Abstract:
According to a related art for evaluating the position accuracy of heaters with respect to the plate, it is necessary to attach an energizing electrode to the heaters, and energize the heaters for a predetermined period to heat the entire plate, before measuring the temperature distribution map. Therefore, there is a problem in that several tens of minutes are required until the temperature distribution map can be measured. As the plate becomes larger, the time required for energizing the heaters to heat the entire plate becomes longer. A technique for evaluating the position accuracy of heaters with respect to the plate, without executing a process for energizing the heaters to heat the plate is disclosed.

Description:
CROSS REFERENCE TO RELATED APPLICATION  
       [0001]     This application is based upon and claims the benefit of priority from a Japanese Patent Application No. TOKUGAN 2005-077929, filed on Mar. 17, 2005; the entire contents of which are incorporated herein by reference.  
       BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the invention  
         [0003]     The present invention relates to a method and an apparatus for evaluating position accuracy indicating, when members made of a second material are arranged within a disk-shaped first material so as to form a first circle of the second material having a radius of a first length and a second circle of the second material having a radius of a second length, deviation amounts of the actual first circle and the second circle from designed positions.  
         [0004]     2. Description of the Related Art  
         [0005]     There is conventionally known, as disclosed in Japanese Patent Application Laid-Open No. 2004-079440, a technique for evaluating whether heaters made of a second material and embedded within a plate made of a first material are evenly arranged by energizing the heaters to generate heat and measuring a temperature distribution map to evaluate whether the plate is evenly heated.  
       SUMMARY OF THE INVENTION  
       [0006]     However, according to the above-mentioned technique, it is necessary to attach an energizing electrode to the heaters, and energize the heaters for a predetermined period to heat the entire plate, before measuring the temperature distribution map. Therefore, there is a problem in that several tens of minutes are required until the temperature distribution map can be measured. As the plate becomes larger, the time required for energizing the heaters to heat the entire plate becomes longer.  
         [0007]     It is therefore an object of the present invention to provide a technique for evaluating the position accuracy of heaters with respect to the plate, without executing a process for energizing the heaters to heat the plate.  
         [0008]     According to a first aspect of the present invention, there is provided a method for evaluating position accuracy indicating, when members made of a second material are arranged within a disk-shaped first material so as to form a first circle of the second material having a radius of a first length and a second circle of the second material having a radius of a second length, deviation amounts of the first circle and the second circle from designed positions, comprising steps of: (1) substantially equally dividing an outer circumference of the disk-shaped first material into n and measuring a first position to an n-th position; (2) measuring an (n+1)th position, which is an intersection of a first radius connecting the center of the disk-shaped first material and the first position and a circular arc of the first circle, to a 2n-th position, which is an intersection of an n-th radius connecting the center of the disk-shaped first material and the n-th position and the circular arc of the first circle; (3) measuring a (2n+1)th position, which is an intersection of the first radius and a circular arc of the second circle, to a 3n-th position, which is an intersection of the n-th radius and the circular arc of the second circle; (4) calculating a first vector starting from the (n+1)th position and ending at the first position to an n-th vector starting from the 2n-th position and ending at the n-th position; (5) calculating an (n+1)th vector starting from the (2n+1)th position and ending at the (n+1)th position to a 2n-th vector starting from the 3n-th position and ending at the 2n-th position; (6) calculating a first combined vector by adding the first to the n-th vectors; (7) calculating a second combined vector by adding the (n+1) th to the 2n-th vectors; and (8) evaluating the position accuracy of the first and the second circles with respect to the outer circumference of the disk-shaped first material, based on a third combined vector obtained by adding the first combined vector and the second combined vector, wherein “n” is a natural number of four or more.  
         [0009]     For the disk-shaped first material, nitride ceramics such as silicon nitride, aluminum nitride, boron nitride, and sialon, and an alumina-silicon carbide composite material are preferably used.  
         [0010]     For the second material, refractory metals such as tantalum, tungsten, molybdenum, platinum, rhenium, and hafnium, or alloys thereof are preferably used. Carbon, TiN, and TiC can be used as a conductive material other than the metal.  
         [0011]     “Members made of a second material are arranged . . . so as to form a first circle having a radius of a first length” means that the members made of the second material need not be arranged so as to form a “complete” circle. As described later, a part of a circular arc may be missing. Further, “so as to form a circle . . . ” means that it is “intended” to form a circle. Generally, even if it is intended to arrange the members made of the second material within the disk-shaped first material so as to form a predetermined circle, it is not easy to arrange the members as designed. The present invention is to evaluate how much the members intended to be arranged as designed actually deviate from the designed positions.  
         [0012]     According to a second aspect of the present invention, the members made of the second material are arranged also between the center and the second circle so as to form a third, . . . , and an m-th circle, the members made of the second material are arranged between the second circle and the first circle so as to form an (m+1)th, . . . , and an (m+k)th circle, and differences in a radial length between respective adjacent circles are substantially equal.  
         [0013]     For example, if it is assumed that m=4, and k=4, the smallest circle is a third circle, a circle slightly larger than the third circle is a fourth circle, a circle slightly larger than the fourth circle is a fifth circle, a circle slightly larger than the fifth circle is a sixth circle, a circle slightly larger than the sixth circle is the second circle, a circle slightly larger than the second circle is a seventh circle, a circle slightly larger than the seventh circle is an eighth circle, and a circle slightly larger than the eighth circle is the first circle.  
         [0014]     When it is assumed that a difference in the radial length between adjacent two circles is Δr, then, the following relations are substantially established: 
 
(radial length of the third circle)+Δr≈(radial length of the fourth circle) 
 
(radial length of the fourth circle)+Δr≈(radial length of the fifth circle) 
 
(radial length of the fifth circle)+Δr≈(radial length of the sixth circle) 
 
(radial length of the sixth circle)+Δr≈(radial length of the second circle) 
 
(radial length of the second circle)+Δr≈(radial length of the seventh circle) 
 
(radial length of the seventh circle)+Δr≈(radial length of the eighth circle); and 
 
(radial length of the eighth circle)+Δr≈(radial length of the first circle) 
 
         [0015]     According to a third aspect of the present invention, the radius of the first circle is the longest among the radii of the first, the second, the third, . . . , the m-th, the (m+1)th, . . . , and the (m+k) th circles, and the radius of the second circle is substantially half the length of the radius of the first circle.  
         [0016]     For example, a relation of (radial length of the third circle) &lt;(radial length of the fourth circle)&lt;(radial length of the fifth circle)&lt;(radial length of the sixth circle)&lt;(radial length of the second circle)&lt;(radial length of the seventh circle)&lt;(radial length of the eighth circle)&lt;(radial length of the first circle) is established, and a relation of (radial length of the second circle) ≈(radial length of the first circle)/2 is established.  
         [0017]     According to the first aspect of the present invention, the position accuracy of the first and the second circle made of the second material with respect to the outer circumference of the disk-shaped first material can be evaluated in a short period of time, based on the third combined vector.  
         [0018]     According to the second aspect of the present invention, the combined vector obtained by using the above method agrees well with an eccentric direction obtained from a temperature distribution map, and hence, the position accuracy of the first and the second circle made of the second material with respect to the outer circumference of the first disk-shaped material can be accurately evaluated. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0019]     Exemplary embodiments of the invention will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only exemplary embodiments and are, therefore, not to be considered limiting of the invention&#39;s scope, the exemplary embodiments of the invention will be described with additional specificity and detail through use of the accompanying drawings in which:  
         [0020]      FIGS. 1A, 1B  show a schematic configuration of a position accuracy evaluation apparatus, in which  FIG. 1A  is an overall block diagram of the position accuracy evaluation apparatus, and  FIG. 1B  is a plan view for explaining movement of an XY stage;  
         [0021]      FIG. 2  is a flowchart showing a flow from rough machining of a plate to a final evaluation stage;  
         [0022]      FIG. 3  is a flowchart showing a flow of a position accuracy evaluation;  
         [0023]      FIG. 4  shows an example of basic information for calculating designed positions;  
         [0024]      FIG. 5  shows an example of the designed positions;  
         [0025]      FIG. 6A, 6B  show an example of a designed heater element position and an actual heater element position, in which  FIG. 6A  shows an image of a heater element photographed by an X-ray camera, and  FIG. 6B  is an enlarged view of a central part of  FIG. 6A ;  
         [0026]      FIG. 7  shows a distance and the like between the actual heater element position (measurement result) and a measurement position calculated from the measurement result;  
         [0027]      FIG. 8  shows a distance d 1  between an outer circumference of the plate and an outermost heater element, and a distance d 2  between the outermost heater element and a fifth perimeter heater element:  
         [0028]      FIG. 9  shows an example of a vector or a combined vector calculated from the actual measurement positions; and  
         [0029]      FIG. 10  shows a result of a conventional method for evaluating the temperature distribution using an infrared thermometer. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0030]     Various embodiments of the invention are now described with reference to the Figures. The embodiments of the present invention, as generally described and illustrated in the Figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of several exemplary embodiments of the present invention, as represented in the Figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of the embodiments of the invention.  
         [0031]     The word “exemplary” is used exclusively herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.  
         [0000]     &lt;Configuration of Position Accuracy Evaluation Apparatus&gt; 
         [0032]      FIGS. 1A, 1B  show a schematic configuration of a position accuracy evaluation apparatus.  FIG. 1A  is an overall block diagram of the position accuracy evaluation apparatus, and  FIG. 1B  is a plan view for explaining movement of an XY stage. As shown in  FIGS. 1A and 1B , a position accuracy evaluation apparatus  100  includes an X-ray camera  101 , an XY stage  102  movable in X and Y directions with a measurement object (sample)  103  placed thereon, and a personal computer (PC)  104  that controls the X-ray camera  101  and the XY stage  102 . The PC  104  includes a display device  105  such as a CRT or a liquid crystal display, a pointing device  106  such as a mouse, a track pad, or a stick pointer, a character/numeric input unit  107  such as a keyboard, a hard disk drive (HDD) (not shown) and a central processing unit (CPU). The HDD is one example of a storage unit that can store measurement object positions of the sample and members therein, and the CPU is one example of a calculating unit that can calculate a vector starting from one of the measurement object positions and ending at the other measurement object position, and also calculate the sum of two or more vectors.  
         [0033]     The position accuracy evaluation apparatus  100  also includes an XY stage drive unit (not shown). Even if the X-ray camera  101  cannot observe the entire measurement object  103  by one shot, the entire measurement object  103  can be observed without exception by appropriately moving the XY stage in X and Y directions. For example, even if the observable range by the X-ray camera  101  by one shot is 200 mm in diameter, if the XY stage  102  can move 100 mm in X and Y directions, respectively, a photographable range is 400 mm by dividing photographing to five shots.  
         [0034]     Photographing the entire measurement object  103  by a plurality of shots means that the range to be observed by the X-ray camera  101  by one shot becomes narrower as compared to photographing the entire measurement object  103  by one shot, which has a merit in that measurement errors decrease.  
         [0000]     &lt;Positioning of Position Accuracy Evaluation Process in Entire Plate Machining&gt; 
         [0035]      FIG. 2  shows a flow from rough machining of the plate to a final evaluation stage. As shown in  FIG. 2 , an unprocessed plate is roughly machined (step S 201 ), position accuracy is evaluated (step S 203 ), and it is determined whether eccentric machining is required (step S 205 ). When the eccentric machining is required, the eccentric machining is performed (step S 207 ), and then primary machining is performed (step S 209 ). When the eccentric machining is not required, the eccentric machining is omitted and the primary machining is performed (step S 209 ). Thereafter, a shaft is connected to the primary-machined plate (step S 211 ), secondary machining is performed (step S 213 ), and then, final evaluation is performed (step S 215 ).  
         [0036]     Thus, position accuracy evaluation (step S 203 ) and determination whether the eccentric machining is required (step S 205 ) in the embodiment are performed between the rough machining of the plate (step S 201 ) and the eccentric machining (step S 207 ). It is determined whether the eccentric machining is required based on the position accuracy evaluation (step S 203 ) (step S 205 ).  
         [0037]     For example, it is assumed that a first perimeter heater element, a second perimeter heater element, . . . , and an eighth perimeter heater element are embedded in the plate from the center of the plate toward an outer circumference thereof. In this case, a distance between the outer circumference of the plate and the outermost heater element (the eighth perimeter heater element) is measured at a plurality of points, and a distance between the outermost heater element and the fifth perimeter heater element is measured at a plurality of points. Based on measurement data, the relative position of the outermost heater element with respect to the outer circumference of the plate, and the relative position of the fifth perimeter heater element with respect to the outermost heater element are calculated.  
         [0000]     &lt;Flow of Position Accuracy Evaluation&gt; 
         [0038]      FIG. 3  is a flowchart showing the flow of the position accuracy evaluation. As shown in  FIG. 3 , the outer circumstance of the disk-shaped first material is substantially evenly divided into n, and a first position to an n-th position is measured (step S 301 ).  
         [0039]     In the embodiment, the disk-shaped first material is a ceramic plate, and the outer circumstance of the plate is divided into twelve, and the first position to the twelfth position is measured.  
         [0040]     The (n+1) th position, which is an intersection of the first radius and a circular arc of the first circle, the first radius connecting the center of the disk-shaped first material and the first position, to the 2n-th position, which is an intersection of the n-th radius and the circular arc of the first circle, the n-th radius connecting the center of the disk-shaped first material and the n-th position, is measured next (step S 303 ).  
         [0041]     In the embodiment, the first perimeter heater element, the second perimeter heater element, . . . , and the eighth perimeter heater element are formed in the ceramic plate. The first perimeter heater element is the heater element closest to the center of the plate, and the eighth perimeter heater element is the heater element closest to the outer circumference of the plate.  
         [0042]     A radius connecting the center of the plate and the first position on the outer circumference of the plate is the first radius;  
         [0043]     a radius connecting the center of the plate and the second position on the outer circumference of the plate is the second radius;  
         [0044]     a radius connecting the center of the plate and the third position on the outer circumference of the plate is the third radius; . . . ; and  
         [0045]     a radius connecting the center of the plate and the twelfth position on the outer circumference of the plate is a twelfth radius, that is, n=12.  
         [0046]     An intersection of the first radius and the eighth perimeter heater element is the thirteen-th position;  
         [0047]     an intersection of the second radius and the eighth perimeter heater element is the fourteen-th position;  
         [0048]     an intersection of the third radius and the eighth perimeter heater element is the fifteen-th position; . . . ; and  
         [0049]     an intersection of the twelfth radius and the eighth perimeter heater element is the twenty-fourth position.  
         [0050]     The (2n+1) th position, which is an intersection of the first radius and the circular arc of the second circle, to the 3n-th position, which is an intersection of the n-th radius and the circular arc of the second circle, is measured (step S 305 ).  
         [0051]     In the embodiment, the second circle is the fifth perimeter heater element.  
         [0052]     An intersection of the first radius and the fifth perimeter heater element is the twenty-fifth position;  
         [0053]     an intersection of the second radius and the fifth perimeter heater element is the twenty-sixth position;  
         [0054]     an intersection of the third radius and the fifth perimeter heater element is the twenty-seven-th position; . . . ; and  
         [0055]     an intersection of the twelfth radius and the fifth perimeter heater element is the thirty-sixth position.  
         [0056]     The first vector starting from the (n+1)th position and ending at the first position to the n-th vector starting from the 2n-th position and ending at the n-th position is calculated (step S 307 ).  
         [0057]     In the embodiment, a vector starting from the thirteen-th position and ending at the first position is the first vector;  
         [0058]     a vector starting from the fourteen-th position and ending at the second position is the second vector;  
         [0059]     a vector starting from the fifteen-th position and ending at the third position is the third vector; . . . ; and  
         [0060]     a vector starting from the twenty-fourth position and ending at the twelfth position is the twelfth vector.  
         [0061]     The (n+1) th vector starting from the (2n+1)th position and ending at the (n+1)th position to the 2n-th vector starting from the 3n-th position and ending at the 2n-th position is calculated, respectively (step S 309 ).  
         [0062]     In the embodiment, a vector starting from the twenty-fifth position and ending at the thirteen-th position is the thirteen-th vector;  
         [0063]     a vector starting from the twenty-sixth position and ending at the fourteen-th position is the fourteen-th vector;  
         [0064]     a vector starting from the twenty-seven-th position and ending at the fifteen-th position is the fifteen-th vector; . . . ; and  
         [0065]     a vector starting from the thirty-sixth position and ending at the twenty-fourth position is the twenty-fourth vector.  
         [0066]     The first vector to the n-th vector is then added to calculate a first combined vector (step S 311 ).  
         [0067]     In the embodiment, all of the first vector, the second vector, the third vector, . . . , and the twelfth vector are added to calculate the first combined vector.  
         [0068]     The (n+1) th vector to the 2n-th vector is added to calculate a second combined vector (step S 313 ).  
         [0069]     In the embodiment, all of the thirteen-th vector, the fourteen-th vector, the fifteen-th vector, . . . , and the twenty-fourth vector are added to calculate the second combined vector.  
         [0070]     Lastly, the second material position accuracy of the first circle and the second circle with respect to the outer circumference of the first material is evaluated based on the third combined vector obtained by adding the first and the second combined vectors (step S 315 )  
         [0000]     &lt;Coordinate Information of Measurement Position&gt; 
         [0071]     When respective positions are to be measured, a mark is respectively displayed at the designed positions. The outer circumference of the first material, the circular arc of the first circle of the second material, or the circular arc of the second circle of the second material closest to the mark is designated as an actually measured position.  
         [0072]     In an example in which the outer circumference is divided into 12, marks are displayed at positions obtained by dividing the circular arc of a circle having a designed radius into 12, and the outer circumference closest to the marks is designated as the actually measured position. If the ceramic plate has a dimension as designed, all the marks relating to the positions on the outer circumference should be displayed on the outer circumference of the plate photographed by the X-ray camera. Due to various reasons, however, all the marks are not always displayed on the outer circumference. Likewise, if the heaters are embedded at positions as designed, all the marks relating to the positions of the eighth perimeter heater element should be displayed on the eighth perimeter heater element photographed by the X-ray camera. Due to various reasons, however, all the marks are not always displayed on the eighth perimeter heater element. The same applies to the fifth perimeter heater element.  
         [0073]     An example of a method for calculating the designed position (hereinafter, appropriately referred to as “design value”) will be explained with reference to  FIGS. 4 and 5 . An example of a state in which the actually measured position deviates from the designed position is shown in  FIG. 6A, 6B .  
         [0074]      FIG. 4  shows an example of basic information for calculating the designed position. As shown in  FIG. 4 , an article name of the measurement object is input in an column  401 , a number for a measurement object shape in an column  402 , a score in outer circumference measurement information in an column  403 , an offset angle in the outer circumference measurement information in an column  404 , a hole diameter for PCD in an column  405 , whether the coordinate system is an XY coordinate system or Rθ coordinate system is input in an column  406 , and in the case of the Rθ coordinate system, radius R, or in the case of the XY coordinate system, X coordinate value is input in an column  407 , in the case of the Rθ coordinate system, angle θ, or in the case of the XY coordinate system, Y coordinate value is input in an column  408 , a diameter when the object shape is the outer circumference or PCD is input in an column  409 , a coordinate number in an column  410 , and coordinate numbers of two points, a distance of which is to be measured, are input in an column  411 , respectively.  
         [0075]     For example, object shape number “1” indicates that the object shape is “point”, object shape number “2” indicates that the object shape is “hole (three point measurement)”, object shape number “3” indicates that the object shape is “outer circumference (n-point measurement)”, and object shape number “4” indicates that the object shape is “PCD measurement”.  
         [0076]     When “object shape: name” corresponding to the coordinate number input in the column  411  is “hole” or “outer circumference”, a distance between the hole or the outer circumference and the “center” is measured. The “PCD” in the object shape is a pitch circle diameter, and a diameter of a circle connecting central positions of lift pin holes. The “measurement angle” in the outer circumference measurement information is an angle between radial lines connecting the respective measurement points and the center, and “hole diameter” for PCD is a diameter of the lift pin hole.  
         [0000]     &lt;Designed Measurement Positions&gt; 
         [0077]      FIG. 5  shows one example of designed positions. Designed measurement positions (design values) as shown in  FIG. 5  are calculated based on the coordinate information shown in  FIG. 4 . In the example shown in  FIG. 5 , the design value is expressed by radius r and angle θ.  
         [0078]     “Point  2 , object number  1 ” in  FIG. 5  corresponds to coordinate information No.  1  in  FIG. 4 . As shown in  FIG. 4 , in coordinate information No.  1 , as the Rθ coordinate system, radius r=123 [mm] and angle θ=180 degrees are given initially. Therefore, the design value for “Point  2 , object number  1 ” indicates radius r=123.00 [mm] and angle θ=180.00 degrees.  
         [0079]     “Point  3 , object number  2 ” to “Point  11 , object number  2 ” in  FIG. 5  correspond to coordinate information No.  2  in  FIG. 4 . As shown in  FIG. 4 , in coordinate information No.  2 , offset angle =30 degrees and diameter=318 [mm] are given as the outer circumference measurement information. Therefore, the design value for “Point  3 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=30.00 degrees. Further, in the coordinate information No.  2 , since score=9 is given as the outer circumference measurement information, the interval between “Point  3 , object number  2 ” and “Point  4 , object number  2 ” is 360/9=40 degrees. Accordingly, the design value for “Point  4 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=70.00 degrees.  
         [0080]     Likewise, the design value for “Point  5 , object number  2 ” in  FIG. 5  indicates radius r=159.00 [mm] and angle θ=110.00 degrees;  
         [0081]     “Point  6 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=150.00 degrees;  
         [0082]     “Point  7 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=190.00 degrees;  
         [0083]     “Point  8 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=230.00 degrees;  
         [0084]     “Point  9 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=270.00 degrees;  
         [0085]     “Point  10 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=310.00 degrees; and  
         [0086]     “Point  11 , object number  2 ” indicates radius r=159.00 [mm] and angle θ=350.00 degrees. “Point  12 , object number  3 ” in  FIG. 5  corresponds to coordinate information No.  3  in  FIG. 4 . As shown in  FIG. 4 , in coordinate information No.  3 , X coordinate value=11.2 [mm] and Y coordinate value=8 [mm] are given as the XY coordinate system. Based on these values, radius r=13.76 [mm] and angle θ=35.54 degrees are calculated as the design value for “Point  12 , object number  3 ” in  FIG. 5 .  
         [0087]     Likewise, based on X coordinate value=−4.8 [mm] and Y coordinate value=8 [mm] in coordinate information No.  4 , radius r=9.33 [mm] and angle θ=120.96 degrees are calculated as the design value for “Point  13 , object number  4 ” in  FIG. 5 .  
         [0088]     Based on X coordinate value=−4.8 [mm] and Y coordinate value =−8 [mm] in coordinate information No.  5 , radius r=9.33 [mm] and angle θ=239.04 degrees are calculated as the design value for “Point  14 , object number  5 ” in  FIG. 5 .  
         [0089]     Based on X coordinate value=11.2 [mm] and Y coordinate value =−8 [mm] in coordinate information No.  6 , radius r=13.76 [mm] and angle θ=324.46 degrees are calculated as the design value for “Point  15 , object number  6 ” in  FIG. 5 . In this manner, designed heater positions are determined for each article.  
         [0000]     &lt;Actual Heater Position&gt; 
         [0090]      FIG. 6A, 6B  shows an example of a designed heater position (hereinafter, referred to as “heater element position”) and an actual heater element position. As shown in  FIG. 6A , an image  601  of a heater element photographed by using the X-ray camera  101  is displayed on a display screen of the device  105 .  
         [0091]      FIG. 6B  is an enlarged view of the central part of  FIG. 6A . As shown in  FIG. 6B , a cursor  603  is displayed at the predetermined designed heater element position in the image of the photographed heater element. As shown in  FIG. 6B , the designed heater element position indicated by the cursor  603  may displace from the actual heater element position photographed by the X-ray camera. In this case, the cursor  603  is moved onto the heater element displayed on the display device, by using a pointing device such as a mouse  106 . Then the position of the cursor  603  at the time of occurrence of such an event is fetched in the storage unit of the PC  104  as the actual heater element position, by clicking a button on the mouse  106 , or pressing an “Enter” key on the keyboard  11 . The confirming process of the actual heater element position is repeated for the preset number of coordinates.  
         [0092]     The confirming process of the actual heater element position coil position may be automated. For example, a difference between the position according to design information and the actual position can be automatically fetched, by using a heater element position determination image processing function.  
         [0000]     &lt;Processing of Measurement Result&gt; 
         [0093]      FIG. 7  shows a distance and the like between the actual heater element position (measurement result) and a measurement position calculated from the measurement result. As shown in  FIG. 7 , radius r and angle θ obtained from the measurement result are displayed in a display column  701 . Specifically, radius r=147 [mm] and angle θ=0 are displayed as a measurement result corresponding to point  1 , radius r=123 [mm] and angle θ=180.27 are displayed as a measurement result corresponding to point  2 , radius r=158.2 [mm] and angle θ=19.99 are displayed as a measurement result corresponding to point  3 , radius r=158.29 [mm] and angle θ=59.99 are displayed as a measurement result corresponding to point  4 , and radius r=158.31 [mm] and angle θ=99.99 are displayed as a measurement result corresponding to point  5 .  
         [0094]     The X coordinate value or the radius r, and the Y coordinate value or the angle θ obtained from the measurement result are displayed in a display column  703 . The first line in the display column  703  relates to a reference point at the angle θ, and indicates that the reference point at the angle θ indicates radius R=147.00 mm, and angle θ=0.0 degree.  
         [0095]     The second line in the display column  703  relates to a point of coordinate information No.  1 , and the measurement result indicates radius r=123.00 mm, and angle θ=180.27 degrees.  
         [0096]     The third line in the display column  703  relates to the outer circumference of coordinate information No.  2 , and the measurement result indicates radius R=0.20 mm, and angle θ deviates by 237.83 degrees.  
         [0097]     The fourth line in the display column  703  relates to a point of coordinate information No.  3 , and the measurement result indicates X coordinate value=10.94 [mm] and Y coordinate value=7.81 [mm].  
         [0098]     The fifth line in the display column  703  relates to a point of coordinate information No.  4 , and the measurement result indicates X coordinate value=11.51 [mm] and Y coordinate value=−8.23 [mm].  
         [0099]     The sixth line in the display column  703  relates to a point of coordinate information No.  5 , and the measurement result indicates X coordinate value=−4.95 [mm] and Y coordinate value=−8.25 [mm].  
         [0100]     The seventh line in the display column  703  relates to a point of coordinate information No.  6 , and the measurement result indicates X coordinate value=−4.52 [mm] and Y coordinate value=7.54 [mm].  
         [0101]     The eighth line in the display column  703  relates to a point of coordinate information No.  7 , and the measurement result indicates X coordinate value=0.00 mm and Y coordinate value=0.00 mm.  
         [0102]     A hole diameter, a diameter of the outer circumference, and a PCD diameter are displayed in a display column  705 . The “hole diameter” is a diameter of the lift pin hole, the “diameter of the outer circumference” is a diameter in the outermost portion of the heater element, and the “PCD diameter” is a pitch circle diameter connecting central positions of the lift pin holes.  
         [0103]     A difference in the X coordinate value between two points, a difference in the Y coordinate value between two points, and a distance between two points are displayed in a display column  707 . The first line in the display column  707  relates to point  3  and point  4 , indicating X coordinate value of point  3 +0.57 [mm]=X coordinate value of point  4 , Y coordinate value of point  3 −16.04 [mm]=Y coordinate value of point  4 , and distance between point  3  and point  4 =16.05.  
         [0104]     The second line in the display column  707  relates to point  4  and point  5 , indicating X coordinate value of point  4 −16.46 [mm]=X coordinate value of point  5 , Y coordinate value of point  4 −0.02 [mm]=Y coordinate value of point  5 , and distance between point  4  and point  5 =16.46.  
         [0105]     The third line in the display column  707  relates to point  5  and point  6 , indicating X coordinate value of point  5 +0.43 [mm]=X coordinate value of point  6 , Y coordinate value of point  5 +15.79 [mm]=Y coordinate value of point  6 , and distance between point  5  and point  6 =15.80.  
         [0000]     &lt;Outer Circumference of Plate, Outermost Heater Element, and Fifth Perimeter Heater Element&gt; 
         [0106]     A distance between the outer circumference of the plate and the outermost heater element, and a distance between the outermost heater element and the fifth perimeter heater element are shown in  FIG. 8 . As shown in  FIG. 8 , the distance between the outer circumference of the plate and the outermost heater element stands for a distance d 1  between the outer circumference  801  of the plate and the outermost heater element  803 . The distance between the outermost heater element and the fifth perimeter heater element stands for a distance d 2  between the outermost heater element  803  and the fifth perimeter heater element  805 . The distances d 1  and d 2  are calculated based on the actual measurement values.  
         [0000]     &lt;Position Accuracy Analysis of Heater Element&gt; 
         [0107]      FIG. 9  shows one example of a vector or a combined vector calculated from the actual measurement positions. Position accuracy analysis of the heater element is explained with reference to  FIG. 9 . In the example shown in  FIG. 9 , a position at an angle of 15 degrees on the outer circumference of the plate is designated as a first position, a position at an angle of 45 degrees is designated as a second position, a position at an angle of 75degrees is designated as a third position, . . . , and a position at an angle of 345 degrees is designated as a twelfth position. Further, the distance d 1  between the outer circumference of the plate and the outermost heater element on the outermost heater element is plotted respectively for the angle θ=15 degrees, 45 degrees, 75 degrees, 105 degrees, 135 degrees, 165 degrees, 195 degrees, 225 degrees, 255 degrees, 285 degrees, 315 degrees, and 345 degrees.  
         [0108]     Graph  901  indicates the content of Table 1 with regard to article name: heater sample A.  
                                             TABLE 1                           POSITION   POSITION               NUMBER   NUMBER ON           ON OUTER   OUTERMOST       ANGLE θ   CIRCUMFERENCE   HEATED   DISTANCE d1       [DEGREES]   OF PLATE   ELEMENT   [mm]                                15   1   13   7.0       45   2   14   7.0       75   3   15   6.1       105   4   16   5.4       135   5   17   4.2       165   6   18   4.0       195   7   19   3.2       225   8   20   3.0       255   9   21   4.1       285   10   22   5.1       315   11   23   6.2       345   12   24   6.0                  
 
         [0109]     A vector  903  starting from the central point in the graph  901  is the first vector starting from the thirteen-th position on the outermost heater element and ending at the first position on the outermost circumference of the plate;  
         [0110]     a vector  904  is the second vector starting from the fourteen-th position and ending at the second position;  
         [0111]     a vector  905  is the third vector starting from the fifteen-th position and ending at the third position; and  
         [0112]     a vector  914  is the twelfth vector starting from the twenty-fourth position and ending at the twelfth position.  
         [0113]     A vector  916  obtained by combining vectors  903  to  914  corresponds to the first combined vector. The vector  916  has an angle θof 25 degrees and a length of 10.2 [mm].  
         [0114]     A graph  920  indicates the content of Table 2 with regard to article name: heater sample A.  
                                             TABLE 2                           POSITION   POSITION               NUMBER ON   NUMBER           OUTERMOST   ON FIFTH       ANGLE θ   HEATER   PERIMETER   DISTANCE d2       [DEGREES]   ELEMENT   HEATER ELEMENT   [mm]                                15   13   25   39.6       45   14   26   38.5       75   15   27   39.1       105   16   28   39.0       135   17   29   38.9       165   18   30   38.6       195   19   31   39.9       225   20   32   40.0       255   21   33   40.0       285   22   34   39.5       315   23   35   40.0       345   24   36   38.5                  
 
         [0115]     A vector  923  starting from the central point in the graph  920  is the thirteen-th vector starting from the twenty-fifth position on the fifth perimeter heater element and ending at the thirteen-th position on the outermost heater element;  
         [0116]     a vector  924  is the fourteen-th vector starting from the twenty-sixth position and ending at the fourteen-th position;  
         [0117]     a vector  925  is the fifteen-th vector starting from the twenty-seven-th position and ending at the fifteen-th position; . . . ; and  
         [0118]     a vector  934  is the twenty-fourth vector starting from the thirty-sixth position and ending at the twenty-fourth position.  
         [0119]     A vector  936  obtained by combining vectors  923  to  934  corresponds to the second combined vector. The vector  936  has an angle θof 251 degrees and a length of 5.7 [mm].  
         [0120]     The third combined vector obtained by combining the vector  916  and the vector  936  has an angle θ of 351 degrees and a length of 7.4 [mm].  
         [0121]     A graph  940  indicates the content of Table 3 with regard to article name: heater sample B.  
                                             TABLE 3                           POSITION   POSITION               NUMBER   NUMBER ON           ON OUTER   OUTERMOST       ANGLE θ   CIRCUMFERENCE   HEATED   DISTANCE d1       [DEGREES]   OF PLATE   ELEMENT   [mm]                                15   1   13   5.6       45   2   14   4.4       75   3   15   4.0       105   4   16   4.1       135   5   17   3.9       165   6   18   4.7       195   7   19   4.9       225   8   20   6.0       255   9   21   6.1       285   10   22   7.1       315   11   23   6.6       345   12   24   6.3                  
 
         [0122]     A Vector  943  starting from the central point in the graph  940  is the first vector starting from the thirteen-th position on the outermost heater element and ending at the first position on the outer circumference of the plate;  
         [0123]     a vector  944  is the second vector starting from the fourteen-th position and ending at the second position;  
         [0124]     a vector  945  is the third vector starting from the fifteen-th position and ending at the third position; . . . ; and  
         [0125]     a vector  954  is the twelfth vector starting from the twenty-fourth position and ending at the twelfth position.  
         [0126]     A vector  956  obtained by combining vectors  943  to  954  corresponds to the first combined vector. The vector  956  has an angle θ of 291 degrees and a length of 9.1 [mm].  
         [0127]     A graph  960  indicates the content of Table 4 with regard to article name: heater sample B.  
                                             TABLE 4                           POSITION   POSITION               NUMBER ON   NUMBER           OUTERMOST   ON FIFTH       ANGLE θ   HEATER   PERIMETER   DISTANCE d2       [DEGREES]   ELEMENT   HEATER ELEMENT   [mm]                                15   13   25   39.5       45   14   26   39.0       75   15   27   39.6       105   16   28   39.5       135   17   29   39.0       165   18   30   38.9       195   19   31   39.6       225   20   32   40.0       255   21   33   40.5       285   22   34   40.1       315   23   35   40.0       345   24   36   39.9                  
 
         [0128]     A vector  963  starting from the central point in the graph  960  is the thirteen-th vector starting from the twenty-fifth position on the fifth perimeter heater element and ending at the thirteen-th position on the outermost heater element;  
         [0129]     a vector  964  is the fourteen-th vector starting from the twenty-sixth position and ending at the fourteen-th position;  
         [0130]     a vector  965  is the fifteen-th vector starting from the twenty-seven-th position and ending at the fifteen-th position; . . . ; and  
         [0131]     a vector  974  is the twenty-fourth vector starting from the thirty-sixth position and ending at the twenty-fourth position.  
         [0132]     A vector  976  obtained by combining vectors  963  to  974  corresponds to the second combined vector. The vector  976  has an angle θ of 259 degrees and a length of 2.6 [mm].  
         [0133]     The third combined vector obtained by combining the vector  916  and the vector  936  has an angle θ of 284 degrees and a length of 11.4 [mm].  
         [0000]     &lt;Position Accuracy Evaluation by Conventional Method&gt; 
         [0134]     On the other hand,  FIG. 10  shows a result of a conventional method for evaluating the temperature distribution using an infrared thermometer, by energizing the heater elements to heat the entire plate with respect to an article name: HC46302-00089, for which various vectors are shown in graphs  940  and  960  in  FIG. 9 .  
         [0135]     As shown in  FIG. 10 , a radial range is 4.5 to 7.5° C., the maximum value of a temperature difference on the same circumference is 4.8° C., and the maximum value of a temperature difference on the plate is 9.0° C. A vector  1001  has an angle θ of 280 degrees and a length of 1.1 [mm].  
         [0136]     The radial range stands for the maximum value when a plurality of temperature differences are obtained on the same radial. A method for obtaining the angle and the length of the vector  1001  is such that an angle for changing the obtained temperature distribution to symmetrical distribution is obtained by multivariate analysis based on the obtained temperature distribution. As for the length, the maximum temperature difference on the same radial on the outer circumference of the obtained temperature distribution map is first obtained, and an eccentricity required for modifying a 1° C. of temperature difference stored in a database is multiplied to the maximum temperature difference, giving the length.  
         [0000]     &lt;Comparison Between Method According to Embodiment and Conventional Method&gt; 
         [0137]     The third combined vector obtained by the method according to the embodiment has the angle θ of 284 degrees and the length of 11.4 [mm]. Since an eccentricity conversion rate of the combined vector value is 10%, the eccentricity after conversion becomes 1.14 [mm].  
         [0138]     On the other hand, the vector  1001  obtained by the conventional method has the angle θ of 280 degrees and the length of 1.1 [mm]. That is, an equivalent result to that obtained by the conventional method can be obtained by the method according to the embodiment with regard to the eccentricity and the eccentric direction.  
         [0139]     Thus, the eccentricity and the eccentric direction with the accuracy equal to the conventional method can be obtained by the method according to the embodiment. The method according to the embodiment does not require energizing the heater elements to heat up the entire plate. Accordingly, there is an effect that the method according to the embodiment can perform process to get the eccentricity and the eccentric direction in a shorter period of time than that required in the conventional method.