JP5275853B2 - Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a surface shape measurement machine, a measurement method, and a method of analyzing a surface shape measurement value capable of precisely measuring an error of a contour shape in a short time without setting as an object the entire range of a symmetrical effective diameter across an axis in the measurement of the contour shape of an aspherical surface of an aspherical member that is rotationally symmetrical about the axis. <P>SOLUTION: In a range M asymmetrical across the axis A, the contour shape of an aspherical surface is measured from a prescribed position at one side of the axis A to another prescribed position at the other side, and the measurement value of the contour shape of the aspherical surface in the range M is used to be complemented in a prescribed range at the other side across the axis A for which the measurement value is not obtained as a tentative measurement value. Next, in the total range of the asymmetrical range across the axis A and the range complemented with the tentative measurement value, a convergence calculation is performed by using the measurement value, the tentative measurement value, and a design value of the contour shape of the aspherical surface until a prescribed convergence condition is satisfied to calculate the error of the contour shape of the aspherical surface. <P>COPYRIGHT: (C)2010,JPO&amp;INPIT

Description

  The present invention relates to a surface shape measuring machine, a surface shape measuring method, and a surface shape measurement value analysis method.

  A surface shape measuring machine is used to measure and evaluate the surface shape of an optical element, its mold, and parts. In particular, when the object to be measured is a member having an aspherical surface that is rotationally symmetric about an axis (hereinafter referred to as an aspherical member), the overall shape of the aspherical surface is the contour shape on one side from the axis. It becomes substantially equal to the shape rotated once as the center.

Generally, the aspherical member is processed through a rotary processing machine such as a lathe. The rotary machine rotates the work piece around the axis and moves the work piece in a rotationally symmetric aspherical shape by moving the work piece in the axial direction and the rotation radius direction while applying the blade to the work piece. Process.
For this reason, when an aspherical member is used as an object to be measured, the contour shape on one side is measured from the axis, and the measured value and the design value are compared through a predetermined calculation, so that the contour shape error is determined as a deviation. It can be calculated. Then, by feeding back the calculation result to the rotary processing machine, it is possible to perform processing with high accuracy while correcting the aspherical shape of the object to be measured.

Here, the rotary machine will be described in more detail. A rotary machine is a surface of a member that includes an effective diameter by moving in a rotational radius direction from a position that is a predetermined distance away from the shaft to the position of the shaft while applying a blade to the workpiece that is rotated about the shaft. Process the whole.
For this reason, the surface shape correction data for feeding back to the rotary machine need only be the calculation result of the error of the contour shape for one range from the axis of one contour shape passing through the axis of the object to be measured. .

In other words, in the case of an aspherical member, it is possible to evaluate and correct the surface shape by calculating an error in the contour shape for at least one range from the axis.
However, in order to accurately calculate the contour shape error in the aspherical member, it is necessary to measure the contour shape in the range on both sides across the axis.

The reason will be described in detail below with reference to FIG.
In FIG. 29, a predetermined range (X) of one contour shape passing through the axis in an optical member having an aspheric surface that is rotationally symmetric about the axis is measured, and the measured value of the contour shape and the contour shape are measured in the measured range. It is a graph showing the result of comparing the design value with a predetermined calculation as an error (ΔZ) of the contour shape, (a) is a graph when the range of the symmetric effective diameter across the axis, (b) is a graph when the alignment error is removed for the asymmetric range across the axis from the outermost diameter position on one side separated by the axis to the predetermined position on the other side, (c) It is a graph which shows the result of having further performed convergence calculation with respect to the error of the contour shape calculated in (b).

  Usually, the surface shape is measured by measuring one contour shape passing through the axis of the object to be measured within an effective diameter range symmetrical to the axis through a surface shape measuring machine. When the contour shape is evaluated, the shape error is calculated by comparing the measured value of the contour shape with the design value of the contour shape through a predetermined calculation. In the predetermined calculation, a calculation method such as a least square method or a Newton method is used, for example, a convergence calculation (common name: fitting) is performed so that the convergence condition shown in Patent Document 3 or the RMS value (root mean square) is minimized. Do. And by this convergence calculation, the error due to the installation posture (common name: alignment) of the object to be measured can be removed, and the error of only the shape can be calculated.

Here, for example, an optical member having an aspherical surface that is rotationally symmetric about an axis is an object to be measured, and out of one outline shape passing through the axis, the outline in an asymmetric range sandwiching the axis in the one outline shape Consider the case of measuring the shape. In that case, the measurement value of the contour shape cannot be obtained in a part of the range. Then, if the above-described convergence calculation is performed from the measured value and the design value for an asymmetric range with the axis interposed therebetween, an error having a value different from the error value of the desired shape is calculated. This is because, for example, an RMS value (square) is used in the convergence calculation without considering the range in which the measured value of the contour shape is missing or insufficient with respect to the design formula that determines the design value for the entire range of the contour shape. This is because the convergence is performed so that the average square root) is minimized. As a result, when there is a range C in which the measurement values are missing or insufficient, as shown in FIG. 29B, the error value of the contour shape is the original contour shape as shown in FIG. The error value is greatly deviated.
Furthermore, in evaluating the error of the aspherical contour shape, in addition to the convergence calculation for removing the error in the installation posture of the object to be measured as described above, as shown in Patent Document 1, R in the design formula By changing (curvature radius), convergence calculation for obtaining R (curvature radius) that minimizes the error of the contour shape of the aspherical surface may be performed. When this evaluation is performed on the measurement result shown in FIG. 29 (b) where there is a range C in which the measurement value is missing or insufficient, as shown in FIG. 29 (c), the value of the contour shape error becomes larger. It will be shifted.

  For this reason, in a conventional general surface shape measuring machine, when evaluating the contour shape of an aspheric surface using a member having a rotationally asymmetric aspheric surface about the axis as the object to be measured, the surface shape measuring machine passes through the axis of the object to be measured. In one contour shape, the contour shape is measured for the entire range of the symmetric effective diameter across the axis, and the measured value and the design value of the contour shape in the range are subjected to the predetermined calculation as described above. By comparing, the error of the contour shape was calculated (see Patent Document 1 and Patent Document 2).

Japanese Patent No. 2885422 Japanese Patent No. 3322210 Japanese Patent No. 2520202

However, if the contour shape in the range on both sides across the axis is measured, the measurement time becomes longer.
Moreover, in the conventional surface shape measuring machine including the surface shape measuring machine described in Patent Document 1, as described above, the measurement of the contour shape of the aspheric surface of the member having the aspheric surface rotationally symmetric about the axis is performed. In this case, the contour shape error cannot be evaluated with high accuracy unless the entire range of the symmetric effective diameter across the axis in one contour shape passing through the axis of the object to be measured is targeted.

  The present invention has been made in view of the above-mentioned conventional problems, and in the measurement of the contour shape of an aspheric surface in a member having an aspheric surface that is rotationally symmetric about an axis, the range of a symmetric effective diameter across the axis. An object of the present invention is to provide a surface shape measuring machine, a surface shape measuring method, and a surface shape measurement value analysis method capable of measuring an outline shape error with high accuracy in a short time without targeting the whole. And

In order to achieve the above object, a surface shape measuring instrument according to the present invention is a surface shape measuring device for a member having an aspheric surface rotationally symmetric about an axis, the contour shape measuring means for measuring the contour shape of the aspheric surface. And a shape error calculating means for calculating a shape error with a design value of the contour shape of the aspheric surface, and the contour shape measuring means has one of the axes sandwiched in an asymmetric range with the shaft sandwiched therebetween. Measuring the contour shape of the aspheric surface from a predetermined position on the other side to another predetermined position on the other side, and the shape error calculating means measures the measured value of the aspheric contour shape in an asymmetric range across the axis. Is used to supplement the predetermined range on the other side separated by the axis from which the measured value is not obtained as a provisional measurement value, and then the asymmetric range across the axis and the range supplemented with the provisional measurement value, In the range where I said in an asymmetric range and the measured value of the aspheric contour the provisional measurement value with the design value of the aspheric contour of the aspherical contour in an asymmetric range sandwiching the shaft Until the difference between the measured value and the provisional measurement value and the design value satisfies a predetermined convergence condition , the measurement value of the aspherical contour shape and the provisional measurement value in an asymmetric range across the axis, or Calculating to obtain a difference between the design value and the measured value of the aspherical contour shape and the provisional measurement value in an asymmetrical range with the axis interposed, while converting at least one of the design values. It is characterized by that.

Further, the surface shape measuring method according to the present invention is a surface shape measuring method for a member having an aspherical surface that is rotationally symmetric about an axis, and in one asymmetrical range across the axis, one side across the axis. Measuring the contour shape of the aspheric surface from a predetermined position to another predetermined position on the other side, and then using the measured value of the contour shape of the aspheric surface in an asymmetric range across the axis, In the range that combines the asymmetric range across the axis and the range supplemented with the temporary measurement value, supplemented as a provisional measurement value to the predetermined range on the other side separated by the axis not obtained, using the design values of the aspherical surface of the measured value and the provisional measurement value and the aspherical profile of the contour in an asymmetric range across the said axis, said in an asymmetric range sandwiching the shaft aspherical The measured value of the contour shape of the And value, the the design value, until the difference is a predetermined convergence condition is satisfied, the measurement value and the provisional measurement value of the non-spherical contour in an asymmetric range across the said axis, or at least of the design value The calculation is performed to obtain the difference between the measured value and the provisional measurement value of the aspherical contour shape in the asymmetric range across the axis while the one side is coordinate-transformed, and the design value .

In addition, the method for analyzing a surface shape measurement value according to the present invention is a method for analyzing a surface shape measurement value of a member having an aspherical surface that is rotationally symmetric about an axis, and is measured in an asymmetric range across the axis. Using the measured value of the aspherical contour shape from a predetermined position on one side across the axis to another predetermined position on the other side, the other separated by the axis from which no measured value is obtained Is supplemented as a provisional measurement value in a predetermined range on the side of, and then in a range where the asymmetric range across the axis and the range supplemented with the provisional measurement value are combined, the asymmetrical range across the axis Using the measurement value of the aspherical contour shape, the provisional measurement value, and the design value of the aspherical contour shape, the measurement value of the aspherical contour shape in the asymmetric range across the axis and the provisional measurement values and the design values and the difference is a predetermined convergence condition of Until they meet the measured value and the provisional measurement value of the non-spherical contour in an asymmetric range sandwiching the shaft, or, while allowed to coordinate transformation at least one of the design value, an asymmetric range sandwiching the shaft And calculating the difference between the measured value of the aspherical contour shape and the temporary measured value and the design value .

  In the surface shape measuring machine according to the present invention, in the surface shape measuring machine, the shape error calculating unit may measure the measured value of the aspherical contour shape in an asymmetric range across the axis with respect to the axis. Inverted symmetrically, in the range where the measured value of the contour shape of the aspheric surface before inversion overlaps with the measured value of the contour shape of the aspheric surface after inversion, the measured value of the contour shape of the aspheric surface before the inversion And coordinate conversion so that the error between the measured value of the aspherical contour shape after the inversion is minimized, and the measured value of the aspherical contour shape before the inversion and the aspherical shape after the inversion It is characterized in that it is complemented as the temporary measurement value by superimposing the measurement value of the contour shape.

  Further, the surface shape measuring method according to the present invention is the above surface shape measuring method, wherein the measurement value of the aspherical contour shape in the asymmetric range across the axis is inverted symmetrically with respect to the axis. In the range where the previous measurement value of the aspheric contour shape overlaps the measurement value of the aspheric contour shape after inversion, the measurement value of the aspheric contour shape before the inversion and the non-inversion Coordinate transformation is performed so that an error from the measurement value of the spherical contour shape is minimized, and the measurement value of the aspheric contour shape before the reversal and the measurement value of the aspheric contour shape after the reversal are obtained. It is characterized in that it is complemented as the provisional measurement value by overlapping.

  The surface shape measurement value analysis method according to the present invention is the surface shape measurement value analysis method described above, wherein the measurement value of the aspherical contour shape in an asymmetric range across the axis is obtained with respect to the axis. The measurement of the aspherical contour shape before inversion is performed in a range where the measured value of the aspherical contour shape before the inversion and the measured value of the aspherical contour shape after the inversion overlap with each other by axisymmetric inversion. Coordinate conversion so that an error between the measured value and the measured value of the contour shape of the aspheric surface after the inversion is minimized, and the measured value of the contour shape of the aspheric surface before the inversion and the aspheric surface after the inversion The measured value of the contour shape is complemented as the temporary measured value by superimposing the measured value.

The surface shape measuring machine according to the present invention is a surface shape measuring device for a member having an aspheric surface rotationally symmetric about an axis, the contour shape measuring means for measuring the contour shape of the aspheric surface, and the aspheric surface. A shape error calculating means for calculating a shape error with respect to the design value of the contour shape of the contour shape, and the contour shape measuring means from a predetermined position on one side across the axis in an asymmetric range across the axis. the aspherical profile to another predetermined position of the other side is measured, the shape error calculating means, the measured value of the profile shape of said aspheric surface contour measuring means has measured said aspherical Until the difference between the design value of the contour shape and a predetermined convergence condition is satisfied , coordinate conversion is performed on at least one of the measurement value of the aspherical contour shape in the asymmetric range across the axis or the design value. , Non-clamping the shaft The measured values of the aspheric contour in the referred range, the conducted and the design value, the difference between the first calculation seeking of, among the measurement values of the aspheric contour after the first calculation The first processing step of complementing the measured values in the range excluding the symmetric range across the axis as a tentative measured value in an axially symmetrical manner to the predetermined range on the other side separated by the axis from which no measured value is obtained When,
If there is a step at the boundary between the provisional measurement value of the measurement value and the complementary range of the contour shape of the asymmetric range after sandwiching the shaft the first calculation, the first sandwiching said shaft in the provisional measurement value and the range of the combined measurements and the complementary range of asymmetric range of the contour shape after calculation, using the design values of the aspherical contour, the first sandwiching said shaft The first sandwiching the axis until a difference between the measured value of the aspherical contour shape in the asymmetric range after the calculation, the provisional measurement value, and the design value satisfies a predetermined convergence condition . The asymmetrical shape after the first calculation across the axis while coordinate-transforming at least one of the measurement value and the provisional measurement value of the aspherical contour shape in the asymmetrical range after the calculation, or the design value Measured value of the aspherical contour shape in the range and the preliminary measurement Values and, with the design value, and performing a second calculation to determine the difference between the steps of deleting the measured value of the complementary range, asymmetric after the second calculation across the said shaft among the range measurements of the axial measurements in the range excluding the second count symmetrical range after calculation across the said axis in a predetermined range on the other side that are separated by the shaft not obtain a measure The non-obtained processing obtained through the second processing step, the first processing step, and the second processing step, which are repeated until the step satisfies a predetermined matching condition, And a third processing step of calculating an error of the aspheric contour shape from the measured value of the spherical contour shape and the design value of the aspheric contour shape.

Further, the surface shape measuring method according to the present invention is a method for analyzing a measured value of a surface shape of a member having an aspheric surface that is rotationally symmetric about an axis, and is measured in an asymmetric range across the axis, Using the measured value of the contour shape of the aspherical surface from a predetermined position on one side of the shaft to another predetermined position on the other side, one side of the shaft in an asymmetrical range of the shaft of the measured value of the non-spherical contour from the predetermined position to another predetermined position of the other side of the side, said the design value of the aspheric contour, until the difference is a predetermined convergence condition is satisfied, the Measured value of the aspherical contour shape in the asymmetrical range with the axis sandwiched, or measured value of the aspherical contour shape in the asymmetrical range with the axis sandwiched while transforming at least one of the design values. And the design value It performs a first calculation that, among the measurement values of the aspheric contour after the first calculation, the measured value in a range excluding the symmetrical range across the shaft, has obtained a measurement value a first processing step to complement as not the axis provisional measurement value axisymmetrically in a predetermined range on the other side was separated, the measurement of the profile of the asymmetric range after the shaft the first calculation across the If the boundary between the provisional measurement value in a range that is the complement to the value there is a step, the provisional measurement value and the complementary range of the contour shape of the asymmetric range after the first calculation sandwiching said shaft In the range combined with the measured value, the measured value of the aspheric contour shape in the asymmetrical range after the first calculation across the axis and the temporary value using the design value of the aspheric contour shape the measured values, the difference between the design value, until a predetermined convergence condition is satisfied, the first sandwiching said shaft The coordinate value of at least one of the measurement value and the provisional measurement value of the aspherical contour shape in the asymmetric range after calculation, or the design value is transformed, and the asymmetric value after the first calculation across the axis. the measured values and the temporary measured value of the non-spherical contour in the region, and the design value, and performing a second calculation to determine the difference between the steps of deleting the measured value of the complementary range , among the measurement values of the asymmetrical range after the second calculation across the said axis, the measurement value in the range excluding the second count symmetrical range after calculation sandwiching the axis, to obtain a measurement value A second processing step that repeats a process comprising a step of axisymmetrically complementing a predetermined range on the other side not separated by the axis until the step satisfies a predetermined matching condition, and the first process The aspherical contour shape obtained through the step and the second processing step And a third processing step of calculating an error of the aspheric contour shape from the measured value of the aspheric surface and a design value of the aspheric contour shape.

In addition, the method for analyzing a surface shape measurement value according to the present invention is a method for analyzing a surface shape measurement value of a member having an aspherical surface that is rotationally symmetric about an axis, and is measured in an asymmetric range across the axis. The measured value of the contour shape of the aspheric surface from a predetermined position on one side across the axis to another predetermined position on the other side is used to determine the axis in an asymmetric range across the axis. the measured values of the non-spherical contour to another predetermined position on the other side from one predetermined position on the side of the sandwiching, the the design value of the aspheric contour, the difference is a predetermined convergence condition The aspherical contour in the asymmetric range across the axis while transforming at least one of the measured value of the aspherical contour shape in the asymmetrical range across the axis or the design value until the axis is satisfied The shape measurement value and the design value It performs a first calculation to determine the difference between, among the measurement values of the aspheric contour after the first calculation, the measured value in a range excluding the symmetrical range across the shaft, the measured value a first processing step to complement the axially symmetric as a temporary measure in a predetermined range on the other side that are separated by the shaft not getting, asymmetric range of contour after the first calculation sandwiching said shaft If the boundary between the provisional measurement value of the measurement value and the complementary range of shapes there is a step, wherein supplemented with measurement of the contour shape of the asymmetric range after the first calculation sandwiching said shaft The measured value of the aspherical contour shape in the asymmetric range after the first calculation using the design value of the aspherical contour shape in the range combined with the temporary measurement value of the range. and wherein the provisional measurement value, and the design value, the difference until a predetermined convergence condition is satisfied, and across the axis The first calculation across the axis while coordinate-transforming at least one of the measurement value and the provisional measurement value of the aspherical contour shape in the asymmetric range after the first calculation, or the design value the measured values and the temporary measured value of the non-spherical contour in an asymmetric range of post, with the design value, and performing a second calculation to determine the difference between the measured value of the complementary range a step of deleting, among the measured values of the asymmetrical range after the second calculation across the said axis, the measurement value in the range excluding the second count symmetrical range after calculation sandwiching said shaft, A second processing step of repeating a process consisting of a step of axisymmetrically complementing a predetermined range on the other side separated by the axis from which measurement values are not obtained until the step satisfies a predetermined matching condition; The aspheric surface obtained through the first processing step and the second processing step. And a third processing step of calculating an error of the aspheric contour shape from the measured value of the contour shape and the design value of the aspheric contour shape.

  According to the present invention, in measuring an aspherical contour shape of a member having an aspherical surface that is rotationally symmetric about an axis, the contour can be formed in a short time without targeting the entire range of the symmetric effective diameter across the axis. A surface shape measuring machine, a surface shape measuring method, and a surface shape measurement value analysis method capable of measuring a shape error with high accuracy are obtained.

(a) is an explanatory view showing a state of measuring the contour shape of the aspheric surface in an optical member having an aspheric surface rotationally symmetric about an axis, using the surface shape measuring instrument according to one embodiment of the present invention, b) is an explanatory view showing the measurement results when measured using the surface shape measuring machine shown in (a). It is a graph showing the relationship between the measured value (measurement result) and the design value (design formula) in the convergence calculation that is generally performed in the conventional surface shape measuring machine, (a) in the measurement range before the convergence calculation (B) is a graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation, and (c) is the measured value and design in the measurement range after the convergence calculation. A graph showing each value, (d) is a graph showing the difference between the measured value and the design value in the measurement range after the convergence calculation. It is a flowchart which shows an example of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a graph which shows the relationship between a measured value (measurement result) and a design value (design formula) in the convergence calculation of the surface shape measuring machine of the present invention which performs processing in the processing procedure shown in FIG. (B) is a graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation, and (c) is the graph after the convergence calculation. A graph showing the measured value and the design value in the measurement range, respectively, (d) is a graph showing the difference between the measured value and the design value in the measurement range after the convergence calculation. FIG. 5 is a graph showing the relationship between the measured value and the design value after the processing step shown in FIG. 4 in the convergence calculation of the surface shape measuring machine of the present invention that performs processing according to the processing procedure shown in FIG. Is a graph showing the measured value and the design value when a part of the measured value in the measurement range after the convergence calculation is performed with respect to the reference axis of the design coordinate in the insufficient range, and (b) is the complementary processing of (a) After that, a graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation, (c) shows the difference between the measurement value and the design value in the measurement range after the complementary processing (a) and the convergence calculation. (D) is a graph showing the measured value and design value in the measurement range after execution of the complement processing and convergence calculation of (a), and (e) is insufficient from the measurement range after execution of the convergence calculation of (d). It is a graph which shows a measured value when a range is deleted, and a design value, respectively. FIG. 6 is a graph showing the relationship between the measured value and the design value after the processing step shown in FIG. 5 in the convergence calculation of the surface shape measuring machine of the present invention that performs processing according to the processing procedure shown in FIG. A graph showing the measured value and design value when a part of the measured value in the measurement range after the convergence calculation is completed with respect to the reference axis of the design coordinate in the insufficient range, (b) is after the supplement processing of (a) , A graph showing the difference between the measurement value and the design value in the measurement range before the convergence calculation, (c) shows the difference between the measurement value and the design value in the measurement range after the complementary processing of (a) and the convergence calculation Graph, (d) is a process consisting of the step of deleting the shortage range from the measurement range after the convergence calculation, the step of complementing the partial shortage of the measurement values in the measurement range after the convergence calculation, and the step of calculating the convergence Is repeated until the step is minimized, The results of the design values of the contour shape of the surface were compared through a predetermined calculation is a graph showing an error contour. It is a flowchart which shows the modification with respect to the example of FIG. 3 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the other modification with respect to the example of FIG. 3 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the further another modification with respect to the example of FIG. 3 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the other example of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. FIG. 11 is a graph showing a difference between a measured value and a design formula at each step in the flowchart of FIG. 10, and (a) converges to a design formula only for a measured value in a range Ma symmetric with respect to the axis A. FIG. A graph showing the measured value of the entire range M as a difference from the design value, (b) is a range where the measured value is not obtained, a range M asymmetric with respect to the axis A to a range Ma symmetric with respect to the axis A A graph in which the measured values in the range Mb excluding the range are complemented as temporary measured values with respect to the reference axis of the design coordinates as tentative measured values, and the measured values in the entire range including these ranges are expressed as differences from the designed values, (c ) For the measurement values in the entire range shown in (b), the convergence calculation to remove the installation error of the object to be measured, and the curvature and aspheric coefficient to minimize the error of the aspherical contour shape Measurement of the design value when the convergence calculation is performed until the specified convergence condition is satisfied. (D) is a graph showing the difference between the measured values of the range complemented with the predetermined range C supplemented in (c), and the axis of the asymmetrical measured values with the axis after the coordinate conversion is changed. (E) a graph showing a difference between measured values with respect to a design value when the measured values in a range excluding the sandwiched symmetrical range are complemented to a predetermined range C with respect to one coordinate axis Z in the design coordinates, Is the curvature that minimizes the error of the aspherical contour shape and the convergence calculation to remove the installation error of the object to be measured in the range of the measured value of the entire new effective diameter after coordinate transformation shown in (d) And a graph showing the difference of the measured value with respect to the design value when the convergence calculation for obtaining the aspheric coefficient is performed until a predetermined convergence condition is satisfied, (f) complements the predetermined range C supplemented in (e) The measured value in the specified range is deleted, and the axis after the coordinate conversion is asymmetric Of the measured values, the measured values in the range excluding the symmetrical range across the axis are supplemented as a temporary measured value symmetrically with respect to one coordinate axis Z in the design coordinates in the predetermined range C, and a new value after coordinate conversion is obtained. Convergence calculation for removing the installation error of the measured object, and convergence calculation for obtaining the curvature and aspheric coefficient that minimize the error of the aspheric contour 5 is a graph showing a difference between measured values with respect to design values when performing until a predetermined convergence condition is satisfied. It is a flowchart which shows one modification with respect to the example of FIG. 10 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the other modification with respect to the example of FIG. 10 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the further another modification with respect to the example of FIG. 10 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the other example of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the modification with respect to the example of FIG. 15 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the other modification with respect to the example of FIG. 15 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the further another modification with respect to the example of FIG. 15 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. It is a flowchart which shows the other example of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. FIG. 20 is a flowchart showing a modified example of the processing procedure in the surface shape measurement method including the measurement value analysis method of the present invention with respect to the example of FIG. It is a flowchart which shows the other modification with respect to the example of FIG. 19 of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. FIG. 20 is a flowchart showing still another modified example of the processing procedure in the surface shape measurement method including the measurement value analysis method of the present invention with respect to the example of FIG. It is a flowchart which shows an example of the process sequence in the measuring method of the surface shape provided with the analysis method of the measured value of this invention. FIG. 24 is a graph showing the relationship between the measured value and the design value in the convergence calculation of the surface shape measuring machine of the present invention that performs the processing in the processing procedure shown in FIG. 23, and (a) inverts the measured value with respect to the axis. (B) is a graph showing the difference between the measured value and the design value at the time of inversion processing of (a), (c) is a graph of the inversion after the inversion processing of (a). In the range where the previous measured value and the measured value after inversion overlap, the difference between the measured value and the design value when coordinate conversion is performed so that the error between the measured value before inverted and the measured value after inverted is minimized. (D) is a graph showing the result of comparing the measured value of the aspherical contour shape after coordinate conversion and the design value of the aspherical contour shape through a predetermined calculation as an error of the contour shape. It is explanatory drawing which shows a state when the holding | maintenance part of the surface shape measuring machine shown to Fig.1 (a) is inclined, and is a figure which shows a mode that a to-be-measured object with a big inclination angle is measured. It is a flowchart which shows the measurement procedure when measuring the to-be-measured object which needs to incline the holding | maintenance part of a surface shape measuring machine, and to measure. In the surface shape measuring method using the surface shape measuring machine shown in FIG. 1A, the rotation center of the rotating base of the holding unit and the center of curvature near the axis of the surface to be measured of the object to be measured do not coincide with each other. (A) is a diagram showing a state in which the part to be measured is placed at the center of the placing part of the turntable in the holding part set at an inclination angle of 0 degree. b) is a diagram showing a state in which the turntable in the holding unit is tilted by a predetermined tilt angle. It is explanatory drawing which shows a mode that the outline shape of the aspherical surface of a to-be-measured object is measured using the surface shape measuring apparatus and surface shape measuring method concerning other embodiment of this invention, (a) is 0 degree of inclination angles. FIG. 5B is a diagram showing the positional relationship between the position of the probe tip set to 1 and the rotation center of the means for tilting the probe, and FIG. 5B is a diagram showing a state in which the probe is tilted by a certain tilt angle. An optical member having a rotationally symmetric aspheric surface about the axis is measured for a predetermined range of one contour shape passing through the axis, and in the measured range, the measured value of the contour shape and the design value of the contour shape are It is a graph showing the result of comparison through calculation as an error of the contour shape, (a) is a graph when the effective diameter range symmetrical to the axis is targeted, (b) one separated by the axis It is a graph when the alignment error is removed for an asymmetric range sandwiching the axis from the outermost diameter position on the other side to a predetermined position on the other side. (c) is a graph showing the result of further convergence calculation performed on the contour shape error calculated in (b).

  First, the basic concept of the analysis method of the measurement value of the surface shape that constitutes an essential part in the present invention will be described, and then a configuration for carrying out the analysis method of the measurement value of the surface shape according to the embodiment of the present invention will be provided. The surface shape measuring machine and the surface shape measuring method including the surface shape measurement value analysis method will be described.

  According to the present invention, a method for analyzing a measured value of a surface shape is a conventional method for measuring the contour shape of an aspheric surface of a member having an aspheric surface that is rotationally symmetric about an axis (hereinafter simply referred to as an aspheric member). In consideration of the fact that the error of the contour shape could not be evaluated unless the entire range of the symmetric effective diameter across the axis of the object to be measured, it is not necessary to measure the entire range of the symmetric effective diameter across the axis. This is a method for evaluating the error of the contour shape with high accuracy. This method is provided in an arithmetic processing unit (not shown) as software constituting the shape error calculation means in the surface shape measuring machine of the present invention. In the case of an optical member having an aspherical surface, the rotationally symmetric axis is located at the same position as the optical axis of the optical member.

FIG. 1 (a) is an explanatory diagram showing a state in which the contour shape of an aspheric surface in an optical member having an aspheric surface rotationally symmetric about an axis is measured using the surface shape measuring instrument of the present invention. In the following description, the optical member O having an aspherical surface that is rotationally symmetric about the axis A is simply referred to as an aspherical member O.
The surface shape measuring machine 10 has a probe 11. This probe 11 is a contour shape measuring means for measuring the contour shape of the object to be measured.
The probe 11 is configured to be movable in the X-axis direction and the Z-axis direction via a known mechanism (not shown).
Here, the cross-sectional shape measuring machine 10 of the present invention has a predetermined axisymmetric contour shape on the aspherical surface of the aspherical member O, which is the object to be measured, via the probe 11 as shown in FIG. Among (for example, the axially symmetric contour shape passing through the position of the axis A or the vicinity of the position of the axis A), the contour shape of the asymmetric range M across the axis A is measured. This asymmetric range M is a range from a position P1 of the outermost diameter on one side across the axis A to a predetermined position P2 on the other side.

  When the measurement value of the contour shape for the range M is graphed, the measurement result is asymmetric with respect to the axis A as shown by the solid line in FIG. In FIG. 1B, the alternate long and two short dashes line indicates the design value for the entire effective diameter range of the contour shape.

  When the alignment error of the object to be measured is large, a design value or a design formula (a formula showing a line connecting the design values in the design coordinates) is used for this measurement value (measurement result), or the design value or design By using the measurement value (measurement result) for the equation and performing convergence calculation until a predetermined convergence condition is satisfied, an error in the surface shape of the object to be measured is calculated by removing the alignment error of the object to be measured. In the convergence calculation, a convergence method disclosed in Patent Document 3, an RMS value (root mean square), or the like may be minimized by using a calculation method such as a least square method or a Newton method.

Here, in the method for analyzing the measured value of the cross-sectional shape according to the present invention, the measured value of the aspherical contour shape in the asymmetric range across the axis is inverted symmetrically with respect to the axis, and the aspherical surface before the inversion is inverted. In the range where the measured value of the contour shape overlaps with the measured value of the aspherical contour shape after inversion, there is an error between the measured value of the aspherical contour shape before inversion and the measured value of the aspherical contour shape after inversion. Coordinate conversion is performed so as to be the minimum, and the measured value of the aspherical contour shape before inversion and the measured value of the aspherical contour shape after inversion are overlapped to supplement as a provisional measurement value.
In this way, in the measurement of the aspherical contour shape of a member having an aspherical surface that is rotationally symmetric about the axis, the contour can be contoured in a short time without covering the entire range of the symmetric effective diameter across the axis. The shape error can be measured with high accuracy.
Hereinafter, this point will be described in detail.

  For example, in the method for analyzing a measured value of a cross-sectional shape according to the present invention, after a predetermined first convergence calculation, during a predetermined first convergence calculation repeated in this calculation method, or after a predetermined first convergence calculation Among the measured values of the contour shape of the aspherical surface, the measured value in the range Mb excluding the symmetrical range Ma across the axis A is changed to a predetermined range C on the other side separated by the axis A from which no measured value is obtained. One coordinate axis in the design coordinates (Z coordinate axis, for convenience of explanation in FIG. 1, axis A is shown at a position coincident with the Z coordinate axis) is supplemented as a provisional measurement value in axisymmetric manner (the above processing) Hereinafter, the process is referred to as a first treatment process.)

  Next, if there is a step at the boundary between the measurement value of the asymmetric range M across the axis A and the provisional measurement value of the complemented range C, the measurement value of the asymmetric range M across the axis A is complemented. Performing a predetermined second convergence calculation using the measured value of the aspherical contour shape and the design value of the aspherical contour shape for the range obtained by combining the provisional measurement values of the range C. The measured value of the range Mb excluding the symmetrical range Ma across the axis A among the measured value of the aspherical contour shape after the second convergence calculation and the step of deleting the provisional measured value of the range C A process comprising a step of supplementing a predetermined range C on the other side separated by an axis A from which no measurement value is obtained as a provisional measurement value with respect to one coordinate axis in design coordinates (Z coordinate axis in FIG. 1) as a provisional measurement value; Are repeated until the step at the boundary satisfies a predetermined matching condition (the above processing The following, a second processing step.).

Next, the error of the aspherical contour shape is calculated from the measured value of the aspherical contour shape and the design value of the aspherical contour shape obtained through the first processing step and the second processing step.
As described above, in the method for analyzing the measurement value of the surface shape according to the present invention, the measurement values in the range Mb excluding the symmetric range Ma across the axis A among the measurement values in the asymmetric range M across the axis A are obtained. Focusing on an error (that is, a step at the boundary) generated in complementing one coordinate axis in the design coordinates in the range C where no measurement value is obtained, The predetermined convergence calculation, the deletion of the provisional measurement value in the complemented range, and the complement processing using the measurement value after the convergence calculation are repeated.

  In this way, a highly accurate contour shape error can be obtained even if the measured value is complemented in a range where the measured value is not obtained.

Here, the process in the method for analyzing the measured value of the surface shape according to the present invention will be described in comparison with the process of calculating the convergence between the measured value and the design value generally performed in the conventional surface shape measuring machine.
As a comparative example for the present invention, a convergence calculation using a measured value and a design value for the entire effective diameter range symmetric with respect to an axis, which is generally performed in a conventional surface shape measuring machine, is illustrated in FIG. 2 will be described.
Fig. 2 is a graph showing the relationship between the measured value (measurement result) and the design value (design formula) in the convergence calculation generally performed in the conventional surface shape measuring machine. (A) is before the convergence calculation. A graph showing the measured value and design value in the measurement range, (b) is a graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation, and (c) is a measurement in the measurement range after the convergence calculation. (D) is a graph showing the difference between the measured value and the design value in the measurement range after the convergence calculation.
For convenience of explanation, FIG. 2 shows that the coordinate axis of the measurement coordinate (coordinate serving as the reference for the measurement value of the object to be measured) and the coordinate axis of the design coordinate (coordinate serving as the reference for the design value) coincide with each other.

  In the convergence calculation that is generally performed in the conventional surface shape measuring machine, the measured value or design value is applied to the design value or design formula (the equation that shows the line connecting the design values in the measurement range). Then, it is converged while transforming the coordinates so that the translation and tilt change. Note that the convergence calculation is usually repeated without converging at one time. The difference between the measured value and the design value (FIG. 2 (b)) is reduced by repeating the convergence calculation. In this way, when the convergence calculation is performed in which one of the measured value and the design value is coordinate-transformed so that the translation or inclination changes with respect to the other, the alignment error (measured object) shown in FIG. As shown in FIG. 2 (c), position shifts such as the parallel direction and inclination of the measurement object in the measurement coordinates when the measurement object is placed on the measuring instrument are removed. Then, FIG. 2D, which is a calculation result when a predetermined convergence condition is finally satisfied, is an error of the aspherical contour shape. Note that the predetermined convergence condition here is determined according to the accuracy of the required error. For example, the convergence condition disclosed in Patent Document 3 and the conditions such as when the RMS value becomes the standard value can be applied.

Further, in evaluating the error of the aspherical contour shape, in addition to the convergence calculation for removing the alignment error of the object to be measured as described above, as disclosed in Patent Document 1 and Patent Document 2, By changing R (curvature radius) and aspheric coefficient in the equation, convergence calculation is performed to obtain R (curvature radius) and aspheric coefficient that minimize the error of the contour shape of the aspheric surface.
Then, in the analysis of the measured value of the surface shape, after the convergence calculation for removing the installation error of the object to be measured, the convergence for obtaining R (curvature radius) and the aspheric coefficient that minimize the error of the aspherical contour shape. A procedure for performing calculations and a procedure for performing these convergence calculations simultaneously can be taken.

Therefore, in the method of analyzing the measured value of the surface shape according to the present invention, first, convergence calculation for removing the installation error of the object to be measured, and R (curvature radius) or aspherical surface that minimizes the error of the aspherical contour shape. An example of a procedure for performing the convergence calculation for obtaining the coefficients separately will be described with reference to FIG. Also, the difference between the measured value and the design value at each step in the processing procedure is shown in FIG.
FIG. 3 is a flowchart showing an example of a processing procedure in the surface shape measuring method provided with the method for analyzing a surface shape measurement value of the present invention.
FIG. 4 is a graph showing the relationship between the measured value and the design value in the convergence calculation of the surface shape measuring machine of the present invention that performs the processing in the processing procedure shown in FIG. 3, and (a) is a measurement before the convergence calculation is performed. (B) is a graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation, and (c) is the measured value in the measurement range after the convergence calculation. And (d) is a graph showing the difference between the measured value and the designed value in the measurement range after the convergence calculation. FIG. 5 is a graph showing the relationship between the measurement results after the processing steps shown in FIG. 4 and the design formula in the convergence calculation of the surface shape measuring machine of the present invention that performs processing in the processing procedure shown in FIG. (a) is a graph showing the measured value and the design value when a part of the measured value in the measurement range after the convergence calculation is performed with respect to the reference axis of the design coordinate in the insufficient range, and (b) is a graph showing the design value. (C) is a graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation after the supplement processing of (a). (D) is a graph showing the measured value and design value in the measurement range after performing the complementing process and convergence calculation of (a), and (e) is the measurement range after performing the convergence calculation of (d). FIG. 6 is a graph showing measured values and design values when a shortage range is deleted. FIG. 6 is a graph showing the relationship between the measurement results after the processing steps shown in FIG. 5 and the design formula in the convergence calculation of the surface shape measuring machine of the present invention which performs processing in the processing procedure shown in FIG. a) is a graph showing the measured value and the design value when a part of the measured value in the measurement range after the convergence calculation is completed with respect to the reference axis of the design coordinate in the insufficient range, and (b) is the graph of (a). A graph showing the difference between the measured value and the design value in the measurement range before the convergence calculation after the supplement processing, (c) is the difference between the measured value and the design value in the measurement range after the supplement processing and the convergence calculation in (a). A graph showing the difference, (d) is a step of deleting the shortage range from the measurement range after the convergence calculation is performed, a step of complementing a partial shortage of the measurement values in the measurement range after the convergence calculation is performed, and a step of convergence calculation After repeating the process consisting of until the step is minimized, the aspherical contour shape is measured. It is a graph showing the results of the design value of the values and non-spherical contour and compared with a predetermined operation as an error contour.
For convenience of explanation, FIG. 4 shows that the coordinate axis of the measurement coordinate (coordinate serving as the reference for the measurement value of the object to be measured) and the coordinate axis of the design coordinate (coordinate serving as the reference for the design value) coincide with each other. Further, the graph in FIG. 4 represents the difference in the measured value in the range M shown in FIG. 1 with respect to the design value in the entire range of the symmetric effective diameter across the axis.

First, measurement results (x _i , z _i ) in the range M shown in FIG. 4A [i is the number of measured values obtained at predetermined measurement points in the range M: 1, 2,... N] And the design formula Y is converged (fitted) (steps S1 _{1 to} S2 ₁ ). Here, the convergence calculation for removing the installation error is performed until a predetermined convergence condition is satisfied.
Through this convergence calculation, the measurement value is subjected to coordinate conversion such that the design value or the measurement value with respect to the design value changes in parallel movement or inclination. Here, the coordinates of the measured value are converted with respect to the design value, and as shown in FIG. 4C, the measured value (x _ij , z _ij ) after coordinate conversion [here j = 1 (step S1 ₁ )] have gained.

Next, among the measured values (x _ij , z _ij ) of the asymmetric range M across the axis after coordinate conversion, the measured values are obtained in the range Mb excluding the symmetric range Ma across the axis. The measured value (x _{ij +} , z _{ij +} ) of the entire effective diameter is created by complementing the predetermined range C on the other side separated by a non-axial axis as a provisional measurement value with respect to one coordinate axis Z in the design coordinates. (Step S3 ₁ ).
Originally, if the aspheric surface of an optical member having an aspheric surface that is rotationally symmetric about the axis is measured, the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measurement of the complemented predetermined range C There should be no step at the boundary between the value or the line connecting it.
However, in the actual measurement of the surface shape, since the reference axis of the measured value of the object to be measured and the reference axis of the design value do not coincide with each other, accurate convergence cannot be achieved even if the convergence calculation is performed. A step Δ is likely to occur.

Therefore, in order to reduce the step difference Δ, a coordinate calculation is performed by performing a convergence calculation for removing an installation error of the object to be measured for a range of measured values (x _{ij +} , z _{ij +} ) of the entire effective diameter. Measurement values (xi _{(j + 1) +} , zi _{(j + 1) +} ) are obtained. Then, from the measured values (xi _{(j + 1) +} , zi _{(j + 1) +} ) of the range M that is asymmetric with respect to the axis after coordinate conversion, the symmetrical range Ma with the axis sandwiched is excluded. The measurement value in the range Mb is replaced with the measurement value supplemented in the previous processing step. That is, first, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion, provisional measurement supplemented to a predetermined range C supplemented in the previous process. Delete the value. Then, the range Mb excluding the symmetrical range Ma with the axis sandwiched among the measured values (xi _{(j + 1)} , z _{i (j + 1)} ) of the asymmetric range M with the axis after the coordinate conversion. The measured values are complemented in a predetermined range C in a symmetrical manner with respect to one coordinate axis Z in the design coordinates. Thereby, a measurement value (x _{ij +} , z _{ij +} ) [here j = j + 1] of the entire effective diameter is created. Then, a process of performing convergence calculation to remove the installation error of the object to be measured, and a temporary measurement in which the measured values in the range Mb excluding the symmetric range Ma across the axis are complemented in the previous processing steps. The process of replacing the value is repeated until a predetermined matching condition (for example, the step is equal to or less than a predetermined value) for allowing the step to be recognized as being minimum (substantially disappear) is satisfied.

When converged until the step is minimized, the reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the installation error of the object to be measured is removed.
As a result, the measurement value exists substantially axisymmetrically with respect to the reference axis of the design coordinates, so by calculating the deviation between the measurement value and the design value, the aspheric contour that can be fed back to the processing machine or the like Shape errors and evaluation results can be obtained.

  It should be noted that the convergence calculation for removing the installation error of the object to be measured, which is performed in a process that is repeated until a predetermined coincidence condition for allowing the step to be recognized as the minimum is satisfied, may be performed once or a predetermined convergence. It may be performed until the condition is satisfied. In addition, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured value is an error in setting the measured object. It may be performed either before or after the convergence calculation for removing.

In the example of FIG. 3, in the repetitive process (steps S3 _{1 to} S7 ₁ ), the convergence calculation for removing the installation error of the object to be measured is performed until a predetermined convergence condition is satisfied (step S4 ₁ ).
Further, in the iterative process, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured values is performed. This is performed after the convergence calculation for removing the object installation error (step S5 ₁ ).

The relationship between the measurement coordinates and the design coordinates at this time is shown in FIG.
In the iterative process, the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate transformation through the convergence calculation (step S 4 ₁ ) are complemented in the previous process. The temporary measurement value supplemented to the predetermined range C is deleted (step S6 ₁ , FIG. 5 (e)).
Then, the range Mb excluding the symmetric range Ma with the axis between the measured values (x _ij , z _ij ) [j = j + 1 (step S7 ₁ )] of the asymmetric range M with the axis after the coordinate conversion. Is supplemented as a provisional measurement value with respect to one coordinate axis Z in the design coordinates in a predetermined range C (step S3 ₁ ). As a result, a measurement value (x _{ij +} , z _{ij +} ) in the entire range of the new effective diameter after coordinate conversion is obtained.
Then, the convergence calculation for removing the installation error of the object to be measured is again performed on the design formula until a predetermined convergence condition is satisfied (step S4 ₁ ). The relationship between the measured value and the design value at this time is as shown in FIGS. 6 (a) and 6 (b).

When repeating this step S3 ₁ ~S7 ₁ process step, as shown in FIG. 6 (c), the step converges gradually, ultimately, the temporary measured value complemented to a predetermined range C or it The connecting line coincides with the measurement value of the asymmetric range M across the axis or the connecting line with almost no step at the boundary.

In other words, in such a state, the measurement coordinate (reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the measurement value ( x _ij , z _ij ) are set. Here, j indicates the number of convergence calculations. The confirmation that the step has converged can be made based on the RMS value in the vicinity of the step Δ or the difference between the overlapped measurement values.

After completing the iterative process by satisfying the step matching condition, the measurement value of the aspherical contour shape transformed by the convergence calculation to remove the installation error of the object to be measured and the design of the aspherical contour shape calculating an error of the aspherical profile and a value (step S8 _1). This calculated value can be evaluated as an accurate error from which the installation error of the object to be measured is removed. FIG. 6D shows the difference between the measured value and the design value when calculating the error of the aspherical contour shape.

Furthermore, measurements of effective径全body _{(x i (j + 1)} +, z i (j + 1) +) as a target range of relative error of aspheric contour calculated in step S8 ₁ Then, the convergence calculation for obtaining the curvature and the aspherical coefficient that minimizes the error is performed until a predetermined convergence condition is satisfied (step S9 ₁ ). In this way, it is possible to evaluate R (curvature radius) and aspheric coefficient that minimize the error of the contour shape.

Modification 1
FIG. 7 is a flowchart showing a modified example of the processing procedure in the surface shape measuring method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 7, in the repetitive process (steps S3 _{2 to} S7 ₂ ), the number of convergence calculations performed to remove the installation error of the object to be measured is set to one (step S4 ₂ ).
That is, in the example of FIG. 7, for each convergence calculation, the measurement value in the range Mb excluding the symmetrical range Ma with the axis interposed therebetween is replaced with the provisional measurement value supplemented in the previous processing step. (Steps S6 ₂ , S7 ₂ , S3 ₂ ).
In the example of FIG. 7, satisfy the matching condition of the step, after completion of the repeated process, the convergence calculation for removing the installation error of the object to be measured, is performed until a predetermined convergence condition is satisfied (step S8 ₂ ).
Other processing procedures are substantially the same as those in the example of FIG.

Modification 2
FIG. 8 is a flowchart showing another modification of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 8, in the repetitive process (steps S3 _{3 to} S7 ₃ ), the measurement value of the asymmetric range M across the axis or a line connecting the measurement value and the provisional measurement value of the complemented predetermined range C or the connection thereof. The level difference at the boundary with the line is checked before the convergence calculation for removing the installation error of the object to be measured (step S4 ₃ ).
Other processing procedures are substantially the same as those in the example of FIG.

Modification 3
FIG. 9 is a flowchart showing still another modified example of the processing procedure in the surface shape measurement method including the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 9, in the repetitive process (steps S3 _{4 to} S7 ₄ ), the measurement value of the asymmetric range M across the axis or a line connecting the measurement value and the provisional measurement value of the complemented predetermined range C or the connection thereof. A step check at the boundary with the line is performed before the convergence calculation for removing the installation error of the object to be measured (step S4 ₄ ).
In the example of FIG. 9, the number of times of convergence calculation for removing the installation error of the object to be measured is set to 1 in the repetition process (step S5 ₄ ).
That is, in the example of FIG. 9, for each convergence calculation, the measurement values in the range Mb excluding the symmetric range Ma across the axis are replaced with provisional measurement values supplemented in the previous processing steps. (Steps S6 ₄ , S7 ₄ , S3 ₄ ).
Further, in the example of FIG. 9, satisfies the matching condition of the step, after completion of the repeated process, the convergence calculation for removing the installation error of the object to be measured, is performed until a predetermined convergence condition is satisfied (step S8 ₄ ).
Other processing procedures are substantially the same as those in the example of FIG.

In the examples of FIGS. 3 and 7 to 9 described above, the convergence calculation for obtaining R (curvature radius) and aspheric coefficient that minimize the contour shape error after performing the convergence calculation to remove the installation error of the object to be measured. However, the surface shape measuring method provided with the measurement value analysis method of the present invention is not limited to this processing procedure. Convergence calculation for removing the installation error of the object to be measured and convergence calculation for obtaining R (curvature radius) or aspheric coefficient that minimizes the contour shape error may be performed simultaneously.
Therefore, an example including a processing procedure for simultaneously performing convergence calculation for removing the installation error of the object to be measured and convergence calculation for obtaining R (curvature radius) and an aspherical coefficient that minimize the contour shape error will be described. .

FIG. 10 is a flowchart showing another example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention.
The convergence calculation is generally repeated until a predetermined convergence condition is indicated. However, in a state where there is a region C where no measurement value is obtained, in addition to the convergence calculation for removing the installation error, the convergence calculation for obtaining the R (curvature radius) and the aspheric coefficient that minimizes the contour shape error is performed. If it is repeated until a predetermined convergence condition is satisfied at the same time, an erroneous R (curvature radius) or aspheric coefficient that minimizes the contour shape error is calculated for the contour shape error including the installation error.

  Therefore, in the surface shape measurement method provided with the measurement value analysis method of FIG. 10, the convergence calculation and contour shape error for removing the installation error in the state where the region C where the measurement value is not obtained exist. Convergence calculation for obtaining the minimum R (curvature radius) and aspherical coefficient is performed only once at the same time, and based on the result of the convergence calculation, interpolation processing to the data deficient portion, convergence calculation processing, from the deficient portion The process including the data deletion process is repeated until the level difference is minimized.

First, the measured values _{(x i, z i) [} i measurement data number: 1, 2, · · · n] as the target asymmetric range M across the axis to obtain the measured value (x _i, z _i ) [I is the number of measurement values obtained at predetermined measurement points in the range M: 1, 2,... N] and the design equation Y are converged (fitting) (steps S11 _{1 to} S12 ₁ ). Here, the convergence calculation for removing the installation error with respect to the design value and the convergence calculation for obtaining R (curvature radius) and aspheric coefficient that minimize the contour shape error are performed only once at the same time.
Through this convergence calculation, the design value for the measurement value, or the measurement value for the design value is coordinate-transformed so that the translation and inclination change, and at the same time, the design equation R (curvature radius) is transformed. Let
By the way, as described above, normally, the convergence calculation does not satisfy the convergence condition at one time. For this reason, it becomes an asymmetrical state across the reference axis of the design value. Here, the coordinates of the measurement result are converted with respect to the design value, and the measurement result (x _ij , z _ij ) after the coordinate conversion [here j = 1 (step S11) as shown in FIG. ₁ )] have gained.

Next, as shown in FIG. 11 (b), the range Mb excluding the symmetrical range Ma with the axis sandwiched among the measured values (x _ij , z _ij ) of the asymmetric range M with the axis after coordinate transformation interposed therebetween. As a provisional measurement value that is axisymmetric with respect to one coordinate axis Z in the design coordinates, a predetermined range C on the other side separated by this axis where the measurement value is not obtained is supplemented as a range of the entire effective diameter. (X _{ij +} , z _{ij +} ) are created (step S13 ₁ ).
In FIG. 11 (b), for the sake of simplicity, the difference between the measured values with respect to the design value is shown as being supplemented as a provisional measured value in the predetermined range C. Data processing for complementing the measured value to the predetermined range C instead of the difference is performed.

As described above, if the aspherical surface of an optical member having an aspherical surface that is rotationally symmetric about the axis is measured, the measured value of the asymmetric range M across the axis or a line connecting the measured value and the complemented predetermined range C There should be no step at the boundary between the temporary measurement value or the line connecting the temporary measurement value.
The cause of the step is that the actual measurement of the surface shape does not match the reference axis of the measurement result of the object to be measured and the reference axis of the design formula. It is in.

Therefore, in order to reduce this step Δ, the convergence calculation for removing the installation error of the object to be measured and the aspherical contour shape for the range of the measured values (x _{ij +} , z _{ij +} ) of the entire effective diameter Convergence calculation is performed to obtain the curvature and aspheric coefficient that minimize the error, and the coordinate-converted measurement values (x _{i (j + 1) +} , z _{i (j + 1) +} ) are obtained. Then, from the measured values (xi _{(j + 1) +} , zi _{(j + 1) +} ) of the range M that is asymmetric with respect to the axis after coordinate conversion, the symmetrical range Ma with the axis sandwiched is excluded. The measurement value in the range Mb is replaced with the measurement value supplemented in the previous processing step. That is, first, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion, provisional measurement supplemented to a predetermined range C supplemented in the previous process. Delete the value. Then, the range Mb excluding the symmetrical range Ma with the axis sandwiched among the measured values (xi _{(j + 1)} , z _{i (j + 1)} ) of the asymmetric range M with the axis after the coordinate conversion. The measured values are complemented in a predetermined range C in a symmetrical manner with respect to one coordinate axis Z in the design coordinates. As a result, a measurement value (x _{ij +} , z _{ij +} ) [here j = j + 1] in the entire effective diameter is created. Then, a convergence calculation for removing the installation error of the object to be measured, and a convergence calculation for obtaining a curvature or an aspheric coefficient that minimizes the error of the aspherical contour shape, and a symmetry across the axis. Predetermined matching conditions (for example, a step difference) for the step of replacing the measurement value in the range Mb excluding the range Ma with the provisional measurement value supplemented in the previous processing step to be recognized as having a minimum step (substantially disappear). Repeat until the value is below the specified value.

When converged until the step is minimized, the reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the installation error of the object to be measured is removed.
As a result, the measured value exists substantially symmetrically with respect to the reference axis of the design coordinates, so by calculating the deviation between the measured value and the designed value, the aspherical contour shape that can be fed back to the processing machine etc. Error and evaluation results can be obtained.

  Convergence calculation for removing the installation error of the object to be measured, and the curvature that minimizes the error of the aspherical contour shape, which are repeated until a predetermined matching condition for satisfying the minimum step is satisfied. The convergence calculation for obtaining the aspherical coefficient may be performed once or until a predetermined convergence condition is satisfied. In addition, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured value is an error in setting the measured object. The calculation may be performed either before or after the convergence calculation for removing the image and the convergence calculation for obtaining the curvature or aspheric coefficient that minimizes the error of the aspherical contour shape.

In the example of FIG. 10, in a repetitive process (steps S13 _{1 to} S17 ₁ ), a convergence calculation for removing the installation error of the object to be measured, and a curvature and an aspheric coefficient that minimize the error of the aspherical contour shape are obtained. The convergence calculation is performed until a predetermined convergence condition is satisfied (step S14 ₁ ).
Further, in the iterative process, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured values is performed. The calculation is performed after the convergence calculation for removing the object installation error and the convergence calculation for obtaining the curvature and aspheric coefficient that minimize the error of the aspherical contour shape (step S15 ₁ ).

FIG. 11C shows the difference between the measured values and the design values at this time.
In the iterative process, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion through convergence calculation (step S14 ₁ ), it is complemented in the previous process. The provisional measurement value in the range complemented by the predetermined range C is deleted (step S16 ₁ ).
Then, as shown in FIG. 11 (d), among the measured values (x _ij , z _ij ) [j = j + 1 (step S17 ₁ )] of the asymmetric range M across the axis after coordinate conversion, the axis is sandwiched. The measured value in the range Mb excluding the symmetrical range Ma is supplemented as a temporary measured value in the predetermined range C with respect to one coordinate axis Z in the design coordinates as a provisional measured value (step S13 ₁ ). As a result, a measurement value (x _{ij +} , z _{ij +} ) in the entire range of the new effective diameter after coordinate conversion is obtained.
Then, the convergence calculation for removing the installation error of the object to be measured and the convergence calculation for obtaining the curvature and aspheric coefficient that minimize the error of the aspherical contour shape are performed until a predetermined convergence condition is satisfied. (Step S14 ₁ ).

When repeating this step S13 ₁ ~S17 ₁ process step, the difference between the measured value for the design values, FIG. 11 (c), the shown in FIG. 11 (d), FIG. 11 (e), the FIG. 11 (f) Thus, the level difference gradually converges, and finally, the provisional measurement value supplemented to the predetermined range C or the line connecting the same is the measurement value of the asymmetric range M across the axis or the line connecting the boundary and the boundary portion. In FIG.

In other words, in such a state, the reference value of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the measured value ( x _ij , z _ij ) are set. Here, j indicates the number of convergence calculations. The confirmation that the step has converged can be made based on the RMS value in the vicinity of the step Δ or the difference between the overlapped measurement values.

Convergence calculation to remove the installation error of the object to be measured after completion of the iterative process after satisfying the step matching condition, and convergence calculation to find the curvature and aspheric coefficient that minimize the error of the aspherical contour shape The error of the aspherical contour shape is calculated from the measured value of the aspherical contour shape that has been coordinate-converted via the above and the design value of the aspherical contour shape (step S18 ₁ ). This calculated value can be evaluated as an accurate error from which the installation error of the object to be measured is removed.

Modification 4
FIG. 12 is a flowchart showing a modified example of the processing procedure in the surface shape measuring method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 12, in a repetitive process (steps S13 _{2 to} S17 ₂ ), in order to obtain a curvature or an aspheric coefficient that minimizes an aspherical contour shape error, a convergence calculation for removing an installation error of the object to be measured. Is calculated once (step S14 ₂ ).
That is, in the example of FIG. 12, for each convergence calculation, the measurement values in the range Mb excluding the symmetric range Ma with the axis in between are replaced with the provisional measurement values supplemented in the previous processing steps. (Steps S16 ₂ , S17 ₂ , S13 ₂ ).
In the example of FIG. 12, the convergence calculation for removing the installation error of the object to be measured after completion of the iterative process after satisfying the step matching condition, and the curvature or non-uniformity that minimizes the error of the aspherical contour shape. The convergence calculation for obtaining the spherical coefficient is performed until a predetermined convergence condition is satisfied (step S18 ₂ ).
Other processing procedures are substantially the same as those in the example of FIG.

Modification 5
FIG. 13 is a flowchart showing another modified example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 13, in the repetitive process (steps S13 _{3 to} S17 ₃ ), the measurement value of the asymmetric range M across the axis or a line connecting the measurement value and the provisional measurement value of the supplemented predetermined range C are connected. Check the step at the boundary with the line before the convergence calculation to remove the installation error of the object to be measured and the convergence calculation to find the curvature and aspheric coefficient that minimize the error of the aspherical contour shape. (Step S14 ₃ ).
Other processing procedures are substantially the same as those in the example of FIG.

Modification 6
FIG. 14 is a flowchart showing still another modified example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 14, in the repetitive process (steps S13 _{4 to} S17 ₄ ), the measurement value of the asymmetric range M across the axis or a line connecting the measurement value and the provisional measurement value of the complemented predetermined range C or the connection thereof. Check the step at the boundary with the line before the convergence calculation to remove the installation error of the object to be measured and the convergence calculation to find the curvature and aspheric coefficient that minimize the error of the aspherical contour shape. (Step S14 ₄ ).
In the example of FIG. 14, the convergence calculation for removing the installation error of the object to be measured and the convergence calculation for obtaining the curvature and aspheric coefficient that minimize the error of the aspherical contour shape are 1 in the repetition process. (Step S15 ₄ ).
That is, in the example of FIG. 14, for each convergence calculation, the measurement values in the range Mb excluding the symmetric range Ma across the axis are replaced with the measurement values supplemented in the previous processing steps. (Steps S16 ₄ , S17 ₄ , S13 ₄ ).
Further, in the example of FIG. 14, satisfies the matching condition of the step, after completion of the repeated process, the convergence calculation for removing the installation error of the object to be measured, is performed until a predetermined convergence condition is satisfied (Step S18 ₄ ).
Other processing procedures are substantially the same as those in the example of FIG.

In the example of the processing procedure shown in FIG. 3, FIG. 7 to FIG. 9, FIG. 10, and FIG. 12 to FIG. Convergence calculation is performed at least once to remove the installation error from the design value, targeting an asymmetric range with a gap in between. When the design value is converged and calculated with respect to the measured value, the design formula Y changes to the design formula Y ₁ . Therefore, a part of the measurement result (x, z) is complemented symmetrically with respect to the reference axis of the design formula Y ₁ .

  It should be noted that the surface shape measurement method provided with the measurement value analysis method of the present invention is designed such that a part of the measurement value is designed in a measuring machine capable of reducing the installation error (particularly shift error) of the object to be measured. A processing procedure that, after supplementing the reference axis of coordinates symmetrically with respect to the coordinate axis, performs a convergence calculation to remove the installation error for the design value for the measured value of the entire effective diameter range including the complemented range. It is also possible to adopt.

If the installation error (especially shift error) of the object to be measured is large, the deviation between the measurement coordinates and the design coordinates becomes large. In such a case, among the measurement values in the asymmetric range M across the axis (of the object to be measured), the design values are not obtained for the measurement values in the range Mb excluding the symmetrical range Ma across the axis. When a predetermined range C on the other side separated by an axis is supplemented as a provisional measurement value with respect to one reference axis Z of design coordinates as a provisional measurement value, a measurement value of an asymmetric range M across the axis or a line connecting the measurement value The shape of the shape obtained by using the result of the convergence calculation for removing the installation error with respect to the design value will be greatly separated from the boundary between the provisional measurement value of the complemented range C or the line connecting it. The accuracy of the error becomes worse.
However, if the work of making the origin of the measurement coordinates in the vicinity of the axis of the object to be measured (that is, setting the probe position coordinate to zero) can be performed before the measurement, the installation error of the object to be measured (in particular, (Shift error) can be reduced. Specifically, since the position of the probe is measured with a linear scale or laser, it is possible to set the linear scale or laser to zero.
Therefore, in the surface shape measurement method provided with the measurement value analysis method of the present invention, among the measurement values in the asymmetric range M across the axis, the measurement values in the range Mb excluding the symmetric range Ma across the axis are obtained. After supplementing as a temporary measurement value axisymmetrically with respect to one reference axis of the design coordinates, the convergence calculation for removing the installation error is performed on the design value for the entire effective diameter range including the complemented range. An example in which the processing procedure is adopted will be described.

FIG. 15 is a flowchart showing another example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention.
In the surface shape measurement method provided with the measurement value analysis method of the example of FIG. 15, first, measurement values (x _i , z _i ) [i is the number of measurement data: 1, 2,... N] were obtained. Among the asymmetrical range M with the axis sandwiched, the measured value of the range Mb excluding the symmetric range Ma with the axis sandwiched is designated as the design coordinate in the predetermined range C on the other side separated by this axis where the measured value is not obtained. As a provisional measurement value that is axisymmetric with respect to one coordinate axis Z in FIG. 1, a measurement value (x _{ij +} , z _{ij +} ) [here j = 1 (step S21 ₁ )] of the entire effective diameter is created (step S21 ₁ ). S22 ₁ ).

Next, the measured values (x _{ij +} , z _{ij +} ) and the design formula Y are measured for the range of the measured values (x _{ij +} , z _{ij +} ) [i is the number of measured data: 1, 2 _,. Is converged (fitted) (step S23 ₁ ). Here, the convergence calculation for removing the installation error is performed on the design formula until a predetermined convergence condition is satisfied.
Through this convergence calculation, coordinate conversion is performed so that the measured value is converted into the design formula or the measured value with respect to the design formula is changed in translation and inclination. Here, the coordinates of the measurement result are converted with respect to the design formula, and the measurement result after the coordinate conversion (xi _{(j + 1) +} , zi _{(j + 1) +} ) [here j = 1 ( Step S21 ₁ )] is obtained.

Next, a step difference check is performed at the boundary between the measurement value of the asymmetric range M across the axis or a line connecting the measurement value and the provisional measurement value of the complemented predetermined range C or the line connecting it (step S24 ₁ ).
As described above, if the aspherical surface of an optical member having an aspherical surface that is rotationally symmetric about the axis is measured, the measured value of the asymmetrical range M on the axis or a line connecting the measured value and the provisional range C supplemented There should be no step at the boundary between the measured value or the line connecting it.
The cause of the step is that the actual measurement of the surface shape does not match the reference axis of the measurement result of the object to be measured and the reference axis of the design formula. It is in.

Therefore, in order to reduce this level difference Δ, the axis of the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) of the asymmetric range M across the axis after coordinate transformation is The measurement value in the range Mb excluding the sandwiched symmetrical range Ma is replaced with the measurement value supplemented in the previous processing step. That is, first, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion, provisional measurement supplemented to a predetermined range C supplemented in the previous process. Delete the value. Then, in the measurement value (x _ij , z _ij ) [here j = j + 1] of the asymmetric range M across the axis after coordinate conversion, measurement of the range Mb excluding the symmetric range Ma across the axis The value is complemented as a provisional measurement value in the predetermined range C in a symmetrical manner with respect to one coordinate axis Z in the design coordinates. As a result, a measurement value (x _{ij +} , z _{ij +} ) of the entire effective diameter is created. Then, a step of replacing the measured value in the range Mb excluding the symmetrical range Ma across the axis with a temporary measured value supplemented in the previous processing step, a convergence calculation for removing the installation error of the object to be measured The step of performing the above is repeated until a predetermined matching condition (for example, the step becomes equal to or less than a predetermined value) for which the step is recognized to be minimum (substantially disappear) is satisfied.

When converged until the step is minimized, the reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the installation error of the object to be measured is removed.
As a result, the measured value exists substantially symmetrically with respect to the reference axis of the design coordinates, so by calculating the deviation between the measured value and the designed value, the aspherical contour shape that can be fed back to the processing machine etc. Error and evaluation results can be obtained.

  It should be noted that the convergence calculation for removing the installation error of the object to be measured, which is performed in a process that is repeated until a predetermined coincidence condition for allowing the step to be recognized as the minimum is satisfied, may be performed once or a predetermined convergence. It may be performed until the condition is satisfied. In addition, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured value is an error in setting the measured object. It may be performed either before or after the convergence calculation for removing.

In the example of FIG. 15, in the repetitive process (steps S23 _{1 to} S27 ₁ ), the convergence calculation for removing the installation error of the object to be measured is performed until a predetermined convergence condition is satisfied (step S23 ₁ ).
Further, in the iterative process, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured values is performed. This is performed after the convergence calculation for removing the object installation error (step S24 ₁ ).

In the iterative process, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion through convergence calculation (step S24 ₁ ), it is complemented in the previous process. The provisional measurement value in the range complemented by the predetermined range C is deleted (step S25 ₁ ).
Then, the range Mb excluding the symmetric range Ma with the axis between the measured values (x _ij , z _ij ) [j = j + 1 (step S26 ₁ )] of the asymmetric range M with the axis after coordinate conversion. Is supplemented as a provisional measurement value with respect to one coordinate axis Z in the design coordinates in a predetermined range C (step S27 ₁ ). As a result, a measurement value (x _{ij +} , z _{ij +} ) in the entire range of the new effective diameter after coordinate conversion is obtained.
Then, the convergence calculation for removing the installation error of the device under test is again performed on the design formula until a predetermined convergence condition is satisfied (step S23 ₁ ).

When repeating this step S23 ₁ ~S27 ₁ process step, the difference between the measured value for the design values, step converges gradually and eventually joining the provisional measurement or it complemented the predetermined range C The line coincides with the measurement value of the asymmetric range M across the axis or the line connecting the measurement line with almost no step.

In other words, in such a state, the reference value of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the measured value ( x _ij , z _ij ) are set. Here, j indicates the number of convergence calculations. The confirmation that the step has converged can be made based on the RMS value in the vicinity of the step Δ or the difference between the overlapped measurement values.

Aspheric surface shape measurement values that have undergone coordinate conversion via convergence calculation to eliminate the installation error of the object to be measured after the step matching condition is satisfied, and design of the aspheric surface shape The error of the contour shape of the aspherical surface is calculated from the value (step S28 ₁ ). This calculated value can be evaluated as an accurate error from which the installation error of the object to be measured is removed.

Furthermore, measurements of effective径全body _{(x i (j + 1)} +, z i (j + 1) +) as a target range of relative error of aspheric contour calculated in step S28 ₁ Then, the convergence calculation for obtaining the curvature and the aspherical coefficient that minimizes the error is performed until a predetermined convergence condition is satisfied (step S29 ₁ ). In this way, it is possible to evaluate R (curvature radius) and aspheric coefficient that minimize the error of the contour shape.

Modification 7
FIG. 16 is a flowchart showing a modification of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 16, in the repetitive process (steps S23 _{2 to} S27 ₂ ), the convergence calculation for removing the installation error of the object to be measured is performed once (step S23 ₂ ).
That is, in the example of FIG. 16, for each convergence calculation, the measurement values in the range Mb excluding the symmetric range Ma across the axis are replaced with the measurement values supplemented in the previous processing steps. (Steps S25 ₂ , S26 ₂ , S27 ₂ ).
In the example of FIG. 16, the convergence calculation for removing the installation error of the object to be measured is performed until the predetermined convergence condition is satisfied after the step matching condition is satisfied and the repetition process is completed (step S < _b > 29 _2). ).
Other processing procedures are substantially the same as in the example of FIG.

Modification 8
FIG. 17 is a flowchart showing another modified example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 17, in the repetitive process (steps S23 _{3 to} S27 ₃ ), the measurement value of the asymmetric range M across the axis or a line connecting the same and the provisional measurement value of the complemented predetermined range C or the same are connected. A step check at the boundary with the line is performed before the convergence calculation for removing the installation error of the object to be measured (step S23 ₃ ).
It should be noted that among the asymmetrical ranges M across the axis from which the measured values (x _i , z _i ) [i are the number of measurement data: 1, 2,. The measured value in the excluded range Mb is complemented as a temporary measured value in a symmetrical manner with respect to one coordinate axis Z in the design coordinates in the predetermined range C on the other side separated by this axis where the measured value is not obtained. The measured value (x _{ij +} , z _{ij +} ) [here j = 1 (step S21 ₃ )] of the entire diameter range is created (step S22 ₃ ). When the line connecting the measured values in the asymmetrical range M across the axis or the line connecting the two coincides with almost no step at the boundary, the process is not repeated and the convergence calculation is not performed once. It will be. Therefore, in such a case, the convergence calculation for removing the installation error of the object to be measured is performed until the predetermined convergence condition is satisfied for the range of the measured values (x _{ij +} , z _{ij +} ) of the entire effective diameter. A coordinate-transformed measurement value (x _{i (j + 1) +} , z _{i (j + 1) +} ) is obtained (step S29 ₃ ).
Other processing procedures are substantially the same as in the example of FIG.

Modification 9
FIG. 18 is a flowchart showing still another modified example of the processing procedure in the surface shape measurement method including the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 18, in the repetitive process (steps S23 _{4 to} S27 ₄ ), the measurement value of the asymmetric range M across the axis or a line connecting it is connected to the provisional measurement value of the complemented predetermined range C or the same. The level difference at the boundary with the line is checked before the convergence calculation for removing the installation error of the object to be measured (step S23 ₄ ).
In the example of FIG. 18, the number of convergence calculations for removing the installation error of the object to be measured is set to 1 in the repetition process (step S25 ₄ ).
That is, in the example of FIG. 18, for each convergence calculation, the measured values in the range Mb excluding the symmetrical range Ma across the axis are replaced with temporary measured values supplemented in the previous processing steps. (Steps S25 ₄ , S26 ₄ , S27 ₄ ).
In the example of FIG. 18, the convergence calculation for removing the installation error of the object to be measured is performed until the predetermined convergence condition is satisfied after the step matching condition is satisfied and the repetition process is completed (step S28 _4). ).
Other processing procedures are substantially the same as in the example of FIG.

In the example of FIGS. 15 to 18 described above, after performing the convergence calculation to remove the installation error of the object to be measured, the process of performing the convergence calculation to obtain R (curvature radius) and aspheric coefficient that minimize the contour shape error. Although the procedure is shown, as described above, the surface shape measurement method provided with the measurement value analysis method of the present invention is not limited to this processing procedure. Convergence calculation for removing the installation error of the object to be measured and convergence calculation for obtaining R (curvature radius) or aspheric coefficient that minimizes the contour shape error may be performed simultaneously.
Therefore, an example including a processing procedure for simultaneously performing convergence calculation for removing the installation error of the object to be measured and convergence calculation for obtaining R (curvature radius) and an aspherical coefficient that minimize the contour shape error will be described. .

FIG. 19 is a flowchart showing another example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention.
The convergence calculation is generally repeated until a predetermined convergence condition is indicated. However, in a state where there is a region C where no measurement value is obtained, in addition to the convergence calculation for removing the installation error, the convergence calculation for obtaining the R (curvature radius) and the aspheric coefficient that minimizes the contour shape error is performed. If it is repeated until a predetermined convergence condition is satisfied at the same time, an erroneous R (curvature radius) or aspheric coefficient that minimizes the contour shape error is calculated for the contour shape error including the installation error.

  Therefore, in the surface shape measurement method including the measurement value analysis method of FIG. 19, the convergence calculation and the contour shape error for removing the installation error in the state where the region C where the measurement value is not obtained exist. Convergence calculation for obtaining the minimum R (curvature radius) and aspherical coefficient is performed only once at the same time, and based on the result of the convergence calculation, interpolation processing to the data deficient portion, convergence calculation processing, from the deficient portion The process including the data deletion process is repeated until the level difference is minimized.

First, among the asymmetrical ranges M with respect to the axes where the measured values (x _i , z _i ) [i is the number of measured data: 1, 2,. The measured value in the excluded range Mb is complemented as a temporary measured value in a symmetrical manner with respect to one coordinate axis Z in the design coordinates in the predetermined range C on the other side separated by this axis where the measured value is not obtained. A measurement value (x _{ij +} , z _{ij +} ) [here j = 1 (step S41 ₁ )] of the entire diameter range is created (step S42 ₁ ).

Next, the measured values (x _{ij +} , z _{ij +} ) and the design formula Y are measured for the range of the measured values (x _{ij +} , z _{ij +} ) [i is the number of measured data: 1, 2 _,. Is converged (fitted) (step S43 ₁ ). Here, the convergence calculation for removing the installation error in the design formula and the convergence calculation for obtaining the R (curvature radius) and the aspheric coefficient that minimize the contour shape error are performed only once at the same time.
Through this convergence calculation, the design equation for the measurement value, or the measurement value for the design equation is coordinate-transformed so that the translation and inclination change, and at the same time, the R (curvature radius) of the design equation is transformed. Let
By the way, as described above, normally, the convergence calculation does not satisfy the convergence condition at one time. For this reason, it becomes an asymmetrical state with respect to the reference axis of the design formula. Here, the coordinate of the measurement result is converted with respect to the design formula, and the measured value after the coordinate conversion (xi _{(j + 1) +} , zi _{(j + 1) +} ) [here j = 1 ( Step S41 ₁ )] is obtained.

As described above, if the aspherical surface of an optical member having an aspherical surface that is rotationally symmetric about the axis is measured, the measured value of the asymmetric range M across the axis or a line connecting the measured value and the complemented predetermined range C There should be no step at the boundary between the temporary measurement value or the line connecting the temporary measurement value.
The cause of the step is that the actual measurement of the surface shape does not match the reference axis of the measured value of the object to be measured and the reference axis of the design formula. It is in.

Therefore, in order to reduce this level difference Δ, the axis of the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) of the asymmetric range M across the axis after coordinate transformation is The measurement value in the range Mb excluding the sandwiched symmetrical range Ma is replaced with the measurement value supplemented in the previous processing step. That is, first, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion, provisional measurement supplemented to a predetermined range C supplemented in the previous process. Delete the value. Then, a range Ma excluding a range symmetric with respect to the axis among the measured values (x _{i (j + 1)} , z _{i (j + 1)} ) of the range M that is asymmetric with respect to the axis after coordinate conversion is obtained. The measured value in the excluded range Mb is supplemented as a provisional measured value in the predetermined range C, symmetrically about one coordinate axis Z in the design coordinates. As a result, a measurement value (x _{ij +} , z _{ij +} ) [here j = j + 1] in the entire effective diameter is created. Furthermore, for the range of measured values (x _{ij +} , z _{ij +} ) of the entire effective diameter, a convergence calculation for removing the installation error of the object to be measured, and a curvature or aspheric surface that minimizes the aspherical contour shape error. Convergence calculation for obtaining the coefficient is performed to obtain coordinate-converted measurement values (xi _{(j + 1) +} , zi _{(j + 1) +} ). Then, the process of replacing the measured values in the range excluding the symmetric range across the axis with the measured values supplemented in the previous processing process, the convergence calculation for removing the installation error of the measured object, and the non- A step of performing a convergence calculation for obtaining a curvature or an aspherical coefficient that minimizes an error in the contour shape of the sphere, and a predetermined matching condition for the step to be recognized as being minimum (substantially disappear) (for example, the step is predetermined) Repeat until satisfied.

When converged until the step is minimized, the reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the installation error of the object to be measured is removed.
As a result, the measurement value exists approximately axisymmetrically with respect to the reference axis of the design coordinates, so by calculating the deviation between the measurement result and the design formula, an aspheric contour shape that can be fed back to the processing machine etc. Error and evaluation results can be obtained.

  In addition, the convergence calculation for removing the installation error of the object to be measured, and the error of the aspherical contour shape are minimized in the process of repeating until a predetermined coincidence condition for satisfying that this step is recognized as the minimum is satisfied. The convergence calculation for obtaining the curvature and the aspherical coefficient may be performed once or until a predetermined convergence condition is satisfied. In addition, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured value is an error in setting the measured object. The calculation may be performed either before or after the convergence calculation for removing the image and the convergence calculation for obtaining the curvature or aspheric coefficient that minimizes the error of the aspherical contour shape.

In the example of FIG. 19, in a repetitive process (steps S44 _{1 to} S48 ₁ ), a convergence calculation for removing an installation error of the object to be measured, and a curvature and an aspheric coefficient that minimize the error of the aspherical contour shape are obtained. The convergence calculation is performed until a predetermined convergence condition is satisfied (step S48 ₁ ).
Further, in the iterative process, a step difference check at the boundary between the measured value of the asymmetric range M across the axis or a line connecting the measured value and the provisional measured value of the complemented predetermined range C or the line connecting the measured values is performed. This is performed after convergence calculation for removing an object installation error and convergence calculation for obtaining a curvature and an aspheric coefficient that minimize the error of the aspherical contour shape (step S44 ₁ ).

In the iterative process, among the measured values (x _{i (j + 1) +} , z _{i (j + 1) +} ) after coordinate conversion, the provisional range supplemented to the predetermined range C supplemented in the previous process is performed. The measured value is deleted (step S45 ₁ ).
Then, the range Mb excluding the range Ma that is symmetric with respect to the axis out of the measurement values (x _ij , z _ij ) [j = j + 1 (step S46 ₁ )] that are asymmetric with respect to the axis after coordinate conversion Is supplemented as a provisional measurement value with respect to one coordinate axis Z in the design coordinates in a predetermined range C (step S47 ₁ ). As a result, a new measurement value (x _{ij +} , z _{ij +} ) of the entire effective diameter after coordinate conversion is obtained.
Then, the convergence calculation for removing the installation error of the object to be measured and the convergence calculation for obtaining the curvature and aspheric coefficient that minimize the error of the aspherical contour shape are performed until a predetermined convergence condition is satisfied. (Step S48 ₁ ).

Then, when the processing steps of Steps S44 _{1 to} S48 ₁ are repeated, the difference in the measured value with respect to the design value gradually converges on the step, and finally the measured value supplemented to the predetermined range C or a line connecting it Coincides with the measurement value asymmetrical to the axis or the line connecting the measurement values with almost no step at the boundary.

In other words, when such a state is reached, the measured value (with respect to the entire effective diameter range in which the reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide and are symmetric with respect to the axis of the object to be measured ( x _ij , z _ij ) are set. Here, j indicates the number of convergence calculations. The confirmation that the step has converged can be made based on the RMS value in the vicinity of the step Δ or the difference between the overlapped measurement values.

Convergence calculation to remove the installation error of the object to be measured after completion of the iterative process after satisfying the step matching condition, and convergence calculation to find the curvature and aspheric coefficient that minimize the error of the aspherical contour shape Then, the error of the aspherical contour shape is calculated from the measured value of the aspherical contour shape that has been coordinate-converted via, and the design value of the aspherical contour shape (step S49 ₁ ). This calculated value can be an accurate error from which the installation error of the object to be measured is removed.

Modification 10
FIG. 20 is a flowchart showing a modification of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 20, in a repetitive process (steps S <b> 43 _{2 to} S <b> 47 ₂ ), a convergence calculation for removing an installation error of the object to be measured, and a curvature or an aspheric coefficient that minimizes an aspheric contour shape error are obtained. Is calculated once (step S43 ₂ ).
That is, in the example of FIG. 20, for each convergence calculation, the measurement values in the range Mb excluding the symmetric range Ma with the axis in between are replaced with the provisional measurement values supplemented in the previous processing steps. (Steps S45 ₂ , S46 ₂ , S47 ₂ ).
Further, in the example of FIG. 20, the convergence calculation for removing the installation error of the object to be measured and the curvature or non-uniformity that minimizes the error of the aspherical contour shape after satisfying the step matching condition and finishing the repetition process. The convergence calculation for obtaining the spherical coefficient is performed until a predetermined convergence condition is satisfied (step S48 ₂ ).
Other processing procedures are substantially the same as in the example of FIG.

Modification 11
FIG. 21 is a flowchart showing another modified example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 21, in the repetitive process (steps S43 _{3 to} S47 ₃ ), the measurement value of the range M asymmetric to the axis or a line connecting it, and the provisional measurement value of the complemented predetermined range C or the line connecting it Are checked before the convergence calculation to remove the installation error of the object to be measured and the convergence calculation to find the curvature and aspheric coefficient that minimize the error of the aspherical contour shape. (Step S43 ₃ ).
It should be noted that among the asymmetrical ranges M across the axis from which the measured values (x _i , z _i ) [i are the number of measurement data: 1, 2,. The entire effective diameter is measured by complementing the measured value of the excluded range Mb with the predetermined range C on the other side separated by the axis from which the measured value is not obtained, symmetrically with respect to one coordinate axis Z in the design coordinates. When the value (x _{ij +} , z _{ij +} ) [here j = 1 (step S41 ₃ )] is created (step S42 ₃ ), the measurement value supplemented to the predetermined range C or the line connecting it is When there is almost no step at the boundary between the measured value of the asymmetric range M or the line connecting it, the convergence calculation has not been performed even once without repeating the process. Therefore, in such a case, the convergence calculation for removing the installation error of the object to be measured is performed until the predetermined convergence condition is satisfied for the range of the measured values (x _{ij +} , z _{ij +} ) of the entire effective diameter. A coordinate-converted measurement value (x _{i (j + 1) +} , z _{i (j + 1) +} ) is obtained (step S49 ₃ ).
Other processing procedures are substantially the same as in the example of FIG.

Modification 12
FIG. 22 is a flowchart showing still another modified example of the processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention with respect to the example of FIG.
In the example of FIG. 22, in the repetitive process (steps S43 _{4 to} S47 ₄ ), the measurement value of the asymmetric range M across the axis or a line connecting the measurement value and the provisional measurement value of the complemented predetermined range C is connected. Check the step at the boundary with the line before the convergence calculation to remove the installation error of the object to be measured and the convergence calculation to find the curvature and aspheric coefficient that minimize the error of the aspherical contour shape. (Step S43 ₄ ).
In the example of FIG. 22, the convergence calculation for removing the installation error of the object to be measured is performed once in the repetition process (step S44 ₄ ).
That is, in the example of FIG. 22, for each convergence calculation, the measurement values in the range Mb excluding the symmetric range Ma across the axis are replaced with the measurement values supplemented in the previous processing steps. (Steps S45 ₄ , S46 ₄ , S47 ₄ ).
In the example of FIG. 22, the convergence calculation for removing the installation error of the object to be measured is performed until the predetermined convergence condition is satisfied after the step matching condition is satisfied and the repetition process is completed (step S <b> 48 _4). ).
Other processing procedures are substantially the same as in the example of FIG.

In the example of the processing procedure shown in FIGS. 15 to 22 described above, after a part of the measurement value is complemented as a temporary measurement value with respect to the reference axis of the design coordinates as a provisional measurement value, an asymmetric range with the axis interposed therebetween is targeted. As a result, the convergence calculation for removing the installation error is performed on the design formula at least once. When the design formula is converged and calculated with respect to the measurement result, the design formula Y changes to the design formula Y ₁ . Therefore, it will complement the part of the measurement results in axial symmetry with respect to the reference axis of the design equation Y ₁ (x, z) as a temporary measure.

Next, an example of a processing procedure in the method for analyzing a measured value of a surface shape according to the present invention will be described with reference to FIG. Further, FIG. 24 shows the difference between the measured value and the design value at each step in the processing procedure.
FIG. 23 is a flowchart showing an example of a processing procedure in the surface shape measurement method provided with the measurement value analysis method of the present invention.
FIG. 24 is a graph showing the relationship between the measured value and the design value in the convergence calculation of the surface shape measuring machine of the present invention that performs the processing in the processing procedure shown in FIG. 23, and (a) shows the measured value with respect to the axis. (B) is a graph showing the difference between the measured value and the design value during the inversion process of (a), (c) is the inversion process of (a) Then, in the range where the measured value before inversion and the measured value before inversion overlap, the measured value and design value when coordinate conversion is performed so that the error between the measured value before inversion and the measured value after inversion is minimized. (D) is a graph showing the result of comparing the measured value of the aspherical contour shape after coordinate conversion and the design value of the aspherical contour shape through a predetermined calculation as an error of the contour shape. It is.

In the measurement value analysis method of the present invention, measurement values (x _i , z _i ) [i are the number of measurement values respectively obtained at predetermined measurement points in the range M: 1 ,... N] are reversed axisymmetrically with respect to the axis A so as to partially overlap the original measured values (x _i , z _i ), and the entire effective diameter Measurement values (x _{i +} , z _{i +} ) are created (step S51). In the examples of FIGS. 23 and 24, among the measured values (x _i , z _i ) in the asymmetric range M across the axis A, the value on the side where the measured value of the effective diameter is obtained across the axis A However, if the measurement value of the entire effective diameter can be created by inverting so that it partially overlaps with the original measurement value (x _i , z _i ), the range to be inverted is not limited. For example, all the measurement values (x _i , z _i ) in the asymmetric range M across the axis A may be inverted.
Originally, if an aspheric surface of an optical member having an aspheric surface that is rotationally symmetric about an axis is measured, the measured value of an asymmetric range M across the axis or a line connecting the measured value and the measured value of an inverted range or There should be no step between the connecting lines.
However, in the actual measurement of the surface shape, since the reference axis of the measured value of the object to be measured and the reference axis of the design value do not coincide with each other, accurate convergence cannot be achieved even if the convergence calculation is performed, and the step Δ It is likely to occur.

Therefore, in order to reduce this step Δ, the measured value of the aspherical contour shape before inversion and the aspherical contour shape after inversion out of the range of measured values (x _{i +} , z _{i +} ) of the entire effective diameter. In the range where the measured values overlap, the coordinates are transformed and complemented so that the error between the measured value of the aspherical contour shape before inversion and the measured value of the aspherical contour shape after inversion is minimized. Are obtained in the entire range (x _{i1 +} , Z _{i1 +} ) (step S52).

  Next, the error of the aspherical contour shape is calculated from the measured value of the aspherical contour shape coordinate-transformed through the convergence calculation to remove the installation error of the object to be measured and the design value of the aspherical contour shape. (Step S53). This calculated value can be evaluated as an accurate error from which the installation error of the object to be measured has been removed. FIG. 24D shows the difference between the measured value and the design value when calculating the error of the aspherical contour shape.

At this time, the reference axis of the measurement coordinate and the reference axis of the design coordinate substantially coincide with each other, and the installation error of the object to be measured is removed.
As a result, the measurement value exists substantially axisymmetrically with respect to the reference axis of the design coordinates, so by calculating the deviation between the measurement value and the design value, the aspheric contour that can be fed back to the processing machine or the like Shape errors and evaluation results can be obtained.

Further, with respect to the range of measured values (x _{i1 +} , z _{i1 +} ) of the entire effective diameter, the curvature and aspheric coefficient that minimize the error are obtained with respect to the error of the aspherical contour shape calculated in step S54. Is performed until a predetermined convergence condition is satisfied (step S54). In this way, it is possible to evaluate R (curvature radius) and aspheric coefficient that minimize the error of the contour shape.

Note that when the alignment error of the object to be measured is large, may be performed convergence calculation for removing the same installation error that shown in step S2 ₁ in FIG.
That is, prior to the processing of step S51 described above, for example, first, measurement results (x _i , z _i ) [i in the range M shown in FIG. 4A are respectively obtained at predetermined measurement points in the range M. The number of measurement values: 1, 2,... N] and the design formula Y are converged (fitted) (steps S1 _{1 to} S2 ₁ ), and the convergence calculation for removing installation errors is performed until a predetermined convergence condition is satisfied. Let it be implemented.
Through this convergence calculation, the measurement value is subjected to coordinate conversion such that the design value or the measurement value with respect to the design value changes in parallel movement or inclination. For example, the coordinate of the measured value is converted with respect to the design value, and the measured value (x _i1 , z _i1 ) after the coordinate conversion is obtained as shown in FIG.
Then, using the measured values (x _i1 , z _i1 ) after the coordinate conversion, the same processing as in steps S51 to S54 described above is performed.

Next, an embodiment of the surface shape measuring machine of the present invention that performs the method of analyzing the surface shape measurement value of the present invention will be described with reference to the drawings. In addition, the surface shape measuring machine of this invention is not limited to the following embodiment.
Fig.1 (a) is explanatory drawing showing the holding | maintenance part of the to-be-measured object in the surface shape measuring machine concerning one Embodiment of this invention.
The holding part 12 has a base 12a and a turntable 12b. The turntable 12b has a placement portion 12b1 on which the object to be measured O is placed, and a sliding surface 12b2 having a curvature centered on a predetermined axis B perpendicular to the XZ plane. . The base 12a is fixed. The inside of the base 12a has a sliding surface 12a1 having a curvature that the sliding surface 12b2 matches with the sliding. Then, the holding unit 12 rotates the rotating base 12b about the predetermined axis B with respect to the base 12a. For example, as shown in FIG. It can be tilted.
In the present embodiment, a contact type probe 11 is used, but a non-contact type probe may be used. Further, the object to be measured O may have either a concave surface or a convex surface as long as it is an optical member having an aspherical surface that is rotationally symmetric about an axis.

  In FIG. 25, the turntable 12b of the holding unit 12 is tilted so that the angle a formed by the normal line of the contacting surface when the tip of the probe 11 is brought into contact with the axis A is 90 degrees. It is explanatory drawing which shows a mode that the outline shape of the aspherical surface in the optical member which has an aspherical surface rotationally symmetrical centering on the axis | shaft which is the measurement object O is measured. In FIG. 25, D is the center axis of the holding part 12, and B is the center of rotation of the turntable 12b.

Here, if the rotation center B of the turntable 12b and the center of curvature in the vicinity of the axis A on the surface to be measured of the object to be measured O coincide with each other, the predetermined range M in the object to be measured can be easily measured. So desirable.
However, for this purpose, every time a measurement object having a different aspherical shape is measured, the rotation center B of the turntable 12b and the center of curvature near the axis A on the measurement object surface of the measurement object coincide with each other. It is not realistic because a jig is required.
For this reason, in the surface shape measuring method using the surface shape measuring machine of this embodiment, the rotation center B of the turntable 12b and the center of curvature near the axis A on the surface to be measured of the object to be measured O do not coincide. Also, the measurement of the contour shape is possible. The method will be described later.

The surface shape measuring method using the surface shape measuring machine of this embodiment is demonstrated using FIG.
FIG. 26 is an explanatory diagram showing a contour shape measurement procedure in the surface shape measuring method using the surface shape measuring instrument according to the present embodiment.
First, using the design equation of the object to be measured O, the maximum contact angle between the probe 11 and the surface to be measured (that is, the normal of the contact surface when the tip of the probe 11 is brought into contact with the axis A). The angle a) is calculated (step S61). Next, it is determined whether or not the calculated contact angle is within a range that can be measured by the surface shape measuring machine (step S62). In the initial state, the turntable 12b of the holding unit 12 is arranged with the surface on which the object to be measured O is placed kept horizontal, as shown in FIG.
When the calculated contact angle is within a range that can be measured by the surface shape measuring instrument, the measurement is performed without correcting the posture of the object to be measured O. That is, the contour shape of the surface to be measured on the object to be measured O is measured while the surface on which the object to be measured O is placed on the turntable 12b of the holding unit 12 is kept horizontal (step S64).

  When the calculated contact angle is outside the range that can be measured by the surface shape measuring instrument, that is, for the part that is outside the measurable range of the surface shape measuring instrument on the surface to be measured, the posture of the object to be measured is corrected. (Step S63) and measure. That is, the turntable 12b on which the object to be measured O is placed is inclined with respect to the base 12a in the holding unit 12 by a predetermined angle α from the horizontal state. Accordingly, the object to be measured O is inclined by a predetermined angle α from the horizontal state.

Here, the inclination angle α for correcting the posture of the object to be measured is determined as follows.
Usually, the measurable range of the contact-type probe is such that the angle (contact angle) a formed by the normal line of the surface contacting the tip of the probe and the axis A is within 60 degrees.
Further, the measurable range of the non-contact type probe is such that the angle a formed by the normal line of the surface contacting the tip of the probe and the axis A is within 30 degrees.
Here, when the maximum contact angle between the axis A and the normal of the surface contacting the tip of the probe calculated from the design equation of the object to be measured O is b, the inclination angle α is as follows: Can be determined.
When b ≦ a, the turntable 12b in the holding unit 12 maintains a horizontal state, and the inclination angle α = 0.
b> a, and
When b / 2 <a, the inclination angle α of the turntable 12b in the holding unit 12 satisfies ba−α ≦ α <a.
When b / 2 ≧ a, the inclination angle α is selected for each measurement as the angle at which the measurement value is superimposed within the measurable range.

  For example, the tip of the probe via a surface shape measuring machine having a contact type probe (the angle a formed by the axis A and the normal of the surface of the object to be measured that contacts the tip of the probe is within 60 degrees) When measuring an object to be measured O in which the maximum contact angle b formed by the normal of the surface contacting the part and the axis A is 90 degrees, b> a and b / 2 <a, and the inclination angle α is 30 ° or more and less than 60 ° because ba−α ≦ α <a. In the example of FIG. 25, the turntable 12b is inclined at an inclination angle α = 30 degrees.

Here, a measurement method in the case where the rotation center B of the turntable 12b does not coincide with the center of curvature in the vicinity of the axis A on the surface to be measured of the object to be measured O will be described with reference to FIG.
The position P of the tip of the probe 11 and the rotation center B of the turntable 12b can be easily understood from the design values of the surface shape measuring machine. Therefore, as shown in FIG. 27A, the object to be measured O is placed at the center of the placement portion 12b1 of the turntable 12b in the holding portion 12 set to the inclination angle α = 0. Next, the probe 11 is brought into contact with the vicinity of the position of the optical axis A in the object to be measured O, and the position information of the probe tip is acquired.
Since the positional relationship (distance S) between the position P of the tip of the probe 11 and the rotation center B of the turntable 12b in the holding portion 12 is known, if the amount of movement L of the probe 11 to the surface to be measured is known, The positional relationship between the measurement object O is also clarified, and the positional relationship between the probe 11 and the measurement object O can be grasped.
That is, as shown in FIG. 27 (b), the lateral movement amount Δx of the surface top position of the object to be measured O when the turntable 12b of the holding unit 12 is inclined by a predetermined inclination angle α is expressed by the following equation. Calculate according to (1). As a result, the measurement position on the measurement surface of the object to be measured O can be accurately grasped.
Here, the distance S is S> 0 if there is a rotation center B of the turntable 12b in the holding unit 12 in the direction of the object to be measured O with respect to the position P at the tip of the probe 11, and is in the opposite direction. S <0.
(Equation 1)
Deviation of the top position of the object under test O:
Δx = | LS−sin α (1)

After correcting the posture of the object to be measured O, the contour shape is measured (step S64).
The processing of step S61 to step S64 is performed for an asymmetric range M across the axis A from the outermost diameter position P1 on one side separated by the axis A to the predetermined position P2 on the other side (step S65, S66).

Next, in order to evaluate the measurement result of the contour shape, analysis processing by the above-described analysis method is performed.
For this reason, according to the present embodiment, the contour shape error can be obtained with high accuracy without measuring a part of one side of the symmetrical effective diameter across the axis in the range of the symmetrical effective diameter across the axis. It can be calculated and evaluated.

In the above-described embodiment of the present invention, the maximum angle b formed by the normal of the surface of the object to be measured O contacting the tip of the probe 11 and the axis A is a measurable range with the surface shape measuring instrument. An example in which the rotation base 12a of the holding unit 12 is inclined by a predetermined inclination angle α in order to change the posture of the object to be measured has been described.
By the way, when it exceeds the measurable range with the surface shape measuring instrument, basically the relative angle between the probe 11 and the object to be measured O may be changed. For this reason, it is good also as a structure and measuring method which change the inclination-angle (alpha) of the probe 11 with respect to a to-be-measured object. The analysis method of the present invention can be used for measurement values obtained by any configuration / method.

Therefore, as another embodiment of the present invention, an example in which a predetermined inclination angle α of the probe with respect to the object to be measured is changed will be described. In this case, the calculation method of the positional relationship between the probe and the object to be measured when the inclination angle α is changed is different from the calculation method described above.
Accordingly, a method for calculating the positional relationship between the probe and the object to be measured in this case will be described with reference to FIG.
FIG. 28 is an explanatory view showing a state in which the aspherical contour shape of the object to be measured is measured by using the surface shape measuring instrument and the surface shape measuring method according to another embodiment of the present invention, and (a) shows an inclination. The figure which shows the positional relationship of the position of the probe front-end | tip set to 0 degree | times, and the rotation center of the means to incline a probe, (b) is a figure which shows the state which inclined the probe by the fixed inclination angle.
In the measurement method of this embodiment, the probe 11 is inclined with respect to the object O to be measured.
First, an angle (inclination angle) formed by the axis A ′ of the probe 11 and the axis A of the object to be measured O is an angle α ′. Here, the means for inclining the probe 11 is not particularly limited, such as an air spindle (not shown) or a gonio stage.

First, when α ′ = 0, the probe 11 is brought into contact with the top of the object to be measured O, and the position information of the tip of the probe 11 is acquired.
Positional relationship between the rotational center O _P means for inclining the position P and the probe 11 of the probe 11 tip which is set to the inclination angle 0 degrees shown in FIG. 28 (a) (distance S _P), since it is known in the design The lateral movement amount Δx ′ of the position of the probe 11 when the probe 11 shown in FIG. 28B is changed by a certain inclination angle α ′ can be calculated according to the equation (2). As a result, the measurement position on the measurement surface of the object to be measured O can be accurately grasped.
Here, the distance S _P is S _P > 0 when the rotation center O _{P of the} means for inclining the probe 11 is located in the direction of the object to be measured O with respect to the position P of the tip of the probe 11, and is positioned in the opposite direction. When doing so, S _P <0.
(Equation 2)
Deviation between the probe contact point and the surface top position of the object to be measured:
Δx ′ = | L _P −S _P | sin α ′ (2)

After correcting the tilt angle of the probe 11, the contour shape is measured. Then, the processes of steps S61 to S64 described above are performed for an asymmetric range M sandwiching the axis A from the outermost diameter position P1 on one side separated by the axis A to the predetermined position P2 on the other side.
Subsequently, in order to measure the error of the contour shape, analysis processing by the above-described analysis method is performed.

Therefore, according to the surface shape measuring apparatus of the present invention, as in the prior art, in the measurement of the contour shape of the aspheric surface in a member having an aspheric surface that is rotationally symmetric about the axis, the symmetry effective across the axis is effective. The contour shape error can be evaluated with high accuracy without measuring the entire diameter range.
And as a result of not having to measure the entire range of the symmetric effective diameter across the axis, for the object to be measured having a contour shape in which the contact angle with the probe is equal to or greater than the allowable tilt angle range of the measuring machine, In the case of measuring the effective diameter range by tilting the object to be measured, the number of measurements and the measurement time can be greatly reduced.
In addition, since the convergence calculation in the analysis after the measurement is performed via a computer, the convergence calculation result can be obtained instantaneously. For this reason, even if the number of iterations of the convergence calculation in the present invention is larger than the number of iterations when the convergence calculation is performed on the measurement result measured for the entire effective diameter range, the processing time is affected. There is almost no influence, and the effect of reducing the measurement time is not impaired.

  INDUSTRIAL APPLICABILITY The present invention is useful in a field in which it is required to measure and evaluate the surface shape of an optical member having a rotationally symmetric aspherical surface about its axis, its mold, and parts.

DESCRIPTION OF SYMBOLS 10 Surface shape measuring machine 11 Probe 12 Holding part 12a Base 12b Rotating base 12a1 Sliding surface 12b1 Mounting part 12b2 Sliding surface A Axis of measured object A 'Probe axis B Rotation base of rotating base C Measurement Missing or lacking range M Asymmetrical range across axis A Ma Out of range M, symmetrical range across axis A Mb Out of range M, range Ma excluded O Object to be measured P Probe tip position P1 Position of the outermost diameter on one side separated by the axis A P2 Predetermined position on the other side a Angle between the normal of the surface contacting the tip of the probe and the axis A α Inclination angle of the turntable α 'Probe tilt angle

Claims (12)

A surface shape measuring device for a member having an aspheric surface rotationally symmetric about an axis,
A contour shape measuring means for measuring the contour shape of the aspheric surface, and a shape error calculating means for calculating a shape error with a design value of the contour shape of the aspheric surface,
The contour shape measuring means measures the contour shape of the aspheric surface from a predetermined position on one side to the other predetermined position on the other side in the asymmetric range across the shaft,
The shape error calculating means includes
Using the measurement value of the aspherical contour shape in the asymmetric range across the axis, supplemented as a temporary measurement value to a predetermined range on the other side separated by the axis that has not obtained a measurement value,
Next, in the range where the asymmetric range across the axis and the range supplemented with the temporary measurement value are combined, the measured value of the aspherical contour shape and the temporary measurement value in the asymmetric range across the axis And the design value of the aspherical contour shape,
Until the difference between the measured value of the aspherical contour shape in the asymmetric range across the axis and the provisional measurement value and the design value satisfies a predetermined convergence condition ,
While transforming at least one of the measurement value and the provisional measurement value of the aspherical contour shape in the asymmetric range across the axis, or the design value,
A surface shape measuring machine for calculating a difference between a measured value and a provisional measured value of the contour shape of the aspherical surface in an asymmetric range across the axis, and the design value . A method for measuring a surface shape of a member having an aspheric surface rotationally symmetric about an axis,
Measuring the contour shape of the aspherical surface from a predetermined position on one side of the shaft to another predetermined position on the other side in an asymmetrical range with the shaft sandwiched;
Then, using the measured value of the aspherical contour shape in the asymmetric range across the axis, supplemented as a temporary measured value to a predetermined range on the other side separated by the axis not obtaining the measured value,
Next, in the range where the asymmetric range across the axis and the range supplemented with the temporary measurement value are combined, the measured value of the aspherical contour shape and the temporary measurement value in the asymmetric range across the axis And the design value of the aspherical contour shape,
Until the difference between the measured value of the aspherical contour shape in the asymmetric range across the axis and the provisional measurement value and the design value satisfies a predetermined convergence condition ,
While transforming at least one of the measurement value and the provisional measurement value of the aspherical contour shape in the asymmetric range across the axis, or the design value,
A method for measuring a surface shape , comprising: calculating a difference between a measured value and a temporary measured value of the contour shape of the aspherical surface in an asymmetric range across the axis, and the design value . An analysis method of a measured value of a surface shape of a member having an aspheric surface that is rotationally symmetric about an axis,
Using a measured value of the aspherical contour shape from a predetermined position on one side of the axis to another predetermined position on the other side, measured in an asymmetric range with the axis interposed therebetween, a measured value Supplemented as a tentative measurement value to the predetermined range on the other side separated by the axis,
Next, in the range where the asymmetric range across the axis and the range supplemented with the temporary measurement value are combined, the measured value of the aspherical contour shape and the temporary measurement value in the asymmetric range across the axis And the design value of the aspherical contour shape,
Until the difference between the measured value of the aspherical contour shape in the asymmetric range across the axis and the provisional measurement value and the design value satisfies a predetermined convergence condition ,
While transforming at least one of the measurement value and the provisional measurement value of the aspherical contour shape in the asymmetric range across the axis, or the design value,
A method for analyzing a measured value of a surface shape , comprising: calculating a difference between the measured value of the aspherical contour shape in the asymmetric range across the axis, the temporary measured value, and the design value. .   The shape error calculation means reverses the measurement value of the aspheric contour shape in an asymmetric range across the axis to be axisymmetric with respect to the axis, and measures the aspheric contour shape before inversion. In the range where the measured value of the aspherical contour shape after inversion overlaps, the error between the measured value of the aspherical contour shape before the inversion and the measured value of the aspherical contour shape after the inversion is Coordinate conversion is performed so as to be minimized, and the measured value of the aspherical contour shape before the inversion and the measured value of the aspherical contour shape after the inversion are superimposed on each other to complement the provisional measurement value. The surface shape measuring machine according to claim 1.   The measured value of the aspherical contour shape in an asymmetric range across the axis is inverted symmetrically with respect to the axis, and the measured value of the aspherical contour shape before inversion and the aspherical surface after inversion are reversed. In the range where the measured values of the contour shape overlap, the coordinate conversion is performed so that the error between the measured value of the contour shape of the aspheric surface before the inversion and the measured value of the contour shape of the aspheric surface after the inversion is minimized. Then, the measured value of the aspherical contour shape before the reversal and the measured value of the aspherical contour shape after the reversal are overlapped to complement the temporary measured value. 2. The surface shape measuring method according to 2.   The measured value of the aspherical contour shape in an asymmetric range across the axis is inverted symmetrically with respect to the axis, and the measured value of the aspherical contour shape before inversion and the aspherical surface after inversion are reversed. In the range where the measured values of the contour shape overlap, the coordinate conversion is performed so that the error between the measured value of the contour shape of the aspheric surface before the inversion and the measured value of the contour shape of the aspheric surface after the inversion is minimized. Then, the measured value of the aspherical contour shape before the reversal and the measured value of the aspherical contour shape after the reversal are overlapped to complement the temporary measured value. 4. A method for analyzing a measured value of a surface shape according to 3. A surface shape measuring device for a member having an aspheric surface rotationally symmetric about an axis,
A contour shape measuring means for measuring the contour shape of the aspheric surface, and a shape error calculating means for calculating a shape error with a design value of the contour shape of the aspheric surface,
The contour shape measuring means measures the contour shape of the aspheric surface from a predetermined position on one side to the other predetermined position on the other side in the asymmetric range across the shaft,
The shape error calculating means includes
Wherein the measurement of the aspheric contour of the contour shape measuring means to measure the the design value of the aspheric contour, until the difference is a predetermined convergence condition is satisfied,
Measurement of the aspherical contour shape in the asymmetrical range with the axis sandwiched between the measured values of the aspherical contour shape in the asymmetrical range with the axis and the coordinate conversion of at least one of the design values performed and values and the design values, the difference between the first calculation seeking of,
Among the measurement values of the aspheric contour after the first calculation, the other side of the measurement values in the range excluding the symmetrical range across the shaft, spaced by said shaft not obtain a measure A first processing step that complements as a temporary measurement value axisymmetrically within a predetermined range of
If there is a step at the boundary between the provisional measurement value of the measurement value and the complementary range of the contour shape of the asymmetric range after sandwiching the shaft the first calculation, the first sandwiching said shaft in the provisional measurement value and the range of the combined measurements and the complementary range of asymmetric range of the contour shape after calculation, using the design values of the aspherical contour,
Until the difference between the measured value of the aspherical contour shape and the provisional measurement value in the asymmetric range after the first calculation across the axis satisfies the predetermined convergence condition ,
The axis is sandwiched while at least one of the measured value of the aspherical contour shape and the provisional measurement value or the design value in the asymmetric range after the first calculation with the axis sandwiched. the measured values and the temporary measured value of the non-spherical contour in an asymmetric range after the first calculation, and the design value, and performing a second calculation to determine a difference, which is the complement a step of deleting a measurement of range, out of the measured values of the asymmetrical range after the second calculation across the said axis, a range excluding the second count symmetrical range after calculation sandwiching said shaft The process consisting of the step of complementing the measured value of the second axis in a symmetrical manner to a predetermined range on the other side separated by the axis from which no measured value is obtained is repeated until the step satisfies a predetermined matching condition. Processing steps;
The error of the aspheric contour shape is calculated from the measured value of the aspheric contour shape and the design value of the aspheric contour shape obtained through the first processing step and the second processing step. A third processing step;
A surface shape measuring machine characterized by comprising: A method for measuring a surface shape of a member having an aspheric surface rotationally symmetric about an axis,
Measuring the contour shape of the aspherical surface from a predetermined position on one side of the shaft to another predetermined position on the other side in an asymmetrical range with the shaft sandwiched;
Until the difference between the measured value of the aspheric contour shape and the design value of the aspheric contour shape satisfies a predetermined convergence condition ,
Measurement of the aspherical contour shape in the asymmetrical range with the axis sandwiched between the measured values of the aspherical contour shape in the asymmetrical range with the axis and the coordinate conversion of at least one of the design values performed and values and the design values, the difference between the first calculation seeking of,
Among the measurement values of the aspheric contour after the first calculation, the other side of the measurement values in the range excluding the symmetrical range across the shaft, spaced by said shaft not obtain a measure A first processing step that complements as a temporary measurement value axisymmetrically within a predetermined range of
If there is a step at the boundary between the provisional measurement value of the measurement value and the complementary range of the contour shape of the asymmetric range after sandwiching the shaft the first calculation, the first sandwiching said shaft in the provisional measurement value and the range of the combined measurements and the complementary range of asymmetric range of the contour shape after calculation, using the design values of the aspherical contour,
The measured values and the temporary measured value of the non-spherical contour in an asymmetric range after the first calculation across the shaft, the difference between the design value, is at a predetermined convergence Joukenwomitasuma,
The axis is sandwiched while at least one of the measured value of the aspherical contour shape and the provisional measurement value or the design value in the asymmetric range after the first calculation with the axis sandwiched. the measured values and the temporary measured value of the non-spherical contour in an asymmetric range after the first calculation, and the design value, and performing a second calculation to determine a difference, which is the complement a step of deleting a measurement of range, out of the measured values of the asymmetrical range after the second calculation across the said axis, a range excluding the second count symmetrical range after calculation sandwiching said shaft The process consisting of the step of complementing the measured value of the second axis in a symmetrical manner to a predetermined range on the other side separated by the axis from which no measured value is obtained is repeated until the step satisfies a predetermined matching condition. Processing steps;
The error of the aspheric contour shape is calculated from the measured value of the aspheric contour shape and the design value of the aspheric contour shape obtained through the first processing step and the second processing step. A third processing step;
A surface shape measuring method characterized by comprising: An analysis method of a measured value of a surface shape of a member having an aspheric surface that is rotationally symmetric about an axis,
Using the measured value of the aspherical contour shape from a predetermined position on one side of the axis to another predetermined position on the other side, measured in an asymmetric range with the axis interposed therebetween, the axis in asymmetric extent across the, the measured value of the non-spherical contour from a predetermined position of the side of the one sandwiching said axis to another predetermined position on the other side, the non-spherical contour design value Until the difference between and
Measurement of the aspherical contour shape in the asymmetrical range with the axis sandwiched between the measured values of the aspherical contour shape in the asymmetrical range with the axis and the coordinate conversion of at least one of the design values performed and values and the design values, the difference between the first calculation seeking of,
Among the measurement values of the aspheric contour after the first calculation, the other side of the measurement values in the range excluding the symmetrical range across the shaft, spaced by said shaft not obtain a measure A first processing step that complements as a temporary measurement value axisymmetrically within a predetermined range of
If there is a step at the boundary between the provisional measurement value of the measurement value and the complementary range of the contour shape of the asymmetric range after sandwiching the shaft the first calculation, the first sandwiching said shaft in the provisional measurement value and the range of the combined measurements and the complementary range of asymmetric range of the contour shape after calculation, using the design values of the aspherical contour,
Until the difference between the measured value of the aspherical contour shape and the provisional measurement value in the asymmetric range after the first calculation across the axis satisfies the predetermined convergence condition ,
The axis is sandwiched while at least one of the measured value of the aspherical contour shape and the provisional measurement value or the design value in the asymmetric range after the first calculation with the axis sandwiched. the measured values and the temporary measured value of the non-spherical contour in an asymmetric range after the first calculation, and the design value, and performing a second calculation to determine a difference, which is the complement a step of deleting a measurement of range, out of the measured values of the asymmetrical range after the second calculation across the said axis, a range excluding the second count symmetrical range after calculation sandwiching said shaft The process consisting of the step of complementing the measured value of the second axis in a symmetrical manner to a predetermined range on the other side separated by the axis from which no measured value is obtained is repeated until the step satisfies a predetermined matching condition. Processing steps;
The error of the aspheric contour shape is calculated from the measured value of the aspheric contour shape and the design value of the aspheric contour shape obtained through the first processing step and the second processing step. A third processing step;
A method for analyzing a measured value of a surface shape, comprising: 8. The shape error calculating unit according to claim 1, wherein the shape error calculating unit changes at least one of a curvature, a radius of curvature, or an aspherical coefficient of the design value together with the coordinate conversion or after the coordinate conversion. Surface shape measuring machine. 9. The surface shape measuring method according to claim 2, wherein at least one of a curvature, a radius of curvature, or an aspherical coefficient of the design value is changed together with or after the coordinate conversion. The analysis of the measured value of the surface shape according to any one of claims 3, 6 and 9, wherein at least one of a curvature, a radius of curvature, or an aspherical coefficient of the design value is changed together with or after the coordinate conversion. Method.

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