JP2007240465A - Method and instrument for measuring three-dimensional displacement and distortion - Google Patents

Method and instrument for measuring three-dimensional displacement and distortion Download PDF

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JP2007240465A
JP2007240465A JP2006066766A JP2006066766A JP2007240465A JP 2007240465 A JP2007240465 A JP 2007240465A JP 2006066766 A JP2006066766 A JP 2006066766A JP 2006066766 A JP2006066766 A JP 2006066766A JP 2007240465 A JP2007240465 A JP 2007240465A
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Yoshiharu Morimoto
吉春 森本
Motoharu Fujigaki
元治 藤垣
Toru Matsui
徹 松井
Shunsuke Okazawa
俊介 岡澤
Toshiyuki Kita
俊行 喜多
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Kansai Technology Licensing Organization Co Ltd
Wakayama University
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Abstract

<P>PROBLEM TO BE SOLVED: To provide a method and an instrument for measuring a distribution of a three-dimensional displacement or distortion of a three-dimensional object, at one stroke, in a short time, in displacement measurement using a phase shift digital holography. <P>SOLUTION: The three-dimensional displacement of the measuring object is measured (a) by irradiating the measuring object with the same wavelength of object lights from three different directions, (b) by photographing a plurality of interference images of three reference lights having the same wavelength as that of the object lights and a reflected light from the measuring object, by a two-dimensional imaging element, while changing phases of the respective reference lights at each different speed with respect to the object lights, (c) by extracting interference components different in the phase changing speeds, using Fourier transformation, to separate the interference images due to the three object lights, and (d) by measuring the displacement distribution of the measured object along a direction in response to the irradiation direction of the each object light, based on the respective interference images. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

本発明は、３次元物体（立体物）の３次元変位及びひずみを計測する方法及び装置に関する。   The present invention relates to a method and apparatus for measuring three-dimensional displacement and strain of a three-dimensional object (three-dimensional object).

鋼構造物、コンクリート構造物、樹脂・セラミック構造物等の構造物の欠陥検査や、産業現場などにおいて、立体物の３次元変位やひずみの分布を計測する手法が求められている。従来のひずみ計測では、ほとんどの場合にひずみゲージが用いられているが、ひずみゲージを貼ることのできる場所は限られるため、広い領域や或る物体の全面のひずみの分布を得ることは困難であった。また、マイクロマシンの材料試験や特性評価試験に際しても微小な変位やひずみの計測が必要とされる。   There is a demand for a technique for measuring a three-dimensional displacement and strain distribution of a three-dimensional object in a defect inspection of a structure such as a steel structure, a concrete structure, a resin / ceramic structure, or an industrial site. In conventional strain measurement, strain gauges are used in most cases, but because the places where strain gauges can be attached are limited, it is difficult to obtain strain distribution over a wide area or a certain object. there were. In addition, it is necessary to measure minute displacements and strains in micromachine material tests and characteristic evaluation tests.

３次元物体の変位を高精度に計測する手法の一つに、位相シフトデジタルホログラフィ法がある（例えば、非特許文献１参照）。位相シフトデジタルホログラフィ法では、物体に主レーザ光（物体光）と、それに対して位相をシフトさせた参照光とを照射し、物体の変位前後の両光の干渉像をCCDカメラにより撮影する。こうして撮影した干渉像を逆フーリエ変換することにより、物体表面の各部位の変位分布をデジタルデータとして計測する。この方法は、分布表面の変形量や変位量を非接触で、しかも高速で計測することができるという大きな特長を持つため、種々の用途に適用することができる。   One method for measuring the displacement of a three-dimensional object with high accuracy is a phase shift digital holography method (see, for example, Non-Patent Document 1). In the phase shift digital holography method, an object is irradiated with main laser light (object light) and reference light whose phase is shifted with respect to the object, and an interference image of both lights before and after the displacement of the object is taken by a CCD camera. By performing inverse Fourier transform on the captured interference image, the displacement distribution of each part of the object surface is measured as digital data. Since this method has a great feature that it can measure the deformation amount and displacement amount of the distribution surface in a non-contact manner and at a high speed, it can be applied to various applications.

特許文献１には、位相シフトデジタルホログラフィ法の一つの改良方法が開示されている。これは、ハレーションやスペックルノイズによる影響を低減することにより高精度の変位・ひずみ計測を行うことを目的としたものである。
非特許文献１には、2光波の照射で計測物体の3方向の変位（3次元変位）を求めることができる位相シフトデジタルホログラフィ法が記載されている。
特許文献２には、計測物体に対して2方向からレーザを照射し、方向ごとにシャッタを使って照射方向を順番に切り替え、それぞれの画像を順に撮影することにより、計測物体の面内方向および面外方向の変位を高精度に計測することができる方法が記載されている。 Patent Document 1 discloses an improved method of the phase shift digital holography method. The purpose of this is to perform highly accurate displacement / strain measurement by reducing the influence of halation and speckle noise.
Non-Patent Document 1 describes a phase shift digital holography method capable of obtaining displacement (three-dimensional displacement) in three directions of a measurement object by irradiation with two light waves.
In Patent Document 2, a measurement object is irradiated with a laser from two directions, the irradiation direction is switched in order using a shutter for each direction, and each image is taken in order, whereby the in-plane direction of the measurement object and A method capable of measuring the displacement in the out-of-plane direction with high accuracy is described.

特開2005-265441号公報JP 2005-265441 A 特願2005-256593号明細書Japanese Patent Application No. 2005-256593 Specification 大瀧博貴, 坂上賢一, 隆雅久「位相シフトデジタルイメージプレーンホログラフィ干渉法による変位計測」, 日本実験力学会2005年度年次講演会, No. 5, 130-135(2005)Hiroki Ohtsuki, Kenichi Sakagami, Masahisa Takah “Displacement Measurement by Phase Shift Digital Image Plane Holography Interferometry”, 2005 Annual Conference of the Japan Society for Experimental Force, No. 5, 130-135 (2005)

特許文献１に記載の方法によれば計測物体の面外方向の変位を高精度に計測することができるが、この方法は、計測対象物体に正面から物体光を照射するとともに、それに対して位相をシフトさせた参照光を重畳して撮影し、干渉縞を得るものであるため、1方向の変位(面外変位)しか計測することしかできない。
非特許文献２に記載の方法では、2光波の照射で3方向の変位を求めているため、面内方向の精度が不十分である。
特許文献２に記載の方法では、計測物体に対して2方向からレーザを照射するが、方向ごとにシャッタを使って照射方向を順番に切り替え、それぞれの画像を順に撮影しているため、計測に多くの時間を要する。 According to the method described in Patent Document 1, it is possible to measure the displacement in the out-of-plane direction of the measurement object with high accuracy. This method irradiates the measurement target object with object light from the front, and the phase relative thereto. Since the interference light is obtained by superimposing the reference light with shifted reference light, only displacement in one direction (out-of-plane displacement) can be measured.
In the method described in Non-Patent Document 2, since displacement in three directions is obtained by irradiation with two light waves, the accuracy in the in-plane direction is insufficient.
In the method described in Patent Document 2, laser irradiation is performed on the measurement object from two directions, but the irradiation direction is switched in order using the shutter for each direction, and each image is taken in order. It takes a lot of time.

本発明はこれら従来の方法の欠点を解決するものであって、位相シフトデジタルホログラフィを用いた変位計測において、3次元変位計測を一挙に且つ短時間で行う手法を提供する。また、変位計測手法によって得られた変位分布からひずみ分布を算出する手法も提供する。   The present invention solves the drawbacks of these conventional methods, and provides a technique for performing three-dimensional displacement measurement in a short time in a displacement measurement using phase shift digital holography. Also provided is a method for calculating a strain distribution from a displacement distribution obtained by a displacement measurement method.

上記課題を解決するために成された本発明に係る３次元変位計測方法は、
a) 計測物体に３つの異なる方向から同一波長の物体光を照射し、
b) 物体光と同一波長を有する３つの参照光と計測物体からの反射光との干渉像を、各参照光の位相を互いに異なる速度で物体光に対して変化させつつ複数枚、２次元撮像素子で撮影し、
c) フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離し、
d) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する
ことにより計測物体の３次元変位を計測するものである。 The three-dimensional displacement measuring method according to the present invention, which has been made to solve the above problems,
a) Irradiate the object with the same wavelength from three different directions,
b) Two or two-dimensional imaging of interference images of three reference lights having the same wavelength as the object light and the reflected light from the measurement object while changing the phase of each reference light with respect to the object light at different speeds Shoot with the element,
c) Extracting interference components with different phase change rates using Fourier transform to separate the interference images of the three object beams,
d) The three-dimensional displacement of the measurement object is measured by measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image.

また、次のような方法であってもよい。すなわち、
a) 計測物体に３つの異なる方向から、同一波長であって互いに異なる速度で位相が変化する物体光を照射し、
b) 物体光と同一波長を有する参照光と計測物体からの反射光との干渉像を複数枚、２次元撮像素子で撮影し、
c) フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離し、
d) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する
ことにより計測物体の３次元変位を計測する。 Further, the following method may be used. That is,
a) Irradiate the object to be measured from three different directions with the same wavelength and object light whose phase changes at different speeds.
b) Taking a plurality of interference images between the reference light having the same wavelength as the object light and the reflected light from the measurement object with a two-dimensional image sensor,
c) Extracting interference components with different phase change rates using Fourier transform to separate the interference images of the three object beams,
d) The three-dimensional displacement of the measurement object is measured by measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image.

この３次元変位計測方法を用いて計測物体の未知の３次元変位量の絶対値を計測するには、基準面に既知の３次元変位を与えつつ前記方法で該変位を計測しておき、その結果に基づいて計測物体の未知の３次元変位量を計測する。   In order to measure the absolute value of the unknown three-dimensional displacement amount of the measurement object using this three-dimensional displacement measuring method, the displacement is measured by the above method while giving the known three-dimensional displacement to the reference surface, Based on the result, an unknown three-dimensional displacement amount of the measurement object is measured.

上記の３次元変位計測方法において、既知変位の計測を複数回行い、その平均を取ることにより未知変位の計測精度を高めることができる。   In the above three-dimensional displacement measuring method, the measurement accuracy of the unknown displacement can be increased by measuring the known displacement a plurality of times and taking the average.

計測精度を高めるには、２次元撮像素子の各画素における演算結果に基づいて平滑化処理を行うという方法をとることもできる。   In order to increase the measurement accuracy, a method of performing a smoothing process based on a calculation result in each pixel of the two-dimensional image sensor can be used.

そして、計測物体の３次元ひずみは、２次元撮像素子の各画素毎に、該画素及び周辺画素の位置とそれら画素について前記方法により計測された変位とに基づき算出することができる。   Then, the three-dimensional distortion of the measurement object can be calculated for each pixel of the two-dimensional image sensor based on the positions of the pixel and the peripheral pixels and the displacement measured by the method for the pixels.

上記方法に対応する、本発明に係る３次元変位計測装置は、
a) 計測物体に３つの異なる方向から同一波長の物体光を照射する物体光照射手段と、
b) 物体光と同一波長を有し、互いに異なる速度で物体光に対する位相が変化する３つの参照光を生成する参照光生成手段と、
c) 計測物体からの反射光と前記３つの参照光の干渉像を撮影する２次元撮像素子と、
d) ２次元撮像素子により複数枚撮影された干渉像に基づき、フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離する分離手段と、
e) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する変位計測手段と
を備える。 The three-dimensional displacement measuring apparatus according to the present invention corresponding to the above method is
a) Object light irradiation means for irradiating the measurement object with object light of the same wavelength from three different directions;
b) reference light generating means for generating three reference lights having the same wavelength as the object light and changing the phase with respect to the object light at different speeds;
c) a two-dimensional image sensor that captures an interference image of reflected light from the measurement object and the three reference lights;
d) separation means for separating interference images of three object beams by extracting interference components having different phase change speeds using Fourier transform based on interference images captured by a two-dimensional image sensor;
e) Displacement measuring means for measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image.

また、
a) 計測物体に３つの異なる方向から、同一波長であって互いに異なる速度で位相が変化する物体光を照射する物体光照射手段と、
b) 物体光と同一波長を有する参照光を生成する参照光生成手段と、
c) 計測物体からの反射光と参照光の干渉像を撮影する２次元撮像素子と、
d) ２次元撮像素子により複数枚撮影された干渉像に基づき、フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離する分離手段と、
e) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する変位計測手段と
を備えるものであってもよい。 Also,
a) Object light irradiating means for irradiating a measurement object with object light having the same wavelength and changing phase at different speeds from three different directions;
b) reference light generating means for generating reference light having the same wavelength as the object light;
c) a two-dimensional image sensor that captures an interference image of the reflected light from the measurement object and the reference light;
d) separation means for separating interference images of three object beams by extracting interference components having different phase change speeds using Fourier transform based on interference images captured by a two-dimensional image sensor;
e) Displacement measuring means for measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image may be provided.

更に、３次元変位ひずみ計測装置とするため、２次元撮像素子の各画素毎に、該画素及び周辺画素の位置とそれら画素について計測された変位とに基づきひずみを算出するひずみ算出手段を設けてもよい。   Further, in order to obtain a three-dimensional displacement strain measuring device, a strain calculating means is provided for each pixel of the two-dimensional image sensor to calculate strain based on the positions of the pixels and peripheral pixels and the displacement measured for these pixels. Also good.

なお、上記方法・装置では物体光・参照光を３つの異なる方向から照射するとしたが、本発明の原理より、これを２方向を含む複数の方向の場合に一般化することはもちろん可能である。   In the above method and apparatus, the object light and the reference light are emitted from three different directions. However, it is of course possible to generalize this in a plurality of directions including two directions based on the principle of the present invention. .

本発明に係る3次元物体変位・ひずみ計測方法では、3つの異なる方向から物体に光を照射し、フーリエ変換位相シフト法を用いてそれら3つの光の位相解析を一挙に行うことにより、3方向からの光を同時に解析し、3次元の変位を一挙に計測することができる。すなわち、３光束の照射方向をシャッターにより切り替える必要がないため、特許文献２に記載の方法よりも短時間で計測を行うことができる。また、シャッター機構（照射光の切り替え機構）が不要であることから、装置を小型化することもできる。なお、解析に際しては、光源の座標など、実測し難いパラメータを使う必要がないため、計測精度が向上する。   In the three-dimensional object displacement / strain measurement method according to the present invention, the object is irradiated with light from three different directions, and the phase analysis of the three lights is performed at once by using the Fourier transform phase shift method, so that three directions are obtained. 3D displacement can be measured at once by analyzing the light from That is, since it is not necessary to switch the irradiation direction of the three light beams by the shutter, measurement can be performed in a shorter time than the method described in Patent Document 2. Further, since the shutter mechanism (irradiation light switching mechanism) is unnecessary, the apparatus can be downsized. In the analysis, since it is not necessary to use parameters that are difficult to measure, such as the coordinates of the light source, the measurement accuracy is improved.

また、この方法に、基準面を用いて画素ごとに感度ベクトルを3方向の変位量に変換するキャリブレーションを行う手法を組み合わせることで、変位の実際の値（絶対値）を瞬時に得ることができる。さらに、この変位計測手法によって得られた変位分布からひずみ分布を算出することもできる。   In addition, by combining this method with a calibration method that converts the sensitivity vector into displacement in three directions for each pixel using the reference plane, the actual displacement value (absolute value) can be obtained instantaneously. it can. Furthermore, the strain distribution can be calculated from the displacement distribution obtained by this displacement measurement method.

本発明に係る３次元変位・ひずみ計測方法及び装置は、鋼構造物、コンクリート構造物、樹脂・セラミック構造物等の構造物の欠陥検査や、産業現場などにおいて、立体物の３次元変位やひずみの分布を高精度に計測することに用いることができる。また、マイクロマシンの材料試験や特性評価試験にも用いることができる。更に、非接触で物体の形状や変形、応力、歪み等の計測を全視野で行うことができるという特長より、情報通信、医療等の種々の分野にも利用することができる。   The three-dimensional displacement / strain measuring method and apparatus according to the present invention are used for defect inspection of structures such as steel structures, concrete structures, resin / ceramic structures, and in three-dimensional displacement and strain of three-dimensional objects in industrial sites. It can be used to measure the distribution of. It can also be used for micromachine material tests and characteristic evaluation tests. Furthermore, it can be used in various fields such as information communication and medical care because it can measure the shape, deformation, stress, strain, etc. of an object in a non-contact manner over the entire visual field.

以下、本発明の実施の形態を順を追って説明する。
(1) フーリエ変換位相シフト法を用いた多光束同時解析法の原理
フーリエ変換位相シフト法は位相解析に非常に有効な手法であり、従来の位相シフト法と異なり複数枚の画像から位相を解析することができる。3光束を用いた変位計測を例に挙げると、物体に照射する3光束には3つの波長が等しいレーザを用いる。波長を等しくする理由は、位相シフトデジタルホログラフィにおける再生範囲が波長に左右されるためである。 Hereinafter, embodiments of the present invention will be described in order.
(1) Principle of simultaneous analysis of multi-beams using Fourier transform phase shift method The Fourier transform phase shift method is a very effective method for phase analysis. Unlike the conventional phase shift method, the phase is analyzed from multiple images. can do. Taking displacement measurement using three light beams as an example, lasers with three equal wavelengths are used for the three light beams that irradiate an object. The reason for making the wavelengths equal is that the reproduction range in phase shift digital holography depends on the wavelength.

物体に3つの異なる方向から物体光を照射し、物体で反射された物体光と3つの参照光の3種類の干渉縞を同時にCCDで撮影する。ここで、3つの参照光の位相シフト量を変化させて干渉像を撮影する。例えば、図１(a)に示すように、所定時間内に7枚の干渉像を撮影するものとし、その間の各参照光の位相シフト量をそれぞれ2π、4π、6πとする。図１(b)の左側に示すように、位相シフト量が2πのものは周波数成分が1の部分を抽出し、その実部と虚部の逆正接を求めることで位相を求めることができる。全画素に対して同様の計算を行うことで位相分布を求めることができる。位相シフト量が4π、6πのものも同様に、図１(b)の中央及び右側に示すように、周波数成分が2、3の部分を抽出して計算することで位相分布を求めることができる。このように、3つの干渉縞を同時に撮影しても、位相シフト量と抽出する周波数成分を変えることで、図１(c)に示すように、位相シフト量が2π、4π、6πのものがそれぞれ周波数成分1、2、3の部分に現れるため、それぞれの成分を抽出することで3光束の解析を同時に行うことができる。   The object is irradiated with object light from three different directions, and three types of interference fringes of the object light reflected by the object and the three reference lights are simultaneously photographed with the CCD. Here, an interference image is taken by changing the phase shift amounts of the three reference lights. For example, as shown in FIG. 1 (a), it is assumed that seven interference images are taken within a predetermined time, and the phase shift amount of each reference light during that period is 2π, 4π, and 6π, respectively. As shown on the left side of FIG. 1 (b), when the phase shift amount is 2π, the phase can be obtained by extracting the part having the frequency component of 1 and obtaining the arctangent of the real part and the imaginary part. The phase distribution can be obtained by performing the same calculation for all the pixels. Similarly, for phase shift amounts of 4π and 6π, as shown in the center and right side of FIG. 1 (b), the phase distribution can be obtained by extracting and calculating the frequency components of 2 and 3. . Thus, even if three interference fringes are photographed simultaneously, by changing the phase shift amount and the frequency component to be extracted, the ones with phase shift amounts of 2π, 4π, and 6π as shown in FIG. Since they appear in the frequency components 1, 2, and 3, respectively, it is possible to simultaneously analyze the three light beams by extracting the respective components.

(2) 感度ベクトルを用いた3次元変位計測原理
計測物体にある角度から光を照射したときの光源と物体と観測面の位置関係を図２に示す。物体上の或る点Pに入射角θで光を照射したとき、観測場所によって物体からの反射光の強度に違いが生じる。点Pからの反射光の方向毎の強度を表す感度ベクトルeは、物体の変位ベクトルdとその変位によって生じるCCDカメラへの入射光の位相変化Δφを用いると、式(1)のように表すことができる。
1方向からの入射光に対して、変位ベクトルと感度ベクトルともにx、y、z方向に成分を持っているため、式(1)のベクトル演算を成分式で表すと、
となる。3方向から光を照射すると、それぞれの入射光に対する感度ベクトル成分のパラメータが増える。このことから、式(2)は式(3)のように表すことができる。
ここで、添え字の1、2、3は3つの入射光を意味する。式(3)から
とおき、Sの逆行列S-1を求めてそれを位相差ベクトルφにかけることで変位ベクトルdを求めることができる。
上式から、3つの入射光を用いることで、それぞれの入射光に応じた感度ベクトル方向の変位成分を表す位相差を得ることができ、上式を用いることによりx、y、z方向の変位成分をそれぞれ求めることができる。 (2) Principle of three-dimensional displacement measurement using sensitivity vectors Fig. 2 shows the positional relationship between the light source, the object, and the observation surface when the measurement object is irradiated with light from a certain angle. When a certain point P on the object is irradiated with light at an incident angle θ, the intensity of reflected light from the object varies depending on the observation location. The sensitivity vector e representing the intensity of the reflected light from the point P in each direction is expressed as in Equation (1) using the displacement vector d of the object and the phase change Δφ of the incident light to the CCD camera caused by the displacement. be able to.
For incident light from one direction, both the displacement vector and the sensitivity vector have components in the x, y, and z directions.
It becomes. When light is irradiated from three directions, the parameter of the sensitivity vector component for each incident light increases. From this, equation (2) can be expressed as equation (3).
Here, the subscripts 1, 2, and 3 mean three incident lights. From equation (3)
The displacement vector d can be obtained by obtaining the inverse matrix S −1 of S and applying it to the phase difference vector φ.
From the above equation, by using three incident lights, it is possible to obtain a phase difference representing the displacement component in the sensitivity vector direction according to each incident light. By using the above equation, displacement in the x, y, and z directions can be obtained. Each component can be determined.

(3) 基準面を用いたキャリブレーション手法の原理
上記方法によりx、y、z方向の変位成分を求めることができるが、これらは未だ具体的な数値（絶対値）として求めることはできない。絶対値を求めるためには、上記方法を実際に変位する物体に適用し、その変位量と位相差との関係を求めておいて、校正を行わなければならない。 (3) Principle of calibration method using reference plane Although displacement components in the x, y, and z directions can be obtained by the above method, these cannot be obtained as specific numerical values (absolute values) yet. In order to obtain the absolute value, the above method must be applied to an object that is actually displaced, and the relationship between the displacement amount and the phase difference must be obtained for calibration.

そこで、基準面を用いた校正手法の手順について述べる。校正に用いる基準面は3軸PZTステージに取り付けることでそれぞれx、y、z方向に動かすことができる。
校正に用いる光学系の一例を図３に示す。この光学系では、上記の通り、3つの物体光と、3つの参照光を生成し、参照光に互いに異なる位相シフトを設けて干渉像を撮影する。
なお、参照光ではなく物体光に位相シフト装置をつけ、参照光を共通化することによっても、同様の手法で変位分布を計測することが可能である。その光学系を図４に示す。 Therefore, the procedure of the calibration method using the reference plane will be described. The reference plane used for calibration can be moved in the x, y, and z directions by attaching it to a 3-axis PZT stage.
An example of an optical system used for calibration is shown in FIG. In this optical system, as described above, three object beams and three reference beams are generated, and an interference image is photographed by providing different phase shifts to the reference beams.
Note that it is also possible to measure the displacement distribution by the same method by attaching a phase shift device to the object light instead of the reference light and sharing the reference light. The optical system is shown in FIG.

まず、次の手順により、位相−変位変換テーブルを作成する。
1) 図５に示すように、光源1から基準面に光を照射し、基準面をx方向にΔx1だけ移動させ、その移動によって生じる位相差分布Δφ1xを求める。
2) Δx1とΔφ1xから、光源1の感度ベクトルeのx方向の成分e1xを求める。
3) 同様にy方向、z方向にΔy1、Δz1だけ移動させ、その移動によって生じる位相差分布Δφ1y、Δφ1zを求め、光源1の感度ベクトルeのy方向成分、z方向成分e1y、e1zをそれぞれ求める。
4) 光源2と光源3から照射する光に対しても、x、y、z方向にそれぞれΔx2、Δy2、Δz2、Δx3、Δy3、Δz3移動させ、その移動によって生じる位相差分布Δφ2x、Δφ2y、Δφ2z、Δφ3x、Δφ3y、Δφ3zをそれぞれ求める。
5) 2)と同様に、光源2、3の感度ベクトルeのx、y、z方向成分e2x、e2y、e2z、e3x、e3y、e3zをそれぞれ求める。
6) 1)〜5)を複数回行い、結果を平均することで、感度ベクトル成分の信頼度を高める。なお、精度よりも時間が優先される場合は、この行程を省略することも可能である。
7) 得られた感度ベクトル成分e1x、e1y、e1z、e2x、e2y、e2z、e3x、e3y、e3zより式(4)の行列Sを作成し、その逆行列S-1を演算して各成分f1x、f1y、f1z、f2x、f2y、f2z、f3x、f3y、f3zの値を求める。 First, a phase-displacement conversion table is created by the following procedure.
1) As shown in FIG. 5, the light source 1 emits light to the reference surface, the reference surface is moved by Δx 1 in the x direction, and a phase difference distribution Δφ 1x generated by the movement is obtained.
2) The component e 1x in the x direction of the sensitivity vector e of the light source 1 is obtained from Δx 1 and Δφ 1x .
3) Similarly, move Δy 1 and Δz 1 in the y direction and z direction, obtain phase difference distributions Δφ 1y and Δφ 1z caused by the movement, and obtain y direction component and z direction component e 1y of sensitivity vector e of light source 1 , E 1z are obtained respectively.
4) The light emitted from light source 2 and light source 3 is also moved by Δx 2 , Δy 2 , Δz 2 , Δx 3 , Δy 3 , Δz 3 in the x, y, and z directions, respectively, and the phase difference caused by the movement Distributions Δφ 2x , Δφ 2y , Δφ 2z , Δφ 3x , Δφ 3y , Δφ 3z are obtained, respectively.
5) Similarly to 2), the x, y, and z direction components e 2x , e 2y , e 2z , e 3x , e 3y , and e 3z of the sensitivity vector e of the light sources 2 and 3 are obtained, respectively.
6) Perform 1) to 5) multiple times and average the results to increase the reliability of the sensitivity vector component. If time is given priority over accuracy, this step can be omitted.
7) Create matrix S of equation (4) from the obtained sensitivity vector components e 1x , e 1y , e 1z , e 2x , e 2y , e 2z , e 3x , e 3y , e 3z , and its inverse matrix S calculates the -1 components f 1x, f 1y, f 1z , f 2x, f 2y, f 2z, f 3x, f 3y, obtaining the value of f 3z.

以上の行程を各画素について行うことで、各画素毎に逆行列S-1を得ることができる。さらに、逆行列S-1の各成分のノイズを除去するために、f1x、f1y、f1z、f2x、f2y、f2z、f3x、f3y、f3zの値を必要に応じて平滑化する。位相−変位変換テーブルは、各画素ごとにf1x、f1y、f1z、f2x、f2y、f2z、f3x、f3y、f3zの値を持つテーブルである。 By performing the above process for each pixel, an inverse matrix S −1 can be obtained for each pixel. Furthermore, in order to remove the noise of each component of the inverse matrix S - 1 , the values of f 1x , f 1y , f 1z , f 2x , f 2y , f 2z , f 3x , f 3y , f 3z are used as necessary To smooth. The phase-displacement conversion table is a table having values of f 1x , f 1y , f 1z , f 2x , f 2y , f 2z , f 3x , f 3y , and f 3z for each pixel.

次に、位相−変位変換テーブルを用いて計測対象物の変位分布計測を次の手順で行う。
8) 校正実験の基準面の位置に計測物体を置き、各光源から照射する光で基準となる画像(変位前)と物体に力が加わった画像(変位後)を順に撮影する。
9) 計測物体の変形によって生じた位相差分布Δφ1、Δφ2、Δφ3と、校正実験で求めた位相−変位変換テーブルの各成分より、計測物体のx、y、z方向の変位ベクトル成分を求めることができる。 Next, the displacement distribution measurement of the measurement object is performed by the following procedure using the phase-displacement conversion table.
8) Place the measurement object at the position of the reference plane in the calibration experiment, and take the reference image (before displacement) and the image with force applied to the object (after displacement) in order with the light emitted from each light source.
9) From the phase difference distributions Δφ 1 , Δφ 2 , Δφ 3 generated by the deformation of the measuring object and the components of the phase-displacement conversion table obtained in the calibration experiment, the displacement vector components in the x, y, and z directions of the measuring object Can be requested.

(4) 変位分布を用いたひずみ分布算出原理
次に、変位分布からひずみ分布を算出する方法を示す。
1) 縦の画素iと横の画素jとx方向の変位dxによる図６のような3次元座標を考える。この3次元座標において、検出する画素とその画素を中心とする周囲の画素について平面近似を行う。この平面は、式 (7)のようにパラメータax、bx、cxを用いて表すことができる。
この式について最小2乗法を行うことでax、bx、cxを求める。i方向、j方向の傾きはそれぞれ、式(8)、(9)のようになる。
(4) Strain distribution calculation principle using displacement distribution Next, a method for calculating the strain distribution from the displacement distribution is shown.
1) Consider a three-dimensional coordinate as shown in FIG. 6 by a vertical pixel i, a horizontal pixel j, and a displacement dx in the x direction. In this three-dimensional coordinate, planar approximation is performed for the pixel to be detected and the surrounding pixels centered on the pixel. This plane can be expressed using parameters a x , b x , and c x as shown in Equation (7).
A x , b x , and c x are obtained by performing the least square method on this expression. The inclinations in the i and j directions are as shown in equations (8) and (9), respectively.

2) dxと同様に、y方向の変位dyについても図６のような3次元座標を考え、i方向、j方向の傾きを検出する。近似した平面、i方向、j方向の傾きはそれぞれ、式(10)、(11)、(12)のようになる。
2) Similar to dx, the displacement dy in the y direction is also considered for the three-dimensional coordinates as shown in FIG. 6, and the inclinations in the i and j directions are detected. The slopes of the approximate plane, i direction, and j direction are expressed by equations (10), (11), and (12), respectively.

3) 再生面におけるi方向、j方向の1画素の幅Δx、Δyはそれぞれ、
となる。ここで、Rは物体とCCDカメラとの光学的距離(再生距離)、wはカメラのi方向の画素数、hはカメラのj方向の画素数、ΔXはカメラの1画素のi方向のサイズ、ΔYはカメラの1画素のj方向のサイズである。ここからx方向の垂直ひずみは、
となる。同様にy方向の垂直ひずみは、
となる。またせん断ひずみγxyは、
となる。 3) The widths Δx and Δy of one pixel in the i and j directions on the playback surface are
It becomes. Where R is the optical distance (reproduction distance) between the object and the CCD camera, w is the number of pixels in the i direction of the camera, h is the number of pixels in the j direction of the camera, and ΔX is the size of one pixel of the camera in the i direction. , ΔY is the size of one pixel of the camera in the j direction. From here, the vertical strain in the x direction is
It becomes. Similarly, the vertical strain in the y direction is
It becomes. The shear strain γ xy is
It becomes.

(5) 感度ベクトルを用いたひずみ計測原理
式(5)、(6)より、x、y方向の変位は、
となる。式(18)、(19)を偏微分すると引張ひずみεx、εy、せん断ひずみγxyは、
となる。ここで、∂Δφ1/∂x、∂Δφ2/∂x、∂Δφ3/∂x、∂Δφ1/∂y、∂Δφ2/∂y、∂Δφ3/∂yはΔφ1〜Δφ3に(4)のひずみ算出原理を適用して求めた傾き分布を表している。 (5) Strain measurement principle using sensitivity vector From equations (5) and (6), the displacement in the x and y directions is
It becomes. When partial differentiation of equations (18) and (19), tensile strains ε x , ε y and shear strain γ xy are
It becomes. Here, ∂Δφ 1 / ∂x, ∂Δφ 2 / ∂x, ∂Δφ 3 / ∂x, ∂Δφ 1 / ∂y, ∂Δφ 2 / ∂y, ∂Δφ 3 / ∂y are Δφ 1 to Δφ 3 Represents the slope distribution obtained by applying the strain calculation principle (4).

しかし、位相差分布はラッピングされた分布(すなわち、位相差が−πから＋πの間になるように2nπ(nは整数）を加算された位相差の分布)であるため、位相の切れ目の部分では位相接続を行わないと傾き分布を検出することはできない。そこで、基準となる位相を決め、図７(a)のようにその画素を基準とし平滑化差分に用いる画素の位相差ΔφをΔφ0移動し、図７(b)のようにラッピングすることで(すなわち、位相差が−πから＋πの間になるように2nπ(nは整数）を加算することで)傾きの検出を可能にする。
式(20)〜(22)を用いることで、変位分布を算出するのに必要な位相接続などの処理を必要とせず、位相差分布から直接ひずみ分布を検出することができる。 However, since the phase difference distribution is a wrapping distribution (that is, a phase difference distribution obtained by adding 2nπ (n is an integer) so that the phase difference is between −π and + π), the phase break portion Then, the slope distribution cannot be detected unless the phase connection is performed. Therefore, a reference phase is determined, and the phase difference Δφ of the pixel used for the smoothing difference is shifted by Δφ 0 with reference to that pixel as shown in FIG. 7A, and is wrapped as shown in FIG. 7B. In other words, the inclination can be detected (by adding 2nπ (n is an integer) so that the phase difference is between −π and + π).
By using the equations (20) to (22), it is possible to detect the strain distribution directly from the phase difference distribution without requiring processing such as phase connection necessary for calculating the displacement distribution.

本発明の作用(作動)を実施例により具体的に説明する。
(1) 3次元変位計測装置
レーザ3台を光源とし、それぞれを物体光と参照光に分ける。物体光は球面波とし物体に3方向から光を照射する。参照光は平行光とし位相シフト装置を通してカメラで撮影する。解析手順の概要を図８に示す。 The operation (operation) of the present invention will be specifically described with reference to examples.
(1) Three-dimensional displacement measuring device Three lasers are used as light sources, and each is divided into object light and reference light. The object light is a spherical wave, and the object is irradiated with light from three directions. The reference light is parallel light and photographed with a camera through a phase shift device. An outline of the analysis procedure is shown in FIG.

(2) 3光束同時解析実験
(i)図３に示す光学系を用いて3つの物体光と参照光を同時にカメラで記録する。なお、前記の通り、図４に示す光学系を用いてもよい。計測物体には回転ステージに取り付けた平板を用いた。回転前の状態を変位前として、物体光と参照光の干渉縞を記録する。次に回転ステージによって変位を与え、変位後の状態を記録する。 (2) 3-beam simultaneous analysis experiment
(i) Using the optical system shown in FIG. 3, three object beams and reference beams are recorded simultaneously by a camera. As described above, the optical system shown in FIG. 4 may be used. A flat plate attached to a rotary stage was used as the measurement object. The interference fringes between the object beam and the reference beam are recorded with the state before the rotation as the state before displacement. Next, a displacement is given by the rotary stage, and the state after the displacement is recorded.

(ii)フーリエ変換位相シフト法によって各光束を分離解析する。得られた3種の周波数成分のそれぞれの再生像および変位量を表す位相分布を図９に示す。図９の位相分布には、位相の切れ目である不連続線が表れている。全体の変位分布を求めるには位相が連続でなければならないので、前記方法により位相接続をおこなう。位相接続によって得られた位相分布を図１０に示す。この位相差分布では、位相差平均化手法を用いた16分割処理によってスペックルノイズの影響を軽減している（特許文献１）。   (ii) Each light beam is separated and analyzed by the Fourier transform phase shift method. FIG. 9 shows phase distributions representing the reproduced images and the displacement amounts of the obtained three types of frequency components. In the phase distribution of FIG. 9, discontinuous lines that are phase breaks appear. Since the phase must be continuous in order to obtain the entire displacement distribution, the phase connection is performed by the above method. FIG. 10 shows the phase distribution obtained by the phase connection. In this phase difference distribution, the influence of speckle noise is reduced by 16 division processing using a phase difference averaging method (Patent Document 1).

(3) 基準面を用いた校正実験
(i)図３(又は図４)に示す光学系を用いて、3つの物体光と参照光を同時にカメラで記録する。計測物体には基準面を取り付けた3軸PZTステージを用いた。まず、変位前の計測物体における物体光と参照光の干渉縞を記録する。次に、3軸PZTステージによって各方向に100 nmずつ変位を与え、変位後の状態を記録する。 (3) Calibration experiment using reference plane
(i) Using the optical system shown in FIG. 3 (or FIG. 4), three object beams and reference beams are recorded simultaneously by a camera. A three-axis PZT stage with a reference plane was used as the measurement object. First, the interference fringes between the object light and the reference light in the measurement object before displacement are recorded. Next, a displacement of 100 nm is given in each direction by a 3-axis PZT stage, and the state after the displacement is recorded.

(ii)フーリエ変換位相シフト法によって各光束を分離解析し、得られた位相差分布と3軸PZTステージの変位量から感度ベクトル成分を求める。そして、各感度ベクトル成分から位相−変位変換テーブルを作成する。位相差分布には位相差平均化手法を用いた16分割処理によってスペックルノイズの影響を軽減した。   (ii) Separate and analyze each light beam by the Fourier transform phase shift method, and obtain a sensitivity vector component from the obtained phase difference distribution and the displacement amount of the three-axis PZT stage. Then, a phase-displacement conversion table is created from each sensitivity vector component. The effect of speckle noise was reduced by 16-division processing using phase difference averaging method for the phase difference distribution.

(4) 3次元変位計測実験
(i)(2)で求めた位相接続後の位相分布と(3)で求めた位相−変位変換テーブルからx、y、z方向の相対変位分布を求める。各方向の相対変位分布を図１１に示す。 (4) 3D displacement measurement experiment
(i) The relative displacement distribution in the x, y, and z directions is obtained from the phase distribution after phase connection obtained in (2) and the phase-displacement conversion table obtained in (3). The relative displacement distribution in each direction is shown in FIG.

(5) ひずみ分布検出
(i)面内変位計測光学系から得た位相差分布を図１２に示す。これは片持ち梁に変形を加えたときのx方向(図の横方向)の位相差分布である。本分布からx方向のひずみ分布を算出したものを図１３に示す。 (5) Strain distribution detection
(i) The phase difference distribution obtained from the in-plane displacement measurement optical system is shown in FIG. This is the phase difference distribution in the x direction (lateral direction in the figure) when the cantilever is deformed. FIG. 13 shows the x-direction strain distribution calculated from this distribution.

フーリエ変換を用いて干渉像を分離する方法を説明するための図The figure for demonstrating the method of isolate | separating an interference image using a Fourier transform 光源と、変位する計測物体と、観測装置の位置関係を示す図Diagram showing the positional relationship between the light source, the displacement measuring object, and the observation device 参照光位相シフトによる干渉像撮影光学系の光路図Optical path diagram of interference imaging optical system by phase shift of reference beam 物体光位相シフトによる干渉像撮影光学系の光路図Optical path diagram of interference imaging optical system by phase shift of object light 基準面を用いた校正の方法を示す位置関係図Positional relationship diagram showing calibration method using reference plane ひずみ計測の原理を説明するための画素平面＋変位の３次元座標図3D coordinate diagram of pixel plane + displacement for explaining the principle of strain measurement 位相の切れ目における接続処理を説明するための図Diagram for explaining connection process at phase break ３次元変位計測の解析手順を説明するための図Diagram for explaining the analysis procedure of 3D displacement measurement 各周波数成分の再生像と位相分布の図Reconstructed image and phase distribution of each frequency component 各周波数成分の位相接続後の位相分布図Phase distribution after phase connection of each frequency component xyz各方向の相対変位分布図xyz Relative displacement distribution map 計測された位相差分布図の一例Example of measured phase difference distribution map 計測されたひずみ分布図の一例Example of measured strain distribution

Claims (11)

a) 計測物体に３つの異なる方向から同一波長の物体光を照射し、
b) 物体光と同一波長を有する３つの参照光と計測物体からの反射光との干渉像を、各参照光の位相を互いに異なる速度で物体光に対して変化させつつ複数枚、２次元撮像素子で撮影し、
c) フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離し、
d) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する
ことにより計測物体の３次元変位を計測する方法。 a) Irradiate the object with the same wavelength from three different directions,
b) Two or two-dimensional imaging of interference images of three reference lights having the same wavelength as the object light and the reflected light from the measurement object while changing the phase of each reference light with respect to the object light at different speeds Shoot with the element,
c) Extracting interference components with different phase change rates using Fourier transform to separate the interference images of the three object beams,
d) A method of measuring the three-dimensional displacement of the measurement object by measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image. a) 計測物体に３つの異なる方向から、同一波長であって互いに異なる速度で位相が変化する物体光を照射し、
b) 物体光と同一波長を有する参照光と計測物体からの反射光との干渉像を複数枚、２次元撮像素子で撮影し、
c) フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離し、
d) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する
ことにより計測物体の３次元変位を計測する方法。 a) Irradiate the object to be measured from three different directions with the same wavelength and object light whose phase changes at different speeds.
b) Taking a plurality of interference images between the reference light having the same wavelength as the object light and the reflected light from the measurement object with a two-dimensional image sensor,
c) Extracting interference components with different phase change rates using Fourier transform to separate the interference images of the three object beams,
d) A method of measuring the three-dimensional displacement of the measurement object by measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image. 基準面に既知の３次元変位を与えつつ前記方法で該変位を計測しておき、その結果に基づいて計測物体の未知の３次元変位量を計測する請求項１又は２に記載の３次元変位計測方法。   The three-dimensional displacement according to claim 1 or 2, wherein the displacement is measured by the method while giving a known three-dimensional displacement to a reference surface, and an unknown three-dimensional displacement amount of the measurement object is measured based on the result. Measurement method. 前記既知変位の計測を複数回行い、その平均を取ることにより未知変位の計測精度を高める請求項３に記載の３次元変位計測方法。   The three-dimensional displacement measurement method according to claim 3, wherein the measurement accuracy of the unknown displacement is increased by measuring the known displacement a plurality of times and taking an average thereof. ２次元撮像素子の各画素における演算結果に基づいて平滑化処理を行うことによりノイズ除去を行い、未知変位の計測精度を高める請求項１〜４のいずれかに記載の３次元変位計測方法。   The three-dimensional displacement measurement method according to any one of claims 1 to 4, wherein noise is removed by performing a smoothing process based on a calculation result in each pixel of the two-dimensional image sensor, thereby increasing measurement accuracy of an unknown displacement. ２次元撮像素子の各画素毎に、該画素及び周辺画素の位置とそれら画素について請求項１〜４のいずれかに記載された方法により計測された変位とに基づき、ひずみを算出する３次元ひずみ計測方法。   For each pixel of the two-dimensional image sensor, a three-dimensional strain for calculating the strain based on the positions of the pixel and the peripheral pixels and the displacement measured by the method according to any one of claims 1 to 4 Measurement method. a) 計測物体に３つの異なる方向から同一波長の物体光を照射する物体光照射手段と、
b) 物体光と同一波長を有し、互いに異なる速度で物体光に対する位相が変化する３つの参照光を生成する参照光生成手段と、
c) 計測物体からの反射光と前記３つの参照光の干渉像を撮影する２次元撮像素子と、
d) ２次元撮像素子により複数枚撮影された干渉像に基づき、フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離する分離手段と、
e) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する変位計測手段と
を備える３次元変位ひずみ計測装置。 a) Object light irradiation means for irradiating the measurement object with object light of the same wavelength from three different directions;
b) reference light generating means for generating three reference lights having the same wavelength as the object light and changing the phase with respect to the object light at different speeds;
c) a two-dimensional image sensor that captures an interference image of reflected light from the measurement object and the three reference lights;
d) separation means for separating interference images of three object beams by extracting interference components having different phase change speeds using Fourier transform based on interference images captured by a two-dimensional image sensor;
e) A three-dimensional displacement strain measuring device comprising: displacement measuring means for measuring a displacement distribution of a measuring object in a direction corresponding to the irradiation direction of each object light from each interference image. a) 計測物体に３つの異なる方向から、同一波長であって互いに異なる速度で位相が変化する物体光を照射する物体光照射手段と、
b) 物体光と同一波長を有する参照光を生成する参照光生成手段と、
c) 計測物体からの反射光と参照光の干渉像を撮影する２次元撮像素子と、
d) ２次元撮像素子により複数枚撮影された干渉像に基づき、フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより３つの物体光による干渉像を分離する分離手段と、
e) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する変位計測手段と
を備える３次元変位ひずみ計測装置。 a) Object light irradiating means for irradiating a measurement object with object light having the same wavelength and changing phase at different speeds from three different directions;
b) reference light generating means for generating reference light having the same wavelength as the object light;
c) a two-dimensional image sensor that captures an interference image of the reflected light from the measurement object and the reference light;
d) separation means for separating interference images of three object beams by extracting interference components having different phase change speeds using Fourier transform based on interference images captured by a two-dimensional image sensor;
e) A three-dimensional displacement strain measuring device comprising: displacement measuring means for measuring a displacement distribution of a measuring object in a direction corresponding to the irradiation direction of each object light from each interference image. 更に、２次元撮像素子の各画素毎に、該画素及び周辺画素の位置とそれら画素について計測された変位とに基づきひずみを算出するひずみ算出手段を備える請求項７又は８に記載の３次元変位ひずみ計測装置。   The three-dimensional displacement according to claim 7 or 8, further comprising, for each pixel of the two-dimensional image sensor, a strain calculating means for calculating a strain based on the positions of the pixel and the peripheral pixels and the displacement measured for the pixels. Strain measuring device. a) 計測物体に異なる複数の方向から同一波長の物体光を照射し、
b) 物体光と同一波長を有する複数の参照光と計測物体からの反射光との干渉像を、各参照光の位相を互いに異なる速度で物体光に対して変化させつつ複数枚、２次元撮像素子で撮影し、
c) フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより前記複数の物体光による干渉像を分離し、
d) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する
ことにより計測物体の変位を計測する方法。 a) Irradiate the object with the same wavelength object light from different directions,
b) Two or two-dimensional imaging of interference images of multiple reference beams having the same wavelength as the object beam and reflected light from the measurement object while changing the phase of each reference beam with respect to the object beam at different speeds Shoot with the element,
c) Separating interference images of the plurality of object beams by extracting interference components having different phase change rates using Fourier transform,
d) A method of measuring the displacement of the measurement object by measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image. a) 計測物体に異なる複数の方向から、同一波長であって互いに異なる速度で位相が変化する物体光を照射し、
b) 物体光と同一波長を有する参照光と計測物体からの反射光との干渉像を複数枚、２次元撮像素子で撮影し、
c) フーリエ変換を用いて位相変化速度の異なる干渉成分を抽出することにより、前記複数の物体光による干渉像を分離し、
d) 各干渉像より、各物体光の照射方向に応じた方向の計測物体の変位分布を計測する
ことにより計測物体の変位を計測する方法。

a) Irradiate the object to be measured from different directions with the same wavelength and different object speeds at different speeds.
b) Taking a plurality of interference images between the reference light having the same wavelength as the object light and the reflected light from the measurement object with a two-dimensional image sensor,
c) Extracting interference components having different phase change speeds using Fourier transform to separate the interference images of the plurality of object lights,
d) A method of measuring the displacement of the measurement object by measuring the displacement distribution of the measurement object in the direction corresponding to the irradiation direction of each object light from each interference image.

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