JPH05340843A - Method for connecting phase of wave front by fringe scanning interference measurement system - Google Patents
Method for connecting phase of wave front by fringe scanning interference measurement systemInfo
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- JPH05340843A JPH05340843A JP4171718A JP17171892A JPH05340843A JP H05340843 A JPH05340843 A JP H05340843A JP 4171718 A JP4171718 A JP 4171718A JP 17171892 A JP17171892 A JP 17171892A JP H05340843 A JPH05340843 A JP H05340843A
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Abstract
Description
【０００１】[0001]
【産業上の利用分野】本発明はフリンジスキャニング干
渉測定方式における波面の位相つなぎ方法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for connecting wavefront phases in a fringe scanning interferometry system.
【０００２】[0002]
【従来の技術】フリンジスキャニング干渉測定方式は、
参照光の位相変化により物体光と参照光との位相差をＮ
段階（但し、Ｎは整数）に変化させ、その各段階での干
渉縞パターンを２次元エリアセンサーで読み取り、光電
変換し、デジタル化して、2. Description of the Related Art The fringe scanning interferometry method is
The phase difference between the object light and the reference light is N by the phase change of the reference light.
The number of steps (however, N is an integer) is changed, the interference fringe pattern at each step is read by a two-dimensional area sensor, photoelectrically converted, digitized,
【０００３】[0003]
【数１】 [Equation 1]
【０００４】上記数１により、位相Ｗ（Ｘ，Ｙ）を求め
る方法として知られている。ただし、数１において、Ｉ
j （Ｘ，Ｙ）はｊ段階目の位相変化における干渉縞パタ
ーンの（Ｘ，Ｙ）位置における光強度であり、ｋはλを
光の波長とするときの波数２π／λである。また、ｌj
＝（λ／２π）ｊでｊ段階目の位相変化量である。数１
に従って波面形状を求めるのであるが、ｔａｎ-1演算は
値が主値（−π／２からπ／２）に限られ、実際には連
続的な位相分布もπだけ位相が不連続となる所が生じ
る。従って、位相飛びの方向（−π／２からπ／２か、
またはπ／２から−π／２）を２次元的に判断し、補正
して連続的な位相分布を求める必要がある。It is known as a method for obtaining the phase W (X, Y) by the above-mentioned equation 1. However, in Equation 1, I
j (X, Y) is the light intensity at the (X, Y) position of the interference fringe pattern in the j-th phase change, and k is the wave number 2π / λ when λ is the wavelength of the light. Also, l j
= (Λ / 2π) j, which is the phase change amount at the j-th stage. Number 1
However, the tan -1 calculation is limited to the main value (-π / 2 to π / 2), and in reality, the continuous phase distribution has a phase discontinuity of π. Occurs. Therefore, the direction of phase jump (-π / 2 to π / 2,
Alternatively, it is necessary to two-dimensionally determine (π / 2 to −π / 2) and correct it to obtain a continuous phase distribution.
【０００５】従来知られている位相分布の求め方として
は、特開平３−２１８４３１号公報に開示された技術が
ある。これは、図８のフローチャートに示すように、前
記数１によって求められた位相データをＸ方向にスキャ
ンして各画素（Ｘi ，Ｙi ）における補正値δ
x （Ｘi ，Ｙi ）をＸ＝Ｘc のライン上での値を基準と
して求める。次に、Ｘ＝Ｘc のライン上でＹ方向の補正
値δy （Ｘi ，Ｙi ）をＹ＝Ｙc での値を基準として求
める。最後に、上記の如く求められた補正値δ
x （Ｘi，Ｙi ）、δy （Ｘi ，Ｙi ）を各画素
（Ｘi ，Ｙi ）での位相データに加え合わせて連続的な
位相分布を得ていた。As a conventionally known method for obtaining the phase distribution, there is a technique disclosed in Japanese Patent Laid-Open No. 3-218431. This is because, as shown in the flowchart of FIG. 8, the correction value δ at each pixel (X i , Y i ) is obtained by scanning the phase data obtained by the equation 1 in the X direction.
x (X i , Y i ) is calculated with reference to the value on the line of X = X c . Next, on the line of X = X c , the correction value δ y (X i , Y i ) in the Y direction is obtained with the value at Y = Y c as a reference. Finally, the correction value δ obtained as described above
x (X i , Y i ) and δ y (X i , Y i ) are added to the phase data at each pixel (X i , Y i ) to obtain a continuous phase distribution.
【０００６】[0006]
【発明が解決しようとする課題】ところが、上述の従来
技術においては、一方向でのスキャニングライン上の前
後２点間での位相のみから位相飛びを判定していたた
め、前の画素の位相データが欠落している場合には位相
飛びを判定することができず、位相つなぎが不連続にな
るという問題点があった。However, in the above-mentioned conventional technique, since the phase jump is determined only from the phase between two points before and after on the scanning line in one direction, the phase data of the previous pixel is If it is missing, the phase jump cannot be determined and the phase connection becomes discontinuous.
【０００７】本発明は上記問題点に鑑みてなされたもの
で、干渉縞パターン中にゴミや欠陥が存在して、一部の
位相データが欠落しても連続的な位相分布を得ることの
できる位相つなぎ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 problems, and it is possible to obtain a continuous phase distribution even if a part of phase data is lost due to dust or defects existing in the interference fringe pattern. The purpose is to provide a phase connecting method.
【０００８】[0008]
【課題を解決するための手段】上記目的を達成するため
に本発明の位相つなぎ方法では、フリンジスキャニング
干渉測定方式により、測定光と参照光とをエリアセンサ
ー上で干渉せしめ、参照光の位相を段階的に変化させ、
その各段階での干渉縞の強度値を読み取り、そのデータ
に基づき演算処理を行って各点での位相を求める方法に
おいて、求めた位相データ領域を一方向でスキャンし、
各スキャニングライン毎に位相データが連続して存在す
る連続位相領域中で位相つなぎを行う第一ステップと、
前記方向と直交する方向で前記連続位相領域同士の位相
つなぎを行う第二ステップとにより、連続的な位相分布
を求めることを特徴としている。In order to achieve the above object, in the phase joining method of the present invention, the measurement light and the reference light are caused to interfere with each other on the area sensor by the fringe scanning interferometry, and the phase of the reference light is changed. Change in stages,
Reading the intensity value of the interference fringes at each stage, in the method of calculating the phase at each point by performing arithmetic processing based on the data, scan the phase data area obtained in one direction,
The first step of connecting the phases in the continuous phase region where the phase data continuously exists for each scanning line,
A continuous phase distribution is obtained by a second step of connecting the phases of the continuous phase regions in a direction orthogonal to the direction.
【０００９】[0009]
【作用】次に、本発明の位相つなぎ方法の作用を図１の
フローチャートにより説明する。まず、ステップＳ１で
は、Ｘ方向での連続位相領域Ｌjkを検出する。即ち、前
記数１によって求められた位相データを、図２に示すよ
うに、Ｘ方向に順次スキャンして各スキャニングライン
上で位相データが連続して存在する領域を検出する。こ
こで、ｊ番目のスキャニングライン上でのｋ番目の連続
位相領域をＬjkとする。Next, the operation of the phase connecting method of the present invention will be described with reference to the flowchart of FIG. First, in step S1, the continuous phase region L jk in the X direction is detected. That is, as shown in FIG. 2, the phase data obtained by the equation 1 is sequentially scanned in the X direction to detect a region where the phase data continuously exists on each scanning line. Here, the k-th continuous phase area on the j-th scanning line is L jk .
【００１０】次に、ステップＳ２では、連続位相領域Ｌ
jk内で位相つなぎを行う。即ち、領域Ｌjk内での位相分
布は、図３に示すように、−π／２からπ／２までの値
をとり、πだけの位相飛びを生じる部分がある。これを
補正する手段として隣合う２点（Ｘi-1 ，Ｙj ），（Ｘ
i ，Ｙj ）間の位相差ΔＷ、すなわち、 ΔＷ＝Ｗ（Ｘi ，Ｙj ）−Ｗ（Ｘi-1 ，Ｙj ） ・・・（２） の絶対値｜ΔＷ｜が、あるしきい値θよりも大きい場合
は位相飛びがあると判定し、そうでなければ連続である
と判定する。そして、位相飛びが生じた場合にはΔＷの
正負に応じて次のような補正値δ（Ｘi ，Ｙj ） （但
し、（Ｘi ，Ｙj ）∈Ｌjk）を与える。 ｜ΔＷ｜＞θ かつ ΔＷ＜０ のとき δ（Ｘi ，Ｙj ）＝δ（Ｘi-1 ，Ｙj ）＋π ｜ΔＷ｜＞θ かつ ΔＷ＞０ のとき δ（Ｘi ，Ｙj ）＝δ（Ｘi-1 ，Ｙj ）−π それ以外の場合には、 δ（Ｘi ，Ｙj ）＝δ（Ｘi-1 ，Ｙj ） とする。ただし、各領域Ｌjkの始点での補正値を０とす
る。以上の如く求められた補正値δ（Ｘi ，Ｙj ）を各
領域Ｌjk中の全ての位相データＷ（Ｘi ，Ｙj ）に加え
合わせたものをＷ’（Ｘi ，Ｙj ）とする。即ち、 Ｗ’（Ｘi ，Ｙj ）＝Ｗ（Ｘi ，Ｙj ）＋δ（Ｘi ，Ｙj ） ・・・（３） である。Next, in step S2, the continuous phase region L
Perform phase connection in jk . That is, as shown in FIG. 3, the phase distribution in the region L jk takes a value from −π / 2 to π / 2, and there is a portion where a phase jump of π occurs. As a means for correcting this, two adjacent points (X i-1 , Y j ) and (X
There is a phase difference ΔW between i , Y j ), that is, ΔW = W (X i , Y j ) −W (X i-1 , Y j ) ... (2) absolute value | ΔW | If it is larger than the threshold value θ, it is determined that there is a phase jump, and if not, it is determined to be continuous. When a phase jump occurs, the following correction value δ (X i , Y j ) (where (X i , Y j ) εL jk ) is given according to the positive or negative of ΔW. When | ΔW |> θ and ΔW <0 δ (X i , Y j ) = δ (X i-1 , Y j ) + π | ΔW |> θ and ΔW> 0 δ (X i , Y j ) = Δ (X i-1 , Y j ) -π In other cases, δ (X i , Y j ) = δ (X i-1 , Y j ). However, the correction value at the start point of each area L jk is set to 0. The correction value δ (X i , Y j ) obtained as described above is added to all the phase data W (X i , Y j ) in each region L jk , and W ′ (X i , Y j ) is added. And That is, W '(X i , Y j ) = W (X i , Y j ) + δ (X i , Y j ) ... (3).
【００１１】次に、ステップＳ３では、上記の処理で得
られた連続位相領域Ｌjkでの位相データとＹ方向に隣合
う連続位相領域Ｌ(j-1)1またはＬ(j+1)mでの位相データ
とが連続的につながるように以下の処理を行う。即ち、
図４に示すように、ｊ行目のｋ番目の連続位相領域Ｌjk
中での任意の位相データのうち同じ列でＹ方向に１行だ
け上の画素に位相データＷｐ’（Ｌ(j-1)k）が存在する
ものをＷｐ’（Ｌjk）とする。Ｗｐ’（Ｌjk）とＷｐ’
（Ｌ(j-1)k）との位相差ΔＷｐ’、即ち、 ΔＷｐ’＝Ｗｐ’（Ｌjk）−Ｗｐ’（Ｌ(j-1)k） ・・・（４） の絶対値｜ΔＷｐ’｜があるしきい値θより小さい場合
は、Ｗｐ’（Ｌjk）にπを加減して、 ΔＷｐ’＝（Ｗｐ’（Ｌjk）±ｎπ）−Ｗｐ’（Ｌ(j-1)k） （ｎ：整数）・・・（５） により、｜ΔＷｐ’｜がθより小さくなるまでπの加減
をｎ回繰り返す。そして、｜ΔＷｐ’｜＜θとなったら
領域Ｌjk中の全ての位相データＷ’（Ｘi ，Ｙj）に対
して、 Ｗ”（Ｘi ，Ｙj ）＝Ｗ’（Ｘi ，Ｙj ）±ｎπ （但し、（Ｘi ，Ｙj ）∈Ｌjk）・・・（６） を計算する。ここで、Ｌjk中の全ての位相データＷｐ’
（Ｌjk）に対してＷｐ’（Ｌ(j-1)k）が存在しない場合
は全ての位相領域の処理が終了した後に、領域Ｌjk中の
位相データのうち同じ列でＹ方向に１行だけ下の画素に
位相データＷｑ”（Ｌ(j+1)k）が存在するものをＷｑ’
（Ｌjk）とすると、Ｗｑ’（Ｌjk）とＷ”（Ｌ(j+1)k）
との位相差ΔＷｑ’、即ち、 ΔＷｑ’＝Ｗｑ’（Ｌjk）−Ｗ”（Ｌ(j+1)k） ・・・（７） の絶対値｜ΔＷｑ’｜があるしきい値θより小さくなる
ようにＷｑ’（Ｌjk）にπを加減して、 ΔＷｑ’＝（Ｗｑ’（Ｌjk）±ｎπ）−Ｗｑ”（Ｌ(j-1)k） （ｎ：整数）・・・（８） により、｜ΔＷｑ’｜がθより小さくなるまでπの加減
をｎ回繰り返す。｜ΔＷｑ’｜＜θとなったら、（６）
式に従ってＷ”（Ｘi ，Ｙj ）を計算する。Ｗ”
（Ｘi ，Ｙj ）が求めるべき連続位相分布である。Next, in step S3, the continuous phase region L (j-1) 1 or L (j + 1) m adjacent to the phase data in the continuous phase region L jk obtained in the above process in the Y direction. The following processing is performed so that the phase data in 1 is continuously connected. That is,
As shown in FIG. 4, the j-th row k-th continuous phase region L jk
Among arbitrary phase data among them, data having phase data Wp ′ (L (j−1) k ) in the pixel on the same column and one row above in the Y direction is defined as Wp ′ (L jk ). Wp '(L jk ) and Wp'
(L (j-1) k ) Phase difference ΔWp ', that is, ΔWp' = Wp '(L jk ) -Wp' (L (j-1) k ) ... (4) Absolute value | ΔWp If '| is smaller than a certain threshold value θ, π is added to or subtracted from Wp' (L jk ), and ΔWp '= (Wp' (L jk ) ± nπ) -Wp '(L (j-1) k ) (N: integer) (5), the addition and subtraction of π is repeated n times until | ΔWp ′ | becomes smaller than θ. Then, when | ΔWp ′ | <θ, for all the phase data W ′ (X i , Y j ) in the region L jk , W ″ (X i , Y j ) = W ′ (X i , Y j ) ± nπ (where (X i , Y j ) εL jk ) ... (6) is calculated, where all the phase data Wp ′ in L jk are calculated.
When Wp '(L (j-1) k ) does not exist for (L jk ), after processing of all the phase regions is completed, 1 in the same column in the phase data in the region L jk in the Y direction. If the phase data Wq ″ (L (j + 1) k ) exists in the pixel just below the row, Wq ′
(L jk ), Wq ′ (L jk ) and W ″ (L (j + 1) k ).
ΔWq ', that is, ΔWq' = Wq '(L jk ) -W "(L (j + 1) k ) ... (7) absolute value | ΔWq' | Π is added to or subtracted from Wq ′ (L jk ) so as to be small, and ΔWq ′ = (Wq ′ (L jk ) ± nπ) −Wq ″ (L (j-1) k ) (n: integer) ... By (8), the adjustment of π is repeated n times until | ΔWq ′ | becomes smaller than θ. When | ΔWq '| <θ, (6)
Compute W ″ (X i , Y j ) according to the formula. W ″
(X i , Y j ) is the continuous phase distribution to be obtained.
【００１２】以上説明した手順に従って処理を行えば、
図５（Ａ）に示したような、位相飛びが生じた位相分布
から、図５（Ｂ）に示すような、連続的な位相分布を得
ることができる。If processing is performed according to the procedure described above,
A continuous phase distribution as shown in FIG. 5 (B) can be obtained from the phase distribution with the phase jump as shown in FIG. 5 (A).
【００１３】[0013]
【実施例１】以下、添付図面を参照して本発明に係る位
相つなぎ方法の実施例を説明する。まず、本発明の実施
例１を説明する。図６は本発明の実施例１を説明する図
である。実施例１では、図１のステップＳ１に対応する
手順、即ち、Ｘ方向で領域Ｌjkを検出する際に、各領域
Ｌjkの始点と終点との座標を記憶しておいて、その座標
から各領域の中点Ｍjkを算出し、その点での位相データ
を用いてＹ方向で各領域Ｌjk同士の位相つなぎ（図１の
ステップＳ３に対応する）を行う。[Embodiment 1] An embodiment of a phase connecting method according to the present invention will be described below with reference to the accompanying drawings. First, a first embodiment of the present invention will be described. FIG. 6 is a diagram for explaining the first embodiment of the present invention. In the first embodiment, the procedure corresponding to step S1 in FIG. 1, that is, when the area L jk is detected in the X direction, the coordinates of the start point and the end point of each area L jk are stored, and the coordinates are calculated from the coordinates. The midpoint M jk of each area is calculated, and the phase data at that point is used to connect the phases of the areas L jk in the Y direction (corresponding to step S3 in FIG. 1).
【００１４】各領域Ｌjkの端点付近の位相データはノイ
ズの影響を受けやすく誤差が含まれている可能性がある
が、本実施例では中点での位相データを用いるので、よ
り測定精度が向上する。The phase data near the end point of each region L jk is susceptible to noise and may include an error. However, since the phase data at the midpoint is used in this embodiment, the measurement accuracy is higher. improves.
【００１５】[0015]
【実施例２】次に、本発明の実施例２を説明する。図７
は本発明の実施例２を説明する図である。実施例２で
は、図１のステップＳ１に対応する手順、即ち、Ｘ方向
で領域Ｌjkを検出する際に、Ｙ方向で上下端での領域
と、それ以外の領域の始点と終点での位相データをカッ
トした後で、図１のステップＳ２以下の処理を行う。Second Embodiment Next, a second embodiment of the present invention will be described. Figure 7
FIG. 8 is a diagram illustrating a second embodiment of the present invention. In the second embodiment, the procedure corresponding to step S1 in FIG. 1, that is, when detecting the region L jk in the X direction, the regions at the upper and lower ends in the Y direction and the phases at the start and end points of the other regions After the data is cut, the processing of step S2 and thereafter in FIG. 1 is performed.
【００１６】干渉縞のアパーチャ周辺付近及びゴミや欠
陥等による位相データの欠落領域付近の位相データはノ
イズの影響を受けやすく誤差が含まれている可能性があ
るが、本実施例ではかかる誤差を含むデータを排除する
ので、より測定精度が向上する。The phase data in the vicinity of the aperture of the interference fringes and in the vicinity of the missing area of the phase data due to dust or defects are likely to be affected by noise and may contain an error. Since the included data is excluded, the measurement accuracy is further improved.
【００１７】[0017]
【発明の効果】以上説明したように、本発明の位相つな
ぎ方法によれば、ゴミや欠陥の存在する干渉縞や、形状
的に穴が明いている被検物の干渉縞にも適用が可能であ
り、しかも、測定精度を向上することができる。As described above, according to the phase connecting method of the present invention, it is possible to apply it to the interference fringes having dust or defects, or the interference fringes of a test object having a hole in shape. In addition, the measurement accuracy can be improved.
【図１】本発明の位相つなぎ方法を示すフローチャート
である。FIG. 1 is a flowchart showing a phase connecting method according to the present invention.
【図２】図１のステップＳ１の処理を説明する図であ
る。FIG. 2 is a diagram illustrating a process of step S1 of FIG.
【図３】図１のステップＳ２の処理を説明する図であ
る。FIG. 3 is a diagram illustrating a process of step S2 of FIG.
【図４】図１のステップＳ３の処理を説明する図であ
る。FIG. 4 is a diagram illustrating a process of step S3 of FIG.
【図５】本発明により得られる連続位相分布を説明する
図である。FIG. 5 is a diagram illustrating a continuous phase distribution obtained by the present invention.
【図６】本発明の実施例１を説明する図である。FIG. 6 is a diagram illustrating a first embodiment of the present invention.
【図７】本発明の実施例２を説明する図である。FIG. 7 is a diagram illustrating a second embodiment of the present invention.
【図８】従来の位相つなぎ方法を示すフローチャートで
ある。FIG. 8 is a flowchart showing a conventional phase connecting method.
Claims (1)
り、測定光と参照光とをエリアセンサー上で干渉せし
め、参照光の位相を段階的に変化させ、その各段階での
干渉縞の強度値を読み取り、そのデータに基づき演算処
理を行って各点での位相を求める方法において、求めた
位相データ領域を一方向でスキャンし、各スキャニング
ライン毎に位相データが連続して存在する連続位相領域
中で位相つなぎを行う第一ステップと、前記方向と直交
する方向で前記連続位相領域同士の位相つなぎを行う第
二ステップとにより、連続的な位相分布を求めることを
特徴とする位相つなぎ方法。1. A fringe scanning interferometry method causes measurement light and reference light to interfere on an area sensor, the phase of the reference light is changed stepwise, and the intensity value of interference fringes at each step is read, In the method of calculating the phase at each point by performing arithmetic processing based on that data, scan the calculated phase data area in one direction, and phase in the continuous phase area where the phase data continuously exists for each scanning line. A phase connecting method, wherein a continuous phase distribution is obtained by a first step of connecting and a second step of connecting phases of the continuous phase regions in a direction orthogonal to the direction.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP17171892A JP3148001B2 (en) | 1992-06-05 | 1992-06-05 | Wavefront phase joining method by fringe scanning interferometry |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP17171892A JP3148001B2 (en) | 1992-06-05 | 1992-06-05 | Wavefront phase joining method by fringe scanning interferometry |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH05340843A true JPH05340843A (en) | 1993-12-24 |
| JP3148001B2 JP3148001B2 (en) | 2001-03-19 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP17171892A Expired - Lifetime JP3148001B2 (en) | 1992-06-05 | 1992-06-05 | Wavefront phase joining method by fringe scanning interferometry |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009236706A (en) * | 2008-03-27 | 2009-10-15 | Kobe Steel Ltd | Shape calculator, shape calculation program, shape calculating method, and shape-measuring device |
| JP2010121977A (en) * | 2008-11-17 | 2010-06-03 | Keyence Corp | Optical displacement gauge |
-
1992
- 1992-06-05 JP JP17171892A patent/JP3148001B2/en not_active Expired - Lifetime
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009236706A (en) * | 2008-03-27 | 2009-10-15 | Kobe Steel Ltd | Shape calculator, shape calculation program, shape calculating method, and shape-measuring device |
| JP2010121977A (en) * | 2008-11-17 | 2010-06-03 | Keyence Corp | Optical displacement gauge |
Also Published As
| Publication number | Publication date |
|---|---|
| JP3148001B2 (en) | 2001-03-19 |
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