JP2012052998A - Optical measurement method and optical measurement device for measuring refraction factor of solid body having rough surface - Google Patents

Optical measurement method and optical measurement device for measuring refraction factor of solid body having rough surface Download PDF

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JP2012052998A
JP2012052998A JP2010197613A JP2010197613A JP2012052998A JP 2012052998 A JP2012052998 A JP 2012052998A JP 2010197613 A JP2010197613 A JP 2010197613A JP 2010197613 A JP2010197613 A JP 2010197613A JP 2012052998 A JP2012052998 A JP 2012052998A
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rough surface
refractive index
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Kuniharu Takizawa
國治 滝沢
Yasushi Haraguchi
康史 原口
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SIGMAKOKI Co Ltd
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PROBLEM TO BE SOLVED: To provide an optical measurement method and optical measurement device capable of measuring a refraction index of a rough surface of a solid body and a volume ratio γ of the solid body and a gas when the rough surface is regarded as a mixture layer of the solid body and the gas contacted to the solid body.SOLUTION: The optical measurement method includes a first step in which p-polarized light is incident on a rough surface 32 of a sample 30 which is in contact with the gas, and an apparent refraction index nof the rough surface 32 which is in contact with the gas is measured based on an incidence angle φwhere the intensity of the reflection light reflected from the rough surface 32 is minimum; and a second step in which the p-polarized light is incident on the rough surface 32 of the sample 30 which is in contact with a liquid, an apparent refraction index nof the rough surface 32 which is in contact with the liquid is measured based on an incidence angle φwhere the intensity of the reflection light reflected from the rough surface 32 is minimum, and a volume ratio γ in the mixture layer of the solid body and the gas and a refraction index nof the sample 30 when the rough surface 32 is regarded as a mixture layer of the solid body and the gas, based on the refraction indices of nand n.

Description

本発明は、粗面を有する固体の屈折率を測定する光学測定方法及び光学測定装置に関する。   The present invention relates to an optical measurement method and an optical measurement apparatus for measuring a refractive index of a solid having a rough surface.

従来から、代表的な屈折率測定法として、最小偏角法、臨界角法、エリプソメトリー(偏光解析法)、液浸法などが知られている。最小偏角法(非特許文献1参照)は、プリズムに加工された試料の頂角と、最小偏角を測定して屈折率を求めるもので、最も精密に屈折率を測定することができる。臨界角法(非特許文献2参照)は、液体の屈折率測定に適している。試料液の屈折率は、参照プリズムに対する相対値として求められる。エリプソメトリー(非特許文献3参照)は、既知の屈折率をもつ基板上の試料薄膜にP偏光とS偏光を入射し、反射による偏光状態の変化から、薄膜の厚さ、屈折率および消衰係数などを求める手法である。液浸法(非特許文献4参照)は、粉末状の試料と屈折率が段階的に変化した多数の透明液体を用いて、これらの液体に粉末試料を混ぜ、試料の輪郭が最も見にくい液体を選択することで、屈折率を求める方法である。この方法では、試料を鏡面加工せずに屈折率を測定できる。   Conventionally, as a typical refractive index measurement method, a minimum deviation method, a critical angle method, an ellipsometry (an ellipsometry), an immersion method, and the like are known. The minimum deviation method (see Non-Patent Document 1) is a method for obtaining the refractive index by measuring the apex angle and the minimum deviation angle of a sample processed into a prism, and can measure the refractive index most precisely. The critical angle method (see Non-Patent Document 2) is suitable for measuring the refractive index of a liquid. The refractive index of the sample liquid is obtained as a relative value with respect to the reference prism. In ellipsometry (see Non-Patent Document 3), P-polarized light and S-polarized light are incident on a sample thin film on a substrate having a known refractive index, and the thickness, refractive index, and extinction of the thin film are determined from changes in the polarization state due to reflection. This is a method for obtaining a coefficient. The immersion method (see Non-Patent Document 4) uses a powder sample and a large number of transparent liquids whose refractive index changes stepwise, and mixes the liquid sample with these liquids to obtain a liquid in which the outline of the sample is most difficult to see. This is a method for obtaining the refractive index by selecting. In this method, the refractive index can be measured without mirror-treating the sample.

Everitt Charles, "Refraction." The Encyclopedia Britannica, 11th Ed. vol. 23, The Encyclopedia Britannica Company, New York (1911) 26-27.Everitt Charles, "Refraction." The Encyclopedia Britannica, 11th Ed. Vol. 23, The Encyclopedia Britannica Company, New York (1911) 26-27. Tilton, Leroy W., and John K. Taylor,"Refractive Index Measurement," in Physical Methods in Chemical Analysis Vol. 1, 2nd ed. ; Walter G. Berl, editor (1961) 411-62. (E ABBE, "Carl's Repertorium der Physik", Vol. 15, 643 (1879). C. PULFRICH, "Zeitschrift fuer Instrumentenkunde", Vol. 18, 107 (1898))Tilton, Leroy W., and John K. Taylor, "Refractive Index Measurement," in Physical Methods in Chemical Analysis Vol. 1, 2nd ed .; Walter G. Berl, editor (1961) 411-62. (E ABBE, " Carl's Repertorium der Physik ", Vol. 15, 643 (1879). C. PULFRICH," Zeitschrift fuer Instrumentenkunde ", Vol. 18, 107 (1898)) 藤原裕之,分光エリプソメトリー,丸善株式会社2003,7-124.Hiroyuki Fujiwara, Spectroscopic Ellipsometry, Maruzen Co., Ltd. 2003, 7-124. 都城秋穂,久城育夫,「岩石学I」,共立出版 2000,pp.90-93.Miyakonojo Akiho, Hisagi Ikuo, “Iwagaku I”, Kyoritsu Shuppan 2000, pp.90-93.

最小偏角法には、試料をプリズムに加工するため、非破壊測定を行うことができないという問題点がある。また、臨界角法には、固体試料の屈折率を測定できない、最小偏角法ほどの測定精度が得られない、参照プリズムの屈折率より大きな屈折率を測定できないといった問題点がある。また、エリプソメトリーは、光学研磨や蒸着などにより表面をフラットにした固体あるいは液体を測定試料とする方法であり、粗面を有する固体試料の測定には適さない。また、液浸法は、破壊検査であること、浸液の屈折率(1.44〜1.88)の範囲内の素材に限られること、測定精度が先の3つの方法に比べて劣るといった問題点を抱えている。   The minimum deviation method has a problem that non-destructive measurement cannot be performed because the sample is processed into a prism. In addition, the critical angle method has problems that the refractive index of a solid sample cannot be measured, the measurement accuracy as low as the minimum deviation method cannot be obtained, and the refractive index larger than the refractive index of the reference prism cannot be measured. Ellipsometry is a method in which a solid or liquid whose surface is flattened by optical polishing or vapor deposition is used as a measurement sample, and is not suitable for measurement of a solid sample having a rough surface. In addition, the immersion method is a destructive inspection, limited to materials within the refractive index of the immersion liquid (1.44 to 1.88), and has problems such as inferior measurement accuracy compared to the previous three methods. ing.

本発明は、以上のような課題に鑑みてなされたものであり、その目的とするところは、固体の粗面になんらの加工を施すことなく、粗面を有する固体の屈折率を測定することが可能な光学測定方法及び光学測定装置を提供することにある。   The present invention has been made in view of the above problems, and its object is to measure the refractive index of a solid having a rough surface without any processing on the rough surface of the solid. It is an object of the present invention to provide an optical measurement method and an optical measurement apparatus capable of performing the above.

(1)本発明は、粗面を有する固体の屈折率を測定する光学測定方法において、
前記固体の粗面に気体を接触させて、前記固体の粗面の見掛けの屈折率ncsを測定する第1ステップと、
前記固体の粗面に吸収係数又は散乱係数の大きな液体を接触させて、前記固体の粗面の見掛けの屈折率nciを測定し、前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciとに基づいて、前記固体の粗面を固体と前記気体の混合層とみなしたときの前記混合層における固体と気体の体積比γと、前記固体の屈折率nとを求める第2ステップとを有することを特徴とする。
(1) The present invention provides an optical measurement method for measuring a refractive index of a solid having a rough surface.
A first step of measuring an apparent refractive index n cs of the solid rough surface by bringing a gas into contact with the rough surface of the solid;
A liquid having a large absorption coefficient or scattering coefficient is brought into contact with the solid rough surface, the apparent refractive index n ci of the solid rough surface is measured, and the apparent refractive index n cs of the rough surface with which the gas is in contact Based on the apparent refractive index n ci of the rough surface in contact with the liquid, the volume ratio γ of the solid and the gas in the mixed layer when the rough surface of the solid is regarded as the mixed layer of the solid and the gas characterized by a second step of obtaining a refractive index n m of the solid.

ここで、固体粗面に入射した光が粗面において反射もしくは屈折する際に実際に感じる屈折率を見掛けの屈折率と呼ぶ。見掛けの屈折率は、固体本来の屈折率とは異なり、固体の屈折率とそれを取り巻く雰囲気の屈折率や粗面の凹凸状態から定められる。また、屈折率が異なる2つの媒質の界面からの戻り光のうち、反射の法則に従う光を反射光と呼び、それ以外の戻り光を散乱光と呼ぶことにする。また、屈折率が異なる2つの媒質の界面を透過する光のなかで、スネルの法則に従う光を透過光と呼び、それ以外の光を散乱光と呼ぶことにする。さらに、入射光の電界と反射光の電界の比を、電界反射率と定義し、入射光パワーと反射光パワーの比を、パワー反射率と定義する。   Here, the refractive index actually felt when light incident on the solid rough surface is reflected or refracted on the rough surface is referred to as an apparent refractive index. The apparent refractive index is determined from the refractive index of the solid, the refractive index of the atmosphere surrounding it, and the uneven state of the rough surface, unlike the original refractive index of the solid. Of the return light from the interface between two media having different refractive indexes, the light that follows the law of reflection is called reflected light, and the other return light is called scattered light. In addition, among the light transmitted through the interface between two media having different refractive indexes, light complying with Snell's law is called transmitted light, and the other light is called scattered light. Furthermore, the ratio of the electric field of incident light and the electric field of reflected light is defined as electric field reflectance, and the ratio of incident light power and reflected light power is defined as power reflectance.

本発明によれば、粗面を有する固体の屈折率を非破壊で測定することができる。   According to the present invention, the refractive index of a solid having a rough surface can be measured nondestructively.

(2)また本発明において、
前記第1ステップでは、
直線偏光の電界成分が入射面内で振動するp偏光を前記気体が接触した粗面に入射角度φで入射させ、前記固体の粗面から反射の法則に従って反射角度φで反射した反射光の強度が最小になる入射角度φminを求め、前記入射角度φminと、前記固体の粗面と接触している気体の屈折率nとに基づいて、前記気体が接触した粗面の見掛けの屈折率ncsを求めるようにしてもよい。
(2) In the present invention,
In the first step,
The p-polarized light whose electric field component of linearly polarized light vibrates in the incident plane is incident on the rough surface in contact with the gas at an incident angle φ 1 , and the reflected light reflected at the reflection angle φ 1 from the solid rough surface according to the law of reflection. It obtains the incident angle phi min the strength is minimized, and the incident angle phi min, based on the refractive index n s of the gas in contact with the rough surface of the solid, the apparent rough surface on which the gas is in contact The refractive index n cs may be obtained.

(3)また本発明において、
前記第1ステップでは、
に基づいて前記気体が接触した粗面の見掛けの屈折率ncsを求めるようにしてもよい。
(3) In the present invention,
In the first step,
The apparent refractive index n cs of the rough surface in contact with the gas may be obtained based on the above.

(4)また本発明において、
前記第2ステップでは、
透明プリズムを前記液体を介して前記固体の粗面に圧着することで前記固体の粗面に前記液体を接触させ、直線偏光の電界成分が入射面内で振動するp偏光を前記透明プリズムに入射させ、前記透明プリズムと前記固体の粗面との界面で反射の法則に従って反射した反射光の強度が最小になる入射角度φを求め、前記入射角度φと、前記透明プリズムの屈折率nと、前記透明プリズムの出射面と対峙する頂角δと、前記透明プリズムと接触している気体の屈折率nとに基づいて、前記液体が接触した粗面の見掛けの屈折率nciを求めるようにしてもよい。
(4) In the present invention,
In the second step,
The liquid is brought into contact with the solid rough surface by pressing the transparent prism to the solid rough surface via the liquid, and the p-polarized light whose electric field component of linearly polarized light vibrates in the incident surface is incident on the transparent prism. The incident angle φ i that minimizes the intensity of the reflected light reflected at the interface between the transparent prism and the solid rough surface according to the law of reflection is obtained, and the incident angle φ i and the refractive index n of the transparent prism are determined. g and, a top angle δ which faces the exit surface of the transparent prism, on the basis of the refractive index n s of the gas in contact with the transparent prism, the refractive index n ci apparent rough surface on which the liquid is in contact May be requested.

ここで、前記透明プリズムは、光の入射面、出射面及び反射面を光学研磨した透明プリズムであることが好ましい。   Here, it is preferable that the transparent prism is a transparent prism obtained by optically polishing a light incident surface, an output surface, and a reflective surface.

(5)また本発明において、
前記第2ステップでは、
に基づいて前記液体が接触した粗面の見掛けの屈折率nciを求めるようにしてもよい。
(5) In the present invention,
In the second step,
The apparent refractive index n ci of the rough surface in contact with the liquid may be obtained based on the above.

(6)また本発明において、
前記第2ステップでは、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciと、前記液体の屈折率nとに基づいて、前記混合層における固体と気体の体積比γを求めるようにしてもよい。
(6) In the present invention,
In the second step,
Based on the apparent refractive index n cs of the rough surface in contact with the gas, the apparent refractive index n ci of the rough surface in contact with the liquid, and the refractive index n i of the liquid, the solid in the mixed layer The gas volume ratio γ may be obtained.

(7)また本発明において、
前記第2ステップでは、
前記混合層における固体の体積Vと気体の体積Vの体積比をγ=V/Vとすると、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciと、前記液体の屈折率nとを、
(7) In the present invention,
In the second step,
When the volume ratio of the solid volume V m to the gas volume V s in the mixed layer is γ = V s / V m ,
The refractive index n cs apparent rough surface on which the gas is in contact, and the refractive index n ci apparent rough surface on which the liquid is in contact, and a refractive index n i of said liquid,

で表し、 Represented by

に基づいて前記体積比γを求めるようにしてもよい。 The volume ratio γ may be obtained based on the above.

(8)また本発明において、
前記第2ステップでは、
前記体積比γと、前記気体が接触した粗面の見掛けの屈折率ncsとに基づいて、前記固体の屈折率nを求めるようにしてもよい。
(8) In the present invention,
In the second step,
It said volume ratio gamma, on the basis of the refractive index n cs apparent rough surface on which the gas is in contact, may be obtained refractive index n m of the solid.

(9)また本発明において、
前記第2ステップでは、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記固体の屈折率nを、
(9) In the present invention,
In the second step,
Refractive index and n cs apparent rough surface on which the gas is in contact, the refractive index n m of the solid,

で表し、 Represented by

に基づいて前記固体の屈折率nを求めるようにしてもよい。 It may be obtained refractive index n m of the solid based on.

(10)本発明は、
粗面を有する固体の屈折率を測定する光学測定装置において、
直線偏光の電界成分が入射面内で振動するp偏光を前記固体の粗面に入射させる光照射部と、
気体或いは液体を接触させた前記固体の粗面から反射の法則に従って反射した反射光の強度を検出する光検出部と、
前記固体を回転させることで前記p偏光の入射角度を変化させる回転駆動部と、
前記p偏光を前記気体が接触した粗面に入射させた場合に、前記固体の粗面から反射の法則に従って反射した反射光の強度が最小になる入射角度φminに基づいて、前記気体が接触した粗面の見掛けの屈折率ncsを算出し、
透明プリズムを前記液体を介して前記固体の粗面に圧着することで前記固体の粗面に前記液体を接触させて前記p偏光を前記透明プリズムに入射させた場合に、前記透明プリズムと前記固体の粗面との界面で反射の法則に従って反射した反射光の強度が最小になる入射角度φに基づいて、前記液体が接触した粗面の見掛けの屈折率ncsを算出し、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciとに基づいて、前記固体の粗面を固体と前記気体の混合層とみなしたときの前記混合層における固体と気体の体積比γと、前記固体の屈折率nとを算出する演算処理を行う演算処理部とを含むことを特徴とする。
(10) The present invention
In an optical measuring device for measuring the refractive index of a solid having a rough surface,
A light irradiator that causes p-polarized light whose electric field component of linearly polarized light oscillates in the incident plane to be incident on the solid rough surface;
A light detection unit for detecting the intensity of reflected light reflected according to the law of reflection from the rough surface of the solid contacted with gas or liquid;
A rotation drive unit that changes the incident angle of the p-polarized light by rotating the solid;
When the p-polarized light is incident on the rough surface in contact with the gas, the gas comes into contact based on an incident angle φ min that minimizes the intensity of reflected light reflected from the solid rough surface according to the law of reflection. And calculating the apparent refractive index n cs of the rough surface,
When the liquid is brought into contact with the rough surface of the solid by pressing the transparent prism to the rough surface of the solid through the liquid and the p-polarized light is incident on the transparent prism, the transparent prism and the solid Calculating an apparent refractive index n cs of the rough surface in contact with the liquid, based on the incident angle φ i at which the intensity of the reflected light reflected at the interface with the rough surface is minimized according to the law of reflection;
Based on the apparent refractive index n cs of the rough surface in contact with the gas and the apparent refractive index n ci of the rough surface in contact with the liquid, the solid rough surface is regarded as a mixed layer of the solid and the gas. wherein the volume ratio γ of the solid and gas in the mixed layer, characterized in that it comprises a processing unit for performing arithmetic processing for calculating the refractive index n m of the solid when the.

本発明によれば、粗面を有する固体の屈折率を非破壊で測定することができる。   According to the present invention, the refractive index of a solid having a rough surface can be measured nondestructively.

気体が接触した固体表面における光の反射及び散乱の様子を模式的に示す図。The figure which shows typically the mode of reflection and scattering of the light in the solid surface which gas contacted. 気体が接触した固体の粗面を、固体と気体の混合層とみなしたモデルを示す図。The figure which shows the model which considered the solid rough surface which gas contacted as the mixed layer of a solid and gas. 気体が接触した粗面固体における入射角度φminと、混合層の散乱係数αの関係を示す図。The figure which shows the relationship between incident angle (phi) min in the rough surface solid which gas contacted, and the scattering coefficient (alpha) of a mixed layer. 液体が接触した粗面固体の見掛けの屈折率測定について説明するための図。The figure for demonstrating the apparent refractive index measurement of the rough surface solid which the liquid contacted. 液体が接触した粗面固体の見掛けの屈折率測定について説明するための図。The figure for demonstrating the apparent refractive index measurement of the rough surface solid which the liquid contacted. 本実施形態の光学測定装置の構成の一例を示す図。The figure which shows an example of a structure of the optical measuring device of this embodiment. 試料台を回転させる第1の回転機構と、光検出器台を回転させる第2の回転機構の構成の一例を示す側面図。The side view which shows an example of a structure of the 1st rotation mechanism which rotates a sample stand, and the 2nd rotation mechanism which rotates a photodetector stand. 光学測定装置の変形例を示す図。The figure which shows the modification of an optical measuring device. 光学測定装置の変形例を示す図。The figure which shows the modification of an optical measuring device. 光学測定装置の変形例を示す図。The figure which shows the modification of an optical measuring device. 試料と透明プリズムを固定する一方法を示す図。The figure which shows one method of fixing a sample and a transparent prism. 試料と試料台の位置関係を示す図。The figure which shows the positional relationship of a sample and a sample stand. 透明プリズム、透明ダブプリズムおよびその他のプリズムの構成図。The block diagram of a transparent prism, a transparent dove prism, and other prisms. 図14(A)は、軽度粗面で反射した反射光を撮像した画像であり、図14(B)は、重度粗面で反射した反射光を撮像した画像である。14A is an image obtained by imaging reflected light reflected by a light rough surface, and FIG. 14B is an image obtained by imaging reflected light reflected by a heavy rough surface. 入射光と試料面の角度を決定する初期設定について説明するための図。The figure for demonstrating the initial setting which determines the angle of incident light and a sample surface. 入射光と試料面の角度を決定する初期設定について説明するための図。The figure for demonstrating the initial setting which determines the angle of incident light and a sample surface. 吸収係数の大きな液体の屈折率測定について説明するための図。The figure for demonstrating the refractive index measurement of the liquid with a big absorption coefficient. 空気中に置かれたLT結晶のパワー反射率Rと入射角度φとの関係を示す図。The figure which shows the relationship between power reflectivity Rp and incident angle (phi) 1 of LT crystal | crystallization put in the air. 吸収係数の大きな液体に接触したLT結晶のパワー反射率Rと入射角度φとの関係を示す図。Drawing showing the relationship between the power reflectivity R p of the contacted LT crystal large liquid the incident angle phi i of the absorption coefficient.

以下、本実施形態について説明する。なお、以下に説明する本実施形態は、特許請求の範囲に記載された本発明の内容を不当に限定するものではない。また本実施形態で説明される構成の全てが、本発明の必須構成要件であるとは限らない。   Hereinafter, this embodiment will be described. In addition, this embodiment demonstrated below does not unduly limit the content of this invention described in the claim. In addition, all the configurations described in the present embodiment are not necessarily essential configuration requirements of the present invention.

1.測定原理
本実施形態の光学測定方法及び光学測定装置が採用する測定原理を説明する。
1. Measurement Principle The measurement principle employed by the optical measurement method and the optical measurement apparatus according to this embodiment will be described.

1−1.粗面の凹凸に気体が接触した固体粗面(固体と気体からなる混合層)の見掛けの屈折率の測定(第1ステップ)
図1(A)に、気体雰囲気中に置かれた固体の粗面における光の反射と散乱の様子を模式的に示す。図1に示すように、すりガラスやアズカット結晶などの表面は、微細凹凸を有する粗面となっており、固体とそれを取り囲む雰囲気である気体(例えば、空気)が複雑に入り組んだ構造となっている。この粗面の構造の微細部分が入射光の波長と同程度かそれよりも小さい場合、図1(B)に示すように、固体の粗面は、固体と気体の混合層と看做すことができる。この混合層は、例えば、粗面の最も高い部分に接する面を上面とし、粗面の最も低い部分に接する面であって上面と平行な面を下面とするとき、上面と下面の間に存在する固体(粗面を構成する固体)と気体(粗面に接触している気体)とを構成要素とする層である。
1-1. Measurement of apparent refractive index of solid rough surface (mixed layer of solid and gas) with gas in contact with rough surface irregularities (first step)
FIG. 1A schematically shows how light is reflected and scattered on a solid rough surface placed in a gas atmosphere. As shown in FIG. 1, the surface of frosted glass or as-cut crystal is a rough surface having fine irregularities, and has a structure in which a solid and a gas (for example, air) surrounding it are intricately complicated. Yes. When the fine portion of the rough surface structure is equal to or smaller than the wavelength of the incident light, the solid rough surface is regarded as a mixed layer of solid and gas as shown in FIG. Can do. This mixed layer exists, for example, between the upper surface and the lower surface when the surface that is in contact with the highest portion of the rough surface is the upper surface and the surface that is in contact with the lowest portion of the rough surface and is parallel to the upper surface is the lower surface. It is a layer which makes the solid (solid which comprises a rough surface) and gas (gas which is in contact with the rough surface) to constitute.

本実施形態における第1ステップでは、固体の粗面を、固体と気体の混合層とみなしたモデルを用いて、気体が接触した固体の粗面の見掛けの屈折率を測定する。   In the first step in the present embodiment, the apparent refractive index of the solid rough surface in contact with the gas is measured using a model in which the solid rough surface is regarded as a mixed layer of solid and gas.

図2に示すように、混合層(固体の粗面)に入射するp偏光(電界成分が入射面内で振動する直線偏光)の入射角度をφとし、混合層の屈折角度をφとし、固体の屈折角度をφとし、混合層の散乱係数と厚さをそれぞれα、dとすると、p偏光の入射光に対する混合層のパワー反射率Rφは、次式のように表される。 As shown in FIG. 2, the incident angle of the mixed layer p-polarized light incident on the (solid rough surface) (linear polarization electric field component vibrates in the plane of incidence) and phi 1, the refraction angle of the mixed layer and phi 2 When the solid refraction angle is φ 3 and the scattering coefficient and thickness of the mixed layer are α and d, respectively, the power reflectivity R p φ 1 of the mixed layer with respect to the incident light of p-polarized light is expressed as follows: Is done.

式(1)において、rは、気体から混合層に光が入射するときのフレネル反射による振幅反射率(光の電界の反射率)であり、rは、混合層と固体の境界で光が反射するときのフレネル反射による振幅反射率であり、それぞれ次式のように表される。 In equation (1), r 1 is the amplitude reflectivity (reflectance of the electric field of light) due to Fresnel reflection when light enters the mixed layer from the gas, and r 2 is the light at the boundary between the mixed layer and the solid. Is the amplitude reflectivity due to Fresnel reflection, and is expressed by the following equations, respectively.

ここで、nは、気体の屈折率であり、ncsは、混合層の見掛けの屈折率であり、nは、固体の屈折率である。 Here, n s is the refractive index of the gas, n cs is the apparent refractive index of the mixed layer, and n m is the refractive index of the solid.

また式(1)において、Lは、光が混合層を1往復するときの物理的光路長であり、Ψは、隣接する反射光間の位相差であり、それぞれ次式のように表される。ただし、λは入射光の波長である。   In Expression (1), L is a physical optical path length when light makes one round trip through the mixed layer, and Ψ is a phase difference between adjacent reflected lights, each represented by the following expression: . Where λ is the wavelength of the incident light.

ここで、散乱係数αと混合層内の光路長Lの積αLが非常に小さい場合、混合層表面の反射光(図2に示す光線100)だけでなく、混合層内部から反射の法則に従って反射する反射光の存在も無視できないため、反射光のパワー反射率Rφ1は、式(1)にしたがって、φ1の変化とともに周期的な変化を示す。一方、前記αLが非常に大きい場合、混合層に入射した光は、様々な方向に散乱し、混合層内部からの反射光は極めて小さくなる。このとき、混合層表面の反射光(図2に示す光線100)が、混合層からの反射光のパワー反射率Rφ1を支配することになり、反射光のパワー反射率Rは、 Here, when the product αL of the scattering coefficient α and the optical path length L in the mixed layer is very small, not only the reflected light on the surface of the mixed layer (light ray 100 shown in FIG. 2) but also the reflection from the inside of the mixed layer according to the law of reflection. Since the presence of reflected light that cannot be ignored is also negligible, the power reflectivity R p φ 1 of the reflected light shows a periodic change with the change of φ 1 according to the equation (1). On the other hand, when the αL is very large, the light incident on the mixed layer is scattered in various directions, and the reflected light from the inside of the mixed layer becomes extremely small. At this time, the reflected light of the mixed layer surface (ray 100 shown in FIG. 2) is, thus dominating the power reflectivity R p phi 1 of the reflected light from the mixed layer, the power reflectivity R p of the reflected light,

となる。 It becomes.

ここで、図1に示すように散乱光は全方位に放射されるのに対して、反射光は、入射角度と同じ反射角度を保つため、後述する図6〜図10に示す光学系を用いれば、殆どの散乱光を遮断して、反射光を選択的に取り出すことができる。図6〜図10に示す光検出器40に入射する光の主成分が反射光になれば、ブリュースター(Brewster)の法則を利用して混合層(すなわち粗面)の見掛けの屈折率ncsを求めることができる。混合層と気体の界面のブリュースター角をφとすると、混合層の屈折率ncsは、次式のように表される。 Here, the scattered light is radiated in all directions as shown in FIG. 1, whereas the reflected light uses the optical system shown in FIGS. 6 to 10 described later in order to maintain the same reflection angle as the incident angle. For example, most of the scattered light can be blocked and the reflected light can be selectively extracted. If the main component of the light incident on the photodetector 40 shown in FIGS. 6 to 10 is reflected light, the apparent refractive index n cs of the mixed layer (that is, the rough surface) is obtained using Brewster's law. Can be requested. When the Brewster angle at the interface between the mixed layer and the gas and phi B, the refractive index n cs of the mixed layer is expressed by the following equation.

このとき、ブリュースターの法則よりr=0であるから、式(1)から、ブリュースター角φにおけるパワー反射率Rφは、次式のように表される。 At this time, since r 1 = 0 by Brewster's law, the power reflectivity R p φ B at the Brewster angle φ B is expressed by the following equation from the equation (1).

式(8)が成立する条件を探るため、式(1)に式(2)〜(5)を代入し、変数φ1に関する偏導関数∂Rφ)/φを求め、これがゼロとなるときの入射角度を求める。ここでは、固体の屈折率n=2.5とし、気体の屈折率n=1とし、混合層の屈折率ncs=1.6〜2.4とし、混合層の厚さd=1000nmとし、p偏光の入射光の波長λ=632.8nmとする条件で計算を行った。 In order to find a condition for satisfying the equation (8), the equations (2) to (5) are substituted into the equation (1) to obtain a partial derivative ∂R p φ 1 ) / φ 1 related to the variable φ 1 , which is zero. Find the angle of incidence when Here, the solid refractive index n m = 2.5, the gas refractive index n s = 1, the mixed layer refractive index n cs = 1.6 to 2.4, and the mixed layer thickness d = 1000 nm. And the calculation was performed under the condition that the wavelength λ of the incident light of p-polarized light was 632.8 nm.

図3は、パワー反射率Rφ1が最小値になる入射角度φminと、混合層の散乱係数αの関係を示す解析結果を示す図である。図3は、αd>2のときに、入射角度φminが一定値になることを示している。混合層の屈折率ncsを、1.6〜2.4の範囲で変化させて、入射角度φminを求めた結果を表1に示す。 FIG. 3 is a diagram showing an analysis result showing a relationship between the incident angle φ min at which the power reflectivity R p φ 1 is the minimum value and the scattering coefficient α of the mixed layer. FIG. 3 shows that the incident angle φ min becomes a constant value when αd> 2. Table 1 shows the results of calculating the incident angle φ min by changing the refractive index n cs of the mixed layer in the range of 1.6 to 2.4.

表1に示した、入射角度φminは、それぞれ、式(7)で表されるブリュースター角φと一致している。図3や表1の解析結果は一例であり、n、ncs、n、d及びλを変化させても、混合層がαd>2の条件を満たす限り、φmin=φが成立する。従って、本解析から、αd>2を満たす混合層の屈折率ncsは、次式により求められることが明らかである。 The incident angle φ min shown in Table 1 is in agreement with the Brewster angle φ B expressed by the equation (7). The analysis results in FIG. 3 and Table 1 are examples, and even if n s , n cs , n m , d, and λ are changed, φ min = φ B is established as long as the mixed layer satisfies the condition of αd> 2. To do. Therefore, it is clear from this analysis that the refractive index n cs of the mixed layer satisfying αd> 2 is obtained by the following equation.

従って、p偏光を気体に接触している固体の粗面に入射させ、粗面で反射した反射光の強度(すなわち、パワー反射率Rφ1)が最小になる入射角度φminを測定し、測定した入射角度φminと、気体の屈折率nを式(9)に代入することで、固体の粗面を固体と気体の混合層とみなしたときの混合層の屈折率ncs(すなわち、固体の粗面の見掛けの屈折率)を求めることができる。 Therefore, p-polarized light is incident on a solid rough surface in contact with gas, and the incident angle φ min at which the intensity of reflected light reflected by the rough surface (ie, power reflectivity R p φ 1 ) is minimized is measured. By substituting the measured incident angle φ min and the refractive index n s of the gas into the equation (9), the refractive index n cs of the mixed layer when the rough surface of the solid is regarded as a mixed layer of the solid and the gas ( That is, the apparent refractive index of the solid rough surface can be obtained.

このように、本実施形態によれば、固体の粗面を固体と気体雰囲気の混合層とみなして、粗面の見掛けの屈折率を測定することができる。   Thus, according to this embodiment, the apparent refractive index of the rough surface can be measured by regarding the rough surface of the solid as a mixed layer of a solid and a gas atmosphere.

1−2.粗面の凹凸に気体が接触した固体粗面(固体と気体からなる混合層)における固体と気体の体積比γと固体の屈折率nを未知数とする方程式の導出
次に、αd>2を満たす混合層における固体と気体の体積比γと固体の屈折率nとを関係付ける方程式の導出について説明する。
1-2. Derivation of equations to the refractive index n m of the solid rough surface gas contacts the irregularities of the rough surface of the solid and gas in (solid and mixed layer composed of gas) volume ratio γ and solid unknowns Next, the .alpha.d> 2 the derivation of equations describing relating the refractive index n m of the solid and gas volume ratio γ and the solid in the mixed layer satisfying.

固体の密度をρとし、気体の密度をρとし、混合層の密度をρcsとすると、固体、気体及び混合層のそれぞれの密度と屈折率の間には、ローレンツ-ローレンツ(Lorentz-Lorenz)の公式から、次式に示す関係が成立する。 If the density of the solid is ρ m , the density of the gas is ρ s, and the density of the mixed layer is ρ cs , the Lorentz-Lorentz (Lorentz-) From the Lorenz formula, the following relationship is established:

ここで、βは、混合層中での気体の重量(%)である。   Here, β is the weight (%) of the gas in the mixed layer.

また、固体の体積をVとし、気体の体積をVとし、混合層の体積をVcsとすると、次式が成立することも明白である。 It is also apparent that the following equation holds, where V m is the solid volume, V s is the gas volume, and V cs is the volume of the mixed layer.

式(11)〜(13)から、次式を得る。   From the equations (11) to (13), the following equation is obtained.

ここで、γは、混合層における固体の体積Vと気体の体積Vの比である。 Here, γ is the ratio of the volume V m of the solid and the volume V s of the gas in the mixed layer.

式(13)を書き直すと、
となり、式(12)を書き直すと、
Rewriting equation (13),
And rewriting equation (12),

となる。式(17)を式(16)に代入すると、次式を得る。 It becomes. Substituting equation (17) into equation (16) yields:

式(14)を式(18)に代入すると、次式を得る。   Substituting equation (14) into equation (18) yields:

ここで、固体の屈折率n、気体の屈折率n及び混合層の屈折率ncsのそれぞれの関数f、f、fcsを、 Here, the functions f m , f s , f cs of the refractive index n m of the solid, the refractive index n s of the gas, and the refractive index n cs of the mixed layer are expressed as follows :

と定義し、式(20)と式(14)を、式(10)に代入すると、次式を得る。 And substituting Expression (20) and Expression (14) into Expression (10), the following expression is obtained.

式(21)に式(19)を代入すると、次式を得る。   Substituting equation (19) into equation (21) yields:

ここで、気体の屈折率nは凡そ1(例えば、空気ならば、0℃、1気圧の条件でns=1.000292)であるから、式(20)より屈折率nの関数fは凡そ0となる。そこで、f=0を式(22)に代入することで、次式に示すように、混合層における固体と気体の体積比γと固体の屈折率nの関数fを関係付けても良い。 Here, the refractive index of the gas n s is approximately 1 (e.g., if air, 0 ° C., n s = 1.000292 under the conditions of 1 atm) because it is a function f s of the refractive index n s from equation (20) Approximately 0. Therefore, by substituting f s = 0 in equation (22), as shown in the following equation, even if related functions f m of the refractive index n m of the volume ratio γ and solid solid and a gas in the mixed layer good.

1−3.吸収係数又は散乱係数の大きな液体が、粗面に接触した固体粗面(固体と前記液体から成る混合層)における固体と前記気体の体積比γと固体の屈折率nを未知数とする方程式の導出、および前記体積比γと固体の屈折率nの導出(第2ステップ)
次に、粗面を有する固体の屈折率n(固体の真の屈折率)と体積比γを同時に測定する原理を説明する。
1-3. Large liquid absorption coefficient or scattering coefficient, equation of solid rough surface in contact with the rough surface of the refractive index n m of the volume ratio γ and a solid solid and the gas in the (mixed layer made of the solid liquid) and unknown Derivation and derivation of the volume ratio γ and the refractive index nm of the solid (second step)
Next, the principle of simultaneously measuring the refractive index nm (solid true refractive index) and volume ratio γ of a solid having a rough surface will be described.

式(22)および式(23)は、どちらも2つの変数γとfを含む。これらの変数を決定するためには、空気以外の別の雰囲気(例えば液体)を粗面の凹凸に接触させ、式(22)に相当する新たな見掛けの屈折率nciと前記体積比γを関係付ける方程式を求め、この方程式と式(22)あるいは式(23)との連立方程式を解くことが必要である。 Equation (22) and (23) are both include two variables γ and f m. In order to determine these variables, another atmosphere (for example, liquid) other than air is brought into contact with the unevenness of the rough surface, and a new apparent refractive index n ci corresponding to the equation (22) and the volume ratio γ are set. It is necessary to obtain an equation to be related and solve a simultaneous equation of this equation and Equation (22) or Equation (23).

空気以外のもう1種類の雰囲気として、(a)真空、(b)空気と屈折率の異なる同一圧力の気体、(c)圧力の異なる空気あるいはそれ以外の気体、(d)透明度の高い液体、(e)大きな吸収係数と大きな散乱係数のうちどちらか一方を少なくとも有する液体、が考えられる。   As another type of atmosphere other than air, (a) vacuum, (b) gas of the same pressure having a refractive index different from that of air, (c) air of different pressure or other gas, (d) liquid with high transparency, (E) A liquid having at least one of a large absorption coefficient and a large scattering coefficient is conceivable.

(a)と(b)は、第1ステップにおける気体(例えば、空気)との屈折率差が非常に小さいため適当でない。(c)は、2種類の気体の気圧差を非常に大きくすれば屈折率差を大きくできるため測定可能であるが、装置が大掛かりになり適当でない。(d)は、混合層における固体と液体の屈折率差が、固体と空気の屈折率差よりも小さくなるため、αd<2になる可能性があり適当でない。(e)は、混合層における固体と液体の反射率は低下するが、その代わりに混合層を伝播する光は、液体に吸収される効果、あるいは液体中で散乱される効果、あるいはこれら二つの効果により、大きく減衰するため、混合層内部からの反射光を無視して差し支えない。すなわち、ウエット状態を厭わない試料の場合、大きな吸収係数と大きな散乱係数のうちどちらか一方を少なくとも有する液体が最も適している。   (A) and (b) are not suitable because the difference in refractive index from the gas (for example, air) in the first step is very small. Although (c) can be measured because the difference in refractive index can be increased if the pressure difference between the two gases is greatly increased, the apparatus becomes large and is not suitable. (D) is not appropriate because the difference in refractive index between the solid and the liquid in the mixed layer is smaller than the difference in refractive index between the solid and air, and αd <2. In (e), the reflectance of the solid and the liquid in the mixed layer is lowered, but instead, the light propagating through the mixed layer is absorbed in the liquid, or is scattered in the liquid, or these two Because of the large attenuation due to the effect, the reflected light from inside the mixed layer can be ignored. That is, in the case of a sample that does not have a wet state, a liquid having at least one of a large absorption coefficient and a large scattering coefficient is most suitable.

ここでは、空気以外のもう1種類の雰囲気として、高吸収率の液体(吸収係数の大きな液体)を用いる方法について説明する。液体の吸収係数をηとすると、図3の解析結果から、吸収係数ηは以下の値が望ましい。   Here, a method of using a liquid having a high absorption rate (a liquid having a large absorption coefficient) as another type of atmosphere other than air will be described. Assuming that the absorption coefficient of the liquid is η, the following value is desirable for the absorption coefficient η from the analysis result of FIG.

図4に示すように、高吸収率の液体を、固体の粗面に均一に塗布し、その上から透明プリズム(光の入射面、出射面及び反射面を光学研磨した透明プリズム)を圧着して、厚さdの混合層を形成する。混合層は、固体と吸収係数ηの液体で構成される。   As shown in FIG. 4, a liquid having a high absorptance is uniformly applied to a solid rough surface, and a transparent prism (a transparent prism having an optically polished light incident surface, an output surface, and a reflective surface) is pressure-bonded thereon. Thus, a mixed layer having a thickness d is formed. The mixed layer is composed of a solid and a liquid having an absorption coefficient η.

図5に示すように、固体と透明プリズムで挟まれた混合層にp偏光を照射し、混合層からの反射光の強度が最小値になる混合層の入射角度φ’minを求める。入射角度φ’minを直接測定することはできないが、反射光の強度が最小値になる透明プリズムの入射角度φを測定して、スネルの法則よりφとφ’minを関係付ければよい。 As shown in FIG. 5, the mixed layer sandwiched between the solid and the transparent prism is irradiated with p-polarized light, and the incident angle φ ′ min of the mixed layer at which the intensity of the reflected light from the mixed layer becomes the minimum value is obtained. Although the incident angle φ ′ min cannot be directly measured, the incident angle φ i of the transparent prism that minimizes the intensity of the reflected light can be measured, and φ i and φ ′ min can be related from Snell's law. .

透明プリズム、固体および混合層の屈折率を、それぞれn、n、nciとすると、式(24)が成立する場合には、反射光の強度が最小になるとき、次式が近似的に成り立つ。 Assuming that the refractive indexes of the transparent prism, the solid, and the mixed layer are n g , n m , and n ci , respectively, the following equation is approximated when the intensity of the reflected light is minimized when Equation (24) is satisfied. It holds.

また、透明プリズムと、屈折率nの気体(空気)の間には、次式のスネルの法則が成立する。 Further, a transparent prism, between the gas of the refractive index n s (air), Snell's law of the following equation holds.

ここで、φgは、図5に示すように透明プリズムと気体の界面における屈折角度である。 Here, φ g is a refraction angle at the interface between the transparent prism and the gas as shown in FIG.

式(25)、式(26)より、混合層の屈折率nciは、次式により求めることができる。 From the equations (25) and (26), the refractive index n ci of the mixed layer can be obtained by the following equation.

ここで、δは、図5に示すように、透明プリズムの出射面と対峙する頂角(透明プリズムの入射面と反射面とがなす角度)である。   Here, as shown in FIG. 5, δ is an apex angle (angle formed by the incident surface of the transparent prism and the reflecting surface) facing the output surface of the transparent prism.

従って、p偏光を透明プリズムの入射面に入射させ、固体の粗面(透明プリズムと固体の粗面との界面)で反射した反射光の強度が最小になる入射角度φを測定し、測定した入射角度φと、透明プリズムの屈折率nと、透明プリズムの頂角δと、気体の屈折率nを式(27)に代入することで、固体と高吸収率の液体とで構成される混合層の屈折率nci(すなわち、高吸収率の液体と接触している固体粗面の見掛けの屈折率)を求めることができる。 Accordingly, p-polarized light is incident on the incident surface of the transparent prism, and the incident angle φ i at which the intensity of the reflected light reflected by the solid rough surface (interface between the transparent prism and the solid rough surface) is minimized is measured. in to the incident angle phi i was, the refractive index n g of transparent prisms, the apex angle δ of the transparent prism, the refractive index n s of the gas by substituting the equation (27), and a liquid of solid and high absorption rate The refractive index n ci (that is, the apparent refractive index of the solid rough surface in contact with the liquid having a high absorption rate) can be obtained.

ここで、固体の屈折率n、高吸収率の液体の屈折率n及び混合層の屈折率nciのそれぞれの関数f、f、fciを、 Here, the respective functions f m , f i , and f ci of the refractive index n m of the solid, the refractive index n i of the liquid having a high absorption rate, and the refractive index n ci of the mixed layer are expressed as

と定義すると、混合層は固体と液体で構成されるから、式(22)から、次式が成立する。 Since the mixed layer is composed of a solid and a liquid, the following equation is established from the equation (22).

式(23)を式(29)に代入して整理すると、次式を得る。   Substituting equation (23) into equation (29) and rearranging results in the following equation.

従って、高吸収率の液体の屈折率n(すなわち、nの関数f)が明らかな場合には、第1ステップの測定値である混合層の屈折率ncs(すなわち、ncsの関数fcs)と、第2ステップの測定値である混合層の屈折率nci(すなわち、nciの関数fci)とを式(30)に代入することで、混合層における固体と前記気体の体積比γを求めることができる。 Therefore, when the refractive index n i (ie, the function f i of n i ) of the liquid having a high absorptance is clear, the refractive index n cs (ie, n cs of the mixed layer) which is the measurement value of the first step the function f cs), the refractive index of the mixed layer is a measure of the second step n ci (i.e., the function f ci) and n ci by substituting the equation (30), solid in the mixed layer and the gas Can be obtained.

すなわち、式(9)により求めた混合層の屈折率ncs(気体と接触している固体粗面の見掛けの屈折率)を、式(20)に代入することでfcsを求め、式(27)により求めた混合層の屈折率nci(高吸収率の液体と接触している固体粗面の見掛けの屈折率)を、式(28)に代入することでfciを求め、求めたfcsとfciとfを式(30)に代入することで、固体の粗面を固体と気体の混合層とみなしたときの混合層における固体と気体の体積比γを求めることができる。 That is, f cs is obtained by substituting the refractive index n cs (apparent refractive index of the solid rough surface in contact with the gas) of the mixed layer obtained by the equation (9) into the equation (20). 27) Substituting the refractive index n ci (apparent refractive index of the solid rough surface in contact with the liquid having a high absorption rate) of the mixed layer obtained by (27) into the equation (28), the f ci was obtained and obtained. By substituting f cs , f ci and f i into equation (30), the volume ratio γ of the solid and the gas in the mixed layer when the solid rough surface is regarded as a mixed layer of the solid and the gas can be obtained. .

また、式(30)により求めた体積比γと、第1ステップの測定値である混合層の屈折率ncs(すなわち、ncsの関数fcs)とを式(23)(或いは、式(22))に代入することで、固体の屈折率nの関数fを求め、求めたfを式(20)に代入することで、固体の真の屈折率nを求めることができる。 Moreover, the volume ratio γ obtained by the equation (30), the refractive index of the mixed layer is a measurement of the first step n cs (i.e., the function f cs of n cs) and the formula (23) (or formula ( by substituting 22)), determine the function f m of the refractive index n m of solid, f m obtained by substituting the equation (20) can be determined the true refractive index n m of solid .

このように本実施形態によれば、第1ステップで気体雰囲気での粗面の見掛けの屈折率ncsを測定し、第2ステップで高吸収率の液体雰囲気での粗面の見掛けの屈折率nciとを測定することにより、粗面を有する固体の屈折率nと混合層の体積比γとを非破壊で測定することができる。また、本実施形態によれば、反射光強度を測定するため、吸収の大きな物質の屈折率も測定することができる。また従来の臨界角法や液浸法では、測定可能な屈折率の範囲が限られているが、本実施形態によれば、混合層がαd>2の条件を満たす限り、あらゆる範囲の屈折率を測定することができる。 As described above, according to the present embodiment, the apparent refractive index n cs of the rough surface in the gas atmosphere is measured in the first step, and the apparent refractive index of the rough surface in the liquid atmosphere having a high absorption rate in the second step. by measuring the n ci, and a volume ratio γ of the refractive index n m and the mixed layer of a solid can be measured nondestructively with a rough surface. Moreover, according to this embodiment, since the reflected light intensity is measured, the refractive index of a substance with large absorption can also be measured. In addition, in the conventional critical angle method and the liquid immersion method, the range of the refractive index that can be measured is limited. However, according to the present embodiment, as long as the mixed layer satisfies the condition of αd> 2, the refractive index in any range. Can be measured.

2.構成
図6は、本実施形態の光学測定装置の構成の一例を示す図である。
2. Configuration FIG. 6 is a diagram illustrating an example of the configuration of the optical measurement apparatus of the present embodiment.

本実施形態の光学測定装置1は、測定対象である試料30(粗面を有する固体)の粗面32の見掛けの屈折率ncs、及び混合層における固体と気体の体積比γを測定する装置である。光学測定装置1は、レーザダイオードからなる光源10と、ビームスプリッタ12と、円形の開口を有するアパーチャ14と、p偏光を透過させる偏光子20及び検光子22と、光電センサ(フォトディテクタ)からなる第1及び第2の光検出器40、42と、連続光をチョッピングするチョッパー50と、チョッパー制御部52と、ロックインアンプ54と、試料30が載置される試料台60と、第1の光検出器40が載置される光検出器台62と、試料台60を回転軸RAを中心に回転させる第1の回転機構(図示せず)と、光検出器台62を回転軸RAを中心に回転させる第2の回転機構(図示せず)と、演算装置70とを含む。回転軸RAはZ軸と平行で、試料30の粗面32の面内あるいはその近傍に存在し、粗面32の法線33と直交する。 The optical measuring device 1 of the present embodiment is a device that measures the apparent refractive index n cs of the rough surface 32 of the sample 30 (solid having a rough surface) to be measured, and the volume ratio γ of the solid and gas in the mixed layer. It is. The optical measuring device 1 includes a light source 10 composed of a laser diode, a beam splitter 12, an aperture 14 having a circular aperture, a polarizer 20 and an analyzer 22 that transmit p-polarized light, and a photoelectric sensor (photo detector). First and second photodetectors 40 and 42, a chopper 50 for chopping continuous light, a chopper controller 52, a lock-in amplifier 54, a sample stage 60 on which the sample 30 is placed, and a first light A photodetector stage 62 on which the detector 40 is placed, a first rotation mechanism (not shown) for rotating the sample stage 60 around the rotation axis RA, and a photodetector stage 62 around the rotation axis RA. A second rotation mechanism (not shown) that rotates the first rotation mechanism, and an arithmetic unit 70. The rotation axis RA is parallel to the Z axis, exists in or near the rough surface 32 of the sample 30, and is orthogonal to the normal 33 of the rough surface 32.

光源10から出射した光は、偏光子20を透過して、水平面(図6のX軸とY軸を含む面)内で振動するp偏光になる。すなわち、p偏光の電界は、試料30の粗面32の法線33を含む水平面で振動する。このp偏光は、チョッパー50によりパルス変調され、試料30の粗面32の面内に入射する。入射光と反射光の交点は、回転軸RAに一致する、あるいは、少なくとも回転軸RAの近傍であることが望ましい。   The light emitted from the light source 10 passes through the polarizer 20 and becomes p-polarized light that vibrates in a horizontal plane (a plane including the X axis and the Y axis in FIG. 6). That is, the p-polarized electric field vibrates on a horizontal plane including the normal line 33 of the rough surface 32 of the sample 30. The p-polarized light is pulse-modulated by the chopper 50 and is incident on the rough surface 32 of the sample 30. The intersection of the incident light and the reflected light is preferably coincident with the rotation axis RA or at least near the rotation axis RA.

粗面32で反射したp偏光の反射光は、図6に示すように入射角φと等しい反射角φの方向に進む。一方、散乱光は、入射光と反射光の交点から全方向に放射される。反射光と散乱光の強度を測定するために、光検出器台62に、入射光のビーム径とほぼ同一径の開口を有するアパーチャ14、検光子22および第1の光検出器40が設置されている。   The p-polarized reflected light reflected by the rough surface 32 travels in the direction of the reflection angle φ equal to the incident angle φ as shown in FIG. On the other hand, scattered light is radiated in all directions from the intersection of incident light and reflected light. In order to measure the intensity of the reflected light and scattered light, an aperture 14, an analyzer 22 and a first light detector 40 having an opening having substantially the same diameter as the beam diameter of the incident light are installed on the light detector table 62. ing.

第1の光検出器40(光検出部)は、光検出器台62の回転にともない粗面32で反射した反射光および散乱光を受光し、受光した光の強度を電流もしくは電圧に変換(光電変換)して、光強度情報(検出信号)としてロックインアンプ54に出力する。   The first photodetector 40 (light detector) receives the reflected light and scattered light reflected by the rough surface 32 as the photodetector base 62 rotates, and converts the intensity of the received light into a current or voltage ( Photoelectrically converted) and output to the lock-in amplifier 54 as light intensity information (detection signal).

また、チョッパー制御部52は、チョッパー50に制御信号(駆動信号)を出力して、チョッパー50の駆動を制御するとともに、当該制御信号を参照信号としてロックインアンプ54に出力する。ロックインアンプ54は、第1の光検出器40から出力された検出信号のうち、チョッパー制御部52から出力された参照信号と等しい周波数成分を検出し、演算装置70に出力する。チョッパー50、チョッパー制御部52、ロックインアンプ54を用いることで、測定精度を向上させることができる。   The chopper controller 52 outputs a control signal (drive signal) to the chopper 50 to control the drive of the chopper 50 and outputs the control signal to the lock-in amplifier 54 as a reference signal. The lock-in amplifier 54 detects a frequency component equal to the reference signal output from the chopper control unit 52 among the detection signals output from the first photodetector 40, and outputs the detected frequency component to the arithmetic device 70. By using the chopper 50, the chopper controller 52, and the lock-in amplifier 54, the measurement accuracy can be improved.

ビームスプリッタ12は、光源10から出射された光の一部を反射する。第2の光検出器42は、ビームスプリッタ12で反射した光を受光し光電変換し、検出信号を演算装置70に出力する。ビームスプリッタ12と、第2の光検出器42を用いて、光源10からの出射光強度の変動を検出することで、出射光強度の変動に伴う第1の光検出器40によって検出される光強度の変動を補償することができ、測定精度を向上させることができる。   The beam splitter 12 reflects a part of the light emitted from the light source 10. The second photodetector 42 receives the light reflected by the beam splitter 12, performs photoelectric conversion, and outputs a detection signal to the arithmetic device 70. The light detected by the first photodetector 40 due to the fluctuation of the emitted light intensity by detecting the fluctuation of the emitted light intensity from the light source 10 using the beam splitter 12 and the second photodetector 42. Variations in intensity can be compensated for and measurement accuracy can be improved.

なお、ここでは半導体レーザを光源とする一例を示したが、半導体レーザの代わりにガスレーザ、色素レーザ、固体レーザを用いることもできる。また、ハロゲンランプやキセノンランプなどのいわゆるインコヒーレント光源を用いることも可能である。ただし、インコヒーレント光は一般に非常に広い発光スペクトルを有しているため、光源10とビームスプリッタ12の間にスペクトルを狭める光バンドパスフィルタを挿入する必要がある。   Although an example using a semiconductor laser as a light source is shown here, a gas laser, a dye laser, or a solid-state laser can be used instead of the semiconductor laser. A so-called incoherent light source such as a halogen lamp or a xenon lamp can also be used. However, since incoherent light generally has a very wide emission spectrum, it is necessary to insert an optical bandpass filter that narrows the spectrum between the light source 10 and the beam splitter 12.

図7(A)は、試料台60を回転させる第1の回転機構61と、光検出器台62を回転させる第2の回転機構63の構成の一例を示す側面図である。   FIG. 7A is a side view showing an example of the configuration of a first rotation mechanism 61 that rotates the sample stage 60 and a second rotation mechanism 63 that rotates the photodetector stage 62.

図7(A)に示すように、試料台60は、試料台60を回転させる第1の回転機構61、試料台60のあおり角を調整するあおり機構64(ゴニオ)、及び試料台60をXYZ軸方向に空間移動させるXYZ移動機構65の上に設けられている。XYZ移動機構65は、第1の支持ポール67によって支持されている。   As shown in FIG. 7A, the sample stage 60 includes a first rotation mechanism 61 that rotates the sample stage 60, an tilt mechanism 64 (gonio) that adjusts the tilt angle of the sample stage 60, and the sample stage 60 as XYZ. It is provided on an XYZ moving mechanism 65 that moves in the axial direction. The XYZ moving mechanism 65 is supported by a first support pole 67.

光検出器台62は、光検出器台62を回転させる第2の回転機構63に取り付けられている。光検出器台62には、アパーチャ14を支持する支持ポール(図示せず)と、検光子22を支持する第2の支持ポール68と、第1の光検出器40を垂直移動させる垂直移動機構66が設けられ、垂直移動機構66には、第1の光検出器40を支持する第3の支持ポール69が設けられている。第1及び第2の回転機構61、63は、手動回転ステージや自動回転ステージ等により構成することができる。   The photodetector base 62 is attached to a second rotation mechanism 63 that rotates the photodetector base 62. The photodetector base 62 includes a support pole (not shown) that supports the aperture 14, a second support pole 68 that supports the analyzer 22, and a vertical movement mechanism that vertically moves the first photodetector 40. 66 is provided, and the vertical movement mechanism 66 is provided with a third support pole 69 that supports the first photodetector 40. The first and second rotation mechanisms 61 and 63 can be configured by a manual rotation stage, an automatic rotation stage, or the like.

第1の回転機構61と第2の回転機構63の回転軸RAは一致しており、また、回転軸RAは円形の試料台60の中心と一致している。試料台60は、第1の回転機構61によって回転軸RAを中心に回転し、光検出器台62、アパーチャ14、検光子22及び第1の光検出器40は、第2の回転機構63によって回転軸RAを中心に回転する。   The rotation axes RA of the first rotation mechanism 61 and the second rotation mechanism 63 coincide with each other, and the rotation axis RA coincides with the center of the circular sample stage 60. The sample stage 60 is rotated around the rotation axis RA by the first rotation mechanism 61, and the photodetector stage 62, the aperture 14, the analyzer 22, and the first photodetector 40 are rotated by the second rotation mechanism 63. It rotates around the rotation axis RA.

上述したように本実施形態では、試料30の粗面で反射した反射光の強度が最小になる入射角度φmin(或いは、入射角度φ)を求める。そのため、第1の回転機構61により試料台60を回転することで、p偏光の入射角度φ(図6参照)を変化させ、p偏光の入射角度φの変化に応じて、第2の回転機構63により光検出器台62を回転することで、試料30の粗面32で反射した反射光がアパーチャ14及び検光子22を介して第1の光検出器40に入射するように構成している。 As described above, in this embodiment, the incident angle φ min (or the incident angle φ i ) that minimizes the intensity of the reflected light reflected by the rough surface of the sample 30 is obtained. Therefore, by rotating the sample stage 60 by the first rotating mechanism 61, the incident angle φ of the p-polarized light (see FIG. 6) is changed, and the second rotating mechanism is changed according to the change of the incident angle φ of the p-polarized light. By rotating the photodetector table 62 by 63, the reflected light reflected by the rough surface 32 of the sample 30 enters the first photodetector 40 via the aperture 14 and the analyzer 22. .

図7(B)は、試料台60の上面図と側面図である。図7(B)に示すように、円形の試料台60には、回転軸RAを示す点とそれを通る直線が示されている。この直線と粗面32の表面が同一平面になるように、試料30は載置される(設置に必要な装置については図示を省略する)。   FIG. 7B is a top view and a side view of the sample stage 60. As shown in FIG. 7B, the circular sample stage 60 shows a point indicating the rotation axis RA and a straight line passing therethrough. The sample 30 is placed so that the surface of the straight line and the rough surface 32 are flush with each other (illustration of devices necessary for installation is omitted).

再び図6を参照すると、演算装置70は、演算処理部72と、記憶部74とを含む。演算処理部72は、ロックインアンプ60から出力された光強度情報に基づいて、試料30の粗面32で反射した反射光の強度が最小になるp偏光の入射角度φminを求め、入射角度φminと気体の屈折率nとに基づいて、気体と接触している試料30の粗面32の見掛けの屈折率ncsを算出する演算処理(第1ステップの演算処理)を行う。 Referring to FIG. 6 again, the arithmetic device 70 includes an arithmetic processing unit 72 and a storage unit 74. Based on the light intensity information output from the lock-in amplifier 60, the arithmetic processing unit 72 obtains the incident angle φ min of p-polarized light that minimizes the intensity of the reflected light reflected by the rough surface 32 of the sample 30. Based on φ min and the refractive index n s of the gas, a calculation process (first calculation process) is performed to calculate the apparent refractive index n cs of the rough surface 32 of the sample 30 in contact with the gas.

また、演算処理部72は、試料30の粗面32に吸収係数ηの液体を介して透明プリズムを圧着させた状態において、p偏光を前記透明プリズムに入射させたときに、ロックインアンプ60から出力された光強度情報に基づいて、試料30の粗面32で反射した反射光の強度が最小になるp偏光の入射角度φを求め、前記入射角度φと、前記透明プリズムの屈折率nと、前記透明プリズムの頂角δと、前記透明プリズムと接触している気体の屈折率nとに基づいて、前記液体と接触している試料30の粗面32の見掛けの屈折率nciを求め、前記気体と接触している粗面32の見掛けの屈折率ncsと、前記液体と接触している粗面32の見掛けの屈折率nciと、前記液体の屈折率nとに基づいて、試料30の粗面32を固体と気体の混合層とみなしたときの前記混合層における固体と気体の体積比γを算出する演算処理(第2ステップの演算処理)を行う。また、演算処理部72は、前記体積比γと、気体と接触している粗面32の見掛けの屈折率ncsとに基づいて、試料30の屈折率nを算出する演算処理(第2ステップの演算処理)を行う。 In addition, the arithmetic processing unit 72 receives the p-polarized light from the lock-in amplifier 60 when the p-polarized light is made incident on the rough surface 32 of the sample 30 through the liquid having the absorption coefficient η. Based on the output light intensity information, the incident angle φ i of p-polarized light that minimizes the intensity of the reflected light reflected by the rough surface 32 of the sample 30 is obtained, and the incident angle φ i and the refractive index of the transparent prism are obtained. and n g, and the top angle δ of the transparent prism, on the basis of the refractive index n s of the gas in contact with the transparent prism, the refractive index of the apparent rough surface 32 of the sample 30 in contact with the liquid n ci is obtained, the apparent refractive index n cs of the rough surface 32 in contact with the gas, the apparent refractive index n ci of the rough surface 32 in contact with the liquid, and the refractive index n i of the liquid. Based on the above, the rough surface 32 of the sample 30 is fixed. A calculation process (calculation process of the second step) is performed to calculate the volume ratio γ of the solid and the gas in the mixed layer when it is regarded as a mixed layer of body and gas. Further, the arithmetic processing unit 72, the volume ratio and gamma, based on the refractive index n cs apparent rough surface 32 in contact with the gas, calculation processing for calculating a refractive index n m of the sample 30 (second Step calculation processing).

なお、光学測定装置1が、チョッパー50、チョッパー制御部52及びロックインアンプ54を備えない場合には、演算処理部72は、第1の光検出器40から出力された光強度情報に基づき前記演算処理を行う。   When the optical measurement device 1 does not include the chopper 50, the chopper control unit 52, and the lock-in amplifier 54, the arithmetic processing unit 72 is based on the light intensity information output from the first photodetector 40. Perform arithmetic processing.

記憶部74は、種々のデータを一時記憶する機能を有し、例えばロックインアンプ60から出力された光強度情報を、p偏光の入射角度φと対応付けて記憶する。   The storage unit 74 has a function of temporarily storing various data, and stores, for example, light intensity information output from the lock-in amplifier 60 in association with the incident angle φ of p-polarized light.

図8〜図10は、光学測定装置1の変形例を示す図である。   8-10 is a figure which shows the modification of the optical measuring device 1. As shown in FIG.

図8に示す光学測定装置1では、試料台60とアパーチャ14との間に凸レンズ16を設けている。ここで、凸レンズ16とアパーチャ14間の距離は、凸レンズ16の焦点距離fと一致する。従って、平行光である試料30からの反射光は、アパーチャ14の開口を通過して、第1の光検出器40に入射する。一方、試料30と凸レンズ16間の距離aは、凸レンズ16の焦点距離f以下となっており、試料30からの散乱光は、アパーチャ14により遮断される。また、図8に示す構成によれば、図6に示す構成と比べて、光検出器台62の光路に沿った方向の長さを短くすることができる。   In the optical measuring device 1 shown in FIG. 8, the convex lens 16 is provided between the sample stage 60 and the aperture 14. Here, the distance between the convex lens 16 and the aperture 14 coincides with the focal length f of the convex lens 16. Therefore, the reflected light from the sample 30 that is parallel light passes through the opening of the aperture 14 and enters the first photodetector 40. On the other hand, the distance a between the sample 30 and the convex lens 16 is equal to or shorter than the focal length f of the convex lens 16, and scattered light from the sample 30 is blocked by the aperture 14. Further, according to the configuration shown in FIG. 8, the length of the photodetector base 62 in the direction along the optical path can be shortened as compared with the configuration shown in FIG.

図9に示す光学測定装置1では、光源10と試料台60との間にビームエクスパンダ18を設けて、光源10から出射された光のビーム径を大きくしている。試料30に入射するp偏光のビーム径を大きくすることで、平行光である試料30からの反射光は、凸レンズ16によってより小さなスポットに集光されるため、図8に示す構成と比較してアパーチャ14の開口をより小さくすることができ、試料30からの散乱光の影響をより小さくすることができる。   In the optical measuring apparatus 1 shown in FIG. 9, a beam expander 18 is provided between the light source 10 and the sample stage 60 to increase the beam diameter of the light emitted from the light source 10. By increasing the beam diameter of the p-polarized light incident on the sample 30, the reflected light from the sample 30 that is parallel light is condensed into a smaller spot by the convex lens 16, and thus compared with the configuration shown in FIG. The aperture of the aperture 14 can be made smaller, and the influence of scattered light from the sample 30 can be made smaller.

図10に示す光学測定装置1では、チョッパー50に代えて光変調器51(例えば、光弾性変調器)が設けられ、チョッパー制御部52に変えて信号発生器53及び増幅器55が用いられている。光変調器51を用いることで、光源10から出射された光の強度を、矩形波状ばかりでなく正弦波状にも変化させることができ、また、変調周波数を低周波から高周波まで自在に選択することができる。   In the optical measuring apparatus 1 shown in FIG. 10, an optical modulator 51 (for example, a photoelastic modulator) is provided instead of the chopper 50, and a signal generator 53 and an amplifier 55 are used instead of the chopper control unit 52. . By using the optical modulator 51, the intensity of light emitted from the light source 10 can be changed not only to a rectangular wave shape but also to a sine wave shape, and the modulation frequency can be freely selected from a low frequency to a high frequency. Can do.

図6〜図10は、粗面が気体に接触する第1ステップにおける構成である。第2ステップでは、前記透明プリズムを吸収係数の大きな前記液体を介して試料30の粗面32に圧着することで試料30の粗面32に前記液体を接触させること以外は、第1ステップと同じ構成で計測を行うことができる。   6 to 10 are configurations in the first step in which the rough surface contacts the gas. The second step is the same as the first step except that the liquid is brought into contact with the rough surface 32 of the sample 30 by pressing the transparent prism to the rough surface 32 of the sample 30 through the liquid having a large absorption coefficient. Measurements can be made with the configuration.

試料30と透明プリズムを接触させる手法の1例を図11に示す。試料30と透明プリズム110は、V溝ブロック111と台座112の間に設置され、ねじ113とばね114を用いて、試料30、透明プリズム110、V溝ブロック111及び台座112が一体となって保持される。これらは、図12に示すように、試料台60の回転軸RAを通る直線と粗面32が一致するように調整される。ここでは、試料30やそれを支持するV溝ブロック111などを試料台60に設置する装置の図示を省略している。   An example of a technique for bringing the sample 30 and the transparent prism into contact is shown in FIG. The sample 30 and the transparent prism 110 are installed between the V-groove block 111 and the pedestal 112, and the sample 30, the transparent prism 110, the V-groove block 111, and the pedestal 112 are held together using a screw 113 and a spring 114. Is done. These are adjusted so that the straight line passing through the rotation axis RA of the sample stage 60 and the rough surface 32 coincide as shown in FIG. Here, illustration of an apparatus for installing the sample 30 and the V-groove block 111 for supporting the sample 30 on the sample stage 60 is omitted.

透明プリズムに与えられる条件は、図13(A)に示すように、入射面、反射面および出射面が鏡面であり、かつ、出射面と対峙する頂角δが、δ<90°である。   As shown in FIG. 13A, the condition given to the transparent prism is that the incident surface, the reflection surface, and the output surface are mirror surfaces, and the apex angle δ facing the output surface is δ <90 °.

図13(B)に、透明ダブプリズムを示し、図13(C)に、その他のプリズムを示す。いずれも透明プリズムに代わる光学部品であり、反射面と対峙する面が反射面と平行になっているため、図11のV溝ブロックを用いずに、平行平板ブロックを用いて試料30とそれに接触したプリズムを安定、かつ容易に保持することができるという特徴をもつ。   FIG. 13B shows a transparent dove prism, and FIG. 13C shows other prisms. All of these are optical components that replace the transparent prism, and the surface facing the reflecting surface is parallel to the reflecting surface, so that the sample 30 and the contact with the sample using the parallel plate block instead of the V-groove block of FIG. The prism can be held stably and easily.

3.測定方法
第1ステップの測定に先立って、入射光と試料面(試料30の粗面32)の角度を決定する初期設定を行う。まず、試料30の粗面32を含む無限平面内に、試料台60の回転軸RAを通る直線が含まれるように、試料30を設置する。厳密には粗面は微細な凹凸を有するが、これを平面とみなしても、測定精度に影響を及ぼすことはない。
3. Measurement Method Prior to the measurement in the first step, initial setting for determining the angle between the incident light and the sample surface (rough surface 32 of the sample 30) is performed. First, the sample 30 is installed so that a straight line passing through the rotation axis RA of the sample stage 60 is included in an infinite plane including the rough surface 32 of the sample 30. Strictly speaking, the rough surface has fine irregularities, but even if this is regarded as a flat surface, the measurement accuracy is not affected.

試料30が軽度な粗面を有する場合には、図14(A)に示すように、散乱光に混じって反射光の存在(図14(A)に示す画像の中央付近の明るい部分)が認められる。この場合には、図15(A)に示すごく一般的な方法で入射光の光軸と試料面の法線を一致させることができる。すなわち、レーザ光の直径とほぼ一致した開口をもつアパーチャを光源10と試料30の間に設け、試料30からの反射光がこの開口を通過するように試料台60の角度を調整すればよい。この状態を0度として、図15(B)に示すように、試料台60を回転軸RAを中心に角度φだけ回転させれば、φが入射角度になる。このとき、試料30からの反射光がアパーチャ14及び検光子22を介して第1の光検出器40に入射するように光検出器台62を回転軸RAを中心に回転させるようにすると、入射角度φの場合における試料30からの反射光の強度を測定することができる。   When the sample 30 has a light rough surface, as shown in FIG. 14A, the presence of reflected light (a bright portion near the center of the image shown in FIG. 14A) mixed with scattered light is recognized. It is done. In this case, the optical axis of the incident light and the normal of the sample surface can be matched by a very general method shown in FIG. That is, an aperture having an opening that substantially matches the diameter of the laser beam is provided between the light source 10 and the sample 30, and the angle of the sample stage 60 may be adjusted so that the reflected light from the sample 30 passes through this opening. If this state is set to 0 degree and the sample stage 60 is rotated about the rotation axis RA by the angle φ as shown in FIG. 15B, φ becomes the incident angle. At this time, if the photodetector base 62 is rotated about the rotation axis RA so that the reflected light from the sample 30 enters the first photodetector 40 via the aperture 14 and the analyzer 22, the incident light is incident. The intensity of the reflected light from the sample 30 in the case of the angle φ can be measured.

また、試料30が重度な粗面を有する場合には、図14(B)に示すように、肉眼では散乱光と反射光を区別することはできない。この場合には、図16に示すように、アパーチャと試料30の間とビームスプリッタと第2の光検出器42の間に、それぞれ凸レンズ101、102を設け、試料30からの反射光を凸レンズ101を介してビームスプリッタにより反射させ、ビームスプリッタからの反射光を別の凸レンズ102を介して第2の光検出器42に入射させる。第2の光検出器42によって検出された光強度が最大になるように、試料台60の角度を調整することで、入射光の光軸と試料面の法線を一致させることができる。   Further, when the sample 30 has a severe rough surface, as shown in FIG. 14B, the scattered light and the reflected light cannot be distinguished with the naked eye. In this case, as shown in FIG. 16, convex lenses 101 and 102 are provided between the aperture and the sample 30, and between the beam splitter and the second photodetector 42, respectively, and the reflected light from the sample 30 is transmitted to the convex lens 101. And the reflected light from the beam splitter is incident on the second photodetector 42 via another convex lens 102. By adjusting the angle of the sample stage 60 so that the light intensity detected by the second photodetector 42 is maximized, the optical axis of the incident light and the normal line of the sample surface can be matched.

以上の初期設定が終了したら、初期設定用のアパーチャや凸レンズを光路から外して第1ステップの測定を行う。すなわち、試料台60を回転させることでp偏光の入射角度φを変化させ、且つ光検出器台62を回転させて、第1の光検出器40により、試料30の粗面32で反射した反射光の強度Iを測定する。このとき、光源10から出射された光の強度Iも第2の光検出器42により測定し、次式の規格化されたパワー反射率Rを算出する。 When the above initial settings are completed, the initial setting aperture and convex lens are removed from the optical path, and the first step measurement is performed. In other words, the incident angle φ of the p-polarized light is changed by rotating the sample stage 60, and the light detector stage 62 is rotated to reflect the light reflected by the rough surface 32 of the sample 30 by the first photodetector 40. measuring the intensity I R of light. At this time, the intensity I i of the light emitted from the light source 10 is also measured by the second photodetector 42, and a normalized power reflectance R p of the following equation is calculated.

反射光強度を入射光強度で割ることにより、入射光強度の変動をキャンセルすることができ、パワー反射率Rの測定精度を向上させることができる。そして、パワー反射率Rが最小になるp偏光の入射角度φminを求め、入射角度φminに基づき、気体が接触した粗面32の見掛けの屈折率ncs(固体と気体からなる混合層の屈折率)を算出する。 The reflected light intensity divided by the incident light intensity, it is possible to cancel the variation of the incident light intensity, it is possible to improve the measurement accuracy of the power reflectivity R p. Then, the incident angle φ min of the p-polarized light that minimizes the power reflectivity R p is obtained, and the apparent refractive index n cs of the rough surface 32 in contact with the gas (mixed layer of solid and gas) based on the incident angle φ min Is calculated).

第2ステップの測定に先立って、まず、透明プリズムと大きな吸収係数をもつ液体の屈折率を予め測定しておく。   Prior to the measurement in the second step, first, the refractive index of a transparent prism and a liquid having a large absorption coefficient is measured in advance.

透明プリズムの屈折率測定に最も適した方法は、従来の最小偏角法であり、その測定方法はよく知られているため、ここではその説明を省略する。   The most suitable method for measuring the refractive index of the transparent prism is the conventional minimum deflection angle method, and its measurement method is well known, and therefore the description thereof is omitted here.

次に、図17を用いて、吸収係数の大きな液体の屈折率nを測定する手法について説明する。前記液体を容器に入れ、前記透明プリズムで蓋をする。このとき、液体と基板の間に空気が入らないように、液体と透明プリズムを完全に接触させる。図11と同様に台座とV溝ブロックで透明プリズムと容器を軽く圧着し、これを図6〜図10に示すいずれかの光学系に、試料(液体)の表面を含む無限平面内に試料台60の回転軸RAを通る直線が含まれるように、試料30を設置する。 Next, with reference to FIG. 17, described a technique for measuring the refractive index n i of a large liquid absorption coefficient. The liquid is put into a container and covered with the transparent prism. At this time, the liquid and the transparent prism are brought into full contact so that air does not enter between the liquid and the substrate. As in FIG. 11, the transparent prism and the container are lightly pressure-bonded by the pedestal and the V-groove block, and this is attached to any one of the optical systems shown in FIGS. 6 to 10 in an infinite plane including the surface of the sample (liquid). The sample 30 is placed so that a straight line passing through the 60 rotation axes RA is included.

そして、第2ステップの測定手順で測定すれば、前記液体の屈折率nを求めることができる。すなわち、反射光の強度が最小になる入射角度をξmin(図17参照)とすれば、式(24)が成立する場合には、次式が近似的に成り立つ。 Then, by measuring the measurement procedure of the second step, it is possible to determine the refractive index n i of the liquid. That is, if the incident angle at which the intensity of the reflected light is minimized is ξ min (see FIG. 17), the following equation is approximately established when Equation (24) is satisfied.

また、透明プリズムと屈折率nの気体(空気)との間には、次式のスネルの法則が成立する。 Between the gas transparent prism and the refractive index n s (air), Snell's law of the following equation holds.

ここで、φgは、図17に示すように屈折角度である。 Here, φ g is a refraction angle as shown in FIG.

式(32)、式(33)より、吸収係数の大きな液体の屈折率nは、次式により求めることができる。 Equation (32), the equation (33), the refractive index n i of a large liquid absorption coefficient can be calculated by the following equation.

ここで、δは、図17に示すように、透明プリズムの出射面と対峙する頂角である。   Here, δ is an apex angle opposite to the exit surface of the transparent prism, as shown in FIG.

前記透明プリズムと前記液体の屈折率測定が終了したら、試料30である粗面固体に前記液体を十分に垂らし、透明プリズムを粗面に密着させる。固体と透明プリズムを図11に示す台座とV溝ブロックで軽く圧着し、試料30の粗面32を含む無限平面内に試料台60の中心RAを通る直線が含まれるように、試料30を設置する。つぎに図6〜図10に示すいずれかの光学系にセットし、第1ステップと同様の測定手順で測定すれば、前記液体に接触した粗面の見掛けの屈折率nciを求めることができる。すなわち、反射光の強度が最小になる入射角度φi(図5参照)を測定し、式(27)に代入すれば、前記液体に接触した粗面の見掛けの屈折率nciを求めることができる。 When the refractive index measurement of the transparent prism and the liquid is completed, the liquid is sufficiently dropped on the rough surface solid that is the sample 30, and the transparent prism is brought into close contact with the rough surface. The sample 30 is placed so that the solid and the transparent prism are lightly pressed by the pedestal and the V-groove block shown in FIG. 11 and the straight line passing through the center RA of the sample table 60 is included in the infinite plane including the rough surface 32 of the sample 30. To do. Next, if the optical system is set in any one of the optical systems shown in FIGS. 6 to 10 and measured by the same measurement procedure as the first step, the apparent refractive index n ci of the rough surface in contact with the liquid can be obtained. . That is, if the incident angle φ i (see FIG. 5) at which the intensity of the reflected light is minimized is measured and substituted into the equation (27), the apparent refractive index n ci of the rough surface in contact with the liquid can be obtained. it can.

本実施形態では、透明プリズムとしてアクリル製プリズムを用いた。また、大きな吸収係数をもつ液体として、インクジェット式プリンターに用いられる黒色インク液を用いた。   In this embodiment, an acrylic prism is used as the transparent prism. Moreover, the black ink liquid used for an ink jet printer was used as a liquid with a large absorption coefficient.

4.測定結果
図18及び表2に、本実施形態の光学測定装置及び光学測定方法における第1ステップでの測定結果を示す。ここでは、図6に示す光学測定装置1において、試料としてアズカットのLiTaO3結晶(LT結晶)を用い、光源として632.8nm波長のHe−Neレーザを用いて測定を行った。
4). Measurement Results FIG. 18 and Table 2 show the measurement results at the first step in the optical measurement apparatus and the optical measurement method of the present embodiment. Here, in the optical measuring apparatus 1 shown in FIG. 6, the measurement was performed using an as-cut LiTaO 3 crystal (LT crystal) as a sample and a 632.8 nm wavelength He—Ne laser as a light source.

図18に、軽度の粗面を有するLT結晶のパワー反射率Rと入射角度φとの関係を示す。これらの測定結果から得られる入射角度φminに基づいて、軽度の粗面を有するLT結晶の粗面の見掛けの屈折率ncs(粗面を固体(結晶)と気体(空気)の混合層とみなしたときの混合層の屈折率)を求めた。測定結果を表2に示す。 FIG. 18 shows the relationship between the power reflectivity R p of the LT crystal having a light rough surface and the incident angle φ 1 . Based on the incident angle φ min obtained from these measurement results, the apparent refractive index n cs of the rough surface of the LT crystal having a light rough surface (the rough surface is a mixed layer of solid (crystal) and gas (air)) The refractive index of the mixed layer when considered). The measurement results are shown in Table 2.

次に図19及び表3に本実施形態の光学測定装置及び光学測定方法における第2ステップでの測定結果を示す。ここでは、第1ステップでの測定結果と同様に図6に示す光学測定装置1において、試料として軽度粗面のLT結晶を用い、光源として632.8nm波長のHe−Neレーザを用いて測定を行った。   Next, FIG. 19 and Table 3 show the measurement results in the second step in the optical measurement apparatus and optical measurement method of the present embodiment. Here, similarly to the measurement result in the first step, the optical measurement apparatus 1 shown in FIG. 6 performs measurement using a light rough surface LT crystal as a sample and a He—Ne laser having a wavelength of 632.8 nm as a light source. It was.

図19に、軽度の粗面を有するLT結晶のパワー反射率Rと入射角度φiとの関係を示す。この測定結果から得られる出射光が最小になる入射角度φ’min=52.7°に基づいて、軽度の粗面を有するLT結晶の前記黒色インク液に接触した粗面の見掛けの屈折率nci(粗面を固体(結晶)と黒色インク液の混合層とみなしたときの混合層の屈折率)を求めた。測定結果を表3に示す。 FIG. 19 shows the relationship between the power reflectivity R p and the incident angle φ i of an LT crystal having a light rough surface. Based on the incident angle φ ′ min = 52.7 ° at which the output light obtained from the measurement result is minimized, the apparent refractive index n ci of the rough surface in contact with the black ink liquid of the LT crystal having a light rough surface is obtained. The refractive index of the mixed layer when the rough surface was regarded as a mixed layer of solid (crystal) and black ink liquid was determined. Table 3 shows the measurement results.

表2及び表3に示す見掛けの屈折率ncs、nciより、LT結晶の屈折率nと、混合層における固体と気体の体積比γを求めた。測定結果を表4に示す。 Table 2 and the refractive index n cs apparent in Table 3, from n ci, calculated refractive index and n m of LT crystals, the volume ratio γ of the solid and gas in the mixed layer. Table 4 shows the measurement results.

公表されているLT結晶の常光線屈折率は、実験と同じ632.8nmでは、2.1774であることが良く知られている(K. -H. Hellwege, Editor in chief, LANDOLT BOERNSTEIN, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, Vol.11, Elastic, Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals (Springer-Verlag Berlin, Heidelberg, New York 1979) p.616.を参照)。表4の結果は、公表値より、0.75%ほど小さいだけである。また、空気と接触した粗面LT結晶の体積比γの測定値は、0.230であった。表2の結果とLT結晶の公知の屈折率(2.1774)とを用いて求めた前記体積比γは、0.241であり、両者の差異(4.6%)は小さかった。これらの結果は、本実施形態の光学測定装置及び光学測定方法が、粗面を有する固体試料の屈折率n及び体積比γを高精度に測定できることを示している。 It is well known that the published ordinary refractive index of LT crystal is 2.1774 at the same 632.8 nm as in the experiment (K. -H. Hellwege, Editor in chief, LANDOLT BOERNSTEIN, Numerical Data and Functional Relationships). in Science and Technology, New Series, Group III: Crystal and Solid State Physics, Vol.11, Elastic, Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals (Springer-Verlag Berlin, Heidelberg, New York 1979) (See p.616.) The results in Table 4 are only about 0.75% smaller than the published values. The measured value of the volume ratio γ of the rough LT crystal in contact with air was 0.230. The volume ratio γ determined by using the results in Table 2 and the known refractive index (2.1774) of the LT crystal was 0.241, and the difference between the two (4.6%) was small. These results indicate that the optical measurement apparatus and optical measurement method of the present embodiment can measure the refractive index nm and volume ratio γ of a solid sample having a rough surface with high accuracy.

本発明の技術範囲は上記実施形態に限定されるものではなく、本発明の趣旨を逸脱しない範囲で適宜変更を加えることができる。   The technical scope of the present invention is not limited to the above-described embodiment, and appropriate modifications can be made without departing from the spirit of the present invention.

高価な物質、化石、美術品など加工の許されない試料の屈折率測定や、化粧品(ファンデーションやパウダー)の定量的光学評価などに利用することができる。また、粗面の屈折率を正確に知ることが出来るため、分光画像処理で多用されるフォンモデル(三宅洋一,「分光画像処理入門」,東京大学出版会 2006,pp.37-61.を参照)の解析に利用することができる。このモデルは、コンピュータグラフィックス(CG)技術に繋がっているため、CG画像やアニメーションなどの高画質化に寄与できる。   It can be used for refractive index measurement of samples that are not allowed to be processed, such as expensive substances, fossils, art works, and quantitative optical evaluation of cosmetics (foundation and powder). Also, since the refractive index of the rough surface can be accurately determined, the phone model often used in spectral image processing (see Yoichi Miyake, “Introduction to Spectral Image Processing”, The University of Tokyo Press 2006, pp. 37-61. ) Can be used for analysis. Since this model is connected to computer graphics (CG) technology, it can contribute to high image quality such as CG images and animations.

10 光源、12 ビームスプリッタ、14 アパーチャ、16 凸レンズ、18 ビームエクスパンダ、20 偏光子、22 検光子、30 試料、32 粗面、33 粗面の法線、40 第1の光検出器、42 第2の光検出器、50 チョッパー、51 光変調器、52 チョッパー制御部、53 信号発生器、54 ロックインアンプ、55 増幅器、60 試料台、61 第1の回転機構、62 光検出器台、63 第2の回転機構、70 演算装置、72 演算処理部、74 記憶部、100 混合層からの最初の反射光線、101 凸レンズ、102 凸レンズ、110 透明プリズム、 111 V溝ブロック、112 台座、113 ねじ、114 ばね DESCRIPTION OF SYMBOLS 10 Light source, 12 Beam splitter, 14 Aperture, 16 Convex lens, 18 Beam expander, 20 Polarizer, 22 Analyzer, 30 Sample, 32 Rough surface, 33 Rough surface normal, 40 1st photodetector, 42 1st 2 photodetectors, 50 choppers, 51 optical modulators, 52 chopper controllers, 53 signal generators, 54 lock-in amplifiers, 55 amplifiers, 60 sample stands, 61 first rotation mechanism, 62 photodetector stands, 63 Second rotating mechanism, 70 arithmetic device, 72 arithmetic processing unit, 74 storage unit, 100 first reflected light from mixed layer, 101 convex lens, 102 convex lens, 110 transparent prism, 111 V groove block, 112 pedestal, 113 screw, 114 spring

Claims (10)

粗面を有する固体の屈折率を測定する光学測定方法において、
前記固体の粗面に気体を接触させて、前記固体の粗面の見掛けの屈折率ncsを測定する第1ステップと、
前記固体の粗面に吸収係数又は散乱係数の大きな液体を接触させて、前記固体の粗面の見掛けの屈折率nciを測定し、前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciとに基づいて、前記固体の粗面を固体と前記気体の混合層とみなしたときの前記混合層における固体と気体の体積比γと、前記固体の屈折率nとを求める第2ステップとを有する光学測定方法。
In an optical measurement method for measuring the refractive index of a solid having a rough surface,
A first step of measuring an apparent refractive index n cs of the solid rough surface by bringing a gas into contact with the rough surface of the solid;
A liquid having a large absorption coefficient or scattering coefficient is brought into contact with the solid rough surface, the apparent refractive index n ci of the solid rough surface is measured, and the apparent refractive index n cs of the rough surface with which the gas is in contact Based on the apparent refractive index n ci of the rough surface in contact with the liquid, the volume ratio γ of the solid and the gas in the mixed layer when the rough surface of the solid is regarded as the mixed layer of the solid and the gas an optical measuring method and a second step of obtaining a refractive index n m of the solid.
請求項1において、
前記第1ステップでは、
直線偏光の電界成分が入射面内で振動するp偏光を前記気体が接触した粗面に入射角度φで入射させ、前記固体の粗面から反射の法則に従って反射角度φで反射した反射光の強度が最小になる入射角度φminを求め、前記入射角度φminと、前記固体の粗面と接触している気体の屈折率nとに基づいて、前記気体が接触した粗面の見掛けの屈折率ncsを求める光学測定方法。
In claim 1,
In the first step,
The p-polarized light whose electric field component of linearly polarized light vibrates in the incident plane is incident on the rough surface in contact with the gas at an incident angle φ 1 , and the reflected light reflected at the reflection angle φ 1 from the solid rough surface according to the law of reflection. It obtains the incident angle phi min the strength is minimized, and the incident angle phi min, based on the refractive index n s of the gas in contact with the rough surface of the solid, the apparent rough surface on which the gas is in contact An optical measurement method for obtaining the refractive index n cs of the film .
請求項2において、
前記第1ステップでは、
に基づいて前記気体が接触した粗面の見掛けの屈折率ncsを求める光学測定方法。
In claim 2,
In the first step,
The optical measurement method which calculates | requires apparent refractive index ncs of the rough surface which the said gas contacted based on.
請求項1又は2において、
前記第2ステップでは、
透明プリズムを前記液体を介して前記固体の粗面に圧着することで前記固体の粗面に前記液体を接触させ、直線偏光の電界成分が入射面内で振動するp偏光を前記透明プリズムに入射させ、前記透明プリズムと前記固体の粗面との界面で反射の法則に従って反射した反射光の強度が最小になる入射角度φを求め、前記入射角度φと、前記透明プリズムの屈折率nと、前記透明プリズムの出射面と対峙する頂角δと、前記透明プリズムと接触している気体の屈折率nとに基づいて、前記液体が接触した粗面の見掛けの屈折率nciを求める光学測定方法。
In claim 1 or 2,
In the second step,
The liquid is brought into contact with the solid rough surface by pressing the transparent prism to the solid rough surface via the liquid, and the p-polarized light whose electric field component of linearly polarized light vibrates in the incident surface is incident on the transparent prism. The incident angle φ i that minimizes the intensity of the reflected light reflected at the interface between the transparent prism and the solid rough surface according to the law of reflection is obtained, and the incident angle φ i and the refractive index n of the transparent prism are determined. g and, a top angle δ which faces the exit surface of the transparent prism, on the basis of the refractive index n s of the gas in contact with the transparent prism, the refractive index n ci apparent rough surface on which the liquid is in contact Optical measurement method for obtaining
請求項4において、
前記第2ステップでは、
に基づいて前記液体が接触した粗面の見掛けの屈折率nciを求める光学測定方法。
In claim 4,
In the second step,
An optical measurement method for obtaining an apparent refractive index n ci of the rough surface in contact with the liquid based on the above.
請求項1乃至5のいずれかにおいて、
前記第2ステップでは、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciと、前記液体の屈折率nとに基づいて、前記混合層における固体と気体の体積比γを求める光学測定方法。
In any one of Claims 1 thru | or 5,
In the second step,
Based on the apparent refractive index n cs of the rough surface in contact with the gas, the apparent refractive index n ci of the rough surface in contact with the liquid, and the refractive index n i of the liquid, the solid in the mixed layer An optical measurement method for obtaining a gas volume ratio γ.
請求項6において、
前記第2ステップでは、
前記混合層における固体の体積Vと気体の体積Vの体積比をγ=V/Vとすると、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciと、前記液体の屈折率nとを、
で表し、
に基づいて前記体積比γを求める光学測定方法。
In claim 6,
In the second step,
When the volume ratio of the solid volume V m to the gas volume V s in the mixed layer is γ = V s / V m ,
The refractive index n cs apparent rough surface on which the gas is in contact, and the refractive index n ci apparent rough surface on which the liquid is in contact, and a refractive index n i of said liquid,
Represented by
An optical measurement method for obtaining the volume ratio γ based on the above.
請求項6又は7において、
前記第2ステップでは、
前記体積比γと、前記気体が接触した粗面の見掛けの屈折率ncsとに基づいて、前記固体の屈折率nを求める光学測定方法。
In claim 6 or 7,
In the second step,
It said volume ratio gamma, the gas on the basis of the refractive index n cs apparent rough surface in contact, an optical measuring method for determining the refractive index n m of the solid.
請求項8において、
前記第2ステップでは、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記固体の屈折率nを、
で表し、
に基づいて前記固体の屈折率nを求める光学測定方法。
In claim 8,
In the second step,
Refractive index and n cs apparent rough surface on which the gas is in contact, the refractive index n m of the solid,
Represented by
Optical measuring method for determining the refractive index n m of the solid based on.
粗面を有する固体の屈折率を測定する光学測定装置において、
直線偏光の電界成分が入射面内で振動するp偏光を前記固体の粗面に入射させる光照射部と、
気体或いは液体を接触させた前記固体の粗面から反射の法則に従って反射した反射光の強度を検出する光検出部と、
前記固体を回転させることで前記p偏光の入射角度を変化させる回転駆動部と、
前記p偏光を前記気体が接触した粗面に入射させた場合に、前記固体の粗面から反射の法則に従って反射した反射光の強度が最小になる入射角度φminに基づいて、前記気体が接触した粗面の見掛けの屈折率ncsを算出し、
透明プリズムを前記液体を介して前記固体の粗面に圧着することで前記固体の粗面に前記液体を接触させて前記p偏光を前記透明プリズムに入射させた場合に、前記透明プリズムと前記固体の粗面との界面で反射の法則に従って反射した反射光の強度が最小になる入射角度φに基づいて、前記液体が接触した粗面の見掛けの屈折率nciを算出し、
前記気体が接触した粗面の見掛けの屈折率ncsと、前記液体が接触した粗面の見掛けの屈折率nciとに基づいて、前記固体の粗面を固体と前記気体の混合層とみなしたときの前記混合層における固体と気体の体積比γと、前記固体の屈折率nとを算出する演算処理を行う演算処理部とを含む光学測定装置。
In an optical measuring device for measuring the refractive index of a solid having a rough surface,
A light irradiator that causes p-polarized light whose electric field component of linearly polarized light oscillates in the incident plane to be incident on the solid rough surface;
A light detection unit for detecting the intensity of reflected light reflected according to the law of reflection from the rough surface of the solid contacted with gas or liquid;
A rotation drive unit that changes the incident angle of the p-polarized light by rotating the solid;
When the p-polarized light is incident on the rough surface in contact with the gas, the gas comes into contact based on an incident angle φ min that minimizes the intensity of reflected light reflected from the solid rough surface according to the law of reflection. And calculating the apparent refractive index n cs of the rough surface,
When the liquid is brought into contact with the rough surface of the solid by pressing the transparent prism to the rough surface of the solid through the liquid and the p-polarized light is incident on the transparent prism, the transparent prism and the solid Calculating an apparent refractive index n ci of the rough surface in contact with the liquid, based on the incident angle φ i at which the intensity of the reflected light reflected at the interface with the rough surface is minimized according to the law of reflection;
Based on the apparent refractive index n cs of the rough surface in contact with the gas and the apparent refractive index n ci of the rough surface in contact with the liquid, the solid rough surface is regarded as a mixed layer of the solid and the gas. optical measuring device which includes solids and a volume ratio γ of the gas, and a calculation processing unit for performing arithmetic processing for calculating the refractive index n m of the solids in the mixed layer upon the.
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