Abstract:
In a spherical shape measurement method for measuring a surface shape, a sphere to be measured is made freely rotatable. The partial spherical shape of each measurement area, which is established so as to have an area overlapping with another measurement area adjacent to each other, is measured at each rotation position, and the surface shape is measured by joining the partial spherical shapes of the measurement areas by a stitching operation based on the shape of the overlapping area. In the state of detaching the sphere from the sphere hold mechanism to which the sphere is freely attachable and detachable, the sphere support table holds the sphere. The sphere is re-held at a different position, so that the shape of the entire sphere can be measured with high accuracy.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    The disclosure of Japanese Patent Application No. 2014-147226 filed on Jul. 17, 2014 including specifications, drawings and claims is incorporated herein by reference in its entirety. 
       TECHNICAL FIELD 
       [0002]    The present invention relates to a spherical shape measurement method and apparatus, and in particular, to a spherical shape measurement method and apparatus that can measure the shape of an entire sphere (surface) with high accuracy. 
       BACKGROUND ART 
       [0003]    Spherical parts or partly spherical parts, such as a ball of a bearing, a reference sphere used as a standard in a measurement device, and a lens are widely used in an industrial field. In order to measure the shapes of these spherical parts, a number of surface shape measurement methods and devices are proposed. An interferometer device, which is a representative example thereof, can measure the surface shapes of the spherical parts with high accuracy and high density. Furthermore, for the purpose of measuring the shape of a spherical surface that is out of a surface area measurable by the surface shape measurement device, U.S. Pat. No. 6,956,657 B2 (hereinafter called Patent Literature 1) and “sphericity measurement using stitched interferometry” proceedings of JSPE autumn meeting, 2011, p. 868-869 (hereinafter called Non-Patent Literature 1) propose an apparatus that includes surface shape measurement unit and measurement position change mechanism for holding the spherical surface and changing a measurement position. 
         [0004]    In such an apparatus, while the measurement position change mechanism changes the measurement position by shifting the spherical surface, the surface shape measurement unit measures the shapes of a plurality of partial areas. By joining the measured shapes of the plurality of partial areas by a computation called stitching, the shape of the wide spherical surface is measured. 
         [0005]    A summary of the spherical shape measurement apparatus described in Non-Patent Literature 1 will be explained.  FIG. 1  is a side view showing the structure of the apparatus. The spherical shape measurement apparatus includes a part of a laser interferometer  20  being the surface shape measurement unit, for example, a Fizeau interferometer, and a part of a measurement position change mechanism  40  being the measurement position change mechanism. The laser interferometer  20  used in this apparatus is a device that measures the surface shape of a sphere  10  by using a reference spherical surface  22  having a spherical shape and comparing the wavelength of laser light  26  generated by a laser light source  24 , which is used as a yardstick, with the reference spherical surface  22 . In the drawings, a reference numeral  28  refers to a beam splitter. A reference numeral  30  refers to a collimator lens for making the laser light  26  into parallel rays. A reference numeral  32  refers to an image sensor for detecting interference light synthesized by the beam splitter  28 . 
         [0006]    The sphere  10  (hereinafter simply called sphere) is disposed in a focal point of the reference spherical surface  22 . Since an area measured by the laser interferometer  20  is a part of the surface of the sphere  10  to which the laser light  26  is applied, it is required to provide unit for moving the position of the laser interferometer  20  itself or the sphere  10 , for the purpose of measuring a wider area. The apparatus described in Non-Patent Literature 1, which measures the shape of a sphere having a shaft, such as the sphere  10  having a support shaft  12  fixed thereto, is provided with the measurement position change mechanism  40  for moving an arbitrary surface of the sphere  10  to a measurement area of the laser interferometer  20  by a biaxial rotation mechanism having a θ rotation axis  42  and a φ rotation axis  44  orthogonal to the θ rotation axis  42 , while holding the sphere  10  through the support shaft  12 . 
         [0007]      FIG. 2  is a top plan view of the apparatus according to Non-Patent Literature 1. The φ rotation axis  44  is adjusted so as to form a right angle with a measurement optical axis (perpendicular direction in the drawing of  FIG. 2 ) and coincide with the focal point of the reference spherical surface  22  positioned thereon. By rotating the φ rotation axis  44 , a bracket  46  for supporting the θ rotation axis  42  is rotated about a φ axis. The θ rotation axis  42  is rotatable thereon by 360 degrees or more. At this time, the length of the support shaft  12  and an arm of the bracket  46  is adjusted such that the center of the sphere  10  is positioned on the φ rotation axis  44 , whereby the sphere  10  can be rotated by an arbitrary angle at a focus position of the reference spherical surface  22 . In this structure, to measure an area extending to a half of the sphere  10  by the laser interferometer  20 , the sphere  10  is rotated about the θ rotation axis  42  by 360 degrees and the φ rotation axis  44  by 90 degrees from a position at which the support shaft  12  is orthogonal to the measurement optical axis to a position at which the support shaft  12  is parallel to the measurement optical axis. 
         [0008]      FIGS. 3A and 3B  show the relation among a measurable area by the apparatus with such a configuration, and the θ and φ rotation axes of the apparatus. In  FIGS. 3A and 3B , the apparatus shown in  FIG. 1  is viewed from above. First, the angle of the φ rotation axis  44  at which the support shaft  12  is orthogonal to the measurement optical axis of the laser interferometer  20  is defined as a first support angle φ 1 .  FIG. 3A  shows this state. Defining a central axis of the support shaft  12  as a polar axis of the sphere  10 , contours in the surface of the sphere  10  at positions orthogonal to the polar axis are considered as latitude lines of the sphere  10 , and the contour having a maximum diameter is the equator (a first measurement latitude line). At the first support angle φ 1 , rotating the θ rotation axis  42  directs an arbitrary point in the first measurement latitude line in the sphere  10  toward the laser interferometer  20 . By performing measurement at the position, the shape of a single measurement area is measured at an arbitrary position of the θ rotation axis  42 . It is desirable that rotation intervals of the θ rotation axis  42  be determined so as to have an overlapping area between the single measurement areas adjacent to each other, for the sake of a stitching operation performed afterward. This overlapping area may be approximately of the order of a half of a viewing angle of the laser interferometer  20 , for example. Here, the first support angle φ 1  is defined as a position at which the support shaft  12  is orthogonal to the measurement optical axis, but is not necessarily such a position and may be set at any arbitrary position. 
         [0009]    Then, the φ rotation axis  44  is rotated to set the support shaft  12  at a position different from the first support angle φ 1 . This position is referred to as a second support angle φ 2 .  FIG. 3B  shows this state. By rotating the θ rotation axis  42  at this position, points on the spherical surface intersecting with the measurement optical axis of the laser interferometer  20  draw a trail. A contour line represented by this trail is referred to as a second measurement latitude line. Just as with an operation at the first support angle φ 1 , rotating the θ rotation axis  42  allows measurement of the shape of the single measurement area at an arbitrary position of the θ rotation axis  42  in the second measurement latitude line in the spherical surface. Just as with the rotation intervals of the θ rotation axis  42 , the distance between the first support angle φ 1  and the second support angle φ 2  may be approximately of the order of a half of the viewing angle of the laser interferometer  20 , for example. 
         [0010]    A plurality of support angles φ are set in a rotation range of the φ rotation axis  44 , and the θ rotation axis  42  is operated at each position. This procedure is performed until the single measurement areas corresponding to the individual positions cover a hemispherical part of the sphere  10 . The shapes of a number of the single measurement areas obtained in this manner are stitched together by the stitching operation with reference to positional information of the θ rotation axis  42  and the φ rotation axis  44 , to measure the surface shape of the sphere  10 . The rotation range of the φ rotation axis  44  is not limited to 90 degrees as shown in  FIG. 2 , and can be set in an arbitrary range as long as there is no physical contact between the laser interferometer  20  and the measurement position change mechanism  40 , or the like. A necessary prerequisite for the plurality of single measurement areas covering the half of the sphere  10  is a rotation range of 90 degrees of the φ rotation axis  44 . 
         [0011]    When the measurement position change mechanism  40  has a dimensional error, that is, each constituting part has a dimension different from a design value, or a movement error, the sphere  10  may be displaced from the focus position of the reference spherical surface  22  with rotation of the θ rotation axis  42  and the φ rotation axis  44 . In the interferometer device for measuring the spherical surface, this positional displacement causes a measurement error. Accordingly, the apparatus of Non-Patent Literature 1 may be provided with, for example, three axes movement mechanism  46  having stages  48   x,    48   y,  and  48   z,  as shown in  FIG. 4 . This positional displacement can be corrected by moving the sphere  10  with reference to an interference fringe image of the laser interferometer  20  so as to minimize the number of interference fringes. 
       SUMMARY OF INVENTION 
     Technical Problem 
       [0012]    The conventional techniques described in Patent Literature 1 and Non-Patent Literature 1 measure a partly spherical shape such as a lens or a sphere held by a fixed shaft. Thus, an area around the shaft and an area around a held portion are difficult to measure, and a measurement range of the conventional techniques is limited to approximately a half part of a sphere at the most. An area beyond the half part of the sphere can be measured, depending on the size of a field of view of the laser interferometer or a movement range of the measurement position change mechanism, but it is still impossible to measure the held portion of the sphere. Therefore, it is desirable to provide an apparatus and a measurement method for measuring the shape of the entire sphere with high accuracy. 
         [0013]    The present invention has been made in order to solve the above-described problem in the conventional technique, and an object thereof is to measure the shape of an entire sphere with high accuracy. 
       Solution to Problem 
       [0014]    To solve the above-described problem, a spherical shape measurement method according to the present invention for measuring a surface shape include: freely rotating a sphere to be measured; measuring a partial spherical shape of each measurement area, which is established so as to have an area overlapping with another measurement area adjacent to each other, at each rotation position; and joining the partial spherical shapes of the measurement areas by a stitching operation based on a shape of the overlapping area, thereby measuring the surface shape. The method further includes the step of enabling a sphere support table to hold the sphere in a state of detaching the sphere from a sphere hold mechanism to which the sphere is freely attachable and detachable, and the step of changing a position at which the sphere is held, so that the shape of the entire sphere can be measured. 
         [0015]    The sphere support table may be rotatable. 
         [0016]    The positions of the sphere and surface shape measurement unit may be adjustable. 
         [0017]    The present invention provides a spherical shape measurement apparatus that includes surface shape measurement unit for measuring the partial shape of a spherical surface, and measurement position change mechanism for freely rotating a sphere to be measured relative to the surface shape measurement unit. The surface shape measurement unit measures the partial spherical shape of each measurement area, which is established so as to have an area overlapping with another measurement area adjacent to each other, at each rotation position, and the surface shape is measured by joining the partial spherical shapes of the measurement areas by a stitching operation based on the shape of the overlapping area. The spherical shape measurement apparatus further includes unit that has a sphere hold mechanism to which the sphere is freely attachable and detachable, and a sphere support table for holding the sphere detached from the sphere hold mechanism, and that changes a position at which the sphere is held, so that the shape of the entire sphere is measured. 
         [0018]    The surface shape measurement unit may be a laser interferometer, and the measurement position change mechanism may rotate the sphere about a first rotation axis and a second rotation axis orthogonal to the first rotation axis. 
         [0019]    The sphere support table may have a recess at a top surface thereof to receive and support the sphere detached from the sphere hold mechanism therein. 
         [0020]    The spherical shape measurement apparatus may further include a mechanism for moving up and down the sphere support table. 
         [0021]    The spherical shape measurement apparatus may further include a mechanism for retracting the sphere hold mechanism, while the sphere is detached. 
         [0022]    The spherical shape measurement apparatus may further include a mechanism for rotating the sphere support table. 
         [0023]    A rotation axis of the mechanism for rotating the sphere support table and the second rotation axis of the measurement position change mechanism may be coaxial with each other. 
         [0024]    The spherical shape measurement apparatus may further include a movement mechanism in three axes directions to adjust the relative position between the sphere and the surface shape measurement unit. 
       Advantageous Effects of Invention 
       [0025]    According to the present invention, it is possible to measure the shape of an entire sphere with high accuracy. 
         [0026]    These and other novel features and advantages of the present invention will become apparent from the following detailed description of preferred embodiments. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0027]    The preferred embodiments will be described with reference to the drawings, wherein like elements have been denoted throughout the figures with like reference numerals, and wherein: 
           [0028]      FIG. 1  is a side view illustrating a spherical shape measurement apparatus described in Non-Patent Literature 1; 
           [0029]      FIG. 2  is a plan view of the spherical shape measurement apparatus of  FIG. 1 ; 
           [0030]      FIG. 3A  and  FIG. 3B  are enlarged plan views for explaining a measurement procedure of the spherical shape measurement apparatus of  FIG. 1 ; 
           [0031]      FIG. 4  is a side view of the spherical shape measurement apparatus of  FIG. 1 , having three axes movement mechanism; 
           [0032]      FIG. 5  is a side view illustrating a first embodiment of the present invention; 
           [0033]      FIG. 6  is a flowchart of a procedure for measuring the shape of an entire sphere according to the first embodiment of the present invention; 
           [0034]      FIG. 7  is a flowchart of a procedure for re-holding the sphere according to the first embodiment of the present invention; 
           [0035]      FIG. 8  is a side view illustrating a second embodiment of the present invention; 
           [0036]      FIG. 9  is a flowchart of a procedure for re-holding the sphere according to the second embodiment of the present invention; 
           [0037]      FIG. 10  is a side view illustrating a third embodiment of the present invention; and 
           [0038]      FIG. 11  is a side view illustrating a fourth embodiment of the present invention. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0039]    Embodiments of the present invention will be described below in detail with reference to the drawings. Note that, the present invention is not limited to descriptions of the below embodiments and practical examples. Components of the below embodiments and practical examples include what is easily assumed by those skilled in the art, what is substantially the same, and what is in a so-called equivalent scope. Moreover, the components described in the below embodiments and practical examples may be appropriately combined or appropriately selectively used. 
         [0040]      FIG. 5  shows the structure of a first embodiment of the present invention. In the first embodiment, a sphere hold mechanism  50 , a sphere support table  52 , a lift axis  54  in Z direction, a base  56  for supporting the sphere support table  52  and the lift axis  54  in Z direction, and an adjustment axis  60  in R direction are newly added to the apparatus described in Non-Patent Literature 1, which includes the laser interferometer  20  and the measurement position change mechanism  40  having the θ rotation axis  42 , the φ rotation axis  44 , and the bracket  46 , in order to enable measurement of the shape of an entire sphere by re-holding the sphere. 
         [0041]    The sphere hold mechanism  50  has a mechanism to arbitrarily attach and detach the sphere  10  to and from the support shaft  12 . By vacuum attraction, magnetic force in the case of a magnetized sphere, or the like, the sphere  10  can be freely attracted or detached. 
         [0042]    The sphere support table  52  is a table having a recess  52 A, in its top surface, to temporarily receive and support the sphere  10  detached from the sphere hold mechanism  50 . While the sphere hold mechanism  50  is attracting the sphere  10 , the sphere support table  52  is preferably retracted by the lift axis  54  in Z direction so as not to contact the sphere  10 . Also, while the sphere  10  is detached, the sphere hold mechanism  50  is preferably retracted by the adjustment axis  60  in R direction so as not to contact the sphere  10 . 
         [0043]    Note that, the φ rotation axis  44  is rotatable, for example, ±90 degrees=180 degrees, for the sake of re-holding the sphere  10 . 
         [0044]    In the drawing, a reference numeral  34  refers to a computer for the laser interferometer  20 . A reference numeral  62  refers to a controller for controlling rotation of the θ rotation axis  42  and the φ rotation axis  44  of the measurement position change mechanism  40 , attraction of the sphere hold mechanism  50 , ascent and descent of the lift axis  54  in Z direction, expansion and contraction of the adjustment axis  60  in R direction, and the like. A reference numeral  64  refers to a computer for analyzing a spherical shape on the basis of information obtained by the computer  34 , while controlling the measurement position change mechanism  40  and the re-holding of the sphere  10  through the controller  62 . 
         [0045]    A procedure for measurement of an entire sphere will hereinafter be described with reference to  FIG. 6 . 
         [0046]    First, the sphere  10  is attracted to the sphere hold mechanism  50  in step  100 . The φ rotation axis  44  is rotated and set at a predetermined angle in step  110 . Then, the rotation of the θ rotation axis  42  in step  120  and the measurement of the single measurement area in step  130  are repeated, until it is judged in step  140  that measurement covering an entire predetermined latitude line has been performed. 
         [0047]    Then, the φ rotation axis  44  is rotated in step  110  to change the latitude line and a repetition of steps  120  to  140  is performed, until it is judged in step  150  that measurement covering a first half part of the sphere (surface) has been performed. 
         [0048]    When it is judged that the measurement of the first half part of the sphere has been completed in step  150 , the sphere  10  is re-held in step  160 . More specifically, as shown in  FIG. 7 , the lift axis  54  in Z direction is moved up while the sphere hold mechanism  50  is attracting the sphere  10 , so that the sphere support table  52  comes into contact with the sphere  10  (step  162 ). Then, the sphere  10  is detached from the sphere hold mechanism  50 , and supported by the sphere support table  52  (step  164 ). Then, the sphere hold mechanism  50  is retracted (moved backward in a right direction of the drawing) by operation of the adjustment axis  60  in R direction to keep the sphere hold mechanism  50  from contact with the sphere  10  (step  166 ). In this state, the measurement position change mechanism  40  can move to an arbitrary rotation position by the rotation of the φ rotation axis  44  (step S 168 ). After the rotation position is changed, the adjustment axis  60  in R direction is operated (moved forward in a left direction of the drawing), so that the sphere hold mechanism  50  makes tight contact with the sphere  10  (step  170 ), and the sphere hold mechanism  50  attracts the sphere  10  again (step  172 ). After that, the lift axis  54  in Z direction is operated to move down the sphere support table  52  (step  174 ). 
         [0049]    This sequential operation changes the position of holding the sphere  10 , and allows the re-holding of the sphere  10 . To be more specific, by 180 degrees rotation of the φ rotation axis  44  from a position shown in  FIG. 2  at which the θ rotation axis  42  is orthogonal to the measurement optical axis, the sphere  10  is re-held at a position inverted by 180 degrees. 
         [0050]    After the re-holding, a second half part of the sphere (surface) is measured at steps  210  to  250 , corresponding to steps  110  to  150 . By doing so, measurement is performed in the state of directing a portion that the sphere has been held by and cannot be measured by the apparatus described in Non-Patent Literature 1 toward the laser interferometer  20 , and it becomes possible to collect measurement results of the single measurement areas that cover the entire sphere. Provided that the first half part of the sphere is measured before the re-holding and the second half part of the sphere is measured after the re-holding, the shape of the entire sphere can be measured by the stitching operation of the two half parts of the sphere in step  300 . An operation flow to measure each of the first and second half part of the sphere is the same as that of Non-Patent Literature 1. The sphere  10  is re-held between the measurement of the two half parts of the sphere, and the stitching operation is performed to join the two half parts of the sphere after the measurement. 
         [0051]    The rotation range of the φ rotation axis  44  in a re-holding operation of the sphere  10  is not limited to 180 degrees, and an arbitrary angle is adoptable. However, the most efficient way to measure the shape of the entire sphere is that the sphere  10  is re-held at a position of 180 degrees and measured half by half. 
         [0052]    In this embodiment, the φ rotation axis  44  is used for re-holding the sphere  10 , resulting in simple structure. 
         [0053]    Next,  FIG. 8  illustrates the structure of a second embodiment according to the present invention. In this embodiment, a φ 2  rotation axis  70  is further provided between the lift axis  54  in Z direction and the sphere support table  52  of the apparatus according to the first embodiment, to make the sphere support table  52  rotatable. The φ 2  rotation axis  70  is coaxial with the φ rotation axis  44 . The rotation range of the φ rotation axis  44  may be 0 degree to 90 degrees, just as with the conventional technique shown in  FIG. 1 . Note that, the position of providing the φ 2  rotation axis  70  is not limited to between the lift axis  54  in Z direction and the sphere support table  52 , and may be between the lift axis  54  in Z direction and the base  56 . 
         [0054]    Since the other structure is the same as that of the first embodiment, the description thereof will be omitted. 
         [0055]    In the measurement method according to the present invention, the position of the single measurement area in the spherical surface to be measured corresponds to the position of each of the θ rotation axis  42  and the φ rotation axis  44 , in a procedure for measuring the half part of the sphere while the sphere  10  is being held. However, since the re-holding of the sphere  10  once separates the measurement position change mechanism  40  from the sphere  10 , there is no continuity between before and after the re-holding in the position of the single measurement area on the spherical surface and the position of each of the θ rotation axis  42  and the φ rotation axis  44 . For this reason, the sphere  10  has to be re-held with as much care as possible to prevent the occurrence of an error such as a positional displacement. According to the structure of the first embodiment, in a case where there is an eccentricity of the support shaft  12  or a mechanical error of the φ rotation axis  44  owing to whirling or the like, the center of the rotation of the measurement position change mechanism  40  does not necessarily coincide with the center of the sphere  10 , and hence an error owing to the re-holding possibly occurs. 
         [0056]    In this embodiment, the re-holding operation of the sphere  10  is performed by rotating the sphere support table  52  about the φ 2  rotation axis  70 , which is coaxial with the φ rotation axis  44 . Thereby, it is possible to stably re-hold the sphere  10 , even if there is the eccentricity of the support shaft  12  or the whirling of the φ rotation axis  44 . 
         [0057]    A procedure for re-holding the sphere according to the second embodiment of the present invention will be hereinafter described with reference to  FIG. 9 . 
         [0058]    The lift axis  54  in Z direction is moved up while the sphere hold mechanism  50  is attracting the sphere  10 , such that the sphere support table  52  comes into contact with the sphere  10  (step  162 ). Then, the sphere  10  is detached from the sphere hold mechanism  50 , and supported by the sphere support table  52  (step  164 ). Then, the sphere hold mechanism  50  is retracted (moved backward in a right direction of  FIG. 8 ) by operation of the adjustment axis  60  in R direction to keep the sphere hold mechanism  50  from being brought into contact with the sphere  10  (step  166 ). In this state, the φ 2  rotation axis  70 , which is adjusted to be coaxial with the φ rotation axis  44 , is rotated to move the sphere  10  to an arbitrary rotation position relative to the measurement position change mechanism  40  (step  180 ). After the rotation position is changed, the adjustment axis  60  in R direction is operated (moved forward in a left direction of  FIG. 8 ) such that the sphere hold mechanism  50  makes tight contact with the sphere  10  (step  170 ), and the sphere hold mechanism  50  attracts the sphere  10  again (step  172 ). After that, the lift axis  54  in Z direction is operated to move down the sphere support table  52  (step  174 ). 
         [0059]    This sequential operation changes the position of holding the sphere  10 , and allows the re-holding of the sphere  10 . A procedure for measuring the spherical surface is the same as that of the first embodiment except for step  180  of the re-holding operation, and hence the description thereof will be omitted. 
         [0060]    According to this embodiment, even if the measurement position change mechanism  40  has a movement error or the like, it is possible to precisely re-hold the sphere  10  and measure the shape of the entire sphere  10  with high accuracy. Also, the φ rotation axis  44  is not used in the re-holding operation, and hence may have a rotation range of 0 degree to 90 degrees, just as with the conventional technique. 
         [0061]    Next,  FIG. 10  illustrates the structure of a third embodiment of the present invention. According to this embodiment, the apparatus of the first embodiment is additionally provided with a base  80  on which the φ rotation axis  44  and the base  56  are mounted, and movement mechanism  82  for translationally moving the base  80  in three axes directions of x, y, and z. In the drawing, a reference numeral  82   x  refers to an x axial direction movement mechanism. A reference numeral  82   y  refers to a y axial direction movement mechanism. A reference numeral  82   z  refers to a z axial direction movement mechanism. 
         [0062]    The other components are the same as those of the first embodiment, a description thereof will be omitted. 
         [0063]    When there is a difference in dimension of each part constituting the measurement position change mechanism  40  from a design value or a movement error, the sphere  10  may be displaced from the center of surface shape measurement unit with the rotation of the θ rotation axis  42  and the φ rotation axis  44 . This displacement sometimes causes a measurement error of the surface shape measurement unit. For example, when the laser interferometer  20  for measuring the spherical surface is used as the surface shape measurement unit, a displacement occurring between the sphere  10  and the center of the reference spherical surface  22  causes a measurement error. Accordingly, the three axes movement mechanism  82  is provided to correct this positional displacement. When the laser interferometer  20  is used as the surface shape measurement unit, this positional displacement can be corrected by moving the sphere  10  with reference to an interference fringe image so as to minimize the number of interference fringes. 
         [0064]    According to this embodiment, it is possible to reduce an effect of the measurement error that is associated with the positional displacement between the sphere  10  and the surface shape measurement unit owing to the movement error of the measurement position change mechanism  40  or the difference in dimension of the component from the design value, and therefore measure the shape of the entire sphere with high accuracy. 
         [0065]    Next,  FIG. 11  illustrates the structure of a fourth embodiment in which the three axes movement mechanism  82  described in the third embodiment is added to the apparatus of the second embodiment. 
         [0066]    The other structure and effects are the same as those of the first to third embodiments, so a description thereof will be omitted. 
         [0067]    According to this embodiment, it is possible to precisely re-hold the sphere  10  even with a movement error of the measurement position change mechanism  40  or the like, and reduce an effect of the measurement error that is associated with a positional displacement between the sphere  10  and the surface shape measurement unit owing to a movement error of the measurement position change mechanism  40  or a difference in dimension of components from a design value. Therefore, it becomes possible to measure the shape of the entire sphere  10  with high accuracy. 
         [0068]    The structures of the apparatuses described above are just examples, and other structures are adoptable so long as the apparatus can operate equivalently. For example, the position of the lift axis  54  in Z direction and the φ 2  rotation axis  70  according to the fourth embodiment may be changed, and the lift axis  54  in Z direction may be provided on the φ 2  rotation axis  70 . Like this example, order of configuration of the axes and the like are flexibly changeable so long as the entire apparatus can operate equivalently. Moreover, the positional relation between the θ rotation axis  42  and the φ rotation axis  44  is not necessarily orthogonal, and is changeable so long as the θ rotation axis  42  and the φ rotation axis  44  can operate equivalently. 
         [0069]    It should be apparent to those skilled in the art that the above-described embodiments are merely illustrative which represent the application of the principles of the present invention. Numerous and varied other arrangements can be readily devised by those skilled in the art without departing from the spirit and the scope of the invention.