Patent Publication Number: US-2013235385-A1

Title: Surface shape measurement method and measurement apparatus

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a surface shape measurement method and measurement apparatus. 
     2. Description of the Related Art 
     In order to simultaneously measure information of surface shapes (heights) over the entire surface of a target object from image information of the target object, a method using a wavelength scanning interferometry is available. However, it is difficult for this wavelength scanning interferometry to quickly measure the surface shapes since a large number of images have to be obtained using an image sensor required to obtain an interference signal. 
     With a method described in APPLIED OPTICS, Vol. 33, No. 34, a target object is irradiated with coherent light while scanning a wavelength (or frequency), and a large number of images of interference light between light reflected by the target object and that reflected by a reference surface are sensed at a plurality of times using an image sensor. With the method described in APPLIED OPTICS, Vol. 33, No. 34, pieces of information of surface shapes (heights) of the target object are simultaneously measured from interference signals obtained for respective pixels of the image sensor. It is difficult for the method described in APPLIED OPTICS, Vol. 33, No. 34 to quickly measure the surface shapes of the target object since a large number of images (for example, one hundred and several ten images) have to be obtained by the image sensor. 
     SUMMARY OF THE INVENTION 
     The present invention provides a novel setting method of a frequency change rate of light used in the wavelength scanning interferometry, which method contributes to, for example, quick measurements of the surface shapes. 
     The present invention in the first aspect provides a method of measuring a surface shape of a target object by irradiating a target object and a reference surface with coherent light while changing a frequency of the coherent light, and sensing interference fringes between measurement light reflected by the target object and reference light reflected by the reference surface, the method comprising: a setting step of setting a rate of changing the frequency of the coherent light based on at least one of first information of a contour of an image of the target object projected onto a surface and known second information of the surface shape; an obtaining step of obtaining, by an image sensor, a plurality of images of the interference fringes while changing the frequency of the coherent light with which the target object and the reference surface are irradiated at the rate set in the setting step; and a step of obtaining the surface shape of the target object based on the plurality of images obtained in the obtaining step. 
     The present invention in the second aspect provides a apparatus for measuring a surface shape of a target object by irradiating a target object and a reference surface with coherent light while changing a frequency of the coherent light, and sensing interference fringes between measurement light reflected by the target object and reference light reflected by the reference surface, the apparatus comprising: a light source configured to emit the light; an image sensor configured to sense interference fringes; and a processor configured to obtain the surface shape based on a plurality of images of the interference fringes sensed by the image sensor, wherein the processor sets a rate of changing the frequency of the coherent light based on at least one of first information of a contour and a position of an image of the target object projected onto a surface perpendicular to an optical axis of the measurement light and known second information of the surface shape, the processor controls the image sensor to obtain the plurality of images of the interference fringes while changing the frequency of the coherent light which with the target object and the reference surface are irradiated at the set rate, and the processor obtains the surface shape of the target object based on the plurality of images obtained by the image sensor. 
     Further features 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 diagram showing a measurement apparatus according to the first embodiment; 
         FIG. 2  is a flowchart of a measurement method according to the first and second embodiments; 
         FIG. 3  is a view showing approximate value data of Z dimensions of a target object; 
         FIG. 4  is a diagram showing a measurement apparatus according to the second embodiment; 
         FIG. 5  is a graph showing a frequency scan timing according to the second embodiment; 
         FIG. 6  is a diagram showing a measurement apparatus according to the third embodiment; 
         FIG. 7  is a flowchart of a measurement method according to the third embodiment; 
         FIG. 8  is a view showing a case in which a readout pixel region is not limited; 
         FIG. 9  is a view showing a case in which a readout pixel region is limited; 
         FIG. 10  is a view for explaining binning; and 
         FIG. 11  is a view showing projected sizes on an X-Y plane. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     First Embodiment 
       FIG. 1  shows the arrangement of an apparatus (measurement apparatus) according to the first embodiment, which quickly measures surface shapes of a target object from known information (second information) of the surface shapes of the target object using a wavelength scanning interferometry. The measurement apparatus includes, as a light source, a wavelength-variable laser  1  which emits coherent light while changing its frequency (and wavelength). A processor  8  changes the frequency of the coherent light emitted from the wavelength-variable laser  1  within a certain time range. A light beam emitted from the wavelength-variable laser  1  is magnified by a magnifying lens  2   a,  is then collimated into parallel light by a collimator lens  2   b,  and is divided by a beam splitter  3  into light traveling toward a reference surface  4   a  and that traveling toward a target object  5 . 
     The light with which the reference surface  4   a  is irradiated is reflected by the reference surface  4   a,  and returns to the beam splitter  3  as reference light. On the other hand, the target object  5 , which is placed on a stage  6  arranged at a position separated by a distance D from a position  4   b  conjugate with the reference surface  4   a,  is irradiated with the light traveling toward the target object  5 . The light with which the target object  5  is irradiated is reflected by the target object  5 , returns to the beam splitter  3  as measurement light, and interferes with the reference light reflected by the reference surface  4   a,  thus forming interference fringes on an image sensor  7 . The processor  8  obtains a plurality of images as the interference fringes by the image sensor  7  while changing (scanning) the frequency of the wavelength-variable laser  1 . The processor  8  applies frequency analysis to the interference fringes at respective pixels from the plurality of sensed images, thus measuring surface shapes (Z dimensions) at respective points on the surface of the target object  5  projected in an optical axis direction. 
     A method of measuring the surface shapes according to the first embodiment will be described below with reference to  FIG. 2 . In step S 101 , the processor  8  obtains known information (second information) of the surface shapes of the target object  5 . The second information is obtained by inputting, for example, the known information of the surface shapes to the processor  8 . The second information includes approximate value data of the Z dimensions at respective positions on the surface of the target object  5 , that is, data which indicate distributions of Z dimensions H 1  and H 2  from a surface that contacts the stage  6 , as shown in  FIG. 3 . Design information of the target object  5  and information indicating measurement results of the target object  5  using a prototype correspond to the second information. 
     When the design information is used as the second information, it is directly input from an input device such as a keyboard to the processor  8 . When the measurement results using the prototype are used as the second information, the target object  5  is actually measured using the prototype, and the measurement results are registered in a database of the processor  8 . Alternatively, CAD data as pieces of design information of various target objects  5  or measurement results of surface shapes of various target objects  5  are registered in advance, and the second information may be input by designating one of the registered target objects  5 . 
     In step S 102 , the processor  8  sets a frequency change rate for respective sensing operations of the wavelength-variable laser  1  based on the second information input in step S 101  (setting step). In the wavelength scanning interferometry, a maximum frequency v max  of interference signals at respective points of the target object  5  is expressed using a maximum value OPD max  of optical path length differences between the reference light and measurement light and a change rate Δf of the frequency by: 
         v   max =(4·π·Δ f ·OPD max )/ C    (1)
 
     where C is a light speed. 
     From the sampling theorem, a condition that allows the quickest sensing operation is a case which satisfies: 
         v   max =FR/2   (2)
 
     where FR is a frame rate of the image sensor  7 . 
     For every target objects  5 , the maximum frequency v max  of interference signals need only match a Nyquist frequency as a frequency ½ of the frame rate FR of the image sensor  7 . However, the maximum value OPD max  of the optical path length differences varies depending on target objects  5 . Therefore, when the change rate Δf of the frequency is constant, the maximum frequency v max  does not always match the Nyquist frequency FR/ 2  with respect to the frame rate FR of the image sensor  7 . 
     Hence, in step S 102 , the processor  8  sets the maximum value OPD max  of the optical path length differences between the reference light and measurement light based on the second information of the known surface shapes of the target object  5  input in step S 101 , and sets the change rate Δf of the frequency based on the set value OPD max . In the first embodiment, the mounting surface of the target object  5  with respect to the stage  6  is set at a place separated by the distance D from the position  4   b  conjugate with the reference surface  4   a.  For this reason, letting H be approximate value data of the Z dimensions of the target object  5 , the maximum value OPD max  of the optical path length difference is expressed by: 
       OPD max =MAX( H )+ D    (3)
 
     where MAX is a function required to obtain a maximum value of the approximate value data H of the Z dimensions of the target object  5 . 
     Hence, by substituting equation (1) which expresses the maximum frequency v max  of the interference signal into conditional formula (2) that allows the quickest sensing operation, and arranging that equation for Δf, we have: 
       Δ f ≦( FR·C )/(8·π·OPD max )   (4)
 
     The processor  8  sets the change rate Δf of the frequency of the wavelength-variable laser  1  so as to meet inequality (4) above. 
     In this case, a maximum rate Δf upon letting H max  be a maximum value of the approximate value data of the Z dimensions of the target object  5  is given by: 
       Δ f =(α·FR· C )/{8·π·( H   max   +D)}   (5)
 
     where α is an offset. In actual measurement, in order to prevent aliasing caused by noise due to manufacturing errors of the target object  5  and noise at the time of measurement, the interference signal frequency is desirably set to be a value about 10% lower than the Nyquist frequency. For this reason, the value a is set to be about 0.9. 
     In step S 103 , the processor  8  obtains an image required to measure the Z dimensions using the image sensor  7  while changing the wavelength of the wavelength-variable laser  1  based on the change rate Δf of the frequency of the wavelength-variable laser  1  set in step S 102  (obtaining step). Letting ΔF be a scan width of the frequency of the wavelength-variable laser  1 , a measurement time t upon measuring the target object  5  at the change rate Δf of the frequency given by equation (5) is expressed by: 
         t=ΔF/Δf={ 8·π·( H   max   +D )·Δ F }/(α·FR· C )   (6)
 
     As can be seen from equation (6), the measurement time t changes when the Z dimension (H max ) of the target object  5  changes. A quicker measurement can be done with decreasing Z dimension of the target object. Letting Δf be the frequency change rate set according to the Z dimensions of the target object  5 , the measurement time can be shortened compared to the rate Δf which is fixed independently of the Z dimensions of the target object  5 . For example, assume that the Z dimensions of the target object having a maximum value=10 mm of the approximate values of the Z dimensions are measured under the conditions that the distance D from the position  4   b  conjugate with the reference surface  4   a  is 10 mm and a measurable range of the Z dimensions is 50 mm, and α=0.9. In this case, when the change rate Δf of the frequency is set according to the Z dimensions of the target object, the measurement time can be shortened to about ⅓ compared to the fixed rate Δf. 
     In step S 104 , the processor  8  executes frequency analysis by applying processing such as Fourier transformation to respective pixels of the image sensor  7  based on the plurality of pieces of image information obtained in step S 103 , and sets an obtained frequency v m,n  of the interference signal (where m is the number of a row direction of the image sensor, and n is the number of a column direction of the image sensor). 
     In this embodiment, a total of the Z dimensions of the target object  5  and the distance D from the position  4   b  conjugate with the reference surface  4   a  corresponds to the optical path length difference. Hence, the processor  8  obtains a Z dimension H m,n  of the target object  5  from the set frequency v m,n  of the interference signal using: 
         H   m,n ={( v   m,n   ·C )/(4·π·Δ f )}− D    (7)
 
     Step S 104  is the step of obtaining the surface shapes of the target object  5 . The measurement apparatus of the first embodiment can quickly and simultaneously measure the Z dimensions at respective points of the target object  5  by executing measurements while changing the frequency of the wavelength-variable laser  1  at the change rate Δf of the frequency set according to the Z dimensions of the target object  5 . When Z dimensions of target objects  5  of the same type are to be continuously measured, step S 101  need not be executed for the second or subsequent target object  5 , and only steps S 102  to S 104  need only be executed. 
     Second Embodiment 
     A measurement apparatus according to the second embodiment executes a wavelength scanning interferometry by setting a wavelength of a light source to be multi-wavelengths. As a result, if the measurement precision remains the same, the second embodiment can reduce a scan width ΔF of a frequency of the light source compared to the measurement method of the first embodiment. As can be seen from equation (6), the measurement time can be further shortened compared to the first embodiment. 
       FIG. 4  is a schematic diagram showing the arrangement of a three-dimensional measurement apparatus of a target object  5  according to the second embodiment. The measurement apparatus uses a wavelength-variable laser  1 , which emits coherent light while changing a frequency, as one light source. A processor  8  changes a frequency (wavelength) of a light beam emitted by the wavelength-variable laser  1  within a certain time range. Light having a frequency f 1  emitted by the wavelength-variable laser  1  is divided by a beam splitter  3   a.  One of divided light beams is incident on a frequency shifter  11   a  which shifts a frequency by an arbitrary amount, and is converted into light, the frequency of which is shifted by an arbitrary frequency shift amount df 1 . 
     The traveling direction of the frequency-shifted light is deflected by a reflective mirror  10   a,  and that light is divided by the beam splitter  3   a  to be combined with light, the traveling direction of which is deflected by a reflective mirror  10   b,  by a beam splitter  3   b.  This combined light beam will be referred to as a light beam  1  hereinafter. The frequency shift amount df 1  corresponds to a frequency of a beat signal of the light beam  1 , and is required to be ½ FR or less of an image sensor  7  so as to correctly obtain an interference signal. 
     The measurement apparatus uses a wavelength-fixed laser  9  which emits coherent light, the frequency of which is fixed, as the other light source. Light having a frequency f 2  emitted by the wavelength-fixed laser  9  is divided by a beam splitter  10   c  in the same manner as the wavelength-variable laser  1 . One of the divided light beams is converted by a frequency shifter  11   b  into light, the frequency of which is shifted by an arbitrary frequency df 2 , and its traveling direction is deflected by a reflective mirror  10   d.    
     The traveling direction of the other light beam divided by the beam splitter  10   c  is deflected by a reflective mirror  10   e  while the frequency emitted by the wavelength-fixed laser  9  remains unchanged. The light, the frequency of which is shifted by the frequency df 2  and that, the frequency of which remains unchanged from that emitted by the wavelength-fixed laser  9 , are combined by a beam splitter  3   d.  This light beam will be referred to as a light beam  2  hereinafter. The frequency shift amount df 2  corresponds to a frequency of a beat signal of the light beam  2 , and is required to be ½ FR or less of the image sensor  7  so as to correctly obtain an interference signal. 
     The light beam  2  and the light beam  1 , the traveling direction of which is deflected by a reflective mirror  4   c,  are combined by a beam splitter  3   e,  the combined light beam is magnified by a magnifying lens  2   a,  and the magnified light beam is collimated into a parallel light beam by a collimator lens  2   b.  The parallel light beam is divided by a beam splitter  3   f  into a light beam traveling toward a reference surface  4   a  and that traveling toward the target object  5  placed on a stage  6 . 
     The light incident on the reference surface  4   a  is reflected by the reference surface  4   a,  and returns to the beam splitter  3   f  as reference light. On the other hand, the target object  5 , which is placed on the stage  6  arranged at a place separated by a distance D from a position  4   b  conjugate with the reference surface  4   a,  is irradiated with the light beam traveling toward the target object  5 . The light beam, with which the target object  5  is irradiated is reflected by the target object  5 , and returns to the beam splitter  3   f  as measurement light. The measurement light interferes with the reference light reflected by the reference surface  4   a,  and forms interference fringes on the image sensor  7 . At this time, on the image sensor  7 , interference fringes are formed by superposing a beat interference signal  1  by the light beam  1  generated by combining the light of the frequency f 1  and that of the frequency (f 1 +df 1 ), and a beat interference signal  2  generated by combining the light of the frequency f 2  and that of the frequency (f 2 +df 2 ). 
     The measurement apparatus senses the interference fringes from time t 0  shown in  FIG. 5  in this state. The measurement apparatus senses a plurality of images of interference fringes using the image sensor  7  while changing the frequency of the wavelength-variable laser  1  from f 1  to f 1′  during a period from time t 1  to time t 2 . The measurement apparatus senses a plurality of images of interference fringes using the image sensor  7  while maintaining the frequency of the wavelength-variable laser  1  at f 1′  during a period from time t 2  to time t 3 . 
     The processor  8  obtains the beat interference signal  1  from the plurality of images sensed during a period from time t 0  to t 1 . The processor  8  makes calculations such as a 4-bucket method, 13-bucket method, or discrete Fourier transformation for the beat interference signal  1  to calculate phases φ 1m,n  of respective pixels of the beat interference signal  1  of the frequency f 1  (where m is the number of a row direction of pixels of the image sensor, and n is the number of a column direction). Next, the processor  8  obtains the number of changes in beat interference signal during a frequency scan by a method of, for example, counting the numbers of bright points and dark points of interference fringes on respective pixels from the plurality of images sensed during the period from time t 1  to time t 2 , and sets interference orders M 1m,n . 
     Next, the processor  8  obtains beat interference signals  1 ′ of respective pixels from the plurality of images sensed during the period from time t 2  to time t 3 , and makes calculations such as discrete Fourier transformation to calculate phases φ 1′m,n  of the beat interference signals  1 ′ having the frequency f 1 . Then, the processor  8  calculates Z dimensions H 1m,n  using a synthetic wavelength Λ 11′  from the phases φ 1m,n  and φ 1′m,n  and the interference orders M 1m,n  calculated at respective timings using: 
       Λ 1m,n =(Λ 11′ /2){ M   1m,n +(φ 1′,n −φ m,n )/2π}  (8)
 
     where Λ 11′  is a combined frequency of the light frequencies f 1  and f 1′ , and is expressed by: 
       Λ 11′   =C/|f   1   −f   1′ |  (9)
 
     where C is a light speed. 
     Next, the processor  8  obtains the beat interference signal  2  from the plurality of images based on the wavelength-fixed laser  9 , which are sensed during the period from time t 0  to time t 3 . The processor  8  makes calculations such as a 4-bucket method, 13-bucket method, or discrete Fourier transformation to the beat interference signal  2  to calculate phases φ 2m,n  on respective pixels of the beat interference signal  2  of the frequency f 2 . The processor  8  calculates Z dimensions H 2m,n  from a synthetic wavelength Λ 1′2  from the obtained phases φ 2m,n  and the previously calculated phases φ 1′m,n  using: 
         H   2m,n =(Λ 1′2 /2){ M   2m,n +(φ 1′m,n −φ 2m,n )/2π}  (10)
 
     where Λ 1′2  is a synthetic wavelength of the light frequencies f 1′  and f 2 , and is expressed by: 
       Λ 1′2   =C/|f   1′   −f   2 |  (11)
 
     M 2m,n  are interference orders when the synthetic wavelength Λ 1′2  is used, and can be calculated by: 
         M   2m,n =round{(2 H   1m,n /Λ 11′ −(φ 1′m,n −φ 2m,n )/π}  (12)
 
     In the example of  FIG. 5 , since |f 1 −f 1′ |&lt;|f 1′ −f 2 |, the synthetic wavelength Λ 1′2  is shorter than the synthetic wavelength Λ 11′ . Therefore, the Z dimensions H 2m,n  calculated using equation (10) have higher precision than the Z dimensions H 1m,n  calculated using equation (8). 
     Also, the processor  8  calculates Z dimensions H 3m,n  using a wavelength (C/f 2 ) of the wavelength-fixed laser  9  from the light frequency f 2  of the wavelength-fixed laser  9  and the interference orders M 2m,n  calculated using equation (10) using: 
         H   3m,n =( C/ 2 f   2 ){ M   3m,n +(φ 2m,n /2π)}  (13)
 
     where M 3m,n  are interference orders, and can be calculated by: 
         M   3m,n =round{(2 H   2m,n   C/f   2 )−(φ 2m,n /2π)}  (14)
 
     In this embodiment, the wavelength (C/f 2 ) of the wavelength-fixed laser  9  is shorter than the synthetic wavelength Λ 12′ . Therefore, the Z dimensions H 3m,n  calculated using equation (13) have higher precision than the Z dimensions H 2m,n . The processor  8  measures Z dimensions at respective points on the surface of the target object  5  by the aforementioned method. The sequence of the measurement method according to the second embodiment will be described below with reference to  FIG. 2 . 
     Steps S 101  to S 103  are the same as those in the first embodiment. In step S 104 , the processor  8  obtains the interference orders from the number of changes in beat interference signal during a frequency scan at respective pixels of the image sensor  7  from a plurality of pieces of image information obtained in step S 103 , concatenates phases using the synthetic wavelength, and analyzes the Z dimensions of the target object  5 . 
     The measurement apparatus of the second embodiment performs measurements while changing the frequency of the wavelength-variable laser  1  at a change rate Δf of a frequency set according to the Z dimensions of the target object  5 , thereby quickly and simultaneously measuring Z dimensions at respective points of the target object  5 . When Z dimensions of target objects  5  of the same type are to be continuously measured, step S 101  need not be executed for the second or subsequent target object  5 , and only steps S 102  to S 104  need only be executed. 
     Third Embodiment 
     In the third embodiment, a light source which generates incoherent light is added, and a measurement apparatus sets approximate value data of Z dimensions of a target object  5 , a position, orientation, and the like of the target object  5  from images based on the incoherent light. The measurement apparatus of the third embodiment changes a frame rate of an image sensor  7  from these set data, measures the Z dimensions of the target object  5  more quickly, and also measures dimensions of a two-dimensional shape projected from the image based on the incoherent light onto an X-Y plane. 
       FIG. 6  shows the arrangement of a three-dimensional measurement apparatus of the third embodiment. The measurement apparatus further includes a light source  9 , which generates incoherent light, as a light source. A light beam emitted by the light source  9  is magnified by a magnifying lens  2   c,  and is collimated into parallel light by a collimator lens  2   d.  The traveling direction of the incoherent light collimated into the parallel light is deflected by a beam splitter  3   a,  that light passes through a beam splitter  3   b,  and strikes on the target object  5 . The incoherent light with which the target object  5  is irradiated is reflected by the target object  5 , its traveling direction is deflected by the beam splitter  3   b,  and that light is incident on the image sensor  7 . The image sensor  7  senses an image of the target object  5  formed by the incoherent light, and the processor  8  executes processing such as edge detection based on strengths of light of the obtained image to measure projected dimensions on the X-Y plane of the target object  5 . The same as in the first embodiment applies to the measurements of Z dimensions. 
       FIG. 7  shows the sequence of the measurement method according to the third embodiment. In step S 201 , pieces of information respectively for a plurality of target objects are registered in the processor  8  (registering step). Pieces of information of each target object registered in the processor  8  are as follows. 
     Information of contours of images of the target objects projected onto a surface (X-Y plane) perpendicular to the optical axis of measurement light (first information). This information is used to set a type of the target object  5  in step S 203 . 
     Known information of surface shapes (second information). This information is used to set a frequency change rate of a wavelength-variable laser  1  in step S 206 . 
     Information indicating a measurement target region of surface shapes. This information is used to set imaging conditions of the image sensor  7  in step S 205 . 
     Information of a measurement density indicating the number of points used to measure Z dimensions per unit area at measurement positions of surface shapes. This information is used to set imaging conditions of the image sensor  7  in step S 205 . 
     Information indicating measurement positions of dimensions of a two-dimensional shape on an X-Y plane. This information is used to set measurement position upon measuring dimensions of the two-dimensional shape in step S 209 . 
     The pieces of information of the target objects registered in step S 201  include those pieces of information. In step S 202 , the processor  8  obtains an image using incoherent light. More specifically, the processor  8  obtains the image by irradiating the target object  5  with incoherent light emitted by the light source  9 , and sensing reflected light by the image sensor  7 . 
     In step S 203 , the processor  8  specifies the type of the target object  5  and the position and orientation on the image sensor  7  by comparing the image obtained in step S 202  with the information of the contours of projected images of the plurality of target objects registered in step S 201  (first information) (comparing step). The processor  8  applies image processing such as edge detection to the image obtained in step S 202  to calculate the position of the target object  5  on the image sensor  7  and a contour of the projected shape. The processor  8  sets the type and orientation of the target object  5  by comparing the calculated contour of the projected shape with the information of the contours of the projected images registered in the processor  8  in step S 201 . The processor  8  checks a correlation between two contours while moving and rotating information of the contour of the projected image of the target object  5  registered in advance, as denoted by reference numeral  8   b  in  FIG. 8 , on the frame of the image sensor  7  with respect to the data of the image obtained in step S 202 . The processor  8  sets the type, position, and orientation of the target object  5  by calculating a two-dimensional projected shape, position, and orientation of the target object  5  in a state in which the contour of the projected image  8   b  overlaps a broken line portion shown in  FIG. 8 , that is, to have the highest correlation. 
     In step S 204 , the processor  8  sets known information of Z dimensions of the target object  5 , a Z-dimension measurement target region, and a Z-dimension measurement density based on the information registered in step S 201 . In step S 205 , the processor  8  sets at least one of a readout pixel region and binning as imaging conditions of the image sensor  7  from the position and orientation of the target object  5  on the image sensor  7  set in step S 203  and the Z-dimension measurement target region and measurement density set in step S 204 . Then, the processor  8  sets and changes a frame rate upon setting the readout pixel region or binning. 
     To set the readout pixel region is to set pixels from which data are to be read out on the image sensor  7 , that is, a Z-dimension measurement target region when a CMOS sensor is mainly used as the image sensor  7 . The processor  8  recognizes pixels of the image sensor  7 , on which the entire target object  5  is located, from the position of the target object  5  on the image sensor  7  set in step S 204 , that is, those of a minimum region including the entire target object  5  indicated by a bold solid line  8   c  in  FIG. 8 . When a Z-dimension measurement target region is not registered, the processor  8  sets the readout pixel region as the region  8   c,  and sets the imaging conditions of the image sensor  7  so as not to read out data of pixels other than those bounded by the bold solid line. In this manner, the number of data to be read out is reduced, thus improving the frame rate. 
     When the Z-dimension measurement target region is registered, the processor  8  recognizes pixels of the image sensor  7  on which the Z-dimension measurement target region (hatched portion  8   a ) is located from those of a minimum region including the entire target object  5 , the orientation of the target object  5 , and the Z-dimension measurement positions. Note that the orientation of the target object  5  is obtained in step S 203 , and the Z-dimension measurement target region is obtained in step S 204 . The processor  8  sets pixels of a region ( 8   d  in  FIG. 9 ) bounded by a bold sold line as a minimum region including the Z-dimension measurement positions as those from which data are to be read out, and sets the imaging conditions of the image sensor  7  so as not to read out data of pixels other than the measurement target region  8   d.  Thus, the number of data to be read out is further reduced, thus improving the frame rate. On a general CMOS sensor, although depending on a size of a limited region, a frame rate higher by several to several ten times than a case in which data of all pixels are read out can be obtained. 
     “Binning” is a method of reading out data of pixels around a certain pixel together by adding them, and reducing the number of data to be read out when a CCD sensor is mainly used as the image sensor  7 . Assume that a region as a unit of a Z-dimension measurement range of the target object  5  corresponds to four pixels of the image sensor  7 , as shown in  FIG. 10 . In this case, the processor  8  sets the imaging conditions of the image sensor  7  so as to add data of four pixels (hatched portion  10   b ) corresponding to the unit region of the Z-dimension measurement range of the target object  5  and to read out them simultaneously. Thus, the number of data to be read out is reduced, thus improving the frame rate. 
     As is known, by simultaneously reading out N×N pixels in a square region on a general CCD, a higher frame rate about N to N 2  times of a case in which data of all pixels are read out can be obtained. The processor  8  obtains a higher frame rate by setting and changing the number N of pixels to be read out together by binning based on a Z-dimension measurement density p set in step S 204  and a pixel scale S of the image sensor  7 , so as to satisfy: 
         N =round{(ρ/ S   2 ) (1/2)}   (15)
 
     where the Z-dimension measurement density ρ is the number of measurement points per unit area of the target object  5 , and round represents a function of rounding to a closest integer. The binning is effective when the Z-dimension measurement density is not so high compared to resolutions required for X and Y projected dimension measurements (for example, when only a flatness or step of the target object  5  is to be measured). 
     In step S 206 , the processor  8  sets a frequency change rate Δf of the wavelength-variable laser  1  from a maximum value OPD max  of optical path length differences of interference light between measurement light and reference light, and a frame rate FR′ of the image sensor based on: 
       Δ f ≦(FR′· C )/(8·π·OPD max )   (16)
 
     The processor  8  sets the frequency change rate to satisfy the sampling theorem as in step S 102  of the first embodiment. The maximum value OPD max  of the optical path length differences is obtained from the known information of the Z dimensions and the Z-dimension measurement target region of the target object  5  set in step S 204 . The frame rate FR′ is that when the measurement target region of the image sensor  7  or the binning set in step S 205  is set. In this embodiment, a surface of a stage on which the target object  5  is placed is arranged at a place separated by a distance D from a position  4   b  conjugate with a reference surface  4   a.  For this reason, the maximum value OPD max  of the optical path length differences can be expressed by {MAX(H)+D} using an approximate value H of the Z dimension of the target object  5  as in the first embodiment. 
     The frame rate FR′ of the image sensor  7  is faster by about several to several ten times than a case in which neither the measurement target region nor the binning is set. For this reason, although depending on the value OPD max , the frequency change rate Δf can be similarly set to be larger by about several to several ten times than the case in which neither the measurement target region nor the binning is set. Even when a target object  5  having the same approximate value of the Z dimension, but a different shape, that is, a target object  5  whose OPD max  value remains unchanged is to be measured, or when a change in OPD max  is not considered, when the frame rate of the image sensor  7  is changed, Δf is required to be changed in step S 206 . 
     In step S 207 , the processor  8  obtains Z-dimension measurement images using the image sensor  7  while changing the frequency of the wavelength-variable laser  1  based on the frame rate FR′ of the image sensor changed in step S 205  and the frequency change rate Δf of the wavelength-variable laser  1  set in step S 206 . In this embodiment, the frame rate FR is speeded up by setting the measurement target region of the image sensor  7  or the binning. For this reason, according to the third embodiment, the frequency change rate Δf of the wavelength-variable laser can be set to be still larger by about several to several ten times than the settings in step S 102  of the first and second embodiments. Hence, in the third embodiment, a measurement time can be shortened by about several to several ten times compared to the first and second embodiments. 
     In step S 208 , the processor  8  applies frequency analysis to respective pixels of the image sensor  7  from the plurality of images obtained in step S 207 , sets frequencies v m,n  of obtained interference signals, and obtains Z dimensions H m,n  of the target object  5  from the set frequencies v m,n  (where m is the number of a row direction of the image sensor, and n is the number of a column direction of the image sensor). In step S 208 , the processor  8  executes processing such as Fourier transformation to attain frequency analysis as in step S 104  of the first and second embodiments. 
     In step S 209 , the processor  8  analyzes the projected dimensions on the X-Y plane from the images obtained based on incoherent light illumination in step S 202 , the position and orientation of the target object  5  set in step S 203 , and the measurement positions of the projected dimensions on the X-Y plane. This method will be described with reference to  FIG. 11 . Reference numerals L 1  and L 2  in  FIG. 11  denote measurement positions of projected dimensions on the X-Y plane of the target object  5 . The processor  8  calculates the number of pixels between L 1  and L 2  from the position and orientation of the target object  5  on the image sensor  7  and the measurement positions of the projected dimensions on the X-Y plane. Next, the processor  8  analyzes the projected dimensions on the X-Y plane by, for example, a method of calculating L 1  and L 2  dimensions from the pixel scale S and the number of pixels between L 1  and L 2 . The precision of the projected dimensions on the X-Y plane depends on the resolution of the image sensor  7 , and is higher with increasing the number of pixels. Therefore, it is desirable to obtain images based on incoherent light using data of all the pixels of the image sensor  7  without setting the measurement target region or binning. 
     By executing steps S 201  to S 209 , the Z dimensions at respective points on the target object  5  can be simultaneously and quickly measured, and the projected dimensions on the X-Y plane can also be measured from images obtained based on incoherent light. Also, in this embodiment, since the frame rate is speeded up by several to several ten times even by setting only the measurement target region or binning, the Z dimensions can be quickly measured. In this embodiment, when data of the target objects  5  are registered once in step S 201  to perform measurements, the processing can be started from step S 202  in the next and subsequent measurements. Also, the wavelength of the light source of this embodiment may be set to be multi-wavelength to measure the Z dimensions. 
     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. 2012-053684 filed Mar. 9, 2012, which is hereby incorporated by reference herein in its entirety.