post-magnetic field

In a modern electron microscope, a specimen is placed in the objective lens. The magnetic field produced below the specimen (at the intermediate lens side) is called "post-magnetic field." Since the spherical aberration and chromatic aberration of the post-magnetic field determine the image resolution, this field is the most important part for image formation.

32. fifth-order spherical aberration

Among the aberrations of rotationally symmetric magnetic and electrostatic lenses, the aberration proportional to α5 (α: an angle between an electron beam and the optical axis) is called "fifth-order spherical aberration." Not only the third-order spherical aberration, but also the fifth-order spherical aberration inevitably exists in an electron lens. The term, "spherical aberration," normally indicates the third-order aberration proportional to α3, and a symbol Cs is used as the spherical aberration coefficient. On the other hand, a symbol C5 is normaly used as the fifth-order spherical aberration coefficient. In recent years, the third-order spherical aberration has been corrected, thus the fifth-order spherical aberration has been needed to be considered. Fortunately, the use of a Cs corrector with the two-stage hexapoles and transfer lenses between them makes possible the value of C5 variable, thus C5 = 0 being available.

Related term
spherical aberration, Five Seidel aberrations, combination aberration

33. 5th order aberrations

"Five Seidel aberrations" are proportional to the cube of α (angle between the incident electron beam and optical axis) and r (distance of the electron beam from the optical axis). "The 5th order aberrations" or so called "nine Schwarzschild aberrations" mean the aberrations of the next order to the Seidel aberrations or those proportional to the fifth power of α and r. Due to the development of Cs correctors, the third-order spherical aberration and third-order axial (parasitic) aberrations have nowadays been successfully corrected. The fourth-order axial (parasitic) aberrations can be corrected by the alignment of the optical axis. Thus, the fifth-order axial aberrations must be considered to decrease blurring of an image. If we have a Cs corrector with transfer lenses, the value of the fifth-order spherical aberration C5α5 is adjustable, thus C5α5 = 0 being possible. In the case of two-stage hexapole type correctors, efforts to minimize the axial (parasitic) 6-fold rotation astigmatism among the 5th order aberrations have been made.

Related term 
Five Seidel aberrations

34. (off-axial) coma aberration

34-1. (off-axial) coma aberration

Electron beams exit from a point that is not located at the optical axis on the object plane at various angles with respect to the optical axis do not come to one point on the image plane after passing through the lens but produce a cone-shaped (comet-shaped) image. This phenomenon is called "(off-axial) coma aberration." In this case, the vertex angle of the cone (divergence angle of the tail of the comet) is 60°. This is one of five Seidel aberrations which are inherent to the lens. It is noted that this is different from the axial parasitic coma aberration. Coma aberration is theoretically the next most important aberration to the spherical aberration for the objective lens. Although an example of off-axial coma correction has been reported, the effect of coma aberration is small for high magnification images. The name of "coma" originates from "comet.

Related term
Five Seidel aberrations, axial coma aberration

34-2. axial coma aberration

"Axial coma aberration" is a parasitic aberration due to incomplete axial symmetry of an electromagnetic lens (objective lens). This aberration deforms a circular image of the electron source to a cone-shaped (comet-shaped) image. The axial coma aberration arises from asymmetry of the pole piece bore of the lens, magnetic non-uniformity of the pole piece material, electron charging on the aperture, etc.

Related term
parasitic aberration

35. condenser aperture

The "condenser aperture" is classified into the fixed aperture and the movable aperture. As for the former case, a fixed condenser aperture with a diameter of ～0.5 mm to 1 mm is inserted into the first condenser lens to cut unnecessary beams. As for the latter case, about five movable apertures with different diameters ranging from ～10 μm to 200 μm are inserted into the second condenser lens, which determine the divergence angle and the dose of the incident beam.

Related term
fixed aperture, movable aperture

36. condenser lens

36-1. condenser lens

The "condenser lens" consists of two lenses: The first lens demagnifies the crossover of the electron beam emitted from the electron gun to ～1/10 in size. The second lens transfers the demagnified beam onto the object plane of the objective lens with a magnification of ～1×.

Related term
condenser-objective lens (C-O lens), condenser mini lens

36-2. condenser mini lens

The "condenser mini lens" is placed between the condenser lens and the objective lens for producing an electron beam with an appropriate convergence angle suitable for respective observation modes. The condenser mini lens does not have a polepiece that strengthens the magnetic field as the objective lens does. When the excitation of condenser mini lens is weak, convergent illumination of an electron beam for a nano-area for STEM, CBED and analytical use is achieved. On the other hand, when the lens excitation is strong, parallel illumination of electron beam for observation of the bright-field image, dark-field image and HREM image is achieved.

Related term
condenser-objective lens (C-O lens), condenser lens, objective mini lens, scanning transmission electron microscope (STEM) image, convergent-beam electron diffraction, CBED, high-resolution electron microscopy, HREM

36-3. condenser-objective lens (C-O lens)

The "condenser-objective lens (C-O lens)" makes the pre-magnetic field of the objective lens act as a condenser lens so that the electron beam is focused onto the specimen, and makes the post-magnetic field act as an objective lens to form the specimen image at the image plane. Since the electron beam is demagnfied to ～1/100 by the pre-magnetic field on the specimen, the C-O lens is essential for various purposes, such as CBED that requires sub-nanometer-area illumination, improvement of STEM image resolution, and decreasing of analysis region for EDS and EELS. To produce a parallel beam for HREM in the TEM mode, a condenser mini lens is used.

Related term
condenser mini lens

37. combination aberration

If two thin optical elements (lenses, multi-poles, etc.) are placed at a free space, higher order aberrations than those inherent to the elements can arise due to a synergetic effect of the inherent aberrations. The higher order aberrations induced are called "combination aberrations." A thick hexapole spherical aberration corrector produces a third-order negative spherical aberration by a self-conbination effect of two three-fold astigmatism fields (second-order aberration). With the use of this third-order negative spherical aberration, the third-order positive aberration of the objective lens can be corrected. In the case of the combination between a spherical aberration (Cs) corrector and an objective lens with a free space (incomplete image transfer) between them, a positive or negative fifth-order spherical aberration is induced by a cross combination between the third-order negative aberration of the Cs corrector and the third-order positive aberration of the objective lens. Using the fifth-order spherical aberration produced, the residual fifth-order spherical aberration of the system can be removed.

Related term
spherical aberration, geometrical aberration, Five Seidel aberrations

38. disk of least confusion

Since the electron lens has spherical aberration, electron beams, which exit from a point at the optical axis on the object plane while traveling in various directions, do not come to one point at the optical axis on the ideal image plane (Gaussian plane). An exiting beam, whose angle to the optical axis is small, nearly comes to the optical axis on the ideal image plane. An exiting beam, whose angle with respect to the optical axis is large, intersects the optical axis above the ideal image plane, thus deviates from the optical axis on the ideal image plane. Adding these formed images produces a least circle (disk) image at a position shifted a little from the ideal image plane to the objective lens. This circle is called "disk of least confusion." The diameter of the disk of least confusion, ds, is given by ds = (1/2)Csα3, which is 1/4 of blur on the Gaussian plane. Here, Cs is spherical aberration coefficient, α is the angle between the electron beam and the optical axis.

Related term
spherical aberration, Gaussian focus

39. Aperture

39-1. aperture

The "aperture" includes the condenser aperture, the objective aperture and the selector aperture. The aperture is classified into the fixed type aperture and the movable type aperture.

Related term
fixed aperture, movable aperture, aperture diameter, condenser aperture, objective aperture, selected-area aperture (intermediate-lens aperture)

39-2．aperture diameter

A diameter of a lens aperture. The condense-aperture diameter determines the divergence angle of an electron beam. The objective-aperture diameter determines scattering angle of electrons exiting from a specimen (the number of diffracted beams used for forming a TEM image). The selector-aperture diameter determines an area from which a diffraction pattern is obtained.

Related term
divergence angle

39-3．condenser aperture

The "condenser aperture" is classified into the fixed aperture and the movable aperture. As for the former case, a fixed condenser aperture with a diameter of ～0.5 mm to 1 mm is inserted into the first condenser lens to cut unnecessary beams. As for the latter case, about five movable apertures with different diameters ranging from ～10 μm to 200 μm are inserted into the second condenser lens, which determine the divergence angle and the dose of the incident beam.

Related term
fixed aperture, movable aperture

39-4．fixed aperture

An aperture with a certain size fixed at an appropriate position. It includes various apertures: An fixed aperture is placed below the condenser lens to cut unnecessary beams from the electron source. A fixed aperture made of tantalum is inserted into the illumination system to cut X-rays excited in the column for achieving high-accuracy analysis. A fixed aperture is inserted at the entrance of the intermediate lens system of the imaging system to cut reflection electrons in the column. A fixed aperture is inserted below the projector lens to enable differential pumping between the camera chamber and the column part.

Related term 
movable aperture

39-5．movable aperture

An aperture that allows selection of its hole diameter and adjustment of its position from the outside of vacuum. The "movable aperture" includes the condenser aperture, the objective aperture and the selector aperture.

Related term 
fixed aperture

39-6．objective aperture

The "objective aperture" is used for accepting a transmitted wave or one of diffracted waves to obtain a bright-field image or a dark-field image. The objective aperture is inserted into the back focal plane of the objective lens. The diameter of the objective aperture is 5 μm to 100 μm. It is noted that this aperture was inserted when obtaining a lattice image or a structure image, but recently, it has not been used. The reason for this is as follows. If computer processing is applied to the data which has a sharp cut due to the aperture, artifacts can appear in the processed image.

Related term
bright-field image, dark-field image, high-contrast polepiece

39-7. selected-area aperture (intermediate-lens aperture)

An aperture for selecting a specimen area in the selected area diffraction (SAD) mode. The aperture is inserted into the image plane of the objective lens (or object plane of the intermediate lens). The aperture diameter ranges normally from 10 μm to 100 μm.

Related term
selected-area diffraction, SAD

40．focusing

"Focusing" is to focus an electron beam to carry out focusing.

41. convergence angle

When a cone shaped, convergent electron beam illuminates a specimen, the semi-angle of the cone is termed "convergence angle."

42. convergence illumination

"Convergence illumination" is to illuminate a specimen with a converged beam.

43．illumination-lens system

The "illumination-lens system" consists of the condenser lens and condenser mini lens. The pre-magnetic field of the condenser-objective lens (C-O lens) is also included in the illumination-lens system.

Related term
condenser lens, condenser mini lens, condenser-objective lens (C-O lens)

44. focal step

The "focal step" means the amount of change of the focal length of the objective lens, when a knob for the objective lens current is varied. The minimum focal step of a recent electron microscope is ～1 nm.

45. focal length

When an electron passes parallel to the optical axis of a lens, the electron intersects with the optical axis at the back focal plane. The "focal length" is the distance from the center of the lens to the focal plane along the optical axis. The focal length of the objective lens ranges 0.5 to 4 mm depending on the target of observation.

46. focal depth (depth of focus)

The "focal depth (depth of focus)" is the range of distances for which the object is imaged with an acceptable sharpness on the image plane. The focal depth is proportional to the spatial resolution of a microscope and to the square of magnification, and inversely proportional to the aperture angle. In the case of a TEM, since the aperture angle is smaller than that of an optical microscope, the focal depth is large. For example, if the magnification is 10,000×, the aperture angle is 1×10-3 rad, and the resolution is 1 nm, the focal depth reaches 100 m.

47. focal plane

47-1. focal plane

A plane that is normal to the optical axis and passes through the focal point.

47-2. back focal plane

A focal plane located in the opposite side of the object (plane) with respect to a lens is called the back focal plane. A diffraction pattern is formed on the "back focal plane," thus the plane corresponds to the reciprocal space of the specimen.

Related term 
reciprocal space

48. stigmatic focus

"Stigmatic focus" means image formation without off-axial astigmatism. For example, in the original Wien filter, focusing action occurs only in the electric field direction but does not occur in the magnetic field direction. Thus, even when an incident beam to the filter is circular, a liner beam is obtained on the image plane. To accomplish astigmatism-free imaging in the Wien filter, application of curved electric and magnetic fields produces magnetic components in the original electric field direction and thus attains the focusing action in the original magnetic field direction.

Related term
Wien filter

49. stigmator

An instrument inserted below the objective lens, which is used to correct the axial astigmatism. This astigmatism can be corrected by a set of four-pole electromagnetic coils (quadrupole), but a real "stigmator" uses two pairs of quadrupoles for operation convenience.

Related term
axial astigmatism, quadrupole

50. selected-area aperture (intermediate-lens aperture)

An aperture for selecting a specimen area in the selected area diffraction (SAD) mode. The aperture is inserted into the image plane of the objective lens (or object plane of the intermediate lens). The aperture diameter ranges normally from 10 μm to 100 μm.

Related term
selected-area diffraction, SAD

51. electrostatic lens

A lens that converges electron beams by an electrostatic field. Since the "electrostatic lens" has larger aberration than the magnetic field lens, the former lens is not used for imaging but used for acceleration and deceleration of the electron beams.

Related term
electromagnetic lens

52. pre-magnetic field

In a modern electron microscope, a specimen is placed in the objective lens. The magnetic field produced above the specimen (at the condenser lens side) is called "pre-magnetic field."

53. image rotation

53-1．image rotation

A phenomenon of an image rotation when the magnification is changed in a TEM, which is inconvenient for image observation. The second and third parts of the intermediate lens system that have opposite excitations to each other are designed to cancel or to minimize the image rotation.

Related term
rotation-free image

53-2．rotation-free image

"Rotation-free image" means an image that does not rotate even when the magnification is changed. To prevent both inconvenience caused by the change of an observation position and disappearance of the orientation relationship between the diffraction pattern (magnification: zero) and the corresponding image, an image rotation created by the first two-parts of the intermediate lens are corrected by the final-part of the intermediate lens, so that the image rotation is eliminated or minimized. When the excitation of the third- (final-) part is changed, the magnification is also changed. Thus, it is necessary to change the excitation of the second part of the lens. Combinations of appropriate excitation of each part in obtaining a rotation-free image are available in tables.

Related term 
intermediate lens

54. scanning coil

Electromagnetic coil(s) used to scan a target area with an electron beam.

55. objective lens

55-1．condenser-objective lens (C-O lens)

The "condenser-objective lens (C-O lens)" makes the pre-magnetic field of the objective lens act as a condenser lens so that the electron beam is focused onto the specimen, and makes the post-magnetic field act as an objective lens to form the specimen image at the image plane. Since the electron beam is demagnfied to ～1/100 by the pre-magnetic field on the specimen, the C-O lens is essential for various purposes, such as CBED that requires sub-nanometer-area illumination, improvement of STEM image resolution, and decreasing of analysis region for EDS and EELS. To produce a parallel beam for HREM in the TEM mode, a condenser mini lens is used.

Related term
condenser mini lens

55-2. objective lens

The "objective lens" is the first-stage lens to form an image using electrons exiting from the specimen. The objective lens is the most important lens in the imaging lens system because the performance of this lens determines the image quality (resolution, contrast, etc). A good objective lens has both a small spherical aberration (Cs) coefficient and a small chromatic aberration (Cc) coefficient. To decrease these coefficients, shortening the distance between the two magnetic poles and decreasing the bore diameter of the polepiece and are required. Since the side-entry-type specimen holder is inserted between the two magnetic poles, there is a limitation on shortening the distance. For the top-entry-type specimen holder, an asymmetric popiece whose upper bore diameter is larger than that of the lower one is used.

Related term 
ultra-high-resolution polepiece, multiuse polepiece, high-contrast polepiece

55-3. objective mini lens

The "objective mini lens" is a weakly excited lens placed below the objective lens. This lens does not have a polepiece to strengthen a magnetic field as the objective lens does. This lens is used to form an image on the selector aperture in Low MAG mode (～50× to 3,000×) by stopping the excitation of the objective lens. The magnification at the objective mini lens is 1× to 2×. This lens is also used to obtain a high quality low magnification image of about 1,000× in the MAG mode. That is, the excitation of the objective lens is kept strong to maintain image quality of the objective-lens, and the image is demagnified (to ～0.5×) by the objective mini lens, thus a wide view image is formed on the object plane of the intermediate lens.

Related term 
objective lens, condenser mini lens

56. multiuse polepiece

The "multiuse polepiece" allows the specimen holder to be tilted to more than ±35°. This polepiece makes it possible to attain a Cs of 1.0 mm, a Cc of 1.4 mm and a spatial resolution for TEM image of 0.23 nm at an accelerating voltage of 200 kV. For analytical case, the objective aperture is inserted below the lower pole of the polepiece to avoid unnecessary X-rays from the aperture. This aperture setting causes a problem that the diffraction pattern is not formed on the aperture plane, which leads to a difficulty in acquiring the dark field image from one diffraction spot and the bright field image without the influence of surrounding diffraction spots. It is noted that there is option to insert a special aperture at the polepiece gap to obtain correct bright- and dark-field images.

Related term
ultra-high-resolution polepiece, high-contrast polepiece

57. intermediate lens

57-1. intermediate lens

The "intermediate lens" is placed between the objective lens and the projector lens. The intermediate lens works in the following way. The intermediate lens changes focusing position either on a diffraction pattern or a TEM image produced by the objective lens by adjusting its excitation, and forms the magnified pattern or image on the object plane of the projector lens. Normally, the intermediate lens consists of three parts: The first part mainly selects focusing position, the second part magnifies the focused pattern or image, and the third part mainly achieves rotation-free condition. The magnification of the intermediate lens is varied from ～0.5× to ～100×. When the total magnification is 100×, the magnifications for the first, second and third parts are 4× to 5×, ～10×, and 2× to 3×, respectively.

Related term
objective lens, projector (projection) lens

57-2. selected-area aperture (intermediate-lens aperture)

An aperture for selecting a specimen area in the selected area diffraction (SAD) mode. The aperture is inserted into the image plane of the objective lens (or object plane of the intermediate lens). The aperture diameter ranges normally from 10 μm to 100 μm.

Related term
selected-area diffraction, SAD

58. accelerating (acceleration) voltage center

When fluctuations are added to accelerating voltage using a high-tension wobbler, a TEM image spirally enlarges and shrinks. The center of this enlargement and shrinkage is called "accelerating (acceleration) voltage center." Alignment of the accelerating voltage center is carried out to bring the accelerating voltage center to the center of the fluorescent screen for viewing the image by the use of a double-deflection coil system. Since the fluctuations of the high voltage are small (<10-6), this alignment is used to minimize the effect of energy spread due to inelastic scattering (plasmon scattering) in a specimen rather than the effect of high-voltage fluctuations. This alignment is required when taking images at a medium magnification lower than 100,000×.

Related term
high-tension wobbler, double-deflection system, objective current center

59. electron trajectory

An "electron trajectory" is defined as the path of motion of an electron in an electromagnetic field, where the electron is regarded as a mass point having a negative charge.

60. electron optics

A field of optics that discusses electron trajectories in electromagnetic fields in analogue of geometrical light optics.

61. electron optical system

A system composed of basic elements, such as electromagnetic lenses，electrostatic lenses and deflection coils to execute the magnification, demagnification, energy dispersion etc. of the electron beam.

Related term
electromagnetic lens, electrostatic lens

62. electron biprism

An "electron biprism" is an electron-wave interferometer to obtain an electron hologram in the first step of electron holography. The electron biprism consists of a fine string electrode placed at the center of the incident electron beam (perpendicular to the electron beam) and parallel-plate ground electrodes placed at the both sides of the string electrode (parallel to the electron beam). The biprism is located below the objective lens in a TEM. A positive voltage is applied to the string electrode, so that the scattered wave transmitted through the object (object wave) passes through one side of the electrode whereas the wave directly coming from the electron source passes through the other side of the electrode. These two waves are attracted each other by the positive potential, and are superposed to form interference fringes (hologram). The interference fringes contain information on the change of the amplitude and phase of the object wave.

Related term
electron holography, electron hologram

63. electron lens

A lens that performs action of convergence on electron beams similar to the lens action of an optical lens on light rays. The "electron lens" is classified into the magnetic-field type and the electric-field type. The former is called the electromagnetic lens, and the latter is the electrostatic lens.

Related term
electromagnetic lens, electrostatic lens

64. electromagnetic lens

A lens that converges electron beams by a magnetic field. The magnetic field in the lens, which bends electron beams, is generated by a solenoid magnet. By changing the electric current to the solenoid, the generated magnetic field is changed, leading to changes of the focal length and magnification.

Related term
electrostatic lens

65. objective current center

When fluctuations are added to the excitation current of the objective lens, a TEM image spirally enlarges and shrinks. The center of this enlargement and shrinkage is called "objective current center." Alignment of the objective current center is carried out to bring the objective current center to the center of the fluorescent screen for viewing the image by the use of a double-deflection coil system. Since the fluctuations of objective-lens current are small, normally the alignment of the objective current center is not performed, but the alignment of the accelerating voltage center is carried out.

Related term 
double-deflection system, accelerating (acceleration) voltage center

66. projector (projection) lens

The "projector (projection) lens" is the final lens in the imaging lens system. The projector lens further magnifies the image magnified by the intermediate lens, and then forms the final image on the fluorescent screen or the detector. The magnification of this lens is fixed at a value of ～150×.

67. inverted image

An image inverted in the vertical and horizontal directions. That is, an "inverted image" is obtained by a 180° rotation of a real image.

68. acceptance angle

An angle that accepts electrons or X-rays exiting from the specimen with the objective aperture or the detector when acquiring a TEM image, an EELS spectrum, or an EDS spectrum.

69. double-deflection system

The "double-deflection system" is designed in such a way that two pairs of deflection coils are arranged in the vertical direction. The "double-deflection system" is composed of two pairs of deflection coils. It is placed between the objective lens and the second condenser lens. The electron beam is deflected by the first-stage coils and then, the deflected electron beam is deflected again by the second-stage coils. The system is used for various purposes, such as adjustment of the accelerating voltage center, acquisition of a dark-field image without blurring due to spherical aberration of the objective lens, taking a STEM image, and hollow-cone beam illumination.

Related term
accelerating (acceleration) voltage center, scanning transmission electron microscope (STEM) image, hollow-cone beam illumination

70. incidence angle

The angle between the normal of a specimen plane and the incident electron beam. In HREM image observation, it is essential to align the incidence direction of the electron beam with the zone axis of the specimen crystal with high accuracy.

Related term
high-resolution electron microscopy, HREM

71. high-contrast polepiece

When the high-resolution polepiece or the multiuse polepiece is used, the lens excitation is strong. As a result, the focal length of the objective lens is shortened and a diffraction pattern is formed above the objective aperture. The aperture cannot often select one diffraction spot but contain the effect of neighboring diffraction spots. The bright-field and dark-field images are influenced by other diffraction spots. To improve this failure, a polepiece that enables acquisition of one diffraction spot is available, which is called the "high-contrast polepiece." In this polepiece, the magnetic field produced is weakened a little by broadening the polepiece gap so that the diffraction pattern is formed on the objective aperture. For this polepiece, a Cs of 3.3 mm, a Cc of 3.0 mm and a spatial resolution for TEM image of 0.31 nm at an accelerating voltage of 200 kV have been attained. Also, the high-contrast polepiece allows the specimen holder to be tilted to ±(30° to 35°). It is used for bright and dark field microscopy of texture analysis of materials and for the studies of biological specimens.

Related term
ultra-high-resolution polepiece, multiuse polepiece

72. octupole (octopole)

A component consisting of eight magnetic coils symmetrically placed with respect to the optical axis, which is used for spherical aberration correction of the objective lens.

Related term
Cs corrector

73. wave aberration

The difference between the wavefront W of ideal imaging with no aberrations (Gauss imaging) and the wavefront S in actual imaging with various aberrations is called “wave aberration.” It is defined as the optical path difference between wavefronts W and S measured along an electron trajectory given by geometrical optics. The wave aberrations neccessary for the interpretation of a high-resolution image are axial aberrations (spherical aberration and parasitic aberrations).

Related term
geometrical aberration, Five Seidel aberrations, spherical aberration, parasitic aberration

74. hysteresis

"Hysteresis" is a phenomenon where the state of a system depends on its undergoing progress, and a physical effect occurs at a delayed time against a given physical impact. In the case of TEM, the relevant phenomenon occurs in the lens action. The accuracy of the positional reproducibility of the electron probe on a specimen due to the hysteresis of the condenser lens affects the operability of a TEM. The excitation of the intermediate lens is frequently changed in obtaining different magnifications and at switching between the diffraction mode and image mode. The error of magnifications due to the hysteresis of the intermediate lens ranges from 5 to 10% though depending on the operation mode. For the objective and projector lenses, the hysteresis does not become a problem because the excitations of those lenses are almost fixed.

75. astigmatic difference

A measure of the axial astigmatism of an objective lens. This is expressed as the difference of the focal length in the two orthogonal directions. The "astigmatic difference" of an objective lens has been decreased down to 1.5 μm or less.

Related term
axial astigmatism

76. axial astigmatism

76-1．axial astigmatism

If an electromagnetic lens (objective lens) does not have perfect axial symmetry, a circular image of the light source (electron source) deforms to an ellipse image. This aberration is called "axial astigmatism." The axial aberration arises from asymmetry of the polepiece bore of the lens, magnetic non-uniformity of the polepiece material, charging on the aperture, etc.

Related term
stigmator, astigmatic difference, parasitic aberration

76-2．off-axial astigmatism and curvature of image field

When electron beams exiting from a circular object centered on the optical axis do not form a perfect circle but form an ellipse on the image plane, this defect is called "off-axial astigmatism." This astigmatism arises from the fact that the lens action (curvature of the lens) is different for the rays in the two orthogonal planes, that is, for the rays in the plane including the optical axis (tangential plane) and for the rays in the plane normal to the tangential plane but not including the optical axis (sagittal plane). "Curvature of image field" is the aberration that the image plane is deformed from a flat plane to a curved plane. The distance from an off-axis object point to the principal point of the lens (the center of the lens) is longer than the distance from the point on the optical axis at the object plane to the principal point. Thus, the distance from the principal point to the image point for the former ray becomes shorter than that for the latter ray. As a result, the image plane deviates from the Gaussian (flat) plane to a curved plane as the image point goes away from the optical axis. The curvature of image field is different for the two orthogonal directions or for the tangential and sagittal directions due to the off-axial astigmatism.

Related term 
Five Seidel aberrations

77. stigmator

An instrument inserted below the objective lens, which is used to correct the axial astigmatism. This astigmatism can be corrected by a set of four-pole electromagnetic coils (quadrupole), but a real "stigmator" uses two pairs of quadrupoles for operation convenience.

Related term
axial astigmatism, quadrupole

78．divergence angle

The "divergence angle" expresses the divergence of an electron beam as a semi-angle. The divergence angle of the electron beam to a specimen is determined by the excitation of the second condenser lens and the condenser mini lens, and the diameter of the condenser aperture, when the objective-lens excitation is fixed.

Related term
aperture diameter

79．deflection coil

Coil(s) that produce a magnetic field to deflect an electron beam.

Related term
double-deflection system

80．hollow-cone beam illumination

A beam illumination method by which a cone-shaped electron beam is produced. In the method, the beam is tilted to a certain angle against the optical axis by the first-stage deflection coils and is tilted back by the second-stage deflection coils to illuminate the same position on the specimen, and then the beam is rotated with respect to the optical axis kept the same illumination position. The method is used to wipe out diffraction contrast in the bright- and dark-field images and to observe the symmetries produced only by HOLZ lines without strong intensity due to ZOLZ interaction in the CBED pattern.

Related term
double-deflection system

81. rotation-free image

"Rotation-free image" means an image that does not rotate even when the magnification is changed. To prevent both inconvenience caused by the change of an observation position and disappearance of the orientation relationship between the diffraction pattern (magnification: zero) and the corresponding image, an image rotation created by the first two-parts of the intermediate lens are corrected by the final-part of the intermediate lens, so that the image rotation is eliminated or minimized. When the excitation of the third- (final-) part is changed, the magnification is also changed. Thus, it is necessary to change the excitation of the second part of the lens. Combinations of appropriate excitation of each part in obtaining a rotation-free image are available in tables.

elated term
intermediate lens

82. yoke

A "yoke" is made of ferromagnetic iron, encloses the excitation coil of a lens and efficiently guides the magnetic flux produced by the coil to the magnetic polepiece.

Related term
polepiece

83. quadrupole

A component consisting of four magnetic coils symmetrically placed with respect to the optical axis, which is used for correction of axial astigmatism of the objective lens by varying the focal lengths in the two orthogonal directions.

Related term
stigmator

84. excitation current

An electric current flowing through the lens coil to generate a magnetic field. The "excitation current" is varied to change the magnification and the focal length of the lens. Fluctuations of the excitation current give rise to chromatic aberration.

85. Lorentz force

A force that acts on electrons moving in electric and magnetic fields.

86. six-fold astigmatism

"Six-fold astigmatism" is one of the fifth-order parasitic aberrations having six-fold symmetry. ("Two-fold astigmatism," which is conventionally called "astigmatism" has two-fold symmetry.) In the case of a current Cs corrector of the two-stage three-fold-field type, a six-fold astigmatism is generated as a combination of the aberrations of the three-fold fields in the two stages. The six-fold astigmatism is the largest aberration when the third-order spherical aberration, parasitic aberrations up to the fourth order and the fifth-order spherical aberration are successfully corrected. Thus, the aberration-corrected range is restricted by the six-fold astigmatism. A Ronchigram clearly shows a hexagonal shape pattern at its peripheral part, when the Cs corrector is incorporated in the illumination system. Two aberration correctors that can correct the six-fold astigmatism have been developed. One is an aberration corrector of a three-stage three-fold-field type composed of dodecapoles. This corrects the six-fold astigmatism by making the vector sum of the astigmatism produced in each three-fold field to be zero. Another is an aberration corrector of a two-stage three-fold-field type composed of hexapoles. This corrects the six-fold astigmatism using that of the opposite sign produced by the combination of the effect of the transfer lens and the three-fold field through optimizing the length of the hexapoles.

Related term
axial astigmatism, combination aberration

87. hexapole (sextupole)

A component consisting of six magnetic coils symmetrically placed with respect to the optical axis, which is used for spherical aberration correction of the objective lens.

Related term
Cs corrector

88．distortion

88-1. S-shaped distortion

"S-shaped distortion" means the distortion characteristic of the electromagnetic lens for the electron beam. Unlike the light beam in the optical lens, the electron beam suffers rotation in the electromagnetic lens. The rotation magnitude increases as the electron beam deviates from the optical axis, and then an image that should be observed as a line on the image plane (fluorescent screen) is viewed as an s-shaped image. The distortion becomes a problem for the projector lens because there exist electron beams which pass largely apart from the optical axis. Combination of lenses with opposite polarity can cancel the distortion, but this technique has not been used yet.

88-2．distortion

An aberration where an image does not exhibit rectilinear projection of an object. This aberration, "distortion" produces pin-cushion and barrel distortion for a square object. It should be noted that this aberration distorts the image but does not produce a blurred image as other aberrations do. In a TEM, the distortion becomes a matter of concern for the projector lens. In TEMs of previous generations, a distortion correction method was adopted, in which the barrel distortion of the intermediate lens was compensated by the pin-cushion distortion of the projector lens by setting the excitations of the intermediate and projector lenses to a similar value. In modern TEMs, however, the technique is not used to fix the projector lens to a strong excitation and to vary the excitation of the intermediate lens. In a real TEM, the image distortion is not serious because the distance from the projector lens to the viewing plane is large.

Related term
Five Seidel aberrations

89. three-fold astigmatism

The three-fold astigmatism, one of the second-order axial geometrical aberrations, is a parasitic aberration exhibiting three-fold symmetry. (Note that it is called a third-order aberration in terms of the wave aberration.) The aberration is corrected using magnetic fields produced by hexapoles. A widely used two-stage hexapole Cs corrector corrects the spherical aberration of the objective lens using a combination effect in the three-fold astigmatism field. In the Cs correction system, the first hexapole simultaneously produces a large three-fold astigmatism and a negative spherical aberration. Then, the second hexapole placed below the first hexapole produces a three-fold astigmatism having an opposite sense to the former and a negative spherical aberration. The three-fold astigmatism produced in the first stage is canceled by that with an opposite sense produced in the second stage. The positive spherical aberration of the objective lens is corrected by the negative spherical aberration produced in the two stages.

Related term
parasitic aberration, wave aberration, axial geometrical aberration, combination aberration, Cs corrector

90. star aberration

The star aberration, one of the third-order axial geometrical aberrations, is a parasitic aberration exhibiting two-fold symmetry. (Note that it is called a fourth-order aberration in terms of the wave aberration.) The star aberration cannot usually be detected due to the existence of a large spherical aberration of the objective lens, but is detected after correcting the spherical aberration of the objective lens. The star aberration appears as a pattern with a two-fold symmetry in high angle areas of a Ronchigram. In the case of a TEM equipped with a Cs corrector, prior to microscope observation, aberrations are measured and then the aberrations including the star aberration are corrected by the automatic aberration correction function with the use of the deflectors of the Cs corrector.

Related term
parasitic aberration, axial geometrical aberration, wave aberration

91. four-fold astigmatism

The four-fold astigmatism, one of the third-order axial geometrical aberrations, is a parasitic aberration exhibiting four-fold symmetry. (Note that it is called a fourth-order aberration in terms of the wave aberration.) The four-fold astigmatism appears as a pattern with four-fold symmetry in a Ronchigram. In the case of a TEM equipped with a Cs corrector, prior to microscope observation, aberrations are measured and then the aberrations including the four-fold astigmatism are corrected by the automatic aberration correction function with the use of the deflectors of the Cs corrector. It is possible to produce a four-fold astigmatism using magnetic octupole fields. In an octupole Cs corrector, the spherical aberration of the objective lens is corrected using the four-fold astigmatism by utilizing the fact that the four-fold astigmatism has the same order as that of the third-order spherical aberration of the objective lens to be corrected.

Related term
parasitic aberration, axial geometrical aberration, wave aberration, star aberration

92. three-lobe aberration

The three-lobe aberration, one of the fourth-order axial geometrical aberrations, is a parasitic aberration exhibiting three-fold symmetry. (Note that it is called a fifth-order aberration in terms of the wave aberration.) In addition to the three-lobe aberration, the fourth-order axial geometrical aberrations include the fourth-order coma aberration and the five-fold astigmatism. In the aberrations exhibiting three-fold symmetry, there is the three-fold astigmatism which is the second-order axial geometrical aberration and a low order aberration compared to the three-lobe aberration. In a two-stage hexapole Cs corrector, even when the three-fold astigmatism is corrected, a Ronchigram sometimes exhibits a three-fold symmetry pattern at its high angle areas. This pattern can be due to the residual three-lobe aberration.

Related term
parasitic aberration, axial geometrical aberration, wave aberration, three-fold astigmatism

93. axial geometrical aberration

The axial geometrical aberrations are aberrations depending only on α, angle between the beam and the optical axis. The axial geometrical aberrations are defocus, two-fold astigmatism, three-fold astigmatism, axial coma aberration, spherical aberration, four-fold astigmatism, star aberration, etc. On the other hand, aberrations that depend on α and r, distance of an electron beam from the optical axis, are called “off-axial (geometrical) aberrations.” As an example of the off-axial aberrations, the coma aberration of Five Seidel aberrations is mentioned. In the case of high-resolution electron microscopy (HREM), the field of view is very narrow because its magnification is very high. Thus, the off-axial geometrical aberrations can be ignored, enabling us to account for only the axial geometrical aberrations. In the case of scanning transmission electron microscopy (STEM), a converged electron probe on the optical axis scans a specimen area. Only the axial geometrical aberrations are accounted for in STEM image formation as in the case of HREM.

Related term
geometrical aberration

94. Cc corrector

The Cc corrector makes the chromatic aberration of the image-forming lens or the probe-forming lens to be 0 (zero) by producing a negative chromatic aberration. To produce the negative chromatic aberration, the corrector uses a quadrupole field formed by the superposition of an electrostatic field and a magnetostatic field. Multi-stage multi-poles are used to create the quadrupole field. The cylindrically symmetric convex lens of the magnetic field type or the electric filed type, which is used for electron microscopes, always possesses a positive chromatic aberration. Thus, electrons having a lower velocity are more largely deflected toward the convergence direction (inward). On the other hand, the quadrupole field of the Cc corrector exhibits a negative energy dispersion, which is opposite to that of the convex lens. Thus, the Cc corrector makes the electrons having a lower velocity to deflect more largely toward the divergence direction (outward). Therefore, incorporation of the Cc corrector into the convex lens system enables the positive chromatic aberration of the lens system to cancel with the negative chromatic aberration produced by the quadrupole field, making the chromatic aberration of the entire lens system of the electron microscope to be zero.

Related term
chromatic aberration, Cs corrector

95. Zernike phase contrast

In TEM, "Zernike phase contrast" means contrast which is obtained by converting the phase change of electron waves scattered by a specimen into the amplitude change. The conversion is performed by using a phase plate or a combined effect of the spherical aberration of the electron lens and defocus.

(a) Conventional TEM (C-TEM) image. (b) Zernike phase contrast (ZPC-TEM) image of an ice-embedded T4 phage taken at an accelerating voltage of 200 kV. (c) Schematic of T4 phage.

Compared with the C-TEM image, the ZPC-TEM image clearly visualizes the fine structures of DNA in a capsid, the hair-like structural objects and the cylindrical structures on the capsid surface.