JP5275853B2 - Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value - Google Patents
Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value Download PDFInfo
- Publication number
- JP5275853B2 JP5275853B2 JP2009054108A JP2009054108A JP5275853B2 JP 5275853 B2 JP5275853 B2 JP 5275853B2 JP 2009054108 A JP2009054108 A JP 2009054108A JP 2009054108 A JP2009054108 A JP 2009054108A JP 5275853 B2 JP5275853 B2 JP 5275853B2
- Authority
- JP
- Japan
- Prior art keywords
- range
- value
- axis
- contour shape
- measured
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Images
Landscapes
- Length Measuring Devices With Unspecified Measuring Means (AREA)
Abstract
Description
本発明は、面形状測定機、面形状の測定方法、及び面形状の測定値の解析方法に関する。 The present invention relates to a surface shape measuring machine, a surface shape measuring method, and a surface shape measurement value analysis method.
光学素子やその金型、部品などの面形状を測定し、評価するために、面形状測定機が利用されている。特に、被測定物が軸を中心として回転対称な非球面を持つ部材(以下、非球面部材とする。)である場合、非球面の全体形状は、その軸から片側の輪郭形状をその軸を中心として一回転させた形状に略等しくなる。 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.
一般に、非球面部材は、旋盤などの回転加工機を介して加工されている。回転加工機は、軸を中心として被加工物を回転させた状態で、刃物を被加工物に当てながら、軸方向及び回転半径方向に動かすことによって、被加工物を回転対称な非球面形状に加工する。
このため、非球面部材を被測定物とした場合、その軸から片側の輪郭形状を測定し、測定値と設計値とを所定の演算を介して比較することにより、輪郭形状の誤差を偏差として算出できる。そして、この算出結果を回転加工機にフィードバックすることで、被測定物の非球面の形状を補正しながら高精度に加工することができる。
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.
ここで、回転加工機について、さらに詳しく説明する。回転加工機は、軸を中心として回転させている被加工物に刃物を当てながら、軸から所定量離れた位置から軸の位置まで回転半径方向に移動させることで、有効径を含む部材の面全体を加工する。
このため、回転加工機へフィードバックするための面形状補正用のデータは、被測定物における軸を通る一つの輪郭形状のうち、その軸から片側の範囲についての輪郭形状の誤差の算出結果で足りる。
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. .
言い換えれば、非球面部材においては、少なくとも軸から片側の範囲についての輪郭形状の誤差を算出すれば、面形状の評価および補正加工が可能である。
しかし、非球面部材における輪郭形状の誤差を精度良く算出するためには、軸を挟んだ両側の範囲についての輪郭形状の測定値が必要となる。
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.
その理由を以下に、図29を用いて詳細に説明する。
図29は軸を中心として回転対称な非球面を持つ光学部材における軸を通る一つの輪郭形状の所定範囲(X)を対象として測定し、測定した範囲において、輪郭形状の測定値と輪郭形状の設計値とを所定の演算を介して比較した結果を輪郭形状の誤差(ΔZ)として示すグラフであり、(a)はその軸を挟んだ対称な有効径の範囲を対象としたときのグラフ、(b)はその軸で隔てた一方の側の最外径位置から他方の側の所定位置までの軸を挟んだ非対称な範囲を対象として、アライメント誤差を取り除いたときのグラフ、(c)は(b)で算出した輪郭形状の誤差に対して、さらに収束計算を実施した結果を示すグラフである。
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).
通常、面形状の測定は面形状測定機を介して、被測定物における軸を通る一つの輪郭形状を、その軸に対称な有効径の範囲を対象として測定する。そして、その輪郭形状の評価を行なう際は、輪郭形状の測定値と輪郭形状の設計値とを所定の演算を介して比較することで形状の誤差を算出する。所定の演算では、最小二乗法やニュートン法という計算手法を用いて、例えば、特許文献3に示す収束条件や、RMS値(二乗平均平方根)が最小となるように収束計算(通称:フィッティング)を行なう。そして、この収束計算により、被測定物の設置姿勢(通称:アライメント)による誤差を取り除いて、形状のみの誤差を算出できる。 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.
ここで、例えば、軸を中心として回転対称な非球面を持つ光学部材を被測定物とし、その軸を通る一つの輪郭形状のうち、その一つの輪郭形状における軸を挟んだ非対称な範囲の輪郭形状を測定した場合について考える。その場合には、一部の範囲において輪郭形状の測定値が得られない。そして、軸を挟んだ非対称な範囲を対象として、測定値と設計値とから、上述したような収束計算を行なうと、所望する形状の誤差の値とは異なる値の誤差が算出されてしまう。これは、収束計算において、輪郭形状の全体の範囲についての設計値を定める設計式に対して、輪郭形状の測定値が欠落または不足している範囲を考慮せずに、例えば、RMS値(二乗平均平方根)が最小となるように収束させてしまうからである。その結果、測定値が欠落または不足する範囲Cがある場合には、図29(b)に示すように、輪郭形状の誤差の値が、図29(a)に示すような本来の輪郭形状の誤差の値から、大きくずれたものとなってしまう。
さらに、非球面の輪郭形状の誤差の評価に際しては、上述したような被測定物の設置姿勢の誤差を取り除くための収束計算に加えて、特許文献1に示されるように、設計式中のR(曲率半径)を変化させることによって、非球面の輪郭形状の誤差が最小となるR(曲率半径)を求める収束計算を行なう場合がある。この評価を、測定値が欠落または不足する範囲Cがある図29(b)に示す測定結果に対して実施すると、図29(c)に示すように、輪郭形状の誤差の値が、さらに大きくずれたものとなってしまう。
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
このため、従来一般の面形状測定機においては、軸を中心として回転対称な非球面を持つ部材を被測定物とするその非球面の輪郭形状の評価に際しては、被測定物の軸を通る一つの輪郭形状における、その軸を挟んだ対称な有効径の範囲全体を対象として、輪郭形状を測定し、その範囲における輪郭形状の測定値と設計値とを上述したような所定の演算を介して比較することによって、輪郭形状の誤差を算出していた(特許文献1及び特許文献2参照)。
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
しかし、軸を挟んで両側の範囲の輪郭形状を測定すると、測定時間が長くなる。
しかも、特許文献1に記載の面形状測定機を含め、従来の面形状測定機では、上述したように、軸を中心として回転対称な非球面を持つ部材における、その非球面の輪郭形状の測定においては、被測定物の軸を通る一つの輪郭形状における、その軸を挟んだ対称な有効径の範囲全体を対象としなければ、輪郭形状の誤差を高精度に評価することができない。
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
本発明は、上記従来の問題点に鑑みてなされたものであり、軸を中心として回転対称な非球面を持つ部材における非球面の輪郭形状の測定において、軸を挟んだ対称な有効径の範囲全体を対象とすることなく、短い時間で輪郭形状の誤差を高精度に測定することが可能な面形状測定機、面形状測定方法、及び面形状の測定値の解析方法を提供することを目的とする。 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
上記目的を達成するため、本発明による面形状測定機は、軸を中心として回転対称な非球面を持つ部材の面形状測定機であって、前記非球面の輪郭形状を測定する輪郭形状測定手段と、前記非球面の輪郭形状の設計値との形状誤差を算出する形状誤差算出手段とを備え、前記輪郭形状測定手段は、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、前記形状誤差算出手段は、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を用いて、測定値を得ていない前記軸で隔てた他方の側の所定範囲に仮測定値として補完し、次いで、前記軸を挟んだ非対称な範囲と前記仮測定値を補完された範囲とを合わせた範囲において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と前記仮測定値と前記非球面の輪郭形状の設計値とを用いて、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める計算を行なうことを特徴としている。 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.
また、本発明による面形状測定方法は、軸を中心として回転対称な非球面を持つ部材の面形状測定方法であって、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、次いで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を用いて、測定値を得ていない前記軸で隔てた他方の側の所定範囲に仮測定値として補完し、次いで、前記軸を挟んだ非対称な範囲と前記仮測定値を補完された範囲とを合わせた範囲において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と前記仮測定値と前記非球面の輪郭形状の設計値とを用いて、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める計算を行なうことを特徴としている。 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 .
また、本発明による面形状の測定値の解析方法は、軸を中心として回転対称な非球面を持つ部材の面形状の測定値の解析方法であって、前記軸を挟んだ非対称な範囲において測定された、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値を用いて、測定値を得ていない前記軸で隔てた他方の側の所定範囲に仮測定値として補完し、次いで、前記軸を挟んだ非対称な範囲と前記仮測定値を補完された範囲とを合わせた範囲において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と前記仮測定値と前記非球面の輪郭形状の設計値とを用いて、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める計算を行なうことを特徴としている。 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 .
また、本発明による面形状測定機は、上記面形状測定機において、前記形状誤差算出手段は、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を前記軸に対して軸対称に反転させて、反転前の前記非球面の輪郭形状の測定値と反転後の前記非球面の輪郭形状の測定値とが重なり合う範囲において、前記反転前の前記非球面の輪郭形状の測定値と前記反転後の前記非球面の輪郭形状の測定値との誤差が最小となるように座標変換して、前記反転前の前記非球面の輪郭形状の測定値と前記反転後の前記非球面の輪郭形状の測定値とを重ね合わせることにより前記仮測定値として補完することを特徴としている。 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.
また、本発明による面形状測定方法は、上記面形状測定方法において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を前記軸に対して軸対称に反転させて、反転前の前記非球面の輪郭形状の測定値と反転後の前記非球面の輪郭形状の測定値とが重なり合う範囲において、前記反転前の前記非球面の輪郭形状の測定値と前記反転後の前記非球面の輪郭形状の測定値との誤差が最小となるように座標変換して、前記反転前の前記非球面の輪郭形状の測定値と前記反転後の前記非球面の輪郭形状の測定値とを重ね合わせることにより前記仮測定値として補完することを特徴としている。 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.
また、本発明による面形状の測定値の解析方法は、上記面形状の測定値の解析方法において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を前記軸に対して軸対称に反転させて、反転前の前記非球面の輪郭形状の測定値と反転後の前記非球面の輪郭形状の測定値とが重なり合う範囲において、前記反転前の前記非球面の輪郭形状の測定値と前記反転後の前記非球面の輪郭形状の測定値との誤差が最小となるように座標変換して、前記反転前の前記非球面の輪郭形状の測定値と前記反転後の前記非球面の輪郭形状の測定値とを重ね合わせることにより前記仮測定値として補完することを特徴としている。 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.
また、本発明による面形状測定機は、軸を中心として回転対称な非球面を持つ部材の面形状測定機であって、前記非球面の輪郭形状を測定する輪郭形状測定手段と、前記非球面の輪郭形状の設計値との形状誤差を算出する形状誤差算出手段とを備え、前記輪郭形状測定手段は、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、前記形状誤差算出手段は、前記輪郭形状測定手段が測定した前記非球面の輪郭形状の測定値と、前記非球面の輪郭形状の設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と、前記設計値と、の差を求める第一の計算を行ない、前記第一の計算後の非球面の輪郭形状の測定値のうち、前記軸を挟んだ対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に仮測定値として補完する第一の処理工程と、
前記軸を挟んだ前記第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値との境界部に段差がある場合、前記軸を挟んだ第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値とを合わせた範囲において、前記非球面の輪郭形状の設計値を用いて、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める第二の計算を行なう工程と、前記補完された範囲の測定値を削除する工程と、前記軸を挟んだ第二の計算後の非対称な範囲の測定値のうち、前記軸を挟んだ第二の計算後の対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に補完する工程とからなる処理を、前記段差が所定の一致条件を満足するまで繰り返す第二の処理工程と、前記第一の処理工程及び第二の処理工程を介して得た、前記非球面の輪郭形状の測定値と前記非球面の輪郭形状の設計値とから前記非球面の輪郭形状の誤差を算出する第三の処理工程と、を有することを特徴としている。
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.
また、本発明による面形状測定方法は、軸を中心として回転対称な非球面を持つ部材の面形状の測定値の解析方法であって、前記軸を挟んだ非対称な範囲において測定された、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値を用いて、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値と、前記非球面の輪郭形状の設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と、前記設計値と、の差を求める第一の計算を行ない、前記第一の計算後の非球面の輪郭形状の測定値のうち、前記軸を挟んだ対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に仮測定値として補完する第一の処理工程と、前記軸を挟んだ前記第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値との境界部に段差がある場合、前記軸を挟んだ第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値とを合わせた範囲において、前記非球面の輪郭形状の設計値を用いて、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める第二の計算を行なう工程と、前記補完された範囲の測定値を削除する工程と、前記軸を挟んだ第二の計算後の非対称な範囲の測定値のうち、前記軸を挟んだ第二の計算後の対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に補完する工程とからなる処理を、前記段差が所定の一致条件を満足するまで繰り返す第二の処理工程と、前記第一の処理工程及び第二の処理工程を介して得た、前記非球面の輪郭形状の測定値と前記非球面の輪郭形状の設計値とから前記非球面の輪郭形状の誤差を算出する第三の処理工程と、を有することを特徴としている。 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.
また、本発明による面形状の測定値の解析方法は、軸を中心として回転対称な非球面を持つ部材の面形状の測定値の解析方法であって、前記軸を挟んだ非対称な範囲において測定された、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値を用いて、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値と、前記非球面の輪郭形状の設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と、前記設計値と、の差を求める第一の計算を行ない、前記第一の計算後の非球面の輪郭形状の測定値のうち、前記軸を挟んだ対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に仮測定値として補完する第一の処理工程と、前記軸を挟んだ前記第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値との境界部に段差がある場合、前記軸を挟んだ第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値とを合わせた範囲において、前記非球面の輪郭形状の設計値を用いて、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める第二の計算を行なう工程と、前記補完された範囲の測定値を削除する工程と、前記軸を挟んだ第二の計算後の非対称な範囲の測定値のうち、前記軸を挟んだ第二の計算後の対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に補完する工程とからなる処理を、前記段差が所定の一致条件を満足するまで繰り返す第二の処理工程と、前記第一の処理工程及び第二の処理工程を介して得た、前記非球面の輪郭形状の測定値と前記非球面の輪郭形状の設計値とから前記非球面の輪郭形状の誤差を算出する第三の処理工程と、を有することを特徴としている。 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.
本発明によれば、軸を中心として回転対称な非球面を持つ部材における非球面の輪郭形状の測定において、軸を挟んだ対称な有効径の範囲全体を対象とすることなく、短い時間で輪郭形状の誤差を高精度に測定することが可能な面形状測定機、面形状測定方法、及び面形状の測定値の解析方法が得られる。 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.
まず、本発明において本質的部分をなす面形状の測定値の解析方法について基本概念を説明し、次いで、本発明の実施形態にかかる面形状の測定値の解析方法を実施するための構成を備えた面形状測定機、及び面形状の測定値の解析方法を備えた面形状の測定方法について説明する。 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.
本発明による面形状の測定値の解析方法は、軸を中心として回転対称な非球面を持つ部材(以下、単に非球面部材とする。)におけるその非球面の輪郭形状の測定において、従来は被測定物の軸を挟んだ対称な有効径の範囲全体を対象としなければ輪郭形状の誤差の評価ができなかったことに鑑み、軸を挟んだ対称な有効径の範囲全体を測定しなくても輪郭形状の誤差を高精度に評価するための方法である。この方法は、本発明の面形状測定機における形状誤差算出手段を構成するソフトウェアとして、図示を省略した演算処理装置に備えられている。なお、非球面を持つ光学部材の場合の回転対称な軸は、その光学部材の光軸と同じ位置に位置する。 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.
図1(a)は本発明の面形状測定機を用いて、軸を中心として回転対称な非球面を持つ光学部材におけるその非球面の輪郭形状を測定する様子を示す説明図である。なお、以下の説明では、軸Aを中心として回転対称な非球面を持つ光学部材Oを、単に非球面部材Oと称する。
面形状測定機10は、プローブ11を有している。このプローブ11は、被測定物の輪郭形状を測定するための輪郭形状測定手段である。
プローブ11は、公知の機構(図示省略)を介してX軸方向及びZ軸方向に移動可能に構成されている。
ここで、本発明の断面形状測定機10は、図1(a)に示すように、プローブ11を介して、被測定物である、非球面部材Oの非球面における所定の軸対称な輪郭形状(例えば、軸Aの位置又は軸Aの位置の近傍を通る軸対称な輪郭形状)のうち、軸Aを挟んだ非対称な範囲Mの輪郭形状を測定する。この非対称な範囲Mは、軸Aを挟んだ一方の側の最外径の位置P1から他方の側の所定位置P2までの範囲である。
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
The
Here, the cross-sectional
範囲Mを対象とした輪郭形状の測定値をグラフ化すると、測定結果は、図1(b)に実線で示すように、軸Aを挟んで非対称になる。なお、図1(b)中、二点鎖線は、輪郭形状の有効径の範囲全体についての設計値を示している。 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.
被測定物のアライメント誤差が大きい場合には、この測定値(測定結果)に対して設計値又は設計式(設計座標における設計値を結んだ線を示す式)を用いるか、或いは設計値又は設計式に対して測定値(測定結果)を用いて、所定の収束条件を満たすまで収束計算を行なうことで、被測定物のアライメント誤差を取り除いた被測定物の面形状の誤差が算出される。収束計算では、最小二乗法やニュートン法等の計算手法を用いて、例えば特許文献3に開示されている収束条件や、RMS値(二乗平均平方根)等が最小となるようにすれば良い。 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.
ここで、本発明による断面形状の測定値の解析方法では、軸を挟んだ非対称な範囲における非球面の輪郭形状の測定値を軸に対して軸対称に反転させて、反転前の非球面の輪郭形状の測定値と反転後の非球面の輪郭形状の測定値とが重なり合う範囲において、反転前の非球面の輪郭形状の測定値と反転後の非球面の輪郭形状の測定値との誤差が最小となるように座標変換して、反転前の非球面の輪郭形状の測定値と反転後の非球面の輪郭形状の測定値とを重ね合わせることにより仮測定値として補完する。
このようにすれば、軸を中心として回転対称な非球面を持つ部材における非球面の輪郭形状の測定において、軸を挟んだ対称な有効径の範囲全体を対象とすることなく、短い時間で輪郭形状の誤差を高精度に測定することが可能となる。
以下、この点について詳しく説明する。
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.
例えば、本発明による断面形状の測定値の解析方法では、この計算手法において繰り返される所定の第一の収束計算の際、又は所定の第一の収束計算の後に、所定の第一の収束計算後の非球面の輪郭形状の測定値のうち、軸Aを挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていない軸Aで隔てた他方の側の所定範囲Cに設計座標における一つの座標軸(Z座標軸、なお、図1では説明の便宜上、軸AはZ座標軸に一致した位置に示してある。)に対して軸対称に仮測定値として補完する(以上の処理工程を以下、第一の処理工程とする。)。 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.)
次いで、軸Aを挟んだ非対称な範囲Mの測定値と補完された範囲Cの仮測定値との境界部に段差がある場合、この軸Aを挟んだ非対称な範囲Mの測定値と補完された範囲Cの仮測定値とを合わせた範囲を対象として、非球面の輪郭形状の測定値と非球面の輪郭形状の設計値とを用いて所定の第二の収束計算を行なう工程と、補完された範囲Cの仮測定値を削除する工程と、第二の収束計算後の非球面の輪郭形状の測定値のうち、軸Aを挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていない軸Aで隔てた他方の側の所定範囲Cに設計座標における一つの座標軸(図1ではZ座標軸)に対して軸対称に仮測定値として補完する工程からなる処理とを、この境界部の段差が所定の一致条件を満足するまで繰り返す(以上の処理工程を以下、第二の処理工程とする。)。 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.).
次いで、上記第一の処理工程及び第二の処理工程を介して得た、非球面の輪郭形状の測定値と非球面の輪郭形状の設計値とから非球面の輪郭形状の誤差を算出する。
このように、本発明の面形状の測定値の解析方法では、軸Aを挟んだ非対称な範囲Mの測定値のうち、軸Aを挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていない範囲Cに、設計座標における一つの座標軸に対して軸対称に補完する際に生じる誤差(即ち、上記境界部の段差)に着目し、その誤差が収束するまで、上記のような所定の収束計算、補完された範囲の仮測定値の削除、収束計算後の測定値を用いた補完処理を繰り返すようにしている。
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.
このようにすると、測定値を得ていない範囲に測定値を補完しても高精度な輪郭形状の誤差が得られるようになる。 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.
ここで、本発明による面形状の測定値の解析方法における処理を従来の面形状測定機において一般に行われている測定値と設計値との収束計算の処理と対比して説明する。
本発明に対する比較例として、従来の面形状測定機において一般に行われている、軸に対して対称な有効径の範囲全体を対象とした、測定値と設計値とを用いた収束計算を、図2を用いて説明する。
図2は従来の面形状測定機において一般に行われている収束計算における、測定値(測定結果)と設計値(設計式)との関係を示すグラフであり、(a)は収束計算実施前の測定範囲における測定値と設計値を各々示すグラフ、(b)は収束計算実施前の測定範囲における測定値と設計値との差を示すグラフ、(c)は収束計算実施後の測定範囲における測定値と設計値を各々示すグラフ、(d)は収束計算実施後の測定範囲における測定値と設計値との差を示すグラフである。
なお、説明の便宜上、図2では測定座標(被測定物の測定値の基準となる座標)の座標軸と設計座標(設計値の基準となる座標)の座標軸とが一致するように示してある。
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.
従来の面形状測定機において一般に行われている収束計算では、設計値又は設計式(測定範囲における設計値を結んだ線を示す式)に対して測定値、又は測定値に対して設計値を、平行移動や傾きが変化するように座標変換させながら、収束させていく。なお、収束計算は、通常、一回では収束せず、繰り返し行なわれる。測定値と設計値との差分(図2(b))は、収束計算を繰り返すことによって小さくなる。このように、測定値と設計値の一方を他方に対し平行移動や傾きが変化するように座標変換をさせる収束計算を行なうと、図2(a)に示した被測定物のアライメント誤差(被測定物を測定機に配置したときの測定座標における被測定物の平行方向や傾きなどの位置ズレ)が図2(c)に示すように取り除かれていく。そして、最終的に所定の収束条件を満たしたときの算出結果である図2(d)が非球面の輪郭形状の誤差となる。なお、ここでの所定の収束条件は、求められる誤差の精度に応じて決める。例えば、特許文献3に開示されている収束条件や、RMS値等が規格値になったとき等の条件が適用できる。 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.
さらに、非球面の輪郭形状の誤差の評価に際しては、上記したような被測定物のアライメント誤差を取り除くための収束計算に加えて、特許文献1及び特許文献2に開示されているように、設計式のR(曲率半径)や非球面係数を変化させることによって、非球面の輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を行なう。
そして、面形状の測定値の解析においては、被測定物の設置誤差を取り除くための収束計算の後に、非球面の輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を行なう処置手順と、これらの収束計算を同時に行なう処理手順を取り得る。
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
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.
そこで、本発明の面形状の測定値の解析方法において、まず、被測定物の設置誤差を取り除くための収束計算と、非球面の輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算とを別々に実施する処置手順の一例について図3を用いて説明する。また、その処理手順における各ステップでの測定値と設計値との差分を図4に示すこととする。
図3は本発明の面形状の測定値の解析方法を備えた面形状測定方法における処理手順の一例を示すフローチャートである。
図4は図3に示した処理手順で処理を行なう本発明の面形状測定機の収束計算における、測定値と設計値との関係を示すグラフであり、(a)は収束計算実施前の測定範囲における測定値と設計値を各々示すグラフ、(b)は収束計算実施前の測定範囲における測定値と設計値との差を示すグラフ、(c)は収束計算実施後の測定範囲における測定値と設計値を各々示すグラフ、(d)は収束計算実施後の測定範囲における測定値と設計値との差を示すグラフである。図5は図3に示した処理手順で処理を行なう本発明の面形状測定機の収束計算における、図4に示した処理工程以降での測定結果と設計式との関係を示すグラフであり、(a)は収束計算実施後の測定範囲における測定値の一部を不足範囲に設計座標の基準軸に対して補完したときの測定値と設計値を各々示すグラフ、(b)は(a)の補完処理後、収束計算実施前の測定範囲における測定値と設計値との差を示すグラフ、(c)は(a)の補完処理及び収束計算実施後の測定範囲における測定値と設計値との差を示すグラフ、(d)は(a)の補完処理及び収束計算実施後の測定範囲における測定値と設計値を各々示すグラフ、(e)は(d)の収束計算実施後の測定範囲から、不足範囲を削除したときの測定値と設計値を各々示すグラフである。図6は図3に示した処理手順で処理を行なう本発明の面形状測定機の収束計算における、図5に示した処理工程以降の測定結果と設計式との関係を示すグラフであり、(a)は収束計算実施後の測定範囲における測定値の一部を不足範囲に設計座標の基準軸に対して補完したときの測定値と設計値を各々示すグラフ、(b)は(a)の補完処理後、収束計算実施前の測定範囲における測定値と設計値との差を示すグラフ、(c)は(a)の補完処理及び収束計算実施後の測定範囲における測定値と設計値との差を示すグラフ、(d)は収束計算実施後の測定範囲からの不足範囲を削除する工程、収束計算実施後の測定範囲における測定値の一部の不足範囲へ補完する工程、収束計算する工程からなる処理を段差が最小になるまで繰り返した後に、非球面の輪郭形状の測定値と非球面の輪郭形状の設計値とを所定の演算を介して比較した結果を輪郭形状の誤差として示すグラフである。
なお、説明の便宜上、図4では測定座標(被測定物の測定値の基準となる座標)の座標軸と設計座標(設計値の基準となる座標)の座標軸とが一致するように示してある。また、図4におけるグラフでは、軸を挟んだ対称な有効径の範囲全体における設計値に対する図1で示した範囲Mにおける測定値の差を表している。
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.
まず、図4(a)に示す範囲Mにおける測定結果(xi、zi)[iは範囲Mにおける所定の測定点で各々得られた測定値の個数:1、2、・・・n]と設計式Yを収束計算(フィッティング)させる(ステップS11〜S21)。ここでは、設置誤差を除くための収束計算を所定の収束条件を満たすまで実施させている。
この収束計算を介して、測定結果に対して設計値、または設計値に対して測定値を、平行移動や傾きが変化するように座標変換させる。ここでは、設計値に対して測定値の座標を変換させて、図4(c)に示すように、座標変換後の測定値(xij、zij)[ここでは、j=1(ステップS11)]を得ている。
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.
次いで、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xij、zij)のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていない軸で隔てた他方の側の所定範囲Cに設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完して、有効径全体の測定値(xij+、zij+)を作成する(ステップS31)。
本来、軸を中心として回転対称な非球面を持つ光学部材の非球面を測定すれば、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部には段差が生じないはずである。
しかし、実際の面形状の測定においては、被測定物の測定値の基準軸と設計値の基準軸が一致していないために、収束計算をしても正確な収束ができず、上記境界部に段差Δが生じ易い。
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.
そこで、この段差Δを低減するために、有効径全体の測定値(xij+、zij+)の範囲を対象として、被測定物の設置誤差を取り除くための収束計算を実施して、座標変換された測定値(xi(j+1)+、zi(j+1)+)を得る。そして、座標変換後の軸に対して非対称な範囲Mの測定値(xi(j+1)+、zi(j+1)+)のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替える。即ち、まず、座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された仮測定値を削除する。そして、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xi(j+1)、zi(j+1))のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に補完する。これにより、有効径全体の測定値(xij+、zij+)[ここでは、j=j+1]を作成する。そして、この被測定物の設置誤差を取り除くための収束計算を実施する工程、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替える工程を段差が最小(略なくなる)と認められるための所定の一致条件(例えば、段差が所定の値以下になる)を満足するまで繰り返す。 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.
段差が最小になるまで収束させたとき、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の設置誤差が取り除かれたことになる。
これにより、測定値は、設計座標の基準軸に対して略軸対称に存在することになるので、測定値と設計値との偏差を計算することで、加工機等にフィードバックできる非球面の輪郭形状の誤差と評価結果を得ることができるようになる。
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.
なお、この段差が最小と認められると認められるための所定の一致条件を満足するまで繰り返す工程において行なう、被測定物の設置誤差を取り除くための収束計算は、1回でもよいし、所定の収束条件を満たすまで行なってもよい。また、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックは、被測定物の設置誤差を取り除くための収束計算の前、後いずれに行なってもよい。 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.
図3の例では、繰り返し工程(ステップS31〜S71)において、被測定物の設置誤差を取り除くための収束計算は、所定の収束条件を満たすまで行なっている(ステップS41)。
また、繰り返し工程において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算の後に行なっている(ステップS51)。
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 ).
このときの測定座標と設計座標の関係を図5(d)に示す。
繰り返し工程においては、収束計算(ステップS41)を経て座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された仮測定値を削除する(ステップS61、図5(e))。
そして、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xij、zij)[j=j+1(ステップS71)]のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完する(ステップS31)。これにより、座標変換後の新たな有効径全体の範囲の測定値(xij+、zij+)が得られる。
そして、再度、設計式に対し、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なう(ステップS41)。このときの測定値と設計値との関係は、図6(a)、図6(b)のようになる。
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).
そして、このステップS31〜S71の処理工程を繰り返すと、図6(c)に示すように、段差が次第に収束し、最終的には、所定範囲Cに補完された仮測定値又はそれを結ぶ線は、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と境界部において殆ど段差がなく一致する。 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.
つまり、このような状態になったときに、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の軸を挟んで対称となる有効径の範囲全体に測定値(xij、zij)が設定されたことになる。なお、ここで、jは収束計算の回数を示している。なお、段差が収束したことの確認は、段差Δ近傍のRMS値や重なる測定値の差分より行なうことができる。 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.
段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を介して座標変換された非球面の輪郭形状の測定値と、非球面の輪郭形状の設計値とから非球面の輪郭形状の誤差を算出する(ステップS81)。この算出値は、被測定物の設置誤差が取り除かれた正確な誤差として評価することができる。この非球面の輪郭形状の誤差の算出時における測定値と設計値との差を図6(d)に示す。 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.
さらに、有効径全体の測定値(xi(j+1)+、zi(j+1)+)の範囲を対象として、ステップS81で算出された非球面の輪郭形状の誤差に対して、誤差が最小となる曲率や非球面係数を求めるための収束計算を所定の収束条件を満たすまで行なう(ステップS91)。このようにすれば、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を評価することができる。 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.
変形例1
図7は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図3の例に対する一変形例を示すフローチャートである。
図7の例では、繰り返し工程(ステップS32〜S72)において、被測定物の設置誤差を取り除くために行なう収束計算の回数を1回にしている(ステップS42)。
即ち、図7の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替えている(ステップS62、S72、S32)。
また、図7の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS82)。
その他の処理手順は、図3の例と略同じである。
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.
変形例2
図8は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図3の例に対する他の変形例を示すフローチャートである。
図8の例では、繰り返し工程(ステップS33〜S73)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算の前に行なっている(ステップS43)。
その他の処理手順は、図3の例と略同じである。
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.
変形例3
図9は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図3の例に対するさらに他の変形例を示すフローチャートである。
図9の例では、繰り返し工程(ステップS34〜S74)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算の前に行なっている(ステップS44)。
また、図9の例では、繰り返し工程において、被測定物の設置誤差を取り除くための収束計算の回数を1回にしている(ステップS54)。
即ち、図9の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替えている(ステップS64、S74、S34)。
また、図9の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS84)。
その他の処理手順は、図3の例と略同じである。
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.
上述した図3、図7〜図9の例において、被測定物の設置誤差を取り除く収束計算を行なった後に、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を行なう処理手順を示したが、本発明の測定値の解析方法を備えた面形状測定方法は、この処理手順に限定されるものではない。被測定物の設置誤差を取り除く収束計算と、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を同時に行なうようにしても良い。
そこで、次に、被測定物の設置誤差を取り除く収束計算と、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を同時に行なう処理手順を備えた例について説明する。
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. .
図10は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の他の例を示すフローチャートである。
収束計算は、一般には、所定の収束条件を示すまで繰り返し行なう。しかし、測定値が得られていない領域Cが存在する状態で、設置誤差を取り除くための収束計算に加えて輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を同時に所定の収束条件を満たすまで繰り返すと、設置誤差を含んだ輪郭形状の誤差に対して、その輪郭形状の誤差が最小となる間違ったR(曲率半径)や非球面係数が算出されてしまう。
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.
そこで、図10の測定値の解析方法を備えた面形状測定方法においては、測定値が得られていない領域Cが存在する状態での、設置誤差を取り除くための収束計算と輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算とを同時に1回のみ行なうようにし、その収束計算の結果に基づいて、データ不足部への補完処理、収束計算処理、不足部からのデータ削除処理からなる処理を段差が最小となるまで繰り返すようにしている。 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.
まず、測定値(xi、zi)[iは測定データ数:1、2、・・・n]を得た軸を挟んだ非対称な範囲Mを対象として、測定値(xi、zi)[iは範囲Mにおける所定の測定点で各々得られた測定値の個数:1、2、・・・n]と設計式Yを収束(フィッティング)させる(ステップS111〜S121)。ここでは、設計値に対して設置誤差を取り除くための収束計算と、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算とを同時に1回のみ行なう。
この収束計算を介して、測定値に対して設計値、または設計値に対して測定値を、平行移動や傾きが変化するように座標変換させると同時に、設計式のR(曲率半径)を変形させる。
ところで、上述したように、通常、収束計算は、1回では収束条件を満たさない。このため、設計値の基準軸を挟んで非対称な状態となる。ここでは、設計値に対して測定結果の座標を変換させて、図11(a)に示すように、座標変換後の測定結果(xij、zij)[ここでは、j=1(ステップS111)]を得ている。
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.
次いで、図11(b)に示すように、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xij、zij)のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていないこの軸で隔てた他方の側の所定範囲Cに設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完して、有効径全体の範囲の測定値(xij+、zij+)を作成する(ステップS131)。
なお、図11(b)においては、説明を簡略化するため便宜的に、設計値に対する測定値の差分を所定範囲Cに仮測定値として補完しているように示してあるが、実際には、差分ではなく測定値を所定範囲Cに補完するデータ処理を行なう。
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.
上述したように、軸を中心として回転対称な非球面を持つ光学部材の非球面を測定すれば、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部には段差が生じないはずである。
段差が生じる原因は、実際の面形状の測定において、被測定物の測定結果の基準軸と設計式の基準軸が一致していないため、収束計算をしても正確な収束ができていないことにある。
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.
そこで、この段差Δを低減するために、有効径全体の測定値(xij+、zij+)の範囲を対象として、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を実施し、座標変換した測定値(xi(j+1)+、zi(j+1)+)を得る。そして、座標変換後の軸に対して非対称な範囲Mの測定値(xi(j+1)+、zi(j+1)+)のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替える。即ち、まず、座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された仮測定値を削除する。そして、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xi(j+1)、zi(j+1))のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に補完する。これにより、有効径全体の範囲の測定値(xij+、zij+)[ここでは、j=j+1]を作成する。そして、この被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を実施する工程、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替える工程を段差が最小(略なくなる)と認められるための所定の一致条件(例えば、段差が所定の値以下になる)を満足するまで繰り返す。 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.
段差が最小になるまで収束させたとき、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の設置誤差が取り除かれたことになる。
これにより、測定値は、設計座標の基準軸に対して略対称に存在することになるので、測定値と設計値との偏差を計算することで、加工機等にフィードバックできる非球面の輪郭形状の誤差と評価結果を得ることができるようになる。
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.
なお、この段差が最小と認められるための所定の一致条件を満足するまで繰り返す工程において行なう、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算は、1回でもよいし、所定の収束条件を満たすまで行なってもよい。また、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックは、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の前、後いずれに行なってもよい。 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.
図10の例では、繰り返し工程(ステップS131〜S171)において、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を、所定の収束条件を満たすまで行なっている(ステップS141)。
また、繰り返し工程において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の後に行なっている(ステップS151)。
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 ).
このときの設計値に対する測定値の差分を図11(c)に示す。
繰り返し工程においては、収束計算(ステップS141)を経て座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された範囲の仮測定値を削除する(ステップS161)。
そして、図11(d)に示すように、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xij、zij)[j=j+1(ステップS171)]のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完する(ステップS131)。これにより、座標変換後の新たな有効径全体の範囲の測定値(xij+、zij+)が得られる。
そして、再度、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を、所定の収束条件を満たすまで行なう(ステップS141)。
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 ).
そして、このステップS131〜S171の処理工程を繰り返すと、設計値に対する測定値の差分は、図11(c)、図11(d)、図11(e)、図11(f)に示すように、段差が次第に収束し、最終的には、所定範囲Cに補完された仮測定値又はそれを結ぶ線は、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と境界部において殆ど段差がなく一致する。 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.
つまり、このような状態になったときに、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の軸を挟んだ対称となる有効径の範囲全体に測定値(xij、zij)が設定されたことになる。なお、ここで、jは収束計算の回数を示している。なお、段差が収束したことの確認は、段差Δ近傍のRMS値や重なる測定値の差分より行なうことができる。 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.
段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を介して座標変換された非球面の輪郭形状の測定値と、非球面の輪郭形状の設計値とから非球面の輪郭形状の誤差を算出する(ステップS181)。この算出値は、被測定物の設置誤差が取り除かれた正確な誤差として評価することができる。 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.
変形例4
図12は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図10の例に対する一変形例を示すフローチャートである。
図12の例では、繰り返し工程(ステップS132〜S172)において、被測定物の設置誤差を取り除くための収束計算、非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を1回にしている(ステップS142)。
即ち、図12の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替えている(ステップS162、S172、S132)。
また、図12の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を、所定の収束条件を満たすまで行なっている(ステップS182)。
その他の処理手順は、図10の例と略同じである。
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.
変形例5
図13は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図10の例に対する他の変形例を示すフローチャートである。
図13の例では、繰り返し工程(ステップS133〜S173)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の前に行なっている(ステップS143)。
その他の処理手順は、図10の例と略同じである。
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.
変形例6
図14は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図10の例に対するさらに他の変形例を示すフローチャートである。
図14の例では、繰り返し工程(ステップS134〜S174)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の前に行なっている(ステップS144)。
また、図14の例では、繰り返し工程において、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を1回にしている(ステップS154)。
即ち、図14の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替えている(ステップS164、S174、S134)。
また、図14の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS184)。
その他の処理手順は、図10の例と略同じである。
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.
上述した図3、図7〜図9、図10、図12〜図14に示した処理手順の例では、測定値の一部を設計座標の基準軸に対して対称に補完する前に、軸を挟んだ非対称な範囲を対象として、設計値に対して設置誤差を取り除くための収束計算を少なくとも1回行なっている。なお、測定値に対して設計値を収束計算した場合は、設計式Yは設計式Y1に変化する。そこで、設計式Y1の基準軸に対して対称に測定結果(x、z)の一部を補完することになる。 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 .
なお、本発明の測定値の解析方法を備えた面形状測定方法は、被測定物の設置誤差(特に、シフト誤差)を小さくすることが可能な測定機においては、測定値の一部を設計座標の基準軸に対して軸対称に補完した後に、補完した範囲を含む有効径の全範囲の測定値を対象として、設計値に対して設置誤差を取り除くための収束計算を行なうような処理手順を採用することも可能である。 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.
被測定物の設置誤差(特に、シフト誤差)が大きいと、測定座標と設計座標のずれが大きくなる。そのような場合に、(被測定物の)軸を挟んだ非対称な範囲Mの測定値のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、設計値を得ていない軸で隔てた他方の側の所定範囲Cに設計座標の一つの基準軸Zに対して軸対称に仮測定値として補完すると、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された範囲Cの仮測定値又はそれを結ぶ線との境界部が大きく離れることになり、設計値に対して設置誤差を取り除くための収束計算を行なった結果を用いて得られる形状の誤差の精度が悪くなる。
しかし、測定前に、被測定物の軸近傍で、測定座標の原点を作る(即ち、プローブの位置座標をゼロに設定する)作業を実施することができれば、被測定物の設置誤差(特に、シフト誤差)を小さくすることができる。具体的には、プローブの位置は、リニアスケールやレーザで測長しているため、リニアスケールやレーザをゼロに設定するようにすることで可能となる。
そこで、本発明の測定値の解析方法を備えた面形状測定方法において、軸を挟んだ非対称な範囲Mの測定値のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を設計座標の一つの基準軸に対して軸対称に仮測定値として補完した後に、補完した範囲を含む有効径の全範囲を対象として、設計値に対して設置誤差を取り除くための収束計算を行なう処理手順を採用した例について説明する。
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.
図15は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の他の例を示すフローチャートである。
図15の例の測定値の解析方法を備えた面形状の測定方法では、まず、測定値(xi、zi)[iは測定データ数:1、2、・・・n]を得た軸を挟んだ非対称な範囲Mのうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていないこの軸で隔てた他方の側の所定範囲Cに設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完して、有効径全体の測定値(xij+、zij+)[ここでは、j=1(ステップS211)]を作成する(ステップS221)。
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 ).
次いで、有効径全体の測定値(xij+、zij+)[iは測定データ数:1、2、・・・n]の範囲を対象として、測定値(xij+、zij+)と設計式Yを収束計算(フィッティング)させる(ステップS231)。ここでは、設計式に対して設置誤差を取り除くための収束計算を所定の収束条件を満たすまで実施させている。
この収束計算を介して、測定値に対して設計式、または設計式に対して測定値を、平行移動や傾きが変化するように座標変換させる。ここでは、設計式に対して測定結果の座標を変換させて、座標変換後の測定結果(xi(j+1)+、zi(j+1)+)[ここでは、j=1(ステップS211)]を得ている。
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.
次いで、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを行なう(ステップS241)。
上述したように、軸を中心として回転対称な非球面を持つ光学部材の非球面を測定すれば、軸に非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部には段差が生じないはずである。
段差が生じる原因は、実際の面形状の測定において、被測定物の測定結果の基準軸と設計式の基準軸が一致していないため、収束計算をしても正確な収束ができていないことにある。
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.
そこで、この段差Δを低減するために、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xi(j+1)+、zi(j+1)+)のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替える。即ち、まず、座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された仮測定値を削除する。そして、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xij、zij)[ここでは、j=j+1]のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完する。これにより、有効径全体の範囲の測定値(xij+、zij+)を作成する。そして、この軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替える工程、被測定物の設置誤差を取り除くための収束計算を実施する工程を段差が最小(略なくなる)と認められるための所定の一致条件(例えば、段差が所定の値以下になる)を満足するまで繰り返す。 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.
段差が最小になるまで収束させたとき、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の設置誤差が取り除かれたことになる。
これにより、測定値は、設計座標の基準軸に対して略対称に存在することになるので、測定値と設計値との偏差を計算することで、加工機等にフィードバックできる非球面の輪郭形状の誤差と評価結果を得ることができるようになる。
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.
なお、この段差が最小と認められると認められるための所定の一致条件を満足するまで繰り返す工程において行なう、被測定物の設置誤差を取り除くための収束計算は、1回でもよいし、所定の収束条件を満たすまで行なってもよい。また、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックは、被測定物の設置誤差を取り除くための収束計算の前、後いずれに行なってもよい。 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.
図15の例では、繰り返し工程(ステップS231〜S271)において、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS231)。
また、繰り返し工程において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算の後に行なっている(ステップS241)。
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 ).
繰り返し工程においては、収束計算(ステップS241)を経て座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された範囲の仮測定値を削除する(ステップS251)。
そして、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xij、zij)[j=j+1(ステップS261)]のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完する(ステップS271)。これにより、座標変換後の新たな有効径全体の範囲の測定値(xij+、zij+)が得られる。
そして、再度、設計式に対し、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なう(ステップS231)。
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 ).
そして、このステップS231〜S271の処理工程を繰り返すと、設計値に対する測定値の差分は、段差が次第に収束し、最終的には、所定範囲Cに補完された仮測定値又はそれを結ぶ線は、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と境界部において殆ど段差がなく一致する。 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.
つまり、このような状態になったときに、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の軸を挟んだ対称となる有効径の範囲全体に測定値(xij、zij)が設定されたことになる。なお、ここで、jは収束計算の回数を示している。なお、段差が収束したことの確認は、段差Δ近傍のRMS値や重なる測定値の差分より行なうことができる。 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.
段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を介して座標変換された非球面の輪郭形状の測定値と、非球面の輪郭形状の設計値とから非球面の輪郭形状の誤差を算出する(ステップS281)。この算出値は、被測定物の設置誤差が取り除かれた正確な誤差として評価することができる。 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.
さらに、有効径全体の測定値(xi(j+1)+、zi(j+1)+)の範囲を対象として、ステップS281で算出された非球面の輪郭形状の誤差に対して、誤差が最小となる曲率や非球面係数を求めるための収束計算を所定の収束条件を満たすまで行なう(ステップS291)。このようにすれば、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を評価することができる。 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.
変形例7
図16は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図15の例に対する一変形例を示すフローチャートである。
図16の例では、繰り返し工程(ステップS232〜S272)において、被測定物の設置誤差を取り除くための収束計算を1回にしている(ステップS232)。
即ち、図16の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替えている(ステップS252、S262、S272)。
また、図16の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS292)。
その他の処理手順は、図15の例と略同じである。
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.
変形例8
図17は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図15の例に対する他の変形例を示すフローチャートである。
図17の例では、繰り返し工程(ステップS233〜S273)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算の前に行なっている(ステップS233)。
なお、測定値(xi、zi)[iは測定データ数:1、2、・・・n]を得た軸を挟んだ非対称な範囲Mのうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていないこの軸で隔てた他方の側の所定範囲Cに設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完して、有効径全体の範囲の測定値(xij+、zij+)[ここでは、j=1(ステップS213)]を作成した(ステップS223)ときに、所定範囲Cに補完された仮測定値又はそれを結ぶ線は、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と境界部において殆ど段差がなく一致した場合には、繰り返し工程を経ず、収束計算を1回も行なっていないことになる。そこで、そのような場合には、有効径全体の測定値(xij+、zij+)の範囲を対象として、被測定物の設置誤差を取り除くための収束計算を所定の収束条件を満たすまで行ない、座標変換した測定値(xi(j+1)+、zi(j+1)+)を得る(ステップS293)。
その他の処理手順は、図15の例と略同じである。
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.
変形例9
図18は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図15の例に対するさらに他の変形例を示すフローチャートである。
図18の例では、繰り返し工程(ステップS234〜S274)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算の前に行なっている(ステップS234)。
また、図18の例では、繰り返し工程において、被測定物の設置誤差を取り除くための収束計算の回数を1回にしている(ステップS254)。
即ち、図18の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替えている(ステップS254、S264、S274)。
また、図18の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS284)。
その他の処理手順は、図15の例と略同じである。
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.
上述した図15〜図18の例において、被測定物の設置誤差を取り除く収束計算を行なった後に、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を行なう処理手順を示したが、上述したように、本発明の測定値の解析方法を備えた面形状測定方法は、この処理手順に限定されるものではない。被測定物の設置誤差を取り除く収束計算と、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を同時に行なうようにしても良い。
そこで、次に、被測定物の設置誤差を取り除く収束計算と、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を同時に行なう処理手順を備えた例について説明する。
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. .
図19は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の他の例を示すフローチャートである。
収束計算は、一般には、所定の収束条件を示すまで繰り返し行なう。しかし、測定値が得られていない領域Cが存在する状態で、設置誤差を取り除くための収束計算に加えて輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算を同時に所定の収束条件を満たすまで繰り返すと、設置誤差を含んだ輪郭形状の誤差に対して、その輪郭形状の誤差が最小となる間違ったR(曲率半径)や非球面係数が算出されてしまう。
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.
そこで、図19の測定値の解析方法を備えた面形状測定方法においては、測定値が得られていない領域Cが存在する状態での、設置誤差を取り除くための収束計算と輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算とを同時に1回のみ行なうようにし、その収束計算の結果に基づいて、データ不足部への補完処理、収束計算処理、不足部からのデータ削除処理からなる処理を段差が最小となるまで繰り返すようにしている。 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.
まず、測定値(xi、zi)[iは測定データ数:1、2、・・・n]を得た軸に対して非対称な範囲Mのうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていないこの軸で隔てた他方の側の所定範囲Cに設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完して、有効径全体の範囲の測定値(xij+、zij+)[ここでは、j=1(ステップS411)]を作成する(ステップS421)。 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 ).
次いで、有効径全体の測定値(xij+、zij+)[iは測定データ数:1、2、・・・n]の範囲を対象として、測定値(xij+、zij+)と設計式Yを収束計算(フィッティング)させる(ステップS431)。ここでは、設計式に対して設置誤差を取り除くための収束計算と、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を求める収束計算とを同時に1回のみ行なう。
この収束計算を介して、測定値に対して設計式、または設計式に対して測定値を、平行移動や傾きが変化するように座標変換させると同時に、設計式のR(曲率半径)を変形させる。
ところで、上述したように、通常、収束計算は、1回では収束条件を満たさない。このため、設計式の基準軸に対して非対称な状態となる。ここでは、設計式に対して測定結果の座標を変換させて、座標変換後の測定値(xi(j+1)+、zi(j+1)+)[ここでは、j=1(ステップS411)]を得ている。
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.
上述したように、軸を中心として回転対称な非球面を持つ光学部材の非球面を測定すれば、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部には段差が生じないはずである。
段差が生じる原因は、実際の面形状の測定において、被測定物の測定値の基準軸と設計式の基準軸が一致していないため、収束計算をしても正確な収束ができていないことにある。
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.
そこで、この段差Δを低減するために、座標変換後の軸を挟んだ非対称な範囲Mの測定値(xi(j+1)+、zi(j+1)+)のうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替える。即ち、まず、座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された仮測定値を削除する。そして、座標変換後の軸に対して非対称な範囲Mの測定値(xi(j+1)、zi(j+1))のうち、軸に対して対称な範囲を除いた範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完する。これにより、有効径全体の範囲の測定値(xij+、zij+)[ここでは、j=j+1]を作成する。さらに、有効径全体の測定値(xij+、zij+)の範囲を対象として、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を実施し、座標変換した測定値(xi(j+1)+、zi(j+1)+)を得る。そして、この軸を挟んだ対称な範囲を除いた範囲の測定値を、それ以前の処理工程において補完されている測定値と入れ替える工程、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を実施する工程、を段差が最小(略なくなる)と認められるための所定の一致条件(例えば、段差が所定の値以下になる)を満足するまで繰り返す。 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.
段差が最小になるまで収束させたとき、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の設置誤差が取り除かれたことになる。
これにより、測定値は、設計座標の基準軸に対して略軸対称に存在することになるので、測定結果と設計式の偏差を計算することで、加工機等にフィードバックできる非球面の輪郭形状の誤差と評価結果を得ることができるようになる。
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.
なお、この段差が最小と認められると認められるための所定の一致条件を満足するまで繰り返す工程において行なう、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算は、1回でもよいし、所定の収束条件を満たすまで行なってもよい。また、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックは、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の前、後いずれに行なってもよい。 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.
図19の例では、繰り返し工程(ステップS441〜S481)において、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算は、所定の収束条件を満たすまで行なっている(ステップS481)。
また、繰り返し工程において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の後に行なっている(ステップS441)。
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 ).
繰り返し工程においては、座標変換後の測定値(xi(j+1)+、zi(j+1)+)のうち、それ以前の工程において補完されている所定範囲Cに補完された仮測定値を削除する(ステップS451)。
そして、座標変換後の軸に対して非対称な範囲Mの測定値(xij、zij)[j=j+1(ステップS461)]のうち、軸に対して対称な範囲Maを除いた範囲Mbの測定値を、所定範囲Cに、設計座標における一つの座標軸Zに対して軸対称に仮測定値として補完する(ステップS471)。これにより、座標変換後の新たな有効径全体の測定値(xij+、zij+)が得られる。
そして、再度、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を、所定の収束条件を満たすまで行なう(ステップS481)。
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 ).
そして、このステップS441〜S481の処理工程を繰り返すと、設計値に対する測定値の差分は、段差が次第に収束し、最終的には、所定範囲Cに補完された測定値又はそれを結ぶ線は、軸に非対称な測定値又はそれを結ぶ線と境界部において殆ど段差がなく一致する。 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.
つまり、このような状態になったときに、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の軸に対して対称となる有効径の範囲全体に測定値(xij、zij)が設定されたことになる。なお、ここで、jは収束計算の回数を示している。なお、段差が収束したことの確認は、段差Δ近傍のRMS値や重なる測定値の差分より行なうことができる。 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.
段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を介して座標変換された非球面の輪郭形状の測定値と、非球面の輪郭形状の設計値とから非球面の輪郭形状の誤差を算出する(ステップS491)。この算出値は、被測定物の設置誤差が取り除かれた正確な誤差とすることができる。 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.
変形例10
図20は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図19の例に対する一変形例を示すフローチャートである。
図20の例では、繰り返し工程(ステップS432〜S472)において、被測定物の設置誤差を取り除くための収束計算、非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を1回にしている(ステップS432)。
即ち、図20の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている仮測定値と入れ替えている(ステップS452、S462、S472)。
また、図20の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算を、所定の収束条件を満たすまで行なっている(ステップS482)。
その他の処理手順は、図19の例と略同じである。
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.
変形例11
図21は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図19の例に対する他の変形例を示すフローチャートである。
図21の例では、繰り返し工程(ステップS433〜S473)において、軸に非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の前に行なっている(ステップS433)。
なお、測定値(xi、zi)[iは測定データ数:1、2、・・・n]を得た軸を挟んだ非対称な範囲Mのうち、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、測定値を得ていない該軸で隔てた他方の側の所定範囲Cに設計座標における一つの座標軸Zに対して軸対称に補完して、有効径全体の測定値(xij+、zij+)[ここでは、j=1(ステップS413)]を作成した(ステップS423)ときに、所定範囲Cに補完された測定値又はそれを結ぶ線は、軸に非対称な範囲Mの測定値又はそれを結ぶ線と境界部において殆ど段差がなく一致した場合には、繰り返し工程を経ず、収束計算を1回も行なっていないことになる。そこで、そのような場合には、有効径全体の測定値(xij+、zij+)の範囲を対象として、被測定物の設置誤差を取り除くための収束計算を所定の収束条件を満たすまで行ない、座標変換した測定値(xi(j+1)+、zi(j+1)+)を得る(ステップS493)。
その他の処理手順は、図19の例と略同じである。
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.
変形例12
図22は本発明の測定値の解析方法を備えた面形状測定方法における処理手順の図19の例に対するさらに他の変形例を示すフローチャートである。
図22の例では、繰り返し工程(ステップS434〜S474)において、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、補完された所定範囲Cの仮測定値又はそれを結ぶ線との境界部の段差チェックを、被測定物の設置誤差を取り除くための収束計算、及び非球面の輪郭形状の誤差が最小となる曲率や非球面係数を求めるための収束計算の前に行なっている(ステップS434)。
また、図22の例では、繰り返し工程において、被測定物の設置誤差を取り除くための収束計算を1回にしている(ステップS444)。
即ち、図22の例では、1回の収束計算ごとに、軸を挟んだ対称な範囲Maを除いた範囲Mbの測定値を、それ以前の処理工程において補完されている測定値と入れ替えている(ステップS454、S464、S474)。
また、図22の例では、段差の一致条件を満たして、繰り返し工程を終了後に、被測定物の設置誤差を取り除くための収束計算を、所定の収束条件を満たすまで行なっている(ステップS484)。
その他の処理手順は、図19の例と略同じである。
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.
上述した図15〜図22に示した処理手順の例では、測定値の一部を設計座標の基準軸に対して軸対称に仮測定値として補完した後に、軸を挟んだ非対称な範囲を対象として、設計式に対して設置誤差を取り除くための収束計算を少なくとも1回行なっている。なお、測定結果に対して設計式を収束計算した場合は、設計式Yは設計式Y1に変化する。そこで、設計式Y1の基準軸に対して軸対称に測定結果(x、z)の一部を仮測定値として補完することになる。 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.
次に、本発明の面形状の測定値の解析方法における処理手順の一例を図23を用いて説明する。また、その処理手順における各ステップでの測定値と設計値との差分を図24に示すこととする。
図23は本発明の測定値の解析方法を備えた面形状の測定方法における処理手順の一例を示すフローチャートである。
図24は図23に示した処理手順で処理を行なう本発明の面形状測定機の収束計算における、測定値と設計値との関係を示すグラフであり、(a)は軸に対して測定値を反転させたときの測定値と設計値を各々示すグラフ、(b)は(a)の反転処理時の測定値と設計値との差を示すグラフ、(c)は(a)の反転処理後、反転前の測定値と反転前の測定値とが重なり合う範囲において、反転前の測定値と反転後の測定値との誤差が最小となるように座標変換したときの測定値と設計値との差を示すグラフ、(d)は座標変換後の非球面の輪郭形状の測定値と非球面の輪郭形状の設計値とを所定の演算を介して比較した結果を輪郭形状の誤差として示すグラフである。
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.
本発明の測定値の解析方法では、軸Aを挟んだ非対称な範囲Mの測定値(xi、zi)[iは範囲Mにおける所定の測定点で各々得られた測定値の個数:1、2、・・・n]の全部又は一部を、もとの測定値(xi、zi)と一部で重なるように、軸Aに対して軸対称に反転して、有効径全体の測定値(xi+、zi+)を作成する(ステップS51)。なお、図23、図24の例では、軸Aを挟んだ非対称な範囲Mの測定値(xi、zi)のうち、軸Aを隔てて有効径の測定値を得ている側の値を反転させたが、もとの測定値(xi、zi)と一部で重なるように反転させることで有効径全体の測定値が作成できれば、反転させる範囲は限定されない。例えば、軸Aを挟んだ非対称な範囲Mの測定値(xi、zi)の全部を反転させても良い。
本来、軸を中心として回転対称な非球面を持つ光学部材の非球面を測定すれば、軸を挟んだ非対称な範囲Mの測定値又はそれを結ぶ線と、反転した範囲の測定値又はそれを結ぶ線とには段差が生じないはずである。
しかし、実際の面形状の測定においては、被測定物の測定値の基準軸と設計値の基準軸が一致していないために、収束計算をしても正確な収束ができず、段差Δが生じ易い。
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.
そこで、この段差Δを低減するために、有効径全体の測定値(xi+、zi+)の範囲のうち、反転前の非球面の輪郭形状の測定値と反転後の非球面の輪郭形状の測定値とが重なり合う範囲において、反転前の非球面の輪郭形状の測定値と反転後の非球面の輪郭形状の測定値との誤差が最小となるように座標変換して補完し、これらの範囲を合わせた全範囲の測定値(xi1+、Zi1+)を得る(ステップS52)。 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).
次いで、被測定物の設置誤差を取り除くための収束計算を介して座標変換された非球面の輪郭形状の測定値と、非球面の輪郭形状の設計値とから非球面の輪郭形状の誤差を算出する(ステップS53)。この算出値は、被測定物の設置誤差が取り除かれた正確な誤差として評価することができる。この非球面の輪郭形状の誤差の算出時における測定値と設計値との差を図24(d)に示す。 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.
このとき、測定座標の基準軸と設計座標の基準軸が略完全に一致し、被測定物の設置誤差が取り除かれたことになる。
これにより、測定値は、設計座標の基準軸に対して略軸対称に存在することになるので、測定値と設計値との偏差を計算することで、加工機等にフィードバックできる非球面の輪郭形状の誤差と評価結果を得ることができるようになる。
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.
さらに、有効径全体の測定値(xi1+、zi1+)の範囲を対象として、ステップS54で算出された非球面の輪郭形状の誤差に対して、誤差が最小となる曲率や非球面係数を求めるための収束計算を所定の収束条件を満たすまで行なう(ステップS54)。このようにすれば、輪郭形状の誤差が最小となるR(曲率半径)や非球面係数を評価することができる。 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.
なお、被測定物のアライメント誤差が大きい場合には、図3のステップS21に示すのと同様の設置誤差を除くための収束計算を行なうようにしてもよい。
即ち、上述したステップS51の処理に先立ち、例えば、まず、図4(a)に示した範囲Mにおける測定結果(xi、zi)[iは範囲Mにおける所定の測定点で各々得られた測定値の個数:1、2、・・・n]と設計式Yを収束計算(フィッティング)させ(ステップS11〜S21)、設置誤差を除くための収束計算を所定の収束条件を満たすまで実施させる。
この収束計算を介して、測定結果に対して設計値、または設計値に対して測定値を、平行移動や傾きが変化するように座標変換させる。例えば、設計値に対して測定値の座標を変換させて、図4(c)に示したように、座標変換後の測定値(xi1、zi1)を得る。
そして、この座標変換後の測定値(xi1、zi1)を用いて、上述したステップS51〜S54と同様の処理を行なう。
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.
次に、本発明の面形状の測定値の解析方法を行なう本発明の面形状測定機の実施形態について図を用いて説明する。なお、本発明の面形状測定機は、以下の実施形態に限定されるものではない。
図1(a)は本発明の一実施形態にかかる面形状測定機における被測定物の保持部を表す説明図である。
保持部12は、基台12aと回動台12bを有している。回動台12bは、被測定物Oを載置する載置部12b1と、X−Z面に対して垂直な所定の軸Bを回転中心とした曲率を有する摺動面12b2を有している。基台12aは固定されている。基台12aの内側は、摺動面12b2が摺動に合わせた曲率を有する摺動面12a1を有している。そして、保持部12は、基台12aに対して回動台12bが所定の軸Bを中心として回動し、例えば、図25に示すように、測定用のプローブ11に対し被測定物Oを傾斜させることが可能となっている。
なお、本実施形態では、プローブ11は、接触式のものを用いているが、非接触式のものを用いてもよい。また、被測定物Oは、軸を中心として回転対称な非球面を持つ光学部材であれば、凹面、凸面のいずれの面形状を持つものでもよい。
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
In the present embodiment, a
図25はプローブ11の先端部を接触させたときの接触する面の法線と軸Aとのなす角度aが90度となるように、保持部12の回動台12bを傾斜させて、被測定物Oである軸を中心として回転対称な非球面を持つ光学部材におけるその非球面の輪郭形状を測定する様子を示す説明図である。図25中、Dは保持部12の中心軸、Bは回動台12bの回転中心である。
In FIG. 25, the
ここで、回動台12bの回転中心Bと被測定物Oの被測定面における軸A付近の曲率中心とが一致するように配置すれば、被測定物における所定の範囲Mを測定しやすくなるので望ましい。
しかし、そのためには、非球面形状の異なる被測定物を測定するたびに、保持部12に回動台12bの回転中心Bと被測定物の被測定面における軸A付近の曲率中心とを一致させるための治具が必要になり、現実的ではない。
このため、本実施形態の面形状測定機を用いた面形状測定方法においては、回動台12bの回転中心Bと被測定物Oの被測定面における軸A付近の曲率中心とが一致しない場合についても、輪郭形状の測定が可能にしている。なお、その方法については後述する。
Here, if the rotation center B of the
However, for this purpose, every time a measurement object having a different aspherical shape is measured, the rotation center B of the
For this reason, in the surface shape measuring method using the surface shape measuring machine of this embodiment, the rotation center B of the
本実施形態の面形状測定機を用いた面形状測定方法について図26を用いて説明する。
図26は本実施形態にかかる面形状測定機を用いた面形状測定方法における輪郭形状の測定手順を示す説明図である。
まず、被測定物Oの設計式を用いて、プローブ11と被測定面との最大接触角度(即ち、プローブ11の先端部を接触させたときの接触する面の法線と軸Aとのなす角度a)を算出する(ステップS61)。次いで、算出した接触角度が、面形状測定機において測定可能な範囲であるか否かを判断する(ステップS62)。なお、初期状態においては、保持部12の回動台12bは、図1(a)に示すように、被測定物Oを載置する面を水平に保った状態にして配置されている。
算出した接触角度が面形状測定機において測定可能な範囲内の場合、被測定物Oの姿勢を補正せずに測定する。すなわち、保持部12の回動台12bにおける被測定物Oを載置する面を水平に保った状態のまま、被測定物Oにおける被測定面の輪郭形状を測定する(ステップS64)。
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
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
算出した接触角度が面形状測定機において測定可能な範囲外の場合、即ち、被測定物の被測定面において面形状測定機の測定可能範囲外となる部位については、被測定物の姿勢を補正(ステップS63)して測定する。すなわち、保持部12における基台12aに対し、被測定物Oを載置した回動台12bを、水平状態から所定角度αだけ傾斜させる。これに伴い、被測定物Oは、水平状態から所定角度αだけ傾斜する。
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
ここで、被測定物の姿勢を補正するための傾斜角度αの決定は、次のようにして行なう。
通常、接触式のプローブの測定可能範囲は、プローブの先端部に対して接触する面の法線と軸Aとのなす角度(接触角度)aが60度以内となっている。
また、非接触式のプローブの測定可能範囲は、プローブの先端部に対して接触する面の法線と軸Aとのなす角度aが30度以内となっている。
ここで、被測定物Oの設計式より算出される、プローブの先端部に対して接触する面の法線と軸Aとのなす最大接触角度をbとすると、次のように傾斜角度αを決定することができる。
b≦aのとき、保持部12における回動台12bは、水平状態を保ち、傾斜角度α=0となる。
b>aであり、且つ、
b/2<aのとき、保持部12における回動台12bの傾斜角度αは、b−a≦α<aとなる。
b/2≧aのとき、傾斜角度αは、測定可能範囲内で測定値が重畳する角度が測定毎に選択される。
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
b> a, and
When b / 2 <a, the inclination angle α of the
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.
例えば、接触式のプローブを有する面形状測定機(プローブの先端部に対して接触する被測定物の面の法線と軸Aとのなす角度aが60度以内)を介して、プローブの先端部に対して接触する面の法線と軸Aとのなす最大接触角度bが90度となる被測定物Oを測定する場合、b>a、且つ、b/2<aであり、傾斜角度αはb−a≦α<aであるから30度以上60度未満である。図25の例では、回動台12bを傾斜角度α=30度で傾斜させている。
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
ここで、回動台12bの回転中心Bと被測定物Oの被測定面における軸A付近の曲率中心とが一致しない場合の測定方法について、図27を用いて説明する。
プローブ11先端の位置Pと回動台12bの回転中心Bは、面形状測定機の設計値から容易に分かる。そこで、図27(a)に示すように、傾斜角度α=0に設定された保持部12における回動台12bの載置部12b1の中心部に被測定物Oを載置する。次いで、プローブ11を被測定物Oにおける光軸A位置近傍に接触させて、プローブ先端の位置情報を取得する。
プローブ11先端の位置Pと、保持部12における回動台12bの回転中心Bの位置関係(距離S)は既知であることから、被測定面までのプローブ11の移動量Lがわかれば、被測定物Oの位置関係も明確になり、プローブ11と被測定物Oの位置関係が把握できる。
つまり、図27(b)に示すように、保持部12における回動台12bを所定の傾斜角度αだけ傾斜させたときの被測定物Oの面頂位置の横方向の移動量Δxは、式(1)に従って計算できる。その結果、被測定物Oの測定面の測定位置を正確に把握することができる。
ここで、距離Sは、プローブ11先端の位置Pに対して、被測定物Oの方向に保持部12における回動台12bの回転中心BがあればS>0とし、逆方向にある場合はS<0とする。
(数1)
被測定物Oの面頂位置のずれ:
Δx=|L−S|sinα …(1)
Here, a measurement method in the case where the rotation center B of the
The position P of the tip of the
Since the positional relationship (distance S) between the position P of the tip of the
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
Here, the distance S is S> 0 if there is a rotation center B of the
(Equation 1)
Deviation of the top position of the object under test O:
Δx = | LS−sin α (1)
被測定物Oの姿勢を補正後、輪郭形状を測定する(ステップS64)。
このステップS61〜ステップS64の処理を、軸Aで隔てた一方の側の最外径の位置P1から他方の側の所定位置P2までの軸Aを挟んだ非対称な範囲Mについて行なう(ステップS65,S66)。
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).
次いで、輪郭形状の測定結果を評価するため、上述した解析方法による解析処理を行なう。
このため、本実施形態によれば、軸を挟んだ対称な有効径の範囲のうち、軸を挟んだ対称な一方の側の一部を測定しなくても、輪郭形状の誤差を高精度に算出・評価することができる。
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.
上述した、本発明の実施形態においては、プローブ11の先端部に対して接触する被測定物Oの面の法線と軸Aとのなす最大角度bが、面形状測定機での測定可能範囲を超えた場合、被測定物の姿勢を変化させるため保持部12の回動台12aを所定の傾斜角度αだけ傾斜させた例について説明した。
ところで、面形状測定機での測定可能範囲を超えた場合、基本的にはプローブ11と被測定物Oとの相対的な角度を変化させればよい。このため、被測定物に対するプローブ11の傾斜角度αを変化させる構成、測定方法としてもよい。本発明の解析方法は、いずれの構成・方法による測定値に対しても用いることができる。
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
By the way, when it exceeds the measurable range with the surface shape measuring instrument, basically the relative angle between the
そこで、本発明の他の実施形態として被測定物に対するプローブの所定の傾斜角度αを変化させる例について説明する。この場合、傾斜角度αを変化させた場合のプローブと被測定物の位置関係の算出方法が、上述した算出方法とは異なる。
そこで、この場合におけるプローブと被測定物の位置関係の算出方法を、図28を用いて説明する。
図28は本発明の他の実施形態にかかる面形状測定機、及び面形状測定方法を用いて被測定物の非球面の輪郭形状を測定する様子を示す説明図であり、(a)は傾斜角度0度に設定されたプローブ先端の位置とプローブを傾斜させる手段の回転中心の位置関係を示す図、(b)はプローブを一定の傾斜角度だけ傾斜させた状態を示す図である。
本実施形態の測定方法では、プローブ11を被測定物Oに対し、傾斜させている。
まず、プローブ11の軸A’と被測定物Oの軸Aとのなす角度(傾斜角度)を角度α’とする。ここで、プローブ11を傾斜させる手段は、不図示のエアースピンドル、ゴニオステージなど、特に限定されない。
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
First, an angle (inclination angle) formed by the axis A ′ of the
まず、α’=0のとき、被測定物Oの面頂にプローブ11を接触させてプローブ11先端の位置情報を取得する。
図28(a)に示す傾斜角度0度に設定されたプローブ11先端の位置Pとプローブ11を傾斜させる手段の回転中心OPの位置関係(距離SP)は、設計上既知であることから、図28(b)に示すプローブ11を一定の傾斜角度α’だけ変化させたときのプローブ11の位置の横方向の移動量Δx’は式(2)に従って計算することができる。その結果、被測定物Oの測定面の測定位置を正確に把握することができる。
ここで、距離SPは、プローブ11を傾斜させる手段の回転中心OPが、プローブ11先端の位置Pに対して被測定物Oの方向に位置するときはSP>0、逆方向に位置するときはSP<0とする。
(数2)
プローブの接触点と被測定物の面頂位置のずれ:
Δx’=|LP−SP|sinα’ …(2)
First, when α ′ = 0, the
Positional relationship between the rotational center O P means for inclining the position P and the
Here, the distance S P is S P > 0 when the rotation center O P of the means for inclining the
(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)
プローブ11の傾斜角度を補正後、輪郭形状を測定する。そして、上述したステップS61〜S64の処理を、軸Aで隔てた一方の側の最外径の位置P1から他方の側の所定位置P2までの軸Aを挟んだ非対称な範囲Mについて行なう。
次いで、輪郭形状の誤差を測定するため、上述した解析方法による解析処理を行なう。
After correcting the tilt angle of the
Subsequently, in order to measure the error of the contour shape, analysis processing by the above-described analysis method is performed.
従って、本発明の面形状の測定装置によれば、従来のように、軸を中心として回転対称な非球面を持つ部材における、その非球面の輪郭形状の測定において、軸を挟んだ対称な有効径の範囲全体を対象として測定することなく輪郭形状の誤差を高精度に評価することができる。
そして、軸を挟んだ対称な有効径の範囲全体を対象として測定しなくて済む結果、プローブとの接触角度が測定機の許容傾斜角度の範囲以上となる輪郭形状を持つ被測定物に対し、その被測定物を傾けて有効径の範囲を測定する場合において、測定回数、測定時間を大幅に低減することができる。
なお、測定後の解析における収束計算は、コンピュータを介して行なうため、収束計算結果を瞬時に得ることができる。このため、仮に、本発明における収束計算の繰り返し回数が、従来の有効径の範囲全体を対象として測定した測定結果に対して収束計算を行なう場合の繰り返し回数より増えたとしても、処理時間に及ぼす影響は殆どなく、測定時間を低減する効果を損ねることはない。
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.
本発明は、軸を中心として回転対称な非球面を持つ光学部材やその金型、部品などの面形状を測定し、評価することが求められる分野に有用である。 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.
10 面形状測定機
11 プローブ
12 保持部
12a 基台
12b 回動台
12a1 摺動面
12b1 載置部
12b2 摺動面
A 被測定物の軸
A’ プローブの軸
B 回動台の回転中心
C 測定値が欠落または不足する範囲
M 軸Aを挟んだ非対称な範囲
Ma 範囲Mのうち、軸Aを挟んだ対称な範囲
Mb 範囲Mのうち、範囲Maを除いた範囲
O 被測定物
P プローブ先端の位置
P1 軸Aで隔てた一方の側の最外径の位置
P2 他方の側の所定位置
a プローブの先端部に対して接触する面の法線と軸Aとのなす角度
α 回動台の傾斜角度
α’ プローブの傾斜角度
DESCRIPTION OF
Claims (12)
前記非球面の輪郭形状を測定する輪郭形状測定手段と、前記非球面の輪郭形状の設計値との形状誤差を算出する形状誤差算出手段とを備え、
前記輪郭形状測定手段は、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、
前記形状誤差算出手段は、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を用いて、測定値を得ていない前記軸で隔てた他方の側の所定範囲に仮測定値として補完し、
次いで、前記軸を挟んだ非対称な範囲と前記仮測定値を補完された範囲とを合わせた範囲において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と前記仮測定値と前記非球面の輪郭形状の設計値とを用いて、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める計算を行なうことを特徴とする面形状測定機。 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 .
前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、
次いで、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値を用いて、測定値を得ていない前記軸で隔てた他方の側の所定範囲に仮測定値として補完し、
次いで、前記軸を挟んだ非対称な範囲と前記仮測定値を補完された範囲とを合わせた範囲において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と前記仮測定値と前記非球面の輪郭形状の設計値とを用いて、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める計算を行なうことを特徴とする面形状測定方法。 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 .
前記軸を挟んだ非対称な範囲において測定された、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値を用いて、測定値を得ていない前記軸で隔てた他方の側の所定範囲に仮測定値として補完し、
次いで、前記軸を挟んだ非対称な範囲と前記仮測定値を補完された範囲とを合わせた範囲において、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と前記仮測定値と前記非球面の輪郭形状の設計値とを用いて、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める計算を行なうことを特徴とする面形状の測定値の解析方法。 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. .
前記非球面の輪郭形状を測定する輪郭形状測定手段と、前記非球面の輪郭形状の設計値との形状誤差を算出する形状誤差算出手段とを備え、
前記輪郭形状測定手段は、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、
前記形状誤差算出手段は、
前記輪郭形状測定手段が測定した前記非球面の輪郭形状の測定値と、前記非球面の輪郭形状の設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と、前記設計値と、の差を求める第一の計算を行ない、
前記第一の計算後の非球面の輪郭形状の測定値のうち、前記軸を挟んだ対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に仮測定値として補完する第一の処理工程と、
前記軸を挟んだ前記第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値との境界部に段差がある場合、前記軸を挟んだ第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値とを合わせた範囲において、前記非球面の輪郭形状の設計値を用いて、
前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める第二の計算を行なう工程と、前記補完された範囲の測定値を削除する工程と、前記軸を挟んだ第二の計算後の非対称な範囲の測定値のうち、前記軸を挟んだ第二の計算後の対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に補完する工程とからなる処理を、前記段差が所定の一致条件を満足するまで繰り返す第二の処理工程と、
前記第一の処理工程及び第二の処理工程を介して得た、前記非球面の輪郭形状の測定値と前記非球面の輪郭形状の設計値とから前記非球面の輪郭形状の誤差を算出する第三の処理工程と、
を有することを特徴とする面形状測定機。 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:
前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状を測定し、
前記非球面の輪郭形状の測定値と、前記非球面の輪郭形状の設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と、前記設計値と、の差を求める第一の計算を行ない、
前記第一の計算後の非球面の輪郭形状の測定値のうち、前記軸を挟んだ対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に仮測定値として補完する第一の処理工程と、
前記軸を挟んだ前記第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値との境界部に段差がある場合、前記軸を挟んだ第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値とを合わせた範囲において、前記非球面の輪郭形状の設計値を用いて、
前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める第二の計算を行なう工程と、前記補完された範囲の測定値を削除する工程と、前記軸を挟んだ第二の計算後の非対称な範囲の測定値のうち、前記軸を挟んだ第二の計算後の対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に補完する工程とからなる処理を、前記段差が所定の一致条件を満足するまで繰り返す第二の処理工程と、
前記第一の処理工程及び第二の処理工程を介して得た、前記非球面の輪郭形状の測定値と前記非球面の輪郭形状の設計値とから前記非球面の輪郭形状の誤差を算出する第三の処理工程と、
を有することを特徴とする面形状測定方法。 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:
前記軸を挟んだ非対称な範囲において測定された、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値を用いて、前記軸を挟んだ非対称な範囲において、前記軸を挟んだ一方の側の所定位置から他方の側の別の所定位置までの前記非球面の輪郭形状の測定値と、前記非球面の輪郭形状の設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ非対称な範囲における前記非球面の輪郭形状の測定値と、前記設計値と、の差を求める第一の計算を行ない、
前記第一の計算後の非球面の輪郭形状の測定値のうち、前記軸を挟んだ対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に仮測定値として補完する第一の処理工程と、
前記軸を挟んだ前記第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値との境界部に段差がある場合、前記軸を挟んだ第一の計算後の非対称な範囲の輪郭形状の測定値と前記補完された範囲の仮測定値とを合わせた範囲において、前記非球面の輪郭形状の設計値を用いて、
前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差が所定の収束条件を満たすまで、
前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値、または、前記設計値の少なくとも一方を座標変換させながら、前記軸を挟んだ前記第一の計算後の非対称な範囲における前記非球面の輪郭形状の測定値及び前記仮測定値と、前記設計値と、の差を求める第二の計算を行なう工程と、前記補完された範囲の測定値を削除する工程と、前記軸を挟んだ第二の計算後の非対称な範囲の測定値のうち、前記軸を挟んだ第二の計算後の対称な範囲を除いた範囲の測定値を、測定値を得ていない前記軸で隔てた他方の側の所定範囲に軸対称に補完する工程とからなる処理を、前記段差が所定の一致条件を満足するまで繰り返す第二の処理工程と、
前記第一の処理工程及び第二の処理工程を介して得た、前記非球面の輪郭形状の測定値と前記非球面の輪郭形状の設計値とから前記非球面の輪郭形状の誤差を算出する第三の処理工程と、
を有することを特徴とする面形状の測定値の解析方法。 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:
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2009054108A JP5275853B2 (en) | 2009-03-06 | 2009-03-06 | Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2009054108A JP5275853B2 (en) | 2009-03-06 | 2009-03-06 | Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value |
Publications (2)
Publication Number | Publication Date |
---|---|
JP2010210289A JP2010210289A (en) | 2010-09-24 |
JP5275853B2 true JP5275853B2 (en) | 2013-08-28 |
Family
ID=42970630
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP2009054108A Expired - Fee Related JP5275853B2 (en) | 2009-03-06 | 2009-03-06 | Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value |
Country Status (1)
Country | Link |
---|---|
JP (1) | JP5275853B2 (en) |
Family Cites Families (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2885422B2 (en) * | 1989-06-30 | 1999-04-26 | 株式会社東芝 | Shape evaluation device and shape evaluation method |
JP3321210B2 (en) * | 1992-10-14 | 2002-09-03 | 株式会社リコー | Analysis and evaluation system for aspherical shapes |
JP3174667B2 (en) * | 1993-07-21 | 2001-06-11 | 株式会社リコー | Aspherical shape evaluation device |
JP3402995B2 (en) * | 1997-03-04 | 2003-05-06 | 株式会社ミツトヨ | Shape analyzer |
JP5322402B2 (en) * | 2007-05-21 | 2013-10-23 | 株式会社東京精密 | Shape measuring apparatus and shape measuring method |
-
2009
- 2009-03-06 JP JP2009054108A patent/JP5275853B2/en not_active Expired - Fee Related
Also Published As
Publication number | Publication date |
---|---|
JP2010210289A (en) | 2010-09-24 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
EP1851509B1 (en) | A metrological instrument | |
JP5706158B2 (en) | Surface sensor offset | |
JP4459264B2 (en) | Three-dimensional shape measurement method | |
US6763319B2 (en) | Profilometer and method for measuring, and method for manufacturing object of surface profiling | |
EP2261629A2 (en) | Asphere measurement method and apparatus | |
JP5600045B2 (en) | CMM calibration method | |
Xie et al. | Pose error estimation using a cylinder in scanner-based robotic belt grinding | |
JP2011206862A (en) | Method of positioning rotary tool in multishaft processing machine | |
JP6496924B2 (en) | Shape measuring method and shape measuring apparatus for cylindrical part of workpiece | |
US10585419B1 (en) | Methods and devices for performing in-situ inspections during a computer assisted setup of a machine tool table | |
JP5275853B2 (en) | Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value | |
JP5281918B2 (en) | Surface shape measuring machine, surface shape measuring method, and method of analyzing surface shape measurement value | |
JP2010032473A (en) | Shape evaluating device, shape evaluating method, and shape evaluating program | |
JP2011214949A (en) | Method for calibration of three-dimensional measuring machine | |
JP2000081329A (en) | Shape measurement method and device | |
JP2006281338A (en) | Machining program generator, machining method, and program | |
JP3182056B2 (en) | Aspherical surface shape measuring method and apparatus / aspherical surface evaluating method | |
JP7169168B2 (en) | Structure manufacturing method | |
JP6456082B2 (en) | Shape measurement method | |
JP5389579B2 (en) | Surface shape measurement method | |
JP5027450B2 (en) | Shape measurement method | |
JP6928982B1 (en) | Non-contact roundness and diameter measurement method | |
JP2002039908A (en) | Method for evaluating shape, and method for manufacturing part | |
TWI402711B (en) | System and method for analyzing errors of aspheric lens | |
JP3818628B2 (en) | Measuring method and measuring device |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
A621 | Written request for application examination |
Free format text: JAPANESE INTERMEDIATE CODE: A621 Effective date: 20120111 |
|
A977 | Report on retrieval |
Free format text: JAPANESE INTERMEDIATE CODE: A971007 Effective date: 20130110 |
|
A131 | Notification of reasons for refusal |
Free format text: JAPANESE INTERMEDIATE CODE: A131 Effective date: 20130115 |
|
A521 | Written amendment |
Free format text: JAPANESE INTERMEDIATE CODE: A523 Effective date: 20130315 |
|
RD02 | Notification of acceptance of power of attorney |
Free format text: JAPANESE INTERMEDIATE CODE: A7422 Effective date: 20130315 |
|
TRDD | Decision of grant or rejection written | ||
A01 | Written decision to grant a patent or to grant a registration (utility model) |
Free format text: JAPANESE INTERMEDIATE CODE: A01 Effective date: 20130507 |
|
A61 | First payment of annual fees (during grant procedure) |
Free format text: JAPANESE INTERMEDIATE CODE: A61 Effective date: 20130516 |
|
R151 | Written notification of patent or utility model registration |
Ref document number: 5275853 Country of ref document: JP Free format text: JAPANESE INTERMEDIATE CODE: R151 |
|
S531 | Written request for registration of change of domicile |
Free format text: JAPANESE INTERMEDIATE CODE: R313531 |
|
R350 | Written notification of registration of transfer |
Free format text: JAPANESE INTERMEDIATE CODE: R350 |
|
R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
LAPS | Cancellation because of no payment of annual fees |