JPS61230002A - Interruption measuring method - Google Patents
Interruption measuring methodInfo
- Publication number
- JPS61230002A JPS61230002A JP60070637A JP7063785A JPS61230002A JP S61230002 A JPS61230002 A JP S61230002A JP 60070637 A JP60070637 A JP 60070637A JP 7063785 A JP7063785 A JP 7063785A JP S61230002 A JPS61230002 A JP S61230002A
- Authority
- JP
- Japan
- Prior art keywords
- window
- area sensor
- measurement
- light beam
- wavefront
- 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.)
- Granted
Links
- 238000000034 method Methods 0.000 title description 11
- 238000005259 measurement Methods 0.000 claims abstract description 31
- 238000005070 sampling Methods 0.000 claims abstract description 13
- 238000001228 spectrum Methods 0.000 claims description 20
- 238000000691 measurement method Methods 0.000 claims description 10
- 230000003595 spectral effect Effects 0.000 claims description 2
- 230000001131 transforming effect Effects 0.000 claims 1
- 230000009466 transformation Effects 0.000 abstract description 3
- 230000004907 flux Effects 0.000 abstract 2
- 238000010586 diagram Methods 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 238000007796 conventional method Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 238000010186 staining Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/02083—Interferometers characterised by particular signal processing and presentation
- G01B9/02084—Processing in the Fourier or frequency domain when not imaged in the frequency domain
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
- G01J9/0215—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods by shearing interferometric methods
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Spectroscopy & Molecular Physics (AREA)
- Engineering & Computer Science (AREA)
- Signal Processing (AREA)
- Mathematical Physics (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
- Instruments For Measurement Of Length By Optical Means (AREA)
- Length Measuring Devices By Optical Means (AREA)
Abstract
Description
【発明の詳細な説明】 （技術分野） 本発明は、干渉測定方法に関する。[Detailed description of the invention] (Technical field) The present invention relates to an interference measurement method.
（従来技術）
干渉測定方法は、基準面からの反射光である参照光と、
測定面からの反射光である測定光とを干渉せしめ、その
干渉縞の解析により測定波面と参照波面との差異を知り
、測定面の形状を、高精度に測定する方法である。(Prior art) The interference measurement method uses a reference light that is reflected light from a reference surface,
This is a method in which the shape of the measurement surface is measured with high precision by interfering with measurement light that is reflected light from the measurement surface and by analyzing the interference fringes to determine the difference between the measurement wavefront and the reference wavefront.
このような干渉測定方法のうちに、フーリエ変換を利用
する方法がある。すなわち、測定光と参照元とを所定面
内で互いに微小角θ傾けてエリアセンサーに入射せしめ
、両者の干渉縞をエリアセンサーによりウィンドウ処理
をして読取り、その結果をフーリエ変換することにより
、傾き角θに惑
より分離された３群の空間周波数のスペクトル群を得、
これらスペクトル群からひとつの単側波帯のみを選択し
、これを周波数軸上で傾き角θに対応する量だけスペク
トル移動し、これによって傾き成分を除去し、得られる
スペクトルに対し逆フーリエ変換と逆ウィンドウ処理と
を行ない、その結果から位相部分を算出することにより
、エリアセンサー上の測定波面の、参照波面からの偏差
を算出する測定方法である。Among such interference measurement methods, there is a method using Fourier transform. In other words, the measurement light and the reference source are incident on the area sensor at a slight angle θ tilted to each other within a predetermined plane, the interference fringes of both are read by window processing by the area sensor, and the result is Fourier transformed to calculate the inclination. Obtaining three groups of spatial frequency spectra separated by the angle θ,
Select only one single sideband from these spectra, shift the spectrum by an amount corresponding to the tilt angle θ on the frequency axis, remove the tilt component, and apply inverse Fourier transform to the resulting spectrum. This measurement method calculates the deviation of the measurement wavefront on the area sensor from the reference wavefront by performing inverse window processing and calculating the phase part from the result.
（目 的）
本発明は、上記の如きフーリエ変換を利用する干渉測定
方法を改良し、演算が容易で測定精度の高い干渉測定方
法の提供を目的としている。(Objective) The present invention aims to improve the interference measurement method using Fourier transform as described above, and to provide an interference measurement method that is easy to calculate and has high measurement accuracy.
（構 成） 以下、本発明を説明する。(composition) The present invention will be explained below.
本発明の特徴は、以下にのべる点にある。The features of the present invention are as follows.
フーリエ変換や、その逆変換の演算は離散的に行なわれ
るのであるが、傾き角θに対応する空間周波数ｆｏ
とサンプリング区間りとの間に、ｎを整数として、ｆｏ
＝ｎ／Ｄ が収立つように、θとＤの関係を定める
。上記空間周波数ｆｏ は、λを波長として、ｆＯ”
ｔａｎ ｆｊ で与えられる。Although Fourier transform and its inverse transform are performed discretely, the spatial frequency fo corresponding to the tilt angle θ
and the sampling interval, where n is an integer, fo
The relationship between θ and D is determined so that =n/D is satisfied. The above spatial frequency fo is fO'' where λ is the wavelength.
It is given by tan fj.
λ
また、フーリエ変換に先立つウィンドウ処理においては
、読取りの各ラインごとに、ウィンドウ両端部を、入力
光束の境界部と一致させるように、スレッシュホールド
レベルヲ設ケル。λ In addition, in window processing prior to Fourier transform, a threshold level is set for each line of reading so that both ends of the window coincide with the boundary of the input beam.
さらに、スペクトル移動の際に、１周期の出力周波数領
域を越える成分については、移動方向と反対方向に−だ
け移動させる。ここにｄはサンプリングピッチである。Furthermore, when moving the spectrum, components exceeding the output frequency range of one cycle are moved by - in the opposite direction to the moving direction. Here, d is the sampling pitch.
以下、図面を参照しながら、説明する。Description will be given below with reference to the drawings.
矛１図において、符号１０はビームスプリッタ−符号１
２は測定対象物、符号１４は平面鏡、符号１６はレンズ
、符号１８はエリアセンサーをそれぞれ示している。測
定対象物１２は測定面を有する。平面鏡１４ の鏡面は
基準面である。またＸ方向、２方向を図の如く定め、ｙ
方向は１図面に直交する方向とする。平面鏡１４は、そ
の鏡面の法線が、所定のｘｚ面内でＸ方向に対して微小
角傾いている。In Figure 1, the code 10 is the beam splitter - code 1
Reference numeral 2 indicates an object to be measured, reference numeral 14 indicates a plane mirror, reference numeral 16 indicates a lens, and reference numeral 18 indicates an area sensor. The measurement object 12 has a measurement surface. The mirror surface of the plane mirror 14 is a reference surface. In addition, the X direction and two directions are determined as shown in the figure, and the y
The direction is perpendicular to one drawing. The plane mirror 14 has a normal line to its mirror surface inclined at a small angle with respect to the X direction within a predetermined xz plane.
今、ビームスプリッタ−１０に対し、平面波が左方から
２方向に入射すると、この平面波はビームスプリッタ−
１０により２分割され、一方は、測定対象物１２Ｖｃ、
他方は平面鏡１４に′入射する。測定対象物１２に入射
した平面波は、測定面により反射され、測定光となりビ
ームスプリッタ−１０に入射し、Ｘ方向へ反射され、レ
ンズ１６を介してエリアセンサー１８に入射し、エリア
センサー１８の受光面上に測定面形状に応じた位相形状
を形成する。この位相形状なＷＡ （ｘ ）とする。こ
の位相形状は、本来はｘ、ｙの関数としてＷＡ（ｘ、
Ｙ） と書くべきものである。一方平面鏡１４に入射
した平面波は、反射されて参照波となり、ビームスプリ
ッタ−１０、レンズ１６を介してエリアセンサー１８に
入射する。この参照波の波面は平面である。参照光は、
平面鏡１４の傾きのため、測定光に対し微小角θだけ傾
いてエリアセンサー１８に入射する。従って参照波面は
Ｘ方向に対して傾いたものとなる。この参照波面〔参照
波の位相形状〕をＷＢ （ｘ ）とする。測定光と参照
元とは干渉しエリアセンサー上に干渉縞を生ずる。Now, when a plane wave enters the beam splitter 10 in two directions from the left, this plane wave enters the beam splitter 10 in two directions.
10, one is the measurement target 12Vc,
The other beam is incident on the plane mirror 14. The plane wave incident on the measurement object 12 is reflected by the measurement surface, becomes measurement light, enters the beam splitter 10, is reflected in the X direction, enters the area sensor 18 via the lens 16, and is received by the area sensor 18. A phase shape corresponding to the shape of the measurement surface is formed on the surface. Let WA (x) be this phase shape. This phase shape is originally WA(x,
It should be written as Y). On the other hand, the plane wave incident on the plane mirror 14 is reflected and becomes a reference wave, which is incident on the area sensor 18 via the beam splitter 10 and the lens 16. The wavefront of this reference wave is a plane. The reference light is
Due to the inclination of the plane mirror 14, the measuring light enters the area sensor 18 at an angle of a small angle θ. Therefore, the reference wavefront is inclined with respect to the X direction. Let this reference wavefront [phase shape of the reference wave] be WB (x). The measurement light and the reference source interfere, producing interference fringes on the area sensor.
測定波面ＷＡ （ｘ ）と参照波面ＷＢ（ｘ）の相対的
な位置関係を、ｔ−１図（１）に示す。The relative positional relationship between the measurement wavefront WA (x) and the reference wavefront WB(x) is shown in t-1 diagram (1).
これらＷＡ（ｘ） 、 ＷＢ（ｘ）の複素振幅分布を、
それぞ０、 ＜ 、 ）、Ｊ （ｗＡ（Ｘ） ” ２
” ｆＯＸ） 、 β（１）トすると、干渉縞の強度
分布ｇ（ｘ） は、ｇ（ｘ） ＝ ａ（ｘ） 十ｏ
（ｘ）ｃｏｓ （ＷＡ（ｘ） ＋ ２ｒｆｏｘ〕＝ａ（
ｘ） ＋ （Ｌ’（ｘ）ｅ””０ｘ＋＊−Ｊ２πｆＯＸ
Ｃ（ｘ）ｅ （１）となる。ただ
し、ｆｏ は、λを波長としてｆＯ” １／λｔａｎ
θ （２）λ
であり、ａ（ｘ）＝α（ｘ）＋ ｂ（ｘ） ＝２α（
Ｘ）β” ｘ） ｊＷＡ（ｘ） ＊
（ｘ）、 Ｃ（ｘ） ＝−ｅ 、 Ｃ（ｘ）
＝０（Ｘ） −ｊＷＡ（ｘ） である。これから
分るように、測定波面ＷＡ （ｘ ）の情報は、（１）
式の２項と６項に入っている。The complex amplitude distribution of WA(x) and WB(x) is
0, < , ), J (wA(X) ” 2
”fOX), β(1), the intensity distribution of interference fringes g(x) is g(x) = a(x)
(x)cos (WA(x) + 2rfox)=a(
x) + (L'(x)e""0x+*-J2πfOX C(x)e (1). However, fo is fO"1/λtan where λ is the wavelength.
θ (2)λ, and a(x)=α(x)+b(x)=2α(
X) β” x) jWA(x) * (x), C(x) =-e, C(x)
=0(X)-jWA(x). As you can see, the information on the measured wavefront WA (x) is (1)
It is included in the 2nd and 6th terms of the equation.
この強度分布ｇ（ｘ）ｋサンプリング区間についてウィ
ンドウ処理を行ない、これをＸに関してフーリエ変換す
ると。Window processing is performed on this intensity distribution g(x)k sampling interval, and this is Fourier-transformed with respect to X.
とい５ス゛ベクトルが得られる。このスペクトル（３）
式は、傾き角θに応じた空間周波数ｆＯにより６群Ａ（
ｆ）、ｃＣｆ−’ｆｏ）、ｃ＊ｃｆ＋ ｆｏ）Ｋ分離し
ている。もとめるべき測定波面ＷＡ（ｘ） ＶＣ関する
清＊
報は、単側波帯Ｃ（ｆ−ｆＯ）とＣＣｆ＋ｆＯ）ＶＣ含
まれている。そこで、このうち、ひとつの単側波帯ｃ
（ｆ−ｆｏ ）を選択する。In this case, a 5-wave vector is obtained. This spectrum (3)
The formula is 6 groups A (
f), cCf-'fo), c*cf+fo)K separated. The detailed information regarding the measurement wavefront WA(x) VC to be determined includes single sidebands C(f-fO) and CCf+fO)VC. Therefore, among these, one single sideband c
Select (f-fo).
そのためには、（３）式の右辺のスペクトル群へ＊
（ｆ）、Ｃ（ｆ＋ｆｏ）をフィルターで除去すればよい
。このようにして得られるＣ （ｆ −ｆｏ ） を
、周波数軸上で、ｆｏ だけ原点にむけて、スペクト
ル移動すると、Ｃ（ｆ）なるスペクトルが得られるが、
このスペクトルＣ（ｆ）では、傾き角θにもとづく傾き
成分が除去されている。そこで、Ｃ’（ｆ）を逆フーリ
エ変換し、逆ウィンドウ処理するとＣ（ｘ）が求められ
る。測定波面ＷＡ（ｘ ）はＣ（ｘ）の位相部分である
から、ＷＡ （ｘ ）は、として与えられる。To do this, *(f) and C(f+fo) may be removed from the spectrum group on the right side of equation (3) using a filter. If the spectrum of C (f − fo ) obtained in this way is moved toward the origin by fo on the frequency axis, a spectrum C(f) will be obtained, but
In this spectrum C(f), the tilt component based on the tilt angle θ has been removed. Therefore, C(x) is obtained by performing inverse Fourier transform on C'(f) and performing inverse window processing. Since the measured wavefront WA(x) is the phase part of C(x), WA(x) is given as.
測定波面ＷＡ（ｘ）は、本来ＷＡ（ｘ、ｙ） と記す
るべきものである背光に述べたが、エリアセンサー１８
ＶＣよろ読取は、ｙ方向につ（・では、１ラインずつ行
なうので各ラインの読取結果についての演算プロセスで
は、これをＸのみの関数ＷＡ（ｘ）としてあつがってよ
い。The measurement wavefront WA(x) should originally be written as WA(x, y), but as mentioned above, the area sensor 18
Since VC wobble reading is performed line by line in the y direction, in the calculation process for the reading results of each line, this can be treated as a function WA(x) of only X.
さて、周知の如く、離散的なフーリエ変換においては、
サンプリングピッチｄでＮ個の値についてフーリエ変換
すると、周波数領域でのスペクトはサンプリング区間で
あってＤ＝ｄ・（Ｎ＋１）で与えられる。Now, as is well known, in the discrete Fourier transform,
When Fourier transform is performed on N values at a sampling pitch d, the spectrum in the frequency domain is a sampling interval and is given by D=d·(N+1).
例えば、矛１図（Ｉ）において、フーリエ変換されるべ
き強度分布ｇ（ｘ）が、破線の如きものとするとき、サ
ンプリングピンチｄで、サンプリング区間り内のＮ点に
ついてフーリエ変換を行なうと、その結果は才１図（ｆ
ｆ）に示す如くなる。スペクトル（）（ｆ）は、ピンチ
が１７Ｄで、周期１ ／ ｄの周期関数である。For example, in Figure 1 (I), when the intensity distribution g(x) to be Fourier transformed is as shown by a broken line, if Fourier transform is performed on N points within the sampling interval with sampling pinch d, then The result is Figure 1 (f
f). The spectrum ()(f) is a periodic function with a pinch of 17D and a period of 1/d.
従って、空間周波数ｆｏ Ｖｃ対して、ｎを整数とし
て、ｆ、 ＝−とすると、スペクトルにおけるｆＯ成分
は１区間にのみ表われることになり、（３）式における
Ｃ （ｆ −ｆｏ ） 、 Ｃ＊（ｆ ＋ ｆｏ ）
の広がりが抑制され、フィルター操作、スペクトル
移動操作を正確に行うことができ、演算も簡単化される
。Therefore, for the spatial frequency fo Vc, if n is an integer and f, = -, the fO component in the spectrum will appear only in one interval, and C (f - fo ), C* in equation (3). (f + fo)
The spread of the spectrum is suppressed, filter operations and spectrum shifting operations can be performed accurately, and calculations are also simplified.
には、予め定められたＤＫ対してｆ、 ＝−を満足り
するように、傾き角θを定める方法（矛１の方法）と、
他の測定器で傾き角θを正確に測定し、ｆ。There is a method of determining the inclination angle θ so as to satisfy f, = - for a predetermined DK (method of spear 1),
Accurately measure the inclination angle θ with another measuring device, and measure f.
＝−を満足するようにサンプリング区間を調整する方法
（矛２の方法）とがある。There is a method (method 2) of adjusting the sampling interval so as to satisfy =-.
矛１の方法は、エリアセンサー１８として、出力がサン
プルホールドされ、す／プリングピッチｄが固定・され
るものを用いる場合に有効である。矛２の方法は、出力
が連続的で、サンプリングピッチｄを可変にできるよう
なエリアセンサーを用いる場合に、角θの許容誤差が厳
しいときに有効である。The first method is effective when using an area sensor 18 whose output is sampled and held and whose spring/pull pitch d is fixed. The second method is effective when using an area sensor with continuous output and variable sampling pitch d, and when the tolerance of the angle θ is strict.
また、エリアセンサー１８による読取りは、Ｘ方向につ
いてはＸ方向の複数ラインとして読みとられるのである
が、この場合に、各ラインについてＤの値を共通にし、
信号強度方向にスレッシュホールドレベルを設けて、ウ
ィンドウの広さを可変とし、各ラインごとに、ウィンド
ウ両端部を入力光束の境界部と一致させることにより、
測定精度を高めることができる。In addition, the reading by the area sensor 18 is read as multiple lines in the X direction, but in this case, the value of D is set in common for each line,
By setting a threshold level in the direction of signal strength, making the width of the window variable, and aligning both ends of the window with the boundary of the input beam for each line,
Measurement accuracy can be improved.
さらに、スペクトル移動を行うとき、ＦＦＴプ周波数領
域での結果が出力される。従って、側波帯Ｃ（ｆ −ｆ
Ｏ） を周波数軸の原点側へｆ、 たけへ移動させ
ることにより、正確かつ容易に逆変換を実行できる。Furthermore, when performing spectral shifting, the results in the FFT frequency domain are output. Therefore, the sideband C(f − f
By moving O) toward the origin of the frequency axis by f, the inverse transformation can be performed accurately and easily.
２次元の波面形状ＶＡ （ｘ 、 ｙ ） を知るに
は、平面鏡１４の法線をｘｙ面に平行な面内でＸ方向に
対して微小角傾け、Ｘ方向について、前記と同様の方法
で１ライン分のみの形状ケもとめ、求められたＸ方向１
２４７分の形状に、先に求められたＸ方向の各ライン（
Ｘ方向へ並列している）の形状をのせてやればよい。To find the two-dimensional wavefront shape VA (x, y), the normal line of the plane mirror 14 is tilted at a small angle with respect to the X direction in a plane parallel to the xy plane, and Find the shape only for the line, and find the X direction 1
In the shape of 247 minutes, each line in the X direction (
It is sufficient to place the shapes (parallel to each other in the X direction).
以下、コンピューターによるシミニレ−ジョン例を示す
。An example of computer-generated staining is shown below.
矛２図において（１）は、エリアセンサー上の測定波面
ＷＡ （ｘ ）を示す。（１）は、測定光と参照光との
おりなす干渉縞の光強度分布、（１）は、（１）に示す
光強度分布に、ウィンドウ処理を行った状態を示す。ウ
ィンドウ関数Ｗは、た、ウィンドウ両端部は入射光東端
部と一致させている。（ＩＶ）は、（■）の結果をフー
リエ変換した状態、（Ｖ）は、単側波帯Ｃ（ｆ −ｆｏ
） をスペクトル移動して傾き成分を除去した状態
、（■）は（Ｖ）のスペクトルに対し、逆フーリエ変換
と逆ウィンドウ処理を捲して得られるＣ（ｘ）Ｋつき、
その絶対値１ｃ（ｘ）ｌと、その位相部公転さネ欠Ｃ（
Ｘ） ）すなわちＷＡ（ｘ）を示す図、才２図（■）は
、才２図（１）に示すＷＡ（ｘ）と、上記の如く算出さ
れたＷＡ（Ｘ） （７２図〔■〕）との差異、すなわち
、測定誤差を示す。この図から明らかなように両端部を
のぞけば、 ＷＡ（Ｘ）は、極めて良好に測定されてい
る。In Figure 2, (1) shows the measured wavefront WA (x) on the area sensor. (1) shows the light intensity distribution of interference fringes formed by the measurement light and the reference light, and (1) shows the state where window processing is performed on the light intensity distribution shown in (1). The window function W has both ends of the window coincident with the east end of the incident light. (IV) is the Fourier transformed state of the result of (■), (V) is the single sideband C(f −fo
) with the spectrum moved and the slope component removed, (■) is the spectrum of (V) with C(x)K obtained by inverse Fourier transform and inverse window processing,
Its absolute value 1c(x)l and its phase part revolution C(
X) ), that is, the diagram showing WA(x), Figure 2 (■) shows the WA(x) shown in Figure 2 (1) and WA(X) calculated as above (Figure 72 [■] ), that is, the measurement error. As is clear from this figure, WA(X) is measured extremely well except at both ends.
矛５図は、従来法による測定のシミュレーションを示す
。（１）〜（■）の各図は１，１７２図における（１〕
〜（■）にそれぞれ対応している。矛３図（ＩＩ）は、
干渉縞ｇ（ｘ）（同図（Ｉ）〕にウィンドウ処理を捲し
た状態を示す。ウィンドウ関数Ｗは、
であって、ウィンドウ両端部は、入力元束の端部と合致
していない。Figure 5 shows a simulation of measurement using the conventional method. Each figure (1) to (■) is (1) in figure 1,172.
~(■) corresponds to each. The spear 3 figure (II) is
The interference fringe g(x) ((I) of the same figure) shows a state in which window processing has been applied.The window function W is as follows, and both ends of the window do not match the ends of the input source bundle.
このため、矛３図（ＶＩ［）に示すように全体にわたっ
て誤差が生じている。Therefore, as shown in Figure 3 (VI[), errors occur throughout.
（効 果）
以上、本発明によれば、新規な干渉測定方法を提供でき
る。本発明は上記の如くに構成されているので、従来法
に比し演算が簡単化され、測定精度も向上する。(Effects) As described above, according to the present invention, a novel interference measurement method can be provided. Since the present invention is configured as described above, calculations are simplified and measurement accuracy is improved compared to conventional methods.
第１図は、本発明を説明するための図、矛２図は、本発
明の測定方法のシミュレーションの１例を示す図、矛３
図は従来の測定方法のシミュレーションの１例を示す図
である。
１０・・・ビームスプリッタ−１１２・・・測定対象物
、１４・・・平面鏡、１６・・・レンズ、１８・・・エ
リアセンサー、ＷＡ（ｘ）・・・測定波面、ＷＢ （ｘ
）・・・参照波面烏？ ■
ｉ
−／ρ」
１十ｆ−
！ （１／１ｗｒ）
−／ρ」
一７ｊｐ、ｊ ｊFigure 1 is a diagram for explaining the present invention, Figure 2 is a diagram showing an example of simulation of the measuring method of the present invention,
The figure is a diagram showing an example of a simulation of a conventional measurement method. 10...Beam splitter-112...Measurement object, 14...Plane mirror, 16...Lens, 18...Area sensor, WA(x)...Measurement wavefront, WB (x
)...Reference wave front crow? ■ i −/ρ” 10f−! (1/1wr) −/ρ” 17jp, j j
Claims (1)
リアセンサーに入射せしめ、測定光と参照光との干渉縞
を、エリアセンサーにより、ウィンドウ処理して上記所
定面に平行な方向へ読取り、読取結果をフーリエ変換す
ることにより、上記傾き角θにより分離された３群の空
間周波数のスペクトル群を得、これらスペクトル群から
ひとつの単側波帯のみを選択し、これを周波数軸上で、
上記傾き角θに対応する量だけずらすスペクトル移動を
行うことによって、傾き成分を除去し、得られるスペク
トルに対し逆フーリエ変換と逆ウィンドウ処理とを行な
い、その結果から位相部分を算出することにより、エリ
アセンサー上における測定光の波面の、参照波面からの
偏差を算出する干渉測定方式において、 空間周波数ｆｏ（＝１／λｔａｎθ，λは波長）が、ｎ
を整数、Ｄをサンプリング区間として、ｆｏ＝ｎ／Ｄを
満足するように、傾き角θとサンプリング区間Ｄとの関
係を定め、 フーリエ変換に先立つウィンドウ処理において各ライン
ごとウィンドウ両端部を、入力光束の境界部と一致させ
るように、スレッシェホールドレベルを設け、 かつ、上記スペクトル移動する際、１周期の出力周波数
領域をこえる成分については、移動方向と反対方向に−
（ｄ；サンプリングピッチ）だけ移動させることを特徴
とする、干渉測定方法。[Claims] The measurement light and the reference light are incident on the area sensor at a slight angle θ tilted to each other within a predetermined plane, and the interference fringes between the measurement light and the reference light are window-processed by the area sensor to obtain the above-mentioned predetermined information. By reading in a direction parallel to the plane and Fourier transforming the reading results, three groups of spatial frequency spectra separated by the above-mentioned inclination angle θ are obtained, and only one single sideband is selected from these spectral groups. , on the frequency axis,
By moving the spectrum by an amount corresponding to the tilt angle θ, the tilt component is removed, and the obtained spectrum is subjected to inverse Fourier transform and inverse window processing, and the phase part is calculated from the result. In an interferometric measurement method that calculates the deviation of the wavefront of measurement light on an area sensor from a reference wavefront, the spatial frequency fo (=1/λtanθ, λ is the wavelength) is n
is an integer and D is the sampling period, the relationship between the tilt angle θ and the sampling period D is determined so that fo=n/D is satisfied, and in the window processing prior to Fourier transform, both ends of the window for each line are A threshold level is set so as to coincide with the boundary of
An interference measurement method characterized by moving by (d; sampling pitch).
Priority Applications (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP60070637A JPH0652162B2 (en) | 1985-04-03 | 1985-04-03 | Interferometry method |
| US06/840,442 US4744659A (en) | 1985-03-20 | 1986-03-17 | Method of and apparatus for measuring the shape of a wavefront |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP60070637A JPH0652162B2 (en) | 1985-04-03 | 1985-04-03 | Interferometry method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS61230002A true JPS61230002A (en) | 1986-10-14 |
| JPH0652162B2 JPH0652162B2 (en) | 1994-07-06 |
Family
ID=13437356
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP60070637A Expired - Lifetime JPH0652162B2 (en) | 1985-03-20 | 1985-04-03 | Interferometry method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH0652162B2 (en) |
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| JP2002162205A (en) * | 2000-09-13 | 2002-06-07 | Fuji Photo Optical Co Ltd | Method for detecting and correcting analytical error of striped image |
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-
1985
- 1985-04-03 JP JP60070637A patent/JPH0652162B2/en not_active Expired - Lifetime
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| JP2002162205A (en) * | 2000-09-13 | 2002-06-07 | Fuji Photo Optical Co Ltd | Method for detecting and correcting analytical error of striped image |
| JP2002202112A (en) * | 2000-11-06 | 2002-07-19 | Fujitsu Ltd | Shape measuring apparatus |
| JP2002296003A (en) * | 2001-03-29 | 2002-10-09 | Fuji Photo Optical Co Ltd | Method and device for analyzing fourier transform fringe |
| JP4610117B2 (en) * | 2001-03-29 | 2011-01-12 | 富士フイルム株式会社 | Fourier transform fringe analysis method and apparatus |
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| JPWO2006030482A1 (en) * | 2004-09-13 | 2008-05-08 | 三菱電機株式会社 | Laser optical path length difference detection device, laser phase control device, and coherent optical coupling device |
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| US7852489B2 (en) | 2006-02-01 | 2010-12-14 | Tokyo Institute Of Technology | Method for measuring surface profile, and apparatus using the same |
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| JP4710078B2 (en) * | 2006-02-01 | 2011-06-29 | 国立大学法人東京工業大学 | Surface shape measuring method and apparatus using the same |
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| JP2015111074A (en) * | 2013-12-06 | 2015-06-18 | 東京エレクトロン株式会社 | Method of determining distance, method of eliminating electricity from electrostatic chuck, and processing apparatus |
Also Published As
| Publication number | Publication date |
|---|---|
| JPH0652162B2 (en) | 1994-07-06 |
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