Patent Publication Number: US-8539814-B2

Title: Material measures for use in evaluating performance of measuring instrument for measuring surface texture

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2009-189864, filed Aug. 19, 2009, the entire contents of which are incorporated herein by this reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the technology of material measures for use in evaluating the performance of a measuring instrument for measuring surface texture. 
     2. Description of the Related Art 
     A means for evaluating the performance of a measuring instrument for measuring surface texture can be a method of using material measures whose surfaces have a plurality of grooves. 
     There are various types of material measures, but the material measures whose surfaces have grooves having the same shapes in a predetermined direction as described in Standard Number JISB0659-1 “Geometrical Product Specifications (GPS)—Surface Texture Profile method; Measurement standards—Part 1: Material Measures” have become widespread lately. 
     The groove shapes of material measures are in many cases simple from the viewpoint of easy evaluation, processing, etc. For example, material measures  100  having the cross-sectional shapes of grooves  101  exemplified in  FIGS. 1A through 1D , that is, a sine wave shape (refer to  FIG. 1A ), a triangle shape (refer to  FIG. 1B ), a trapezoid shape ( FIG. 1C ), and an arc shape (refer to  FIG. 1D ), are known. 
     The performance of a measuring instrument is evaluated by whether or not the shape of the groove  101  of the material measure  100  can be appropriately measured. To be more concrete, for example, there is a method of evaluating the performance of a measuring instrument by checking the change in measurement accuracy of the depth (amplitude) of a groove to the width (cycle) of the groove (hereinafter referred to as a response characteristic) described in the Theses of the Lectures of the Academic Lecture Meeting in Spring 2009 of the Institute of Precision Industry, p. 495-496 (by Akihiro Fujii and Kazuhisa Yanagi “A study on response properties of surface texture measuring instruments in terms of surface wavelengths”. 
     When the response characteristic of a measuring instrument is checked using a material measure formed by arranging the grooves of the same shape on its surface to evaluate the performance of the measuring instrument, for example, a plurality of material measures (material measures  102 ,  103 , and  104 ) having equal depths (depth D) and different widths (widths W 1 , W 2 , and W 3 ) of grooves as exemplified in  FIGS. 2A through 2F  are prepared and measured respectively. 
     In this case, if the cross-section of a groove is triangle-shaped as exemplified in  FIGS. 3A through 3B , the inclination angle of the groove whose cross-section is triangle-shaped changes with the change of the width of the groove. In  FIGS. 3A and 3B , the inclination angles of the grooves change from the angle θ 1  to the angle θ 2 . In addition, as exemplified in  FIGS. 4A and 4B , if the cross-section of a groove is sine-wave-shaped, the maximum inclination angle of the groove whose cross-section is sine-wave-shaped changes. In  FIGS. 4A and 4B , the maximum inclination angles of the grooves change from the angle θ 3  to the angle θ 4 . 
     SUMMARY OF THE INVENTION 
     An aspect of the present invention provides a material measure which is used in evaluating the performance of a measuring instrument for measuring surface texture, which has a measurement area including a plurality of grooves in a predetermined direction, each of whose grooves cross-section and has a simple cross-sectional shape at a cross-section along the predetermined direction, and the length in the predetermined direction of whose cross-sectional shape is different for predetermined number of grooves adjacent in the predetermined direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be more apparent from the following detailed description when the accompanying drawings are referenced. 
         FIG. 1A  exemplifies the cross-sectional shape of the groove of a material measure according to a prior art; 
         FIG. 1B  exemplifies the cross-sectional shape of the groove of another material measure according to a prior art; 
         FIG. 1C  exemplifies the cross-sectional shape of the groove of a further material measure according to a prior art; 
         FIG. 1D  exemplifies the cross-sectional shape of the groove of a further material measure according to a prior art; 
         FIG. 2A  is a perspective view of a material measure according to the prior art for use in checking the response characteristic of the depth of the groove to the width of the groove; 
         FIG. 2B  is a cross-sectional view of a material measure according to the prior art exemplified in  FIG. 2A ; 
         FIG. 2C  is a perspective view of another material measure according to the prior art for use in checking the response characteristic of the depth of the groove to the width of the groove; 
         FIG. 2D  is a cross-sectional view of a material measure according to the prior art exemplified in  FIG. 2C ; 
         FIG. 2E  is a perspective view of a further material measure according to the prior art for use in checking the response characteristic of the depth of the groove to the width of the groove; 
         FIG. 2F  is a cross-sectional view of a material measure according to the prior art exemplified in  FIG. 2E ; 
         FIG. 3A  is an explanatory view of the relationship between the width and the inclination angle of the groove whose cross-section is triangle-shaped; 
         FIG. 3B  is an explanatory view of the relationship between the width and the inclination angle of the groove whose cross-section is triangle-shaped; 
         FIG. 4A  is an explanatory view of the relationship between the width and the maximum inclination angle of the groove whose cross-section is sine-wave-shaped; 
         FIG. 4B  is an explanatory view of the relationship between the width and the maximum inclination angle of the groove whose cross-section is sine-wave-shaped 
         FIG. 5A  is a perspective view exemplifying the material measure according to embodiment 1; 
         FIG. 5B  is an example of a cross-sectional view of the material measure exemplified in  FIG. 5A ; 
         FIG. 5C  is another example of a cross-sectional view of the material measure exemplified in  FIG. 5A ; 
         FIG. 5D  is a further example of a cross-sectional view of the material measure exemplified in  FIG. 5A ; 
         FIG. 6A  exemplifies a variation of the material measure according to embodiment 1; 
         FIG. 6B  exemplifies another variation of the material measure according to embodiment 1; 
         FIG. 6C  exemplifies a further variation of the material measure according to embodiment 1; 
         FIG. 7A  is a perspective view exemplifying a further variation of the material measure according to embodiment 1; 
         FIG. 7B  is a cross-sectional view of the material measure exemplified in  FIG. 7A ; 
         FIG. 8A  is a perspective view exemplifying the material measure according to embodiment 2; 
         FIG. 8B  is a cross-sectional view of the material measure exemplified in  FIG. 8A ; 
         FIG. 9A  exemplifies a variation of the material measure according to embodiment 2; 
         FIG. 9B  exemplifies another variation of the material measure according to embodiment 2; 
         FIG. 9C  exemplifies a further variation of the material measure according to embodiment 2; 
         FIG. 10A  is a perspective view exemplifying the material measure according to embodiment 3; 
         FIG. 10B  is a cross-sectional view of the material measure exemplified in  FIG. 10A ; 
         FIG. 11  illustrates the function indicating the cross-sectional shape of the material measure according to embodiment 3; 
         FIG. 12A  exemplifies a variation of the material measure according to embodiment 3; 
         FIG. 12B  exemplifies another variation of the material measure according to embodiment 3; 
         FIG. 12C  exemplifies a further variation of the material measure according to embodiment 3; 
         FIG. 13A  is a perspective view exemplifying the material measure according to embodiment 4; 
         FIG. 13B  is a cross-sectional view of a cross-section of the material measure exemplified in  FIG. 13A ; 
         FIG. 13C  is a cross-sectional view of another cross-section of the material measure exemplified in  FIG. 13A ; 
         FIG. 14A  is a perspective view exemplifying a variation of the material measure according to embodiment 4; 
         FIG. 14B  is a perspective view exemplifying another variation of the material measure according to embodiment 4; 
         FIG. 14C  is a perspective view exemplifying a further variation of the material measure according to embodiment 4; 
         FIG. 15A  is a perspective view exemplifying the material measure according to embodiment 5; 
         FIG. 15B  is a cross-sectional view of a cross-section of the material measure exemplified in  FIG. 15A ; 
         FIG. 15C  is a cross-sectional view of another cross-section of the material measure exemplified in  FIG. 15A ; and 
         FIG. 16  is a perspective view exemplifying the material measure according to embodiment 6; 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Each embodiment of the present invention is described below with reference to the attached drawings. 
     &lt;Embodiment 1&gt; 
       FIGS. 5A through 5D  exemplify the material measures according to the present embodiment for use in evaluating the performance of a measuring instrument for measuring surface texture.  FIG. 5A  is a perspective view of a material measure  10  according to the present embodiment.  FIGS. 5B through 5D  are cross-sectional views at the cross-sections  1 - 1 ′ of different material measures  10 . 
     In the XYZ coordinate system exemplified in  FIGS. 5A through 5D , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  10 , the XZ plane and the cross-section  1 - 1 ′ of the material measure  10  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     The material measure  10  has a measurement area R including a plurality of grooves arranged in the X direction (predetermined direction) on the surface S. A measuring instrument measures the measurement area R of the material measure  10 , and its performance is evaluated based on the result of the measurement. Each groove formed in the measurement area R on the surface S has a simple cross-sectional shape at the cross-section  1 - 1 ′ along the X direction. In  FIGS. 5A through 5D , the cross-sections of the grooves arranged in the X direction are sine-wave-shaped. 
     In the material measure  10 , the lengths (hereinafter referred to as depths) in the Z direction (depth direction) of the cross-sectional shapes along the grooves arranged in the X direction are constant while the lengths (hereinafter referred to as widths) in the X direction are not constant. 
     The widths of the cross-sectional shapes of the grooves can be different for a predetermined number of adjacent grooves. As exemplified in  FIG. 5B , the width of each cross-sectional shape of the groove arranged in the X direction can be different. In addition, as exemplified in  FIGS. 5C and 5D , the widths of the cross-sectional shapes of grooves can be different every two adjacent grooves. It is desired that the widths of the cross-sectional shapes of the grooves decrease in every predetermined number of adjacent grooves. 
     In  FIGS. 5B and 5C , the adjacent grooves in the X direction are continuous, but the present invention is not limited to the formation. As exemplified in  FIG. 5D , a flat portion FL can be provided between the grooves. The length (hereinafter referred to as a width) of the flat portion FL in the X direction can be arbitrarily changed. For example, the width of the flat portion FL can be adjusted to cyclically generate a groove in the X direction, that is, to obtain a constant sum of the width of the cross-sectional shape of a groove and the width of the adjacent flat portion FL. 
     In  FIGS. 5B through 5D , the surface S of the material measure  10  is positioned at the same level as the top ends of the grooves, but the present invention is not limited to this formation. For example, the measurement area R can be formed at a lower level than the surface S. In this case, the top ends are not positioned at the same level as the surface S. 
     Each of the grooves arranged in the X direction is a linear groove parallel to the Y direction (linear direction), and the depth of each groove is constant in the Y direction. That is, a plurality of parallel and linear grooves are formed in the measurement area R of the material measure  10 . Therefore, the material measure  10  has the same cross-sectional shape at an arbitrary parallel cross-section as the cross-section  1 - 1 ′. 
     The material measure  10  can be manufactured by processing a piece of monocrystal silicon with a focused ion beam. The material and the processing method of the material measure  10  are not limited if a groove of a target shape can be formed. 
     The material of the material measure  10  can be metal such as stainless steel etc. and glass. The processing method of the material measure  10  can also be etching or milling in addition to a processing method using a spattering such as FIB processing. 
     When the performance of a measuring instrument for measuring surface texture is evaluated using the material measure  10  described above, the response characteristic indicating a change in measurement accuracy of the depth of a groove to a change in width of the groove can be checked only by once scanning the measurement area R of the material measure  10  in parallel to the X direction. When the field of view of the measuring instrument is larger than the measurement area R, the response characteristic can be checked by performing the measurement only once with the field of view fixed. 
     Therefore, as compared with the case in which the response characteristic is acquired by sequentially measuring a plurality of material measures having different widths of grooves using a measuring instrument, the working time required to acquire the response characteristic can be shortened and the work load can be reduced. As a result, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     The performance evaluation of the measuring instrument using the response characteristic is performed in the same method as the prior art. For example, assume that the measuring instrument scans the material measure  10  having a cross-section exemplified in  FIG. 5B , and the response characteristic of the measuring instrument is acquired. If the depth D can be measured within an allowance for grooves  10   a  through  10   c  while the depth cannot be measured within the allowance for a groove  10   d , then it can be evaluated that the limit of the width for which the measuring instrument can appropriately measure the depth D is a width W 3 . 
       FIGS. 6A through 6C  exemplify variations of a material measure according to the present embodiment. The material measures exemplified in  FIGS. 6A through 6C  are different from the material measure  10  only in the cross-sectional shape of the groove.  FIG. 6A  exemplifies a material measure  11  in which the cross-section of a groove  11   a  is triangle-shaped.  FIG. 6B  exemplifies a material measure  12  in which the cross-section of a groove  12   a  is trapezoid-shaped.  FIG. 6C  exemplifies a material measure  13  in which the cross-section of a groove  13   a  is circle-arc-shaped or oval-arc-shaped. The cross-sectional shape of the groove of a material measure can be simple, and can be polygon-shaped. 
     The material measures according to the present variations have the same effects as the material measure  10 . That is, the working time and the work load required to evaluate the total performance of a measuring instrument can be shortened and reduced respectively. 
       FIGS. 7A and 7B  exemplify another variation of a material measure according to the present embodiment.  FIG. 7A  is a perspective view of a material measure  14  according to the present variation, and  FIG. 7B  is a cross-sectional view at the cross-section  2 - 2 ′ of the material measure  14 . 
     In the XYZ coordinate system exemplified in  FIGS. 7A and 7B , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  14 , the XZ plane and the cross-section  2 - 2 ′ of the material measure  14  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     The material measure  14  according to the present variation is different from the material measure  10  in that a plurality of concentric grooves about the position O are included. That is, the material measure  14  has a measurement area R including a plurality of grooves in the radial direction (predetermined direction) of the concentric circles on the surface S. 
     Each of the grooves formed in the measurement area R of the surface S is sine-wave-shaped at the cross-section  2 - 2 ′ along the radial direction.  FIG. 7A  exemplifies the case in which the cross-section  2 - 2 ′ is the XZ plane including the center O, but the present invention is not limited to this formation. It is only necessary that the cross-section  2 - 2 ′ includes the center O, and is a plane orthogonal to the XY plane. That is, it is to be a cross-section along the radial direction. The cross-sectional shape of the grooves is not limited to a sine wave shape, but can be any simple shape. 
     In the material measure  14  according to the present variation, the depths of the cross-sectional shapes of the grooves arranged in the radial direction are constant while the lengths in the radial direction (hereinafter referred to as widths) of the cross-sectional shapes are not constant. Since the grooves of the material measure  14  are arranged in a concentric fashion, the widths of the grooves at the symmetrical positions about the center O are equal as exemplified in  FIG. 7B . 
     The depth of each groove  14   a  is constant along the circular direction of the concentric circles. Therefore, the material measure  14  has the same cross-sectional shape as the cross-section  2 - 2 ′ along any radial direction. 
     As described above, the material measure  14  according to the present variation has the same effect as the material measure  10 . That is, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     &lt;Embodiment 2&gt; 
       FIGS. 8A through 8B  exemplify the material measures according to the present embodiment for use in evaluating the performance of a measuring instrument for measuring surface texture.  FIG. 8A  is a perspective view of a material measure  15  according to the present embodiment.  FIG. 8B  is a cross-sectional view at the cross-sections  3 - 3 ′ of the material measure  15 . 
     In the XYZ coordinate system exemplified in  FIGS. 8A and 8B , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  15 , the XZ plane and the cross-section  3 - 3 ′ of the material measure  15  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     The material measure  15  has a measurement area R including a plurality of grooves in the X direction (predetermined direction) on the surface S. Each groove formed in the measurement area R on the surface S has a simple cross-sectional shape at the cross-section  3 - 3 ′ along the X direction. In  FIG. 8B , the cross-sections of the grooves arranged in the X direction are sine-wave-shaped. 
     In the material measure  15  according to the present embodiment, the widths and the depths of the cross-sectional shapes of the grooves arranged in the X direction are not constant. 
     The widths and the depths of the cross-sectional shapes of the grooves can be different for a predetermined number of adjacent grooves. As exemplified in  FIG. 8B , the width and the depth of each cross-sectional shape of the groove arranged in the X direction can be different. It is desired that the widths and the depths of the cross-sectional shapes of the grooves decrease in every predetermined number of adjacent grooves. 
     In  FIG. 8B , the adjacent grooves in the X direction are continuous, but the present invention is not limited to the formation. A flat portion can be provided between the grooves. The width of the flat portion can be arbitrarily changed. For example, the width of the flat portion can be adjusted to cyclically generate a groove in the X direction. 
     In  FIG. 8B , the surface S of the material measure  15  is positioned at the same level as the top ends of the grooves, but the present invention is not limited to this formation. For example, the measurement area R can be formed at a lower level than the surface S. In this case, the top ends are not positioned at the same level as the surface S. In  FIG. 8B , the height of the top end of each groove matches each other, but the present invention is not limited to this formation. The height of the bottom end of each groove or the height of the intermediate portion between the top end and the bottom end can match each other. 
     Each of the grooves arranged in the X direction is a linear groove parallel to the Y direction (linear direction), and the depth of each groove is constant in the Y direction. That is, a plurality of parallel and linear grooves are formed in the measurement area R of the material measure  15 . Therefore, the material measure  15  has the same cross-sectional shape at an arbitrary parallel cross-section as the cross-section  3 - 3 ′. 
     Since the material and the processing method of the material measure  15  are similar to those of the material measure  10  according to embodiment 1, the description of the material and method is omitted here. 
     When the performance of a measuring instrument for measuring surface texture is evaluated using the material measure  15  described above, the response characteristic indicating a change in measurement accuracy of the width and the depth of a groove to a change in width and depth of the groove can be checked only by once scanning the measurement area R of the material measure  15  in parallel to the X direction. When the field of view of the measuring instrument is larger than the measurement area R, the response characteristic can be checked by performing the measurement only once with the field of view fixed. 
     Therefore, as compared with the case in which the response characteristic is acquired by sequentially measuring a plurality of material measures having different widths and depths of grooves using a measuring instrument, the working time required to acquire the response characteristic can be shortened and the work load can be reduced. As a result, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     The performance evaluation of the measuring instrument using the response characteristic is performed in the same method as the prior art. For example, assume that the measuring instrument scans the material measure  15  having a cross-section exemplified in  FIG. 8B , and the response characteristic of the measuring instrument is acquired. If the width and the depth can be measured within an allowance for grooves  15   a  through  15   c  while the width and/or the depth cannot be measured within the allowance for a groove  15   d , then it can be evaluated that the limit of the combination of the width and the depth for which the measuring instrument can appropriately measure is the combination of a width W 3  and a depth D 3 . 
     The material measure according to the present embodiment can also include a plurality of concentric grooves instead of the linear grooves parallel to the Y direction (linear direction) as in the case of embodiment 1. 
       FIGS. 9A through 9C  exemplify variations of a material measure according to the present embodiment. The material measures exemplified in  FIGS. 9A through 9C  are different from the material measure  15  only in the cross-sectional shape of the groove.  FIG. 9A  exemplifies a material measure  16  in which the cross-section of a groove  16   a  is triangle-shaped.  FIG. 9B  exemplifies a material measure  17  in which the cross-section of a groove  17   a  is trapezoid-shaped.  FIG. 9C  exemplifies a material measure  18  in which the cross-section of a groove  18   a  is circle-arc-shaped or oval-arc-shaped. The cross-sectional shape of the groove of a material measure can be simple, and can be polygon-shaped. 
     The material measures according to the present variations have the same effects as the material measure  15 . That is, the working time and the work load required to evaluate the total performance of a measuring instrument can be shortened and reduced respectively. 
     &lt;Embodiment 3&gt; 
       FIGS. 10A and 10B  exemplify the material measures according to the present embodiment for use in evaluating the performance of a measuring instrument for measuring surface texture.  FIG. 10A  is a perspective view of a material measure  19  according to the present embodiment.  FIG. 10B  is a cross-sectional view at the cross-section  4 - 4 ′ of the material measures  19 . 
     In the XYZ coordinate system exemplified in  FIGS. 10A and 10B , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  19 , the XZ plane and the cross-section  4 - 4 ′ of the material measure  19  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     The material measure  19  has a measurement area R including a plurality of grooves arranged in the X direction (predetermined direction) on the surface S. Each groove formed in the measurement area R on the surface S has a simple cross-sectional shape at the cross-section  4 - 4 ′ along the X direction. In  FIG. 10B , the cross-sections of the grooves arranged in the X direction are sine-wave-shaped. 
     In the material measure  19  according to the present embodiment as in the material measure  15  according to embodiment 2, the widths and the depths of the cross-sectional shapes of the grooves arranged in the X direction are not constant. However, the material measure  19  is different from the material measure  15  in that the maximum inclination angle of the profile of the cross-sectional shape of a groove in the X direction (hereinafter referred to simply as the maximum inclination angle) is constant among a plurality of grooves arranged in the X direction. 
     The widths and the depths of the cross-sectional shapes of the grooves can be different for a predetermined number of adjacent grooves. As exemplified in&#39;  FIG. 10B , the width and the depth of each cross-sectional shape of the groove arranged in the X direction can be different. It is desired that the widths and the depths of the cross-sectional shapes of the grooves decrease in every predetermined number of adjacent grooves. 
     In  FIG. 10B , the adjacent grooves in the X direction are continuous, but the present invention is not limited to the formation. A flat portion can be provided between the grooves. The width of the flat portion can be arbitrarily changed. For example, the width of the flat portion can be adjusted to cyclically generate a groove in the X direction. 
     In  FIG. 10B , the surface S of the material measure  19  is positioned at the same level as the top ends of the grooves, but the present invention is not limited to this formation. For example, the measurement area R can be formed at a lower level than the surface S. In this case, the top ends are not positioned at the same level as the surface S. In  FIG. 10B , the height of the top end of each groove matches each other, but the present invention is not limited to this formation. The height of the bottom end of each groove or the height of the intermediate portion between the top end and the bottom end can match each other. 
     Each of the grooves arranged in the X direction exemplified in  FIG. 10B  is a linear groove parallel to the Y direction (linear direction), and the depth of each groove is constant in the Y direction. That is, a plurality of parallel and linear grooves are formed in the measurement area R of the material measure  19 . Therefore, the material measure  19  has the same cross-sectional shape at an arbitrary parallel cross-section as the cross-section  4 - 4 ′. 
     Since the material and the processing method of the material measure  19  are similar to those of the material measure  10  according to embodiment 1, the description of the material and the method is omitted here. 
     Described below is an example of a method of calculating the surface shape of a material measure for maintaining a constant maximum inclination angle α for the grooves having an arbitrary width and arranged in the X direction. The method of calculating the surface shape of a material measure is not limited to the following method, but other methods can be used. 
     First, the width W n  of the cross-sectional shape of the grooves arranged in the X direction is arbitrarily determined. In this example, the width W n  indicates the width of the cross-sectional shape of the n-th groove. For example, the width W n  can be a geometric progression (W n+1 =a*W n ) or a arithmetic progression (W n+1 =W n +b). 
     Next, the function f n  indicating the cross-sectional shape of the groove satisfying the arbitrarily determined width W n  is calculated. In this case, if the cross-section of each groove is sine-wave-shaped, the depth of the cross-sectional shape of each groove is 1, and each groove is continuous with adjacent grooves, then the function f n  is expressed by the following equation (1). 
     
       
         
           
             
               
                 
                   
                     
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     Furthermore, the function F indicating the cross-sectional shape of the material measure satisfying the arbitrarily determined width W n  is calculated by adding up the functions f n  indicating the cross-sectional shapes of the respective grooves. When the number of grooves is N, the function F is expressed by the following equation (2). 
     
       
         
           
             
               
                 
                   
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       FIG. 11  illustrates the function F indicating the cross-sectional shape of the material measure satisfying the arbitrarily determined width W n . As illustrated in  FIG. 11 , the material measure represented by the function F has constant depths of the cross-sectional shapes of grooves while it has different widths of the cross-sectional shapes of the grooves. Therefore, the maximum inclination angle differs for every groove. 
     Next, the function f n  indicating the cross-sectional shape of each groove is differentiated and the maximum inclination m n  of each groove is calculated. The maximum inclination m n  of each groove of the material measure expressed by equation (2) is expressed by the following equation (3). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 x 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             max 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     - 
                                     1 
                                   
                                   2 
                                 
                                 * 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                   
                                     W 
                                     n 
                                   
                                 
                                 * 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           ⁢ 
                                           π 
                                         
                                         
                                           W 
                                           n 
                                         
                                       
                                       * 
                                       
                                         ( 
                                         
                                           x 
                                           - 
                                           
                                             
                                               ∑ 
                                               
                                                 i 
                                                 = 
                                                 1 
                                               
                                               
                                                 n 
                                                 - 
                                                 1 
                                               
                                             
                                             ⁢ 
                                             
                                               W 
                                               i 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               } 
                             
                           
                           = 
                           
                             π 
                             
                               W 
                               n 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The relationship of m n =tan β n  holds between the maximum inclination angle β n  of each groove and the maximum inclination m n  of each groove of the material measure expressed by equation (2). Therefore, in the material measure expressed by equation (2), the maximum inclination angle β n  depends on the width W n  of each groove. 
     Next, the function f n  indicating the cross-sectional shape of each groove is amended and the maximum inclination angle of the cross-sectional shape of each groove is unified. In this case, when the maximum inclination angle is unified as the angle α, the function g n  indicating the cross-sectional shape of each groove is expressed by the following equation (4). 
     
       
         
           
             
               
                 
                   
                     
                       g 
                       n 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           tan 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                         
                           m 
                           n 
                         
                       
                       * 
                       
                         
                           f 
                           n 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             y 
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             W 
                             n 
                           
                           * 
                           tan 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                         π 
                       
                       * 
                       
                         
                           f 
                           n 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             y 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Finally, the following equation (5) is calculated by adding up the functions g n  indicating the cross-sectional shape of respective grooves whose maximum inclination angles are unified. Thus calculated is the function G indicating the cross-sectional shape of the material measure which satisfies the arbitrarily determined width W n  and whose maximum inclination angle is unified as the angle α. 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         1 
                       
                       N 
                     
                     ⁢ 
                     
                       
                         g 
                         n 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     By calculating the cross-sectional shape using the above-mentioned calculating method, a material measure having a groove of an arbitrary width and having a constant maximum inclination angle can be easily manufactured. 
     When the performance of a measuring instrument for measuring surface texture is evaluated using the material measure  19  described above, as in the case according to embodiment 2, the response characteristic indicating a change in measurement accuracy of the width and the depth of a groove to a change in width and depth of the groove can be checked only by once scanning the measurement area R of the material measure  19  in parallel to the X direction. When the field of view of the measuring instrument is larger than the measurement area R, the response characteristic can be checked by performing the measurement only once with the field of view fixed. As a result, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     The material measure  19  can be preferably used especially in evaluating the performance of an optical measuring instrument and comparing the performance between the optical measuring instrument and a probe measuring instrument. Measuring instruments for measuring surface texture can be roughly classified into contact type measuring instruments represented by probe measuring instruments and non-contact type measuring instruments represented by optical measuring instruments. Since optical measuring instruments measure the surface texture by detecting reflected light from a material measure, the inclination angle of a groove affects a measurement result because whether or not the reflected light has been detected depends on the numerical aperture of a measuring instrument (to be more strict, the numerical aperture of an objective of the measuring instrument) and the inclination angle of the grooves. However, since the material measure  19  has a constant maximum inclination angle of each groove, the influence of the inclination angle can be eliminated. Accordingly, the reliability of the performance evaluation of an optical measuring instrument can be improved as high as the performance evaluation of a probe measuring instrument. In addition, the difference in measurement result between the optical measuring instruments and the probe measuring instruments can be suppressed. 
     Furthermore, the material measures according to the present embodiment can include a plurality of concentric grooves instead of linear grooves parallel to the Y direction (linear direction). 
       FIGS. 12A through 12C  exemplify variations of a material measure according to the present embodiment. The material measures exemplified in  FIGS. 12A through 12C  are different from the material measure  19  only in the cross-sectional shape of the groove.  FIG. 12A  exemplifies a material measure  20  in which the cross-section of a groove  20   a  is triangle-shaped.  FIG. 12B  exemplifies a material measure  21  in which the cross-section of a groove  21   a  is trapezoid-shaped.  FIG. 12C  exemplifies a material measure  22  in which the cross-section of a groove  22   a  is circle-arc-shaped or oval-arc-shaped. The cross-sectional shape of the groove of a material measure can be simple, and can be polygon-shaped. 
     The material measures according to the present variations have the same effects as the material measure  19 . That is, the working time and the work load required to evaluate the total performance of a measuring instrument can be shortened and reduced respectively. Furthermore, the reliability of the performance evaluation of an optical measuring instrument can be improved as high as the performance evaluation of a probe measuring instrument. In addition, the difference in measurement result between the optical measuring instruments and the probe measuring instruments can be suppressed. 
     &lt;Embodiment 4&gt; 
       FIGS. 13A through 13C  exemplify the material measures according to the present embodiment for use in evaluating the performance of a measuring instrument for measuring surface texture.  FIG. 13A  is a perspective view of a material measure  23  according to the present embodiment.  FIG. 13B  is a cross-sectional view at the cross-sections  5 - 5 ′ of the material measure  23 , and  FIG. 13C  is a cross-sectional view at the cross-sections  6 - 6 ′ of the material measure  23   
     In the XYZ coordinate system exemplified in  FIGS. 13A through 13C , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  23 , the XZ plane and the cross-section  5 - 5 ′ and the cross-section  6 - 6 ′ of the material measure  23  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     The material measure  23  has a measurement area R including a plurality of grooves in the X direction (predetermined direction) on the surface S. To be more concrete, a plurality of linear grooves parallel to one another are formed in the measurement area R of the material measure  23 , and each groove is parallel to one another in the Y direction (linear direction). 
     Each of the grooves formed in the measurement area R on the surface S has a simple cross-sectional shape at the cross-section along the X direction. In  FIGS. 13A through 13C , the cross-sections of the grooves arranged in the X direction are sine-wave-shaped. 
     The material measure  23  according to the present embodiment is similar to the material measure  19  according to embodiment 3 in that the widths and the depths of the cross-sectional shapes of the grooves arranged in the X direction are not constant and the maximum inclination angle is constant. However, it is different from the material measure  19  in that each of the grooves of the material measure  23  is different from one another in depth and maximum inclination angle in the Y direction (linear direction). 
     For example, as exemplified in  FIG. 13B , the maximum inclination angles of the grooves of the widths W 1 , W 2 , W 3 , and W 4  are unified as the angle α 1  at the cross-section  5 - 5 ′. On the other hand, as exemplified in  FIG. 13C , the maximum inclination angles of the grooves of the widths W 1 , W 2 , W 3 , and W 4  are unified as the angle α 2  at the cross-section  6 - 6 ′. That is, in each groove, the maximum inclination angle is continuously changed with a constant width of the groove in the Y direction. It is desired that, in each groove, the depth of the cross-sectional shape of the groove and the maximum inclination angle gradually decrease in the Y direction. 
     The widths and the depths of the cross-sectional shapes of the grooves can be different for a predetermined number of adjacent grooves. As exemplified in  FIGS. 13B and 13C , the width and the depth of each cross-sectional shape of the groove arranged in the X direction can be different. It is desired that the widths and the depths of the cross-sectional shapes of the grooves decrease in every predetermined number of adjacent grooves. 
     In  FIGS. 13B and 13C , the adjacent grooves in the X direction are continuous, but the present invention is not limited to the formation. A flat portion can be provided between the grooves. The width of the flat portion can be arbitrarily changed. For example, the width of the flat portion can be adjusted to cyclically generate a groove in the X direction. 
     In  FIGS. 13B and 13C , the surface S of the material measure  23  is positioned at the same level as the top ends of the grooves, but the present invention is not limited to this formation. For example, the measurement area R can be formed at a lower level than the surface S. In this case, the top ends are not positioned at the same level as the surface S. In  FIGS. 13B and 13C , the height of the top end of each groove matches each other, but the present invention is not limited to this formation. The height of the bottom end of each groove or the height of the intermediate portion between the top end and the bottom end can match each other. 
     Since the material and the processing method of the material measure  23  are similar to those of the material measure  10  according to embodiment 1, the description of the material and the method is omitted here. 
     Described below is an example of a method of calculating the surface shape of a material measure with the maximum inclination angle α of a groove changed in the Y direction while maintaining the constant maximum inclination angle α of the grooves arranged in the X direction. The method of calculating the surface shape of the material measure is not limited to the following method, but other methods can be used. 
     The surface shape in the X direction is similar to that according to embodiment 3. Therefore, the conditional equations (1), (4), and (5) are used. Then the maximum inclination angle α can be an arbitrary function α (y) in accordance with the Y direction. 
     That is, the function g n  indicating the cross-sectional shape of each groove can be amended by the conditional equations (4) and can be expressed by the follow conditional equation (6). 
     
       
         
           
             
               
                 
                   
                     
                       g 
                       n 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               α 
                               ⁡ 
                               
                                 ( 
                                 y 
                                 ) 
                               
                             
                             ) 
                           
                         
                         
                           m 
                           n 
                         
                       
                       * 
                       
                         
                           f 
                           n 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             y 
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             W 
                             n 
                           
                           * 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 α 
                                 ⁡ 
                                 
                                   ( 
                                   y 
                                   ) 
                                 
                               
                               ) 
                             
                           
                         
                         π 
                       
                       * 
                       
                         
                           f 
                           n 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             y 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     When the maximum inclination angle is linearly changed with respect to the Y direction, the function α (y) indicating the maximum inclination angle is expressed by equation (7).
 
α( y )= by+c   (7)
 
     Furthermore, for example, when the width of the measurement area R in the Y direction is 100, and the maximum inclination angle is changed from 45° to 9°, the function α (y) indicating the maximum inclination angle is expressed by the following equation (8). 
     
       
         
           
             
               
                 
                   
                     α 
                     ⁡ 
                     
                       ( 
                       y 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           π 
                           500 
                         
                       
                       ⁢ 
                       y 
                     
                     + 
                     
                       π 
                       4 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     By calculating the cross-sectional shape by the above-mentioned calculating method, a material measure whose maximum inclination angle changes in the Y direction can be easily manufactured. 
     When the performance of a measuring instrument for measuring surface texture is evaluated using the material measure  23  according to the present embodiment, in the specific inclination angle, the response characteristic indicating a change in measurement accuracy of the width and the depth of a groove to a change in the width and depth of the groove can be checked only by once scanning the measurement area R of the material measure  23  in parallel to the X direction as in the case according to embodiment 3. In addition, only by shifting the relative positions of a measuring instrument and a material measure in the Y direction, the response characteristic at another inclination angle can be easily checked. When the field of view of the measuring instrument is larger than the measurement area R, the response characteristic of various inclination angles can be checked by performing the measurement only once with the field of view fixed. Therefore, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     As with the material measure  19 , the material measure  23  can be preferably used especially in evaluating the performance of an optical measuring instrument and comparing the performance between the optical measuring instrument and a probe measuring instrument. Therefore, the reliability of the performance evaluation of an optical measuring instrument can be improved as high as the performance evaluation of a probe measuring instrument. In addition, the difference in measurement result between the optical measuring instruments and the probe measuring instruments can be suppressed. 
     Furthermore, the material measures according to the present embodiment can include a plurality of concentric grooves instead of linear grooves parallel to the Y direction (linear direction). Each groove can be different in maximum inclination angle in the circular direction of the concentric circles. 
       FIGS. 14A through 14C  exemplify variations of a material measure according to the present embodiment. The material measures exemplified in  FIGS. 14A through 14C  are different from the material measure  23  only in the cross-sectional shape of the groove.  FIG. 14A  exemplifies a material measure  24  in which the cross-section of a groove is triangle-shaped.  FIG. 14B  exemplifies a material measure  25  in which the cross-section of a groove is trapezoid-shaped.  FIG. 14C  exemplifies a material measure  26  in which the cross-section of a groove is circle-arc-shaped or oval-arc-shaped. The cross-sectional shape of the groove of a material measure can be simple, and can be polygon-shaped. 
     The material measures according to the present variations have the same effects as the material measure  23 . That is, the working time and the work load required to evaluate the total performance of a measuring instrument can be shortened and reduced respectively. In addition, the reliability of the performance evaluation of an optical measuring instrument can be improved as high as the performance evaluation of a probe measuring instrument. In addition, the difference in measurement result between the optical measuring instruments and the probe measuring instruments can be suppressed. 
     &lt;Embodiment 5&gt; 
       FIGS. 15A through 15C  exemplify the material measures according to the present embodiment for use in evaluating the performance of a measuring instrument for measuring surface texture.  FIG. 15A  is a perspective view of a material measure  27  according to the present embodiment.  FIG. 15B  is a cross-sectional view at the cross-sections  7 - 7 ′ of the material measure  27 , and  FIG. 15C  is a cross-sectional view at the cross-sections  8 - 8 ′ of the material measure  27   
     In the XYZ coordinate system exemplified in  FIGS. 15A through 15C , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  27 , the XZ plane, the cross-section  7 - 7 ′ and the cross-section  8 - 8 ′ of the material measure  27  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     The material measure  27  has a measurement area R including a plurality of grooves in the X direction (predetermined direction) on the surface S. To be more concrete, a plurality of linear grooves parallel to one another are formed in the measurement area R of the material measure  27 , and each groove is parallel to one another in the Y direction (linear direction). 
     Each of the grooves formed in the measurement area R on the surface S has a simple cross-sectional shape at the cross-section along the X direction. In  FIGS. 15B and 15C , the cross-sections of the grooves arranged in the X direction are sine-wave-shaped, but the present invention is not limited to this application. That is, they cay be polygonal such as triangle-shaped or trapezoid-shaped, and they can also be circle-arc-shaped or oval-arc-shaped. 
     The material measure  27  according to the present embodiment is similar to the material measure  10  according to embodiment 1 in that the widths of the cross-sectional shapes of the grooves arranged in the X direction are not constant and the depth is constant. However, it is different from the material measure  10  in that each of the grooves of the material measure  27  is different from one another in depth in the Y direction (linear direction). 
     For example, as exemplified in  FIG. 15B , the depth of each groove of the widths W 1 , W 2 , W 3 , and W 4  is depth D 1  at the cross-section  7 - 7 ′. On the other hand, as exemplified in  FIG. 15C , the depth of each groove of the widths W 1 , W 2 , W 3 , and W 4  is depth D 2  at the cross-section  8 - 8 ′. That is, in each groove, the depth is continuously changed with a constant width of the groove in the Y direction. It is desired that, in each groove, the depth of the cross-sectional shape of the groove gradually decreases in the Y direction. 
     The widths of the cross-sectional shapes of the grooves can be different for a predetermined number of adjacent grooves. As exemplified in  FIGS. 15B and 15C , the width of each cross-sectional shape of the groove arranged in the X direction can be different. It is desired that the widths of the cross-sectional shapes of the grooves decrease in every predetermined number of adjacent grooves. 
     In  FIGS. 15B and 15C , the adjacent grooves in the X direction are continuous, but the present invention is not limited to the formation. A flat portion can be provided between the grooves. The width of the flat portion can be arbitrarily changed. For example, the width of the flat portion can be adjusted to cyclically generate a groove in the X direction. 
     In  FIGS. 15B and 15C , the surface S of the material measure  27  is positioned at the same level as the top ends of the grooves, but the present invention is not limited to this formation. For example, the measurement area R can be formed at a lower level than the surface S. In this case, the top ends are not positioned at the same level as the surface S. 
     Since the material and the processing method of the material measure  27  are similar to those of the material measure  10  according to embodiment 1, the description of the material and the method is omitted here. 
     When the performance of a measuring instrument for measuring surface texture is evaluated using the material measure  27  described above, in the specific inclination angle, the response characteristic indicating a change in measurement accuracy of the depth of a groove to a change in width of the groove can be checked only by once scanning the measurement area R of the material measure  27  in parallel to the X direction. In addition, the response characteristic at another depth can be easily checked by only shifting the relative positions of the measuring instrument and the material measure in the Y direction. When the field of view of the measuring instrument is larger than the measurement area R, the response characteristic can be checked by performing the measurement only once with the field of view fixed. 
     Therefore, as compared with the conventional method in which the response characteristic is acquired by sequentially measuring a plurality of material measures having different widths and depths of grooves using a measuring instrument, the working time required to acquire the response characteristic can be shortened and the work load can be reduced. As a result, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     The material measure according to the present embodiment can also include a plurality of concentric grooves instead of the linear grooves parallel to the Y direction (linear direction) as in the case of embodiment 1. The depth of the cross-sectional shape of each groove can be different in the circular direction of the concentric circles. In this case, it is desired that the depth of the cross-sectional shape of the groove gradually decreases in the Y direction. 
     &lt;Embodiment 6&gt; 
       FIG. 16  exemplifies the material measures according to the present embodiment for use in evaluating the performance of a measuring instrument for measuring surface texture. The material measure  28  according to the present embodiment has a plurality of measurement areas (measurement areas R 1 , R 2 , and R 3 ) on the surface S. The plurality of measurement areas are arranged in the Y direction (linear direction). 
     In the XYZ coordinate system exemplified in  FIG. 16 , the Z direction and the vertical direction, the XY plane, the horizontal plane, and the surface S of the material measure  28  are parallel to one another. In addition, the X direction, the Y direction and the Z direction are orthogonal to one another. 
     Each measurement area includes a plurality of grooves in the X direction (predetermined direction). In each measurement area, a plurality of linear grooves are formed in parallel, and each groove is parallel to the Y direction (linear direction). In each groove, the width and the depth of the groove are constant in the Y direction. 
     The surface shape of a measurement area is similar to the surface shapes of the material measures according to embodiments 1 through 3. Among the measurement areas, the states such as depths, maximum inclination angles, etc. as variables of the response characteristic are different. 
     For example, when the surface shape of a measurement area is similar to the surface shape of the material measure according to embodiment 1, the depths of the cross-sectional shapes of the grooves are different in the measurement areas R 1 , R 2 , and R 3 . When the surface shape of a measurement area is similar to the surface shape of the material measure according to embodiment 3, the maximum inclination angles of the profiles of the cross-sectional shapes of the grooves in the X direction are different in the measurement areas R 1 , R 2 , and R 3 . 
     Since the material and the processing method of the material measure  28  are similar to those of the material measure  10  according to embodiment 1, the description of the material and the method is omitted here. 
     When the performance of a measuring instrument for measuring surface texture is evaluated using the material measure  28  described above, the response characteristic can be checked only by once scanning any measurement area of the material measure  28  in the X direction. In addition, the response characteristic with different depths and maximum inclination angles can be easily checked by only shifting the relative positions of the measuring instrument and the material measure in the Y direction and scanning another measurement area. When the field of view of the measuring instrument is larger than the measurement area, the response characteristic can be checked by performing the measurement only once with the field of view fixed. 
     Therefore, as compared with the case in which the response characteristic is acquired by sequentially measuring a plurality of material measures having different widths and depths of grooves using a measuring instrument, the working time required to acquire the response characteristic can be shortened and the work load can be reduced. As a result, the working time and the work load required to evaluate the total performance of the measuring instrument can be shortened and reduced respectively. 
     Furthermore, the material measure  28  has a constant cross-sectional shape along the X direction in the area. Therefore, the position accuracy required when the relative position of the material measure to the measuring instrument is shifted in the Y direction can be moderated. As a result, the performance of the measuring instrument can be prevented from being erroneously evaluated by the shift of the position. 
     Described above is the case in which a groove, that is, a concave pattern, is formed on the surface S of a material measure in embodiments 1 through 6. However, the present invention is not limited to this case, and a projection, that is, a convex pattern, can be formed on the surface S of a material measure for a similar effect.