Abstract:
The present invention discloses a method for determining the mineral content represented by the entire SEM-EDS dataset, including initially unknown data points. SEM-EDS data points are taken and compared to a set of known data points. Any data point that is not sufficiently similar to the known data point is classified as unknown and clustered with like unknown data points. After all data points are analyzed, any clusters of unknown data points with a sufficient number of data points are further analyzed to determine their characteristics. All clusters of unknown data points with an insufficient number of data points to allow further analysis are considered outliers and discarded.

Description:
TECHNICAL FIELD OF THE INVENTION 
       [0001]    The present invention relates generally to methods and structures for identifying minerals using charged particle beam systems and energy dispersive spectroscopy systems. 
       BACKGROUND OF THE INVENTION 
       [0002]    Mineral analysis systems, such as the Qemscan and MLA available from FEI Company, Hillsboro, Oreg., have been used for many years to analyze mineral samples. To determine the type and relative quantity of minerals present in a mine, a sample in the form of small granules, is fixed in epoxy in a mold and the mold is placed in a vacuum chamber. An electron beam is directed toward a sample and, in a process called “energy dispersive x-ray spectroscopy” or “EDS,” the energies of x-rays coming from the sample in response to the electron beam are measured and plotted in a histogram to form a spectrum. The measured spectrum can be compared to the known spectra of various elements to determine which elements and minerals are present. 
         [0003]    Mineral analysis systems, such as the QEMSCAN® (Quantitative Evaluation of Minerals by Scanning electron microscopy) and MLA (Mineral Liberation Analyzer) from FEI Company, the assignee of the present invention, have been used for many years to determine minerals present in mines in order to determine the presence of valuable minerals. Such systems direct an electron beam toward the sample and measure the energy of x-rays coming from the material in response to the electron beam. One such process is called “energy dispersive x-ray analysis” or “EDS,” which can be used for elemental analysis or chemical characterization of a sample. Backscattered electron (BSE) detectors are also used for mineral analysis in conjunction with electron beam columns. The intensity of the BSE signal is a function of the average atomic number of the material under the electron beam, and this relationship can be used to develop a useful mineral identification method. 
         [0004]    EDS systems rely on the emission of X-rays from a sample to perform elemental analysis. Each element has a unique atomic structure, which allows x-rays that are characteristic of an element&#39;s atomic structure to be uniquely identified from one another. To stimulate the emission of x-rays from a sample, a beam of charged particles is focused onto the sample, which causes electrons from inner shells to be ejected. Electrons from outer shells seek to fill this electron void, and the difference in energy between the higher energy shell and the lower energy shell is released as an x-ray, which can be detected by an EDS detector. 
         [0005]    QEMSCAN® comprises a SEM, multiple EDS detectors, and software for controlling automated data acquisition. This technology identifies and quantifies elements within an acquired spectrum and then matches this data against a list of mineral definitions with fixed elemental ranges. The size of the ranges depends directly on the number of x-rays in the spectrum and cannot be applied to higher quality spectra without creating a new mineral definition. Thus, it is not possible to define a universal database for an arbitrary number of X-ray counts. Furthermore, the match is not given as a probability value, it is given as either true or false, and it picks the first match it finds even if a better match might be present elsewhere in the mineral database. 
         [0006]    MLA technology also combines a SEM, multiple EDS detectors, and automated quantitative mineralogy software. MLA computes a probability match between a measured mineral spectrum and a reference mineral spectrum. This method works reasonably, but the numerical value obtained tends to be dominated by the size of the largest peak in the x-ray spectrum. 
         [0007]    The acquisition time of a suitable BSE signal is typically on the order of microseconds per pixel. However, EDS systems are usually slower and have a longer acquisition time, typically on the order of several seconds per pixel to uniquely discriminate the spectrum from all other mineral spectra. As a result, the time required to collect an x-ray spectrum to uniquely identify a mineral reduces the number of pixels that can be measured substantially. EDS systems are also typically insensitive to light atoms. Because of the advantages of both EDS detectors and BSE detectors, it is sometimes useful to use both BSE and x-ray spectra to accurately identify minerals, which requires more time and becomes a difficult problem to solve with a commercially viable approach. 
         [0008]    A mineral classification system must be capable of comparing each unknown measured spectrum to a library of known mineral spectrums, and then making a selection based on which known mineral is most similar to the measured spectrum. Typically, to find the most similar spectrum requires the use of a metric that represents the degree of similarity between the measured data and the known material. 
         [0009]    Currently, there are various ways to compare two spectrums directly, either by calculating a distance metric or a similarity metric. An example of a method of comparison used in the prior art is to take the sum of the differences between the two spectrums as a distance. The Mineral Liberation Analyzer manufactured by FEI Company, Inc., the assignee of the present invention, uses a chi-squared statistical test to compare the value at each energy channel of the measured spectrum to the value at the corresponding channel of the known mineral spectrum. These prior art approaches are based around comparing the spectrums on a channel by channel basis. The problem of using a comparison on a channel by channel basis is that there is no guarantee that all required peaks in the mineral spectrum are present in the measured spectrum. It is possible that a measured spectrum appears to be similar to a mineral yet it is missing an element that is required by the definition of that mineral, or has an additional element not found in that definition of a mineral. 
         [0010]    In the XBSE_STD measurement mode of the MLA, each data point is compared against a mineral list. If the data point is not similar to any mineral, then a new mineral entry is created and a high quality EDS spectrum is immediately measured from the sample. However, there are several significant limitations of this approach. First, the user is presented with hundreds of unknown data points and there is no way to distinguish which ones occur most frequently and which ones are outlier&#39;s. Second, the analysis cannot be performed offline as it requires access to the SEM to collect the high quality data during measurement. Finally, only the raw data is presented to the user and there is no analytical tool to give elemental composition. Thus, there is a need for an improved mineral identification method. 
       SUMMARY OF THE INVENTION 
       [0011]    An objection of the invention is to improve the identification of minerals in a sample. The present invention facilitates the determination of the mineral content represented of an SEM-EDS dataset, including initially unknown data points. 
         [0012]    SEM-EDS data points are collected and compared to a set of known data points. Any data point that is not sufficiently similar to the known data point is classified as unknown and clustered with like unknown data points. After all data points are analyzed, any clusters of unknown data points with a sufficient number of data points are further analyzed to determine their characteristics. 
         [0013]    Embodiments of the invention differentiate unknown data points that are simply outliers, from data points that represent a genuine mineral that is occurring in the sample. The clustering analysis can be performed offline, online, or in real time, and re-processed anytime. The results presented to the operator are typically elemental compositions, average atomic number, or other characteristics that are measured by the analysis. The raw EDS and BSE spectrums may also be presented, as well as the raw data of any other tests done. 
         [0014]    The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter. It should be appreciated by those skilled in the art that the conception and specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    For a more thorough understanding of the present invention, and advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
           [0016]      FIG. 1  shows a flow chart of the method to classify all unknown data points into clusters; and 
           [0017]      FIG. 2  shows the analysis of all clusters to determine if they contain only outlier data points or if the mineral definition list needs updating. 
           [0018]      FIG. 3   a - 3   j  are example spectra obtained by energy dispersive x-ray spectroscopy. 
           [0019]      FIGS. 4B and 4B  are x-ray spectra of quartz and pyrite, respectively. 
           [0020]      FIG. 5  is a scanning electron microscope system with EDS capability. 
       
    
    
     DETAILED DESCRIPTION 
       [0021]    Embodiments of the present invention are directed to a method and apparatus for efficiently and easily classifying data points. A “data point” is a group of data, such as an EDS spectrum and/or backscattered electron (“BSE”) value. A data point typically corresponds to a mineral. Characteristics of data points corresponding to known minerals are compared to the characteristics of the measured data points. If the characteristics are identical or very similar, the data point is labeled as a known or similar data point. However, if the characteristics of the data point are not similar to the characteristics of the known data points, the data point is labeled as an unknown or dis-similar data point. Any unknown or dis-similar data points will enter into the clustering analysis. 
         [0022]    Basic Scanning Technology 
         [0023]    A beam is directed toward a sample surface and emissions generated from the surface by the beam impact are detected. The primary beam can comprise, for example, electrons, ions, photons (e.g., a laser beam or x-rays), or atoms. The beam is typically focused to a point on the sample and the point is scanned across the sample. Particles (used herein to include photons and scattered primary particles) that are emitted, backscattered, or transmitted through the sample in response to the primary beam are detected. Different emissions from the sample, such as x-rays, backscattered electrons, secondary electrons, Auger electrons, transmitted electrons, or photons, are detected in various analysis modalities. The invention is not limited to any particular analytical technique. 
         [0024]    The different modalities may provide different information about properties of the sample, such as contour information, compositional information, topographical information, or chemical state information. For example, backscattered electron data may be acquired at the same time as x-ray data, with the x-rays being placed at the correct location in the backscattered electron image to produce a spectrum cube. In some embodiments, the different analysis modalities include detecting emissions generated by different beams at different times. 
         [0025]    In some embodiments, an electron beam is directed toward a sample and scanned across regions having different characteristics, such as different mineral compositions. A first detector may provide information about contour, topography, or atomic number, for example, by detecting backscattered electrons, while a second detector may provide information about composition, for example, by detecting characteristic x-rays. 
         [0026]    Clustering 
         [0027]    Cluster analysis, or clustering, is the task of assigning a set of objects into groups, also called clusters, so that the objects in the same cluster are more similar to each other than to those in other clusters. Cluster analysis groups objects based on the information found in the data describing the objects or their relationships. The goal is that the objects in a group will be similar to one other and different from the objects in other groups. The greater the similarity within a group, and the greater the difference between groups, the “better” or more distinct the clustering. 
         [0028]    Cluster analysis itself is not one specific algorithm, but is an general approach to assigning minerals identifications. It can be achieved by various algorithms that differ significantly in their notion of what constitutes a cluster and how to efficiently find them. Clustering can therefore be formulated as a multi-objective optimization problem. The appropriate clustering algorithm and parameter settings, including values such as the distance function to use, a density threshold or the number of expected clusters, depend on the individual data set and intended use of the results. Cluster analysis is typically an iterative process of knowledge discovery or interactive multi-objective optimization that involves trial and error. It will often be necessary to modify preprocessing and parameters until the result achieves the desired properties. 
         [0029]    Any standard clustering technique, such as Agglomerative, Single-Pass or K-Means, may be used for the analysis of the present invention. For example, one possible distance metric takes the sum of the differences between the EDS Spectrum channel values. 
         [0030]    As shown in  FIG. 1 , the first step in the process is to classify every data point in the SEM-EDS data set,  100 , as a known or unknown,  105 . A data point is “known” if its spectrum matches the known spectrum of a mineral within a predetermined limit. For example, one measurement of how well spectra match is the Cosine Similarity metric analysis as given in Equation 1. 
         [0000]    
       
         
           
             
               
                 
                   similarity 
                   = 
                   
                     
                       cos 
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           A 
                           · 
                           B 
                         
                         
                           
                              
                             A 
                              
                           
                            
                           
                              
                             B 
                              
                           
                         
                       
                       = 
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               n 
                             
                              
                             
                               
                                 A 
                                 i 
                               
                               × 
                               
                                 B 
                                 i 
                               
                             
                           
                           
                             
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   n 
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       A 
                                       i 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             × 
                             
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   n 
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       B 
                                       i 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    Where “i” represents each measurement parameter, such as each normalized energy channel height, average atomic number from back-scattered electron analysis, or other measurement parameter, and the values of data point each spectrum are summed over all the energy channels and other measurements. In some embodiments, a spectrum is considered a match to a reference spectrum when the similarity metric of the two is greater than 90%. 
         [0031]    After excluding known data points, all unknown data points are compared to the clusters of unknown data points,  110 . If the unknown data point&#39;s characteristics are similar to another cluster, that is, the similarity metric is greater than a pre-determined amount, the unknown data point is placed in that cluster,  115 . If the unknown data point is not similar to other clusters, a new cluster is created,  120 . The average value of every cluster for each energy channel is recalculated after the addition of each new data point to further refine the cluster&#39;s characteristics and differentiate each cluster from the others,  125 . 
         [0032]    The results of the clustering analysis will be several clusters, with each cluster containing least one “unknown” data point. As shown in  FIG. 2 , once the SEM-EDS data set is reduced to known data points and clusters of unknown data points, the clusters are sorted by the number of data points in the clusters,  200 . This list can be reduced to only those clusters that matched a significant number of data points,  205 , for example the top 20 clusters, although analysis of all or fewer clusters is possible. As used herein matching means unknown data points are clustered or grouped together when the characteristics of each data point are identical or similar to the characteristics of the other data points in the cluster or group. In one embodiment, the characteristics of each data point in a group should be within at least three percent of the average value of the all data points in the group. The matching criteria can be tightened if more precise measurements are needed. 
         [0033]    Once all clusters have been sorted, it is determined whether or not there are any clusters remaining,  210 . If there are no clusters remaining after removal of those with few data points, the remaining clusters are outliers,  215 , and the process is complete. 
         [0034]    However, if there are clusters remaining, it means that there is a mineral in the sample that has not been identified. The remaining clusters then undergo quantitative EDS analysis to give the elemental composition of the unknown minerals,  220 , and a BSE analysis to determine the average atomic number of the minerals,  225 . The average EDS spectrum and BSE value is calculated from each cluster, by averaging all the data points within a cluster. This gives a high quality EDS spectrum that can be further analyzed to give accurate elemental composition and atomic numbers based on BSE data. 
         [0035]    Once all data is analyzed and placed in the appropriate cluster, the analyzed cluster data is presented to the operator,  230 , who may make use of the data to expand the list of mineral definitions to minimize the unknown data points,  235 , eliminate clusters with minimal data points,  205 , and/or determine that all “unknown” data points are outliers and can be ignored,  215 . If desired the operator can instruct the analysis to be repeated so as to rerun the sample with and updated known data point list which will produce fewer unknown data points. 
       Example 
       [0036]    The following example shows an analysis of 10 different samples having spectra show in  FIGS. 3   a - 3   j . The spectra of the ten samples are being compared to spectra of known minerals in a mineral list. In this example, the mineral list has only two minerals, quartz and pyrite, having spectra as shown in  FIGS. 4   a  and  4   b . Each of the spectra of a sample represents a data point. In this example, the data point does not include back scattered electron data. After obtaining the spectra corresponding to the ten points, each data point is analyzed for its similarities with known spectra, for example, by using a cosine comparison on multiple energy channels. Table 1 shows the results of the comparison, and the classification shows how the result of the analysis. 
         [0037]    In this example the known data points are Quartz and Pyrite. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Sample Data and Cluster Analysis 
               
             
          
           
               
                   
                 Similarity  
                 Similarity  
                 Similarity  
                 Similarity  
                   
               
               
                 Num- 
                 With 
                 With 
                 with 
                 with 
                   
               
               
                 ber 
                 Quartz 
                 Pyrite 
                 Unknown_1 
                 Unknown_2 
                 Classification 
               
               
                   
               
             
          
           
               
                 1 
                 99.2% 
                 4.3% 
                 — 
                 — 
                 Identified  
               
               
                   
                   
                   
                   
                   
                 as quartz 
               
               
                 2 
                 3.73% 
                 54.19% 
                 — 
                 — 
                 New cluster  
               
               
                   
                   
                   
                   
                   
                 added 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_1′ 
               
               
                 3 
                 3.04% 
                 98.18% 
                 — 
                 — 
                 Identified as  
               
               
                   
                   
                   
                   
                   
                 Pyrite 
               
               
                 4 
                 5.77% 
                 43.08% 
                 8.63% 
                 — 
                 New Cluster  
               
               
                   
                   
                   
                   
                   
                 added 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_2′ 
               
               
                 5 
                 4.54% 
                 47.81% 
                 95.37% 
                 10.43% 
                 Matches  
               
               
                   
                   
                   
                   
                   
                 cluster 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_1′ 
               
               
                 6 
                 98.96% 
                 4.7% 
                 4.16% 
                 7.22% 
                 Identified as  
               
               
                   
                   
                   
                   
                   
                 Quartz 
               
               
                 7 
                 6.45% 
                 44.89% 
                 10.72% 
                 91.70% 
                 Matches  
               
               
                   
                   
                   
                   
                   
                 cluster 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_2′ 
               
               
                 8 
                 8.96% 
                 43.72% 
                 11.03% 
                 92.81% 
                 Matches  
               
               
                   
                   
                   
                   
                   
                 cluster 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_2′ 
               
               
                 9 
                 6.02% 
                 43.03% 
                 11.67% 
                 92.42% 
                 Matches  
               
               
                   
                   
                   
                   
                   
                 cluster 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_2′ 
               
               
                 10  
                 9.04% 
                 43.93% 
                 11.45% 
                 93.16% 
                 Matches  
               
               
                   
                   
                   
                   
                   
                 cluster 
               
               
                   
                   
                   
                   
                   
                 ′Unknown_2′ 
               
               
                   
               
             
          
         
       
     
         [0038]    In this example, a spectrum is considered a match when the similarity between samples is greater than ninety percent (90%). As seen in Table 1, samples 1 and 6 have a 99.2% match and 98.96% match respectively with the known values of Quartz, thus the software will designate those samples as Quartz. Sample 2 does not match with either Quartz or Pyrite to a degree of greater than 90%, so it is classified as an unknown sample and place in unknown cluster one. Sample 3 has a match of 98.18% with the known value of Pyrite, thus the software will classify this sample as Pyrite. Sample 4 does not match any of the known samples, and does not match closely with the first unknown sample, sample 3, so it is classified as a second unknown sample and placed in unknown cluster two. Sample 5 has a greater than 90% match to Sample 2 and is placed in unknown cluster one. Samples 7-10 have a greater than 90% match to sample 4, therefore these samples are placed in unknown cluster two. At this point the operator can evaluate the samples in unknown clusters one and two to determine if further analysis is needed, additional known data sets should be added to the software, or if the unknown clusters are simply outlier data points that can be ignored. Thus it can be seen that the current method can quickly and easily cluster unknown samples for more efficient handling. 
         [0039]      FIG. 5  is an example of a scanning electron beam system  500  with an x-ray detector  540  suitable for analyzing samples prepared according to the present invention. A scanning electron microscope  541 , along with power supply and control unit  545 , is provided with system  500 . An electron beam  532  is emitted from a cathode  553  by applying voltage between cathode  553  and an anode  554 . Electron beam  532  is focused to a fine spot by means of a condensing lens  556  and an objective lens  558 . Electron beam  532  is scanned two-dimensionally on the specimen by means of a deflection coil  560 . Operation of condensing lens  556 , objective lens  558 , and deflection coil  560  is controlled by power supply and control unit  545 . 
         [0040]    A system controller  533  controls the operations of the various parts of scanning electron beam system  500 . The vacuum chamber  510  is evacuated with ion pump  568  and mechanical pumping system  569  under the control of vacuum controller  532 . 
         [0041]    Electron beam  532  can be focused onto sample  502 , which is on movable X-Y stage  504  within lower vacuum chamber  510 . When the electrons in the electron beam strike sample  502 , the sample gives off x-rays whose energy correlated to the elements in the sample. X-rays  532  having energy inherent to the elemental composition of the sample are produced in the vicinity of the electron beam incident region. Emitted x-rays are collected by x-ray detector  540 , preferably an energy dispersive detector of the silicon drift detector type, although other types of detectors could be employed, which generates a signal having an amplitude proportional to the energy of the detected x-ray. 
         [0042]    Output from detector  540  is amplified and sorted by the processor  520 , which counts and sorts the total number of X-rays detected during a specified period of time, at a selected energy and energy resolution, and a channel width (energy range) of preferably between 10-20 eV per channel. Processor  520  can comprise a computer processor; operator interface means (such as a keyboard or computer mouse); program memory  522  for storing data and executable instructions; interface means for data input and output, executable software instructions embodied in executable computer program code; and display  544  for displaying the results of a multivariate spectral analysis by way of video circuit  542 . 
         [0043]    Processor  520  can be a part of a standard laboratory personal computer, and is typically coupled to at least some form of computer-readable media. Computer-readable media, which include both volatile and nonvolatile media, removable and non-removable media, may be any available medium that can be accessed by processor  520 . By way of example and not limitation, computer-readable media comprise computer storage media and communication media. Computer storage media include volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. For example, computer storage media include RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and that can be accessed by processor  520 . 
         [0044]    Program memory  522  can include computer storage media in the form of removable and/or non-removable, volatile and/or nonvolatile memory and can provide storage of computer-readable instructions, data structures, program modules and other data. Generally, the processor  520  is programmed by means of instructions stored at different times in the various computer-readable storage media of the computer. Programs and operating systems are typically distributed, for example, on floppy disks or CD-ROMs. From there, they are installed or loaded into the secondary memory of a computer. At execution, they are loaded at least partially into the computer&#39;s primary electronic memory. The invention described herein includes these and other various types of computer-readable storage media when such media contain instructions or programs for implementing the steps described below in conjunction with a microprocessor or other data processor. The invention also includes the computer itself when programmed according to the methods and techniques described herein. 
         [0045]    An x-ray spectrum obtained as described above can be stored in a portion of memory  522 , such as the measured spectra memory portion  523 . Data template memory portion  524  stores data templates, such as definitions of known spectra of elements or, in some embodiments, known diffraction patterns of materials. 
         [0046]    While the embodiment shown includes a scanning electron microscope, related embodiment could use a transmission electron microscope or a scanning transmission electron microscope to generate x-rays from the sample. An x-ray fluorescence system could also be used to generate x-rays from the sample. Other embodiments may detect other characteristic radiation, such as gamma rays, from a sample. 
         [0047]    Further, whenever the terms “automatic,” “automated,” or similar terms are used herein, those terms will be understood to include manual initiation of the automatic or automated process or step. Whenever a scan or image is being processed automatically using computer processing, it should be understood that the raw image data can be processed without ever generating an actual viewable image. In the following discussion and in the claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to . . . .” 
         [0048]    It should be recognized that embodiments of the present invention can be implemented via computer hardware or software, or a combination of both. The methods can be implemented in computer programs using standard programming techniques—including a computer-readable storage medium configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner—according to the methods and figures described in this specification. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the programs can be implemented in assembly or machine language, if desired. In any case, the language can be a compiled or interpreted language. Moreover, the program can run on dedicated integrated circuits programmed for that purpose. 
         [0049]    Further, methodologies may be implemented in any type of computing platform, including but not limited to, personal computers, mini-computers, main-frames, workstations, networked or distributed computing environments, computer platforms separate, integral to, or in communication with charged particle tools or other imaging devices, sensors, and the like. Aspects of the present invention may be implemented in machine readable code stored as memory on a storage medium or device, whether removable or integral to the computing platform, such as a hard disc, optical read and/or write storage mediums, RAM, ROM, and the like, so that it is readable by a programmable computer, for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. Moreover, machine-readable code, or portions thereof, may be transmitted over a wired or wireless network. The invention described herein includes these and other various types of computer-readable storage media when such media contain instructions or programs for implementing the steps described above in conjunction with a microprocessor or other data processor. The invention also includes the computer itself when programmed according to the methods and techniques described herein. 
         [0050]    Computer programs can be applied to input data to perform the functions described herein and thereby transform the input data to generate output data. The output information is applied to one or more output devices such as aberration correctors or to a display monitor. In preferred embodiments of the present invention, the transformed data represents physical and tangible objects, including producing a particular visual depiction of the physical and tangible objects on a display. 
         [0051]    Preferred embodiments of the present invention may make use of a particle beam apparatus, energy beam apparatus, or apparatus using a physical probe tip in order to image a sample. Such beams or physical probes used to image a sample inherently interact with the sample resulting in some degree of physical transformation. Further, throughout the present specification, discussions utilizing terms such as “calculating,” “determining,” “measuring,” “generating,” “detecting,” “forming,” “resetting,” “reading,” “subtracting,” “detecting,” “comparing,” “acquiring,” “mapping,” “recording,” “transforming,” “changing,” or the like, also refer to the action and processes of a computer system, a sensor, or similar electronic device, that manipulates and transforms data represented as physical quantities within the computer system into other data similarly represented as physical quantities within the computer system or other information storage, transmission or display devices. 
         [0052]    The invention has broad applicability and can provide many benefits as described and shown in the examples above. The embodiments will vary greatly depending upon the specific application, and not every embodiment will provide all of the benefits and meet all of the objectives that are achievable by the invention. Particle beam systems suitable for carrying out some embodiments of the present invention are commercially available, for example, from FEI Company, the assignee of the present application. 
         [0053]    To the extent that any term is not specially defined in this specification, the intent is that the term is to be given its plain and ordinary meaning. The accompanying drawings are intended to aid in understanding the present invention and, unless otherwise indicated, are not drawn to scale. Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present invention, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.