JP2000146705A - Method of measuring phase distribution by using grating shearing interferometer - Google Patents
Method of measuring phase distribution by using grating shearing interferometerInfo
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- JP2000146705A JP2000146705A JP10312824A JP31282498A JP2000146705A JP 2000146705 A JP2000146705 A JP 2000146705A JP 10312824 A JP10312824 A JP 10312824A JP 31282498 A JP31282498 A JP 31282498A JP 2000146705 A JP2000146705 A JP 2000146705A
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- interference fringes
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Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、光波の位相分布を
精密に計測するための干渉計に関し、特にグレーティン
グシアリング干渉計によって測定した干渉縞の強度分布
を処理するアルゴリズムに関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an interferometer for accurately measuring the phase distribution of a light wave, and more particularly to an algorithm for processing the intensity distribution of interference fringes measured by a grating shearing interferometer.
【０００２】[0002]
【従来の技術】光波の位相分布を精密に計測するため
に、従来より、グレーティングシアリング干渉計が使用
されている。グレーティングシアリング干渉計とは、実
質的に同一に形成された２枚の位相型回折格子を、互い
に平行に、且つ格子のピッチ方向を同一の方向に向けて
配置し、２枚の回折格子のうちの少なくともいずれか一
方を、ピッチ方向にシフト可能に配置したものである。
ここで、第１の位相型回折格子をｍ次光として通過し、
第２の位相型回折格子を−ｍ次光として通過した光を、
ｍ次結像光と呼ぶこととする。グレーティングシアリン
グ干渉計は、１次結像光と−１次結像光との干渉による
干渉縞の強度分布を測定し、この測定を、一方の位相型
回折格子をシフトしながら繰り返すことによって、干渉
計に入射する光の位相分布を測定するものである。2. Description of the Related Art A grating shearing interferometer has been conventionally used to accurately measure the phase distribution of a light wave. A grating shearing interferometer is a device in which two phase-type diffraction gratings formed substantially identically are arranged parallel to each other and the pitch direction of the gratings is oriented in the same direction. Is arranged so as to be shiftable in the pitch direction.
Here, the light passes through the first phase type diffraction grating as m-order light,
Light that has passed through the second phase type diffraction grating as -m order light,
It is referred to as an m-th order imaging light. The grating shearing interferometer measures the intensity distribution of interference fringes due to interference between the primary imaging light and the primary imaging light, and repeats this measurement while shifting one of the phase-type diffraction gratings. It measures the phase distribution of light incident on the meter.
【０００３】そして、従来より用いられている計測方法
のうち、例えば５バケット法とは、格子のピッチをｐと
するとき、一方の位相型回折格子をｐ／８・ｊ（ｊ＝
０，１，２，３，４）ずつシフトして、都合５個の干渉
縞の強度分布Ｉjを測定し、次式によって、波面の位相
分布θ″を求めるものであった。 [0003] Among the conventionally used measurement methods, for example, the 5-bucket method is such that when the pitch of the grating is p, one of the phase type diffraction gratings is p / 8 · j (j =
0, 1, 2, 3, 4), the intensity distribution I j of five convenient interference fringes is measured, and the phase distribution θ ″ of the wavefront is obtained by the following equation.
【０００４】[0004]
【発明が解決しようとする課題】グレーティングシアリ
ング干渉計を構成する各々の位相型回折格子の段差の高
さは、０次光の強度が０となるように設計されている。
しかしながら、実際の段差は設計値通りの高さになると
は限らず、もしも実際の段差が設計値と異なるときに
は、０次光が存在することとなるから、干渉縞の強度に
影響を与え、測定精度の低下を招くこととなる。したが
って本発明は、グレーティングシアリング干渉計を用い
た位相分布の計測方法において、０次光による影響を受
けにくいアルゴリズムを提供することを課題とする。The height of the step of each phase type diffraction grating constituting the grating shearing interferometer is designed so that the intensity of the zero-order light becomes zero.
However, the actual step does not always have the height as designed, and if the actual step is different from the designed value, the zero-order light will be present. This leads to a decrease in accuracy. Therefore, an object of the present invention is to provide an algorithm that is less affected by zero-order light in a phase distribution measurement method using a grating shearing interferometer.
【０００５】[0005]
【課題を解決するための手段】本発明は上記課題を解決
するためになされたものであり、すなわち、実質的に同
一に形成された２枚の位相型回折格子を、互いに平行
に、且つ格子のピッチ方向を同一の方向に向けて配置
し、該２枚の位相型回折格子のうちの少なくともいずれ
か一方を、前記ピッチ方向にシフト可能に配置したグレ
ーティングシアリング干渉計を用い、該干渉計に入射す
る光の位相分布を計測する方法において、前記格子のピ
ッチをｐとし、Ｎを３以上の自然数とするとき、前記い
ずれか一方の位相型回折格子を、ｐ／２Ｎ・ｊ（ｊ＝
０，１，２，‥‥，２Ｎ）ずつシフトして、都合２Ｎ＋
１個の干渉縞の強度分布を測定する工程と、第ｋ番目
（ｋ＝０，１，２，‥‥，Ｎ）の干渉縞の強度分布と、
第ｋ＋Ｎ番目の干渉縞の強度分布とを平均して得られる
都合Ｎ個の強度分布に基づいて、前記光の位相分布を求
める工程とを有することを特徴とする、グレーティング
シアリング干渉計を用いた位相分布の計測方法である。
なお、平均に代えて合計を用いたとしても、本質的に差
異がないこと明らかである。SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problem, that is, two phase-type diffraction gratings formed substantially identically are arranged in parallel with each other and in parallel with each other. Are arranged in the same direction, and at least one of the two phase-type diffraction gratings is provided with a grating shearing interferometer arranged so as to be shiftable in the pitch direction. In the method for measuring the phase distribution of incident light, when the pitch of the grating is p and N is a natural number of 3 or more, one of the phase type diffraction gratings is set to p / 2N · j (j =
0, 1, 2,..., 2N) by 2N +
Measuring the intensity distribution of one interference fringe, the intensity distribution of the k-th (k = 0, 1, 2,..., N) interference fringe;
Obtaining a phase distribution of the light based on N convenient intensity distributions obtained by averaging the intensity distributions of the (k + N) th interference fringes, using a grating shearing interferometer. This is a method for measuring the phase distribution.
It is clear that there is essentially no difference even if the sum is used instead of the average.
【０００６】その際、Ｎ＝４として一方の位相型回折格
子をｐ／８・ｊ（ｊ＝０，１，２，‥‥，８）ずつシフ
トして、都合９個の干渉縞の強度分布Ｉjを測定し、次
の（２）式によって、光の位相分布θ′を求めことがで
きる。 At this time, one phase type diffraction grating is shifted by p / 8 · j (j = 0, 1, 2, ‥‥, 8) by setting N = 4, and the intensity distribution of nine interference fringes is conveniently obtained. By measuring I j , the phase distribution θ ′ of light can be obtained by the following equation (2).
【０００７】[0007]
【発明の実施の形態】本発明の実施の形態を図面によっ
て説明する。図１は本発明方法を適用するグレーティン
グシアリング干渉計を示す。第１の位相型回折格子１
と、第２の位相型回折格子２とは、実質的に同一に形成
されており、両回折格子１，２は、互いに平行に配置さ
れ、且つ格子のピッチ方向を同一の方向に向けて配置さ
れている。図１では、干渉計に入射する光Ｅの方向、す
なわち波面の進行方向をｗとし、波面方向ｗに直交する
２方向をｘ方向とｙ方向とし、このうち格子のピッチ方
向をｘ方向としている。第２の位相型回折格子２は、ピ
ッチ方向すなわちｘ方向にシフトできるように、ピエゾ
素子３によって駆動されている。２枚の回折格子を通過
した光は、入射光Ｅの波面に応じた干渉縞を作り、その
干渉縞はＣＣＤカメラ４によって撮像される。Embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows a grating shearing interferometer to which the method of the present invention is applied. First phase type diffraction grating 1
And the second phase type diffraction grating 2 are formed substantially identically, the two diffraction gratings 1 and 2 are arranged in parallel with each other, and the pitch directions of the gratings are oriented in the same direction. Have been. In FIG. 1, the direction of the light E incident on the interferometer, that is, the traveling direction of the wavefront is defined as w, and two directions orthogonal to the wavefront direction w are defined as x and y directions, and the pitch direction of the grating is defined as x direction. . The second phase diffraction grating 2 is driven by a piezo element 3 so as to be able to shift in the pitch direction, that is, in the x direction. The light that has passed through the two diffraction gratings forms interference fringes corresponding to the wavefront of the incident light E, and the interference fringes are imaged by the CCD camera 4.
【０００８】また、上記の構成では、入射光Ｅのｘ方向
の波面の差分のみを知ることができる。そこで、入射光
Ｅと干渉計との位置関係を光軸回りに９０°回転するこ
とにより、ｙ方向の波面の差分を知ることができ、これ
らの結果を積分することによって、入射光の位相分布を
求めることができる。入射光と干渉計との位置関係を光
軸回りに９０°回転する方法としては、干渉計を固定し
て入射光を回転しても良いし、入射光を固定して干渉計
の方を回転しても良い。In the above configuration, only the difference between the wavefronts of the incident light E in the x direction can be known. Therefore, by rotating the positional relationship between the incident light E and the interferometer by 90 ° around the optical axis, the difference between the wavefronts in the y direction can be known. By integrating these results, the phase distribution of the incident light can be obtained. Can be requested. As a method of rotating the positional relationship between the incident light and the interferometer by 90 ° around the optical axis, the interferometer may be fixed and the incident light may be rotated, or the incident light may be fixed and the interferometer is rotated. You may.
【０００９】以下の説明において、２枚の回折格子１，
２を通過した後の回折光を結像光と呼び、１枚目の回折
格子１をｍ次光として通過し、２枚目の回折格子２を−
ｍ次光として通過した結像光をｍ次結像光と呼ぶことと
する。また、±３次までの結像光Ｅ0、Ｅ1、Ｅ-1、
Ｅ3、Ｅ-3までを考慮して、より高次の結像光は無視す
ることとし、３次結像光Ｅ3と−３次結像光Ｅ-3との干
渉による干渉縞も無視することとする。In the following description, two diffraction gratings 1
2 is called imaging light, the first diffraction grating 1 is passed as m-order light, and the second diffraction grating 2 is-.
The imaging light that has passed as the m-th order light is referred to as the m-th order imaging light. Further, imaging light E 0 , E 1 , E −1 , up to ± 3 order,
Taking into account the up E 3, E -3, higher order imaging light and ignoring, ignore the interference fringes due to interference between the 3 image-forming light E 3 and -3 image formation light E -3 I decided to.
【００１０】位相差が０の領域とρの領域とが、デュー
ティー比１にて周期的に繰り返す２値の位相型回折格子
に、光が垂直入射すると、 Ａm：回折光の強度比 ρ：位相型回折格子の位相差 ｍ：回折次数 となる。When light is vertically incident on a binary phase type diffraction grating in which a region having a phase difference of 0 and a region having ρ are periodically repeated at a duty ratio of 1, A m : intensity ratio of diffracted light ρ: phase difference of phase type diffraction grating m: diffraction order
【００１１】式（３）より、０次光の光量を０とするた
めには、ρ＝π，３π，５π，‥‥などに設定すれば良
いが、実際には回折格子の製造上の公差があるために、
ρ≠π，３π，５π，‥‥となるおそれがあり、すなわ
ち０次光の光量が０とならないおそれがある。したがっ
て考慮対象となる干渉縞は、（ａ）１次と−１次、
（ｂ）０次と１次、 及び（ｃ）０次と−１次、
（ｄ）０次と３次、 及び（ｅ）０次と−３次、
（ｆ）１次と３次、 及び（ｇ）−１次と−３次、
（ｈ）１次と−３次、 及び（ｉ）−１次と３次、の結
像光の組み合わせによる都合９種類の干渉縞である。但
し、これらの干渉縞の位相分布のうち、（ｂ）は（ｃ）
と等しく、（ｄ）は（ｅ）と等しく、（ｆ）は（ｇ）と
等しく、（ｈ）は（ｉ）と等しい。From equation (3), to set the light quantity of the zero-order light to 0, it is sufficient to set ρ = π, 3π, 5π, ‥‥, etc. Because there is
There is a possibility that ρ ≠ π, 3π, 5π, ‥‥, that is, the light amount of the zero-order light may not become zero. Therefore, the interference fringes to be considered are (a) primary and −1 order,
(B) 0th and 1st order, and (c) 0th and -1st order,
(D) 0th and 3rd order, and (e) 0th and -3rd order,
(F) primary and tertiary, and (g) -1 and -3,
There are nine types of convenient interference fringes due to combinations of (h) primary and tertiary and (i) -1 and tertiary imaging light. However, of the phase distribution of these interference fringes, (b) is (c)
(D) is equal to (e), (f) is equal to (g), and (h) is equal to (i).
【００１２】これらの干渉縞のうち、１次と−１次とに
よる干渉縞の位相分布θが、必要な信号であり、その他
の干渉縞の位相分布はノイズである。また、本発明の目
的とするところは、回折格子の製造上の公差によって０
次光が存在する場合にも、０次結像光を含む組み合わ
せ、すなわち、０次と±１次、及び０次と±３次の干渉
縞の位相分布を、分布のない直流信号として、ノイズと
ならないようにするアルゴリズムを提供するところにあ
る。[0012] Of these interference fringes, the phase distribution θ of the interference fringes due to the first order and the -1st order is a necessary signal, and the phase distribution of the other interference fringes is noise. Further, an object of the present invention is to set the zero due to the manufacturing tolerance of the diffraction grating.
Even in the presence of the secondary light, the combination including the zero-order imaging light, that is, the phase distribution of the 0th-order and ± 1st-order and the 0th-order and ± 3rd-order interference fringes is regarded as a distribution-free DC signal as noise. The algorithm is to provide an algorithm that prevents this from happening.
【００１３】上記（３）式は、第１の位相型回折格子を
通過した時点での強度比であるが、第２の位相型回折格
子を通過する際にも、ほぼ同様の強度比となる。したが
って、２枚の回折格子を通過した後の結像光の強度比は
（Ａm）2となるから、振幅比はＡmとなる。したがっ
て、ｍ次結像光の光波Ｅmは、 ｋ：光の波数 ｗm：波面の位置 と表わされる。The above equation (3) is the intensity ratio at the time of passing through the first phase type diffraction grating, but becomes substantially the same when passing through the second phase type diffraction grating. . Thus, since the two diffraction gratings the intensity ratio of the imaging light which has passed through the (A m) 2, the amplitude ratio is A m. Thus, the light wave E m of the m-th imaging light, k: wave number of light w m : position of wave front
【００１４】０次結像光の波面ｗ0を、 ｗ0＝ｗ（ｘ，ｙ） とし、１次結像光と−１次結像光とのｘ方向のシヤ量を
Δとすると、ｍ次結像光の波面ｗmは、 ｗm＝ｗ（ｘ＋ｍΔ／２，ｙ） である。Assuming that the wavefront w 0 of the zero -order imaging light is w 0 = w (x, y) and the shear amount in the x direction between the primary imaging light and the −1st-order imaging light is Δ, m The wavefront w m of the next imaging light is: w m = w (x + mΔ / 2, y)
【００１５】結像光どうしの干渉による干渉縞強度Ｉ
は、 θm,n：ｍ次光とｎ次光との干渉による干渉縞の位相分
布 θm,n≡ｋ（ｗm−ｗn） となる。Interference fringe intensity I due to interference between imaging light beams
Is θ m, n : The phase distribution of interference fringes due to interference between the m- th light and the n-th light θ m, n ≡k (w m −w n ).
【００１６】ここで、第２の回折格子２をｘ方向にΔｘ
だけシフトすると、ｍ次結像光の位相は、 Δφ：ｍ次結像光の位相シフト量 ｐ：回折格子のピッチ だけシフトする。Here, the second diffraction grating 2 is moved in the x direction by Δx
, The phase of the m-order imaging light becomes Δφ: Phase shift amount of m-order imaging light p: Shift by the pitch of diffraction grating
【００１７】したがって、ｍ次結像光の光波Ｅmは、 となり、結像光どうしの干渉による干渉縞強度Ｉは、 Δm,n：次数差、Δm,n≡｜ｍ−ｎ｜ となる。[0017] Thus, the light wave E m of the m-th imaging light, And the interference fringe intensity I due to the interference between the imaging light is Δ m, n : order difference, Δ m, n ≡ | mn−
【００１８】さて、（７）式において、１次光と−１次
光とによる干渉縞の強度分布が、元の強度分布に復する
ためには、 ２π・［１−（−１）］・Δｘ／ｐ＝２π 故に、 Δｘ＝ｐ／２ となる。すなわち、１次光と−１次光とによる干渉縞
は、ｐ／２のピッチにて変化する。それ故従来は、２枚
の回折格子のシフト量の上限をｐ／２としていた。In the equation (7), in order for the intensity distribution of the interference fringes due to the primary light and the −1st light to return to the original intensity distribution, 2π · [1-(− 1)] · Δx / p = 2π Therefore, Δx = p / 2. That is, the interference fringes due to the first-order light and the minus first-order light change at a pitch of p / 2. Therefore, conventionally, the upper limit of the shift amount of the two diffraction gratings is set to p / 2.
【００１９】しかるに、例えば１次光と０次光とによる
干渉縞の強度分布が、元の強度分布に復するためには、 ２π・［１−０］・Δｘ／ｐ＝２π 故に、 Δｘ＝ｐ となる。すなわち、０次光と±１次光とによる干渉縞
は、ｐのピッチにて変化する。また、３次光と０次光と
による干渉縞の強度分布が、元の強度分布に復するため
には、 ２π・［３−０］・Δｘ／ｐ＝２π 故に、 Δｘ＝ｐ／３ となる。すなわち、０次光と±３次光とによる干渉縞
は、ｐ／３のピッチにて変化する。However, for example, in order for the intensity distribution of the interference fringes by the first-order light and the zero-order light to return to the original intensity distribution, 2π · [1-0] · Δx / p = 2π p. That is, the interference fringes due to the zero-order light and the ± first-order light change at a pitch of p. Further, in order for the intensity distribution of the interference fringes due to the third-order light and the zero-order light to return to the original intensity distribution, 2π · [3-0] · Δx / p = 2π Therefore, Δx = p / 3 Become. That is, the interference fringes due to the 0th-order light and the ± 3rd-order light change at a pitch of p / 3.
【００２０】そこで、シフト量がｐ／２だけ異なる１対
のデータの平均を取ることとすると、１次光と−１次光
とによる干渉縞の強度分布は、両データで同じであるか
ら、単に同一の強度分布を２倍して２で割っただけとな
る。しかるに０次光と±１次光とによる干渉縞の強度分
布は、両データで位相が反転しているから、交流成分は
０となる。同様に、０次光と±３次光とによる干渉縞の
強度分布も、両データで位相が反転しているから、交流
成分は０となる。すなわち０次光との干渉による干渉縞
の交流成分は、すべて０となる。Therefore, if an average of a pair of data whose shift amounts are different by p / 2 is to be averaged, the intensity distribution of interference fringes by the primary light and the −1st light is the same for both data. Simply doubling the same intensity distribution and dividing by two. However, in the intensity distribution of the interference fringes due to the zero-order light and the ± first-order light, the AC component is zero because the phases are inverted in both data. Similarly, the intensity distribution of the interference fringes due to the zero-order light and the ± third-order light also has an AC component of zero because the phases are inverted between the two data. That is, the AC components of the interference fringes due to the interference with the zero-order light are all zero.
【００２１】他方、例えば３次光と１次光とによる干渉
縞の強度分布が、元の強度分布に復するためには、 ２π・［３−１］・Δｘ／ｐ＝２π 故に、 Δｘ＝ｐ／２ となる。すなわち、±１次光と±３次光（複号同順）と
による干渉縞は、ｐ／２のピッチにて変化する。したが
ってシフト量がｐ／２だけ異なる１対のデータの平均を
取ることとしても、元のデータと同じになる。On the other hand, for example, in order for the intensity distribution of the interference fringes due to the third-order light and the first-order light to return to the original intensity distribution, 2π · [3-1] · Δx / p = 2π Therefore, Δx = p / 2. That is, the interference fringes due to the ± 1st-order light and ± 3rd-order light (in the same order of the decoding) change at a pitch of p / 2. Therefore, even if an average of a pair of data whose shift amounts are different by p / 2 is taken, the result is the same as the original data.
【００２２】同様に、３次光と−１次光とによる干渉縞
の強度分布が、元の強度分布に復するためには、 ２π・［３−（−１）］・Δｘ／ｐ＝２π 故に、 Δｘ＝ｐ／４ となる。すなわち、３次光と−１次光とによる干渉縞、
あるいは１次光と−３次光とによる干渉縞は、ｐ／４の
ピッチにて変化する。したがってシフト量がｐ／２だけ
異なる１対のデータの平均を取ることとしても、元のデ
ータと同じになる。Similarly, in order for the intensity distribution of the interference fringes due to the third-order light and the −1st-order light to return to the original intensity distribution, 2π · [3-(− 1)] · Δx / p = 2π Therefore, Δx = p / 4. That is, interference fringes due to the third-order light and the -1st-order light,
Alternatively, the interference fringes due to the primary light and the tertiary light change at a pitch of p / 4. Therefore, even if an average of a pair of data whose shift amounts are different by p / 2 is taken, the result is the same as the original data.
【００２３】以上のように、シフト量がｐ／２だけ異な
る１対のデータの平均を取ることとすると、０次光との
干渉は、次数差が奇数となるために、干渉縞の交流成分
はすべて０となる。他方、次数差が偶数となるその他の
干渉縞についてのデータは変化がないから、０次光によ
る影響を削除することができる。As described above, if an average of a pair of data whose shift amounts are different from each other by p / 2 is to be averaged, the interference with the zero-order light has an odd-order difference, and therefore the AC component of the interference fringe Are all 0. On the other hand, since there is no change in the data on other interference fringes having an even difference in the order, the influence of the zero-order light can be eliminated.
【００２４】次に、１次光と−１次光による干渉縞は、
ｐ／２のピッチにて変化する。そこで、ｐ／２の区間を
４等分して、第２の回折格子２をｐ／８づつシフトする
場合について説明する。この場合、従来の手法では５個
のデータだけを取るために、５バケット法と呼ばれてい
る。しかるに本発明では、ｐだけの区間を８等分して都
合９個のデータを取り、次いでシフト量がｐ／２だけ異
なる１対のデータの平均を取る。したがって２重５バケ
ット法と呼ぶことができる。Next, interference fringes due to the primary light and the −1st light are
It changes at a pitch of p / 2. Therefore, a case in which the section of p / 2 is divided into four equal parts and the second diffraction grating 2 is shifted by p / 8 will be described. In this case, since the conventional method takes only five data, it is called a five-bucket method. However, in the present invention, the section of only p is divided into eight equal parts to obtain nine pieces of data, and then the average of a pair of data having shift amounts different by p / 2 is obtained. Therefore, it can be called a double 5-bucket method.
【００２５】いま、 Δｘ＝ｊｐ／８（ｊ＝０〜８） とした場合の干渉縞の強度分布を、それぞれ、 Ｉj（ｊ＝０〜８） とすると、 となる。If the intensity distribution of interference fringes when Δx = jp / 8 (j = 0 to 8) is I j (j = 0 to 8), Becomes
【００２６】シフト量がｐ／２だけ異なる１対のデータ
の平均に代えて、合計を取ると、 となる。既述のごとく、次数差Δm,nが奇数のときに
は、右辺第２項は０となり、すなわち交流成分が消去さ
れる。When the sum is taken instead of the average of a pair of data in which the shift amount differs by p / 2, Becomes As described above, when the order difference Δ m, n is an odd number, the second term on the right side becomes 0, that is, the AC component is eliminated.
【００２７】簡単のために、結像光の振幅Ａmを±１次
光の振幅Ａ1で規格化して、Ａ1＝１とすると、 となる。但し、θ≡θ1,-1である。[0027] For simplicity, normalized by the amplitude A 1 of the amplitude A m of the imaging light ± 1-order light, when A 1 = 1, Becomes However, θ≡θ 1, -1 .
【００２８】sinθの項を集めると、 となる。同様に、cosθの項を集めると、 となる。すなわち、直流成分の項と次数差が４次となる
項が消去される。When the terms of sin θ are collected, Becomes Similarly, if we collect cosθ terms, Becomes That is, a term having a fourth order difference from the DC component term is eliminated.
【００２９】上記両式より、 となる。From the above equations, Becomes
【００３０】必要とする干渉縞の位相分布はθである
が、（２）式で定義されるθ′を用いることとすると、 となる。したがってθ′を用いることによる誤差Δθ′
は、 となる。The required phase distribution of the interference fringes is θ. If θ ′ defined by equation (2) is used, Becomes Therefore, the error Δθ ′ by using θ ′
Is Becomes
【００３１】他方、従来は前記（１）式によるθ″を用
いていた。そこで、（８）式を（１）式に代入すると、 ｋ≡２1/2／２ となる。On the other hand, conventionally, θ ″ according to the above equation (1) is used. Therefore, when equation (8) is substituted into equation (1), k≡2 1/2 / 2.
【００３２】したがって、（１）式のθ″を用いること
による誤差をΔθ″とすると、 となる。Therefore, assuming that the error caused by using θ ″ in equation (1) is Δθ ″, Becomes
【００３３】（１１）式に示されるように、θ′を用い
ることによる誤差要因は、±１次光と±３次光（複号同
順）との干渉縞だけであり、０次光の影響は除外されて
いる。しかるにθ″を用いることによる誤差要因は、±
１次光と±３次光（複号同順）との干渉縞のほか、０次
光と±１次光との干渉縞、及び０次光と±３次光との干
渉縞がある。それ故、従来の５バケット法に代えて、本
発明による２重５バケット法を用いることにより、測定
精度の向上を図ることができる。As shown in equation (11), the only error factor due to the use of θ 'is the interference fringe between the ± 1st-order light and the ± 3rd-order light (in the same order as the sign), and Effects have been excluded. However, the error factor due to the use of θ ″ is ±
In addition to interference fringes between the primary light and the ± third-order light (in the same order as the double sign), there are interference fringes between the zero-order light and the ± first-order light and interference fringes between the zero-order light and the ± third-order light. Therefore, by using the double 5-bucket method according to the present invention instead of the conventional 5-bucket method, measurement accuracy can be improved.
【００３４】次に具体的な数値を挙げて説明する。
（３）式より、０次光の光量を０とするためには、ρ＝
π，３π，５πなどに設定すれば良い。短波長の光に対
しても適度の段差を持つように、ρ＝３πに設定したと
すると、 λ：光の波長 ｄ：位相型回折格子の段差の高さ ｎ：位相型回折格子の硝材 となる。したがって、 となるように、段差ｄを設計すれば良い。Next, specific numerical values will be described.
From equation (3), in order to set the light quantity of the zero-order light to 0, ρ =
It may be set to π, 3π, 5π, or the like. Assuming that ρ = 3π is set so as to have an appropriate step even for light of short wavelength, λ: wavelength of light d: height of the step of the phase type diffraction grating n: glass material of the phase type diffraction grating Therefore, What is necessary is just to design step d so that it may become.
【００３５】しかるに、段差ｄには製作上の公差を考慮
する必要がある。いま、段差ｄに±Δｄだけの誤差が生
じたとすると、位相型回折格子の位相差ρは、 となる。例えば、 λ＝１９３ｎｍ Δｄ＝±３０ｎｍ ｎ＝１．５ とすると、０次結像光、±１次結像光、±３次結像光の
振幅比Ａ0、Ａ1、Ａ3は、Δｄ＝３０ｎｍの場合も、Δ
ｄ＝−３０ｎｍの場合も、 となる。However, it is necessary to consider a manufacturing tolerance for the step d. Now, assuming that an error of ± Δd occurs in the step d, the phase difference ρ of the phase type diffraction grating becomes Becomes For example, if λ = 193 nm Δd = ± 30 nm n = 1.5, the amplitude ratios A 0 , A 1 , and A 3 of the zero- order imaging light, the ± first-order imaging light, and the ± third-order imaging light are Δd = 30 nm, Δ
When d = −30 nm, Becomes
【００３６】更に、結像光の振幅比ＡmをＡ1で規格化す
ると、 となる。Furthermore, when the amplitude ratio A m of the imaging light is normalized by A 1, Becomes
【００３７】±３次光に起因する測定誤差θ′は、（１
１）式で与えられるが、これとのアナロジーから、０次
光に起因する測定誤差Δθ0は、 によって見積もることができる。但しαは、適当な角度
である。The measurement error θ ′ caused by the ± 3rd-order light is (1
From the analogy with this, the measurement error Δθ 0 due to the zero-order light is Can be estimated by Where α is an appropriate angle.
【００３８】（１３）式の極値を調べるために、Δθ0
をαで微分した結果を０と置くと、 cosα＝−Ａ0＝−0.153 となるから、 α1＝９８．８°；α2＝２６１．２° となる。実際には、α1が（１３）式の最小値を与え、
α2が最大値を与えるから、その差は、 となる。In order to check the extreme value of the equation (13), Δθ 0
If the result obtained by differentiating with respect to α is set to 0, cos α = −A 0 = −0.153, so that α 1 = 98.8 °; α 2 = 261.2 °. In practice, α 1 gives the minimum value of equation (13),
Since α 2 gives the maximum value, the difference is Becomes
【００３９】すなわち、波面ｗの最大誤差（ピーク・バ
レー値）Δｗp-vは、 Δｗp-v＝０．３０７／２π・λ ＝０．０４８９λ となるから、ｒｍｓ（自乗平均平方根）誤差Δｗ
rmsは、 Δｗrms≒Δｗp-v／５ ≒０．０１λ となる。このように本発明による２重５バケット法によ
れは、０次光の光量が残っているとしても、その影響を
受けないので、従来の５バケット法と比べて、ｒｍｓ値
で０．０１λ程度の測定誤差を除外することができる。That is, since the maximum error (peak valley value) Δw pv of the wavefront w is Δw pv = 0.307 / 2π · λ = 0.0489λ, the rms (root mean square) error Δw
rms is Δw rms ≒ Δw pv / 5 0.01λ. As described above, according to the double 5-bucket method according to the present invention, even if the light quantity of the 0th-order light remains, it is not affected by the light quantity. Therefore, compared with the conventional 5-bucket method, the rms value is about 0.01λ. Can be excluded.
【００４０】[0040]
【発明の効果】以上のように本発明方法によれば、回折
格子の製造上の公差などに起因して０次光が存在する場
合にも、０次光を含む干渉縞の位相分布は、一様な信号
となる。したがって、測定しようとする光の位相分布の
測定精度の向上を図ることができる。As described above, according to the method of the present invention, the phase distribution of the interference fringes including the zero-order light can be obtained even when the zero-order light exists due to the manufacturing tolerance of the diffraction grating. It becomes a uniform signal. Therefore, the measurement accuracy of the phase distribution of the light to be measured can be improved.
【図１】本発明方法を適用するグレーティングシアリン
グ干渉計の一例を示す、（Ａ）側面図、（Ｂ）Ａ図中Ｂ
−Ｂ線矢視図である。FIG. 1A is a side view showing one example of a grating shearing interferometer to which the method of the present invention is applied, and FIG.
FIG.
１…第１位相型回折格子 ２…第２位相型回折
格子 ３…ピエゾ素子 ４…ＣＣＤカメラ Ｅ…入射光 Ｅ0、Ｅ1、Ｅ-1、Ｅ
3、Ｅ-3…結像光1 ... first phase type diffraction grating 2 ... second phase type diffraction grating 3 ... piezoelectric elements 4 ... CCD camera E ... incident light E 0, E 1, E -1 , E
3 , E -3 ... imaging light
Claims (2)
折格子を、互いに平行に、且つ格子のピッチ方向を同一
の方向に向けて配置し、該２枚の位相型回折格子のうち
の少なくともいずれか一方を、前記ピッチ方向にシフト
可能に配置したグレーティングシアリング干渉計を用
い、該干渉計に入射する光の位相分布を計測する方法に
おいて、 前記格子のピッチをｐとし、Ｎを３以上の自然数とする
とき、前記いずれか一方の位相型回折格子を、ｐ／２Ｎ
・ｊ（ｊ＝０，１，２，‥‥，２Ｎ）ずつシフトして、
都合２Ｎ＋１個の干渉縞の強度分布を測定する工程と、 第ｋ番目（ｋ＝０，１，２，‥‥，Ｎ）の干渉縞の強度
分布と、第ｋ＋Ｎ番目の干渉縞の強度分布とを平均して
得られる都合Ｎ個の強度分布に基づいて、前記光の位相
分布を求める工程とを有することを特徴とする、グレー
ティングシアリング干渉計を用いた位相分布の計測方
法。1. Two phase-type diffraction gratings formed substantially identically are arranged parallel to each other and with the pitch direction of the gratings oriented in the same direction. At least one of them, using a grating shearing interferometer arranged so as to be shiftable in the pitch direction, in a method of measuring the phase distribution of light incident on the interferometer, wherein the pitch of the grating is p, and N is When a natural number of 3 or more, one of the phase type diffraction gratings is p / 2N
・ J (j = 0, 1, 2, ‥‥, 2N)
Measuring the intensity distribution of the 2N + 1 interference fringes, the intensity distribution of the k-th (k = 0, 1, 2,..., N) interference fringe, the intensity distribution of the k + N-th interference fringe, Obtaining a phase distribution of the light based on the N intensity distributions obtained by averaging the phase distributions, and measuring the phase distribution using a grating shearing interferometer.
／８・ｊ（ｊ＝０，１，２，‥‥，８）ずつシフトし
て、都合９個の干渉縞の強度分布Ｉjを測定する工程
と、 次式によって、前記光の位相分布θを求める工程とを有
することを特徴とする、請求項１記載のグレーティング
シアリング干渉計を用いた位相分布の計測方法。 2. The method according to claim 1, wherein one of the phase type diffraction gratings is a p-type diffraction grating.
/ 8 · j (j = 0, 1, 2, ‥‥, 8) and measuring the intensity distribution I j of nine interference fringes, and the phase distribution θ of the light by the following equation: And measuring the phase distribution using the grating shearing interferometer according to claim 1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP10312824A JP2000146705A (en) | 1998-11-04 | 1998-11-04 | Method of measuring phase distribution by using grating shearing interferometer |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP10312824A JP2000146705A (en) | 1998-11-04 | 1998-11-04 | Method of measuring phase distribution by using grating shearing interferometer |
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| Publication Number | Publication Date |
|---|---|
| JP2000146705A true JP2000146705A (en) | 2000-05-26 |
Family
ID=18033873
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP10312824A Pending JP2000146705A (en) | 1998-11-04 | 1998-11-04 | Method of measuring phase distribution by using grating shearing interferometer |
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| Country | Link |
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