JP4607311B2 - Wavefront shape measurement method and measurement wavefront shape correction method for large observation object by aperture synthesis - Google Patents

Description

【００２１】
ξは前述したように、λを光の波長、ｘを被観察体２の表面の変位量としたとき、ξ＝２πｘ／λで表わせるから上式（１）は下式（２）のように変形できる。
【００２２】
【数２】

ただし、c^*(x，y)はc(x，y)の共役である。
【００２３】
【数３】

【００２４】
上式（２）をフーリエ変換すると、下式（４）を得ることができる。
【００２５】
【数４】

【００２６】
ここで、被観察体２の表面の初期位相をξ_０、被観察体２の移動後の位相をξ_１とすると、開始位置における干渉縞画像データから下式（５）が得られる。
【００２７】
【数５】

【００２８】
次に、被観察体２の移動後における干渉縞画像データから下式（６）が得られる。
【００２９】
【数６】

【００３０】
これにより、下式（７）が得られる。
【００３１】
【数７】

【００３２】
したがって、被観察体２移動前後の位相差は下式（８）で表わされる。
【００３３】
【数８】

【００３４】
したがって、被観察体２の変位量は下式（９）で表わされる。
【００３５】
【数９】

【００３６】
また、所定の被観察体２の移動により得られた各干渉縞画像毎に求めた変位量の平均を求めることにより高精度の変位(傾斜誤差および並進誤差)検出を行なうことができる。なお、フーリエ変換縞解析法により被観察体２の変位を検出する際には、必ずしも縞画像データ全体を用いる必要はなく、一部の縞画像データによっても充分に精度の高い変位検出を行なうことが可能である。
【００３７】
なお、上記ステップ１０１（Ｓ１０１）について、位相シフトの変位量検出補正方法に適用された場合の一例を図４のフローチャートを用いて説明する。
【００３８】
まず、空間キャリア縞が重畳された、被観察体２の形状情報を担持してなる干渉縞画像をＣＣＤカメラ４により得る（Ｓ１）。次に、得られた干渉縞画像データに対してフーリエ変換を施し（Ｓ２）、空間キャリア周波数（f_x，f_y）を抽出し（Ｓ３）、このキャリア周波数に基づきフーリエ変換縞解析を行ない、後述する複素振幅ｃ（x，y）を求める（Ｓ４）。次に、参照（基準）面３の変位量を求め（Ｓ５）、これにより位相シフトの変位量を求めることができ（Ｓ６）、さらに位相シフト法による縞画像解析を行なう場合に、（Ｓ６）で求めた変位量を補正し被観察体２の位相を求める（Ｓ７）。
【００３９】
なお、変位量検出補正方法ではなく傾斜量検出補正方法に適用された場合も、図４に示す場合と同様に表わされる。
また、このように案内誤差を高精度に検出することができるから、この誤差を高精度に補償する補正演算が可能である。
【００４０】
一般に、フーリエ変換方法においては、フィルタリングによって、C(η−f_x ，ζ−f_y)
を求め、図５に示す如く周波数座標系上の位置(f_x ，f_y)に存在するスペクトルのピークを座標原点に移動させ、キャリア周波数を除去する。次に、逆フーリエ変換を用いてc(x，y)を求めることにより、ラップ処理された位相が得られる。次に、アンラップ処理によって被測定物の位相Φ(x，y) が求められる。ここで、(f_x ，f_y) はキャリア周波数であるが、被観察体２の表面と参照面３との間には所定の角度関係（相対姿勢）、具体的には上記式（１ａ）の関係が存在することに着目し、(f_x ，f_y) の各値を求め、その値に基づき、被観察体２表面と参照面３の間の角度関係を求める。
【００４１】
(f_x ，f_y) の各値は、上式（４）の結果から、座標原点にある最大ピーク以外のサブピーク位置、すなわち、C(η−f_x ，ζ−f_y)の位置を求めることで得られる。これにより、被観察体２のＸ方向、Ｙ方向の傾斜（姿勢）であるθ_xとθ_yを求めることができる。
【００４２】
このように、フーリエ変換縞解析法を用いることで、被観察体２の姿勢（傾斜）を検出できる。なお、フーリエ変換縞解析法により被観察体２の姿勢（傾斜）を求める際には、縞画像の全領域を使う必要がなく、一部の縞画像領域を解析することによっても充分に有効なデータを得ることが可能である。
【００４３】
このように、ステップ１０１（Ｓ１０１）における走査案内誤差検出は、ステップ１００（Ｓ１００）において得られた、図３に示すような各小開口画像出力M_IJ[N][M] (Ｘ方向番号I=0,1,2,…、Ｙ方向番号J=0,1,2,…)のそれぞれについてなされる。すなわち、開口のサイズがN×Mの干渉計により、サイズがL×Pである大型被観察体２の表面の形状を測定するときには、隣接する撮影画像との間で、例えばＸ方向、Ｙ方向に各々の一定の領域を重ねあわせるようにして、複数個の測定出力M_IJ[N][M](I=0,1,2,…、J=0,1,2,…)が得られるが、このようにして得られた各測定出力に対して、走査案内の誤差の補正がなされる。
【００４４】
なお、上述した場合における干渉計の出力値は、上記傾き誤差と並進誤差が含まれた下式（１０）で表される。なお、この式（１０）においては参照面３の誤差は考慮されていない。
【００４５】
【数１０】

【００４６】
そして、上述した如くして補正された各干渉縞画像データを、開口合成法を用いてつなぎあわせることになるが、この場合には、上式（１０）を変形した下式（１１）により、各小開口画像出力について、上記傾き誤差と並進誤差を除去する補正がなされ、この状態において各小開口画像が重なり領域（または対向する領域）での複数点での位相関係に基づいてつなぎあわせられる。各小開口画像をつなぎあわせる、開口合成の具体的な処理は干渉計開口合成の周知の技術（例えば特開平4-290905号公報、特開平4-290906号公報）を用いて行われる。
【００４７】
【数１１】

【００４８】
一般に、上記補正がなされない状態では、各小開口形状毎に、各々異なる傾き誤差と並進誤差が生じているから、隣接する２つの小開口形状をそのまま、つなげると、その後の結果に大きな測定誤差が生じてしまう。さらに、多数の小開口形状をつなげていくと、この測定誤差は累積的に拡大してしまう。
【００４９】
そこで、本実施形態方法によれば、干渉計の走査案内により発生した並進誤差と傾き誤差を検出し、演算により補正してから開口合成処理を行うようにしており、これによって、測定誤差のない大型の被測定形状F_IJ[N][M]を求めるようにしている。
【００５０】
また、傾き誤差については、隣接する互いの領域に重なり部分を設けなくとも上記補正を行うことができるが、一般的に、並進誤差については、隣接する互いの領域における相対的な位置の基準が必要であるので、領域の重なり部分が必要である。
【００５１】
上記実施形態方法においては、領域の重なり部分は図３に示す如く、Ｘ方向、Ｙ方向各々が開口の半分となるようにしているが、領域の重なり部分を他の比率とすることも勿論可能であり、重なり部分を線とすることも可能である。
【００５２】
このことは、上述した従来技術において、隣接する領域が互いに面において重なり合うことを必要としていることと相違する点である。
なお、各被測定領域毎に光反射率等が互いに異なることから、この差異を考慮して開口合成時の解析処理を行うことが好ましい。
【００５３】
次に、本発明の実施形態方法を実施するための装置について、上記図２、図６および図７を用いて説明する。
【００５４】
この装置は、上記実施形態方法を実施するためのもので、図２に示すように、マイケルソン型干渉計１において、被観察体２表面と参照（基準）面３からの両反射光束によって形成される干渉縞は、ＣＣＤカメラ４のＣＣＤ素子の撮像面５において形成され、画像入力基板６を介して、ＣＰＵおよび画像処理用のメモリを搭載したコンピュータ７に入力され、入力された干渉縞画像データに対して種々の演算処理が施され、その処理結果はモニタ画面７Ａ上に表示される。なお、ＣＣＤカメラ４から出力される干渉縞画像データはＣＰＵの処理により一旦メモリ内に格納されるようになっている。なお、演算された結果に対応した出力がＤ／Ａ変換基板８を介してピエゾ駆動部９に入力され、ＰＺＴ（ピエゾ素子）アクチュエータ１０を駆動制御する。
【００５５】
コンピュータ７は、図６に示すように、ソフト的に、ＦＦＴ演算複素振幅演算手段１１、位相シフト変位量検出手段１２および位相シフト変位量補正手段１３を備えている。ＦＦＴ演算複素振幅演算手段１１は、前述したように、得られた干渉縞画像データに対してフーリエ変換を施すとともにＦＦＴ演算複素振幅を抽出するステップ３（Ｓ３）の処理を行うものであり、位相シフト変位量検出手段１２は、前記ＦＦＴ演算複素振幅演算手段１１において演算されたＦＦＴ演算複素振幅に基づいて、上記ステップ４（Ｓ４）から上記ステップ６（Ｓ６）に相当する処理を行うものである。さらに、位相シフト変位量補正手段１３は、上記位相シフト変位量検出手段１２において検出された変位量に基づいて該変位量を補償し、被観察体２の誤差補正された位相を求めるものである。
【００５６】
また、コンピュータ７は、図７に示すように、ソフト的に、ＦＦＴ演算キャリア周波数演算手段２１、傾斜量検出手段２２および傾斜量補正手段２３を備えている。ＦＦＴ演算キャリア周波数演算手段２１は、前述したように、得られた干渉縞画像データに対してフーリエ変換を施すとともにＦＦＴ演算キャリア周波数（f_x，f_y）を抽出するステップ１３（Ｓ１３）の処理を行うものであり、傾斜量検出手段２２は、前記ＦＦＴ演算キャリア周波数演算手段２１において演算されたＦＦＴ演算キャリア周波数に基づいて、上記ステップ１４（Ｓ１４）に相当する処理を行うものである。さらに、傾斜量補正手段２３は、上記傾斜量検出手段２２において検出された参照面３の傾斜量に応じて、該傾斜量を補償し、被観察体２の位相を求めるステップ１５、１６(Ｓ１５、Ｓ１６)に相当する処理を行なうものである。
【００５７】
なお、上述した２つの実施形態方法（位相シフト素子の誤差量検出、補正方法および傾斜量の検出、補正方法）は、両者を１つの検査工程あるいは補正工程において行ってもよく、このようにすれば、より効率的に縞画像の解析精度を上げることができる。
【００５８】
このように、本実施形態方法においては、干渉計の走査中に発生した並進誤差と傾き誤差を検出し、演算により補正してから開口合成処理を行うようにしており、これによって、測定誤差のない大型の被測定形状F_IJ[N][M]を求めることができる。
【００５９】
なお、本発明の開口合成による大型被観察体の形状測定方法は、上記実施形態のものに限られるものではなく、その他の種々の態様の変更が可能である。例えば、上記位相シフトを行うための装置構成としてはＰＺＴ（ピエゾ素子）アクチュエータ１０に限られるものではなく、また、ＰＺＴ（ピエゾ素子）アクチュエータ１０としても種々の態様を採りうる。
【００６０】
図８は、上記ＰＺＴ（ピエゾ素子）アクチュエータ１０の２つの態様を示すものである。
【００６１】
すなわち、第１の態様は、図８（Ａ）に示すように、参照面（参照ミラー）３の裏面を支持する３つのピエゾ素子１２１、１２２、１２３を備え、支点部材としても機能するピエゾ素子１２１と各ピエゾ素子１２２、１２３とを結ぶ参照面３を有する参照ミラー上の、２本の直線Ｌｘ、Ｌｙが互いに直交するように構成されたものである。３本のピエゾ素子１２１、１２２、１２３が同量だけ伸縮することにより位相シフトが行なわれ、さらにピエゾ素子１２２のみの伸縮により参照ミラーの参照面３がｙ軸を中心として回転するようにｘ軸方向に傾き、ピエゾ素子１２３のみの伸縮により参照ミラーの参照面３がｘ軸を中心として回転するようにｙ軸方向に傾くことになる。一方、第２の態様は、図８（Ｂ）に示すように、参照面（参照ミラー）３の裏面中央部を円柱状のピエゾチューブ１２４によって支持するように構成されたものである。このピエゾチューブ１２４の偏奇しない伸縮により位相シフトが行なわれ、一方、偏奇した伸縮により参照ミラーの参照面３がｘ軸方向およびｙ軸方向に自在に傾けられることになる。
【００６２】
なお、上記実施形態のものでは位相シフト干渉計を用いたものについて説明しているが、本発明方法を実施し得る測定器としてはその他の干渉計装置、モアレ装置あるいは他の縞解析装置とすることが可能である。
【００６３】
【発明の効果】
本発明の開口合成による大型被観察体の波面形状測定方法によれば、大型被観察体上を干渉計等の測定器の開口により走査して、測定された各小開口領域について測定器の走査中に発生した並進誤差と傾き誤差を検出し、演算により補正してから開口合成処理を行うようにしており、これによって、測定誤差のない大型の被測定形状F_IJ[N][M]を求めることが可能である。
【００６４】
そして、並進誤差と傾き誤差の検出は、前記被観察体の波面形状情報を担持した、走査の前後の２つの縞画像データにフーリエ変換を施し、その変換結果に基づいて演算を行うことによりなされ、別途ハード的な構成を要しないので、装置構成が複雑化したり大型化する虞がない。
【図面の簡単な説明】
【図１】本発明の一実施形態方法を説明するためのフローチャート
【図２】図１に示す実施形態方法を実施するための干渉計装置を示すブロック図
【図３】本実施形態方法における開口合成を説明するための概念図
【図４】図１の一部を詳しく説明するためのフローチャート
【図５】図４に示す方法の一部を説明するための概念図
【図６】図４に示す方法を実施するための構成を示すブロック図
【図７】図４に示す方法とは別の態様の方法を実施するための構成を示すブロック図
【図８】図２の一部を具体的に示すブロック図
【符号の説明】
１ マイケルソン型干渉計
２ 被観察体表面
３ 参照面
４ ＣＣＤカメラ
５ ＣＣＤ
７ コンピュータ
７Ａ モニタ画面
９ ピエゾ駆動部
１０ ＰＺＴアクチュエータ
１１ 複素振幅演算手段
１２ 位相シフト変位量検出手段
１３ 位相シフト変位量補正手段
２１ キャリア周波数演算手段
２２ 傾斜量検出手段
２３ 傾斜量補正手段[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for measuring the wavefront shape of a large object to be observed by aperture synthesis and a method for correcting the wavefront shape of a large object to be observed, and in particular, when observing the wavefront shape of the object to be observed using fringe information such as interference fringes. When the size of the object to be observed is larger than the measurement range of the measuring device, each time the observation position of the object to be observed is scanned, fringes are imaged, each small aperture fringe image is analyzed, and each small aperture fringe image is supported. And finally, a plurality of small aperture phases are connected to each other to obtain a wavefront shape of the entire object to be observed, and a wavefront shape measuring method for a large object to be observed using an aperture synthesis method and a measurement wavefront of the large object to be observed The present invention relates to a shape correction method.
[0002]
[Background Art and Problems to be Solved by the Invention]
In general, in a measuring instrument such as an interferometer, when measuring the surface shape of a large workpiece larger than the opening, the surface of the large workpiece is scanned by the small opening of the measuring instrument, and a large number of small pieces obtained are obtained. An aperture synthesis method is used in which measurement images of aperture shapes are connected to obtain the surface shape of a large workpiece. However, when connecting a large number of measurement images obtained by scanning a small aperture of a measuring instrument, it is extremely difficult to connect the measurement images with high accuracy due to the effects of translation error and tilt error during the scan. It is.
[0003]
Although attempts have been made to solve such problems related to aperture synthesis in measuring instruments, no good concrete measures have been found, and the development of a simple and highly accurate solution method has been desired.
[0004]
The present invention has been made in view of the above circumstances, and when using the aperture synthesis method to connect a large number of small aperture shape measurement images to obtain the surface shape of a large workpiece, the translation error for each measurement wavefront shape. To provide a method for measuring the wavefront shape of a large object to be observed and a method for correcting the measurement wavefront shape of a large object to be observed by the aperture synthesis method, which can connect the measured wavefront shapes with high accuracy by eliminating the influence of the tilt error. It is the purpose.
[0005]
[Means for Solving the Problems]
According to the first aspect of the present invention, there is provided a method for measuring a wavefront shape of a large object to be observed by aperture synthesis, wherein the object to be observed and a measuring instrument divided into a plurality of regions are arranged so that a part of adjacent regions overlap each other. Obtained after obtaining element phase data using fringe analysis based on each of two-dimensional fringe images carrying wavefront shape information of a plurality of spatially continuous objects obtained by scanning . In the method of measuring the wavefront shape of a large object to be observed by aperture synthesis, the element phase data is connected by aperture synthesis to measure the wavefront shape of the object to be observed having a larger area than the observable region of the measuring instrument.
When obtaining each element phase data,
The carrier fringe is superimposed on the carrier fringe to carry the wavefront shape information of the object to be observed, and a Fourier transform is performed on an overlapping portion of a plurality of adjacent carrier fringe images, and calculation is performed based on the transformation result, Detect errors associated with relative scanning,
A plurality of element phase data adjacent to each other are connected after correcting an error accompanying the relative scanning of the plurality of element phase data adjacent to each other based on the detection value. It is.
[0006]
Further, the error due to the relative scanning is a carrier that undergoes Fourier transform on the overlapping portion of the plurality of carrier fringe image regions, and changes with a relative attitude shift between the object to be observed and the measuring instrument. It is possible to obtain a relative inclination amount between the object to be observed and the measuring device, which is obtained by calculating a frequency and performing calculation based on a plurality of carrier frequencies.
[0007]
In addition, the error due to the relative scanning is a complex that changes with a shift in the relative posture between the object to be observed and the measuring instrument by performing Fourier transform on the overlapping portion of the regions of the plurality of carrier fringe images. It is possible to obtain a relative translation error between the object to be observed and the measuring device obtained by calculating the amplitude and performing a calculation based on the plurality of complex amplitudes.
[0008]
Further, the error due to the relative scanning is a carrier that undergoes Fourier transform on the overlapping portion of the plurality of carrier fringe image regions, and changes with a relative attitude shift between the object to be observed and the measuring instrument. It is possible to obtain a relative inclination amount and translation error between the object to be observed and the measuring device, which are obtained by calculating a frequency and a complex amplitude and performing an operation based on the plurality of carrier frequencies and the plurality of complex amplitudes. It is.
[0009]
Further, the wavefront measurement shape correction method for a large object to be observed according to the present invention carries the wavefront shape information of the object to be observed after the detection is performed in the wavefront shape measurement method for the large object to be observed by aperture synthesis. In the fringe analysis of the fringe image, a correction operation for compensating for the detected tilt amount and translation error is performed.
[0010]
Note that each of the above-described methods according to the present invention can be applied to all fringe image analysis methods using the Fourier transform method, and can be applied to, for example, an interference fringe and moire fringe analysis or a three-dimensional projector using fringe projection. It is.
Here, the wavefront shape includes not only the surface shape but also a transmitted wavefront shape (for example, thickness unevenness, refractive index distribution, lens aberration, etc.).
[0011]
[Action]
The method for measuring the wavefront shape of a large object to be observed and the method for correcting the measured wavefront shape of the large object to be observed according to the present invention have been inspired by the following application already invented and disclosed by the present inventors. It came to solve the subject of aperture synthesis that has remained unsolved.
[0012]
That is, when the inventors of the present application perform Fourier transform on the fringe image data of adjacent small regions obtained by scanning guidance, the inventor is generated due to a deviation between the wavefront from the observed object and the wavefront from the reference. A carrier frequency and / or complex amplitude is obtained, and calculation is performed based on the plurality of carrier frequencies and / or the plurality of complex amplitudes before and after scanning, and a relative amount of inclination between the object to be observed and the reference and / or A method for determining the amount of displacement has been invented and already disclosed (Japanese Patent Application No. 2000-277444).
[0013]
With this technique, the relative tilt amount and / or displacement amount between the object to be observed and the reference can be obtained easily and with high accuracy.
Therefore, in the method of the present invention, the above disclosed invention is applied to measure the relative tilt error and / or translation error of each adjacent aperture wavefront shape, and the error is corrected based on the measurement result, thereby achieving high accuracy. It is possible to obtain a simple wavefront shape.
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, a shape measurement method and a measurement shape correction method for a large object to be observed by aperture synthesis according to an embodiment of the present invention will be described with reference to the drawings. Note that the method of the present embodiment will be described by taking as an example a case where it is applied to a phase shift interferometer apparatus.
[0015]
In addition, the method of the present embodiment obtains a plurality of interference fringe image data while scanning the interferometer and the object to be observed while the size of the object to be observed is larger than the aperture size of the interferometer device. It can be applied to the case where they are connected by synthesis.
[0016]
FIG. 1 is a flowchart schematically showing an embodiment method of the present invention, and FIG. 2 shows an interferometer apparatus for carrying out the embodiment method shown in FIG. That is, the aperture of the interferometer is scanned on the observation object 2 and an interference fringe image is acquired each time scanning is performed for a predetermined distance (S100). Next, Fourier transform is performed on the two fringe image data before and after scanning, the carrier frequency and complex amplitude of the fringe image are extracted, and the tilt error and translation error of each small aperture shape due to scanning guidance are detected (S101). ). Finally, as shown in FIG. 3, the scanning guide error is corrected by the aperture synthesis method, and the corrected small aperture shapes are connected (S102).
[0017]
Hereinafter, a method for detecting an inclination error and a translation error associated with scanning guidance and its processing operation in step 101 (S101) will be described with reference to the drawings.
[0018]
In this method, the surface shape of the object to be observed 2 obtained based on the relative shape between the surface of the object to be observed 2 and the reference (reference) plane 3 in the method for obtaining the surface shape of the object to be observed using the fringe analysis method. The fringe image data carrying information is subjected to Fourier transform to obtain the carrier frequency and complex amplitude of the fringe image data before and after scanning, and based on the carrier frequency and the complex amplitude, the relative inclination error of the scanning guide and the translation of the scanning guide An error is detected, and thereafter, a correction operation for compensating for the detected scanning guide error by the fringe image analysis of the fringe image data is performed.
[0019]
In general, in the Fourier transform fringe analysis method, the phase can be obtained using only one fringe image by introducing a carrier frequency (relative inclination between the surface of the observation object 2 and the reference surface 3). When the carrier frequency is introduced, the interference fringe intensity is expressed by the following equation (1).
[0020]
[Expression 1]

[0021]
As described above, ξ can be expressed by ξ = 2πx / λ, where λ is the wavelength of light and x is the amount of displacement of the surface of the object 2 to be observed. Can be transformed into
[0022]
[Expression 2]

However, c ^* (x, y) is a conjugate of c (x, y).
[0023]
[Equation 3]

[0024]
When the above equation (2) is Fourier transformed, the following equation (4) can be obtained.
[0025]
[Expression 4]

[0026]
Here, when the initial phase of the surface of the observation object 2 is ξ ₀ and the phase after the movement of the observation object 2 is ξ ₁ , the following expression (5) is obtained from the interference fringe image data at the start position.
[0027]
[Equation 5]

[0028]
Next, the following expression (6) is obtained from the interference fringe image data after the object 2 is moved.
[0029]
[Formula 6]

[0030]
Thereby, the following formula (7) is obtained.
[0031]
[Expression 7]

[0032]
Therefore, the phase difference before and after the object 2 is moved is expressed by the following equation (8).
[0033]
[Equation 8]

[0034]
Therefore, the displacement amount of the observed object 2 is expressed by the following equation (9).
[0035]
[Equation 9]

[0036]
Further, by obtaining the average of the displacement amounts obtained for each interference fringe image obtained by the predetermined movement of the object 2 to be observed, highly accurate displacement (tilt error and translation error) can be detected. In addition, when detecting the displacement of the observation object 2 by the Fourier transform fringe analysis method, it is not always necessary to use the entire fringe image data, and sufficiently accurate displacement detection is performed even with a part of the fringe image data. Is possible.
[0037]
Note that an example in which the step 101 (S101) is applied to a phase shift displacement amount detection correction method will be described with reference to the flowchart of FIG.
[0038]
First, an interference fringe image on which spatial carrier fringes are superimposed and carrying the shape information of the observation object 2 is obtained by the CCD camera 4 (S1). Next, Fourier transform is performed on the obtained interference fringe image data (S2), spatial carrier frequencies (f _x , f _y ) are extracted (S3), and Fourier transform fringe analysis is performed based on the carrier frequencies. A complex amplitude c (x, y) described later is obtained (S4). Next, the displacement amount of the reference (reference) surface 3 is obtained (S5), whereby the displacement amount of the phase shift can be obtained (S6), and when performing fringe image analysis by the phase shift method (S6). The phase of the object 2 to be observed is obtained by correcting the displacement obtained in step S7.
[0039]
Note that the case where the present invention is applied not to the displacement amount detection correction method but to the inclination amount detection correction method is also expressed in the same manner as the case shown in FIG.
In addition, since the guide error can be detected with high accuracy in this way, correction calculation for compensating for this error with high accuracy is possible.
[0040]
In general, in the Fourier transform method, C (η−f _x , ζ−f _y ) is obtained by filtering.
As shown in FIG. 5, the peak of the spectrum existing at the position (f _x , f _y ) on the frequency coordinate system is moved to the coordinate origin, and the carrier frequency is removed. Next, by obtaining c (x, y) using inverse Fourier transform, a lap-processed phase is obtained. Next, the phase Φ (x, y) of the object to be measured is obtained by unwrapping. Here, (f _x , f _y ) is a carrier frequency, and a predetermined angular relationship (relative posture) between the surface of the observation object 2 and the reference surface 3, specifically, the above formula (1a) In consideration of the existence of the relationship, the values of (f _x , f _y ) are obtained, and the angular relationship between the surface of the observation object 2 and the reference surface 3 is obtained based on the values.
[0041]
For each value of (f _x , f _y ), the sub-peak position other than the maximum peak at the coordinate origin, that is, the position of C (η−f _x , ζ−f _y ) is obtained from the result of the above equation (4). Can be obtained. Thereby, θ _x and θ _y which are inclinations (postures) of the object 2 in the X direction and the Y direction can be obtained.
[0042]
Thus, by using the Fourier transform fringe analysis method, the posture (tilt) of the observation object 2 can be detected. When obtaining the posture (tilt) of the observation object 2 by the Fourier transform fringe analysis method, it is not necessary to use the entire area of the fringe image, and it is sufficiently effective to analyze a part of the fringe image area. Data can be obtained.
[0043]
In this way, the scanning guide error detection in step 101 (S101) is performed in step 100 (S100), and each small aperture image output M _IJ [N] [M] (X direction number I as shown in FIG. 3). .., 0, 1, 2,..., Y direction number J = 0, 1, 2,. That is, when measuring the shape of the surface of the large object 2 having a size of L × P with an interferometer having an aperture size of N × M, for example, the X direction and the Y direction between adjacent captured images. A plurality of measurement outputs M _IJ [N] [M] (I = 0, 1, 2,..., J = 0, 1, 2,. However, the error of the scanning guide is corrected for each measurement output obtained in this way.
[0044]
Note that the output value of the interferometer in the above-described case is represented by the following expression (10) including the tilt error and the translation error. Note that the error of the reference surface 3 is not taken into account in this equation (10).
[0045]
[Expression 10]

[0046]
Then, the interference fringe image data corrected as described above are connected using the aperture synthesis method. In this case, the following equation (11) obtained by modifying the above equation (10) is used. Each small aperture image output is corrected to remove the tilt error and translation error, and in this state, each small aperture image is connected based on the phase relationship at a plurality of points in the overlapping region (or the opposing region). . A specific process of aperture synthesis for joining the small aperture images is performed using a well-known technique of interferometer aperture synthesis (for example, Japanese Patent Laid-Open Nos. 4-290905 and 4-290906).
[0047]
## EQU11 ##

[0048]
In general, in the state where the above correction is not made, different tilt errors and translation errors occur for each small aperture shape. If two adjacent small aperture shapes are connected as they are, a large measurement error is caused in the subsequent results. Will occur. Further, when a large number of small aperture shapes are connected, this measurement error is cumulatively expanded.
[0049]
Therefore, according to the method of the present embodiment, the translational error and the tilt error generated by the scanning guidance of the interferometer are detected, corrected by calculation, and then the aperture synthesis process is performed, whereby there is no measurement error. A large measured shape F _IJ [N] [M] is obtained.
[0050]
In addition, with respect to the tilt error, the above correction can be performed without providing an overlapping portion in each adjacent region. However, in general, with respect to the translation error, the reference of the relative position in each adjacent region is Since it is necessary, an overlapping portion of the area is necessary.
[0051]
In the method of the above embodiment, as shown in FIG. 3, the overlapping portion of the regions is half of the opening in each of the X direction and the Y direction. It is also possible to make the overlapping part a line.
[0052]
This is different from the above-described prior art in that adjacent regions need to overlap each other in plane.
In addition, since the light reflectivity and the like are different for each measurement region, it is preferable to perform analysis processing during aperture synthesis in consideration of this difference.
[0053]
Next, an apparatus for carrying out the method according to the embodiment of the present invention will be described with reference to FIG. 2, FIG. 6, and FIG.
[0054]
This apparatus is for carrying out the above-described embodiment method. As shown in FIG. 2, in the Michelson interferometer 1, this apparatus is formed by both reflected light beams from the surface of the observation object 2 and the reference (reference) surface 3. The interference fringes that are formed are formed on the imaging surface 5 of the CCD element of the CCD camera 4 and are input to the computer 7 equipped with a CPU and a memory for image processing via the image input board 6 and input interference fringe images. Various arithmetic processes are performed on the data, and the processing results are displayed on the monitor screen 7A. The interference fringe image data output from the CCD camera 4 is temporarily stored in the memory by the processing of the CPU. An output corresponding to the calculated result is input to the piezo drive unit 9 via the D / A conversion board 8 to drive and control a PZT (piezo element) actuator 10.
[0055]
As shown in FIG. 6, the computer 7 includes, in software, an FFT calculation complex amplitude calculation means 11, a phase shift displacement amount detection means 12, and a phase shift displacement amount correction means 13. As described above, the FFT calculation complex amplitude calculation means 11 performs the process of step 3 (S3) for performing Fourier transform on the obtained interference fringe image data and extracting the FFT calculation complex amplitude, The shift displacement amount detection means 12 performs processing corresponding to the above step 4 (S4) to step 6 (S6) based on the FFT calculation complex amplitude calculated by the FFT calculation complex amplitude calculation means 11. . Further, the phase shift displacement correction means 13 compensates for the displacement based on the displacement detected by the phase shift displacement detection means 12 and obtains the error-corrected phase of the object 2 to be observed. .
[0056]
Further, as shown in FIG. 7, the computer 7 includes, in software, an FFT calculation carrier frequency calculation means 21, an inclination amount detection means 22, and an inclination amount correction means 23. As described above, the FFT calculation carrier frequency calculation means 21 performs the Fourier transform on the obtained interference fringe image data and extracts the FFT calculation carrier frequency (f _x , f _y ) in step 13 (S13). The tilt amount detection means 22 performs a process corresponding to step 14 (S14) based on the FFT calculation carrier frequency calculated by the FFT calculation carrier frequency calculation means 21. Further, the tilt amount correcting means 23 compensates the tilt amount according to the tilt amount of the reference surface 3 detected by the tilt amount detecting means 22 and obtains the phase of the object 2 to be observed 15, 16 (S 15 , S16) is performed.
[0057]
Note that the above-described two embodiment methods (error amount detection / correction method and inclination amount detection / correction method of the phase shift element) may be performed in one inspection step or correction step. Therefore, the analysis accuracy of the fringe image can be increased more efficiently.
[0058]
As described above, in the method of the present embodiment, the translational error and the tilt error generated during the scanning of the interferometer are detected and corrected by calculation, and then the aperture synthesis process is performed. A large measured shape F _IJ [N] [M] can be obtained.
[0059]
Note that the method for measuring the shape of a large object to be observed by aperture synthesis according to the present invention is not limited to the above-described embodiment, and various other aspects can be changed. For example, the apparatus configuration for performing the phase shift is not limited to the PZT (piezo element) actuator 10, and the PZT (piezo element) actuator 10 can take various forms.
[0060]
FIG. 8 shows two modes of the PZT (piezo element) actuator 10.
[0061]
That is, as shown in FIG. 8A, the first mode includes three piezo elements 121, 122, and 123 that support the back surface of the reference surface (reference mirror) 3, and also functions as a fulcrum member. Two straight lines Lx and Ly on a reference mirror having a reference surface 3 connecting 121 and the piezoelectric elements 122 and 123 are orthogonal to each other. The three piezo elements 121, 122, 123 expand and contract by the same amount to perform phase shift, and the piezo element 122 expands and contracts to rotate the reference plane 3 of the reference mirror about the y axis. The reference surface 3 of the reference mirror is inclined in the y-axis direction so as to rotate about the x-axis by the expansion and contraction of only the piezo element 123. On the other hand, as shown in FIG. 8B, the second mode is configured such that the center of the back surface of the reference surface (reference mirror) 3 is supported by a cylindrical piezo tube 124. The phase shift is performed by the non-uniform expansion / contraction of the piezo tube 124, while the reference surface 3 of the reference mirror is freely tilted in the x-axis direction and the y-axis direction by the uneven expansion / contraction.
[0062]
In addition, although the thing using a phase shift interferometer is demonstrated in the thing of the said embodiment, it is set as other interferometer apparatus, a moire apparatus, or another fringe analysis apparatus as a measuring device which can implement the method of this invention. It is possible.
[0063]
【The invention's effect】
According to the method for measuring the wavefront shape of a large object to be observed by aperture synthesis of the present invention, the large object is scanned with the opening of a measuring instrument such as an interferometer, and the measuring instrument is scanned for each small aperture region measured. A translation error and a tilt error that occur inside are detected, corrected by calculation, and then an aperture synthesis process is performed. This allows a large measured shape F _IJ [N] [M] with no measurement error to be measured. It is possible to ask.
[0064]
Then, the translation error and the tilt error are detected by performing Fourier transform on the two fringe image data before and after the scan carrying the wavefront shape information of the object to be observed, and performing an operation based on the conversion result. Since a separate hardware configuration is not required, there is no possibility that the device configuration becomes complicated or large.
[Brief description of the drawings]
FIG. 1 is a flowchart for explaining a method according to an embodiment of the present invention. FIG. 2 is a block diagram showing an interferometer apparatus for carrying out the method according to the embodiment shown in FIG. FIG. 4 is a conceptual diagram for explaining a part of FIG. 1. FIG. 5 is a conceptual diagram for explaining a part of the method shown in FIG. FIG. 7 is a block diagram showing a configuration for carrying out a method according to a mode different from the method shown in FIG. 4. FIG. 8 is a block diagram showing a part of FIG. Block diagram shown in [Description of symbols]
1 Michelson interferometer 2 Object surface 3 Reference surface 4 CCD camera 5 CCD
7 Computer 7A Monitor screen 9 Piezo drive unit 10 PZT actuator 11 Complex amplitude calculation means 12 Phase shift displacement amount detection means 13 Phase shift displacement amount correction means 21 Carrier frequency calculation means 22 Inclination amount detection means 23 Inclination amount correction means

Claims (6)

Wavefront shape information of a plurality of spatially continuous objects to be observed obtained by relative scanning of the object to be observed divided into a plurality of areas and a measuring instrument so that a part of adjacent areas overlap each other. After obtaining the element phase data using the fringe analysis based on each of the supported two-dimensional fringe images, the obtained element phase data are connected to obtain an object having an area larger than the observable region of the measuring instrument. In the wavefront shape measurement method of a large object to be observed by aperture synthesis to measure the wavefront shape,
When obtaining the element phase data,
A carrier fringe image is formed by superimposing carrier fringes on the fringe image and carrying the wavefront shape information of the object to be observed, and a Fourier transform is performed on an overlapping portion of a plurality of adjacent carrier fringe images, based on the transformation result Perform an operation to detect an error associated with the relative scanning,
The aperture is characterized in that the plurality of element phase data adjacent to each other is connected after correcting an error accompanying the relative scanning of the plurality of element phase data adjacent to each other based on the detection value. A method for measuring the wavefront shape of a large object to be observed by synthesis. A carrier in which the error due to the relative scanning is subjected to a Fourier transform on an overlapping portion of the adjacent plurality of carrier fringe image regions, and changes in accordance with a relative posture deviation between the object to be observed and the measuring device. The aperture synthesis according to claim 1, wherein the frequency is a relative inclination amount between the object to be observed and the measuring device, which is obtained by calculating a spectrum based on the plurality of carrier frequencies. A method for measuring the wavefront shape of a large object. An error caused by the relative scanning is a complex in which a Fourier transform is performed on an overlapping portion of the adjacent plurality of carrier fringe image regions, and the error varies with a relative attitude shift between the object to be observed and the measuring instrument. 2. A large object to be observed by aperture synthesis according to claim 1, characterized in that the amplitude is a relative translation error between the object to be observed and the measuring device obtained by calculating based on the plurality of complex amplitudes. Body wavefront shape measurement method. A carrier in which the error due to the relative scanning is subjected to a Fourier transform on an overlapping portion of the adjacent plurality of carrier fringe image regions, and changes in accordance with a relative posture deviation between the object to be observed and the measuring device. A relative inclination amount and a translation error between the object to be observed and the measuring device, which are obtained by calculating a frequency and a complex amplitude and performing an operation based on the plurality of carrier frequencies and the plurality of complex amplitudes. The wavefront shape measuring method for a large object to be observed by aperture synthesis according to claim 1.   The wavefront shape measuring method for a large object to be observed by aperture synthesis according to any one of claims 1 to 4, wherein the fringe image is an interference fringe image.   5. The method for measuring a wavefront shape of a large object to be observed by aperture synthesis according to claim 4, wherein after the detection, the detected inclination in a fringe analysis of a fringe image carrying the wavefront shape information of the object to be observed. A method for correcting a measured wavefront shape of a large object to be observed by aperture synthesis, comprising performing a correction operation to compensate for an amount and a translation error.

Images