JP5936337B2 - Shape evaluation method, shape evaluation apparatus, program, and recording medium - Google Patents

Description

  The present invention relates to a shape evaluation method, a shape evaluation apparatus, a program, and a recording medium for evaluating the shape of a measured surface by fitting point data and a reference equation when measuring the shape of the measured surface.

  In recent years, optical elements having periodic steps such as diffractive optical elements and Fresnel lenses have been used in the field of optics. Therefore, in the field of shape measurement, there is an increasing need for accurately measuring the shape of an optical element having a periodic step.

  FIG. 6 is an explanatory diagram of a diffractive optical element. FIG. 6A is a perspective view of the diffractive optical element. The surface of the diffractive optical element 102 shown in FIG. 6A is a measurement target surface 102a for measuring the shape. A plurality of concentric steps are formed on the measurement surface 102a. FIG. 6B is an enlarged partial sectional view of a part of the diffractive optical element. On the measured surface 102a of the diffractive optical element 102, annular zones D0, D1, D2, D3,... And wall surfaces E1, E2, E3,. . The position of the x coordinate of the intersection of the annular surface and the outer wall surface is called a step position. As a feature of the diffractive optical element 102, the step position interval often changes. In measuring the shape of the measurement target surface 102a of the diffractive optical element 102, point data obtained by measuring the shape of the annular surface is often evaluated.

  A method for evaluating point data obtained by measuring a general optical element that does not have a step shape with a probe-type shape measuring device is known (see Patent Document 1). Hereinafter, the evaluation method will be described.

  The calculation unit of the shape evaluation apparatus acquires a plurality of point data indicating a shape measurement result obtained by measuring the shape of the measurement target surface of the measurement object. Next, the calculation unit compares each point data with the reference expression. Here, if the setting error is large, the measured point data cannot be compared with the reference equation with high accuracy. The setting error is a coordinate deviation in the translation / rotation direction between the measured point data and the reference expression. In order to reduce setting errors, a process called fitting is performed. In the fitting, the calculation unit first obtains a coordinate conversion parameter by using a design formula or the like as a reference formula. At this time, the square sum of the distance between each measured point data and the reference expression is often used as the evaluation value. When calculating the distance between each point data and the reference formula, the calculation direction such as the optical axis direction or the surface normal direction may be limited. Next, the calculation unit obtains a coordinate conversion parameter so that the evaluation value becomes small using a steepest descent method or the like. The coordinate conversion parameters are six parameters of three translation axes and three rotation axes that correct the translation of the reference formula and measurement data and the deviation in the rotation direction. Next, the calculation unit performs coordinate conversion of each point data using the coordinate conversion parameter. The process of obtaining the coordinate conversion parameters and converting the coordinates is repeated until the evaluation value stops. As a result, the point data and the reference formula are best applied. As described above, the fitting is a process of performing coordinate conversion for the purpose of best fitting each measured point data and the reference expression. The calculation unit outputs difference data relating to the difference (residual) between the fitted point data and the reference expression as an evaluation result to an external device or the like.

  In the manufactured optical element, a shape error may occur due to heat shrinkage or the like. The shape error appears as a deviation of the coefficient of the reference equation. Therefore, when fitting, the coefficient may be changed and applied from the difference between the shape of the reference equation and the measured point data. When the coefficient is changed, coefficient data related to the coefficient is output as an evaluation result to an external device or the like.

JP 2010-32473 A

  However, when the conventional shape evaluation method is applied to the surface to be measured on which the steps are repeatedly formed, the point data may be mistaken as point data for an annular surface that is not an actual annular surface. There was a problem that the fitting of the data and the reference expression could not be performed with high accuracy.

  Hereinafter, a specific description will be given with reference to FIG. FIG. 7 is a diagram comparing reference formula data corresponding to a surface to be measured in which steps are repeatedly formed and measured point data. Here, it is assumed that the xz coordinate system in FIG. 7 is a two-dimensional Cartesian coordinate system of a measurement data coordinate system or a reference type coordinate system with the z axis as the optical axis direction. As shown in FIG. 7A, the point data 1 may be displaced in the x-axis direction with respect to the reference expression 3 due to a setting error or a shape error. As a result, among the plurality of point data 1, there is point data (hereinafter referred to as correspondence deviation data) 715 indicated by a black circle, which is mistakenly recognized as being in the adjacent annular zone surface in the reference expression 3. Note that point data on the correct ring zone surface (hereinafter referred to as correspondence data) is indicated by white circles.

  The ratio of correspondence deviation data to correspondence data increases as the annular zone area decreases. For example, in FIG. 7A, the correspondence deviation data has three points on each annular zone surface, but the correspondence data has seven points in the portion where the annular zone area is relatively large, whereas the correspondence zone data has a relatively large annular zone area. The smaller portion has three points, and the smaller the ring area, the larger the ratio of correspondence deviation data to correspondence data.

  FIG. 7B is a diagram showing the magnitude of the difference (residual) in the optical axis direction between the point data and the reference expression. When the residual between the correspondence error data 715 shown in FIG. 7A and the reference expression 3 is calculated, residual data 82 having a large error is included as shown in FIG. 7B. If the residual data 82 having a large error is included in the fitting evaluation value, the fitting accuracy decreases.

  In particular, since the ratio of the correspondence deviation data to the correspondence data is small in the portion where the ring zone area is relatively large, the influence on the reduction of the fitting accuracy is small. However, since the ratio of the correspondence deviation data to the correspondence data is large in the portion where the ring zone area is relatively small, the influence on the reduction of the fitting accuracy is great. Therefore, since the non-measurement surface on which the annular surface is repeatedly formed includes an annular surface having a small area, the conventional method cannot perform fitting accurately.

  Therefore, an object of the present invention is to improve the fitting accuracy and accurately evaluate the shape.

In the shape evaluation method of the present invention, the calculation unit refers to the surface to be measured having a plurality of band surfaces, in which a band surface and a wall surface extending in a direction intersecting the band surface are alternately connected and formed in a step shape A point data extraction region setting step for setting a point data extraction region that is a range excluding a peripheral region of a portion corresponding to the connection portion with the wall surface with respect to a reference surface indicating one band surface in the equation; An extraction step in which the calculation unit extracts point data included in the point data extraction region from point data indicating the shape measurement result of the surface to be measured, and points extracted by the calculation unit in the extraction step A calculation step for obtaining a coordinate transformation parameter for fitting data to a reference surface in the point data extraction region, and point data indicating the shape measurement result of the surface to be measured by using the coordinate transformation parameter Fittin A correction step of correcting the point data, the calculation unit, when the reference surface adjacent the outside of the point data extraction area to the reference surface of the point data extraction area is present, with respect to the reference surface of the adjacent The point data extraction region is set to expand the extraction range of the point data, and the extraction range expansion step returns to the extraction step, and the calculation unit includes the point data on the reference plane in the point data extraction region. When there is no adjacent reference surface outside the extraction region, the difference data between the point data indicating the shape measurement result of the corrected surface to be measured at that time and the reference formula is obtained as the shape of the surface to be measured. An evaluation step of outputting as an evaluation result.

  According to the present invention, the process of extracting and fitting the point data in the point data extraction area is repeated while sequentially expanding the point data extraction range, so that the corresponding deviation data is used as the point data used when obtaining the coordinate conversion parameters. Extraction is suppressed. Thereby, since fitting accuracy improves, the shape of a to-be-measured surface can be evaluated accurately.

It is explanatory drawing which shows schematic structure of the shape measuring apparatus in which the shape evaluation apparatus which concerns on embodiment of this invention is integrated. It is a block diagram which shows the structure of a shape evaluation apparatus. It is a flowchart for demonstrating the processing operation by CPU of a shape evaluation apparatus. It is a schematic diagram for demonstrating the fitting process operation | movement by CPU. (A) is a figure for demonstrating the process which sets a point data extraction area | region. (B) is a figure which shows the state which performed the correction | amendment of the effective measurement data and the correction | amendment of the coefficient of each reference surface by the calculated coordinate transformation parameter and the correction amount of the coefficient. (C) is a figure which shows the state which correct | amended point data and the coefficient of each reference surface. (D) is a figure which shows the state which expanded the extraction range of point data by setting a point data extraction area | region with respect to an adjacent reference surface. It is a figure for demonstrating the extraction process in an extraction process, (a) is a figure which shows point data, (b) is a figure which shows effective measurement data. It is explanatory drawing of a diffractive optical element, (a) is a perspective view of a diffractive optical element, (b) is the fragmentary sectional view which expanded a part of diffractive optical element. It is the figure which compared the data of the reference type corresponding to the to-be-measured surface in which the level | step difference was repeatedly formed, and the measured point data. (A) is a schematic diagram showing reference formula data and point data, and (b) is a schematic diagram showing a residual between the reference formula data and point data.

  Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the drawings. FIG. 1 is an explanatory diagram showing a schematic configuration of a shape measuring device in which a shape evaluation device according to an embodiment of the present invention is incorporated. The shape measuring apparatus 100 measures the shape of the surface to be measured 102a using the surface of the optical element 102 as the object to be measured as the surface to be measured 102a. The shape measuring apparatus 100 includes a contact probe 101 and a surface plate 103 on which an optical element 102 is placed. The shape measuring apparatus 100 includes a mirror or the like, and includes an interferometer 104 attached to the rear end of the probe 101 and a linear guide 105 that supports the probe 101 so as to be movable in the vertical direction. The surface plate 103 is preferably provided with a vibration isolation function in order to suppress the influence of vibration from the floor. Interferometer 104 measures the three-dimensional position of probe 101.

  In addition, the shape measuring apparatus 100 includes a force generator 106 that is attached to the linear guide 105, compensates the weight of the probe 101, and presses the probe 101 against the measurement target surface 102a of the optical element 102 with a specified force. In addition, the shape measuring apparatus 100 includes a stage 108 attached to the linear guide 105 via a housing 107, and a driving device 109 attached to the stage 108. The driving device 109 moves the stage 108 in the three-axis translation direction. Accordingly, the shape of the surface to be measured 102 a is measured by scanning the surface to be measured 102 a of the optical element 102 using the probe 101.

  In addition, the shape measuring apparatus 100 includes a data sampling apparatus 110 that is connected to the interferometer 104 and samples measurement data indicating the three-dimensional position of the probe 101 at a specified predetermined time interval. The shape measuring apparatus 100 includes a shape evaluation apparatus 111 that is connected to the data sampling apparatus 110 and includes a computer that acquires point data indicating the shape measurement result sampled from the data sampling apparatus 110 and processes the data. The shape evaluation device 111 acquires a plurality of point data (discrete data) sampled by the data sampling device 110, and uses these discrete data for evaluation of the shape of the measured surface 102a.

  In this embodiment, the optical element 102 is a rotationally symmetric diffractive optical element, and this surface is used as the measurement surface 102a. In FIG. 1, the surface to be measured 102 a includes a ring surface D 0, D 1, D 2, D 3, which is a band surface, and a wall surface (step difference) extending in a direction intersecting the ring surfaces D 0, D 1, D 2, D 3,. Surfaces) E1, E2, E3,... Are alternately connected to form a step. Here, the outer shape of the measured surface 102a is circular in plan view. And the circular ring surface D0 located in the center of the to-be-measured surface 102a is called a central ring surface, and the ring-shaped ring formed across the wall surface from the central ring surface D0 toward the radial direction outer side. The band surfaces D1, D2, D3,... Are referred to as a first ring surface, a second ring surface, a third ring surface,. And in this embodiment, the area of central ring zone surface D0 is the largest among several ring zone surfaces D0, D1, D2, D3, ..., and goes to the radial direction outer side from central ring zone surface D0. The ring zone surface is formed to have a small area. That is, it is formed so that the area of the annular zone surface D0> the area of the annular zone surface D1> the area of the annular zone surface D2> the area of the annular zone surface D3>.

  On the surface to be measured 102a, the annular surface and the wall surface intersect with each other to form peaks F1, F2, F3,... And valleys G1, G2, G3,. And step part is between ring zone surface D0, D1, D2, D3 ... by wall surface E1, E2, E3, ..., peak part F1, F2, F3, ... and trough part G1, G2, G3, .... H1, H2, H3,... Are formed.

  The probe 101 is scanned so as to be approximately orthogonal to the peaks F1, F2, F3,... And the valleys G1, G2, G3,. Here, if the probe 101 is scanned in a direction that goes up the wall surfaces E1, E2, E3,..., The probe 101 may collide with the wall surfaces E1, E2, E3,. , E3,...

  FIG. 2 is a block diagram showing a configuration of the shape evaluation apparatus 111. The shape evaluation apparatus 111 is a computer including a CPU 130 as a calculation unit, a ROM 131, a RAM 132, an HDD 133, a recording disk drive 134, and various interfaces 135, 136, and 137.

  These ROM 131, RAM 132, HDD 133, recording disk drive 134, and various interfaces 135, 136, and 137 are connected to the CPU 130 via a bus 138.

  The ROM 131 stores a program 150 for operating the CPU 130. The CPU 130 executes various processes based on the program 150 stored in the ROM 131. The RAM 132 is for temporarily storing the processing result of the CPU 130. The HDD 133 is a storage device, and stores in advance a reference expression that is a design expression of the measurement target surface 102 a of the optical element 102. That is, the reference formula represents an ideal shape of the measured surface 102a of the optical element 102.

  The data sampling device 110 is connected to the interface 135, and a plurality of point data from the data sampling device 110 are output to the bus 138. The HDD 133 stores calculation results, point data, and the like by the CPU 130 under the instruction of the CPU 130.

  The monitor 140 is connected to the interface 136, and various images are displayed on the monitor 140. The interface 137 is configured such that an external storage device 141 such as a rewritable nonvolatile memory or an external HDD can be connected. The recording disk drive 134 can read various data recorded on the recording disk 142.

  FIG. 3 is a flowchart for explaining the processing operation by the CPU 130 of the shape evaluation apparatus 111. FIG. 4 is a schematic diagram for explaining the fitting processing operation by the CPU 130. The CPU 130 executes each process shown in FIG. 3 by executing the program 150 stored in the ROM 131. Hereinafter, each step shown in FIG. 3 will be described.

  The CPU 130 starts processing, and acquires a plurality of point data 1 as shown in FIG. 4A from the data sampling device 110 as data obtained by measuring the shape of the measurement target surface 102a (S101). The point data 1 is stored (stored) in the HDD 133 as a storage device by the CPU 130. Let point data 1 be {p}. As shown in FIG. 4A, the reference formula 3 is obtained from a plurality of reference surfaces 30, 31, 32, 33,... Corresponding to a plurality of annular surfaces D0, D1, D2, D3,. Become. The reference formula is defined by a polynomial.

The point data 1 is position information represented by a three-dimensional orthogonal coordinate system of the shape measuring apparatus 100, and is a coordinate system different from the three-dimensional orthogonal coordinate system of the reference formula 3 stored in the HDD 133. That is, the position / posture of the measured surface 102a does not necessarily match the reference formula position / posture due to setting errors. Therefore, when evaluating the shape of the measurement target surface 102a, it is necessary to convert the point data 1 into a reference coordinate system, that is, fitting. When the coordinate transformation matrix composed of the coordinate transformation parameters is [T], the data {q} after coordinate transformation can be expressed in the form of multiplication of {p} and [T].
{Q} = [T] {p} (1)

  Further, the manufactured optical element 102 may have a shape error due to heat shrinkage or the like. Considering this influence, the coefficient of the reference formula is changed at the time of fitting.

  First, as shown in FIG. 4A, the CPU 130 sets the point data extraction area 20A (S102: point data extraction area setting step). At that time, the CPU 130 sets the range including the reference surface 30 as the designated region 22 and sets the range within the designated region 22 and outside the peripheral region 21A as the point data extraction region 20A. That is, the point data extraction area 20A corresponds to a valley portion G1 that is a connection portion between the annular zone surface D0 and the wall surface E1 with respect to the reference surface 30 indicating one annular zone surface D0 in the reference expression 3. The range excluding the peripheral area 21A of 30A.

  In the present embodiment, the CPU 130 sets the point data extraction region 20A for the reference surface 30 corresponding to the central annular zone surface D0 having the largest area among the plurality of annular zone surfaces. That is, the point data extraction region 20A is set in the region of the reference surface 30 of the central annular surface D0 where the number of point data 1 is larger than the other annular surfaces.

  The peripheral region 21A is a portion 30A corresponding to the valley portion G1 (FIG. 1), that is, a range including the end portion of the reference surface 30, and takes into account the amount of deviation of the step position between the reference surface 30 and the measured point data 1. Determined. As a guideline, it is good to consider the processing error of the object to be measured, the holding error, the measurement error due to the size of the probe tip, and the error at the time of fitting. In addition, it is preferable that this peripheral region 21A also includes a portion 31B corresponding to the mountain portion F1 (FIG. 1). That is, the peripheral region 21A is preferably a region including a portion 41 corresponding to the stepped portion H1 (FIG. 1) between the annular zone surface D0 and the adjacent annular zone surface D1.

  The peripheral region 21B is a region including a portion 31A corresponding to the valley portion G2, and preferably includes a portion 32B corresponding to the peak portion F2, that is, a region including the portion 42 corresponding to the stepped portion H2. Is good. Further, the peripheral region 21C is a region including a portion 32A corresponding to the valley portion G3, and preferably includes a portion 33B corresponding to the peak portion F3, that is, a region including the portion 43 corresponding to the stepped portion H3. Is good.

  As described above, the CPU 130 sets the peripheral areas 21A, 21B, 21C,... Of all the steps as the operation for setting the point data extraction area 20A, and sets the designated area 22 as the outer peripheral portion 30A of the reference plane 30. The range is set and the point data extraction area 20A is obtained.

  Next, the CPU 130 executes an extraction process for extracting point data included in the point data extraction area 20A from the plurality of point data 1 (S103: extraction step). Hereinafter, the extracted point data is referred to as effective measurement data 1A (FIG. 4B).

  The CPU 130 executes a calculation process for obtaining a coordinate conversion parameter for fitting the effective measurement data 1A extracted in step S103 to the reference plane 30 in the point data extraction area 20A (S104: calculation step). Further, the CPU 130 further obtains a correction amount of a coefficient indicating the curvature component of each reference surface so that the effective measurement data 1A is fitted to the reference surface 30 in the point data extraction region in the calculation process of step S104.

  In the present embodiment, the CPU 130 obtains the sum of squares of the difference (residual) between the reference expression 3 and the effective measurement data 1A, and uses the steepest descent method to calculate the coordinate conversion parameter and the coefficient correction amount so that the sum of squares becomes small. Ask for. FIG. 4B shows a state in which the correction of the effective measurement data 1A and the correction of the coefficient of each reference surface are performed using the coordinate conversion parameter and the correction amount of the coefficient obtained in step S104.

  Next, the CPU 130 executes a correction process for correcting by fitting the plurality of point data 1 to the reference expression 3 using the coordinate conversion parameter obtained in step S104 (S105: correction process). That is, the CPU 130 performs coordinate conversion of the plurality of point data 1 using the coordinate conversion parameter obtained in step S104. As a result, the point data 1 stored in the HDD 133 is changed to the corrected point data 1.

  Further, the CPU 130 further corrects the coefficients of the respective reference surfaces 30, 31, 32, 33,... With the correction amount obtained in step S104 in the correction process of step S105. Thereby, the coefficient of each reference surface of the reference formula stored in the HDD 133 is changed to the corrected coefficient. FIG. 4C shows a state where the correction of the point data 1 and the correction of the coefficients of each reference surface are performed in step S105.

  Next, the CPU 130 executes a determination process for determining whether or not to expand the point data extraction range (S106: determination step).

  The case where the point data extraction range is expanded is a case where an adjacent reference surface outside the point data extraction region exists on the reference surface within the point data extraction region. In other words, this is a case where there is a reference surface that is adjacent to the reference surface inside the point data extraction region and has no point data extraction region set outside the point data extraction region. In FIG. 4A, a reference plane 30 exists in the point data extraction area 20A, and the reference plane 31 is outside the point data extraction area 20A and adjacent to the reference plane 30 in the point data extraction area 20A. Exists.

  The case where the point data extraction range is not expanded is a case where there is no adjacent reference surface outside the point data extraction region on the reference surface within the point data extraction region. That is, this is a case where there is no reference plane outside the point data extraction area, which is adjacent to the reference plane inside the point data extraction area and in which the point data extraction area is not set.

  If the CPU 130 determines that the point data extraction range is to be expanded (S106: Yes), the point data extraction region is set for the adjacent reference plane to expand the point data extraction range (S107), and the extraction in step S103 is performed. Return to the process (extraction range expansion process). For example, the CPU 130 sets a point data extraction region 20B for the reference surface 31 adjacent to the reference surface 30 as shown in FIG. Specifically, the CPU 130 expands the designated area 22 to the outer peripheral portion 31 </ b> A of the reference surface 31 so as to include the reference surfaces 30 and 31. Since the peripheral areas 21A and 21B are excluded, a point data extraction area 20A corresponding to the reference plane 30 and a point data extraction area 20B corresponding to the reference plane 31 are set, and the point data extraction range is expanded. That is, the CPU 130 has, as the point data extraction region 20B, the peripheral region 21A of the portion 31B corresponding to the mountain portion F1 that is the connection portion between the annular surface D1 and the wall surface E1, and the connection portion between the annular surface D1 and the wall portion E2. A range excluding the peripheral region 21B of the portion 31A corresponding to the valley portion G2 is set.

  And CPU130 performs the extraction process of step S103, the calculation process of step S104, and the correction process of step S105 again by returning to step S103. At this time, in step S103, the CPU 130 extracts point data included in the point data extraction areas 20A and 20B from the point data 1 corrected in the previous routine. In step S104, the CPU 130 obtains coordinate conversion parameters for fitting the point data extracted by the extraction process to the reference planes 30 and 31 in the point data extraction areas 20A and 20B. In step S105, the CPU 130 fits and corrects the point data 1 using the coordinate conversion parameter obtained by the calculation process.

  By repeating the above steps S106, S103, S104, and S105, the range of the point data extraction area is gradually expanded. FIG. 5 is a diagram for explaining the extraction process in step S103. The designated region 22 extends to the reference surface 33 (fourth step position) of the reference formula 3. For the point data 1 shown in FIG. 5A, effective measurement data 1A is extracted as shown in FIG. 5B.

  By repeating the above steps S106, S103, S104, S105, the point data extraction regions 20A, 20B,... Are finally set corresponding to all the reference planes 30, 31,. Then, the CPU 130 extracts point data in the point data extraction area when the extraction range is set to be expanded on all the reference planes 30, 31,..., Obtains a coordinate conversion parameter using the extracted point data, and performs this coordinate conversion. The point data 1 is fitted to the reference formula 3 with parameters. Thereafter, the CPU 130 determines that the point data extraction range is not expanded because the designated area 22 includes all the reference planes 30, 31,.

  If the CPU 130 determines not to expand the extraction range of the point data (S106: No), the CPU 130 evaluates the difference data regarding the difference between each corrected point data 1 and the reference expression 3 at that time and evaluates the shape of the measurement target surface 102a. The result is output (S108: evaluation step). Then, the process ends. As the difference data, any data relating to a difference value such as a difference value between each point data 1 and the reference expression 3, an absolute value of the difference value, a square value of the difference value, a sum of squares of the difference value, or the like may be used. Good. Note that the case where it is determined not to expand the point data extraction range is a state in which the point data extraction area is set corresponding to each reference plane, so the points adjacent to the reference plane in the point data extraction area This is a case where the reference plane outside the data extraction area no longer exists. At this time, the CPU 130 further outputs coefficient data relating to the coefficient corrected in the reference equation as an evaluation result of the shape of the measured surface 102a. The coefficient data may be a corrected coefficient value or a correction amount obtained by correcting the coefficient.

  Data indicating these evaluation results is output from the CPU 130 to an internal device or an external device. The internal device is, for example, the HDD 133. Also, as the external device, all devices such as a monitor 140, an external storage device 141, and a processing device (not shown) that processes the optical element 102 are assumed.

  As described above, in the present embodiment, the process of extracting and fitting the point data in the point data extraction area is repeated while sequentially expanding the point data extraction range. This is because the uncorrected point data 1 obtained from the data sampling device 110 has a large setting error, and when the optical element 102 is deformed such as heat shrinkage, the shape error is also large. .

  Temporarily, the area excluding the peripheral areas 21A, 21B, 21C,... Corresponding to all the stepped portions H1, H2, H3,. In some cases, correspondence error data may not be completely removed. For example, in FIG. 4A, the measurement data of the second and third zones in the positive x-axis direction are in a state of protruding to the x coordinate of the first and second zones of the reference expression, respectively. . The point data 1 in the protruding range is correspondence deviation data that is not removed. It is conceivable to extract the effective measurement data 1A by taking a wide area around the steps 21A, 21B, 21C,..., But the range used for fitting is reduced accordingly. This makes it impossible to fit with high accuracy.

  On the other hand, in the present embodiment, in the first fitting process, data used for fitting is extracted from the region of the reference surface 30 indicating one annular surface D0 excluding the peripheral region 21A of the stepped portion H1. The point data extraction area 20A to be set is set. Based on the extracted effective measurement data 1A, coordinate correction parameters and coefficient correction amounts are obtained, and the point data 1 is corrected by fitting so that the plurality of point data 1 approaches the position / posture of the reference expression. Further, the shape of the reference equation can be brought closer to the actual distortion of the measured surface 102a by correcting the coefficient.

  For example, before the first fitting, as shown in FIG. 4A, correspondence shift data existed in the region of the reference surface 31 corresponding to the annular surface D1 adjacent to the annular surface D0. However, as a result of the first fitting, as shown in FIG. 4 (d), correspondence error data is detected in the point data extraction area 20B set for the reference surface 31 corresponding to the annular surface D1 adjacent to the annular surface D0. It is gone. That is, in the area of the reference surfaces 30, 31, 32, 33,... Corresponding to each annular surface, the ratio of the correspondence deviation data can be reduced by this fitting.

  Then, the point data extraction range is expanded with respect to the reference surface indicating the adjacent annular surface in a state where the influence of the setting error and the shape error is reduced by the fitting, and the point data extraction range is expanded similarly. The process of correcting the point data 1 is repeated. Therefore, since the point data extraction region is gradually set in the reference surface region where the ratio of the correspondence deviation data is reduced and the extraction range is expanded, the point data 1A used when obtaining the coordinate conversion parameters is supported. Extraction of deviation data is suppressed. Further, since the coefficient of each reference surface of the reference equation is also corrected, it is possible to suppress the correspondence deviation data from being extracted even if there is a distortion such as thermal contraction of the surface to be measured 102a. Thereby, since fitting accuracy improves, the shape of a to-be-measured surface can be evaluated accurately.

  In this embodiment, the point data extraction region is set from the region of the reference surface 30 corresponding to the central annular surface D0 having the largest area, that is, the largest number of point data 1. . As described above, since the effective measurement data 1A having a large number of point data 1 is extracted and fitting is performed, in this ring zone D0, the ratio of the correspondence deviation data to the corresponding data is the other ring zone surface. The first fitting can be performed with high accuracy. Thus, since the first fitting can be performed with high accuracy, it is possible to perform with high accuracy in the next and subsequent fittings.

  In this embodiment, the point data extraction regions are set in descending order of the area of the annular zone surface. Specifically, the point data extraction regions are sequentially set such that the reference surface 31 follows the reference surface 30 and the reference surface 32 follows the reference surface 31. As a result, as fitting errors and shape errors become smaller, point data fitting is performed on a reference surface showing an annular surface with a gradually smaller area, so that the accuracy of fitting can be improved more effectively. it can.

  The present invention is not limited to the embodiments described above, and many modifications can be made by those having ordinary knowledge in the art within the technical idea of the present invention.

  In the above embodiment, the case where the design formula is used as the reference formula has been described. However, the present invention is not limited to this, and the result of measuring the standard sample may be used as the reference formula. Here, it is assumed that the design formula of the standard sample is the same as the design formula of the object to be measured. As a result, the same effect can be obtained as when the design formula is used as a reference formula.

  In the above embodiment, the point data extraction region 20A is set on the reference surface 30 corresponding to the central annular surface D0 in step S102. However, the point data extraction region is set on the reference surface corresponding to a predetermined reference surface. It may be set. Here, the reference plane is a plane where the measured point data 1 and the reference formula 3 are combined, and a contact surface of the object to be measured, an edge surface, a mark, or the like can be considered. The closer to the reference plane, the smaller the setting error and the shape deviation in the rotation direction, and the smaller the proportion of correspondence deviation data. Therefore, the point data extraction region can be expanded from the end of the object to be measured or from the vicinity of the mark, not from the reference surface 30 corresponding to the central annular surface.

  In the above embodiment, uncorrected point data 1 obtained from the data sampling device 110 is used in the first fitting in steps S103 and S104. However, previously corrected point data 1 may be used. Specifically, all the point data 1 may be previously fitted to the reference equation 3 and corrected between step S101 and step S102. In this fitting, since all point data is used, fitting is performed with low accuracy using the correspondence error data, but the proportion of the correspondence error data can be reduced.

  In the above embodiment, the case where the coordinate transformation parameter and the correction amount of the coefficient are obtained by the steepest descent method in step S104 has been described. However, it may be obtained by the bisection method or the GA method, and the same effect as the above embodiment is obtained. can get.

  In the above embodiment, the case has been described in which the range of the set peripheral areas 21A, 21B, 21C,... Is kept constant and the point data extraction area is enlarged by enlarging the designated area 22. However, the present invention is not limited to this. For example, in step S102, the designated area is the entire measurement surface (the entire reference expression), and the areas 21A, 21B, and 21B to be excluded so that the area excluding the portion 30A corresponding to the connection portion of the reference surface 30 becomes the point data extraction area. The width of 21C,... May be set. Then, each time step S107 is repeated, the width of the excluded regions 21A, 21B, 21C,... May be changed so that the gradual point data extraction region is set to the reference surface of the adjacent annular surface. When the widths of these areas 21A, 21B, 21C,... Reach a predetermined width, the change may be finished. The predetermined width may be set in consideration of the point data sampling interval or more when the regions 21A, 21B, 21C,. As a result, the same effect as in the above embodiment can be obtained.

  Moreover, although the said embodiment demonstrated the case where a point data extraction area | region was set by setting a designated area | region and a periphery area | region, it is not limited to this. The data of the point data extraction area may be stored in advance in the HDD 133 which is a storage device, and the CPU 130 may read the data and set the point data extraction area.

  In the above embodiment, the case where the object to be measured is a rotationally symmetric diffractive optical element has been described. However, the present invention is not limited to this, and the diffractive optical element has an elliptical shape in which an annular surface and a wall surface are alternately continuous. A straight parallel shape in which the belt surface and the wall surface alternately continue may be used. Further, it can also be applied to a Fresnel lens having a periodic step shape like the diffractive optical element. Further, it may be a molding die for manufacturing these optical elements, and may be an object to be measured other than these as long as it has a periodic step on the surface to be measured.

  Further, in the above embodiment, the case where the contact type probe is scanned along the surface to be measured to acquire the point data has been described, but the present invention is applicable even when a non-contact type probe is used. is there. Moreover, it is not limited to the case where the surface shape of the surface to be measured is measured using a probe, but may be a case where an interferometer is used to obtain data using a sensor such as a CCD or CMOS.

  In the above embodiment, the case where the coefficient of the reference equation is also corrected has been described. However, this correction process may be omitted as necessary. For example, the case where the object to be measured is not deformed due to heat shrinkage or the like has a small influence on the shape evaluation is omitted. In this case, the calculation process for obtaining the coefficient correction amount is omitted in step S104, the correction process for correcting the coefficient of the reference equation is omitted in step S105, and the process of outputting coefficient data is performed in step S108. It can be omitted.

  In the above embodiment, the point data obtained by the measurement by the shape measuring apparatus has been described. However, the point data indicating the shape of the surface to be measured obtained by ray tracing calculation, finite element calculation, or the like is considered in the same manner. be able to.

  In the above embodiment, the point data or the like is stored in the HDD 133 as a storage device. However, the storage device is not limited to the HDD 133, and any storage device may be used as long as it is a writable storage device. For example, the storage device may be a RAM 132, an external storage device 141 (for example, a rewritable nonvolatile memory such as a USB memory or a memory card, an external HDD), or a recording disk 142 installed in the recording disk drive 134. . The recording disk 142 may be any recording disk as long as it is a writable recording disk such as a CD-R. In addition to these, for example, a flexible disk, an optical disk, a magneto-optical disk, a magnetic tape, an EEPROM, a silicon disk, and the like may be used.

  In the above embodiment, the case where the computer-readable recording medium on which the program is recorded is the ROM 131 is described. However, the present invention is not limited to this, and any recording medium can be used as long as it is a computer-readable recording medium. There may be. For example, the program may be recorded on the HDD 133, the external storage device 141, the recording disk 142, or the like. For example, a non-volatile memory such as a USB memory or a memory card, an external HDD, or the like can be used as the external storage device 141, and a CD-ROM, CD-R, or DVD-ROM can be used as the recording disk 142, for example. Can do. In addition to these, for example, a flexible disk, an optical disk, a magneto-optical disk, a magnetic tape, an EEPROM, a silicon disk, and the like may be used.

  Further, a computer-readable recording medium in which a program code of software that realizes the functions of the above-described embodiments may be supplied to the system or apparatus. The object of the present invention is also achieved by the computer (or CPU or MPU) of the system or apparatus reading and executing the program code stored in the recording medium. In this case, the program code itself read from the recording medium realizes the function of the present invention, and the recording medium on which the program code is recorded constitutes the present invention.

  Further, the program in the above embodiment may be downloaded via a network and executed by a computer.

  Further, the present invention is not limited to the implementation of the functions of the above-described embodiment by executing the program code read by the computer. This includes a case where an OS (operating system) or the like running on the computer performs part or all of the actual processing based on the instruction of the program code, and the functions of the above-described embodiments are realized by the processing. .

  Furthermore, the program code read from the recording medium may be written in a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer. This includes a case where the CPU of the function expansion board or function expansion unit performs part or all of the actual processing based on the instruction of the program code, and the functions of the above embodiments are realized by the processing.

DESCRIPTION OF SYMBOLS 1 ... Point data, 3 ... Reference formula, 20A, 20B ... Point data extraction area | region, 21A, 21B, 21C ... Peripheral area | region, 30, 31, 32, 33 ... Reference surface, 100 ... Shape measuring apparatus, 111 ... Shape evaluation apparatus , 130 ... CPU (calculation unit), 150 ... program

Claims (5)

One of the reference expressions of the surface to be measured, wherein the calculation unit is formed in a stepped shape by alternately connecting the band surface and the wall surface extending in the direction intersecting the band surface, and has a plurality of the band surfaces. A point data extraction region setting step for setting a point data extraction region that is a range excluding the peripheral region of the portion corresponding to the connection portion with the wall surface with respect to the reference surface indicating
An extraction step in which the arithmetic unit extracts point data included in the point data extraction region from point data indicating the shape measurement result of the surface to be measured;
A calculation step for obtaining a coordinate transformation parameter for fitting the point data extracted in the extraction step to a reference plane in the point data extraction region by the arithmetic unit;
A correction step for correcting the point data by fitting the point data indicating the shape measurement result of the surface to be measured using the coordinate conversion parameter;
When there is an adjacent reference surface outside the point data extraction region on the reference surface in the point data extraction region, the calculation unit sets the point data extraction region for the adjacent reference surface and sets the point An extraction range expansion step of expanding the data extraction range and returning to the extraction step;
When the calculation unit no longer has an adjacent reference surface outside the point data extraction region on the reference surface in the point data extraction region, the corrected shape measurement result of the surface to be measured at that time is indicated. An evaluation step of outputting difference data between point data and the reference formula as an evaluation result of the shape of the surface to be measured, and
A shape evaluation method characterized by that. In the calculation step, the calculation unit further calculates a correction amount of a coefficient indicating a curvature component of each reference surface so that the point data extracted in the extraction step fits to the reference surface in the point data extraction region. ,
In the correction step, the calculation unit further corrects the coefficient with the correction amount,
In the evaluation step, the calculation unit further outputs the corrected coefficient data as an evaluation result of the shape of the surface to be measured.
The shape evaluation method according to claim 1. An arithmetic unit that evaluates the shape of the surface to be measured from point data indicating the shape measurement result of the surface to be measured formed in steps by alternately connecting the belt surface and the wall surface extending in the direction intersecting the belt surface In the shape evaluation apparatus comprising
The computing unit is
Set a point data extraction region that is a range excluding a peripheral region of a portion corresponding to the connection portion with the wall surface, with respect to a reference surface indicating one band surface in the reference expression of the surface to be measured,
An extraction process for extracting point data included in the point data extraction area from the point data indicating the shape measurement result of the surface to be measured, and the point data extracted by the extraction process in the point data extraction area A calculation process for obtaining a coordinate transformation parameter to be fitted to a reference surface, and using the coordinate transformation parameter obtained in the calculation process, the point data indicating the shape measurement result of the surface to be measured is fitted to correct the point data. Correction processing to be executed,
When there is an adjacent reference surface outside the point data extraction region on the reference surface in the point data extraction region, the point data extraction region is set for the adjacent reference surface to set the point data extraction range. Enlarging and executing the extraction process, the calculation process, and the correction process again,
Point data indicating the shape measurement result of the measured surface corrected at that time when there is no adjacent reference surface outside the point data extraction region on the reference surface in the point data extraction region and the reference Output the difference data from the equation as an evaluation result of the shape of the measured surface,
A shape evaluation apparatus characterized by that.   The program for making a computer perform each process of the shape evaluation method of Claim 1 or 2.   The computer-readable recording medium which recorded the program of Claim 4.

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