Abstract:
An aberration for correcting higher-order aberrations with a relatively small number of components is by let N1 being the aberration order at a first location, S1 being the symmetry at the first location, N2 being the aberration order at a second location and S2 being the symmetry at the second location. The produced combination aberration satisfies the following condition set  1  as order=N1+N2−1 and symmetry=|S1+S2| or |S2−S1|. That is two aberration-correcting elements (aberration-introducing elements) corresponding to the first and second locations, respectively. An aberration satisfying the condition set  1  is corrected by making use of the produced combination aberration.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a charged-particle beam system and, more particularly, to an aberration corrector and method of aberration correction capable of correcting higher-order aberrations. 
   2. Description of Related Art 
   Spherical aberration that cannot be corrected with a cylindrical symmetrical lens can be corrected using multipole lenses. Since established, this technology has been rapidly introduced into many practical apparatus. In recent years, excellent practical data derived using electron microscopes (TEMs and STEMs) equipped with aberration correctors have been vigorously published. 
   First, a phenomenon in which fifth-order spherical aberrations are created from spherical aberrations in a spherical aberration corrector and in an objective lens is described.  FIG. 1  is a diagram illustrating generation of the fifth-order spherical aberrations from spherical aberrations in the spherical aberration corrector and in the objective lens. 
   In V. Beck, Optik, 53, 241-255 (1979), it is stated that if there is an extra optical distance L between a spherical aberration corrector  1  and a plane at which a correction is made (front or back focal plane of an objective lens  2 ) as shown in  FIG. 1 , extra fifth-order spherical aberration (C 5 ) is introduced because the position of the electron beam is shifted at the correction plane. In this paper, the fifth-order aberration is described as issues produced when the spherical aberration corrector  1  is fabricated. 
   More specifically, because of shift of the position of the electron beam, angles δ 1  and δ 2  given by the following Eqs. (1) and (2) are produced. 
                   δ   1     =       C   s     ·       r   3     /     f   4                 (   1   )                 δ   2     =         r   2     f     +         C   3   2     ⁢     r   2   3         f   4                 (   2   )               
r 2  of the objective lens  2  is given by Eq. (3).
   r   2   =r   1   +C   s   ·r   3   ·L/f   4   (3) 
Therefore, from Eqs. (1)-(3), a relationship given by the following Eq. (4) is derived.
 
                     δ   1     +     δ   2       =         r   2     f     +         3   ⁢           ⁢     C   3   2     ⁢   L       f   2       ·       r   1   5       f   6         +     higher   ⁢           ⁢   order   ⁢           ⁢   terms               (   4   )               
For example, the extra fifth-order spherical aberration (C 5 ) is introduced in the higher-order terms of Eq. (4).
 
   A modern spherical aberration corrector using transfer lenses is free from the above-described problem because the distance L can be set to 0 by means of the transfer lenses. 
   A method of correcting spherical aberration using two hexapole fields is now described by referring to  FIG. 2 , which illustrates a method of correcting spherical aberration using the hexapole fields. In the above-cited reference, Beck also proposes a method of correcting spherical aberration by the use of two hexapole fields. According to Beck, two thin hexapole elements are combined to produce a negative third-order aberration (negative spherical aberration). 
     FIG. 2  shows that a negative spherical aberration given by Eq. (5) is produced by the combination of thin hexapole elements H 1  and H 2  which are spaced from each other by a distance of L.
 δ 1   x=+H ( x   1   2   −y   1   2 ) δ 2   x=−H ( x   2   2   −y   2   2 ) δ 1   y=− 2 Hx   1   y   1  δ 2   y=+ 2 Hx   2   y   2      x   2   =x   1 +δ 1   xL   (5)   y   2   =y   1 +δ 1   yL    δ 1   x+δ   2   x=− 2 LH   2 ( x   1   3   +x   1   y   1   2 )+higher order terms δ 1   y+δ   2   y=− 2 LH   2 ( y   1   3   +y   1   x   1   2 )+higher order terms 
   Eq. (5) gives an example of correction of spherical aberration using a combination of aberrations, though A. V. Crewe and D. Kopf,  Optik,  55, 1-10 (1980) states that a negative spherical aberration was created even from a single hexapole element. 
   JP2001-51613 states a method of removing deformation α n  of an image in an electron optical system. Off-axis image deformations α n γ m  of order n+m which act identically on the deformation α n  are corrected by moving or tilting the beam passage in the direction of the optical axis until compensation of the deformation of the image on the optical axis is completed. Furthermore, in this method, first-, second-, and third-order deformations of the image on the optical axis are corrected by correcting third-order deformation of the image on the optical axis in an electron optical system equipped with hexapole elements. 
   The aforementioned spherical aberration (in terms of order of geometrical aberration) is the third-order aberration. Even if this is corrected, the target resolution cannot be obtained under the condition where the other aberrations are left. Therefore, it is important to obtain a technique for correcting residual higher-order aberrations. Furthermore, in recent years, even electron microscopes have been required to be made up of a less number of components. Of course, the aberration corrector is required to be made up of a less number of components. 
   In the method disclosed in the above-cited JP2001-51613, a correction is made while moving or tilting the beam passage in the direction of the optical axis. Consequently, there is the possibility that labor is required to make adjustments for correcting both an aberration to be corrected and residual aberrations. 
   Especially, in order to correct higher-order aberrations, it is desired that low-order elements be combined, the number of components be reduced, and the correction be made quickly. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide an aberration corrector capable of correcting higher-order aberrations with a relatively small number of components. It is another object of the present invention to provide a method of aberration correction that can be implemented by this aberration corrector. 
   An embodiment of the present invention solves the above-described problem and provides a charged-particle beam system for correcting aberrations possessed by a lens disposed in the direction of travel of an electron beam. The charged-particle beam system comprises an aberration corrector for correcting lower-order aberrations and at least two aberration-correcting elements spaced apart from each other along a path of travel of the electron beam. A higher-order aberration left in the lens after the lower-order aberrations possessed by the lens have been corrected by the aberration corrector is corrected using a combination aberration created by a combination of aberrations produced in the at least two aberration-correcting elements. 
   Another embodiment of the present invention provides a charged-particle beam system comprising an aberration corrector for correcting aberrations possessed by a lens disposed in the direction of travel of an electron beam. At least two aberration-correcting elements are disposed in the aberration corrector. There are further provided first and second control units for applying control voltages to the aberration-correcting elements disposed in the aberration corrector. The second control unit produces its control voltage independent of the first control unit in such a way that the control voltage produced by the second control unit can be superimposed on the control voltage which is produced by the first control unit and to be applied to the aberration-correcting elements disposed in the aberration corrector. A higher-order aberration left in the lens after the lower-order aberrations possessed by the lens have been corrected by the control voltage applied by the first control unit is corrected using a combination aberration created by a combination of aberrations produced in the aberration-correcting elements disposed in the aberration corrector by the control voltage applied by the second control unit. 
   Yet another embodiment of the present invention based on the above-described embodiment comprises: aberration-grasping means for grasping an order and a symmetry of a higher-order aberration that is left in the lens and to be corrected; and aberration-producing means for producing a combination aberration having properties given by an order (N 1 +N 2 −1) and a symmetry |S 1 +S 2 | or |S 2 −S 1 | (where N 1  and S 1  are an order and a symmetry, respectively, of a geometric aberration produced in a first aberration-correcting element disposed in a front stage along the direction of travel of the electron beam and N 2  and S 2  are an order and a symmetry, respectively, of a geometric aberration produced in a second aberration-correcting element disposed in a rear stage) by a combination of the orders and symmetries of the geometric aberrations possessed by the first and second aberration-correcting elements. The first and second aberration-correcting elements are so controlled that the order and symmetry of the aberration grasped by the aberration-grasping means are brought into coincidence with the order and symmetry of the combination aberration produced by the aberration-producing means. 
   In an embodiment of the present invention based on the above-described embodiment, each of the aberration-correcting elements is any one of a multipole element, a deflector, an astigmatic corrector, and a lens. 
   A further embodiment of the present invention provides a charged-particle beam system for correcting aberrations possessed by a lens disposed in the direction of travel of an electron beam. The charged-particle beam system comprises an aberration corrector for correcting lower-order aberrations, and a multipole element having a length in the direction of travel of the electron beam. A higher-order aberration left in the lens after the lower-order aberrations possessed by the lens have been corrected by the aberration corrector is corrected by a higher-order aberration produced as tilt of the electron beam relative to an optical axis is varied when the beam travels through a field produced by the multipole element. The length of the multipole element taken in the direction of travel of the electron beam is set to such a value that the higher-order aberration left in the lens is corrected. 
   In a still further embodiment of the present invention, a method of correcting aberration possessed by a lens disposed in the direction of travel of an electron beam in a charged-particle beam system by means of an aberration corrector is provided. The method comprises the steps of: placing plural aberration-correcting elements at intervals along a path of travel of the electron beam; and producing a combination aberration by combining aberrations produced in the aberration-correcting elements to correct a higher-order aberration left in the lens after lower-order aberrations possessed by the lens have been corrected by the aberration corrector. 
   In a method embodiment of the present invention, a combination aberration is produced which has properties given by an order (N 1 +N 2 −1) and a symmetry |S 1 +S 2 | or |S 2 −S 1 | (where N 1  and S 1  are an order and a symmetry, respectively, of a geometric aberration produced in a first aberration-correcting element disposed in a front stage in the direction of travel of the electron beam and N 2  and S 2  are an order and a symmetry, respectively, of a geometric aberration produced in a second aberration-correcting element disposed in a rear stage) by a combination of the orders and symmetries of the geometric aberrations possessed by the first and second aberration-correcting elements. The order and symmetry of the combination aberration are brought into coincidence with the order and symmetry of the higher-order aberration left in the lens, thus correcting the higher-order aberration left in the lens. 
   A method embodiment of the present invention may further comprise the steps of: grasping an order and a symmetry of a higher-order aberration that is left in the lens and to be corrected; selecting a combination of aberration-correcting elements which produces a combination aberration having properties given by an order (N 1 +N 2 −1) and a symmetry |S 1 +S 2 | or |S 2 −S 1 | from the combinations of plural aberration-correcting elements spaced from each other along the path of travel of the electron beam; and correcting the higher-order aberration left in the lens, using the combination aberration created using the plural aberration-correcting elements. 
   According to the present invention, higher-order aberrations can be produced with a relatively small number of components. This is effective in correcting higher-order aberrations. Furthermore, it is easy to find a procedure for correcting the residual aberrations. In addition, higher-order aberrations can be corrected. 
   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 diagram illustrating generation of fifth-order spherical aberration disclosed in V. Beck,  Optik,  53, 241-255 (1979); 
       FIG. 2  is a diagram illustrating a method of correcting an aberration using a combination of two thin hexapole elements, the method being disclosed in V. Beck,  Optik,  53, 241-255 (1979); 
       FIGS. 3   a  and  3   b  illustrate the principle of the present invention; 
       FIG. 4  is a block diagram of a transmission electron microscope using an aberration corrector in its illumination system, showing the structure of the microscope; 
       FIG. 5  is a block diagram of a transmission electron microscope using an aberration corrector in its imaging system, showing the structure of the microscope; 
       FIG. 6  is a diagram illustrating an example of structure of an aberration corrector associated with the present invention and the operation; and 
       FIG. 7  is a diagram illustrating another example of structure of an aberration corrector associated with the present invention and the operation. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Preferred embodiments of the present invention are hereinafter described with reference to the drawings. After a lens is corrected for an aberration by some aberration corrector, the present invention is intended to correct other higher-order aberration left in the lens. The aberration is corrected by a combination of at least two aberration-producing elements. When the aberration is corrected using two aberration-correcting elements, the geometric aberration orders (hereinafter may be referred to as “aberration orders” or simply as “orders”) of the two aberration-correcting elements and the symmetries of the aberrations in the two aberration-correcting elements (hereinafter may be abbreviated “symmetries”) are combined. 
   In particular, two aberration-correcting elements are prepared. The first aberration-correcting element has an aberration order of N 1  and a symmetry of S 1 . The second aberration-correcting element has an aberration order of N 2  and a symmetry of S 2 . An aberration having an order of N 1 +N 2 −1 and a symmetry of |S 2 −S 1 | is corrected by utilizing a combination aberration produced by the two aberration-correcting elements. 
   The combination aberration referred to herein is described. It is assumed that a first aberration is produced at some location. The first aberration is propagated some distance, varying the point of incidence. When the first aberration is affected by a second aberration, the combination of the first and second aberrations produces a “combination aberration.” In the present invention, aberrations are corrected by making positive use of combination aberrations. 
   The principles of the aberration corrector and method of aberration correction of the present invention are first described. A complex angle Ω is given by Eq. (6).
 
Ω= x+iy 
 
  Ω = x−iy   (6)
 
It is assumed that r=(x,y) indicates a position in a direction perpendicular to the electron beam. Let f be the focal length of the objective lens. The complex angle is given by Eq. (7).
 
Ω= r/f   (7)
 
Let χ be wave aberration. Let C be an aberration coefficient. Generally, wave aberration is given by Eq. (8).
 
χ(Ω,  Ω )=Re {CΩ   n   Ω   m }=Re{χ(Ω,  Ω )}  (8)
 
Where n and m are integers and χ is defined as χ=Re{X}. As a result of computation, a geometrical aberration can be given by Eq. (9).
 
   
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       X 
                     
                     _ 
                   
                   
                     ∂ 
                     Ω 
                   
                 
                 + 
                 
                   
                     ∂ 
                     X 
                   
                   
                     ∂ 
                     
                       Ω 
                       _ 
                     
                   
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
     FIGS. 3   a  and  3   b  illustrate the principles of the present invention. Referring to  FIG. 3   a , it is assumed that aberrations are produced at a first location  11  and a second location  12  that are spaced by a distance of L. The first location  11  can be regarded as a first aberration-producing element. The second location  12  can be regarded as a second aberration-producing element. 
   Let r 1  and r 2  be points of incidence of an electron beam. Using Eq. (9), geometrical aberrations G&#39;s at these points are given by Eqs. (10) and (11).
 
 G (Ω)=    n   1   C   1 Ω n   1   −1 {overscore (Ω)} m     1 + m   1   C   1 Ω n     1     Ω   m     1     −1   (10)
 
 G (Ω)=    n   2   C   2 Ω n     2     −1 {overscore (Ω)} m     2 + m   2   C   2 Ω n     2     Ω   m     2     −1   (11)
 
The order of each geometrical aberration is the sum of a power of Eq. (12) and a power of Eq. (13).
 
Ω  (12)
 
  Ω   (13)
 
   Therefore, the order of the geometrical aberration at the first location  11  is n 1 +m 1 −1, whereas the order of the geometrical aberration at the second location  12  is n 2 +m 2 −1. Using Eqs. (7) and (10), the point of incidence r 2  and complex angle Ω 2  at the second location  12  are given by Eqs. (14) and (15). 
   
     
       
         
           
             
               
                 
                   r 
                   2 
                 
                 = 
                 
                   
                     r 
                     1 
                   
                   - 
                   
                     
                       
                         G 
                         ⁡ 
                         
                           ( 
                           
                             
                               r 
                               1 
                             
                             / 
                             f 
                           
                           ) 
                         
                       
                       / 
                       f 
                     
                     · 
                     L 
                   
                 
               
             
             
               
                 ( 
                 14 
                 ) 
               
             
           
           
             
               
                 
                   
                     
                       
                         Ω 
                         2 
                       
                       = 
                       
                         
                           Ω 
                           1 
                         
                         - 
                         
                           
                             
                               
                                 G 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   Ω 
                                   1 
                                 
                                 ) 
                               
                             
                             / 
                             
                               f 
                               2 
                             
                           
                           · 
                           L 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                       
                         
                           Ω 
                           1 
                         
                         - 
                         
                           
                             L 
                             
                               f 
                               2 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   n 
                                   1 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       
                                         C 
                                         1 
                                       
                                       ⁢ 
                                       Ω 
                                     
                                     _ 
                                   
                                   1 
                                   
                                     
                                       n 
                                       1 
                                     
                                     - 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   Ω 
                                   1 
                                   
                                     m 
                                     1 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   1 
                                 
                                 ⁢ 
                                 
                                   C 
                                   1 
                                 
                                 ⁢ 
                                 
                                   Ω 
                                   1 
                                   
                                     n 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     Ω 
                                     _ 
                                   
                                   1 
                                   
                                     
                                       m 
                                       1 
                                     
                                     - 
                                     1 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 15 
                 ) 
               
             
           
         
       
     
   
   Consequently, by substituting Eq. (15) into Eq. (11), a combination aberration can be calculated as given by Eq. (16). 
                           G   2     ⁡     (     Ω   2     )       =       ⁢           n   2     ⁢     C   2     ⁢     Ω   2       n   2     -   1       ⁢       Ω   _     2     m   2         _     +       m   2     ⁢     C   2     ⁢     Ω   2     n   2       ⁢       Ω   _     2       m   2     -   1                       =       ⁢         G   2     ⁡     (     Ω   1     )       -       L     f   2       ⁢     {         (       n   2     -   1     )     ⁢     n   2     ⁢     n   1       +       n   2     ⁢     m   2     ⁢     m   1         }                         ⁢         C   1     ⁢       C   2     _     ⁢     Ω   1       n   1     +     m   2     -   1       ⁢       Ω   _     1       m   1     +     n   2     -   2         -       L     f   2       ⁢     {         (       n   2     -   1     )     ⁢     n   2     ⁢     m   1       +                               ⁢       n   2     ⁢     m   2     ⁢     n   1       }     ⁢         C   1     ⁢     C   2       _     ⁢     Ω   1       m   1     +     m   2     -   1       ⁢       Ω   _     1       n   1     +     n   2     -   2         -       L     f   2       ⁢     {         n   2     ⁢     m   2     ⁢     n   1       +                             ⁢       (       m   2     -   1     )     ⁢     m   2     ⁢     m   1       }     ⁢       C   1     _     ⁢     C   2     ⁢     Ω   1       m   1     +     n   2     -   1       ⁢       Ω   _     1       n   1     +     m   2     -   2         -                   ⁢       L     f   2       ⁢     {         n   2     ⁢     m   2     ⁢     m   1       +       (       m   2     -   1     )     ⁢     m   2     ⁢     n   1         }                       ⁢         C   1     ⁢     C   2     ⁢     Ω   1       n   1     +     n   2     -   1       ⁢       Ω   _     1       m   1     +     m   2     -   2         +     higher   ⁢           ⁢   order   ⁢           ⁢   terms                     (   16   )               
The order of the geometrical aberration is the sum of a power of Eq. (17) and a power of Eq. (18).
 Ω  (17)   Ω   (18) 
   Therefore, it can be seen that every term of Eq. (16) has an order of (n 1 +m 1 −1)+(n 2 +m 2 −1)−1. That is, the order of a produced combination aberration is obtained by subtracting 1 from the sum of the aberration order at the first location  11  and the aberration order at the second location  12 . 
   Symmetries are next described. Let S 1  and S 2  be the symmetries of an aberration at the first location  11  and the second location  12 , respectively. A combination aberration is given by the following Eq. (19). 
   
     
       
         
           
             
               
                 
                   
                     - 
                     
                       L 
                       
                         f 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               n 
                               2 
                             
                             - 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           n 
                           1 
                         
                       
                       + 
                       
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                         ⁢ 
                         
                           m 
                           1 
                         
                       
                     
                     } 
                   
                   ⁢ 
                   
                     C 
                     1 
                   
                   ⁢ 
                   
                     
                       C 
                       2 
                     
                     _ 
                   
                   ⁢ 
                   
                     Ω 
                     1 
                     
                       
                         m 
                         1 
                       
                       - 
                       
                         S 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       1 
                     
                   
                   ⁢ 
                   
                     
                       Ω 
                       _ 
                     
                     1 
                     
                       
                         m 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       
                         S 
                         2 
                       
                       - 
                       2 
                     
                   
                 
                 - 
                 
                   
                     L 
                     
                       f 
                       2 
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               n 
                               2 
                             
                             - 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           m 
                           1 
                         
                       
                       + 
                       
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                         ⁢ 
                         
                           n 
                           1 
                         
                       
                     
                     } 
                   
                   ⁢ 
                   
                     
                       
                         C 
                         1 
                       
                       ⁢ 
                       
                         C 
                         2 
                       
                     
                     _ 
                   
                   ⁢ 
                   
                     Ω 
                     1 
                     
                       
                         m 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       1 
                     
                   
                   ⁢ 
                   
                     
                       Ω 
                       _ 
                     
                     1 
                     
                       
                         m 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       
                         S 
                         1 
                       
                       - 
                       
                         S 
                         2 
                       
                       - 
                       2 
                     
                   
                 
                 - 
                 
                   
                     L 
                     
                       f 
                       2 
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                         ⁢ 
                         
                           n 
                           1 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               m 
                               2 
                             
                             - 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                         ⁢ 
                         
                           m 
                           1 
                         
                       
                     
                     } 
                   
                   ⁢ 
                   
                     
                       C 
                       1 
                     
                     _ 
                   
                   ⁢ 
                   
                     C 
                     2 
                   
                   ⁢ 
                   
                     Ω 
                     1 
                     
                       
                         m 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       
                         S 
                         2 
                       
                       - 
                       1 
                     
                   
                   ⁢ 
                   
                     
                       Ω 
                       _ 
                     
                     1 
                     
                       
                         m 
                         1 
                       
                       - 
                       
                         S 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       2 
                     
                   
                 
                 - 
                 
                   
                     L 
                     
                       f 
                       2 
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                         ⁢ 
                         
                           m 
                           1 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               m 
                               2 
                             
                             - 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         
                           m 
                           2 
                         
                         ⁢ 
                         
                           n 
                           1 
                         
                       
                     
                     } 
                   
                   ⁢ 
                   
                     C 
                     1 
                   
                   ⁢ 
                   
                     C 
                     2 
                   
                   ⁢ 
                   
                     Ω 
                     1 
                     
                       
                         m 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       
                         S 
                         1 
                       
                       - 
                       
                         S 
                         2 
                       
                       - 
                       1 
                     
                   
                   ⁢ 
                   
                     
                       Ω 
                       _ 
                     
                     1 
                     
                       
                         m 
                         1 
                       
                       + 
                       
                         m 
                         2 
                       
                       - 
                       2 
                     
                   
                 
                 + 
                 
                   higher 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   order 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   terms 
                 
               
             
             
               
                 ( 
                 19 
                 ) 
               
             
           
         
       
     
   
   A symmetry is obtained by taking a power of Eq. (20), adding 1 to the power, subtracting a power of Eq. (21) from the sum, and taking the absolute value of the difference.
 
  Ω   (20)
 
Ω  (21)
 
   Hence, the symmetry of a combination aberration is given by |S 1 +S 2 | or |S 2 −S 1 |. 
   Let N 1  be the aberration order at the first location  11 . Let S 1  be the symmetry at the first location  11 . Let N 2  be the aberration order at the second location  12 . Let S 2  be the symmetry at the second location  12 . The above-described facts indicate that the produced combination aberration satisfies the following condition set  1 .
 
order= N   1   +N   2 −1
 
symmetry=| S   1   +S   2 | or | S   2   −S   1 |
 
   The principle of the present invention has been described taking the case of  FIG. 3   a  as an example. In this case, an aberration having condition  1  is corrected by making use of a combination aberration created by two aberration-producing elements corresponding to first location  11  and second location  12 . 
   Then, a case using a single multipole element having a length (having a thickness) in the direction of travel of an electron beam is described. An aberration similar to a combination aberration created by the aforementioned two correcting elements (aberration-introducing elements) can be produced even using the single multipole element described above. Using this aberration, an aberration in a lens can be corrected. 
   As shown in  FIG. 3   b , when an electron beam enters a multipole element  13  having a thickness, the point of incidence of the electron beam varies gradually as the beam travels through the field produced by the multipole field having the thickness. 
   That is, a combination aberration per unit length of the multipole element having a length (having a thickness) in the direction of travel of the electron beam is given by Eq. (22).
 
{tilde over (Γ)}  (22)
 
The combination aberration in the multipole element having a length (having a thickness) in the direction of travel of the electron beam is given by Eq. (23).
 
                           Γ   ~     ⁡     (   Ω   )       =         -     1     f   2         ⁢     (       n   2     +     m   1     -   1     )     ⁢     (         n   2     ⁢     n   1       +       m   1     ⁢     m   2         )     ⁢     C   1     ⁢       C   2     _     ⁢     Ω   1       n   1     +     m   2     -   1       ⁢       Ω   _     1       n   2     +     m   1     -   2         -       1     f   2       ⁢     (       n   1     +     n   2     -   1     )     ⁢     (         n   2     ⁢     m   1       +       n   1     ⁢     m   2         )     ⁢       C   _     1     ⁢       C   _     2     ⁢     Ω   1       m   1     +     m   2     -   1       ⁢       Ω   _     1       n   1     +     n   2     -   2             )     -       1     f   2       ⁢     (       n   1     +     m   2     -   1     )     ⁢     (         n   2     ⁢     n   1       +       m   1     ⁢     m   2         )     ⁢       C   1     _     ⁢     C   2     ⁢     Ω   1       n   2     +     m   1     -   1       ⁢       Ω   _     1       n   1     +     m   2     -   2         -       1     f   2       ⁢     (       m   1     +     m   2     -   1     )     ⁢     (         n   2     ⁢     m   1       +       n   1     ⁢     m   2         )     ⁢     C   1     ⁢     C   2     ⁢     Ω   1       n   1     +     n   2     -   1       ⁢       Ω   _     1       m   1     +     m   2     -   2           )           (   23   )               
In this case, the tilt r′ of the electron beam caused by the combination aberration is given by Eq. (24).
 
                   r   ′     =       -     1   f       ⁢     ∫         Γ   ~     ⁡     (   Ω   )       ⁢     ⅆ   z                   (   24   )               
where z is the thickness (length taken in the direction of travel of the electron beam) of the multipole element.
 
   In the present invention, an aberration produced by a single multipole element having a length (thickness) in the direction of travel of the electron beam is also referred to as a combination aberration. Correction of a higher-order aberration utilizing the combination aberration also falls within the technical scope of the present invention. 
   While the principles have been described, specific examples of an aberration corrector are described below.  FIG. 4  shows the structure of a transmission electron microscope  20  using an aberration corrector in its illumination system. 
   The microscope has an electron gun  21  using a high-voltage power supply that is controlled by a high-voltage controller  22 . Under this condition, the gun  21  produces an electron beam that is converged by a condenser lens  23  including stigmatic correcting elements. The converged beam reaches an aberration corrector  24  in the illumination system. The corrector  24  has various correcting elements including electron beam-deflecting elements and multipole elements. 
   The electron beam having aberrations which have been corrected by the aberration corrector  24  in the illumination system is converged by another condenser lens  25  including electron beam-deflecting elements. The beam reaches an objective lens and specimen stage  26 . The objective lens causes the beam to hit a specimen placed on the specimen stage. The beam transmitted through the specimen lying on the specimen stage is projected by intermediate and projector lenses  27  and reaches an observation chamber  28 , where an image of the specimen is observed. For example, the image is photographed by a camera. 
     FIG. 5  shows the structure of a transmission electron microscope  30  using an aberration corrector in its imaging system. The microscope has an electron gun  31  producing an electron beam while the high-voltage power supply of the gun is controlled by a high-voltage controller  32 . The beam is converged by a condenser lens  33  including stigmatic correcting elements. The converged beam reaches an objective lens and specimen stage  34 . The objective lens causes the beam to impinge on a specimen placed on the specimen stage. The beam transmitted through the specimen lying on the stage enters an aberration corrector  35  in the imaging system. 
   The aberration corrector  35  in the imaging system has various correcting elements including electron beam-deflecting elements and multipole elements. The electron beam having aberrations which have been corrected by the corrector  35  in the imaging system is projected by intermediate and projector lenses  36  and reaches an observation chamber  37 , where an image of the specimen is observed. For example, the image is photographed by a camera. 
   Furthermore, a transmission electron microscope may be built using a combination of the aberration corrector  24  ( FIG. 4 ) in the illumination system and the aberration corrector  35  in the imaging system. 
   In one feature of the present invention, two of various aberration-correcting elements are used to produce a combination aberration. These various aberration-correcting elements include aberration-correcting elements included in the aberration corrector within the illumination system, aberration-correcting elements included in the aberration correctors incorporated in the deflection system and imaging system, respectively, aberration-correcting elements for correcting spherical aberrations in the deflection system, aberration-correcting elements for correcting spherical aberration in the objective lens, deflection aberration-correcting elements and stigmatic correcting elements incorporated in the condenser lenses, deflecting aberration-correcting elements and stigmatic correcting elements incorporated in the intermediate lenses, and newly introduced aberration-correcting elements. 
   An example of structure of an illumination system aberration corrector associated with the present invention and the operation are described by referring to  FIGS. 6 and 7 . 
   In  FIG. 6 , an aberration corrector  41 , aberration-correcting elements  42 ,  43 , an objective lens OL, and a specimen S are arranged on an optical axis. A first control unit, a second control unit, and a lens control unit operate to apply necessary voltages to the aberration corrector  41 , aberration-correcting elements  42 ,  43 , and objective lens OL, respectively. These control units are made to perform required operations under control of a control and calculation unit  48 . The aberration corrector  41  and aberration-correcting elements  42 ,  43  correspond to the illumination system aberration corrector  24  of  FIG. 4 . 
   In  FIG. 6 , the first control unit applies a control voltage to the aberration corrector such that spherical aberration (geometric third-order aberration), for example, possessed by the objective lens OL is corrected. At this time, higher-order aberrations will still be left in the electron beam hitting the specimen S unless the aberration-correcting elements are in operation. The second control unit applies control voltages to the aberration-correcting elements  42  and  43  to grasp what kinds of higher-order aberrations are left from observation of an image of the specimen and to produce a combination aberration capable of canceling out a residual higher-order aberration. 
     FIG. 7  is a diagram illustrating another example of structure and its operation. In  FIG. 7 , an aberration corrector  51 , an objective lens OL, and a specimen S are arranged on an optical axis. Multipole elements  52  and  53  are built in the aberration corrector  51 . First and second control units operate to apply necessary voltages to the multipole elements  52  and  53 . A lens control unit operates to apply a necessary voltage to the objective lens OL. These control units are made to perform necessary operations under control of a control and calculation unit  58 . Where three or more multipole elements are built in the aberration corrector  51 , any arbitrary combination may be created from them and controlled by the second control unit. The aberration corrector  51  corresponds to the illumination system aberration corrector  24  of  FIG. 4 . 
   In  FIG. 7 , the first control unit applies a control voltage to the aberration corrector such that the spherical aberration (geometric third-order aberration), for example, possessed by the objective lens OL is corrected. At this time, higher-order aberrations will still be left in the electron beam hitting the specimen S unless the second control unit is in operation. 
   The second control unit applies control voltages to the multipole elements  52  and  53  to grasp what kinds of higher-order aberrations are left from observation of an image of the specimen and to produce a combination aberration capable of canceling out a residual higher-order aberration. Superimposition of the voltages from the first and second control units is applied to the multipole elements  52  and  53 . That is, the multipole elements  52  and  53  act also as aberration-correcting elements for producing a combination aberration. 
   Actual examples of the operation are next described by referring to Tables 1-3. The notation of aberrations is first described by referring to Table 1. 
   
     
       
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
               Wave aberration 
               Geometrical 
               Beam 
             
             
               Aberration 
               Symbol 
               function x(Ω) 
               aberration 
               pattern 
             
             
                 
             
           
           
             
               Defocus 
               O 2   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             2 
                           
                           ⁢ 
                           
                             O 
                             2 
                           
                           ⁢ 
                           Ω 
                           ⁢ 
                           
                             Ω 
                             _ 
                           
                         
                         } 
                       
                     
                   
                 
               
               O 2 Ω 
               
                         
               
             
             
                 
             
             
               2-fold astigmatism 
               A 2   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             2 
                           
                           ⁢ 
                           
                             A 
                             2 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             2 
                           
                         
                         } 
                       
                     
                   
                 
               
               A 2   Ω   
               
                         
               
             
             
                 
             
             
               Axial coma 
               P 3   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             3 
                           
                           ⁢ 
                           
                             P 
                             3 
                           
                           ⁢ 
                           Ω 
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             2 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   
                     
                       
                         
                           2 
                           3 
                         
                         ⁢ 
                         
                           P 
                           3 
                         
                         ⁢ 
                         Ω 
                         ⁢ 
                         
                           Ω 
                           _ 
                         
                       
                       + 
                       
                         
                           1 
                           3 
                         
                         ⁢ 
                         
                           
                             P 
                             _ 
                           
                           3 
                         
                         ⁢ 
                         
                           Ω 
                           2 
                         
                       
                     
                   
                 
               
               
                         
               
             
             
                 
             
             
               3-fold astigmatism 
               A 3   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             3 
                           
                           ⁢ 
                           
                             A 
                             3 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             3 
                           
                         
                         } 
                       
                     
                   
                 
               
               A 3   Ω   2   
               
                         
               
             
             
                 
             
             
               Sperical aberration 
               O 4   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             4 
                           
                           ⁢ 
                           
                             O 
                             4 
                           
                           ⁢ 
                           
                             Ω 
                             2 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             2 
                           
                         
                         } 
                       
                     
                   
                 
               
               O 4 Ω 2   Ω   
               
                         
               
             
             
                 
             
             
               Star aberration 
               Q 4   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             4 
                           
                           ⁢ 
                           
                             Q 
                             4 
                           
                           ⁢ 
                           Ω 
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             3 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   
                     
                       
                         
                           1 
                           4 
                         
                         ⁢ 
                         
                           
                             Q 
                             _ 
                           
                           4 
                         
                         ⁢ 
                         
                           Ω 
                           3 
                         
                       
                       + 
                       
                         
                           3 
                           4 
                         
                         ⁢ 
                         
                           Q 
                           4 
                         
                         ⁢ 
                         Ω 
                         ⁢ 
                         
                           
                             Ω 
                             _ 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                         
               
             
             
                 
             
             
               4-fold astigmatism 
               A 4   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             4 
                           
                           ⁢ 
                           
                             A 
                             4 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             4 
                           
                         
                         } 
                       
                     
                   
                 
               
               A 4   Ω   3   
               
                         
               
             
             
                 
             
             
               4th order axial coma 
               P 5   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             5 
                           
                           ⁢ 
                           
                             P 
                             5 
                           
                           ⁢ 
                           
                             Ω 
                             2 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             3 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   
                     
                       
                         
                           3 
                           5 
                         
                         ⁢ 
                         
                           P 
                           5 
                         
                         ⁢ 
                         
                           Ω 
                           2 
                         
                         ⁢ 
                         
                           
                             Ω 
                             _ 
                           
                           2 
                         
                       
                       + 
                       
                         
                           2 
                           5 
                         
                         ⁢ 
                         
                           
                             P 
                             _ 
                           
                           5 
                         
                         ⁢ 
                         
                           Ω 
                           _ 
                         
                         ⁢ 
                         
                           Ω 
                           3 
                         
                       
                     
                   
                 
               
               
                         
               
             
             
                 
             
             
               Three lobe 
               R 6   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             5 
                           
                           ⁢ 
                           
                             R 
                             5 
                           
                           ⁢ 
                           Ω 
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             4 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   
                     
                       
                         
                           1 
                           5 
                         
                         ⁢ 
                         
                           
                             R 
                             _ 
                           
                           5 
                         
                         ⁢ 
                         
                           Ω 
                           4 
                         
                       
                       + 
                       
                         
                           4 
                           5 
                         
                         ⁢ 
                         
                           R 
                           5 
                         
                         ⁢ 
                         Ω 
                         ⁢ 
                         
                           
                             Ω 
                             _ 
                           
                           3 
                         
                       
                     
                   
                 
               
               
                         
               
             
             
                 
             
             
               5-fold astigmatism 
               A 5   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             5 
                           
                           ⁢ 
                           
                             A 
                             5 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             5 
                           
                         
                         } 
                       
                     
                   
                 
               
               A 5   Ω   4   
               
                         
               
             
             
                 
             
             
               5th order spherical aberration 
               O 6   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             6 
                           
                           ⁢ 
                           
                             O 
                             6 
                           
                           ⁢ 
                           
                             Ω 
                             3 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             3 
                           
                         
                         } 
                       
                     
                   
                 
               
               O 6 Ω 3   Ω   2   
               
                         
               
             
             
                 
             
             
               6-fold astigmatism 
               A 6   
               
                 
                   
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             1 
                             6 
                           
                           ⁢ 
                           
                             A 
                             6 
                           
                           ⁢ 
                           
                             
                               Ω 
                               _ 
                             
                             6 
                           
                         
                         } 
                       
                     
                   
                 
               
               A 6   Ω   5   
               
                         
               
             
             
                 
             
             
               Complex angle Ω = α exp(i θ) 
             
             
               α: Angle 
             
             
               θ: Azimuth 
             
           
        
       
     
   
   The kinds of aberrations listed in Table 1 are: defocus, 2-fold astigmatism, axial coma, 3-fold astigmatism, spherical aberration, star aberration, 4-fold astigmatism, 4th-order axial coma, three-lobe aberration, 5-fold astigmatism, 5th-order spherical aberration, and 6-fold astigmatism. Described for each kind of aberration are: symbol, wave aberration function χ(Ω), geometrical aberration, and beam pattern. Two-fold astigmatism A 2 , 3-fold astigmatism A 3 , 4-fold astigmatism A 4 , 5-fold astigmatism A 5 , and 6-fold astigmatism A 6  are primary aberrations. The 2-fold astigmatism A 2  and star aberration Q 4  have the same two-fold symmetry but are different in order of geometrical aberration. That is, A 2  and Q 4  have first-order geometrical aberration and third-order geometrical aberration, respectively. The three-fold astigmatism A 3  and three-lobe aberration R 5  have the same three-fold symmetry but are different in order of geometrical aberration. That is, A 3  and R 5  have second-order geometrical aberration and fourth-order aberration, respectively. 
   The symmetries of the various aberrations and geometrical aberrations are listed in Table 2. The symmetries are arranged vertically in the left end. The orders of geometrical aberrations are arranged horizontally in the top end. 
   
     
       
             
             
             
           
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 2 
             
           
           
             
                 
                 
             
             
                 
               Order of geometrical aberration 
                 
             
           
        
         
             
               Symmetry 
               0 
               1 
               2 
               3 
               4 
               5 
             
             
                 
             
             
               0 
                 
               O 2   
                 
               O 4   
                 
               O 6   
             
             
               1 
                 
                 
               P 3   
                 
               P 5   
             
             
               2 
                 
               A 2   
                 
               Q 4   
                 
               Q 6   
             
             
               3 
                 
                 
               A 3   
                 
               R 5   
             
             
               4 
                 
                 
                 
               A 4   
                 
               S 6   
             
             
               5 
                 
                 
                 
                 
               A 5   
             
             
               6 
                 
                 
                 
                 
                 
               A 6   
             
             
                 
             
           
        
       
     
   
   For example, defocus O 2  has O-fold symmetry and first-order geometrical aberration. Similarly, axial coma P 3  has a 1-fold symmetry and second-order geometrical aberration. Star aberration Q 4  has a 2-fold symmetry and third-order geometrical aberration. 
   It is now assumed, for example, that the aberration to be corrected is 4-fold astigmatism A 4 . It can be seen from Table 2 that 4-fold astigmatism A 4  has a 4-fold symmetry and third-order geometrical aberration. In this case, aberrations which satisfy the condition set  1  described above are 2-fold astigmatism A 2  and star aberration Q 4 . These aberrations are used. Conditions for A 2  and Q 4 , i.e., n 1 =0, m 1 =2, n 2 =1, and m 2 =3, are substituted into Eq. (11). This gives rise to the following Eq. (25). 
   
     
       
         
           
             
               
                 
                   
                     - 
                     6 
                   
                   ⁢ 
                   
                     L 
                     
                       f 
                       2 
                     
                   
                   ⁢ 
                   
                     A 
                     2 
                   
                   ⁢ 
                   
                     Q 
                     4 
                   
                   ⁢ 
                   
                     
                       Q 
                       _ 
                     
                     1 
                     3 
                   
                 
                 - 
                 
                   
                     ( 
                     
                       
                         6 
                         ⁢ 
                         
                           L 
                           
                             f 
                             2 
                           
                         
                         ⁢ 
                         
                           A 
                           2 
                         
                         ⁢ 
                         
                           
                             Q 
                             4 
                           
                           _ 
                         
                       
                       + 
                       
                         12 
                         ⁢ 
                         
                           L 
                           
                             f 
                             2 
                           
                         
                         ⁢ 
                         
                           
                             A 
                             2 
                           
                           _ 
                         
                         ⁢ 
                         
                           Q 
                           4 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     Ω 
                     1 
                     2 
                   
                   ⁢ 
                   
                     
                       Ω 
                       _ 
                     
                     1 
                     1 
                   
                 
               
             
             
               
                 ( 
                 25 
                 ) 
               
             
           
         
       
     
   
   In this Eq. (25), the first term expressed by the Eq. (26) is 4-fold astigmatism A 4 , while the second term expressed by the Eq. (27) is spherical aberration O 4 .
 
  Ω 1     3   (26)
 
Ω 1   2   Ω 1     1   (27)
 
   That is, spherical aberration O 4  and 4-fold astigmatism A 4  are produced from 2-fold astigmatism A 2  and star aberration Q 4 . With respect to the 4-fold astigmatism A 4 , the aberration is corrected using a combination aberration by making use of the first term. 
   Combination aberrations are produced using the orders and symmetries of the various aberrations listed in Table 2 and by referring to the first aberration-correcting element (in the row) and the second aberration-correcting element (in the column). These combination aberrations can be summarized as in the following Table 3. 
   
     
       
             
           
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               First aberration(Row), Second aberration(Column) 
             
           
        
         
             
                 
               O 2   
               A 2   
               P 3   
               A 3   
               O 4   
               A 4   
               Q 4   
               R 5   
             
             
                 
                 
             
           
        
         
             
               O 2   
               O 2   
               A 2   
               P 3 , A 3   
               A 3   
               O 4   
               A 4   
               Q 4   
               R 5   
             
             
               A 2   
               A 2   
               O 2   
               P 3   
               P 3   
               Q 4   
               Q 4   
               Q 4 , A 4   
               P 5 , A 5   
             
             
               P 3   
               P 3   
               P 3 , A 3   
               O 4 , Q 4   
               A 4 , Q 4   
               P 5   
               A 5 , R 5   
               P 5 , R 5   
               Q 6 , S 6   
             
             
               A 3   
               A 3   
               P 3   
               A 4 , Q 4   
               O 4   
               R 5   
               P 5   
               P 5 , A 5   
               O 6 , A 6   
             
             
               O 4   
               O 4   
               Q 4   
               P 5   
               R 5   
               O 6   
               S 6   
               Q 6   
               ⋆ 
             
             
               A 4   
               A 4   
               Q 4   
               A 5 , R 5   
               P 5   
               S 6   
               O 6   
               Q 6 , A 6   
               ⋆ 
             
             
               Q 4   
               Q 4   
               O 4 , A 4   
               P 5 , R 5   
               P 5 , A 5   
               Q 6   
               Q 6 , A 6   
               Q 6 , S 6   
               ⋆ 
             
             
               R 5   
               R 5   
               P 5 , A 5   
               Q 6 , S 6   
               O 6 , A 6   
               ⋆ 
               ⋆ 
               ⋆ 
               ⋆ 
             
             
                 
             
             
               ⋆: Aberration higher than 6th order 
             
           
        
       
     
   
   Where one aberration included in Table 3 should be corrected, the correction can be achieved by preparing first and second aberrations, respectively, in the row and the column. 
   The procedure of corrective processing is summarized as follows. In step S 1 , order and symmetry of an aberration to be corrected are grasped. In step S 2 , two correcting elements (multipole elements or deflecting elements) that are spaced from each other by a distance of L are prepared. The correcting elements satisfy the condition set  1 . In step S 3 , the aberration is corrected using the two correcting elements. 
   For example, three-lobe aberration R 5  can be corrected by preparing spherical aberration O 4  and 3-fold astigmatism A 3  as the first and second aberration-correcting elements, respectively. Furthermore, fifth-order spherical aberration O 6  can be corrected by preparing spherical aberration O 4  as the first aberration-correcting element and also as the second correcting element. In addition, fourth-order coma P 5  and 5-fold astigmatism A 5  can be corrected by preparing 2-fold astigmatism A 2  and three-lobe aberration R 5  as the first and second correcting elements, respectively. 
   In the description provided so far, a combination of two aberration-producing elements is used to make use of a combination aberration. The present invention can also be applied to a combination of three or more aberration-producing elements. 
   In a multipole field having a thickness (i.e., a length in the direction of travel of an electron beam), two aberration-producing elements can be considered to be arranged continuously. Because the point of incidence varies with the progress of the electron beam, an electrooptical effect similar to a combination aberration produced by the two aberration-correcting elements as described so far is produced. A combination aberration is produced on the sample principle as the principle of the present embodiment. In this way, the two aberration-correcting elements of the present embodiment are applied to a combination aberration produced by a multipole element having a thickness. An aberration is corrected by the produced combination aberration. This constitutes a modified embodiment of the present invention. 
   In the case of a multipole element having a thickness or in cases where three or more multipole elements are combined, the combination aberration itself is the original aberration (first or second aberration). An aberration satisfying the condition set  1  can be corrected from the order and symmetry of the combination aberration. Correction of an aberration using this higher-order aberration constitutes a further modified embodiment of the present invention. 
   Having thus described our 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.