Patent Publication Number: US-2015070710-A1

Title: Measurement apparatus

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a measurement apparatus which obtains a measurement value regarding a measurement surface. 
     2. Description of the Related Art 
     The dimensions of the primary mirror of a telescope installed on the ground for astronomic observation are becoming larger to improve the performance of the telescope. For example, in the Subaru Telescope, a primary mirror formed from one mirror has a dimension of 8.2 m. 
     Recently, there has been proposed a telescope using, as a primary mirror, a composite mirror constituted by connecting a plurality of hexagonal mirrors (segment mirrors). For example, the primary mirror of the TMT (Thirty Meter Telescope) tries to implement an effective aperture of 30 m by using a composite mirror formed from 492 segment mirrors (hexagonal mirrors each having a circumscribed circle diameter of 1.5 m and a diagonal line length of 1.44 m). 
     To manufacture a segment mirror forming such a composite mirror at high precision, the shape (surface shape) of a substrate for forming the reflecting surface (mirror surface) needs to be accurately measured. For example, measurement of a segment mirror constituting the primary mirror of the TMT requires a measurement precision as high as about several nm RMS. As a technique of measuring the surface shape of such a large surface at a precision of about several nm RMS, Japanese Patent Laid-Open Nos. 2009-145095 and 11-173835 have proposed measurement apparatuses using a contact probe. 
     Near the summit of Mauna Kea in Hawaii where the installation of the TMT is assumed, the temperature becomes as low as about 2° C., which is different by about 20° C. from a room temperature of 23° C. at which a segment mirror is measured in general. It is therefore necessary to measure (the substrate of) a segment mirror at a low temperature of about 2° C., which is equal to the temperature near the summit of Mauna Kea, in consideration of a measurement error arising from thermal contraction of the substrate of a segment mirror, or thermal deformation of a substrate attachment jig used in measurement or the like. 
     Hence, there has been proposed a measurement apparatus using a non-contact probe in which a measurement object (segment mirror) is accommodated in a thermostatic chamber maintained at a low temperature of about 2° C., a light-transmissive window for transmitting light is arranged on the top surface of the thermostatic chamber, and the shape of the measurement object is measured through the light-transmissive window. 
     In the measurement apparatus, it is important to reduce a measurement error generated in accordance with the accuracy of the installation position when a measurement object such as the substrate of a segment mirror is installed in the measurement apparatus. When a measurement object is measured at a very high precision of about several nm RMS, a measurement error (setting error) arising from an error of the installation position of the measurement object with respect to the measurement probe is not negligible. Japanese Patent Laid-Open No. 11-173835 has disclosed a technique of reducing a setting error. 
     In Japanese Patent Laid-Open No. 11-173835, three spherical surfaces Tb, Tc, and Td indicating the installation position of a measurement object Ta are arranged on the surface of the measurement object Ta, as shown in  FIG. 17 . A contact probe CP scans the three spherical surfaces Tb, Tc, and Td arranged on the surface of the measurement object Ta to reduce an error of the installation position of the measurement object Ta with respect to the contact probe CP that causes a setting error. 
     However, with the technique in Japanese Patent Laid-Open No. 11-173835, it is difficult to perform high-precision alignment between the contact probe and a measurement object because the distal end shape of the contact probe is large and the spherical surface arranged on the surface of the measurement object is also large. As a result, it is difficult to measure the shape of a measurement object at a precision of about several nm RMS. 
     As described above, when measuring a measurement object arranged inside the thermostatic chamber, the contact probe is obstructed by the partition of the thermostatic chamber and cannot scan a spherical surface arranged on the measurement object. Hence, an error of the installation position of the measurement object with respect to the contact probe, which causes a setting error, cannot be reduced. 
     To the contrary, a measurement apparatus using a non-contact probe to measure the shape of a measurement object through a light-transmissive window arranged in a thermostatic chamber does not have an arrangement for reducing an error of the installation position of the measurement object arranged inside the thermostatic chamber. This measurement apparatus cannot reduce a setting error arising from an error of the installation position of a measurement object with respect to the non-contact probe. It is difficult to measure the shape of a measurement object at a precision of about several nm RMS. 
     SUMMARY OF THE INVENTION 
     The present invention provides, for example, a measurement apparatus advantageous in terms of obtaining a measurement value regarding a measurement surface. 
     According to one aspect of the present invention, there is provided a measurement apparatus which obtains a measurement value with respect to a measurement surface based on an interference signal obtained by causing measurement light reflected from the measurement surface and reference light reflected from a reference surface to interfere with each other, the apparatus including a measurement head including an interference optical system configured to generate the interference signal, and a processor configured to obtain a position of an alignment target on the measurement surface based on the interference signal, and obtain the measurement value based on the position of the alignment target and the interference signal. 
     Further aspects of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view showing the arrangement of a measurement apparatus according to the first embodiment of the present invention. 
         FIG. 2  is a schematic view showing the outer appearance of the measurement apparatus shown in  FIG. 1 . 
         FIG. 3  is a view for explaining alignment in the X-Y plane between an interference optical system and a measurement surface. 
         FIGS. 4A to 4D  are views for explaining alignment in the X-Y plane between the interference optical system and the measurement surface. 
         FIG. 5  is a view showing an alignment mark formed on the measurement surface. 
         FIG. 6  is a schematic view showing the arrangement of a measurement apparatus according to the second embodiment of the present invention. 
         FIG. 7  is a schematic view showing the arrangement of a measurement apparatus according to the third embodiment of the present invention. 
         FIG. 8  is a view for explaining alignment between a condensed beam and alignment marks respectively formed on a measurement surface and light-transmissive window. 
         FIGS. 9A and 9B  are views showing alignment marks respectively formed on the light-transmissive window and measurement surface. 
         FIG. 10  is a schematic view showing the arrangement of a measurement apparatus according to the fourth embodiment of the present invention. 
         FIG. 11  is a schematic view showing the arrangement of the light-transmissive window of the measurement apparatus shown in  FIG. 10 . 
         FIGS. 12A and 12B  are views showing alignment marks respectively formed on the first light-transmissive window and measurement surface. 
         FIG. 13  is a schematic view showing the arrangement of a measurement apparatus according to the fifth embodiment of the present invention. 
         FIG. 14  is a view for explaining alignment between an interference optical system and an alignment mark formed on a measurement surface. 
         FIGS. 15A and 15B  are views for explaining alignment between the interference optical system and the alignment mark formed on the measurement surface. 
         FIG. 16  is a view showing the alignment mark formed on the measurement surface. 
         FIG. 17  is a schematic view showing the arrangement of a conventional measurement apparatus. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. Note that the same reference numerals denote the same members throughout the drawings, and a repetitive description thereof will not be given. 
     First Embodiment 
       FIG. 1  is a schematic view showing the arrangement of a measurement apparatus  1  according to the first embodiment of the present invention.  FIG. 2  is a schematic view showing the outer appearance of the measurement apparatus  1 . The measurement apparatus  1  has a function of measuring a change of the optical path length of measurement light reflected by a measurement surface (object surface). In the first embodiment, the measurement apparatus  1  is embodied as a three-dimensional shape measurement apparatus including a non-contact probe (measurement head) using a heterodyne interference method. The measurement apparatus  1  obtains a measurement value regarding a measurement surface (for example, a measurement value regarding the shape of a measurement surface) from an interference signal generated by an interference optical system. The measurement apparatus  1  is suited to measurement of, for example, the shape of a measurement surface having a curvature and a circumscribed circle diameter of more than 1 m (for example, the surface shape of a segment mirror constituting a composite mirror usable as the primary mirror of a telescope, or the surface shape of the substrate of the segment mirror). 
     The measurement apparatus  1  includes, as main components, a light source  102 , stage  112 , reference mirror  111 , interference optical system  103 , autofocus system  140 , detector  107 A, first processor  130 , and second processor  131 . The interference optical system  103  is mainly constituted by an interference optical system  104  and interference optical system  105 . In the measurement apparatus  1 , the interference optical system  103  functions as a non-contact probe (optical probe). 
     A light source  101  and the light source  102  emit two beams having different wavelengths and different directions of polarization, for example, S-polarized light and P-polarized light having directions of polarization perpendicular to each other in the embodiment. As the light sources  101  and  102 , He—Ne lasers having a wavelength of 663 nm are generally used. Lights (parallel lights) emitted by the light sources  101  and  102  are used at a diameter of about 6 mm. An optical fiber, mirror, and the like may be interposed between a subsequent polarizing beam splitter and each of the light sources  101  and  102 . 
     Light emitted by the light source  101  enters the polarizing beam splitter of the interference optical system  104  held by the stage  112 . The polarizing beam splitter is configured to reflect S-polarized light and transmit P-polarized light. Light emitted by the light source  101  is used to obtain a change of the optical path length of the first measurement light reflected by the reference mirror  111  and a double-sided mirror  114 . The light passes through the polarizing beam splitter, a corner cube  113  serving as a reference surface, and the like, and is detected by a detector  107 B. 
     Light emitted by the light source  102  enters a polarizing beam splitter  117  of the interference optical system  105  held by the stage  112 . The interference optical system  105  is an optical system which splits light emitted by the light source  102  into two lights, causes one light to enter a measurement surface  121  through the double-sided mirror  114  and a condenser lens  118 , causes the other light to enter the reference surface, and causes the light reflected by the measurement surface  121  and the light reflected by the reference surface to interfere with each other. In the embodiment, a corner cube  116  serves as the reference surface. 
     Light emitted by the light source  102  is used to obtain a change of the optical path length of the second measurement light reflected by the double-sided mirror  114  and measurement surface  121 . Although lights emitted by the light sources  101  and  102  are illustrated to be parallel to the Y- or Z-axis in  FIG. 1 , they contain a slight inclination error in practice. 
     The measurement apparatus  1  obtains a change of the optical path length of the first measurement light and a change of the optical path length of the second measurement light by using the interference optical system  103  including the interference optical system  104  serving as a double-pass optical system and the interference optical system  105  serving as a single-pass optical system. The measurement apparatus  1  can therefore measure the shape of the measurement surface  121  at high precision. 
     As shown in  FIG. 2 , the stage  112  is driven in the X-Y plane by an X-axis driving unit  201  and Y-axis driving unit  202 . The stage  112  is driven in the Y-Z plane by the Y-axis driving unit  202  and a Z-axis driving unit  203 . The X-axis driving unit  201 , Y-axis driving unit  202 , and Z-axis driving unit  203  function as a positioning mechanism which positions the stage  112  holding the interference optical system  103 . 
     The polarizing beam splitter  117  is configured to reflect S-polarized light and transmit P-polarized light. Of light emitted by the light source  102 , S-polarized light is reflected by the polarizing beam splitter  117 , becomes light almost parallel to the Z-axis, and enters a λ/4 plate  115 . Of the light emitted by the light source  102 , P-polarized light passes through the polarizing beam splitter  117 , becomes light almost parallel to the Y-axis, and enters the corner cube  116  serving as a reference surface. 
     The light (measurement light) entering the λ/4 plate  115  passes through the λ/4 plate  115 , becomes circularly polarized light, and is reflected by the double-sided mirror  114 . The light reflected by the double-sided mirror  114  passes again through the λ/4 plate  115 , becomes P-polarized light, passes through the polarizing beam splitter  117 , and is condensed through the condenser lens  118  on the measurement surface  121  held on a measurement stage  122  (is focused on the measurement surface  121 ). The autofocus system  140  is used to focus measurement light on the measurement surface  121 . 
     The autofocus system  140  will be explained together with a method of condensing measurement light on the measurement surface  121 . In the measurement apparatus  1 , the autofocus system (adjustment unit)  140  controls a position of the condenser lens  118  in a direction along the optical axis. More specifically, the autofocus system  140  adjusts (controls) the distance between the condenser lens  118  and the measurement surface  121  so that a measurement portion on the measurement surface  121  falls (is positioned) within the range of the depth of focus of the condenser lens  118 . 
     The autofocus system  140  includes, for example, a measurement unit  142  and focus control unit  143 . The autofocus system  140  controls the position of the condenser lens  118  in the direction along the optical axis of the condenser lens  118  by using the stage  112  holding the interference optical system  103 , and the Z-axis driving unit  203 . The measurement unit  142  measures a position (the focus state of light condensed by the condenser lens  118 ) of the condenser lens  118  in the direction along the optical axis. Based on the measurement result (focus state) of the measurement unit  142 , the focus control unit  143  controls driving of the stage  112  by the Z-axis driving unit  203  so that a measurement portion on the measurement surface  121  falls within the range of the depth of focus of the condenser lens  118 . Since the Z-axis driving unit  203  is a driving unit which drives the stage  112  in the Z-axis direction, as described above, it can move, in the direction along the optical axis of the condenser lens  118 , the condenser lens  118  of the interference optical system  103  held by the stage  112 . 
     An example of the arrangement of the measurement unit  142  will be explained. When light condensed by the condenser lens  118  falls outside the range of the depth of focus of the condenser lens  118 , light which has been reflected by the measurement surface  121  and has passed again through the condenser lens  118  does not become parallel light, but converges or diverges. In consideration of this, the measurement unit  142  is constituted by a cylindrical lens and four-division sensor. The measurement unit  142  can measure a focus state by causing light reflected by the measurement surface  121  to enter the measurement unit  142  through a half mirror  141 . Note that the half mirror  141  is an optical component which splits, at an appropriate ratio, light (transmission light) passing through the half mirror  141  and light (reflected light) reflected by the half mirror  141 . The half mirror  141  is not limited to an optical component which splits transmission light and reflected light at 50%. In this manner, the measurement unit  142  can measure a focus state by using light which is reflected by the measurement surface  121 , enters again the condenser lens  118 , and returns to the optical system including the polarizing beam splitter  117 . 
     For example, Japanese Patent Laid-Open No. 2012-165139 has disclosed a measurement apparatus including a non-contact probe constituted by combining the interference optical system of a double-pass optical system and the interference optical system of a single-pass optical system. 
     As a main feature of the embodiment, alignment marks  119  and  120  are formed as alignment targets on the upper surface of the measurement surface  121 . In the measurement apparatus  1 , the autofocus system  140  can adjust measurement portions on the measurement surface  121  to fall within the range of the depth of focus of the condenser lens  118 . By using the autofocus system  140 , the measurement apparatus  1  can irradiate the alignment marks  119  and  120  on the measurement surface  121  with light condensed by the condenser lens  118  (can cause the light to be incident on the alignment marks  119  and  120 ). 
     As described above, in the measurement apparatus  1 , measurement portions on the measurement surface  121  are adjusted to fall within the range of the depth of focus of the condenser lens  118 . Light (measurement light) reflected by the measurement surface  121  passes again through the condenser lens  118 , becomes parallel light, passes through the polarizing beam splitter  117 , and enters the λ/4 plate  115 . 
     The measurement light which has passed through the λ/4 plate  115  and is reflected by the double-sided mirror  114  passes again through the λ/4 plate  115 , and becomes S-polarized light. The measurement light having passed through the λ/4 plate  115  is reflected by the polarizing beam splitter  117  and a half mirror  106 , and enters the detector  107 A constituted by a lens  108  and photodiode  109 . Note that the half mirror  106  is an optical component which splits, at an appropriate ratio, light (transmission light) passing through the half mirror  106  and light (reflected light) reflected by the half mirror  106 . The half mirror  106  is not limited to an optical component which splits transmission light and reflected light at 50%. 
     Light entering the corner cube  116  is reflected in the incident direction by the corner cube  116 . The light (reference light) which has been reflected by the corner cube  116  and has entered again the polarizing beam splitter  117  passes through the polarizing beam splitter  117 , and is reflected by the half mirror  106  together with measurement light reflected by the polarizing beam splitter  117 . The measurement light and reference light reflected by the half mirror  106  enter the detector  107 A constituted by the lens  108  and photodiode  109 . 
     The detector  107 A detects interference light between the measurement light and the reference light, and acquires an interference signal corresponding to the interference light, for example, a heterodyne interference signal in the embodiment. In the measurement apparatus  1 , the first processor  130  obtains a change of the light amount of measurement light, or signal light serving as a combination of measurement light and reference light, based on the light amount signal (intensity) of the heterodyne interference signal detected by the detector  107 A. The second processor  131  obtains a change of the optical path length of measurement light based on phase information of the heterodyne interference signal detected by the detector  107 A. 
     In the measurement apparatus  1 , the first processor  130  acquires light amount information of the heterodyne interference signal while the X-axis driving unit  201  and Y-axis driving unit  202  shown in  FIG. 2  drive the stage  112  in the X-Y plane. In other words, the first processor  130  acquires light amount information of the heterodyne interference signal while the interference optical system  103  is positioned so that light traveling from the interference optical system  105 , that is, light condensed by the condenser lens  118  enters a plurality of positions (measurement portions) on the measurement surface  121 . A change of the light amount of measurement light is obtained based on the light amount information of the heterodyne interference signal that is acquired by the first processor  130 . Accordingly, the positions (shapes) of the alignment marks  119  and  120  formed on the upper surface of the measurement surface  121  can be measured at high precision. 
     Also, in the measurement apparatus  1 , the second processor  131  acquires phase information of the heterodyne interference signal while the X-axis driving unit  201  and Y-axis driving unit  202  drive the stage  112  in the X-Y plane. In other words, the second processor  131  acquires phase information of the heterodyne interference signal while the interference optical system  103  is positioned so that light traveling from the interference optical system  105 , that is, light condensed by the condenser lens  118  enters a plurality of positions (measurement portions) on the measurement surface  121 . A change of the optical path length of measurement light is obtained based on the phase information of the heterodyne interference signal that is acquired by the second processor  131 , thereby measuring the shape of the measurement surface  121  (obtaining a measurement value). 
     The embodiment has explained, as the interference optical system  103 , a non-contact probe using the heterodyne interference method. However, the interference optical system  103  may be a non-contact probe using a homodyne interference method. The measurement apparatus  1  according to the embodiment obtains a change of the light amount of measurement light and a change of the optical path length by acquiring an interference signal by the detector  107 A while moving the stage  112  in the X-Y plane. The measurement apparatus  1  can therefore measure not only the surface shape of an object, but also the characteristics of the object that are correlated with these changes. The measurement apparatus  1  can measure, for example, even the surface roughness of the object. 
     Alignment in the X-Y plane (measurement plane) between the interference optical system  103  including the condenser lens  118  and the measurement surface  121  on which the alignment marks  119  and  120  are formed will be explained with reference to  FIGS. 3 and 4A  to  4 D. As shown in  FIG. 3 , the condenser lens  118  constituting the interference optical system  103  condenses measurement light to form a condensed beam  301 . By moving the interference optical system  103  in the X-Y plane, each of the alignment marks  119  and  120  formed on the measurement surface  121  can be irradiated with the condensed beam  301  (the condensed beam  301  can be incident on each alignment mark). The spot size (diameter) of the condensed beam  301  can be narrowed down to a diameter of about 10 μm to 100 μm though it depends on the optical design of the condenser lens  118 . 
     In the measurement apparatus  1 , the autofocus system  140  can control the position of the condenser lens  118  in the optical axis direction so that the alignment marks  119  and  120  on the measurement surface  121  fall within the range of the depth of focus of the condenser lens  118 . By moving the interference optical system  103  in the X-Y plane including the X-axis and Y-axis, the condensed beam  301  condensed by the condenser lens  118  can move to an arbitrary position in the X-Y plane. 
       FIG. 4A  is a schematic view showing an example of the shape of the alignment mark  119 . Since the alignment marks  119  and  120  have the same composition, the alignment mark  119  will be exemplified here. The alignment mark  119  is a 2×2-matrix mark having a rectangular outer frame, and a cross shape arranged inside the outer frame. The alignment mark  119  includes three vertical lines  403 ,  404 , and  405  in the Y-axis direction, and three horizontal lines in the X-axis direction. As shown in  FIG. 4B , a line in each of the X-axis direction and Y-axis direction is formed at a width w and a depth d on the measurement surface  121  serving as a quartz substrate.  FIG. 4B  is a schematic view showing the section of the vertical line  403  of the alignment mark  119 . The alignment mark  119  is constituted so that, for example, the rectangular outer frame is 1 mm square, the width w of a line in each of the X-axis direction and Y-axis direction is 100 μm, and the depth is about 158 nm which is equivalent to λ/4. However, the alignment mark  119  is not limited to the above-described shape as long as the first processor  130  can satisfactorily obtain the light amount signal of a heterodyne interference signal in accordance with the shape of the alignment mark  119 . In other words, it is only necessary to satisfactorily obtain the position of the alignment mark  119  with respect to a reference position from the light amount signal of a heterodyne interference signal. 
       FIG. 4B  shows even a state in which the interference optical system  103  moves in the X-axis direction to move the condensed beam  301  condensed by the condenser lens  118  on (the vertical line  403  of) the alignment mark  119  formed on the measurement surface  121 . As described above, in the interference optical system  103 , the autofocus system  140  controls the position of the condenser lens  118  in the optical axis direction so that the alignment marks  119  and  120  on the measurement surface  121  always fall within the range of the depth of focus of the condenser lens  118 . 
     A case in which the condensed beam  301  condensed by the condenser lens  118  is moved in the X-axis direction or Y-axis direction will be explained.  FIG. 4B  shows condensed spots  301   a ,  301   b ,  301   c ,  301   d , and  301   e  when the condensed beam  301  moves in the X-axis direction on the vertical line  403  of the alignment mark  119 .  FIG. 4C  shows a light amount distribution (light amount information)  408  of heterodyne interference signals corresponding to the respective condensed spots  301   a  to  301   e . Referring to  FIG. 4C , light amounts  408   a ,  408   b ,  408   c ,  408   d , and  408   e  correspond to the condensed spots  301   a ,  301   b ,  301   c ,  301   d , and  301   e , respectively. In  FIG. 4C , the abscissa represents the position of the condensed beam  301  in the X-axis direction (or Y-axis direction) near the alignment mark  119 , and the ordinate represents a light amount Iop of the heterodyne interference signal. 
     For example, the spot size of the condensed beam  301  is 10 μm, the width w of the vertical line  403  of the alignment mark  119  is 5 μm, and the depth d is 158 nm which is equivalent to λ/4 of 633 nm of the He—Ne laser serving as a representative wavelength of measurement light. Also, the light amounts of heterodyne interference signals near the vertical lines  403 ,  404 , and  405  of the alignment mark  119  are light amounts  408 ,  409 , and  410 , as shown in  FIG. 4D . In  FIG. 4D , the abscissa represents the position of the condensed beam  301  in the X-axis direction (or Y-axis direction) near the alignment mark  119 , and the ordinate represents the light amount Iop of the heterodyne interference signal. 
     As shown in  FIGS. 4C and 4D , the measurement apparatus  1  can obtain the satisfactory light amounts  408 ,  409 , and  410  corresponding to the vertical lines  403 ,  404 , and  405  of the alignment mark  119 , respectively. When the condensed beam  301  moves in, for example, the X-axis direction on the alignment mark  119 , a light amount distribution (light amount information)  407  which represents a position of the alignment mark  119  in the X-axis direction at high precision and includes the light amounts  408 ,  409 , and  410  can be acquired. Similarly, by moving the condensed beam  301  in the Y-axis direction on the alignment mark  119 , a light amount distribution (light amount information) which represents a position of the alignment mark  119  in the Y-axis direction at high precision can be acquired. 
     Based on the obtained positions of the alignment mark  119  in the X-axis direction and Y-axis direction, the positional relationship in the X-Y plane between a center position  406  of the alignment mark  119  and the condensed beam  301  can be obtained at high precision. By optimally adjusting design values such as the spot size of the condensed beam  301  and the width w and depth d of the vertical line  403  of the alignment mark  119 , the light amount distribution  408  shown in  FIG. 4C  can become a light amount distribution with a higher contrast. 
     Further, in the measurement apparatus  1 , the center positions of alignment marks formed on the measurement surface  121 , that is, the center positions of the two alignment marks  119  and  120  are known on the measurement surface  121 . Thus, the relative positional relationship between the measurement surface  121  and the condensed beam  301 , or the relative positional relationship between the measurement surface  121  and the interference optical system  103  including the condenser lens  118  can be obtained at a high precision of about several μm on the entire measurement surface  121 . More specifically, the position coordinates (X1, Y1) and (X2, Y2) of the two alignment marks  119  and  120  on the measurement surface  121  are known, as shown in  FIG. 5 . The relative positional relationship between the interference optical system  103  including the condenser lens  118  and the positions of the two alignment marks  119  and  120  is known. Therefore, the condensed beam  301  traveling from the interference optical system  103  can be moved to an arbitrary position on the measurement surface  121  at a high precision of about several μm. 
     Since the interference optical system  103  and measurement surface  121  can be aligned at a high precision of about several μm, a measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  103  can be reduced. For example, as correction processing when obtaining the shape of the measurement surface  121 , alignment between measurement light and the alignment marks  119  and  120  is performed based on a positional shift on the measurement surface between measurement light and the alignment marks  119  and  120 . The shape of the measurement surface  121  is obtained based on a heterodyne interference signal acquired after performing the alignment. The measurement apparatus  1  can greatly suppress a setting error and measure the shape of the measurement surface  121  at a high precision of about several nm RMS. 
     It is also possible to obtain the shape of the measurement surface  121  based on a heterodyne interference signal and remove, from the obtained result, an error arising from a positional shift on the measurement surface between measurement light and the alignment marks  119  and  120 . In other words, it is also possible to estimate a setting error from a relative positional shift between the interference optical system  103  and the measurement surface  121 , and perform numerical correction, thereby removing a setting error. In this case, it is necessary to grasp a setting error generated in accordance with a relative positional shift between the interference optical system  103  and the measurement surface  121  by performing measurement and numerical simulation in advance. However, a setting error can be suppressed to obtain the shape of the measurement surface  121  at high precision without performing alignment between the interference optical system  103  and the measurement surface  121  based on a relative positional shift between the interference optical system  103  and the measurement surface  121 . 
     When removing a setting error by performing numerical correction, a relative positional shift between the interference optical system  103  and the measurement surface  121  may be obtained after obtaining the shape of the measurement surface  121 . 
     As shown in  FIG. 5 , two edge portions  501  and  502  positioned respectively at position coordinates (X3, Y3) and (X4, Y4) on the measurement surface  121  may be used instead of the alignment marks  119  and  120 . By obtaining the positional relationship between the interference optical system  103  including the condenser lens  118  and the positions of the edge portions  501  and  502  of the measurement surface  121 , the condensed beam  301  traveling from the interference optical system  103  can be moved to an arbitrary position on the measurement surface  121  at a high precision of about several μm. 
     Second Embodiment 
       FIG. 6  is a schematic view showing the arrangement of a measurement apparatus  2  according to the second embodiment of the present invention. Similarly to the measurement apparatus  1 , the measurement apparatus  2  has a function of measuring a change of the optical path length of measurement light reflected by a measurement surface. In the second embodiment, the measurement apparatus  2  is embodied as a three-dimensional shape measurement apparatus including a non-contact probe (measurement head) using a heterodyne interference method. 
     The measurement apparatus  2  includes, as main components, a light source  101 , stage  112 , reference mirror  111 , interference optical system  601 , autofocus system  140 , detector  611 , first processor  630 , and second processor  631 . In the second embodiment, the interference optical system  601  constitutes a double-pass heterodyne interference system in which light emitted by the light source  101  reciprocates twice between a measurement surface  121  and the reference mirror  111 . In the measurement apparatus  2 , the interference optical system  601  functions as a non-contact probe (optical probe). As in the first embodiment, alignment marks  607  and  608  are formed as alignment targets on the upper surface of the measurement surface  121 . 
     Light (parallel light) emitted by the light source  101  enters a polarizing beam splitter  603  of the interference optical system  601  held by the stage  112 . The light source  101  emits two lights having different wavelengths and different directions of polarization, that is, S-polarized light and P-polarized light having directions of polarization perpendicular to each other in the embodiment. The polarizing beam splitter  603  is configured to reflect S-polarized light and transmit P-polarized light. Of light emitted by the light source  101 , S-polarized light is reflected by the polarizing beam splitter  603 , becomes light almost parallel to the Z-axis, and enters a λ/4 plate  602 . Of the light emitted by the light source  101 , P-polarized light passes through the polarizing beam splitter  603 , becomes light almost parallel to the Y-axis, and enters a corner cube  604  serving as a reference surface. 
     The light entering the λ/4 plate  602  passes through the λ/4 plate  602 , becomes circularly polarized light, and is reflected by the reference mirror (reference surface)  111 . The light reflected by the reference mirror  111  passes again through the λ/4 plate  602 , becomes P-polarized light, passes through the polarizing beam splitter  603 , and enters a λ/4 plate  605 . The light entering the λ/4 plate  605  passes through the λ/4 plate  605 , becomes circularly polarized light, and is condensed through a condenser lens  606  on the measurement surface  121  held by a measurement stage  122  (is focused on the measurement surface  121 ). The autofocus system  140  is used to focus measurement light on the measurement surface  121 . 
     The light reflected by the measurement surface  121  passes through the condenser lens  606 , becomes parallel light, and enters the λ/4 plate  605 . The light entering the λ/4 plate  605  passes through the λ/4 plate  605 , becomes S-polarized light, is reflected by the polarizing beam splitter  603 , and enters the corner cube  604 . The light reflected by the corner cube  604  is reflected by the polarizing beam splitter  603 , and is condensed again on the measurement surface  121  through the λ/4 plate  605  and condenser lens  606 . The light reflected by the measurement surface  121  passes through the condenser lens  606 , becomes parallel light, and enters the λ/4 plate  605 . In the following description, light reflected twice by the measurement surface  121  will be called measurement light. The measurement light entering the λ/4 plate  605  passes through the λ/4 plate  605 , becomes P-polarized light, passes through the polarizing beam splitter  603 , and enters the λ/4 plate  602 . The light entering the λ/4 plate  602  passes through the λ/4 plate  602 , becomes circularly polarized light, and is reflected by the reference mirror (reference surface)  111 . The light reflected by the reference mirror  111  passes again through the λ/4 plate  602 , becomes S-polarized light, is reflected by the polarizing beam splitter  603 , and enters the detector  611  constituted by a lens  610  and photodiode  609 . 
     Light entering the corner cube  604  is reflected in the incident direction by the corner cube  604 , and enters the polarizing beam splitter  603 . In the following description, light reflected by the corner cube  604  without being reflected by the measurement surface  121  will be called reference light. The reference light entering the polarizing beam splitter  603  passes through the polarizing beam splitter  603 , and enters the detector  611  together with measurement light reflected by the polarizing beam splitter  603 . The detector  611  detects interference light between the measurement light and the reference light, and acquires an interference signal corresponding to the interference light, for example, a heterodyne interference signal in the embodiment. 
     In the measurement apparatus  2 , the first processor  630  obtains a change of the light amount of measurement light based on the light amount signal (intensity) of the heterodyne interference signal detected by the detector  611 . The second processor  631  obtains a change of the optical path length of measurement light based on phase information of the heterodyne interference signal detected by the detector  611 . 
     In the measurement apparatus  2 , the first processor  630  acquires light amount information of the heterodyne interference signal while an X-axis driving unit  201  and Y-axis driving unit  202  drive the stage  112  in the X-Y plane. In other words, the first processor  630  acquires light amount information of the heterodyne interference signal while the interference optical system  601  is positioned so that light traveling from the interference optical system  601 , that is, light condensed by the condenser lens  606  enters a plurality of positions (measurement portions) on the measurement surface  121 . A change of the light amount of measurement light is obtained based on the light amount information of the heterodyne interference signal that is acquired by the first processor  630 . Accordingly, the positions (shapes) of the alignment marks  607  and  608  formed on the upper surface of the measurement surface  121  are measured at high precision. 
     Also, in the measurement apparatus  2 , the second processor  631  acquires phase information of the heterodyne interference signal while the X-axis driving unit  201  and Y-axis driving unit  202  drive the stage  112  in the X-Y plane. In other words, the second processor  631  acquires phase information of the heterodyne interference signal while the interference optical system  601  is positioned so that light traveling from the interference optical system  601 , that is, light condensed by the condenser lens  606  enters a plurality of positions (measurement portions) on the measurement surface  121 . A change of the optical path length of measurement light is obtained based on the phase information of the heterodyne interference signal that is acquired by the second processor  631 , thereby measuring the shape of the measurement surface  121 . 
     Even in the measurement apparatus  2 , as in the measurement apparatus  1 , a position of the condenser lens  606  in the optical axis direction is controlled so that a measurement portion on the measurement surface  121  falls (is positioned) within the range of the depth of focus of the condenser lens  606 . Light (measurement light) which has been reflected by the measurement surface  121  and has entered the condenser lens  606  is reflected as parallel light by the polarizing beam splitter  603 , and detected by the detector  611  together with light (reference light) reflected by the corner cube  604 . The detector  611  therefore detects a satisfactory heterodyne signal. In this manner, even when the interference optical system  601  is constituted by a double-pass heterodyne interference system, the shape of the measurement surface  121  can be measured at high precision. More specifically, the measurement apparatus  2  can measure the shape of the measurement surface  121  at high precision by acquiring a heterodyne interference signal by the detector  611  while moving in the X-Y plane the stage  112  holding the interference optical system  601 . 
     The measurement apparatus  2  according to the embodiment obtains a change of the light amount of measurement light and a change of the optical path length by acquiring an interference signal by the detector  611  while moving the stage  112  in the X-Y plane. The measurement apparatus  2  can measure not only the surface shape of an object, but also the characteristics of the object that are correlated with these changes. The measurement apparatus  2  can measure, for example, even the surface roughness of the object. 
     Alignment in the X-Y plane (measurement plane) between the interference optical system  601  including the condenser lens  606  and the measurement surface  121  on which the alignment marks  607  and  608  are formed will be explained. Each of the alignment marks  607  and  608  is a 2×2-matrix mark having a rectangular outer frame, and a cross shape arranged inside the outer frame. In the embodiment, light condensed by the condenser lens  606  is scanned in the X-axis direction and Y-axis direction on the alignment marks  607  and  608 . The autofocus system  140  is used when condensing measurement light on the measurement surface  121 . Based on a change of light amount information of a heterodyne interference signal, the first processor  630  measures at high precision the relative positions of the interference optical system  601  and the alignment marks  607  and  608  formed on the measurement surface  121 . 
     Even in the measurement apparatus  2  using a double-pass optical system, the interference optical system  601  and measurement surface  121  can be aligned at a high precision of about several μm, as in the measurement apparatus  1  using a single-pass optical system. Accordingly, a measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  601  can be reduced. Similarly to the measurement apparatus  1 , the measurement apparatus  2  can greatly suppress a setting error and measure the shape of the measurement surface  121  at a high precision of about several nm RMS. 
     Third Embodiment 
       FIG. 7  is a schematic view showing the arrangement of a measurement apparatus  3  according to the third embodiment of the present invention. The measurement apparatus  3  has a function of measuring a change of the optical path length of measurement light reflected by a measurement surface. In the third embodiment, the measurement apparatus  3  is embodied as a three-dimensional shape measurement apparatus including a non-contact probe (measurement head) using a heterodyne interference method. In the measurement apparatus  3 , a measurement surface  121  is arranged (accommodated) in a chamber  715 . The shape of the measurement surface  121  is measured through a light-transmissive window  710  arranged in (the wall surface of) the chamber  715 . The light-transmissive window  710  is constituted by a transparent synthetic quartz substrate for a He—Ne laser having a wavelength of 633 nm. Alignment marks  711  and  712  are formed on a surface (surface closer to the measurement surface) of the light-transmissive window  710  on the inner side of the chamber  715 . Alignment marks  713  and  714  are also formed on the measurement surface  121 . 
     In the third embodiment, to measure the shape of the measurement surface  121  based on a change of the phase of measurement light, the light-transmissive window  710  is made of a material, such as synthetic quartz, excellent in optical characteristics regarding the uniformity of the refractive index distribution. These optical characteristics are a homogeneity of about 1 ppm at a wavelength of 365 nm, a birefringence of about 10 nm/cm, and a transmitted wavefront of about λ/4 at a wavelength of 633 nm. 
     In the measurement apparatus  3 , a first processor  730  obtains a change of the light amount of measurement light based on the light amount signal of a heterodyne interference signal detected by a detector  107 A. A second processor  731  obtains a change of the optical path length of measurement light based on phase information of the heterodyne interference signal detected by the detector  107 A. 
     An interference optical system  701  constitutes a single-pass optical system, similarly to the interference optical system  103  of the measurement apparatus  1 . In the measurement apparatus  3 , however, a condenser lens  703  is optically designed in consideration of the optical characteristics of the light-transmissive window  710  in order to measure, through the light-transmissive window  710 , the positions of the alignment marks  713  and  714  formed on the measurement surface  121 . For example, the condenser lens  703  is optically designed to decrease wavefront aberration of measurement light having passed through the light-transmissive window  710 . Thus, the alignment marks  713  and  714  formed on the measurement surface  121 , and the alignment marks  711  and  712  formed on the light-transmissive window  710  can be irradiated with light (condensed beam) which is satisfactorily narrowed down with small wavefront aberration. When measuring the alignment marks  713  and  714  through the light-transmissive window  710 , the measurement apparatus  3  can obtain a change of the light amount of measurement light more satisfactorily, compared to the case in which the interference optical system  105  of the measurement apparatus  1  is used. In other words, the positions of the alignment marks  713  and  714  formed on the measurement surface  121  can be measured satisfactorily. Similarly, the positions of the alignment marks  711  and  712  formed on the light-transmissive window  710  can be measured satisfactorily. 
     The measurement apparatus  3  suffices to condense measurement light on the measurement surface  121  and a surface of the light-transmissive window  710  on the measurement surface side by the autofocus system  140  using surface reflection of measurement light by the measurement surface  121  and light-transmissive window  710 . 
     The measurement apparatus  3  measures alignment marks formed on both the measurement surface  121  and light-transmissive window  710  by using light condensed by the condenser lens  703 . Therefore, the optical system needs to be adjusted to decrease wavefront aberration of light having passed through the light-transmissive window  710  in accordance with which of a surface of the light-transmissive window  710  on the measurement surface side and the surface of the interference optical system bears the alignment marks. For example, when the alignment marks  711  and  712  are formed on a surface of the light-transmissive window  710  on the measurement surface side, the condenser lens  703  is optically designed in consideration of the optical characteristics of the light-transmissive window  710 , as described above. In this case, alignment marks formed on both the measurement surface  121  and light-transmissive window  710  can be measured by light (condensed beam) with small wavefront aberration. In contrast, when alignment marks are formed on a surface of the light-transmissive window  710  on the interference optical system side, an aberration correction optical system is separately used to irradiate alignment marks with satisfactory light from which the optical characteristics of the light-transmissive window  710  are removed. 
     In this way, the measurement apparatus  3  can measure at high precision the relative positional relationship between the interference optical system  701  and the alignment marks  711  and  712  formed on the light-transmissive window  710 . Also, the measurement apparatus  3  can measure at high precision the relative positional relationship between the interference optical system  701  and the alignment marks  713  and  714  formed on the measurement surface  121 . Accordingly, the relative positional relationship between the interference optical system  701 , the light-transmissive window  710 , and the measurement surface  121  can be grasped at high precision. 
     Alignment between a condensed beam  801 , the alignment marks  713  and  714  formed on the measurement surface  121 , and the alignment marks  711  and  712  formed on the light-transmissive window  710  will be explained with reference to  FIG. 8 .  FIG. 8  shows a state in which the first processor  730  obtains a change of the light amount of a heterodyne interference signal while the condensed beam  801  condensed by the condenser lens  703  is moved on the alignment marks  711  and  712 . Similarly,  FIG. 8  shows a state in which the second processor  731  obtains a change of the light amount of heterodyne interference while the condensed beam  801  is moved on the alignment marks  713  and  714  after positions of the interference optical system  701  and condenser lens  703  in the Z-axis direction are changed. 
       FIG. 9A  is a schematic view showing the alignment marks  711  and  712  respectively formed at position coordinates (X5, Y5) and (X6, Y6) on a surface of the light-transmissive window  710  on the measurement surface side.  FIG. 9B  is a schematic view showing the alignment marks  713  and  714  respectively formed at position coordinates (X7, Y7) and (X8, Y8) on a surface of the measurement surface  121  on the measurement surface side. As shown in  FIG. 9A , the positions (position coordinates (X5, Y5) and (X6, Y6)) of the alignment marks  711  and  712  are known on the light-transmissive window  710 . Note that the alignment marks  711  and  712  can also be replaced with the edge portions of the light-transmissive window  710 , as in the first embodiment. Also, as shown in  FIG. 9B , the positions (position coordinates (X7, Y7) and (X8, Y8)) of the alignment marks  713  and  714  are known on the measurement surface  121 . 
     The measurement apparatus  3  obtains the relative positional relationship between the interference optical system  701  (an interference optical system  702 ) including the condenser lens  703  and the positions of the four alignment marks  711  to  714 . Therefore, the condensed beam  801  traveling from the interference optical system  701  can be moved to arbitrary positions on the measurement surface  121  and light-transmissive window  710  at a high precision of about several μm. When measuring an arbitrary position (measurement portion) on the measurement surface  121  with measurement light, a position of the light-transmissive window  710  at which measurement light passes (that is, the passage position of measurement light in the light-transmissive window  710 ) can be obtained. 
     In this fashion, the measurement apparatus  3  can align the interference optical system  701  including the condenser lens  703 , and the measurement surface  121  at a high precision of about several μm, as in a case in which the measurement surface  121  is not arranged inside the chamber  715 . Hence, a measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  701  can be reduced. Similarly to the measurement apparatus  1 , the measurement apparatus  3  can greatly suppress a setting error and measure the shape of the measurement surface  121  at a high precision of about several nm RMS. 
     The light-transmissive window  710  generally has a thickness nonuniformity of about λ/10, that is, 63 nm. To measure the shape of the measurement surface  121  through the light-transmissive window  710  at high precision, it is necessary to grasp, on the entire measurement surface  121 , a position of the light-transmissive window  710  at which measurement light passes, and correct a measurement error arising from the thickness nonuniformity of the light-transmissive window  710 . According to the embodiment, a position of the light-transmissive window  710  at which measurement light passes can be obtained when an arbitrary position of the measurement surface  121  is measured. Therefore, a measurement error arising from the thickness nonuniformity of the light-transmissive window  710  can be corrected. For example, the shape of the measurement surface  121  is obtained based on a heterodyne interference signal acquired when measurement light enters a measurement portion on the measurement surface  121 . An error which arises from the thickness nonuniformity of the light-transmissive window  710  and is obtained based on the positional relationship on the light-transmissive window surface between measurement light and the alignment marks  711  and  712  is removed from the obtained result. Note that the thickness nonuniformity of the light-transmissive window  710  can be measured in advance by using a transmitted wavefront measurement interferometer or the like. 
     As described above, the measurement apparatus  3  can grasp at high precision the relative positional relationship between the interference optical system  701  including the condenser lens  703 , the light-transmissive window  710 , and the measurement surface  121 . The measurement apparatus  3  can reduce a measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  701 . Also, the measurement apparatus  3  can reduce a measurement error arising from the thickness nonuniformity of the light-transmissive window  710 . In other words, the measurement apparatus  3  can compensate for an error arising from the nonuniformity of an optical characteristic such as the thickness nonuniformity of the light-transmissive window  710 . The measurement apparatus  3  can measure at high precision the shape of even the measurement surface  121  arranged inside the chamber  715 . 
     Fourth Embodiment 
       FIG. 10  is a schematic view showing the arrangement of a measurement apparatus  4  according to the fourth embodiment of the present invention. The measurement apparatus  4  has a function of measuring a change of the optical path length of measurement light reflected by a measurement surface. In the fourth embodiment, the measurement apparatus  4  is embodied as a three-dimensional shape measurement apparatus including a non-contact probe (measurement head) using a heterodyne interference method. In the measurement apparatus  4 , a measurement surface  121  is arranged (accommodated) in a chamber  1015 . The shape of the measurement surface  121  is measured through a light-transmissive window  1010  arranged in (the wall surface of) the chamber  1015 . 
     As shown in  FIG. 11 , the light-transmissive window  1010  includes a first light-transmissive window  1010   a  interposed between an interference optical system  1001  and the measurement surface  121 , and a second light-transmissive window  1010   b  arranged on the interference optical system side with respect to the first light-transmissive window  1010   a . In this manner, the light-transmissive window  1010  includes multiple light-transmissive windows on the optical path of measurement light. The first light-transmissive window  1010   a  and second light-transmissive window  1010   b  are integrated by joining members  1019  and  1020 . Each of the first light-transmissive window  1010   a  and second light-transmissive window  1010   b  is constituted by a transparent synthetic quartz substrate for a He—Ne laser having a wavelength of 633 nm. Alignment marks  1011  and  1012  are formed on a surface (surface on the measurement surface side) of the first light-transmissive window  1010   a  on the inner side of the chamber  1015 . Note that a plurality of alignment marks may be formed on each of the first light-transmissive window  1010   a  and second light-transmissive window  1010   b . Alignment marks  1013  and  1014  are also formed on the measurement surface  121 . 
     The measurement apparatus  4  can obtain the positional relationship between the light-transmissive window  1010  and the interference optical system  1001  by using the alignment marks  1011  and  1012  formed on the first light-transmissive window  1010   a . In the measurement apparatus  4 , a first processor  1030  obtains a change of the light amount of measurement light based on the light amount signal of a heterodyne interference signal detected by a detector  107 A. A second processor  1031  obtains a change of the optical path length of measurement light based on phase information of the heterodyne interference signal detected by the detector  107 A. 
     The interference optical system  1001  has the same arrangement as that of the interference optical system  103  of the measurement apparatus  1 . In the measurement apparatus  4 , however, a condenser lens  1003  is optically designed in consideration of the optical characteristics of the light-transmissive window  1010  in order to measure, through the light-transmissive window  1010 , the alignment marks  1013  and  1014  formed on the measurement surface  121 . The measurement apparatus  4  can obtain a change of the light amount of measurement light more satisfactorily, compared to a case in which the interference optical system  105  of the measurement apparatus  1  is used to measure the alignment marks  1013  and  1014  through the light-transmissive window  1010 . The first processor  1030  is optimized to be able to obtain a change of the light amount of measurement light more satisfactorily when measuring the alignment marks  1013  and  1014  through the light-transmissive window  1010 , compared to the first processor  130  of the measurement apparatus  1 . 
     The measurement apparatus  4  can obtain the relative positional relationship between the interference optical system  1001  and the alignment marks  1011  and  1012  formed on the light-transmissive window  1010 . Also, the measurement apparatus  4  can obtain the relative positional relationship between the interference optical system  1001  and the alignment marks  1013  and  1014  formed on the measurement surface  121 . Thus, the measurement apparatus  4  can grasp the relative positional relationship between the interference optical system  1001 , the light-transmissive window  1010 , and the measurement surface  121  at high precision. 
     In the measurement apparatus  4 , as in the measurement apparatus  3 , an autofocus system  140  suffices to condense measurement light on surfaces of the measurement surface  121  and first light-transmissive window  1010   a  on the measurement surface side. 
       FIG. 11  shows a state in which the first processor  1030  obtains a change of the light amount of a heterodyne interference signal while a condensed beam  1016  condensed by the condenser lens  1003  is moved on the alignment marks  1011  and  1012 . Similarly,  FIG. 11  shows a state in which the second processor  1031  obtains a change of the light amount of heterodyne interference while the condensed beam  1016  is moved on the alignment marks  1013  and  1014  after positions of the interference optical system  1001  and condenser lens  1003  in the Z-axis direction are changed. 
       FIG. 12A  is a schematic view showing the alignment marks  1011  and  1012  respectively formed at position coordinates (X9, Y9) and (X10, Y10) on a surface of the first light-transmissive window  1010   a  on the measurement surface side.  FIG. 12B  is a schematic view showing the alignment marks  1013  and  1014  respectively formed at position coordinates (X11, Y11) and (X12, Y12) on a surface of the measurement surface  121  on the measurement surface side. As shown in  FIG. 12A , the positions (position coordinates (X9, Y9) and (X10, Y10)) of the alignment marks  1011  and  1012  are known on the first light-transmissive window  1010   a . Similarly, as shown in  FIG. 12B , the positions (position coordinates (X11, Y11) and (X12, Y12)) of the alignment marks  1013  and  1014  are known on the measurement surface  121 . 
     The measurement apparatus  4  obtains the relative positional relationship between the interference optical system  1001  (an interference optical system  1002 ) including the condenser lens  1003  and the positions of the four alignment marks  1011  to  1014 . The condensed beam  1016  traveling from the interference optical system  1001  can be moved to arbitrary positions on the measurement surface  121  and light-transmissive window  1010  at a high precision of about several μm. When measuring an arbitrary position (measurement portion) on the measurement surface  121  with measurement light, a position of the light-transmissive window  1010  at which measurement light passes (that is, the passage position of measurement light in the light-transmissive window  1010 ) can be obtained. 
     In this way, the measurement apparatus  4  can align the interference optical system  1001  including the condenser lens  1003 , and the measurement surface  121  at a high precision of about several μm, as in a case in which the measurement surface  121  is not arranged inside the chamber  1015 . Hence, a measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  1001  can be reduced. Similarly to the measurement apparatus  3 , the measurement apparatus  4  can greatly suppress a setting error and measure the shape of the measurement surface  121  at a high precision of about several nm RMS. 
     Similarly to the measurement apparatus  3 , when measuring an arbitrary position on the measurement surface  121 , the measurement apparatus  4  can obtain a position of the light-transmissive window  1010  at which measurement light passes, and thus can correct a measurement error arising from the thickness nonuniformity of the light-transmissive window  1010 . Note that the thickness nonuniformity of the light-transmissive window  1010  can be measured in advance by using a transmitted wavefront measurement interferometer or the like. 
     As described above, the measurement apparatus  4  can grasp, at high precision, the relative positional relationship between the interference optical system  1001  including the condenser lens  1003 , the light-transmissive window  1010 , and the measurement surface  121 . The measurement apparatus  4  can reduce a measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  1001 . Also, the measurement apparatus  4  can reduce a measurement error arising from the thickness nonuniformity of the light-transmissive window  1010 . The measurement apparatus  4  can therefore measure at high precision the shape of the measurement surface  121  arranged inside the chamber  1015 . 
     Fifth Embodiment 
       FIG. 13  is a schematic view showing the arrangement of a measurement apparatus  5  according to the fifth embodiment of the present invention. The measurement apparatus  5  has a function of measuring a change of the optical path length of measurement light reflected by a measurement surface. In the fifth embodiment, the measurement apparatus  5  is embodied as a three-dimensional shape measurement apparatus including a non-contact probe (measurement head) using a heterodyne interference method. In the measurement apparatus  5 , an interference optical system  1301  is constituted as a double-pass optical system in which measurement light is reflected twice by a measurement surface  121 , similarly to the interference optical system  601  of the measurement apparatus  2 . In other words, the interference optical system  1301  is an optical system in which, when measuring the shape of the measurement surface  121 , measurement light  1309  enters the measurement surface  121 , and then measurement light  1310  having passed through a plurality of optical systems of the interference optical system  1301  enters again the measurement surface  121 . The measurement apparatus  5  has a simple arrangement in which a condensing optical system such as a condenser lens  606  is not inserted in the optical path of measurement light, unlike the interference optical system  601  of the measurement apparatus  2 . 
     Alignment marks  1307  and  1308  are formed as alignment targets on the upper surface of the measurement surface  121 . Since the measurement apparatus  5  does not use the condensing optical system, measurement light on the measurement surface  121  maintains a size of 6 mm which is the diameter of parallel light emitted by a light source  101 . Hence, no autofocus system need be used for alignment of measurement light in the optical axis direction with respect to the alignment marks  1307  and  1308  formed on the measurement surface  121 . 
     In the measurement apparatus  5 , a first processor  1330  obtains a change of the light amount of measurement light based on the light amount signal (intensity) of a heterodyne interference signal detected by a detector  611 . A second processor  1331  obtains a change of the optical path length of measurement light based on phase information of the heterodyne interference signal detected by the detector  611 . 
     The measurement apparatus  5  can obtain the relative positional relationship between the measurement surface  121  and the interference optical system  1301  by using the alignment marks  1307  and  1308  formed on the measurement surface  121 . The measurement apparatus  5  can easily grasp the relative positional relationship between the measurement surface  121  and the interference optical system  1301  at a precision of 6 mm or less which is the diameter of parallel light. 
     Alignment between (the measurement light  1309  from) the interference optical system  1301  and the alignment marks  1307  and  1308  formed on the measurement surface  121  will be explained with reference to  FIGS. 14 ,  15 A, and  15 B.  FIG. 14  shows a state in which the first processor  1330  obtains a change of the light amount of a heterodyne interference signal while the measurement beam  1309  traveling from the interference optical system  1301  is moved on the alignment marks  1307  and  1308 . As light irradiating the alignment marks  1307  and  1308 , the measurement light  1310  may be used instead of the measurement light  1309 . 
     In the measurement apparatus  5 , the measurement light  1309  traveling from the interference optical system  1301  can be moved to an arbitrary position in the X-Y plane by moving the interference optical system  1301  in the X-Y plane including the X-axis and Y-axis. By moving the interference optical system  1301  in the X-Y plane, each of the alignment marks  1307  and  1308  formed on the measurement surface  121  can be irradiated with the measurement light  1309 . The size of the measurement light  1309  is a diameter of about 6 mm though it depends on the optical design of the light source  101 . 
     In the measurement apparatus  5 , even if the measurement surface  121  slightly shifts from a predetermined position in the Z-axis direction serving as the optical axis direction, the size of the measurement light  1309  irradiating the alignment marks  1307  and  1308  is almost equal to 6 mm which is the diameter of light emitted by the light source  101 . 
       FIG. 15A  is a schematic view showing an example of the shape of the alignment mark  1307 . Since the alignment marks  1307  and  1308  have the same composition, the alignment mark  1307  will be exemplified here. In the embodiment, the alignment mark  1307  is not a 2×2-matrix mark, but is constituted by only a rectangular outer frame in consideration of 6-mmφ parallel light which irradiates the measurement surface  121 . In the alignment mark  1307 , for example, the rectangular outer frame is 1 mm square, the width w of a line in each of the X-axis direction and Y-axis direction is 1 mm, and the depth is about 158 nm which is equivalent to λ/4. However, the alignment mark  1307  is not limited to the rectangular outer frame. 
       FIG. 15B  shows a light amount distribution (light amount information)  1505  obtained when the alignment mark  1307  (or  1308 ) formed on the measurement surface  121  is irradiated with the measurement light  1309  while the interference optical system  1301  is moved in the X-axis direction (or Y-axis direction). In  FIG. 15B , the abscissa represents the position of the measurement light  1309  in the X-axis direction (or Y-axis direction) near the alignment mark  1307 , and the ordinate represents a light amount Iop of the heterodyne interference signal. A light amount  1504  obtained when almost the center of the alignment mark  1307  is irradiated with the measurement light  1309  is different from a light amount  1503  obtained when the periphery of the alignment mark  1307  is irradiated with the measurement light  1309 . By obtaining a light amount by the first processor  1330  while irradiating the alignment marks  1307  and  1308  with the measurement light  1309 , the relative positional relationship between the measurement light  1309  and the alignment marks  1307  and  1308  can be obtained. 
     In the measurement apparatus  5 , when the measurement light  1309  moves in, for example, the X-axis direction on the alignment mark  1307 , a light amount distribution (light amount information) representing a position of the alignment mark  1307  in the X-axis direction at high precision can be acquired. Similarly, by moving the measurement light  1309  in the Y-axis direction on the alignment mark  1307 , a light amount distribution (light amount information) representing a position of the alignment mark  1307  in the Y-axis direction at high precision can be acquired. 
     Based on the obtained positions of the alignment mark  1307  in the X-axis direction and Y-axis direction, the positional relationship in the X-Y plane between the center position of the alignment mark  1307  and the measurement light  1309  can be obtained at high precision. By optimally adjusting the size of the measurement light  1309  and the width w and depth d of the vertical line of the alignment mark  1307 , the light amount distribution  1505  shown in  FIG. 15B  can become a light amount distribution with a higher contrast. 
     In the measurement apparatus  5 , the position coordinates (X13, Y13) and (X14, Y14) of the two alignment marks  1307  and  1308  on the measurement surface  121  are known, as shown in  FIG. 16 . The relative positional relationship between the measurement surface  121  and the measurement light  1309 , or the relative positional relationship between the measurement surface  121  and the interference optical system  1301  can be obtained at high precision on the entire measurement surface  121 . Accordingly, the measurement light  1309  traveling from the interference optical system  1301  can be moved to an arbitrary position on the measurement surface  121  at high precision. 
     Thus, even in the measurement apparatus  5  having no condensing optical system, the interference optical system  1301  and measurement surface  121  can be aligned at high precision. A measurement error, that is, a setting error arising from an error of the installation position of the measurement surface  121  with respect to the interference optical system  1301  can be reduced. Similarly to the measurement apparatus  2 , the measurement apparatus  5  can greatly suppress a setting error and measure the shape of the measurement surface  121  at high precision. 
     In the above-described embodiments, an alignment mark constituted by a 2×2-matrix mark, or an alignment mark constituted by a rectangular outer frame is formed on the measurement surface, and the relative positional relationship between the interference optical system and the measurement surface is obtained based on the alignment mark. However, it is also possible to form a three-dimensional shape mark as an alignment mark, and obtain the relative positional relationship between the interference optical system and the measurement surface based on a change of light amount information obtained when the alignment mark is irradiated with measurement light. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2013-185707 filed on Sep. 6, 2013, which is hereby incorporated by reference herein in its entirety.