Patent Publication Number: US-10782125-B2

Title: Interference fringe projection optical system and shape measurement apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is a Continuing Application based on International Application PCT/JP2015/064837 filed on May 18, 2015, the entire disclosure of this earlier application being incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to an interference fringe projection optical system and to a shape measurement apparatus using the same. 
     BACKGROUND 
     Shape measurement apparatuses such as the one illustrated in  FIG. 25  are known. The shape measurement apparatus illustrated in  FIG. 25 , disclosed in patent literature 1 (PTL 1), is inserted in a body cavity or the like and measures the surface shape of an organ or the like. This shape measurement apparatus includes an interference fringe projection optical system  100 , an imager  200 , and a calculation controller  300  constituted by a computer or the like. The shape measurement apparatus projects an interference fringe  400  onto the object surface of a measured object with the interference fringe projection optical system  100 , images the projected interference fringe  400  with the imager  200 , and measures the three-dimensional shape of the object surface by analyzing the imaged interference fringe  400  with the calculation controller  300 . In  FIG. 25 , the interference fringe  400  is depicted as being planar. 
     The interference fringe projection optical system  100  includes an interference fringe generating optical system  110  and a magnifying optical system  130 . The interference fringe generating optical system  110  includes a light source  111 , a collimator lens  112 , an optical isolator  113 , a coupling lens  114 , a polarization-maintaining optical fiber  115 , a collimator lens  116 , a birefringent plate  117 , and a polarizing plate  118 . The magnifying optical system  130  is constituted by a single projection lens  131 . 
     The light source  111  is, for example, configured by a semiconductor laser and is driven by the calculation controller  300  through a driver  120  to emit linearly polarized light. The light beam emitted from the light source  111  is formed as a parallel light beam by the collimator lens  112 , passes through the optical isolator  113 , is subsequently incident on the polarization-maintaining optical fiber  115  through the coupling lens  114 , is guided by the polarization-maintaining optical fiber  115 , and is emitted. The light beam emitted from the polarization-maintaining optical fiber  115  is formed as a parallel light beam by the collimator lens  116 , is subsequently incident on the birefringent plate  117 , and is separated into a light beam with two polarization components which are further incident on the polarizing plate  118 . Only the coherent components are extracted from among the two polarization components to generate an interference fringe. The interference fringe is magnified by the projection lens  131  and projected onto the object surface as an interference fringe  400 . 
     The shape measurement apparatus illustrated in  FIG. 25  uses the projection lens  131  to magnify and project the interference fringe generated by the interference fringe generating optical system  110 , thus offering the advantage of the collimator lens  116 , the birefringent plate  117 , the polarizing plate  118 , and the projection lens  131  disposed at the tip of the shape measurement apparatus being reducible in size. 
     CITATION LIST 
     Patent Literature 
     
         
         
           
             PTL 1: JP 3009521 B2 
           
         
       
    
     SUMMARY 
     An interference fringe projection optical system according to this disclosure includes: 
     an interference fringe generating optical system configured to generate an interference fringe; and 
     a magnifying optical system configured to magnify the interference fringe and project the interference fringe onto an object surface, wherein 
     the magnifying optical system comprises an incident-side lens group on a side where a light beam forming the interference fringe is incident and an exit-side lens group on a side where the light beam is emitted and the interference fringe is projected towards the object surface, 
     f1/f2&gt;3, where f1 is a focal length of the incident-side lens group, and f2 is a focal length of the exit-side lens group, and 
     the incident-side lens group and the exit-side lens group each have a positive refractive power, and an expression xd/(f1+f2)&lt;2 is satisfied, where xd is a distance from an exit-side principal point of the incident-side lens group to an incident-side principal point of the exit-side lens group. 
     A shape measurement apparatus according to this disclosure includes: 
     the aforementioned interference fringe projection optical system; 
     an imager configured to capture an image of a projected image of the interference fringe; and 
     a calculator configured to calculate unevenness information of the object surface using an image signal from the imager. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings: 
         FIG. 1  schematically illustrates the main structure of a shape measurement apparatus according to Embodiment 1; 
         FIG. 2  is a partial enlargement of  FIG. 1 ; 
         FIG. 3  illustrates contrast characteristics of an interference fringe; 
         FIG. 4  illustrates an intensity distribution of a light beam; 
         FIG. 5A  illustrates the state in which the optical axes of the polarization-maintaining optical fiber and the magnifying optical system in  FIG. 1  match; 
         FIG. 5B  illustrates a state in which the optical axis state in  FIG. 5A  is shifted; 
         FIG. 6A  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes of the polarization-maintaining optical fiber and the magnifying optical system in  FIG. 5A  is 0 mm; 
         FIG. 6B  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes in  FIG. 5B  is 0.01 mm; 
         FIG. 6C  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes in  FIG. 5B  is 0.03 mm; 
         FIG. 6D  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes in  FIG. 5B  is 0.1 mm; 
         FIG. 7A  illustrates the state, for comparison with  FIG. 5A , in which the optical axes of the polarization-maintaining optical fiber and the lens match when the magnifying optical system is configured by a single lens; 
         FIG. 7B  illustrates a state in which the optical axis state in  FIG. 7A  is shifted; 
         FIG. 8A  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes of the polarization-maintaining optical fiber and the lens in  FIG. 7A  is 0 mm; 
         FIG. 8B  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes in  FIG. 7B  is 0.01 mm; 
         FIG. 8C  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes in  FIG. 7B  is 0.03 mm; 
         FIG. 8D  is a photograph illustrating the results of simulating the intensity distribution of the projected interference fringe when the shift amount δ of the optical axes in  FIG. 7B  is 0.1 mm; 
         FIG. 9  illustrates the main structure of an interference fringe projection optical system according to Embodiment 2; 
         FIG. 10  illustrates the main structure of an interference fringe projection optical system according to Embodiment 3; 
         FIG. 11  illustrates a modification to the shape of the birefringent plate of  FIG. 10 ; 
         FIG. 12  illustrates the main structure of an interference fringe projection optical system according to Embodiment 4; 
         FIG. 13  illustrates the main structure of an interference fringe projection optical system according to Embodiment 5; 
         FIG. 14  illustrates the main structure of an interference fringe projection optical system according to Embodiment 6; 
         FIG. 15  illustrates the properties of a focused light beam; 
         FIG. 16  illustrates the relationship between the spot diameter d2 of a focused light beam and the size d of the light beam at distance z; 
         FIG. 17  illustrates the size d(z) of the light beam with respect to the distance z for each reduction in light intensity; 
         FIG. 18  illustrates the RDN surface numbers of the magnifying optical system in Embodiment 4; 
         FIG. 19  is a photograph illustrating the results of simulating the intensity distribution of the interference fringe projected onto an object surface separated from the tip of the magnifying optical system by 20 mm in Embodiment 4; 
         FIG. 20  illustrates an intensity distribution of the interference fringe on the X-X cross section of  FIG. 19 ; 
         FIG. 21  illustrates the contrast distribution of the interference fringe in  FIG. 19 ; 
         FIG. 22  illustrates the intensity distribution in the X-X cross section of  FIG. 19  when the Q value in Expression (10) is greatly shifted from 1; 
         FIG. 23  illustrates the contrast distribution when the Q value in Expression (10) is greatly shifted from 1; 
         FIG. 24  illustrates the relationship between contrast and the Q value at the location where the contrast is reduced the most; 
         FIG. 25  illustrates a conventional shape measurement apparatus; and 
         FIG. 26  is a partial detail drawing of  FIG. 25 . 
     
    
    
     DETAILED DESCRIPTION 
     Upon examination, I discovered a characteristic requiring improvement in the shape measurement apparatus illustrated in  FIG. 25 . Namely, the contrast of the interference fringe  400  projected onto the object surface decreases at the periphery, decreasing the measurement accuracy. The reason is as follows. One light beam is separated into two parallel light beams by the birefringent plate  117  and the polarizing plate  118  to generate an interference fringe. The two parallel light beams are projected separately onto the object surface by the projection lens  131 , as illustrated in the partial detail drawing in  FIG. 26 . As a result, the two light beams do not overlap with the same intensity, leading to the phenomenon of reduced contrast in the interference fringe. In  FIG. 26 , the two projection areas are depicted in planar form. 
     In light of the above considerations, it would be helpful to provide an interference fringe projection optical system, and a shape measurement apparatus using the same, that can alleviate the reduction in contrast of the interference fringe projected onto the object surface and can measure the shape of the object surface to a high degree of accuracy. 
     Embodiments of this disclosure are described below with reference to the drawings. 
     Embodiment 1 
       FIG. 1  schematically illustrates the main structure of a shape measurement apparatus according to Embodiment 1. Like the shape measurement apparatus illustrated in  FIG. 25 , the shape measurement apparatus in Embodiment 1 is inserted in a body cavity or the like to measure the surface shape of an organ or the like and includes an interference fringe projection optical system  1 , an imager  30 , and a calculation controller  50  constituted by a computer or the like. 
     The interference fringe projection optical system  1  includes an interference fringe generating optical system  11  and a magnifying optical system  21 . The interference fringe generating optical system  11  includes a light source  12 , a collimator lens  13 , an optical isolator  14 , a coupling lens  15 , a polarization-maintaining optical fiber  16 , a birefringent plate  17 , and a polarizing plate  18 . The magnifying optical system  21  is constituted by an incident-side lens group  22  and an exit-side lens group  23 . In this embodiment, the incident-side lens group  22  is configured by a single lens  24  having a positive refractive power. Similarly, the exit-side lens group  23  is configured by a single lens  25  having a positive refractive power. 
     The light source  12  is, for example, configured by a semiconductor laser and is driven by the calculation controller  50  through a driver  20  to emit linearly polarized light. The light emitted from the light source  12  is formed as a parallel light beam by the collimator lens  13 , passes through the optical isolator  14 , is subsequently incident on the polarization-maintaining optical fiber  16  through the coupling lens  15 , is guided by the polarization-maintaining optical fiber  16 , and is emitted. The light beam emitted from the polarization-maintaining optical fiber  16  is incident on the birefringent plate  17  and is separated into a light beam with two polarization components which are further incident on the polarizing plate  18 . Only the coherent components are extracted from among the two polarization components to generate the interference fringe. The interference fringe is magnified by the lens  24  and the lens  25  that configure the magnifying optical system  21  and is projected onto an object surface  70  targeted for measurement. 
     The shape measurement apparatus of this embodiment projects the interference fringe onto the object surface  70  with the interference fringe projection optical system  1 , and while scanning the interference fringe with an interference fringe scanner, captures an image of the interference fringe on the object surface  70  with the imager  30  and inputs the resulting image signal to the calculation controller  50 . The calculation controller  50  calculates unevenness information of the object surface  70  using the image signal of the interference fringe and measures a three-dimensional shape. 
     The interference fringe scanner can, for example, be configured by using a tunable laser for the light source  12  and scanning the interference fringe by changing the wavelength of laser light emitted from the light source  12  with the driver  20 . A variety of known configurations, for example as disclosed in PTL 1, may be adopted for the interference fringe scanner, such as changing the difference in scanning path length of two light beams caused by a movable reflecting mirror to interfere, or providing a half-wave plate and a quarter-wave plate at the incident side of the polarization-maintaining optical fiber  16  and rotating the half-wave plate. 
     In this embodiment, as illustrated in the partial enlargement in  FIG. 2 , light emitted from the polarization-maintaining optical fiber  16  is separated by the birefringent plate  17  into two light beams with a divergence angle θ1. These light beams pass through the polarizing plate  18  and are magnified by the magnifying optical system  21  to a divergence angle θ2 and projected onto the object surface  70 . Therefore, the magnifying optical system  21  is arranged so that the focal length f1 of the lens  24  is greater than the focal length f2 of the lens  25 , the emission end face of the polarization-maintaining optical fiber  16  is positioned at the front focal position of the lens  24 , and the front focal position of the lens  25  is positioned at the back focal position. In  FIG. 2 , the projection areas of the two light beams on the object surface  70  are also depicted in planar form. 
     As a result, the magnifying optical system  21  constitutes a bi-telecentric optical system, and the central light rays of the two light beams that are emitted in parallel from the polarizing plate  18  separated by a distance x1 are reduced to a distance x2 by the magnifying optical system  21  and emitted in parallel. On the exit side of the magnifying optical system  21 , the two light beams separated by the birefringent plate  17  each form a spot diameter d2 that is more focused than the spot diameter d1 emitted from the polarization-maintaining optical fiber  16 . Here, the spot diameter d2 is represented by Expression (1) below.
 
 d 2= d 1· f 2/ f 1  (1)
 
     In this embodiment, the central light rays of the two light beams separated by the birefringent plate  17  are thus emitted in parallel by the magnifying optical system  21 , first form a focused spot at the exit side of the magnifying optical system  21 , and then are magnified again and irradiated onto the object surface  70 . Accordingly, the interference fringe is generated over a wide range on the object surface  70 . The light intensity I(r) and the contrast C of the interference fringe generated by light beams a1e i θ 1 e i ω t  and a2e i θ 2 e i ω t  with equivalent wavelengths and different phases are represented by Expressions (2) and (3) below. 
     
       
         
           
             
               
                 
                   
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     As is clear from Expression (3), the condition for maximizing the contrast C is that the amplitude of the two light beams, a1 and a2, be equal. As the difference between the amplitudes a1 and a2 increases, the contrast C decreases, as illustrated in  FIG. 3 . Furthermore, as illustrated in  FIG. 4 , the intensity of the light emitted from the polarization-maintaining optical fiber  16  exhibits a Gaussian distribution, being greatest at the central position and falling at the edges. Therefore, the contrast C of the interference fringe reduces as the separation is greater between the two light beams. 
     According to this embodiment, the two light beams are projected over a wide range of the object surface  70  in a state in which the interval between the central light rays is maintained by the magnifying optical system  21 , thereby allowing generation of an interference fringe with a smaller amount of reduction in contrast. Moreover, the two light beams emitted from the magnifying optical system  21  are magnified as the distance between the magnifying optical system  21  and the object surface  70  is greater, but the interval between the central light rays of the two light beams is constant. Hence, the contrast can be maintained high regardless of the distance between the magnifying optical system  21  and the object surface  70 . Thus, according to this disclosure, a reduction in contrast of the interference fringe projected onto the object surface can be alleviated, and the shape of the object surface can be measured to a high degree of accuracy. 
     According to this embodiment, the effect of a shift between the optical axes of the polarization-maintaining optical fiber  16  and the magnifying optical system  21  can also be kept to a minimum. In other words, if the optical axis state of the polarization-maintaining optical fiber  16  and the magnifying optical system  21  is shifted from the state illustrated in  FIG. 5A  to the state illustrated in  FIG. 5B , no shift in angle occurs in the light beams emitted from the magnifying optical system  21 , though the light beams themselves are shifted. In  FIG. 5A  and  FIG. 5B , the projection areas of the two light beams on the object surface  70  are also depicted in planar form. This shift amount δ1 of the light beams is represented by Expression (4) below, where the shift amount between the optical axes of the polarization-maintaining optical fiber  16  and the magnifying optical system  21  is δ.
 
δ1=δ· f 2/ f 1  (4)
 
     In Expression (4), the focal length f2 of the lens  25  is smaller than the focal length f1 of the lens  24 . Accordingly, the shift amount δ1 of the light beams is a small value relative to the shift amount δ of the optical axes. Moreover, since the shift amount δ1 is constant, regardless of the distance between the magnifying optical system  21  and the object surface  70 , the shift amount δ1 is an extremely small, negligible value relative to the light beams spread on the object surface  70  by the magnifying optical system  21 . Consequently, the center position of intensity of the interference fringe does not shift greatly on the object surface  70 , yielding nearly no change in the intensity of the interference fringe due to the shift amount δ of the optical axes, as illustrated in  FIG. 6A  to  FIG. 6D . Note that  FIG. 6A  to  FIG. 6D  illustrate the results of simulating the intensity distribution of the interference fringe relative to the shift amount δ of the optical axes, where  FIG. 6A  illustrates the case of δ=0 mm,  FIG. 6B  the case of δ=0.01 mm,  FIG. 6C  the case of δ=0.03 mm, and  FIG. 6D  the case of δ=0.1 mm. 
     For the sake of comparison,  FIG. 7A  and  FIG. 7B  illustrate the effect due to optical axis shift between the polarization-maintaining optical fiber  16  and the lens  26  when the magnifying optical system is configured by a single lens  26 . In  FIG. 7A  and  FIG. 7B , the projection areas of the two light beams on the object surface  70  are also depicted in planar form. In this case, as illustrated in  FIG. 7A , in a state with no optical axis shift between the polarization-maintaining optical fiber  16  and the lens  26 , the center position of intensity of the interference fringe matches the optical axis position of the lens  26 . However, if the optical axes of the polarization-maintaining optical fiber  16  and the lens  26  are shifted by a shift amount δ, as illustrated in  FIG. 7B , then the angles of the light beams emitted from the lens  26  change from the case of  FIG. 7A  in accordance with the shift amount δ. As a result, depending on the light beams emitted from the lens  26 , the irradiated position on the object surface  70  shifts, the center position of intensity of the interference fringe shifts, and the intensity of the interference fringe at the shifted side decreases.  FIG. 8A  to  FIG. 8D  illustrate the results of simulating the intensity distribution of the interference fringe relative to the shift amount δ of the optical axes in this case and correspond to  FIGS. 6A to 6D . 
     As is also clear from the above comparison, according to this embodiment, the center position and intensity of the interference fringe on the object surface  70  exhibit nearly no change because of the shift amount δ of the optical axes. In other words, the interference fringe projection optical system  1  according to this embodiment can reduce the eccentric sensitivity of the polarization-maintaining optical fiber  16  and the magnifying optical system  21 . Accordingly, the interference fringe projection optical system  1  is easy to assemble. In particular, the magnifying optical system  21  is easy to assemble. 
     Embodiment 2 
       FIG. 9  illustrates the main structure of an interference fringe projection optical system according to Embodiment 2. In the interference fringe projection optical system  1  according to this embodiment, the interference fringe generating optical system  11  has a different configuration from the configuration illustrated in  FIG. 1 . Specifically, the interference fringe generating optical system  11  includes two polarization-maintaining optical fibers  16   a  and  16   b , and the emission ends thereof are disposed side-by-side at the incident side of the magnifying optical system  21 . As a result, the two emission ends of the polarization-maintaining optical fibers  16   a  and  16   b  constitute two optical emitters. The emission end faces of the polarization-maintaining optical fibers  16   a  and  16   b  are preferably disposed in the same plane, orthogonal to the optical axis of the magnifying optical system  21 , at symmetrical positions about the optical axis. 
     Light from a light source is branched by a fiber-type optical demultiplexer (optical coupler) and caused to enter the polarization-maintaining optical fibers  16   a  and  16   b , for example as disclosed in PTL 1. In the case of scanning the interference fringe, a known configuration may be adopted, for example by changing the phase of light guided through one of the polarization-maintaining optical fibers  16   a  and  16   b  with a fiber-type phase shift that uses stress or the like, or by using a tunable laser for the light source and differing the length of the optical path in the polarization-maintaining optical fibers  16   a  and  16   b.    
     The magnifying optical system  21  is arranged so that the emission end faces of the polarization-maintaining optical fibers  16   a  and  16   b  are positioned on the focal plane at the front focal position of the lens  24 , and so that the front focal position of the lens  25  is positioned at the back focal position. In  FIG. 9 , the projection areas of the two light beams on the object surface  70  are also depicted in planar form. 
     In this embodiment as well, as in Embodiment 1, the magnifying optical system  21  constitutes a bi-telecentric optical system. Furthermore, the central light rays of the two light beams emitted side-by-side in parallel from the polarization-maintaining optical fibers  16   a  and  16   b  are emitted in parallel by the magnifying optical system  21 , first form a focused spot at the exit side of the magnifying optical system  21 , and then are magnified again and irradiated onto the object surface  70 . Accordingly, an interference fringe is generated over a wide range on the object surface  70 , thus obtaining similar effects to those of Embodiment 1. 
     Embodiment 3 
       FIG. 10  illustrates the main structure of an interference fringe projection optical system according to Embodiment 3. The interference fringe projection optical system  1  according to this embodiment differs from the magnifying optical system  21  in Embodiment 1 in that the incident-side lens group  22  is constituted by a plano-convex lens  27 , and the exit-side lens group  23  is constituted by a ball lens  28 . Furthermore, a glass plate  29  that transmits the two light beams generated by the magnifying optical system  21  is disposed at the exit side of the focused spot of the two light beams. The remaining configuration is similar to that of Embodiment 1. 
     According to this embodiment, the incident-side lens group  22  is constituted by a plano-convex lens  27 , and the emission end face of the polarization-maintaining optical fiber  16  is typically a plane perpendicular to the direction of travel of light. Therefore, the inclinations of the flat portion of the piano-convex lens  27  and the emission end face of the polarization-maintaining optical fiber  16  can easily be aligned, allowing a reduction in the performance degradation due to inclination eccentricity of the polarization-maintaining optical fiber  16  and the piano-convex lens  27 . In greater detail, as illustrated in  FIG. 10 , the emission end face of the polarization-maintaining optical fiber  16  and the flat portion of the plano-convex lens  27  are joined by adhesive or the like via the birefringent plate  17  and the polarizing plate  18 . 
     With this approach, the performance degradation due to inclination eccentricity of the polarization-maintaining optical fiber  16  and the piano-convex lens  27  can be reduced, while also reducing the reflection at the flat portion of the birefringent plate  17 , the flat portion of the polarizing plate  18 , and the flat portion of the piano-convex lens  27 , reducing the loss in emission light, and reducing the stray light (unwanted light) due to multiple reflections occurring between the emission end face of the polarization-maintaining optical fiber  16  and the flat portion of the plano-convex lens  27 . As methods for reducing stray light, it is also effective, for example, to incline the birefringent plate  17  relative to the direction of travel of light, or instead of a parallel flat plate shape, to adopt a wedge prism like the one illustrated in  FIG. 11 . The same is also true for the polarizing plate  18  and the glass plate  29 . 
     According to this embodiment, since the exit-side lens group  23  is constituted by a ball lens  28 , the performance degradation due to inclination eccentricity can be eliminated. Furthermore, since the ball lens  28  is typically small and inexpensive to manufacture, this configuration has the advantage of reducing size and cost. 
     In this embodiment as well, the focused spot of the two light beams generated by the magnifying optical system  21  is generated near the exit side of the ball lens  28 . Consequently, when no structure exists between the ball lens  28  and the object surface  70 , it can easily be imagined that the ball lens  28  will constitute the exterior surface. In this case, dirt or the like adhering to the ball lens  28  may lead to a decrease in intensity of the interference fringe, and a decrease in contrast. Moreover, the focused spot of the two light beams generated by the magnifying optical system  21  is smaller than the spot diameter emitted from the polarization-maintaining optical fiber  16 , making the focused spot easily affected by dirt or the like. 
     In this embodiment, however, the glass plate  29  is not affected by dirt or the like and is disposed at the exit side of the focused spot of the two light beams generated by the magnifying optical system  21 , so that light beams with a sufficiently large spot diameter constitute the exterior surface. Also, by providing the glass plate  29 , accidental human contact and injury can be prevented while light is being emitted. 
     Embodiment 4 
       FIG. 12  illustrates the main structure of an interference fringe projection optical system according to Embodiment 4. In the interference fringe projection optical system  1  according to this embodiment, the interference fringe generating optical system  11  has a different configuration from the configuration illustrated in  FIG. 10 . Specifically, the interference fringe generating optical system  11  includes two polarization-maintaining optical fibers  16   a  and  16   b . The two polarization-maintaining optical fibers  16   a  and  16   b  are arranged in the same way as in Embodiment 2. 
     The magnifying optical system  21  is arranged so that the emission end faces of the polarization-maintaining optical fibers  16   a  and  16   b  are positioned on the focal plane at the front focal position of the plano-convex lens  27 , and so that the front focal position of the ball lens  28  is positioned at the back focal position. The remaining configuration is similar to that of Embodiments 2 and 3. 
     Accordingly, as in Embodiment 3, the size and cost can be reduced in this embodiment as well. The glass plate  29  illustrated in  FIG. 10  is preferably disposed at the exit side of the ball lens  28  in this embodiment as well. 
     Embodiment 5 
       FIG. 13  illustrates the main structure of an interference fringe projection optical system according to Embodiment 5. The interference fringe projection optical system  1  according to this embodiment has the configuration illustrated in  FIG. 10 , except that the glass plate  29  is omitted by arranging the birefringent plate  17  and the polarizing plate  18  at the exit side of the ball lens  28 . The remaining configuration is similar to that of Embodiment 3. 
     According to this embodiment, the number of components can be reduced, while also further reducing the size. In other words, in the case of Embodiment 3, the ball lens  28  needs to have a size covering twice the width of the two light beams (see  FIG. 2 ) in addition to the effective diameter of the magnifying optical system  21 . By contrast, since the birefringent plate  17  and the polarizing plate  18  are arranged on the exit side of the ball lens  28  in this embodiment, the size of the ball lens  28  need only take the effective diameter of the magnifying optical system  21  into consideration, thus allowing a more compact configuration. 
     Embodiment 6 
       FIG. 14  illustrates the main structure of an interference fringe projection optical system according to Embodiment 6. An interference fringe projection optical system  10  according to this embodiment includes a plurality of the interference fringe projection optical systems  1  illustrated in Embodiments 1 to 5 above. The plurality of interference fringe projection optical systems  1  may have the same or different configurations. The plurality of interference fringe projection optical systems  1  are arranged so that the projection areas of the interference fringe from adjacent interference fringe projection optical systems  1  complement each other. For the sake of convenience, two of the interference fringe projection optical systems  1  illustrated in  FIG. 1  are depicted in  FIG. 14 . Furthermore, in  FIG. 14 , the projection areas of the light beams from each interference fringe projection optical system  1  on the object surface  70  are also depicted in planar form. 
     In the interference fringe projection optical system  10  according to this embodiment, the plurality of interference fringe projection optical systems  1  project an interference fringe by projection areas of the interference fringe on the object surface  70  complementing each other by time division. Consequently, the shape of the object surface  70  can be measured over a wider range. 
     Next, the interference fringe projection optical systems  1  illustrated in Embodiments 1 to 5 are described in further detail. 
     For example, in the case of a configuration using one polarization-maintaining optical fiber  16 , d2 is represented by Expression (1) above, where d1 is the spot diameter emitted from the polarization-maintaining optical fiber  16 , and d2 is the focused spot diameter formed by the magnifying optical system  21 . The divergence angle θ1 of light emitted from the polarization-maintaining optical fiber  16  (see  FIG. 2 ) typically takes a fixed value. For example, in the case of the wavelength used in a single mode fiber being 635 nm, θ1 is approximately 10°. It is typically desired for the magnifying optical system  21  to be reduced in size until equaling the effective diameter of the light beams. 
     The effective diameter D of the magnifying optical system  21  is calculated by Expression (5) below.
 
 D=f 1×sin θ1  (5)
 
     Expression (6) below follows from Expression (1) and Expression (5).
 
 d 2= d 1×sin θ1× f 2/ D   (6)
 
     To measure the shape over a wide range of the object surface  70 , the light beam needs to be spread over a wide range. The light beam has the property of narrowing and expanding, as illustrated in  FIG. 15 , and therefore as the narrowing light beam is reduced in size, the light beam can be magnified more afterwards. In this case, the size d(z) of the light beam at a distance z from the formation position of the spot diameter d2 focused by the magnifying optical system  21  is represented by Expression (7) below, where the wavelength in use is λ. 
     
       
         
           
             
               
                 
                   
                     d 
                     ⁡ 
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       2 
                       / 
                       2 
                     
                     ⁢ 
                     
                       
                         { 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   λ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   z 
                                 
                                 
                                   
                                     π 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           d 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                         
                                         2 
                                       
                                       ) 
                                     
                                   
                                   2 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         } 
                       
                       
                         1 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
       FIG. 16  illustrates the relationship between the magnitude of d2 and the spot diameter d(20) when the wavelength in use λ is 635 nm and the distance z is 20 mm. As is clear from  FIG. 16 , as d2 is smaller, the spot diameter d(20) increases, and the light is spread over a wider area. 
     In order to decrease the spot diameter d2, either the focal distance f2 of the exit-side lens group  23  needs to be decreased, or the effective diameter D of the magnifying optical system  21  needs to be increased, but to reduce size at the same time, the effective diameter D is preferably not increased. Therefore, in order to reduce the spot diameter d2, it is effective to reduce the focal distance f2. To reduce the focal length f2, it is effective for the glass material of the exit-side lens group  23  to have a high refractive index. For example, using sapphire (nd=1.768) or S-LAH79 (nd=2) as the material for the exit-side lens group  23  is effective. 
     Next, a design example is described. Table 1 lists preconditions. In Table 1, assuming that the effective diameter D, which is an index of the size of the magnifying optical system  21 , is 1 mm and that a typical fiber is used for the polarization-maintaining optical fiber  16 , the spot diameter d1 emitted from the polarization-maintaining optical fiber  16  is calculated from the mode field diameter of the fiber. Also, the divergence angle θ1 of the light beam emitted from the polarization-maintaining optical fiber  16  is calculated from the NA of the fiber. Furthermore, assuming the divergence angle θ2 of the light beams emitted from the magnifying optical system  21  is 75 and that the wavelength in use λ is 635 nm, the magnitude of the most focused spot diameter d2 of the light beams formed by the magnifying optical system  21  is calculated by Expression (7). 
     
       
         
           
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Specifications 
                 Calculated numerical value 
               
               
                   
               
             
            
               
                 Size of magnifying optical system 
                 Effective diameter D = 1 mm 
               
               
                 Divergence angle θ2 
                 Spot diameter d2 = 0.52 μm 
               
               
                 Mode field diameter of fiber 
                 Spot diameter d1 = 5 μm 
               
               
                 NA of fiber 
                 Divergence angle θ1 = 9.2° 
               
               
                   
               
            
           
         
       
     
     From the values of the preconditions in Table 1, the focal distance f2 of the exit-side lens group  23  is calculated as follows, using Expression (6).
 
 f 2= d 2× D /( d 1×sin θ1)=0.00052×1/(0.005×sin 9.2°)=0.65 mm
 
     Furthermore, for example in the case of configuring the exit-side lens group  23  as a ball lens  28 , the size (diameter) Db of the ball lens  28  can be calculated by Expression (8) from the focal length f2 and the refractive index n of the wavelength in use λ.
 
 Db=f 2×4( n− 1)/ n   (8)
 
     Table 2 lists the refractive index n and the size Db of the ball lens  28  when the effective diameter D of the magnifying optical system  21  is 1 mm and the focal length f2 of the ball lens  28  is 0.65 mm. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Refractive index n 
                 Size Db 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 1.5 
                 0.87 
               
               
                   
                 1.6 
                 0.975 
               
               
                   
                 1.7 
                 1.07 
               
               
                   
                 1.8 
                 1.16 
               
               
                   
                 1.9 
                 1.23 
               
               
                   
                 2.0 
                 1.3 
               
               
                   
                   
               
            
           
         
       
     
     The size Db of the ball lens  28  needs to be greater than the effective diameter D of the magnifying optical system  21  to ensure the effective diameter D. Hence, generally a glass material with a refractive index n of 1.7 or greater (glass material with a d-line refractive index nd of 1.7 or greater) is preferably selected. 
     The focal length f1 of the piano-convex lens  27  constituting the incident-side lens group  22  in this case is calculated by Expression (5) as f1=6.25 mm. Accordingly, the ratio between the focal length f1 and the focal length f2 is f1/f2=9.6. 
     To measure the shape over a wide range of the object surface  70 , the light beam needs to be spread over a wide range. In order to spread the light beam, the ratio f1/f2 preferably exceeds 3. The ratio more preferably exceeds 6. In the case of using the ball lens  28 , if D and Db are approximately equal, f1/f2 is calculated by Expression (9) below, using Expression (5) and Expression (8).
 
 f 1/ f 2=4( n− 1)/( n ×sin θ1)  (9)
 
     The size of the light beam emitted from the polarization-maintaining optical fiber  16 , i.e. the NA of the polarization-maintaining optical fiber  16 , is determined by the percentage decrease when the central intensity of the light beam is 100%. Typically, the NA of a fiber is determined for a light beam with an 86.5% light intensity decrease. 
       FIG. 17  illustrates the size d(z) of the light beam with respect to the distance z, calculated by Expression (7), for each reduction in light intensity for the case of setting the core diameter of the polarization-maintaining optical fiber  16  to 10.4 μm and the wavelength in use λ to 1550 nm. Using silicon (refractive index n=3.4 for the wavelength in use λ of 1550 nm) as the material of the ball lens  28  and setting a 50% reduction in intensity with respect to the central intensity as the NA the polarization-maintaining optical fiber  16  yields NA=0.055. Hence, f1/f2=51.33. It is thus reasonable to consider  60  to be the upper limit of f1/f2. 
     As described above, in the magnifying optical system  21 , the front focal position of the incident-side lens group  22  is positioned at the emission end face of the polarization-maintaining optical fiber  16 , and the front focal position of the exit-side lens group  23  is positioned at the back focal position of the incident-side lens group  22 . Consequently, two parallel light beams separated by a distance x1 before traversing the magnifying optical system  21  are emitted by the magnifying optical system  21  in parallel, with the distance therebetween reduced to a distance x2. In other words, Expression (10) below holds between the distance xd and the focal lengths f1 and f2, where xd is the distance from the exit-side principal point of the incident-side lens group  22  to the incident-side principal point of the exit-side lens group  23 .
 
 Q=xd /( f 1+ f 2)=1  (10)
 
     Table 3 lists RDN data of the magnifying optical system  21  in Embodiment 4, illustrated in  FIG. 12 . The RDN surface numbers of Table 3 are listed in  FIG. 18 . 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                   
                 Refrac- 
                   
                   
               
               
                   
                   
                   
                   
                 tive 
                   
                 Spot 
               
               
                 Surface 
                   
                   
                 Glass 
                 index 
                 Focal 
                 diam- 
               
               
                 number 
                 R 
                 D 
                 material 
                 (nd) 
                 length 
                 eter 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1 
                 infinity 
                 5.497 
                   
                   
                   
                 0.005 
               
               
                 2 
                 infinity 
                 1 
                 synthetic quartz 
                 1.458 
                 6.24 
                 1 
               
               
                 3 
                 −2.85 
                 6.3 
                   
                   
                   
                 1 
               
               
                 4 
                  0.55 
                 1.1 
                 sapphire 
                 1.768 
                 0.634 
                 1 
               
               
                 5 
                 −0.55 
                 0.0777 
                   
                   
                   
                 0.135 
               
               
                 6 
                 infinity 
                 20 
                   
                   
                   
                 0.0006 
               
               
                 7 
                 infinity 
                   
                   
                   
                   
                 26.95 
               
               
                   
               
            
           
         
       
     
       FIG. 19  illustrates the results of a simulation, using the magnifying optical system  21  specified by Table 3, of the intensity distribution of the interference fringe projected onto an object surface  70  separated from the tip of the magnifying optical system  21  by 20 mm. The interval x1 between the two polarization-maintaining optical fibers  16   a  and  16   b  is 50 μm. In  FIG. 19 , the horizontal axis indicates an angle of view with a width of 90°, and the vertical axis indicates an angle of view with a width of 60°. Surface number  6  represents the surface (imaginary surface) on which is formed the most focused spot diameter d2 of the light beams formed by the magnifying optical system  21 . 
       FIG. 20  illustrates the intensity distribution of the interference fringe on the X-X cross section of  FIG. 19 .  FIG. 21  illustrates the distribution of the contrast C calculated with Expression (3) above. As is clear from  FIG. 20  and  FIG. 21 , the intensity distribution of the interference fringe is such that while the intensity reduces closer to the edges, the contrast C is a high value of 1 at both the center and the edges. 
       FIG. 22  and  FIG. 23  illustrate the intensity distribution in the X-X cross section of  FIG. 19  when the Q value in Expression (10) above is greatly shifted from 1 and the distribution of the contrast C from Expression (3) above. If the Q value shifts greatly from 1, the intensity distribution of the interference fringe is such that the intensity decreases closer to the edges, as illustrated in  FIG. 22 , but the amount of decrease does not differ greatly from when the Q value is 1. On the other hand, the distribution of the contrast C in  FIG. 23  exhibits an increasingly large reduction at the edges as compared to when the Q value is 1. 
     The contrast C is reduced most at the location of the maximum angle of view (for example, where the angle of view is horizontally (X)  45  and vertically (Y) 30°).  FIG. 24  illustrates the relationship between the contrast C and the Q value at the location where the contrast C is reduced most. As is clear from  FIG. 24 , the contrast C has the highest value when Q=1 and decreases slightly, while remaining a value of almost 1, when the Q value is less than 1. The contrast C rapidly decreases, however, upon the Q value exceeding 2. 
     From the above results, to project an interference fringe without greatly reducing the contrast, the interval between the principal point positions of the incident-side lens group  22  and the exit-side lens group  23 , i.e. the distance xd from the exit-side principal point of the incident-side lens group  22  to the incident-side principal point of the exit-side lens group  23  is preferably configured to satisfy Expression (11) below.
 
 Q=xd /( f 1+ f 2)&lt;2  (11)
 
     This disclosure is not limited to the above embodiments, and a variety of changes or modifications may be made. For example, apart from a configuration using the above-described birefringent plate  17 , the interference fringe generating optical system  11  can adopt any of a variety of known configurations, such as a configuration using the polarization beam splitter or the waveguide disclosed in PTL 1, a configuration using the diffraction element or the wedge prism disclosed in JP 2005-326192 A, or a configuration using the Wollaston prism disclosed in JP H7-280535 A. 
     While a polarization-maintaining optical fiber is used in the above embodiments, a typical fiber, such as a single mode or multi-mode fiber, may be used. Also, depending on the object on which the interference fringe is projected, the optical emitter of the interference fringe generating optical system may be configured by a waveguide or the like, without using a fiber. The glass plate  29  illustrated in  FIG. 10  may be disposed in other embodiments. Furthermore, for the purpose of inspecting shapes only to measure unevenness, the configuration for scanning the interference fringe may be omitted.