Patent Publication Number: US-7723683-B2

Title: Aberration correction system

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an aberration correction system for use in a transmission electron microscope and, more particularly, to an aberration correction system using three stages of multipole elements each producing a field of 3-fold symmetry. 
   2. Description of Related Art 
   One of the factors that limit the spatial resolution of an electron microscope is a variety of aberrations in the optical system. Especially, spherical aberration, which is one of such aberration, limits the spatial resolution because an axisymmetric lens always has a positive spherical aberration coefficient. This creates an intrinsic problem. 
   This problem has been dealt with in A. V. Crewe and D. Kopf,  Optik , Vol. 55 (1980), pp. 1-10, where a result of a theoretical analysis has been shown. That is, a single stage hexapole element having a thickness along the optical axis has a negative spherical aberration coefficient. This suggests that spherical aberration can be reduced by introducing a hexapole element into the optical system. Subsequently, it has been pointed out that if only the single stage hexapole element is used, a second-order aberration occurs. Accordingly, incorporating a single stage hexapole element in a transmission electron microscope results in low usefulness. However, the fact that a hexapole element produces a negative spherical aberration coefficient is very useful to correction of spherical aberration. Techniques for reducing spherical aberration using hexapole elements have been improved further. 
   An example in which an aberration correction system equipped with a hexapole element having a negative spherical aberration and a thickness along the optical axis is applied to a transmission electron microscope is proposed in H. Rose,  Optik , Vol. 85 (1990), pp. 19-24. This aberration correction system has a first transfer lens, a first hexapole element, a second transfer lens, and a second hexapole element arranged in turn. In this system, each transfer lens has two axisymmetric lenses. 
   An aberration correction system having two stages of multipole elements each having a thickness along the optical axis is shown in JP-A-2003-92078. This system has two stages of multipole elements (e.g., hexapole elements) and a transfer lens interposed between them. Each multipole element produces a field of 3-fold symmetry, generating a 3-fold astigmatism and a negative spherical aberration. 
   In the system of the above-cited JP-A-2003-92078, the rear stage of multipole element operates to cancel out the 3-fold astigmatism produced by the front stage multipole element and, therefore, the whole optical system produces a negative spherical aberration. Consequently, where an axisymmetric lens (e.g., an objective lens) producing a positive spherical aberration is disposed ahead of or behind the system, the spherical aberration in the whole optical system is reduced. 
   However, the above-described aberration-correcting techniques correct aberrations only up to the fourth order and cannot achieve complete correction of higher-order aberrations. For example, fifth-order spherical aberration can be corrected by optically controlling the distance between the objective lens and the aberration corrector but astigmatism of the same order (i.e., 6-fold astigmatism) cannot be corrected. Because this is a factor limiting aberration correction, it cannot be expected that the spatial resolution will be improved further. 
   An actual multipole element has a finite thickness along the optical axis. Where this multipole element produces a magnetic or electric field with 3-fold symmetry, if the spherical aberration is corrected by the multipole element, higher-order aberrations dependent on the thickness are induced. Furthermore, the combination of the two stages produces higher-order aberrations. Consequently, the range of incident angles of the electron beam that can be aberration-corrected is limited. This limitation makes it difficult to reduce diffraction aberration. 
   This limitation to the angles is further described by referring to the Ronchigram of  FIG. 7 . This diagram is obtained when an electron beam passing through two stages of multipole elements is corrected for aberrations, each of the multipole elements producing a magnetic field of 3-fold symmetry with respect to the optical axis. A low-contrast region appearing in the center of the diagram corresponds to the angle of incidence of the electron beam on each multipole element, the beam having been appropriately corrected for aberrations. Where a maximum value of the angle of incidence is roughly described, a maximum circle centered at the central point of the region and including only the region is fitted. The angle of incidence of the electron beam is computed from the radius of the circle. It can be seen from the diagram of  FIG. 7  that the maximum incident angle of the electron beam that has been appropriately corrected for aberrations is about 50 mrad. 
   However, where regions located around the circle are noticed, one can observe that a region where an amorphous image is seen is hexagonal, because the fifth-order aberration, or the sixth-order astigmatism, is left as a residual aberration. In the case of the multipole elements producing the diagram of  FIG. 7 , the angle of incidence of the electron beam that can be corrected for aberrations is 50 mrad at maximum. It is difficult to appropriately correct the electron beam having a greater angle of incidence for aberrations. Accordingly, if one tries to reduce diffraction aberration, the spatial resolution is limited due to the limitation on the angle of incidence. 
   Higher-order aberrations (6-fold astigmatisms) produced from multipole elements that generate fields of 3-fold symmetry is induced because the magnetic or electric fields are distributed in directions to cancel out their mutual astigmatisms of 3-fold symmetry. That is, if multipole elements are rotated relative to each other such that each multipole element is rotated through 60° or 180° relative to the magnetic or electric field as in the prior art, higher-order aberrations are produced. 
   SUMMARY OF THE INVENTION 
   Accordingly, it is an object of the present invention to provide an aberration correction system which is for use in an electron microscope and which corrects the above-described higher-order aberrations while holding a negative spherical aberration. 
   This object is achieved by an aberration correction system having three stages of multipole elements arranged in a row along an optical axis, each of the multipole elements having a thickness along the optical axis. The three stages of multipole elements include a front stage of multipole element, a middle stage of multipole element, and a rear stage of multipole element. The front stage of multipole element produces a first magnetic or electric field that shows a 3-fold symmetry with respect to the optical axis. The middle stage of multipole element produces a second magnetic or electric field that shows a 3-fold symmetry with respect to the optical axis. The rear stage of multipole element produces a third magnetic or electric field that shows a 3-fold symmetry with respect to the optical axis. Within the second magnetic or electric field, a distribution of a magnetic or electric field of 3-fold symmetry is produced in a direction not to cancel out an astigmatism of 3-fold symmetry produced from the first magnetic or electric field or from the third magnetic or electric field. Within the third magnetic or electric field, a distribution of a magnetic or electric field of 3-fold symmetry is produced in a direction not to cancel out an astigmatism of 3-fold symmetry produced from the first magnetic or electric field or from the third magnetic or electric field. An aberration of 3-fold symmetry produced by the front stage of multipole element is rotated using the middle stage of multipole element. An aberration of 3-fold symmetry produced by the middle stage of multipole element is rotated using the rear stage of multipole element. The fields produced by the three stages of multipole elements are combined to cancel out their mutual astigmatisms of 3-fold symmetry. The aforementioned rotation is an electron optical angular rotation made when a field produced by one multipole element is transferred to the next multipole element. Rotating action of each lens is taken into consideration. That is, a magnetic lens produces a rotating action about the optical axis, as well as a transferring action and a magnification-varying action. The rotating action is affected by the accelerating voltage and by the strength of the magnetic field. With respect to the distributions of the fields produced by the multipole elements located, respectively, ahead of and behind the magnetic lens, the rotational positional relationship between the 3-fold astigmatisms of two multipole elements must be discussed taking account of rotation induced by the lens. In the present specification, rotational positional relationships are set forth on the assumption that an angle given by this rotation is zero. That the electron optical rotational relation is taken into consideration means that this rotation is taken into consideration. 
   In another feature of the present invention, the angular relational relationship between the magnetic or electric fields produced by the multipole elements is set as follows. Any one of the second and third magnetic or electric field is rotated through an angle of 40° relative to the first magnetic or electric field, taking account of the rotating action of an electron optical lens within a plane perpendicular to the optical axis. The other is rotated through 80° relative to the first magnetic or electric field, taking account of the rotating action of the electron optical lens within the plane perpendicular to the optical axis. The second magnetic or electric field and the third magnetic or electric field are so distributed that they are rotated in the same direction. A field of 3-fold symmetry has a rotational symmetry of 120°. Where a mirror-symmetric system is taken into consideration, rotational positional relationships given by 40° and 80° are equivalent to 120°×m±40° and 120°×m±80°, respectively. 
   In another feature of the present invention, the angular relational relationship between the magnetic or electric fields produced by the multipole elements is set as follows. The second magnetic or electric field is so distributed that it is rotated through 120°×m±about 72° (where m is an integer) relative to the first magnetic or electric field, taking account of the rotating action of an electron optical lens within a plane perpendicular to the optical axis. The third magnetic or electric field is so distributed that it is rotated through 120°×m±about 24° relative to the first magnetic or electric field, taking account of the rotating action of the electron optical lens within the plane perpendicular to the optical axis. 
   According to the above-described configuration, 3-fold astigmatism and 6-fold astigmatism can be removed while producing a negative spherical aberration and, therefore, the spatial resolution is improved. Furthermore, the range of incident angles in which aberration correction can be made can be widened. This reduces diffraction aberration and further improves the spatial resolution. 
   Other objects and features of the invention will appear in the course of the description thereof, which follows. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a ray diagram illustrating aberrations produced by a single stage multipole element having a thickness along an optical axis; 
       FIG. 2   a  is a schematic diagram of an aberration correction system associated with an embodiment of the present invention; 
       FIGS. 2   b - 2   g  are schematic diagrams showing arrangements of multipole elements; 
       FIG. 3  is a schematic ray diagram of an aberration correction system associated with one embodiment of the present invention, and in which first and second transfer lenses are mounted; 
       FIG. 4  is a schematic ray diagram of an aberration correction system associated with one embodiment of the present invention, and in which first, second, and third transfer lenses are mounted; 
       FIG. 5  is a block diagram of a transmission electron microscope having an illumination system aberration corrector made of an aberration correction system associated with one embodiment of the present invention; 
       FIG. 6  is a block diagram of a transmission electron microscope having an imaging system aberration corrector made of an aberration correction system associated with one embodiment of the present invention; 
       FIG. 7  is a representation of a Ronchigram obtained according to the prior art by passing an electron beam through two stages of multipole elements each having a thickness along an optical axis; and 
       FIG. 8  is a graph showing the relationship of the amount of 6-fold astigmatism to the angle made between fields of 3-fold symmetry respectively produced by a front stage of multipole element and a rear stage of multipole element. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   First, aberrations produced when an electron beam passes through both a single stage multipole element and an objective lens are described, the multipole element having a thickness along the optical axis.  FIG. 1  is a schematic ray diagram of aberrations produced on a surface of a specimen when the electron beam has passed through the single stage of multipole element. 
   The single stage of multipole element  102  (e.g., a hexapole element) and the objective lens  103  are arranged in a row along the optical axis  101 . It is assumed that the multipole element  102  produces a magnetic or electric field that shows 3-fold symmetry with respect to the optical axis  101 . After passing through the multipole element  102 , the beam  100  is focused onto the surface  104  of the specimen by the objective lens  103 . The complex angle Ω 0  of the electron beam incident on the multipole element  102  is defined by
 
Ω 0 =α exp( i φ)  (1)
 
   The complex angle Ω 0  is represented by two variables α and φ. The variable α is the angle at which the beam impinges on the specimen. The variable φ is a phase angle (azimuth). Without using α and φ which are employed in a cylindrical coordinate system, the complex angle can be written as follows using coordinate coordinates (u, v):
 
Ω=ω u   +iω   v  
 
Note, however, that if the spatial frequencies of a reciprocal space are given by (u, v), it follows that (ω u , ω v )=λ(u, v). This complex conjugate is given by
 
  Ω   0 =α exp(− i φ)  (2)
 
   Then, let z be the thickness (length) of the multipole element  102  along the optical axis  101 . Let f be the focal distance of the objective lens. It is assumed that the optical distance L between the multipole element  102  and the objective lens  103  is 0. The optical distance L can be adjusted, for example, by inserting a transfer lens between the multipole element  102  and the objective lens  103 . 
   Let r be the position of the electron beam  100  on the specimen surface  104 . Let r′ be the tilt (angle to the optical axis) of the beam. Under the above conditions, the position r and the tilt r′ are given by 
                 r   =         -     1     2   ⁢   f         ⁢     A   3     ⁢       Ω   _     0   2     ⁢     z   2       +         |     A   3     ⁢     |   2         12   ⁢     f   3         ⁢       Ω   _     0     ⁢     Ω   0   2     ⁢     z   4       -             A   _     3     |     A   3     ⁢     |   2         120   ⁢     f   5         ⁢     Ω   0   4     ⁢     z   6       -           A   3     |     A   3     ⁢     |   2         180   ⁢     f   5         ⁢     Ω   0     ⁢       Ω   _     0   3     ⁢     z   6       +           A   3   2     |     A   3     ⁢     |   2         3360   ⁢     f   5         ⁢       Ω   _     0   5     ⁢     z   8                 (   3   )                 r   ′     =         -     1   f       ⁢     A   3     ⁢       Ω   _     0   2     ⁢   z     +         |     A   3     ⁢     |   2         3   ⁢     f   3         ⁢       Ω   _     0     ⁢     Ω   0   2     ⁢     z   3       -             A   _     3     |     A   3     ⁢     |   2         20   ⁢     f   5         ⁢     Ω   0   4     ⁢     z   5       -           A   3     |     A   3     ⁢     |   2         30   ⁢     f   5         ⁢     Ω   0     ⁢       Ω   _     0   3     ⁢     z   5       +           A   3   2     |     A   3     ⁢     |   2         420   ⁢     f   5         ⁢       Ω   _     0   5     ⁢     z   7                 (   4   )               
where A 3  is the 3-fold astigmatism coefficient (per unit length). Let a 3  be the strength of the 3-fold astigmatism. Let  0  be the azimuthal angle of the 3-fold astigmatism. The 3-fold astigmatism coefficient is given by
   A   3   =a   3  exp  i (3θ)  (5)   A 3     (6) 
Eq. (6) gives the complex conjugate of A 3 .
 
   Each term of the right sides of Eqs. (3) and (4) represents an aberration. In particular, the first term of the right side of each equation indicates the second-order, 3-fold astigmatism. The second term indicates the third-order negative spherical aberration. The third and fourth terms indicate the fourth-order, three-lobe aberrations. The fifth term indicates the fifth-order, 6-fold astigmatism. 
   Aberrations appearing when a single stage of multipole element is used have been described so far. 
   Where two stages of multipole elements are prepared and 3-fold astigmatism produced from the first stage of multipole element is canceled, the position of the electron beam assumed after leaving the second stage of multipole element is given by 
   
     
       
         
           
             
               
                 
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   The first term of Eq. (7) is a negative spherical aberration intentionally produced to cancel out the spherical aberration in the objective lens. The second term produces a higher-order aberration (6-fold astigmatism) because the two stages of multipole elements are prepared and that the 3-fold astigmatism produced from the first stage of multipole element is canceled out. 
   Accordingly, in the present invention, three stages of multipole elements are prepared. The multipole elements are so operated that a combination of any two stages does not cancel out a 3-fold astigmatism. Rather, the three stages of multipole elements cancel out 3-fold astigmatisms. In this way, an optical system that cancels out the higher-order aberration is built. 
   One embodiment of the aberration correction system associated with the present invention is described.  FIG. 2   a  is a schematic diagram of an aberration correction system associated with an embodiment of the present invention. 
   As shown in  FIG. 2   a , the aberration correction system associated with the present embodiment is equipped with three stages of multipole elements producing fields of 3-fold symmetry with respect to the optical axis  11 . In this diagram, an electron beam  10  passes from a front stage of multipole element  21  to a rear stage of multipole element  23 . Then, the beam  10  passes through the coma-free plane  41  of an objective lens  40  that substantially corresponds to the front focal plane of the objective lens  40 . Subsequently, the beam is focused onto a specimen surface  42 . One example of each multipole element is a hexapole element. Another example is a dodecapole (12-pole) element. Each multipole element may have any number of poles as long as the element produces a field of 3-fold symmetry with respect to the optical axis  11 . 
   In the aberration correction system associated with the present embodiment, the field of 3-fold symmetry (second field of 3-fold symmetry) produced by the middle stage of multipole element  22  is so distributed that it has been rotated through 40° relative to the field of 3-fold symmetry (first field of 3-fold symmetry) produced by the front stage of multipole element  21  within the plane perpendicular to the optical axis  11 . Furthermore, the field of 3-fold symmetry (third field of 3-fold symmetry) produced by the rear stage of multipole element  23  is so distributed that it has been rotated through 80° relative to the field of 3-fold symmetry produced by the front stage of multipole element  21  within the plane perpendicular to the optical axis  11 . The fields of 3-fold symmetry produced by the middle stage of multipole element  22  and the rear stage of multipole element  23 , respectively, are so distributed that they have been rotated in the same direction relative to the field of 3-fold symmetry produced by the front stage of multipole element  21 . 
   Also, in the case where the three fields of 3-fold symmetry are distributed as described above, the characteristics of aberrations produced by one field of 3-fold symmetry are fundamentally given by Eqs. (3) and (4). Therefore, aberrations produced by the three fields of 3-fold symmetry in the present embodiment are found by a combination of these equations taking account of the rotational positional relationships among the fields of 3-fold symmetry. 
   Accordingly, it is assumed that the fields produced by the front stage of multipole element  21 , middle stage of multipole element  22 , and rear stage of multipole element  23  result in 3-fold astigmatism coefficients A 3A , A 3B , and A 3C , respectively. We now take note of only these coefficients. The 3-fold astigmatism coefficients produced by the fields of 3-fold symmetry are given by
 
 A   3A   =a   3  exp  i (3θ)
 
 A   3B   =a   3  exp  i (3(θ+40°))= a   3  exp  i (3θ+120°)
 
 A   3C   =a   3  exp  i (3(θ+80°))= a   3  exp  i (3θ+240°)  (8)
 
Therefore, the sum of them is given by
 
| A   3A   +A   3B   +A   3C |=0  (9)
 
It can be seen that the 3-fold astigmatisms are canceled out.
 
   On the other hand, a negative spherical aberration coefficient does not depend on the rotational positional relationships among the fields of 3-fold symmetry. Therefore, the negative spherical aberration coefficient has a magnitude that is three times as high as the intensity of the coefficient produced by one field of 3-fold symmetry. Consequently, the negative spherical aberration coefficient can be used for correction of the spherical aberration in the objective lens. 
   The 6-fold astigmatism appearing from within one multipole element is now discussed using Eq. (4). Similarly to Eq. (8), the 6-fold astigmatism coefficients possessed by the multipole elements, respectively, are given by
 
 A   3A   2   =a   3   2  exp  i (6θ)
 
 A   3B   2   =a   3   2  exp  i (6(θ+40°))= a   3   2  exp  i (6θ+240°)
 
 A   3C   2   =a   3   2  exp  i (6(θ+80°))= a   3   2  exp  i (6θ+480°)= a   3   2  exp  i (6θ+120°)  (10)
 
As a result, we obtain
 
| A   3A   2   +A   3B   2   +A   3C   2 |=0  (11)
 
That is, if the fields of 3-fold symmetry produced by the middle stage of multipole element  22  and rear stage of multipole element  23 , respectively, are so distributed that they have been rotated through 40° and 80°, respectively, in the same direction within the plane perpendicular to the optical axis  11  relative to the field of 3-fold symmetry produced by the front stage of multipole element, then the 6-fold astigmatism derived from Eq. (4) is canceled out. Consequently, the three stages of multipole elements  21 ,  22 ,  23  producing the above-described fields of 3-fold symmetry cancel out the 3-fold and 6-fold astigmatisms while producing a negative spherical aberration.
 
   In the above-described configuration, it can be seen that it does not matter which one of the fields of 3-fold symmetry rotated through 40° and 80°, respectively, relative to the field of 3-fold symmetry produced by the front stage of multipole element  21  is located ahead of the other. That is, the middle stage of multipole element  22  may produce a field of 3-fold symmetry rotated through 80° relative to the field of 3-fold symmetry produced by the front stage of multipole element  21 , and the rear stage of multipole element  23  may produce a field of 3-fold symmetry rotated through 40° relative to the field of 3-fold symmetry produced by the front stage of multipole element  21 . Also, in this case, the 3-fold astigmatism and 6-fold astigmatism are canceled out while a negative spherical aberration is produced. 
   The multipole elements producing the above-described three fields of 3-fold symmetry are arranged as follows. Any one of the middle stage of multipole element  22  and the rear stage of multipole element  23  is rotated through 40° relative to the front stage of multipole element  21  within the plane perpendicular to the optical axis  11 . The other is rotated through 80° within the plane perpendicular to the optical axis  11 . At this time, the middle stage of multipole element  22  and the rear stage of multipole element  23  are disposed to be rotated in the same direction.  FIGS. 2   b - 2   d  show one example of the arrangement of the multipole elements based on the above-described arrangement. In these figures, the arrangement of the front stage of multipole element  21  as viewed along the direction indicated by the arrow A from the origin O on the optical axis  11  shown in  FIG. 2   a  is indicated by  21   a . The arrangement of the middle stage of multipole element  22  is indicated by  22   a . The arrangement of the rear stage of multipole element  23  is indicated by  23   a . This rotational positional relationship needs to be noticed after a rotation is made by the transfer lens. If an electron optical rotation of 40° is achieved by the transfer lens, it does not matter whether the rotation of 40° is made physically. A field of 3-fold symmetry has a rotational symmetry of 120°. Where a mirror-symmetric system is considered, the rotational positional relationships given by 40° and 80°, respectively, are equivalent to 120°×m±40° and 120°×m±80°, respectively. 
   In the discussion made thus far using Eq. (4), a 6-fold astigmatism produced within a single multipole element has been noticed. 
   Then, using Eq. (7), a system is discussed in which a 6-fold astigmatism produced by interferences between 3-fold astigmatisms produced by two or more multipole elements is taken into consideration. 
   Three stages of multipole elements are prepared, and 3-fold astigmatisms are canceled out by the three stages. Let A 3A , A 3B , and A 3C  be 3-fold astigmatism coefficients produced by the front, middle, and rear stages of multipole elements, respectively. The tilt of the electron beam leaving the third stage of multipole element with respect to the 6-fold astigmatism is given by 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   As given by Eq. (12), if the three stages of fields of 3-fold symmetry are used, it is possible to make a setting in such a way as to cancel out a higher-order aberration (6-fold astigmatism) of the second term, because the magnitude of the higher-order aberration (6-fold astigmatism) of the second term is made of the coefficient of each 3-fold astigmatism. The three-lobe aberrations (fifth-order aberrations) of the aberrations of 3-fold symmetry can be corrected even by the prior art two-stage design as shown in  FIG. 7 . These aberrations can also be corrected by the three-stage design of the present invention. 
     FIG. 8  is a graph in which the amount of a higher-order aberration (6-fold astigmatism) produced when two stages of multipole elements are used is plotted on the vertical axis and the angle made between the multipole elements producing the 3-fold astigmatism coefficients A 3A  and A 3C  is plotted on the horizontal axis. The amount of the higher-order aberration has been normalized to 1 using Eq. (11) to indicate the relative amount of the 6-fold astigmatism. The system is so set that the 3-fold astigmatisms are canceled out by combining the fields of 3-fold symmetry produced by the three stages of multipole elements. 
   It can be seen that if the rotational positional relationship between the multipole elements producing the 3-fold astigmatism coefficients A 3A  and A 3C , respectively, is varied, the amount of the 6-fold astigmatism decreases and assumes a minimum value around 24°. In a region of less than ±6° about 24° (i.e., the angle made between the multipole elements producing the 3-fold astigmatism coefficients A 3A  and A 3C  is 72°±6°), the amount of the 6-fold astigmatism is less than half of the amount produced when two stages of multipole elements are combined. This demonstrates that the astigmatisms have been corrected effectively. 
   Thus, in the aberration correction system associated with another embodiment of the present invention, the field of 3-fold symmetry (second field of 3-fold symmetry) produced by the middle stage of multipole element  22  is distributed to have been rotated through about 72° relative to the field of 3-fold symmetry (first field of 3-fold symmetry) produced by the front stage of multipole element  21  within the plane perpendicular to the optical axis  11 . Furthermore, the field of 3-fold symmetry (third field of 3-fold symmetry) produced by the rear stage of multipole element  23  is distributed to have been rotated through about 24° relative to the field of 3-fold symmetry produced by the front stage of multipole element  21  within the plane perpendicular to the optical axis  11 . 
   A 3-fold field returns to its original state if rotated through 120°. Furthermore, a 3-fold field can be realized by a mirror-symmetric optical system. The rotational positional relationship described so far can be generalized as follows from geometrical symmetry. The angle made between the first stage of multipole element and the second stage of multipole element can be generalized to 120°×m±about 72° (where m is an integer) within the plane perpendicular to the optical axis  11 . The angle made between the second stage of multipole element and the third stage of multipole element can be generalized to 120°×m±24° within the plane perpendicular to the optical axis  11 . 
   Meanwhile, a negative spherical aberration coefficient does not depend on the rotational positional relationship between the fields of 3-fold symmetry and thus the combination of the intensities created by the three fields of 3-fold symmetry can be used for correction of the spherical aberration in an objective lens. 
     FIGS. 2   e - 2   f  show one example of the arrangement of the multipole elements based on the above-described arrangements. In these figures, the arrangement of the front stage of multipole element  21  as viewed along the direction indicated by the arrow A from the origin O on the optical axis  11  shown in  FIG. 2   a  is indicated by  21   b . The arrangement of the middle stage of multipole element  22  is indicated by  22   b . The arrangement of the rear stage of multipole element  23  is indicated by  23   b . These rotational positional relationships need to be noticed after a rotation is made by the transfer lens. If electron optical rotations of 120°×m±72° and 120°×m±24°, respectively, are achieved by transfer lenses, it does not matter whether these rotations are made physically. 
   Accordingly, the three stages of multipole elements  21 ,  22 , and  23  producing the fields of 3-fold symmetry as described above cancel out the 3-fold astigmatisms while producing a negative spherical aberration. Furthermore, 6-fold astigmatism that is a higher-order aberration is also corrected. 
   In order to produce three fields of 3-fold symmetry as described above, rotating means (not shown) for rotating the multipole elements  21 ,  22 , and  23  within the plane perpendicular to the optical axis  11  may be mounted. 
   Furthermore, in the aberration correction system associated with the present embodiment, a pair of first transfer lenses  31  may be mounted between the front stage of multipole element  21  and the middle stage of multipole element  22 , and a pair of second transfer lenses  32  may be mounted between the middle stage of multipole element  22  and the rear stage of multipole element  23 . 
   The first transfer lenses  31  of the pair have two axisymmetric lenses  31   a  and  31   b  and transfer an image equivalent to the image obtained by the front stage of multipole element  21  to the middle stage of multipole element  22 . Furthermore, the second transfer lenses  32  of the pair have two axisymmetric lenses  32   a  and  32   b  and transfer an image equivalent to the image obtained by the middle stage of multipole element  22  to the rear stage of multipole element  23 . That is, the optical distance between the multipole elements is reduced down to zero by the pairs of transfer lenses  31  and  32 . 
   In this case, the pairs of transfer lenses  31  and  32  only act to transfer the equivalent images to between the multipole elements and so do not affect the optical characteristics relying on the three fields of 3-fold symmetry. In addition, a distance can be secured between the multipole elements. This provides wider latitude in disposing the multipole elements. 
   Additionally, a pair of third transfer lenses  33  may be mounted between the objective lens  40  and the rear stage of multipole element  23 , in addition to the first and second transfer lenses  31 ,  32 . 
   The third transfer lenses of the pair have two axisymmetric lenses  33   a  and  33   b  and transfer an image equivalent to the image obtained by the rear stage of multipole element  23  to the objective lens  40 . That is, the optical distance between them is zero. The third transfer lenses of the pair only act to transfer the equivalent image to the objective lens  40  in the same way as the first and second transfer lenses  31 ,  32 . Therefore, the third lenses do not affect the optical characteristics relying on the three fields of 3-fold symmetry. This offers wider latitude in disposing the rear stage of multipole element  23  and the objective lens  40 . 
   An example in which an aberration correction system associated with one embodiment of the present invention is incorporated in a transmission electron microscope is described by referring to  FIGS. 5 and 6 . 
     FIG. 5  shows an example of transmission electron microscope  50  using the aberration correction system as an illumination system aberration corrector. 
   An electron gun  51  produces an electron beam (not shown) under control of a high-voltage control portion  58  and accelerates the beam to a desired energy. A first condenser lens  52  then focuses the accelerated beam. The focused beam passes through an illumination system aberration corrector  53 . At this time, the aforementioned aberration correction is performed. The beam leaving the aberration corrector  53  is focused by a second condenser lens  54  and passes through an objective lens and a specimen stage  55 . A specimen is placed on the stage  55 . 
   The electron beam transmitted through the specimen is enlarged by an intermediate projector lens  56 . Then, the beam impinges on a fluorescent screen (not shown) in an observation chamber  57 . The image of the specimen projected onto the fluorescent screen is captured by a camera. 
   When the beam passes through the objective lens and specimen stage  55 , the objective lens further focuses the beam. A positive spherical aberration due to the objective lens acts to increase the spot diameter of the beam on the specimen surface. However, the positive spherical aberration is canceled out by a negative spherical aberration produced by the illumination system aberration corrector  53 . Consequently, a very small spot of the beam is obtained on the specimen surface. 
   On the specimen surface, 3-fold astigmatisms, 6-fold astigmatism, and other astigmatisms are removed. Therefore, the range of incident angles of the electron beam capable of being corrected for aberrations is widened in the illumination system. 
   When the range of the incident angles of the electron beam is enlarged, diffraction aberration decreases. This further improves the spatial resolution of the transmission electron microscope. 
   Since the quite small spot is obtained on the specimen surface, analysis of characteristic X-rays can be performed at high spatial resolution when the optical system of the transmission electron microscope  50  has a deflector (not shown). 
     FIG. 6  shows an example of a transmission electron microscope, indicated by 60, using an aberration correction system associated with one embodiment of the present invention as an imaging system aberration corrector. 
   The microscope  60  has an electron gun  61  that produces an electron beam (not shown) under control of a high voltage control portion  68  and accelerates the beam to a desired energy. The accelerated beam is then focused by a first condenser lens  62  and a second condenser lens  63 . The focused beam is then passed through an objective lens and a specimen stage  64 . Then, the beam is made to hit a specimen on the specimen stage. 
   The electron beam transmitted through the specimen passes through an imaging system aberration corrector  65 . At this time, the aforementioned aberration correction is performed. The beam passed through the aberration corrector  65  is enlarged by an intermediate projector lens  66  and impinges on a fluorescent screen (not shown) in an observation chamber  67 . The specimen image projected onto the fluorescent screen is captured by a camera. 
   When the electron beam passes through the imaging system aberration corrector  65 , a positive spherical aberration produced by the objective lens is canceled out by a negative spherical aberration possessed by the aberration corrector  65 . This aberration corrector removes 3-fold astigmatisms, 6-fold astigmatism, and other astigmatisms. Consequently, the spatial resolution of the transmission electron microscope is improved. 
   Aberration correction made by the imaging system aberration corrector  65  widens the range of incident angles of the electron beam in which aberration correction can be made. This, in turn, reduces diffraction aberration induced by an aperture (not shown). In consequence, the spatial resolution of the transmission electron microscope is improved further. 
   In the above examples, any one of the illumination system aberration corrector  53  and imaging system aberration corrector  65  is installed in a transmission electron microscope. A transmission electron microscope may also be equipped with both of these aberration correctors. 
   Having thus described my invention with the detail and particularity required by the Patent Laws, what is desired protected by Letters Patent is set forth in the following claims.