Patent Publication Number: US-9892886-B2

Title: Charged particle beam system and method of aberration correction

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a charged particle beam system and method of aberration correction. 
     Description of Related Art 
     In transmission electron microscopy, aberration correction is a technique that is important in achieving high-resolution imaging. 
     For example, H. Rose, Optik, vol. 85 (1990), pp. 19-24, H. Haider et al., Nature, vol. 392 (1998), pp. 768-769, and H. Muller et al., Microsc., Microanal. 12, pp. 442-455 (2006) disclose two-stage, three-fold field spherical aberration correctors in each of which there are arranged two stages of hexapole elements. In these known spherical aberration correctors, positive spherical aberration in an objective lens is corrected by negative spherical aberration produced by hexapole elements. In two-stage, three-fold field spherical aberration correctors, six-fold astigmatism of the fifth-order geometric aberration normally remains as a dominant aberration. However, the six-fold astigmatism can be corrected by adjusting the thickness of multipole elements or other factors. 
     H. Sawada et al., Journal of Electron Microscopy, vol. 58 (2009), pp. 341-347 and H. Sawada et al., Ultramicroscopy 110 (2010), pp. 958-961 disclose three-stage, three-fold field spherical aberration correctors in each of which there are arranged three stages of three-fold fields. In such a three-stage, three-fold field type spherical aberration corrector, six-fold astigmatism, which is difficult to correct with the above-described two-stage, three-fold field type spherical aberration correctors, is corrected by arranging three stages of three-fold fields. 
     As described above, in a two-stage, three-fold field type spherical aberration corrector, six-fold astigmatism can be corrected by adjusting the thickness of multipole elements or other factors. However, if the six-fold astigmatism is corrected, sixth order three-lobe aberration of sixth order geometric aberration cannot be corrected but rather remains as an aberration that limits the range of aberration correction. 
     Furthermore, as noted above, in a three-stage, three-fold field type spherical aberration corrector, six-fold astigmatism can be corrected. Also, in this three-stage, three-fold field type spherical aberration corrector, after six-fold astigmatism has been corrected, sixth order three-lobe aberration remains as a dominant aberration in the same manner as in a two-stage, three-fold field type spherical aberration corrector. 
     In this way, in a multistage, multipolar aberration corrector, even if aberrations are corrected up to the fifth order, sixth order three-lobe aberration remains. The range of aberration correction will be restricted by the effects of the sixth order three-lobe aberration. That is, the electron beam undergoes greater phase variations by the effects of the sixth order three-lobe aberration. This leads to a deterioration of the image resolution. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing problem, the present invention has been made. One object associated with some aspects of the present invention is to provide a charged particle beam system capable of reducing phase variations in a charged particle beam due to sixth order three-lobe aberration. Another object associated with some aspects of the invention is to provide a method of aberration correction capable of reducing phase variations in a charged particle beam due to sixth order three-lobe aberration. 
     (1) A charged particle beam system associated with the present invention is equipped with an aberration corrector for correcting aberrations in an optical system. The charged particle beam system comprises: an aberration measuring section for measuring sixth order three-lobe aberration of sixth order geometric aberration; a computing section for computing the magnitude of at least one of fourth order three-lobe aberration of fourth order geometric aberration and three-fold astigmatism of second order geometric aberration for reducing phase variations in a charged particle beam due to the sixth order three-lobe aberration on the basis of the measured sixth order three-lobe aberration; and a controller for controlling the aberration corrector to produce at least one of the fourth order three-lobe aberration and the three-fold astigmatism on the basis of the computed magnitude. 
     In this charged particle beam system, at least one of the fourth order three-lobe aberration and the three-fold astigmatism is introduced into the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector, whereby phase variations in the charged particle beam due to the sixth order three-lobe aberration can be reduced. Consequently, in this charged particle beam system, image resolution can be improved. 
     (2) In one feature of the charged particle beam system of (1) above, the computing section may compute the magnitude of the fourth order three-lobe aberration and the magnitude of the three-fold astigmatism. The controller may control the aberration corrector to produce the fourth order three-lobe aberration such that an angular deviation of 60 degrees is induced between a three-fold field generated by the sixth order three-lobe aberration and a three-fold field generated by the fourth order three-lobe aberration. The controller may also control the aberration corrector to produce the three-fold astigmatism such that an angular deviation of 0 degree is induced between the three-fold field generated by the sixth order three-lobe aberration and a three-fold field generated by the three-fold astigmatism. 
     In this charged particle beam system, the fourth order three-lobe aberration and three-fold astigmatism are introduced into the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector. As a result, phase variations in the charged particle beam due to the sixth order three-lobe aberration can be reduced. Furthermore, in this charged particle beam system, the range of aberration correction can be extended as compared with the case where only fourth order three-lobe aberration or only three-fold astigmatism is introduced. 
     (3) In another feature of the charged particle beam system of (1) above, the computing section may compute the magnitude of the fourth order three-lobe aberration. The controller may control the aberration corrector to produce the fourth order three-lobe aberration such that an angular deviation of 60 degrees is induced between a three-fold field generated by the sixth order three-lobe aberration and a three-fold field generated by the fourth order three-lobe aberration. 
     In this charged particle beam system, fourth order three-lobe aberration is introduced into the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector. As a result, phase variations in the charged particle beam due to the sixth order three-lobe aberration can be reduced. 
     (4) In a further feature of the charged particle beam system of (1) above, the computing section may compute the magnitude of the three-fold astigmatism. The controller may control the aberration corrector to produce the three-fold astigmatism such that an angular deviation of 60 degrees is induced between a three-fold field generated by the sixth order three-lobe aberration and a three-fold field generated by the three-fold astigmatism. 
     In this charged particle beam system, three-fold astigmatism is introduced into the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector. As a result, phase variations in the charged particle beam due to the sixth order three-lobe aberration can be reduced. 
     (5) In one feature of the charged particle beam system of any one of (1)-(4) above, the aberration corrector may have a plurality of stages of multipole elements and transfer lens systems disposed between successive ones of the multipole elements. The controller may control the transfer lens systems to produce the fourth order three-lobe aberration. The controller may also control the multipole elements to produce the three-fold astigmatism. 
     In this charged particle beam system, phase variations in the charged particle beam due to the sixth order three-lobe aberration can be reduced easily. 
     (6) A method of aberration correction associated with the present invention is implemented in a charged particle beam system equipped with an aberration corrector having multiple stages of multipole elements. The method starts with measuring sixth order three-lobe aberration of sixth order geometric aberration. The magnitude of at least one of fourth order three-lobe aberration of fourth order geometric aberration and three-fold astigmatism of second order geometric aberration for reducing phase variations in a charged particle beam due to the sixth order three-lobe aberration is computed on the basis of the measured sixth order three-lobe aberration. The aberration corrector is caused to produce at least one of the fourth order three-lobe aberration and the three-fold astigmatism on the basis of the computed magnitude. 
     In this method of aberration correction, at least one of the fourth order three-lobe aberration and the three-fold astigmatism is introduced into the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector, whereby phase variations in the charged particle beam due to the sixth order three-lobe aberration can be reduced. Therefore, in this method of aberration correction, image resolution can be enhanced. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic cross section, partly in block form, of an electron microscope associated with a first embodiment of the present invention. 
         FIG. 2  is a schematic diagram of an aberration corrector included in the electron microscope shown in  FIG. 1 . 
         FIG. 3  is a diagram illustrating an angular relationship between a three-fold field generated by sixth order three-lobe aberration and a three-fold field generated by fourth order three-lobe aberration. 
         FIG. 4A  is a Ronchigram taken computationally under the condition where sixth order three-lobe aberration is assumed to be 10 mm. 
         FIG. 4B  is a diagram showing a phase distribution computed under the condition where sixth order three-lobe aberration is assumed to be 10 mm. 
         FIG. 4C  shows a profile taken along a dotted line shown in  FIG. 4B . 
         FIG. 5A  is a Ronchigram taken computationally under conditions where sixth order three-lobe aberration and fourth order three-lobe aberration are assumed to be 10 mm and 27.3 μm, respectively. 
         FIG. 5B  is a diagram showing a phase distribution computed under conditions where sixth order three-lobe aberration and fourth order three-lobe aberration are assumed to be 10 mm and 27.3 μm, respectively. 
         FIG. 5C  is a diagram showing a profile taken along a dotted line shown in  FIG. 5B . 
         FIG. 6  is a flowchart illustrating one example of subroutine for aberration correction performed by the processor of the electron microscope of  FIG. 1 . 
         FIG. 7  is a diagram illustrating an angular relationship between a three-fold field generated by sixth order three-lobe aberration and a three-fold field generated by three-fold astigmatism. 
         FIG. 8A  is a Ronchigram taken computationally under conditions where sixth order three-lobe aberration and three-fold astigmatism are assumed to be 10 mm and 37.5 nm, respectively. 
         FIG. 8B  is a diagram showing a phase distribution computed under conditions where sixth order three-lobe aberration and three-fold astigmatism are assumed to be 10 mm and 37.5 nm, respectively. 
         FIG. 8C  is a diagram showing a profile taken along a dotted line shown in  FIG. 8B . 
         FIG. 9  is a flowchart illustrating one example of subroutine for aberration correction performed by a processor included in an electron microscope associated with a second embodiment. 
         FIG. 10  is a diagram showing an angular relationship among a three-fold field generated by sixth order three-lobe aberration, a three-fold field generated by fourth order three-lobe aberration, and a three-fold field generated by three-fold astigmatism. 
         FIG. 11A  is a Ronchigram taken computationally under conditions where sixth order three-lobe aberration, fourth order three-lobe aberration, and three-fold astigmatism are assumed to be 10 mm, 63 μm, and 78 nm, respectively. 
         FIG. 11B  is a diagram showing a phase distribution computed under conditions where sixth order three-lobe aberration, fourth order three-lobe aberration, and three-fold astigmatism are assumed to be 10 mm, 63 μm, and 78 nm, respectively. 
         FIG. 11C  is a diagram showing a profile taken along a dotted line shown in  FIG. 11B . 
         FIG. 12  is a flowchart illustrating one example of subroutine for aberration correction performed by a processor included in an electron microscope associated with a third embodiment. 
         FIG. 13  is a cross section similar to  FIG. 1 , but showing an electron microscope associated with a fourth embodiment. 
         FIG. 14  is a schematic diagram of an aberration corrector associated with a modification of the aberration corrector shown in  FIG. 2 . 
     
    
    
     DESCRIPTION OF THE INVENTION 
     The preferred embodiments of the present invention are hereinafter described in detail with reference to the drawings. It is to be understood that the embodiments described below are not intended to unduly restrict the content of the present invention set forth in the appended claims and that not all the configurations described below are essential constituent components of the invention. 
     In the following description, an electron microscope which irradiates a sample with an electron beam to observe, analyze, and otherwise process the sample is taken as one example of a charged particle beam system associated with the present invention. The charged particle beam system associated with the present invention may also be an instrument which irradiates a sample with a charged particle beam other than an electron beam such as ions to observe, analyze, and otherwise process the sample. 
     1. First Embodiment 
     1.1. Configuration of Electron Microscope 
     An electron microscope associated with a first embodiment of the present invention is first described by referring to  FIG. 1 , which schematically shows the electron microscope,  100 . 
     The electron microscope  100  is a scanning transmission electron microscope (STEM) equipped with an aberration corrector  30 . The scanning transmission electron microscope is an instrument for obtaining a scanning transmission electron microscope (STEM) image by scanning an electron probe (focused ion beam) over a sample S and detecting electrons transmitted through the sample S. 
     As shown in  FIG. 1 , the electron microscope  100  includes an electron source  10 , a condenser lens system  12 , scan coils  13 , an objective lens  14 , a sample stage  16 , a sample holder  17 , an intermediate lens  18 , a projector lens  20 , STEM detectors  22   a ,  22   b , an imager  24 , the aberration corrector  30 , a processor  40 , a manual control unit  50 , a display device  52 , and a storage device  54 . 
     The electron source  10  produces electrons. For example, the electron source  10  is an electron gun that emits an electron beam by accelerating electrons, emitted from a cathode, by means of an anode. 
     The condenser lens system  12  focuses the electron beam emitted from the electron source  10 . The condenser lens system  12  may be composed of a plurality of electron lenses (not shown). The condenser lens system  12  and objective lens  14  together constitute an illumination system for focusing the electron beam onto the sample S. 
     The scan coils  13  operate to deflect the electron beam such that the electron beam (electron probe) focused by the condenser lens system  12  and objective lens  14  is scanned over the sample S on the basis of a scan signal generated by a control unit (not shown) of the electron microscope  100 . Thus, the electron probe can be scanned over the sample S. 
     The objective lens  14  is used to focus the electron beam onto the sample S and to form the electron probe. Furthermore, the objective lens  14  focuses the electron beam transmitted through the sample S. 
     The sample stage  16  holds the sample S. In the illustrated example, the sample stage  16  holds the sample S via the sample holder  17 . The sample stage  16  permits the sample S to be moved horizontally or vertically and tilted. 
     The intermediate lens  18  and projector lens  20  cooperate to guide the electrons transmitted through the sample S toward the STEM detectors  22   a  and  22   b . The intermediate lens  18  and projector lens  20  further magnify the image focused by the objective lens  14  and focus the image onto the imager  22 . The objective lens  14 , intermediate lens  18 , and projector lens  20  together constitute an imaging system of the electron microscope  100 . 
     The bright-field STEM detector  22   a  detects electrons which are transmitted through the sample S without being scattered and electrons scattered at angles less than a given angle out of the electrons transmitted through the sample S. Although the bright-field STEM detector  22   a  is disposed on the optical axis, the detector  22   a  can be retracted from the optical axis when the imager  24  is used. 
     The dark-field STEM detector  22   b  detects electrons scattered at a certain angle from the sample S. The dark-field STEM detector  22   b  is an annular detector. 
     The imager  24  captures the image focused by the imaging system. The imager  24  is, for example, a digital camera such as a CCD camera. 
     The aberration corrector  30  is incorporated in the illumination system of the electron microscope  100 . In the illustrated example, the aberration corrector  30  is disposed in a stage following the condenser lens system  12 . The aberration corrector  30  is used to correct aberrations in the illumination system of the electron microscope  100 . In particular, the aberration corrector  30  is a spherical aberration corrector that corrects spherical aberration in the illumination system by creating negative spherical aberration so as to cancel out positive spherical aberration in the illumination system. 
     In the electron microscope  100 , the electron beam emitted from the electron source  10  is focused as an electron probe onto the sample S by the condenser lens system  12  and objective lens  14 . At this time, aberrations in the electron beam made to impinge on the sample S are corrected by the aberration corrector  30 . The electron beam hitting the sample S is scanned over the sample S by the scan coils  13 . The electron beam transmitted through the sample S is guided by the objective lens  14 , intermediate lens  18 , and projector lens  20  onto the STEM detectors  20   a  and  20   b , where the beam is detected. The detectors  22   a  and  22   b  send detection signals indicative of the intensities of the detected electrons to the processor  40 . The processor  40  visualizes the detection signals emanating from the STEM detectors  22   a  and  22   b  in synchronism with a scan signal and generates a bright-field STEM image and a dark-field STEM image, respectively. 
     Furthermore, in the electron microscope  100 , a projected image (Ronchigram) of the sample formed at a diffraction plane can be obtained by the imager  24  by focusing the electron beam to the vicinity of the sample S by means of the illumination system. Information about the image captured by the imager  24  is sent to the processor  40 . 
       FIG. 2  schematically illustrates the aberration corrector  30 . The aberration corrector  30  has three stages of multipole elements  32   a ,  32   b , and  32   c . That is, the aberration corrector  30  is a three-stage, three-fold field type spherical aberration corrector. 
     The aberration corrector  30  is configured including the three stages of multipole elements (first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c ), a first transfer lens system  34 , and a second transfer lens system  35 . In the aberration corrector  30 , the first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c  are arranged in a line along an optical axis OP. 
     The first multipole element  32   a  produces a three-fold field, i.e., a three-fold symmetric field. Similarly, each of the second multipole element  32   b  and third multipole element  32   c  produces a three-fold field. A three-fold field referred to herein is a field whose strength has three-fold symmetry. 
     The first multipole element  32   a  is made, for example, of a dodecapole (12-pole) element. No restriction is placed on the number of poles of the first multipole element  32   a . The three-fold field generated by the first multipole element  32   a  is an electrostatic field, a static magnetic field, or a superimposition thereof. The second multipole element  32   b  and third multipolar element  32   c  are identical in configuration to the first multipole element  32   a.    
     The first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c  have a thickness t along the optical axis OP. In a multipole element having a thickness, aberrations different from aberrations produced in a thin multipole element appear as combination aberrations. Where a three-fold field is produced by a multipole element, negative spherical aberration is induced as the combination aberrations. Utilizing this, positive spherical aberration in the optical system can be corrected. 
     Furthermore, in the aberration corrector  30 , six-fold astigmatism produced by a combination of aberrations produced in three-fold fields which are generated respectively by the three stages of multipole elements  32   a ,  32   b , and  32   c  can be canceled out by establishing a given angular relationship among these 3 three-fold fields. 
     The first transfer lens system  34  is disposed between the first multipole element  32   a  and the second multipole element  32   b . The first transfer lens system  34  is composed of a pair of transfer lenses (first transfer lens  34   a  and second transfer lens  34   b ). An image conjugate to the image formed by the first multipole element  32   a  is formed in the second multipole element  32   b  by the first transfer lens system  34 . 
     The second transfer lens system  35  is disposed between the second multipole element  32   b  and the third multipole element  32   c . The second transfer lens system  35  is composed of a pair of transfer lenses (first transfer lens  35   a  and second transfer lens  35   b ). An image conjugate to the image generated by the second multipole element  32   b  is formed in the third multipole element  32   c  by the second transfer lens system  35 . 
     A further transfer lens system  36  may be positioned between the condenser lens system  12  and the first multipole element  32   a . This transfer lens system  36  is composed of a pair of transfer lenses (first transfer lens  36   a  and second transfer lens  36   b ). 
     The manual control unit  50  performs processing for obtaining a control signal responsive to a user&#39;s manipulation and sending the signal to the processor  40 . The function of the manual control unit  50  can be realized, for example, by buttons, keys, a touch panel display, a microphone, or the like. 
     The display device  52  operates to display the image generated by the processor  40 . The function of the display device  52  can be accomplished by an LCD, a CRT, or the like. Captured STEM images and others are displayed on the display device  52 . 
     Programs, data, and related information permitting the processor  40  to perform various computational operations and control operations are stored in the storage device  54 . Furthermore, the storage device  54  is used as a working area for the processor  40 . The storage device  54  is also used to temporarily store the results of computations executed by the processor  40  in accordance with various programs. The function of the storage device  54  can be implemented by a hard disc, a RAM, or the like. 
     The processor  40  performs various processing operations including a subroutine for aberration correction (described later) and a subroutine for generating STEM images in response to detection signals from the STEM detectors  22   a  and  22   b . The functions of the processor  40  can be implemented either by hardware such as various processors (e.g., a CPU or a DSP) or by software. The processor  40  includes a spherical aberration corrector  42 , an aberration measuring section  44 , a computing section  46 , and a controller  48 . 
     The spherical aberration corrector  42  controls the aberration corrector  30  such that the spherical aberration in the illumination system is corrected. The spherical aberration corrector  42  controls the aberration corrector  30  on the basis of the results of measurements of aberrations made by the aberration measuring section  44  as described later. Furthermore, the spherical aberration corrector  42  controls the aberration corrector  30  in such a way that six-fold astigmatism is corrected in addition to spherical aberration. 
     The aberration measuring section  44  performs processing to measure aberrations, for example, using an SRAM (segmental Ronchigram autocorrelation function matrix) method or a probe tableau method. 
     The SRAM method is a technique for computing aberrations from the shapes of autocorrelation functions by obtaining a Ronchigram, dividing it into segments, and deriving the autocorrelation functions of the segments. A Ronchigram is a projected image (figure) of the sample formed on a diffraction plane by focusing an electron beam to the vicinity of the sample S by the illumination system. 
     The probe tableau method is a technique for measuring aberrations based on a probe image obtained by capturing STEM images with different angles of illumination of the electron beam on the sample surface and deconvoluting the STEM images. 
     The aberration measuring section  44  measures sixth order three-lobe aberration in the subroutine for aberration correction (described later). The sixth order three-lobe aberration referred to herein is sixth order geometric aberration. The sixth order three-lobe aberration creates a three-fold field, i.e., a three-fold symmetric field. The aberration measuring section  44  measures aberrations other than the sixth order three-lobe aberration, for example, fourth order three-lobe aberration of fourth order geometric aberration, three-fold astigmatism of second order geometric aberration, and spherical aberration. 
     In geometric optics where a trajectory of electrons is described as a motion of charged particles within an electromagnetic field, the deviation of an imaging point from an ideal imaging point (Gaussian image point) is referred to as geometric aberration. Generally, optical characteristics are given by a power-series polynomial which makes a mapping from one point on an object plane to one point on an image plane. This polynomial is expanded into a power series, using the distance r of the electron trajectory at the object plane from the optical axis and the angle α to the optical axis as parameters. Where only the first order terms of r and a are taken into account, ideal Gaussian imaging free from aberration is represented. Where second order terms and higher are taken into consideration, the imaging point deviates from the ideal image point. Both the angle α to the optical axis and the order of the distance r from the optical axis give the order of geometric aberration. 
     The computing section  46  computes the magnitude of the fourth order three-lobe aberration for reducing phase variations in the electron beam due to sixth order three-lobe aberration, based on the sixth order three-lobe aberration measured by the aberration measuring section  44 . 
     In the aberration corrector  30 , the sixth order three-lobe aberration remains as a dominant aberration after correction of the spherical aberration and six-fold astigmatism. At this time, the phase variations in the electron beam due to the sixth order three-lobe aberration can be reduced by introducing the fourth order three-lobe aberration into the aberration corrector  30 . 
       FIG. 3  is a diagram illustrating an angular relationship between a three-fold field F 1  generated by the sixth order three-lobe aberration and a three-fold field F 2  generated by the fourth order three-lobe aberration. 
     As illustrated in  FIG. 3 , the fourth order three-lobe aberration for reducing phase variations in the electron beam due to the sixth order three-lobe aberration is introduced in such a way that an angular deviation of 60 degrees occurs between the three-fold field F 1  generated by the sixth order three-lobe aberration and the three-fold field F 2  generated by the fourth order three-lobe aberration. Consequently, the three-fold symmetric aberrations cancel out each other, whereby the phase variations in the electron beam due to the sixth order three-lobe aberration can be reduced. 
     Because the three-fold fields F 1  and F 2  are three-fold symmetric, if they are rotated through 120 degrees or 240 degrees, they return to their original positions. Therefore, the angular deviation between the three-fold fields F 1  and F 2  is herein stipulated to be in the range from 0 degree to less than 120 degrees. 
     Where the magnitude of the sixth order three-lobe aberration is R 7  (mm), if an allowable amount of phase variation is k (rad), the magnitude of the fourth order three-lobe aberration for reducing phase variations in the electron beam due to the sixth order three-lobe aberration is given by 
                     R   5     =       -       (       35   ⁢           ⁢   k   ⁢           ⁢   λ     4     )       2   7         ⁢     R   7     5   7                 (   1   )               
where λ is the wavelength of the electron beam. The allowable amount of phase variation k gives a range within which the phase of the electron beam is allowed to vary and corresponds to the amounts of phase variation at the extreme values of the graph of  FIG. 5C  described later.
 
     For example, where the sixth order three-lobe aberration is 10 mm, assuming that the allowable amount of phase variation k is π/4 and the wavelength λ of the electron beam is 0.0049 nm (accelerating voltage is 60 kV), a computation using Eq. (1) above results in the magnitude R 5  of the fourth order three-lobe aberration to be 27.3 μm. 
     The controller  48  controls the aberration corrector  30  based on the results of computation performed by the computing section  46  to produce fourth order three-lobe aberration. The results of computation performed by the computing section  46  include information about the magnitude of the fourth order three-lobe aberration and information about the angle of the three-fold field generated by the fourth order three-lobe aberration. The fourth order three-lobe aberration can be produced by adjusting the first transfer lens system  34  and second transfer lens system  35 . 
       FIG. 4A  is a Ronchigram taken computationally in a case where the sixth order three-lobe aberration is assumed to be 10 mm.  FIG. 4B  shows a phase distribution computed in a case where the sixth order three-lobe aberration is assumed to be 10 mm.  FIG. 4C  shows a profile taken along a dotted line shown in  FIG. 4B . 
       FIG. 5A  is a Ronchigram taken computationally under conditions where the sixth order three-lobe aberration is 10 mm and the fourth order three-lobe aberration is 27.3 μm.  FIG. 5B  is a phase distribution produced computationally under conditions where the sixth order three-lobe aberration is 10 mm and the fourth order three-lobe aberration is 27.3 μm.  FIG. 5C  shows a profile taken along a dotted line shown in  FIG. 5B . 
     As shown in  FIGS. 4A, 4B, and 4C , in a case where there was only sixth order three-lobe aberration, the range of aberration correction was 46 mrad. On the other hand, as shown in  FIGS. 5A, 5B, and 5C , in a case where fourth order three-lobe aberration was added to the sixth order three-lobe aberration, the magnitude of the sixth order three-lobe aberration was identical to that shown in  FIGS. 4A, 4B, and 4C  but the range of aberration correction was broadened to 65 mrad. That is, the addition of the fourth order three-lobe aberration could reduce phase variations in the electron beam due to the sixth order three-lobe aberration. The range of aberration correction referred to herein is a range in which the amount of phase variation is equal to or less than an allowable amount of phase variation (π/4, here). 
     1.2. Operation of Electron Microscope 
     The operation of the electron microscope  100  is next described. The subroutine for aberration correction performed by the processor  40  of the electron microscope  100  is described below.  FIG. 6  is a flowchart illustrating one example of the subroutine for aberration correction performed by the processor  40  of the electron microscope  100 . 
     First, the processor  40  makes a decision as to whether the user has issued an instruction to start an aberration correction (step S 100 ). If the manual control unit  50  is manipulated to start the correction, the processor  40  determines that the user has issued an instruction for starting an aberration correction. 
     If the decision at step S 100  is YES, indicating that an instruction for starting an aberration correction has been issued, the spherical aberration corrector  42  operates to control the aberration corrector  30  such that spherical aberration and six-fold astigmatism are corrected (step S 102 ). 
     The spherical aberration corrector  42  creates a control signal on the basis of the result of the measurement of aberrations made by the aberration measuring section  44  and sends the signal to an aberration correction power supply controller  31 . The aberration corrector  30  is thus set into operation, and spherical aberration and six-fold astigmatism are corrected. However, the sixth order three-lobe aberration remains as a dominant aberration. 
     Then, the aberration measuring section  44  measures the sixth order three-lobe aberration by an SRAM method or probe-tableau method (step S 104 ). 
     For instance, where an SRAM method is adopted, the aberration measuring section  44  obtains a Ronchigram, divides it into segments, obtains autocorrelation functions of the segments, and computes aberrations. Where a probe tableau method is adopted, the aberration measuring section  44  derives STEM images which have been captured with different angles of impingement of the electron beam on the sample surface, deconvolutes the STEM images to produce a probe image, and measures aberrations. 
     The computing section  46  then computes a magnitude (target value) of the fourth order three-lobe aberration for reducing phase variations in the electron beam due to the sixth order three-lobe aberration on the basis of the sixth order three-lobe aberration measured by the aberration measuring section  44  (step S 106 ). 
     The computing section  46  computes the magnitude (target value) of the fourth order three-lobe aberration using Eq. (1) above. 
     The controller  48  then controls the aberration corrector  30  to produce fourth order three-lobe aberration on the basis of the magnitude of the fourth order three-lobe aberration computed by the computing section  46  (step S 108 ). 
     In particular, the controller  48  generates a control signal based on the computed magnitude of the fourth order three-lobe aberration to control the aberration corrector  30  (first transfer lens system  34  and second transfer lens system  35 ), and sends the signal to the aberration correction power supply controller  31 . As a consequence, fourth order three-lobe aberration is induced in the aberration corrector  30 . 
     The aberration measuring section  44  measures aberrations by an SRAM method or probe-tableau method (step S 110 ). 
     The controller  48  then makes a decision as to whether the difference between the measured magnitude of the fourth order three-lobe aberration and the target value is equal to or below a given value (step S 112 ). 
     If the decision at step S 112  is NO, indicating that the difference between the measured magnitude of the fourth order three-lobe aberration and the target value is not equal to or below the given value, then the controller  48  controls the aberration corrector  30  based on the measured magnitude of the fourth order three-lobe aberration such that the magnitude of the fourth order three-lobe aberration approaches the target value (step S 108 ). 
     During the operation of step S 110 , if the measured aberrations include aberrations other than the sixth order three-lobe aberration and fourth order three-lobe aberration, the processing of step S 108  may include an operation for controlling the aberration corrector  30  so as to correct these other aberrations. 
     The controller  48  and aberration measuring section  44  repeat the steps S 108 , S 110 , and S 112  such that the magnitude of the fourth order three-lobe aberration approaches the target value. 
     If the controller  48  determines that the difference between the measured magnitude of the fourth order three-lobe aberration and the target value is equal to or below the given value (i.e., the decision at step S 112  is YES), the processor  40  ends the subroutine for aberration correction. 
     The electron microscope  100  has the following features. In the electron microscope  100 , the aberration measuring section  44  measures sixth order three-lobe aberration. The computing section  46  computes the magnitude of fourth order three-lobe aberration on the basis of the measured sixth order three-lobe aberration. The controller  48  controls the aberration corrector  30  to produce fourth order three-lobe aberration on the basis of the magnitude computed by the computing section  46 . Therefore, in the electron microscope  100 , fourth order three-lobe aberration is introduced into the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector  30 . Consequently, phase variations in the electron beam due to the sixth order three-lobe aberration can be reduced. That is, the range of aberration correction can be extended. Hence, the electron microscope  100  can provide improved image resolution. 
     In the electron microscope  100 , the controller  48  controls the aberration corrector  30  to produce fourth order three-lobe aberration such that an angular deviation of 60 degrees is induced between the three-fold field produced by the sixth order three-lobe aberration and the three-fold field produced by the fourth order three-lobe aberration. Consequently, the sixth order three-lobe aberration and the fourth order three-lobe aberration cancel out each other, and the range of aberration correction can be extended. 
     In the electron microscope  100 , the controller  48  controls the first transfer lens system  34  and second transfer lens system  35  to produce fourth order three-lobe aberration. Therefore, phase variations in the electron beam due to sixth order three-lobe aberration can be reduced easily. 
     The method of aberration correction associated with the first embodiment involves the steps of: measuring sixth order three-lobe aberration; computing the magnitude of fourth order three-lobe aberration for reducing phase variations in the electron beam due to the sixth order three-lobe aberration on the basis of the measured sixth order three-lobe aberration; and causing the aberration corrector  30  to produce fourth order three-lobe aberration on the basis of the computed magnitude of fourth order three-lobe aberration. Therefore, phase variations in the electron beam due to the sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism in the aberration corrector  30  can be reduced. Consequently, image resolution can be improved. 
     2. Second Embodiment 
     2.1. Configuration of Electron Microscope 
     An electron microscope associated with a second embodiment is next described. Only the differences with the electron microscope  100  associated with the first embodiment are described below; a description of similarities is omitted. 
     In the above-described electron microscope  100  associated with the first embodiment, phase variations in the electron beam due to sixth order three-lobe aberration are reduced by introducing fourth order three-lobe aberration. On the other hand, in the electron microscope associated with the second embodiment, phase variations in the electron beam due to sixth order three-lobe aberration are reduced by introducing three-fold astigmatism. 
     The electron microscope associated with the second embodiment is identical in configuration to the electron microscope  100  associated with the first embodiment shown in  FIG. 1  and consequently its description and illustration is omitted. 
     In the present embodiment, the computing section  46  computes the magnitude of the three-fold astigmatism for reducing phase variations in the electron beam due to sixth order three-lobe aberration on the basis of the sixth order three-lobe aberration measured by the aberration measuring section  44 . 
       FIG. 7  is a diagram illustrating an angular relationship between a three-fold field F 1  generated by sixth order three-lobe aberration and a three-fold field F 3  generated by three-fold astigmatism. As shown in this  FIG. 7 , the three-fold astigmatism is introduced such that an angular deviation of 60 degrees occurs between the three-fold field F 1  generated by the sixth order three-lobe aberration and the three-fold field F 3  generated by the three-fold astigmatism. Consequently, the aberrations of three-fold symmetry cancel each other out and thus phase variations in the electron beam due to the sixth order three-lobe aberration can be reduced. 
     In a case where the magnitude of the sixth order three-lobe aberration is R 7  (mm), if it is assumed that the allowable amount of phase variation is k (rad), then the magnitude A 3  of three-fold astigmatism for reducing phase variations in the electron beam due to the sixth order three-lobe aberration is given by 
     
       
         
           
             
               
                 
                   
                     A 
                     3 
                   
                   = 
                   
                     
                       - 
                       
                         
                           ( 
                           
                             
                               21 
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                               ⁢ 
                               k 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               λ 
                             
                             8 
                           
                           ) 
                         
                         
                           4 
                           7 
                         
                       
                     
                     ⁢ 
                     
                       R 
                       7 
                       
                         3 
                         7 
                       
                     
                   
                 
               
               
                 
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     For example, where the sixth order three-lobe aberration is 10 mm, a computation using Eq. (2) above under conditions where the allowable amount of phase variation k is π/4 and the wavelength of the electron beam λ, is 0.0049 nm (accelerating voltage is 60 kV) results in the magnitude A 3  of the three-fold astigmatism being equal to 37.5 nm. 
     In the present embodiment, the controller  48  controls the aberration corrector  30  based on the results of the computation performed by the computing section  46  to produce three-fold astigmatism. The results of the computation performed by the computing section  46  include information about the magnitude of the three-fold astigmatism and information about the angle of the three-fold field generated by the three-fold astigmatism. The three-fold astigmatism can be produced by adjusting at least one of the first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c.    
       FIG. 8A  is a Ronchigram taken computationally under conditions where the sixth order three-lobe aberration was 10 mm and the three-fold astigmatism was 37.5 nm.  FIG. 8B  shows a phase distribution computed under conditions where the sixth order three-lobe aberration was 10 mm and the three-fold astigmatism was 37.5 nm.  FIG. 8C  shows a profile taken along a dotted line shown in  FIG. 8B . 
     As shown in  FIGS. 4A, 4B, and 4C , in a case where only sixth order three-lobe aberration was present, the range of aberration correction was 46 mrad. On the other hand, as shown in  FIGS. 8A, 8B, and 8C , in a case where three-fold astigmatism was added to the sixth order three-lobe aberration, the magnitude of the sixth order three-lobe aberration remained the same as in the case of  FIGS. 4A, 4B, and 4C  but the range of aberration correction was spread to 58 mrad. 
     2.2. Operation of Electron Microscope 
     The operation of the electron microscope associated with a second embodiment is next described.  FIG. 9  is a flowchart illustrating one example of subroutine for aberration correction performed by the processor  40  of the electron microscope associated with the second embodiment. 
     The operations of steps S 200 , S 202 , and S 204  illustrated in  FIG. 9  are performed similarly to the operations of steps S 100 , S 102 , and S 104 , respectively, illustrated in the above cited  FIG. 6 . 
     After sixth order three-lobe aberration is measured by the aberration measuring section  44  (after step S 204 ), the computing section  46  computes the magnitude (target value) of three-fold astigmatism for reducing phase variations in the electron beam due to the sixth order three-lobe aberration on the basis of the sixth order three-lobe aberration measured by the aberration measuring section  44  (step S 206 ). 
     The computing section  46  computes the magnitude (target value) of the three-fold astigmatism using Eq. (2) above. 
     Then, the controller  48  controls the aberration corrector  30  to produce three-fold astigmatism on the basis of the magnitude of the three-fold astigmatism computed by the computing section  46  (step S 208 ). 
     In particular, the controller  48  generates a control signal for controlling the aberration corrector  30  (i.e., at least one of the first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c ) on the basis of the computed magnitude of the three-fold astigmatism and sends the signal to the aberration correction power supply controller  31 . Consequently, the three-fold astigmatism is produced in the aberration corrector  30 . 
     The aberration measuring section  44  then measures aberrations by an SRAM method or a three-lobe method (step S 210 ). 
     The controller  48  then makes a decision as to whether the difference between the measured magnitude of the three-fold astigmatism and the target value is equal to or below a given value (step S 212 ). 
     If the decision at step S 212  is NO, indicating that the difference between the measured magnitude of the three-fold astigmatism and the target value is not equal to or below a given value, the controller  48  controls the aberration corrector  30  based on the measured three-fold astigmatism such that the magnitude of the three-fold astigmatism approaches the target value (step S 208 ). 
     The controller  48  and aberration measuring section  44  repeat the operations of steps S 208 , S 210 , and S 212  to bring the magnitude of the three-fold astigmatism closer to the target value. 
     If the decision at step S 212  is YES, indicating that the controller  48  has determined that the difference between the measured magnitude of the three-fold astigmatism and the target value is equal to or below a given value, then the processor  40  ends the subroutine for aberration correction. 
     The electron microscope associated with the second embodiment has the following features. In the electron microscope associated with the second embodiment, the aberration measuring section  44  measures sixth order three-lobe aberration. The computing section  46  computes the magnitude of the three-fold astigmatism on the basis of the measured sixth order three-lobe aberration. The controller  48  controls the aberration corrector  30  to produce three-fold astigmatism on the basis of the magnitude computed by the computing section  46 . Therefore, in the electron microscope associated with the second embodiment, the aberration corrector  30  can reduce phase variations in the electron beam due to sixth order three-lobe aberration by introducing three-fold astigmatism into sixth order three-lobe aberration that remains as a dominant aberration after correction of six-fold astigmatism. Consequently, in the electron microscope associated with the second embodiment, image resolution can be improved in the same way as in the above-described electron microscope  100  associated with the first embodiment. 
     In the electron microscope associated with the second embodiment, the controller  48  controls the aberration corrector  30  to produce three-fold astigmatism such that an angular deviation of 60 degrees is produced between the three-fold field generated by the sixth order three-lobe aberration and the three-fold field generated by the three-fold astigmatism. In consequence, the sixth order three-lobe aberration and the three-fold astigmatism cancel each other out. As a result, the range of aberration correction can be extended. 
     In the electron microscope associated with the second embodiment, the controller  48  produces the three-fold astigmatism by controlling at least one of the first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c . Therefore, phase variations in the electron beam due to the sixth order three-lobe aberration can be reduced easily. 
     The method of aberration correction associated with the second embodiment involves the steps of: measuring sixth order three-lobe aberration, computing the magnitude of three-fold astigmatism for reducing phase variations in the electron beam due to the sixth order three-lobe aberration on the basis of the measured magnitude of the sixth order three-lobe aberration, and causing the aberration corrector  30  to produce the three-fold astigmatism on the basis of the computed magnitude of the three-fold astigmatism. Therefore, phase variations in the electron beam due to the sixth order three-lobe aberration that remains as a dominant aberration in the aberration corrector  30  after correction of the six-fold astigmatism can be reduced, and hence image resolution can be improved. 
     3. Third Embodiment 
     3.1. Configuration of Electron Microscope 
     An electron microscope associated with a third embodiment is next described. Only differences with the above-described electron microscopes associated with the first and second embodiments, respectively, are described below; a description of similarities is omitted. 
     In the above-described electron microscope  100  associated with the first embodiment, phase variations in the electron beam due to sixth order three-lobe aberration are reduced by introducing fourth order three-lobe aberration. Furthermore, in the electron microscope associated with the second embodiment, phase variations in the electron beam due to sixth order three-lobe aberration are reduced by introducing three-fold astigmatism. 
     On the other hand, in the electron microscope associated with the third embodiment, phase variations in the electron beam due to sixth order three-lobe aberration are reduced by introducing fourth order three-lobe aberration and three-fold astigmatism. 
     The electron microscope associated with the third embodiment is identical in configuration to the electron microscope  100  associated with the first embodiment shown in  FIG. 1  and so its description and illustration is omitted. 
     In the present embodiment, the computing section  46  computes the magnitude of fourth order three-lobe aberration and the magnitude of three-fold astigmatism for reducing phase variations in the electron beam due to sixth order three-lobe aberration on the basis of the sixth order three-lobe aberration measured by the aberration measuring section  44 . 
       FIG. 10  is a diagram illustrating the angular relationship among the three-fold field F 1  generated by the sixth order three-lobe aberration, the three-fold field F 2  generated by the fourth order three-lobe aberration, and the three-fold field F 3  generated by the three-fold astigmatism. 
     As shown in  FIG. 10 , the fourth order three-lobe aberration is introduced such that an angular deviation of 60 degrees is induced between the three-fold field F 1  generated by the sixth order three-lobe aberration and the three-fold field F 2  generated by the fourth order three-lobe aberration. Furthermore, the three-fold astigmatism is introduced in such a way that an angular deviation of 0 degree occurs between the three-fold field F 1  generated by the sixth order three-lobe aberration and the three-fold field F 3  generated by the three-fold astigmatism. That is, there is no angular deviation between the three-fold field F 1  and the three-fold field F 3 . In this way, the aberrations of three-fold symmetry are made to cancel each other out by introducing fourth order three-lobe aberration and three-fold astigmatism into the sixth order three-lobe aberration. Hence, phase variations in the electron beam caused by the sixth order three-lobe aberration can be reduced. 
     Let χ be an aberration function given by the following Eq. (3). Where the magnitude of the sixth order three-lobe aberration is R 7  (mm), the magnitude R 5  of the fourth order three-lobe aberration and the magnitude A 3  of the three-fold astigmatism for reducing phase variations in the electron beam due to the sixth order three-lobe aberration can be found by solving simultaneous equations of Eqs. (4) for R 5  and R 3 . 
                     χ   ⁡     (   α   )       =         2   ⁢           ⁢   π     λ     ⁢     (         1   3     ⁢     A   3     ⁢     α   3       +       1   5     ⁢     R   5     ⁢     α   5       +       1   7     ⁢     R   7     ⁢     α   7         )               (   3   )               {             χ   ⁡     (         -     R   5       -         R   5   2     -     4   ⁢           ⁢     R   7     ⁢     A   3               2   ⁢           ⁢     R   7         )       =       k   1     ⁢   π                   χ   ⁡     (         -     R   5       +         R   5   2     -     4   ⁢           ⁢     R   7     ⁢     A   3               2   ⁢           ⁢     R   7         )       =       -     k   2       ⁢   π                     (   4   )               
where k 1  is an allowable amount of phase variation on the lower angle side and k 2  is an allowable amount of phase variation on the higher angle side.
 
     For example, where the sixth order three-lobe aberration is 10 mm and assuming that the allowable amount of phase variation k 1  is π/4, the allowable amount of phase variation k 2  is π/4, and the wavelength λ of the electron beam is 0.0049 nm (the accelerating voltage is 60 kV), a computation using Eqs. (4) above leads to results where the magnitude R 5  of the fourth order three-lobe aberration is 63 pill and the magnitude A 3  of the three-fold astigmatism is 78 nm. 
     In the present embodiment, the controller  48  controls the aberration corrector  30  to produce fourth order three-lobe aberration and three-fold astigmatism on the basis of the result of computation performed by the computing section  46 . The fourth order three-lobe aberration can be produced by adjusting the first transfer lens system  34  and the second transfer lens system  35 . The three-fold astigmatism can be generated by adjusting at least one of the first multipole element  32   a , second multipole element  32   b , and third multipole element  32   c.    
       FIG. 11A  is a Ronchigram computed under conditions where the sixth order three-lobe aberration was 10 mm, the fourth order three-lobe aberration was 63 μm, and the three-fold astigmatism was 78 nm.  FIG. 11B  shows a phase distribution computed under conditions where the sixth order three-lobe aberration was 10 mm, the fourth order three-lobe aberration was 63 μm, and the three-fold astigmatism was 78 nm.  FIG. 11  shows a profile taken along a dotted line shown in  FIG. 11B . 
     As shown in  FIGS. 4A, 4B, and 4C , in a case where there was only sixth order three-lobe aberration, the range of aberration correction was 46 mrad. On the other hand, as shown in  FIGS. 11A, 11B, and 11C , in a case where fourth order three-lobe aberration and three-fold astigmatism were added to sixth order three-lobe aberration, the magnitude of the sixth order three-lobe aberration was the same as in the case shown in  FIGS. 4A, 4B, and 4C  but the range of aberration correction was extended to 77 mrad. 
     Note that the allowable amount of phase variation on the lower angle side k 1  corresponds to the amount of phase variation at the extreme value on the lower angle side of the graph of  FIG. 11C , while the allowable amount of phase variation on the higher angle side k 2  corresponds to the amount of phase variation at the extreme value on the higher angle side of the graph of  FIG. 11C . 
     3.2. Operation of Electron Microscope 
     The operation of an electron microscope associated with a third embodiment is next described.  FIG. 12  is a flowchart illustrating one example of subroutine for aberration correction performed by the processor  40  of the electron microscope associated with the third embodiment. 
     The operations of steps S 300 , S 302 , and S 304  illustrated in  FIG. 12  are carried out similarly to the operations of steps S 100 , S 102 , and S 104 , respectively, illustrated in  FIG. 6 . 
     After sixth order three-lobe aberration is measured by the aberration measuring section  44  (after step S 304 ), the computing section  46  computes the magnitude (target value) of fourth order three-lobe aberration and the magnitude (target value) of three-fold astigmatism for reducing phase variations in the electron beam due to sixth order three-lobe aberration and the magnitude (target value) of three-fold astigmatism on the basis of the sixth order three-lobe aberration measured by the aberration measuring section  44  (step S 306 ). 
     The computing section  46  computes the magnitude (target value) of the fourth order three-lobe aberration and the magnitude (target value) of the three-fold astigmatism, using Eqs. (4) above. 
     Then, the controller  48  controls the aberration corrector  30  to produce fourth order three-lobe aberration and three-fold astigmatism, based on the magnitudes of the fourth order three-lobe aberration and of the three-fold astigmatism computed by the computing section  46  (step S 308 ). 
     In particular, the controller  48  generates a control signal for controlling the first transfer lens system  34  and the second transfer lens system  35  on the basis of the computed magnitude of the fourth order three-lobe aberration and sends the signal to the aberration correction power supply controller  31 . Furthermore, the controller  48  generates a control signal for controlling at least one of the first multipole element  32   a , the second multipole element  32   b , and the third multipole element  32   c  on the basis of the computed magnitude of the three-fold astigmatism and sends the signal to the aberration correction power supply controller  31 . Consequently, the aberration corrector  30  produces fourth order three-lobe aberration and three-fold astigmatism. 
     Then, the aberration measuring section  44  measures aberrations using an SRAM method or a probe-tableau method (step S 310 ). 
     The controller  48  then makes a decision as to whether two requirements, i.e., (i) the difference between the measured fourth order three-lobe aberration and the target value is equal to or below a given value and (ii) the difference between the measured magnitude of the three-fold astigmatism and the target value is equal to or below a given value, are met (step S 312 ). 
     If the decision at step S 312  is NO, indicating that the above-described requirements are not met, the controller  48  controls the aberration corrector  30  based on the measured fourth order three-lobe aberration and three-fold astigmatism such that the magnitude of the fourth order three-lobe aberration and the magnitude of the three-fold astigmatism approach their respective target values (step S 308 ). 
     The controller  48  and aberration measuring section  44  repeat the operations of steps S 308 , S 310 , and S 312  to bring the magnitude of the fourth order three-lobe aberration and the magnitude of the three-fold astigmatism closer to their target values. 
     If the controller  48  determines that the decision at step S 312  is YES, indicating that the requirements are met, the processor  40  ends the subroutine for aberration correction. 
     The electron microscope associated with the third embodiment has the following features. In the electron microscope associated with the third embodiment, the aberration measuring section  44  measures sixth order three-lobe aberration. The computing section  46  computes the magnitudes of fourth order three-lobe aberration and three-fold astigmatism on the basis of the measured sixth order three-lobe aberration. The controller  48  controls the aberration corrector  30  to produce fourth order three-lobe aberration and three-fold astigmatism on the basis of the result of the computation performed by the computing section  46 . Therefore, in the electron microscope associated with the third embodiment, phase variations in the electron beam due to sixth order three-lobe aberration can be reduced by introducing fourth order three-lobe aberration and three-fold astigmatism into the sixth order three-lobe aberration that remains as a dominant aberration after correction of the six-fold astigmatism. 
     Furthermore, where fourth order three-lobe aberration and three-fold astigmatism are introduced into the sixth order three-lobe aberration as shown in  FIGS. 11A, 11B, and 11C , the range of aberration correction is wider than both in the case where only fourth order three-lobe aberration is introduced (see  FIGS. 5A, 5B, and 5C ) and the case where only three-fold astigmatism is introduced (see  FIGS. 8A, 8B, and 8C ). Therefore, the electron microscope associated with the third embodiment can provide improved image resolution as compared with the case where only fourth order three-lobe aberration is introduced or the case where only three-fold astigmatism is introduced. 
     In the electron microscope associated with the third embodiment, the controller  48  controls the aberration corrector  30  to produce fourth order three-lobe aberration such that an angular deviation of 60 degrees is induced between the three-fold field generated by the sixth order three-lobe aberration and the three-fold field generated by the fourth order three-lobe aberration. The controller also controls the aberration corrector  30  to produce third order three-lobe aberration such that an angular deviation of 0 degree occurs between the three-fold field generated by the sixth order three-lobe aberration and the three-fold field generated by the three-fold astigmatism. Consequently, the sixth order three-lobe aberration, fourth order three-lobe aberration, and three-fold astigmatism cancel one another out, thus extending the range of aberration correction. 
     The method of aberration correction associated with the third embodiment involves the steps of: measuring sixth order three-lobe aberration, computing the magnitude of fourth order three-lobe aberration and the magnitude of three-fold astigmatism for reducing phase variations in the electron beam due to sixth order three-lobe aberration on the basis of the measured sixth order three-lobe aberration, causing the aberration corrector  30  to produce fourth order three-lobe aberration and three-fold astigmatism on the basis of the computed magnitudes of the fourth order three-lobe aberration and of the three-fold astigmatism. Consequently, it is possible to reduce phase variations in the electron beam due to sixth order three-lobe aberration which remains as a dominant aberration in the aberration corrector  30  after correction of the six-fold astigmatism. As a result, image resolution can be improved. 
     4. Fourth Embodiment 
     An electron microscope associated with a fourth embodiment is next described by referring to  FIG. 13 , which schematically shows the electron microscope,  200 , associated with the fourth embodiment. Those members of the electron microscope  200  which are similar in function to their respective counterparts of the electron microscope  100  associated with the first embodiment are indicated by the same reference numerals as in the above referenced figures and a detailed description thereof is omitted. 
     In the above-described electron microscope  100  associated with the first embodiment, the aberration corrector  30  is incorporated in the illumination system as shown in  FIG. 1 . In contrast, in the electron microscope  200  associated with the second embodiment, the aberration corrector  30  is incorporated in the imaging system as shown in  FIG. 13 . 
     Furthermore, the above-described electron microscope  100  is a scanning transmission electron microscope (STEM). On the other hand, the electron microscope  200  is a transmission electron microscope (TEM). 
     The aberration corrector  30  is incorporated in the imaging system of the electron microscope  100 . In the illustrated example, the aberration corrector  30  is disposed in a stage following the objective lens  14 . The aberration corrector  30  is an instrument for correcting aberrations in the imaging system of the electron microscope  100 . More specifically, the aberration corrector  30  is a spherical aberration corrector that corrects spherical aberration in the imaging system by producing negative spherical aberration so as to cancel out positive spherical aberration in the imaging system. 
     The electron microscope  200  is configured including deflection coils  202  which are located in a stage following the condenser lens system  12 . The deflection coils  202  can deflect the electron beam. The deflection coils  202  make it possible to control the angle of impingement of the electron beam on the sample S (sample surface). 
     In the electron microscope  200 , an electron beam emitted from the electron source  10  is focused onto the sample S by the condenser lens system  12 . The electron beam transmitted through the sample S is focused by the objective lens  14 , intermediate lens  18 , and projector lens  20 . The focused transmission electron microscope (TEM) image is captured by the imager  24 . 
     In the present embodiment, the aberration measuring section  44  measures aberrations using a diffractogram tableau method. This method is a technique for measuring aberrations by capturing plural TEM images of an amorphous sample with different angles of impingement of the electron beam on the sample surface, Fourier transforming the TEM images to produce a diffractogram, and determining the aberrations based on the diffractogram. The angle of impingement of the electron beam can be controlled by the deflection coils  202 . 
     The electron microscope  200  is identical in operation to the above-described electron microscope  100  except that the aberration measuring section  44  measures aberrations using a diffractogram tableau method and so its description is omitted. 
     The electron microscope  200  can yield the same advantageous effects as those provided by the electron microscope  100 . The configuration of the electron microscope  200  is also applicable to the above-described second and third embodiments. 
     5. Other Respects 
     It is to be understood that the present invention is not restricted to the above-described embodiments and that the invention can be implemented in various modified forms without departing from the gist of the present invention. 
     In the above-described embodiments, the aberration corrector  30  is a three-stage, three-fold field type spherical aberration corrector as shown in  FIG. 2 . The aberration corrector  30  may also be a two-stage, three-fold field type spherical aberration corrector as shown in  FIG. 14 . 
     As shown in  FIG. 14 , the aberration corrector  30  has the first multipole element  32   a , the second multipole element  32   b , and the transfer lens system  34 . In this aberration corrector  30 , when fourth order three-lobe aberration is produced, the transfer lens system  34  is used. When three-fold astigmatism is produced, at least one of the first multipole element  32   a  and the second multipole element  32   b  is used. 
     Where the aberration corrector has four or more stages of multipole elements, the technique of the above-described embodiments can also be applied. 
     It is to be noted that the above embodiments and modifications are merely exemplary and that the invention is not restricted thereto. For example, the embodiments and modifications may be combined appropriately. 
     The present invention embraces configurations substantially identical (e.g., in function, method, and results or in purpose and advantageous effects) with the configurations described in the embodiments of the invention. Furthermore, the invention embraces configurations described in the embodiments and including portions which have non-essential portions replaced. In addition, the invention embraces configurations which produce the same advantageous effects as those provided by the configurations described in the embodiments or which can achieve the same objects as the configurations described in the embodiments. Further, the invention embraces configurations which are similar to the configurations described in the embodiments except that well-known techniques have been added. 
     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.