Patent Publication Number: US-7714286-B2

Title: Charged particle beam apparatus, aberration correction value calculation unit therefor, and aberration correction program therefor

Description:
CLAIM OF PRIORITY 
   The present application claims priority from Japanese application JP 2007-131518 filed on May 17, 2007, the content of which is hereby incorporated by reference into this application. 
   BACKGROUND OF THE INVENTION 
   The present invention relates to a charged particle beam apparatus that scans a specimen by irradiation of a charged particle beam to obtain secondary electrons from the specimen, and to an aberration correction value calculation unit therefor and an aberration correction program therefor. 
   A charged particle beam apparatus (for example, an electron microscope such as a scanning electron microscope (SEM) or a transmission electron microscope (TEM)) necessarily uses a lens that utilizes an electric field or magnetic field in order to focus a charged particle beam. Various types of aberration occur inevitably in electric field lenses and magnetic field lenses. As a result, simple narrowing of a spot diameter of a charged particle beam by reducing the magnification of a lens does not lead to an image of good quality if aberration of the charged particle beam is large. 
   Consequently, many charged particle beam apparatuses incorporate an aberration corrector in order to obtain an excellent image. Usually, an aberration corrector comprises multipole lenses arranged in multiple stages, and generates an electric field or a magnetic field within the multipole lenses in order to remove aberration included in a charged particle beam that has passed through the inside of the lenses. 
   Such an aberration corrector, which uses four stages of multipole lenses, is disclosed in the following Non-patent Document 1, for example. 
   Non-patent Document 1: Nuclear Instruments and Methods in Physics Research, A363 (1995), pp. 316-325. 
   Further, there is a technique of detecting and correcting aberration of a charged particle beam apparatus, as disclosed in Japanese Un-examined Patent Application Laid-Open No. 2005-183085 (hereinafter, referred to as Patent Document 1), for example. In this technique, a just-focused (i.e. in-focus) image and a plurality of defocused images are acquired, each item of image data is subjected to Fourier transformation, the Fourier transformed defocused image data are divided by the Fourier transformed in-focus image data, and the obtained value is subjected to inverse Fourier transformation, to obtain beam profile data. Various aberrations are obtained on the basis of the beam profile data, and the various aberrations are removed by operating an aberration corrector according to the various aberrations. Further, Japanese Un-examine Patent Application Laid-Open No. 2001-068048 (hereinafter, referred to as Patent Document 2) discloses a technique of correcting astigmatism by using items of image data having different focus conditions. 
   However, when each aberration is obtained by the method described in Patent Document 1, high S/N (signal to noise) ratio image data should be obtained. Thus, there is a problem in that obtainment of each aberration requires a lot of time, and as a result, obtainment of aberration correction requires a lot of time. 
   The noise in question include noise generated in the course of generation of a charged particle beam and in the course of generation of secondary particles, and noise generated in a detector for detecting the secondary particles, an amplifier for amplifying the output of the detector, and the like. The former noise is stochastic noise concerning particles, and result from, for example, dispersion of the number of generated charged particles or dispersion of the number of generated secondary particles. The latter noise is generated by devices themselves, such as the detector or the amplifier. 
   In the technique of Patent Document 1, division of the Fourier transformed defocused image data by the Fourier transformed in-focus image data means multiplication of random noise included in the defocused image data by random noise included in the in-focus image data. As a result, the final obtained beam profile data include much noise. Thus, it is necessary to obtain high S/N image data, for example by slowing the scanning speed of charged particle beam. 
   Patent Document 2 discloses a technique of correcting astigmatism, but does not disclose a technique of correcting higher-order aberration (second order or higher aberration) such as coma aberration and star aberration. 
   SUMMARY OF THE INVENTION 
   The present invention has been made recognizing such problems of the conventional techniques. An object of the present invention is to provide a charged particle beam apparatus that can shorten the time required for correction of aberration, an aberration correction value calculation unit therefor, and an aberration correction program therefor. 
   According to the present invention, a specimen is scanned with a primary charged particle beam while changing focus conditions; two-dimensional intensity distribution data on the secondary charged particles are acquired by detecting the secondary charged particles (secondary electrons, backscattered electrons, and the like); directional dependency of asymmetry of the acquired two-dimensional distribution data of directional dependency of degree of directional skewness is calculated; and aberration parameters are obtained to control an aberration corrector. 
   Here, “aberration parameter” means parameters required for determining operation conditions of the aberration corrector, and the aberration parameters are quantities that can be converted to and from aberration coefficient by prescribed formulas. When the operation conditions of the aberration corrector are determined in practice, it is sufficient in many cases to obtain the aberration parameters. It is not frequently required to obtain the aberration coefficients. The “asymmetry” or “degree of directional skewness” is the sum of derivative values or amounts of skewness for specific directions at points on a one-dimensional profile cut out along a line segment from the two-dimensional distribution data, and can be calculated from an index called a directional sharpness. The “directional sharpness” is the sum of gradients for specific directions at the points constituting the two-dimensional distribution data. When anisotropies owing to factors other than the beam, i.e. factors such as the inclination or structure information (a pattern biased in a specific direction) of the specimen, are removed, the “directional sharpness” depicts a curve having a local maximum value when the “directional sharpness” (which corresponds physically to the sum of asymmetries of amount of blurring caused by aberration) is plotted with respect to focus values at which the two-dimensional distribution data have been obtained. In the case where the aberration included in the acquired two-dimensional distribution data is two-fold symmetric, the focus-dependent curve of the directional sharpness is distributed symmetrically centering at the local maximum value. On the other hand, in the case where spherical aberration or star aberration exists, the focus-dependent curve of the directional sharpness is distorted in the distribution centering at the local maximum value. Such “asymmetry” or “degree of directional skewness” relates to aberration parameters. The present invention performs fitting of the above “asymmetric” or “degree of directional skewness” curve by using desired aberration parameters as fitting parameters, in order to obtain various aberration parameters. Correction values (i.e., aberration corrector operation conditions) to be given to the aberration corrector are determined. Information on anisotropy and the like of the specimen is cancelled by calculation as far as skewness is not used, and has no effect. Information using skewness is removed by specific processing at the time of fitting. 
   Thus, according to the present invention, directional derivative values in a plurality of directions are obtained for each of a plurality of two-dimensional images of different focal positions, and aberration parameters are obtained from these directional derivative values. When the aberration parameters are obtained from the directional derivative values, random noise is removed in the course of differentiating a two-dimensional image. Thus, the aberration parameters can be obtained accurately even for a relatively coarse two-dimensional image. Thus, according to the present invention, it is possible to acquire an image in a short time, for example, by raising the speed of scanning with a charged particle beam. As a result, the time required for correcting aberration can be shortened. Further according to the present invention, it is possible to reduce damage to a specimen because the speed of scanning with a charged particle beam can be raised. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is an explanatory diagram showing a configuration of a scanning electron microscope as an embodiment of the present invention; 
       FIG. 2  is a flowchart showing aberration correction operation of the scanning electron microscope of the embodiment of the present invention; 
       FIG. 3  is a flowchart showing a detailed flow of step  40   a  in the flowchart of  FIG. 2 ; 
       FIG. 4  is a flowchart showing a detailed flow of step  40   b  in the flowchart of  FIG. 2 ; 
       FIG. 5  is a flowchart showing a detailed flow of step  40   c  in the flowchart of  FIG. 2 ; 
       FIG. 6  is an explanatory diagram showing a method of applying directional differentiation to two-dimensional image data; 
       FIG. 7  is a graph showing a relation between directional sharpness and focal position (focus value) for each direction; 
       FIG. 8A  is a schematic diagram showing a first method of calculating asymmetry; 
       FIG. 8B  is a schematic diagram showing a second method of calculating asymmetry; 
       FIG. 9  is a graph showing a relation between asymmetry of directional sharpness and direction (angular); 
       FIG. 10  is a graph showing a relation between focal position (focus value) at which each focal center position is obtained, and direction (angler), this graph being used for explaining periodicity of astigmatism and a method of extracting parameters of the astigmatism; 
       FIG. 11  is a graph showing a relation between focal position (focus value) at which each focal center is obtained, and direction (angle), this graph being used for explaining periodicity of 4-fold astigmatism and a method of extracting parameters of the 4-fold astigmatism; 
       FIG. 12  is a graph showing a relation between amount of directional skewness and focal position (focus value) for each direction; 
       FIG. 13  is a graph showing a relation between degree of directional skewness and direction (angle); 
       FIG. 14  is a graph showing a relation between degree of directional skewness and direction (angle), this graph being used for explaining periodicity of coma aberration and a method of extracting parameters of the coma aberration; and 
       FIG. 15  is a graph showing a relation between degree of directional skewness and direction (angle), this graph being used for explaining periodicity of 3-fold astigmatism and a method of extracting parameters of the 3-fold astigmatism. 
   

   DETAILED DESCRIPTION 
   In the following, an embodiment of a charged particle beam apparatus according to the present invention will be described referring to the drawings. 
   As shown in  FIG. 1 , the charged particle beam apparatus of the present embodiment is a scanning electron microscope (SEM), and comprises: an electron optical system  10  having a function of scanning a specimen M by irradiating it with an electron beam to output a detection signal indicating detection of secondary charged particles; an optical system control means for controlling the electron optical system  10 ; a specimen chamber for storing the specimen M; an image signal processing unit  40 ; an aberration correction value calculation unit  50 ; an integration control unit  60 ; and the like. Further, the electron optical system  10  comprises: an irradiation optical system for irradiating the specimen with primary charged particles; and a detection optical system for detecting the secondary charged particles generated by irradiation of the primary charged particle beam. 
   The irradiation optical system comprises: an electron gun  11  for generating an electron beam; a condenser lens  12  for converging the electron beam; a beam aperture  13  for narrowing down the electron beam; an astigmatism correction coil  14  for correcting the astigmatism; a deflection coil  15 ; an aberration corrector  16  for correcting various aberrations; a scanning coil  17  for scanning a specimen M with the electron beam; and an objective lens  18  for focusing the electron beam on the specimen M. The detection optical system comprises a detector  20  for detecting secondary electrons from the specimen M. 
   The aberration corrector  16  is a device that gives aberrations that are the reverse of the aberrations generated by the lens system so that the aberrations are finally removed from the electron beam arriving at the specimen M. The aberration corrector  16  comprises four stages of multipole lenses  16   a ,  16   b ,  16   c  and  16   d , and has a function of giving reverse aberrations to the charged particle beam passing through its inside by means of electric fields and magnetic fields generated within the multipole lenses. Aberrations generated in the electron optical system are calculated in advance, and the quantities of the reverse aberrations to give are adjusted so that the aberrations included in the charged particle beam can be removed when the charged particle beam arrives at the surface of the specimen. Although an astigmatism corrector, a deflector and Wien filter for example are each a kind of a multipole lens, each of them is a device for correcting one kind of aberration exclusively. Thus, they are essentially different from the aberration corrector of the present embodiment, which comprises multipole lenses arranged in multiple stages and can correct a plurality of aberrations such as chromatic aberration and spherical aberration at the same time and can correct aberrations as by-products generated at the time of correction. 
   The “optical system control means” comprises: power supply circuits  31 - 38  for supplying drive voltages and driving current respectively to the components of the electron optical system  10 ; and the integration control unit  60 . In the following description, a function of changing the focus of primary charged particles among the functions of the “optical system control means” is also referred to as a “focus control means”. In that case, the “focus control means” comprises the integration control unit  60  and an objective lens power supply circuit  38 . Further, a function of controlling the operation of the aberration corrector is also referred to as a “correction optical system control means”. In that case, the “correction optical system control means” comprises the integration control unit  60  and an aberration corrector power supply circuit  36 . 
   The specimen chamber comprises: a stage  25  for mounting a specimen M; a height sensor  21  for detecting the height of the specimen M; a retarding electrode (not shown) for supplying retarding potential to the specimen M held on the stage  25 ; a sensor controller  39  for controlling the drive of the height sensor  21  and converting an analog signal from the height sensor into a digital signal; and a stage controller  33  for controlling the drive of the stage  25 . The sensor controller  39  receives a control signal from the integration control unit  60 , converts the analog signal from the height sensor  16  into the digital signal as described above, and sends the converted digital signal to the integration control unit  60 . 
   The image processing unit  40  synchronizes the output signal of the detector  20  with the scanning frequency of the primary charged particle beam, and two-dimensional distribution data of the secondary charged particles. An item of data clipped from the obtained two-dimensional distribution data into a range corresponding to a prescribed visual field is referred to as frame data. When such frame data are integrated a predetermined number of times or subjected to prescribed image processing, the obtained data are referred to as an image. The image processing unit  40  of the present embodiment has a function of calculating any of two-dimensional distribution data, frame data and an image. 
   The power supply circuits  31 - 38  include: an electron gun power supply circuit  31 , a condenser lens power supply circuit  32 , an astigmatism correction coil power supply circuit  34 , a deflection coil power supply circuit  35 , the aberration corrector power supply circuit  36 , a scanning coil power supply circuit  37 , and the objective lens power supply circuit  38  for controlling respectively drive of the electron gun  11 , drive of the condenser lens  12 , drive of the astigmatism correction coil  14 , drive of the deflection coil  15 , drive of the aberration corrector  16 , drive of the scanning coil  17 , and drive of the objective lens  18 . These power supply circuits  31 - 38  each receive a control signal from the integration control unit  60 . 
   The aberration correction value calculation unit  50  determines a current value or a voltage value to be outputted from the aberration corrector power supply circuit  36 . The integration control unit  60  controls the power supply circuits and the like  31 - 39 , the image processing unit  40 , and the aberration correction value calculation unit  50  in an integrated manner. The aberration correction value calculation unit  50  further comprises an input-output unit  65  for displaying output from the integration control unit  60  on the one hand and for giving instructions to the integration control unit  60  on the other hand. 
   Functionally, the aberration correction value calculation unit  50  comprises: a storage part  51  for storing two-dimensional image data and the like from the image processing unit  40 ; a correction image acquisition instruction part  52  for giving an instruction to acquire an image for aberration correction; a directional differentiation operation part  53  for obtaining directional derivative values in a plurality of directions with respect to two-dimensional image data; an aberration parameter calculation part  54  for calculating various aberration parameters by using the directional derivative values in the plurality of directions; an aberration correction value calculation part  55  for obtaining correction values for various aberrations by using the aberration parameters; and a control part  56  for controlling the above-mentioned functional parts  52 - 55  and for giving the correction values for the various aberrations to the integration control unit  60  to make it correct the various aberrations by means of the aberration corrector  16 . 
   The parameter calculation part  54  comprises: a directional sharpness operation part  54   a  for obtaining a directional asymmetry of each direction by using the directional derivative values in the plurality of directions; a degree-of-directional-skewness operation part  54   b  for obtaining a degree of directional skewness of each direction by using the plurality of directions; and an aberration parameter operation part  54   c  for obtaining various aberration parameters by using directional sharpness and the directional skewness. In the case where aberration parameters corresponding to n-fold symmetric aberrations (n: an even number, such as 2-fold aberration, 4-fold aberration, etc.) are to be obtained, the aberration parameter operation part  54   c  calculates the aberration parameters by using the operation result of the directional sharpness operation part  54   a . On the other hand, in the case where aberration parameters corresponding to n-fold symmetric aberrations (n: an odd number, such as 1-fold (=astigmatism), 3-fold, etc.) are to be obtained, the aberration parameter operation part  54   c  calculates the aberration parameters by using the operation result of the degree-of-directional-skewness operation part  54   b . According to the configuration of the electron microscope of the present embodiment, the parameter calculation part  54  includes both the directional sharpness operation part  54   a  and the degree-of-directional-skewness operation part  54   b . However, depending on the kinds of aberration parameters to be obtained, the parameter calculation part  54  may include only one of them. The above-mentioned directional derivative values, directional sharpness, directional asymmetry and directional skewness will be described in detail later. 
   Each of these aberration correction value calculation unit  50 , image processing unit  40  and integration control unit  60  is a computer, which comprises a CPU for executing various operations, a memory, an external storage, an input interface, an output interface, and the like. Accordingly, each of the functional parts  52 - 56  of the aberration correction value calculation unit  50  is implemented when the CPU executes a program stored in the external storage or the memory. Further, the storage part  51  of the aberration correction value calculation unit  50  is implemented to have the external storage or the memory. 
   Further, the input-output unit  65  is also a computer, which comprises a display unit for displaying various kinds of data and an input unit for receiving various instructions in addition to a CPU for executing various operations, a memory, an external storage, an input interface, and an output interface. 
   Next, operation of the aberration correction value calculation unit  50  of the present embodiment will be described referring to the flowchart shown in  FIG. 2 . 
   First, the correction image acquisition instruction part  52  of the aberration correction value calculation unit  50  instructs the integration control unit  60  to acquire items of frame data that are to be used for aberration correction and have respective focal positions different from one another (S 10 ). Receiving this instruction, the integration control unit  60  gives a control instruction to the objective lens power supply circuit  38  to control drive of the objective lens  18  in order to change the focal position (focus f) such that the focus is changed sequentially while irradiating an area formed with a pattern including edge components equally in each direction on a specimen M with an electron beam. Here, among the realized focuses, one focus is a just focus and the others defocuses. Further, in the present embodiment, it is assumed that the number of items of frame data is 10 or more. The detector  20  detects secondary electrons from the specimen M each time the focus is changed, and sends them to the image processing unit  40 . The image processing unit  40  generates an item of two-dimensional distribution data for each focus, and sends the generated two-dimensional distribution data to the aberration correction value calculation unit  50 . 
   When the items of two-dimensional distribution data are acquired from the image processing unit  40  (S 20 ), the control part  56  of the aberration correction value calculation unit  50  stores them in the storage part  51 . Next, the directional differentiation operation part  53  of the aberration correction value calculation unit  50  obtains directional derivative values in a plurality of directions for each item of two-dimensional distribution data (S 30 ). Here, derivative values are obtained for directions of 0°, 22.5°, 30°, 45°, 90°, 120° and 135°. 
   Here, a method of obtaining directional derivative values will be described referring to  FIG. 6 . For example, in the case where two-dimensional distribution data as shown in  FIG. 6  are obtained, 0° differentiation mask (i.e., x-direction sobel differential filter) and 90° differentiation mask (i.e., y-direction sobel differential filter) are prepared assuming that one direction of the frame data is an x-axis direction and the direction perpendicular to that direction is a y-axis direction. The stage controller  33  has an x, y-coordinate system for controlling drive of the stage, and usually the above-mentioned x-axis and y-axis are determined in accordance with the x, y-coordinate system for the stage drive control. The x-axis direction is 0° and the y-axis direction is 90°. In the case of the 0° differentiation mask of the present embodiment, “−4”, “0” and “4” are lined up in the 0° direction. In the case of the 90° differentiation mask, “−4”, “0” and “4” are lined up in the 90° direction. To obtain 0° derivative value of some item of pixel data of frame data, the pixel data in question is multiplied by “0” in the center of the 0° differentiation mask, and each item of pixel data around that item of pixel data is also multiplied by the numerical value at the corresponding position in the 0° differentiation mask. Then, the sum of these values becomes the 0° derivative value of the item of pixel data in question. By performing the above processing with respect to all items of pixel data of the frame data, 0° derivative value data of the frame data are obtained. Further, to obtain 90° derivative value data of the frame data, processing similar to the above is performed by using the 90° differentiation mask. In the case of obtaining derivative value data with respect to directions of 22.5°, 30°, 45° and the like, differentiation masks corresponding to those angles may be prepared and used similarly. Otherwise, the two-dimensional distribution data may be rotated by 22.5°, 30°, 45° and the like, and then the 0° differentiation mask and the 90° differentiation mask may be used to perform processing similar to the above. 
   The differentiation masks shown in the figure are examples. It is, however, not necessary to stick to these examples, and other masks may be used if they satisfy requirement for a mask used for directional differentiation (i.e., values in the symmetrical positions with respect to some axis have reversed signs and approximately same values). Further, various variations of differentiation masks can be considered in order to suppress noises and to improve selectivity of differential directions. Further, before calculation of differentiation of frame data, a filtering method and a method of contracting the frame data should be selected appropriately for the frame data. As filtering methods, there are ones that perform smoothing for the purpose of noise suppression and ones that weight the center of frame data in order to avoid effect of drift such as change of frame data boundary. 
   Next, the aberration parameter calculation part  54  obtains various parameters by using directional derivative value data in a plurality of directions with respect to each item of two-dimensional distribution data obtained in step  30  (S 40 ). As processing for obtaining the aberration parameters, there are processing for obtaining parameters of star aberration and spherical aberration (S 40   a ), processing for obtaining parameters of astigmatism, 4-fold astigmatism and focus offset (S 40   b ), and processing for obtaining parameters of 3-fold astigmatism and coma aberration (S 40   c ). Details of these will be described later. Calculated aberration parameters are stored in the storage part  51 . 
   When the parameters are obtained, the control part  56  of the aberration correction value calculation unit  50  judges whether each aberration parameter is less than or equal to a threshold determined previously for that aberration parameter (S 50 ). In the case where all the aberration parameters are less than or equal to the corresponding thresholds, then aberration correction is not performed and the processing is ended. If any aberration parameter is more than its threshold, then the aberration correction value calculation part  55  obtains a correction value for correcting the aberration (S 60 ). The aberration correction value calculation part  55  uses a previously-stored relation between an aberration parameter and a correction value in order to obtain a correction value for the obtained aberration parameter. Then, the control part  56  gives respective correction values for aberrations to the integration control unit  69  to make the aberration corrector  16  perform correction of the aberrations (S 70 ), and the processing returns to step  10  again. Then, the processing of steps  10 - 70  is repeated until it is judged in step  50  that all the aberration parameters are less than or equal to their thresholds. 
   Here, when it is judged in step  50  that a plurality of aberration parameters are more than their thresholds, it is possible that correction values for all the aberrations concerned are obtained in step  60  and all the correction values are given to the integration control unit  60  in step  70  to correct these aberrations all at once. Or, it is possible that only a correction value for the aberration of the lowest order among aberrations whose aberration parameters are judged to be more than their thresholds is obtained in step  60  and only this correction value is given to the integration control unit  60  in step  70 . In other words, it is possible that lower-order aberration is corrected preferentially. Among aberrations, the aberration of the lowest order is focus offset, followed by astigmatism, coma aberration, 3-fold astigmatism, spherical aberration, 4-fold astigmatism and star aberration. Further, in step  50 , the control part  56  of the aberration correction value calculation unit  50  judges whether each aberration parameter is less than or equal to its threshold. In parallel with this, two-dimensional distribution data may be sent to the input-output unit  65  through the integration control unit  60  in order to make the input-output unit  65  display the two-dimensional distribution data, so that two-dimensional frame data are shown to the operator of this scanning electron microscope. 
   Next, among the processes in the aberration parameter calculation processing (S 40 ), details of the processing (S 40   a ) for obtaining the parameters of star aberration and spherical aberration will be described referring to the flowchart shown in  FIG. 3 . 
   First, the directional sharpness operation part  54   a  of the aberration parameter calculation part  54  obtains a directional sharpness dθ(f): {θ: 0°, 45°, 90°, 135°} for each direction by using derivative value data for 0°, 45°, 90° and 135° with respect to each item of two-dimensional distribution data (S 41   a ). In detail, when a directional sharpness d0(f) is to be obtained, then, at the beginning, with respect to two-dimensional distribution data at some focal position f, the sum of absolute values of 0° derivative value data of pixel intensities (gray values) at the points of the two-dimensional distribution data or the sum of square values of the values at those points is obtained. Similarly, by obtaining such sum for each of other focal positions f, f-dependent data on the sum of the absolute values or square values of 0° derivative value data are obtained. The above-mentioned dθ(f) is the thus-obtained f-dependent data on the sum of directional derivative values (gradients at points). 
     FIG. 7  shows the focus value f dependency of the thus-obtained directional sharpness d0(f), d45(f), d90(f), d135(f) for each direction. As shown in the figure, a curve (illustrated as a solid line or a broken line) showing directional sharpness d0(f), d45(f), d90(f), d135(f) for each direction is asymmetric with respect to a specific f at which d takes a local maximum value. In the present embodiment, this position where a directional sharpness d takes the local maximum value is called a center focal position p. In step S 42   a , the directional sharpness operation part  54   a  shown in  FIG. 1  obtains an asymmetry ds0, ds45, ds90, ds135 of directional sharpness d0(f), d45(f), d90(f), d135(f) for each direction 0°, 45°, 90°, 135°. 
   A center focal position p can be obtained by approximating a directional sharpness dθ(f) by a polynomial (for example, a quadratic function) and by taking a local maximum value of this function as a center position pθ. At that time, a function by which the directional sharpness is approximated may be a Gaussian function, and in effect any function can be used as far as it can be used for fitting. Alternatively, with respect to a directional sharpness dθ(f), the center of gravity of a set of points larger than or equal to a threshold may be obtained, to define the center of gravity as a center position pθ. 
   Several methods of obtaining a center focal position p are described. 
   Next, an asymmetry dsθ is obtained by using directional sharpness dθ(f).  FIGS. 8A and 8B  show several methods of obtaining an asymmetry dsθ.  FIG. 8A  shows an example where a curve of directional sharpness dθ(f) is divided into an area of “f&gt;pθ” and an area of “f&lt;pθ” with respect to the center position pθ as a boundary, fitting by a quadratic function is performed for each area independently, and an asymmetry dsθ is determined as a ratio α 1 /α 2  of coefficients α 1 , α 2  of the respective highest-order terms of both quadratic functions or a difference α 1 −α 2  between those coefficients. In this case also, any function (for example, a Gaussian function) that can be used for fitting may be used.  FIG. 8B  shows a method in which integral values S 1 , S 2  are obtained for an area of “f&lt;pθ” and an area of “pθ&lt;f” of a set of points larger than or equal to a threshold, and an asymmetry dsθ is determined as a ratio S 1 /S 2  of the integral values S 1  and S 2  or a difference S 1 −S 2  between those integral values. The method shown in  FIG. 8A  uses the simple calculation formulas requiring shorter calculation times, and thus the load on the operation unit becomes lower. Further, the method shown in  FIG. 8B  has the advantage that an aberration parameter is obtained very accurately because the whole information included in dθ(f) is used. Here, there is also a method in which the value of center of gravity of a set of points larger than or equal to some threshold is obtained with respect to a directional sharpness dθ(f), a local maximum value of the directional sharpness dθ(f) is obtained, and difference between the center-of-gravity value and the local maximum value is determined as an asymmetry dsθ. The calculation time and obtained effects of this method are almost similar to those of  FIG. 8B . However, their characteristics are different with respect to the problem described in the following. In the method of  FIG. 8B , it is possible from the viewpoint of calculation that S 1  equals S 2  (S 1 =S 2 ) although the waveform is different between the area of “f&lt;pθ” and the area of “pθ&lt;f”. On the other hand, also in the method of obtaining a difference between the center-of-gravity value and the local maximum value, it is possible that there is no difference between the center-of-gravity value and the local maximum value although aberration remains. Although the characteristics of these methods do not denote any relative merits on these problems, it is less likely that both problems occur at the same time. Thus, it is possible to select one method, or partially both, depending on the conditions. 
   As shown in  FIG. 9 , an asymmetry dsθ for a direction is periodic with respect to angle, and thus a periodic function such as a sine wave can be fitted. The aberration parameter operation part  54   c  performs fitting of the θ-dependent data of asymmetry dsθ by using a sine wave function as mentioned above; obtains a magnitude δS 3  proportional to the magnitude of a star aberration, a direction δ 3  of the star aberration, and a magnitude δCs proportional to the magnitude of spherical aberration by using the following equations Eq. 1, Eq. 2 and Eq. 3 (S 43   a ); and stores these values in the storage part  51 . 
   
     
       
         
           
             
               
                 
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                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     tan 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             d 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             45 
                           
                           - 
                           
                             d 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             135 
                           
                         
                         
                           
                             d 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                           - 
                           
                             d 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             90 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 2 
               
             
           
           
             
               
                 
                   δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Cs 
                 
                 = 
                 
                   
                     ( 
                     
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       + 
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         45 
                       
                       + 
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         90 
                       
                       + 
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         135 
                       
                     
                     ) 
                   
                   / 
                   4 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 3 
               
             
           
         
       
     
   
   Next, among the processes in the aberration parameter calculation processing (S 40 ), details of the processing (S 40   b ) for obtaining the parameters of astigmatism, 4-fold astigmatism and focus offset will be described referring to the flowchart shown in  FIG. 4 . 
   First, the directional sharpness operation part  54   a  of the aberration parameter calculation part  54  obtains a directional sharpness dθ(f) (d0(f), d22.5(f), d45(f), d90(f), d135(f)) for each direction by using derivative value data for 0°, 22.5°, 45°, 90° and 135° with respect to each item of two-dimensional distribution data (S 41   b ). The method of obtaining each directional sharpness dθ(f) is the same as that of obtaining directional sharpness dθ(f) in the above-described step  41   a.    
   Next, the directional sharpness operation part  54   a  obtains a center focal position p0, p22.5, p45, p90, p135 indicating the peak value with respect to directional sharpness d0(f), d22.5(f), d45(f), d90(f), d135(f) for each direction (S 42   b ). Here, the processing up to obtainment of focus-value-f-dependent data of dθ(f) by using derivative value data for each direction is similar to the processing (S 40   a ) of obtaining parameters of star aberration and spherical aberration. Thus, processing up to the middle of step  40   a  and the processing in step  42   a  may be performed in an integrated manner. 
   The above-described calculation processing obtains angular dependent data of a center focal position pθ, i.e., f at which directional sharpness dθ(f) shows a peak value. By performing fitting of the angular dependent data by using the aberration parameters of astigmatism and the aberration parameters of 4-fold astigmatism as fitting parameters, the above-mentioned aberration parameters can be obtained. For the sake of understandability, a sine wave component for obtaining the aberration parameters of astigmatism and a sine wave component for obtaining the aberration parameters of 4-fold astigmatism are shown schematically in  FIGS. 10 and 11  respectively. As shown in  FIG. 10 , in the case of the sine wave of astigmatism, the magnitude δ of focus displacement (astigmatic difference) owing to the astigmatism appears as the amplitude of this sine wave, and the direction α of focus displacement owing to the astigmatism appears as the angle indicating the peak of this sine wave. Further, the focus offset value z appears as an offset of an inflection point of this sine wave. 
   Thus, the parameter operation part  54   c  obtains the magnitude δ of defocus owing to astigmatism, its direction α and the focus offset value z by using the following Eq. 4, Eq. 5 and Eq. 6 (S 43   b ), and stores the obtained values in the storage part  51 . 
   
     
       
         
           
             
               
                 
                   δ 
                   2 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                         - 
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           90 
                         
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           45 
                         
                         - 
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           135 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 4 
               
             
           
           
             
               
                 α 
                 = 
                 
                   
                     1 
                     2 
                   
                   ⁢ 
                   Arc 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     tan 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             45 
                           
                           - 
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             135 
                           
                         
                         
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                           - 
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             90 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 5 
               
             
           
           
             
               
                 z 
                 = 
                 
                   
                     ( 
                     
                       
                         p 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       + 
                       
                         p 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         45 
                       
                       + 
                       
                         p 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         90 
                       
                       + 
                       
                         p 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         135 
                       
                     
                     ) 
                   
                   / 
                   4 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 6 
               
             
           
         
       
     
   
   Further, as shown in  FIG. 11 , in the case of the sine wave of the 4-fold astigmatism, the magnitude δA 3  of 4-fold astigmatism appears as the amplitude of this sine wave, and its direction α 3  as an angle indicating a peak of this sine wave. Thus, the parameter operation part  54   c  obtains the magnitude δA 3  of 4-fold astigmatism and its direction α 3  by using the following Eq. 7 and Eq. 8 (S 43   b ), and stores the obtained values in the storage part  51 . 
   
     
       
         
           
             
               
                 
                   δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   A 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     3 
                     2 
                   
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   2 
                                   · 
                                   p 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                               - 
                               
                                 δ 
                                 · 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       2 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     α 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 z 
                               
                             
                           
                         
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   2 
                                   · 
                                   p 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 22.5 
                               
                               - 
                               
                                 δ 
                                 · 
                               
                             
                           
                         
                         
                           
                             
                               
                                 cos 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         - 
                                         2 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       α 
                                     
                                     + 
                                     
                                       π 
                                       / 
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 z 
                               
                             
                           
                         
                       
                       ) 
                     
                     2 
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 7 
               
             
           
           
             
               
                 
                   α 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 = 
                 
                   
                     1 
                     4 
                   
                   ⁢ 
                   Arc 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     tan 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             22.5 
                           
                           - 
                           
                             δ 
                             · 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       2 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     α 
                                   
                                   + 
                                   
                                     π 
                                     / 
                                     4 
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           z 
                         
                         
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                           - 
                           
                             δ 
                             · 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     - 
                                     2 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   α 
                                 
                                 ) 
                               
                             
                           
                           - 
                           z 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 8 
               
             
           
         
       
     
   
   In the case of frame data including spherical aberration, as the focus is changed from the just-focused state, the amount of blurring becomes different depending on whether the change is positive or negative while the style of blurring is same. In the case of frame data including star aberration, as the focus is changed from the just-focused state, the style of blurring changes by 90° depending on whether the change is positive or negative while the amount of change of defocus is same. Further, in the case of frame data including 4-fold astigmatism, as the focus is changed from the just-focused state, 4-fold blurring changes its direction by 45° depending on whether the change is positive or negative while the amount of change of defocus is same. As described above, in order to measure these on the basis of frame data in the present embodiment, sharpness at positive or negative change of the focus is analyzed by changing the focal position, to obtain the magnitude of spherical aberration, the magnitude and direction of star aberration, and the magnitude and direction of 4-fold astigmatism. Further, as described above, this method can additionally obtain focus displacement owing to astigmatism and its direction and the focus offset. 
   Next, among the processes in the aberration parameter calculation processing (S 40 ), details of the processing (S 40   c ) for obtaining the parameters of 3-fold astigmatism and coma aberration will be described referring to the flowchart shown in  FIG. 5 . 
   First, the degree-of-directional-skewness operation part  54   b  of the aberration parameter calculation part  54  obtains an amount of directional skewness sθ(f) (s0(f), s30(f), s90(f), s120(f)) for each direction by using the derivative value data for 0°, 30°, 90° and 120° with respect to each item of two-dimensional distribution data (S 41   c ). In detail, when the amount of directional skewness s0(f) is to be obtained, then, at the beginning, with respect to two-dimensional distribution data at some focal position f, the sum of values (gray values) of 0° derivative value data at the points of the two-dimensional distribution data is obtained. Similarly, the sum for each of other focal positions f is obtained. Then, a relation of the sum to the focal position f as a variable is determined as the amount of directional skewness s0(f). Thus, in the case where the sum with respect to the points is determined as an amount of directional skewness, the sum of derivative values become zero if a beam bias (anisotropy of brightness) does not exist while the specimen is a uniform one. However, the sum does not become zero if the bias exists, and the direction of bias appears as a sign, and the magnitude of the bias as the magnitude of a numerical value. As shown in  FIG. 12 , the thus-obtained amount of directional skewness sθ(f) for each direction becomes a quadratic-curve-like function having the base at about the just focus position. 
   Further, as another example of a method of obtaining an amount of directional skewness, there is a method in which a histogram showing derivative value in the horizontal axis and frequency in the vertical axis is obtained with respect to frame data as a result of differentiation, and an amount of skewness is obtained on the basis of the bias of distribution of this histogram. When an amount of directional skewness is obtained from the bias of a histogram, the following Eq. 9 is used. 
   
     
       
         
           
             
               
                 
                   s 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   θ 
                 
                 = 
                 
                   
                     ∑ 
                     i 
                     N 
                   
                   ⁢ 
                   
                     
                       
                         u 
                         i 
                       
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             
                               
                                 t 
                                 i 
                               
                               ⁡ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                             - 
                             
                               μ 
                               ⁡ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                           
                           ) 
                         
                         3 
                       
                       / 
                       
                         ( 
                         
                           U 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             σ 
                             3 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 9 
               
             
           
         
       
     
   
   In any method of obtaining an amount of skewness such as the method of obtaining it from the sum for the points or the method of obtaining it from a histogram, an obtained amount of skewness is affected by an inclination, shading or particle forms of a specimen. Thus, it is favorable to correct the obtained amount on the basis of the value at the just focus. In that case, as shown in the following (Eq. 10) where sθ(f) is expressed as sθ(f) tilt  when there is an inclination or pattern anisotropy of a specimen, effects of the specimen can be cancelled by subtracting the product of an amount of skewness sθ(p) obtained at just focus and a defocus function def(f). 
                       σ   2     =       1   U     ⁢       ∑   i   N     ⁢         u   i     ⁡     (         t   i     ⁡     (   θ   )       -     μ   ⁡     (   θ   )         )       2           ,     
     ⁢       μ   ⁡     (   θ   )       =       1   U     ⁢       ∑   i   N     ⁢         u   i     ⁡     (   θ   )       ⁢       t   i     ⁡     (   θ   )               ,     
     ⁢     U   =       ∑   i   N     ⁢       u   i     ⁡     (   θ   )             ⁢     
     ⁢       s   ⁢           ⁢     θ   ⁡     (   f   )         =       s   ⁢           ⁢       θ   ⁡     (   f   )       tilt       -     s   ⁢           ⁢       θ   ⁡     (   p   )       ·   def     ⁢           ⁢     θ   ⁡     (   f   )                     Eq   .           ⁢   10               
where u i (θ) is frequency, t i (θ) is a derivative value for the direction θ, and N is the total number of t i (θ).
 
   In the case where the directional sharpness dθ(f) is calculated by using the sum of absolute values, the defocus function defθ(f) normalized with respect to f=p is used. On the other hand, in the case where the directional sharpness dθ(f) is calculated by using the sum of the square values, the square root of an amount of skewness is obtained and the defocus function normalized with respect to f=p is used. 
   Next, the degree-of-directional-skewness operation part  54   b  obtains a degree of skewness skθ that indicates a tendency of a change of an amount of skewness as the direction (angle) changes, by using an amount of directional skewness sθ(f) (s0(f), s30(f), s90(f), s120(f) for each direction (S 42   c ). In detail, for example, fitting of an amount of directional skewness sθ(f) by quadratic functions is performed, and a ratio of quadratic coefficients is expressed as a function of θ to determine the function as a degree of skewness skθ. The function used for the fitting may be not a quadratic function but a Gaussian function or the like, and in effect any function can be used as far as it can be used for fitting. Further, although here a ratio of coefficients is defined as a degree of skewness, a difference between coefficients may be defined as a degree of skewness. For example, a degree of skewness skθ becomes a function as shown in  FIG. 13 . 
   Degree of skewness skθ can be divided into a sine wave for coma aberration as shown in  FIG. 14  and a sine wave for 3-fold astigmatism as shown in  FIG. 15 . As shown in  FIG. 14 , in a sine wave for coma aberration, the magnitude δB 2  of coma aberration appears as the amplitude of the sine wave, and its direction β 2  as the angle showing the peak of the sine wave. Further, as shown in  FIG. 15 , in a sine wave for 3-fold astigmatism, its magnitude βA 2  appears as the amplitude of the sine wave, and its direction α 2  as the angle showing the peak of the sine wave. Thus, the parameter operation part  54   c  obtains the magnitude δB 2  and direction β 2  of coma aberration by using the following Eq. 11 and Eq. 12, and obtains the magnitude δA 2  and direction α 2  of 3-fold astigmatism by using the following Eq. 13 and Eq. 14, and stores the obtained values in the storage part  51  (S 43   c ). 
   
     
       
         
           
             
               
                 
                   δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     2 
                     2 
                   
                 
                 = 
                 
                   
                     
                       4 
                       / 
                       3 
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             sk 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                           - 
                           
                             sk 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             120 
                           
                         
                         ) 
                       
                       2 
                     
                   
                   + 
                   
                     
                       4 
                       / 
                       3 
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             sk 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             90 
                           
                           + 
                           
                             sk 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             30 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 11 
               
             
           
           
             
               
                 
                   
                     β 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     Arc 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       tan 
                       ( 
                       
                         
                           
                             3 
                           
                           - 
                           K 
                         
                         
                           1 
                           - 
                           
                             K 
                             ⁢ 
                             
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                 
                 , 
                 
                   K 
                   = 
                   
                     
                       
                         sk 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       - 
                       
                         sk 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         120 
                       
                     
                     
                       
                         sk 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         90 
                       
                       + 
                       
                         sk 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         30 
                       
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 12 
               
             
           
           
             
               
                 
                   δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   A 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     2 
                     2 
                   
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   2 
                                   · 
                                   sk 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       β 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   2 
                                   · 
                                   sk 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 30 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         - 
                                         β 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     + 
                                     
                                       π 
                                       / 
                                       6 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     2 
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 13 
               
             
           
           
             
               
                 
                   α 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 = 
                 
                   
                     1 
                     3 
                   
                   ⁢ 
                   Arc 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     tan 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               2 
                               · 
                               sk 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             30 
                           
                           - 
                           
                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             B 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       β 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                   + 
                                   
                                     π 
                                     / 
                                     6 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               2 
                               · 
                               sk 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                           - 
                           
                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             B 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     - 
                                     β 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 14 
               
             
           
         
       
     
   
   In the case of frame data including 3-fold astigmatism, as the focus is changed from the just-focused state, the frame data do not blur uniformly but blurs in a triangular shape in the same direction without depending on whether the focus change is positive or negative. In the case of frame data including coma aberration, as the focus is changed from the just-focused state, the frame data do not blur uniformly but blurs in one direction without depending on whether the focus change is positive or negative. In order to measure such phenomena on the basis of frame data, the present embodiment defines the degree of directional skewness, obtains the amount of directional skewness by changing the focal position, further obtains the degree of skewness showing a tendency of change in the amount of directional skewness that accompanies a directional change, and obtains the magnitudes and directions of 3-fold astigmatism and coma aberration by using those values. 
   As described above, when the aberration parameters are obtained (S 40 ), it is judged that each of the aberration parameter is less than or equal to its previously-determined threshold (S 50 ). When some aberration parameter is larger than its threshold, a correction value for correcting the aberration is obtained (S 60 ). Then, correction values of aberrations are given to the integration control unit  60 , and the aberration corrector  16  corrects the aberrations (S 70 ). The correction values of aberrations are set in the aberration corrector power supply circuit  36 , and as a result the aberration corrector  16  operates toward the direction of canceling the aberrations. Thus, the aberrations are corrected. Here, it is also possible to correct the focus offset by operating the objective lens  15 . Accordingly, the correction value may be set in the objective lens power supply circuit  38 . 
   As described above, according to the present embodiment, directional derivative value data concerning a plurality of directions are obtained with respect to each item of two-dimensional distribution data of different focal positions, and various aberration parameters are obtained from these items of directional derivative data. Since random noise is removed in the course of differentiating two-dimensional distribution data in obtainment of aberration parameters from directional derivative value data, it is possible to obtain aberration parameter accurately even if two-dimensional distribution data are relatively coarse. This means that aberration parameters can be obtained accurately even if the so-called frame data that have not subjected to image integration or image processing for improving an S/N ratio. Further, aberration parameters can be obtained accurately even when the scanning speed of electron beam is increased (i.e. even when two-dimensional distribution data has a lower S/N ratio). As a result, even when the required number of frames of frame data becomes larger, the acquisition time of one frame of frame data can be reduced, and consequently the time required for adjusting the aberration corrector can be shortened. Further, the scanning speed of an electron beam can be raised, and accordingly damage to a specimen M can be reduced. 
   Further, according to the present embodiment, directional sharpness and degree of directional skewness of frame data of the same specimen M are obtained by changing the focal length, and aberration parameters can be obtained from those values. Thus, the aberration parameters can be obtained without depending on a pattern of the specimen M. As a result, high-precision aberration correction can be performed in parallel with conventional automatic focus operation or automatic stigmatism operation. The calculations of aberration parameters by the methods of the present embodiment are simple processing for a computer used for SEM and the calculations themselves can be performed at high speed. A part of calculations in automatic focusing or automatic stigmatism operation can be shared, and accordingly the aberration parameter calculation part does not need addition of special hardware or conversion of hardware. 
   Further, the present embodiment is provided with a height sensor  39 . As a result, by obtaining previously a relation between change in the height of a specimen M and change in an aberration correction value, it is possible to correct the aberration according to the height of the specimen M, reducing the number of times of repeating aberration correction. 
   In the above embodiment, angles such as 0°, 45°, 90°, 135° are employed as directions for obtaining directional derivative value data. However, it is not necessary to employ these specific angles. Further, the number of angles for obtaining derivative value data is sufficient if the parameters can be obtained. In detail, as for directional sharpness, it is sufficient that sharpness can be obtained for at least five angles. As for degree of directional skewness, it is sufficient that at least four values of skewness can be obtained, and the number of angles may be larger than this. Further, as the number of frames (or items) of frame data having different focal positions, the present embodiment assumes ten or more as described above. However, at least three frames are sufficient. Further, it is not necessary that items of frame data do not include a just-focused item of frame data, and it is sufficient that there is an item of frame data at a focal position near to the just focus. 
   Further, according to the above embodiment, aberration correction values obtained by the aberration correction value calculation unit  50  are set in the aberration corrector power supply circuit  36  through the integration control unit  60 . However, the aberration correction value calculation unit  50  may directly set aberration correction values in the aberration corrector power supply circuit  36 . Further, according to the above embodiment, a computer having a frame data processing function implements the image processing unit  40 ; a computer having an aberration correction value calculation function implements the aberration correction value calculation unit  50 ; and a computer having an integration control function implements the integration control unit  60 . However, a computer having a frame data processing function and an aberration correction value calculation function may implement a frame data processing/aberration correction value calculation unit. A computer having an aberration correction value calculation function and an integration control function may implement an aberration correction value calculation/integration control unit. 
   Further, the above-described embodiment is a case where the present invention is applied to an ordinary scanning electron microscope. The present invention is not limited to this. For example, the present invention can be applied to a critical dimension scanning electron microscope (CD-SEM) or a defect review scanning electron microscope (DR-SEM), of course.