JP2008256590A - Phase difference measuring method and instrument - Google Patents
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Abstract
Description
本発明は位相差の決定方法に関し、特に散乱、吸収または偏光解消により透過率が低下した試料の位相差を、分光器を用いて正確に決定できる位相差の決定方法、および該方法を用いた位相差測定装置に関する。 The present invention relates to a method for determining a phase difference, and in particular, a method for determining a phase difference capable of accurately determining a phase difference of a sample whose transmittance is reduced by scattering, absorption, or depolarization using a spectroscope, and the method. The present invention relates to a phase difference measuring apparatus.
位相差の測定は、液晶ディスプレイ（ＬＣＤ）用の位相差フィルムの評価や光ディスク、プラスチック等の光学素子の品質管理などにおいて、その必要性が増しており、精度と共に、簡便性などが求められている。 The need for phase difference measurement is increasing in the evaluation of retardation films for liquid crystal displays (LCDs) and the quality control of optical elements such as optical discs and plastics. Yes.
位相差測定方法としては、エリプソメトリによる偏光解析を用いる方法が知られている。エリプソメトリは、偏光子や補償子を高速に回転させる機構または光弾性変調器（ＰＥＭ）または左右円偏光ヘテロダイン干渉法など偏光もしくは位相を変調させる方法と、取得したデータを高速演算処理するための装置などからなり、精度の高い位相差の測定が可能である。しかし、この方法は、原理的に複雑で高価な方法である。また、単一波長での測定データを基にする方法であるため、特に液晶ディスプレイ（ＬＣＤ）用の位相差フィルムの評価を行う際のように可視光全域の位相差の測定が必要な場合には、モノクロメータなどで波長をスキャンしてデータを取得する必要があり、高速に位相差の波長分散測定ができないという問題がある。 As a phase difference measuring method, a method using ellipsometry ellipsometry is known. Ellipsometry is a mechanism for rotating polarizers and compensators at high speed, or a method for modulating polarization or phase, such as a photoelastic modulator (PEM) or left and right circularly polarized heterodyne interferometry, and high-speed processing of acquired data. It consists of a device, etc., and can measure the phase difference with high accuracy. However, this method is in principle complicated and expensive. In addition, since this method is based on measurement data at a single wavelength, it is particularly necessary to measure the retardation of the entire visible light range when evaluating a retardation film for a liquid crystal display (LCD). However, it is necessary to scan the wavelength with a monochromator or the like to acquire data, and there is a problem that the chromatic dispersion measurement of the phase difference cannot be performed at high speed.
その他の位相差測定方法としては、例えば特許文献１に記載の方法がある。この方法は、パラニコルの偏光子／検光子間に配置した試料を１回転させたときの単色光の透過光強度の角度依存性から位相差を求める方法であり、偏光や位相の変調の必要がなく必要とするデータ量も少ない。そのためこの方法を用いた測定装置は安価な構成が可能である装置として、現在市販されている。しかし、この方法では位相差は透過光強度を基に求められるため、吸収、散乱あるいは偏光解消などを示す試料の位相差を決定する際には大きな誤差が生じやすい。 As another phase difference measuring method, for example, there is a method described in Patent Document 1. In this method, the phase difference is obtained from the angle dependency of the transmitted light intensity of monochromatic light when the sample placed between the paranicol polarizer / analyzer is rotated once, and it is necessary to modulate the polarization and phase. Less data is required. Therefore, a measuring apparatus using this method is currently marketed as an apparatus that can be configured at a low cost. However, in this method, since the phase difference is obtained based on the transmitted light intensity, a large error is likely to occur when determining the phase difference of the sample exhibiting absorption, scattering, or depolarization.
さらに、非特許文献１や特許文献２及び３に開示されるように、分光光度計などにより得られる透過スペクトルを用いて位相差を測定する方法が知られている。この方法は必要とする波長範囲において、位相差の波長分散を簡便に測定することができる。
位相差フィルムなどの測定対象は無色透明であることが多いため、従来の位相差測定方法においてはいずれも、測定された透過光強度が試料自体の光吸収、散乱あるいは偏光解消の影響は考慮されていない。しかし、試料が有色の場合、積層構造を有するフィルムである場合や、試料に何らかの欠陥がある場合、試料に吸収等が生じることがあるため、透過光強度を利用する従来の位相差測定方法においては正確な測定は不可能である。そこで、本発明においては、散乱、吸収または偏光解消を示す試料の位相差を正確に決定できる方法の提供を課題とする。 Since the measurement object such as a retardation film is often colorless and transparent, in any conventional phase difference measurement method, the measured transmitted light intensity takes into account the effects of light absorption, scattering or depolarization of the sample itself. Not. However, if the sample is colored, if it is a film having a laminated structure, or if the sample has some defect, absorption or the like may occur in the sample, so in the conventional phase difference measurement method using transmitted light intensity It is impossible to measure accurately. Accordingly, an object of the present invention is to provide a method capable of accurately determining the phase difference of a sample exhibiting scattering, absorption, or depolarization.
本発明者らは上記課題の解決のために鋭意研究を行った結果、分光光度計などにより得られる分光スペクトルを用いて位相差を測定する方法として、試料自体の光吸収、散乱あるいは偏光解消の影響を考慮して正確に位相差を測定する方法を見出して、この知見を基に本発明を完成した。すなわち、本発明は下記［１］〜［９］を提供するものである。 As a result of diligent research to solve the above-mentioned problems, the present inventors have measured light absorption, scattering, or depolarization of the sample itself as a method for measuring a phase difference using a spectrum obtained by a spectrophotometer or the like. A method for accurately measuring the phase difference in consideration of the influence was found, and the present invention was completed based on this finding. That is, the present invention provides the following [1] to [9].
［１］光源、偏光子、試料、検光子、及び分光器がこの順に配置されている光学系で測定された分光スペクトルから該試料の位相差を決定する方法であって、
該試料の位相差の影響がない該試料の分光スペクトルデータを用意すること、
該偏光子の透過軸と該試料の光学軸と該検光子の透過軸との配置を該試料の位相差が検出される配置として測定される少なくとも１つの分光スペクトルを測定すること、
および
前記分光スペクトルデータにより前記分光スペクトルを補正すること
を含む方法。
[1] A method for determining a phase difference of a sample from a spectrum measured by an optical system in which a light source, a polarizer, a sample, an analyzer, and a spectrometer are arranged in this order,
Preparing spectral data of the sample not affected by the phase difference of the sample;
Measuring at least one spectroscopic spectrum measured with an arrangement of the transmission axis of the polarizer, the optical axis of the sample, and the transmission axis of the analyzer as an arrangement in which a phase difference of the sample is detected;
And correcting the spectral spectrum with the spectral data.
［２］光源、偏光子、試料、検光子、及び分光器がこの順に配置されている光学系で測定された分光スペクトルから該試料の位相差を決定する方法であって、
（１）偏光子と検光子とをパラニコル配置とし、かつ偏光子の透過軸と試料の光学軸との為す角を０または９０度として分光スペクトルを測定すること、及び
（２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料の光学軸を偏光子の透過軸の為す角を４５度として分光スペクトルを測定すること
（３）（２）で得られるスペクトルにより（１）で得られるスペクトルを補正すること
を含む方法。
[2] A method for determining a phase difference of a sample from a spectrum measured by an optical system in which a light source, a polarizer, a sample, an analyzer, and a spectrometer are arranged in this order,
(1) Measure the spectroscopic spectrum with the polarizer and analyzer in a paranicol arrangement and the angle between the transmission axis of the polarizer and the optical axis of the sample as 0 or 90 degrees; and (2) Polarizer and analyzer. Measure the spectroscopic spectrum with the photon in the paranicol arrangement or the crossed nicol arrangement, and the angle of the optical axis of the sample made by the transmission axis of the polarizer at 45 degrees. Correcting the resulting spectrum.
［３］補正が、（１）で得られるスペクトルの波長λにおける透過率を（２）で得られるスペクトルの該波長λにおける透過率で除算することにより行われる［２］に記載の方法。
［４］光源、偏光子、試料台、検光子、及び分光器がこの順に配置されている光学系、ならびに下記（１１）により（１２）を補正する手段を含む位相差測定装置：
（１１）試料台上に配置される試料の位相差の影響がない該試料の分光スペクトルデータ；
（１２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料台上に配置される試料の光学軸を偏光子の透過軸の為す角を４５度として測定される分光スペクトル。
[3] The method according to [2], wherein the correction is performed by dividing the transmittance at the wavelength λ of the spectrum obtained in (1) by the transmittance at the wavelength λ of the spectrum obtained in (2).
[4] A phase difference measuring apparatus including an optical system in which a light source, a polarizer, a sample stage, an analyzer, and a spectrometer are arranged in this order, and means for correcting (12) according to the following (11):
(11) Spectral spectrum data of the sample not affected by the phase difference of the sample placed on the sample stage;
(12) A spectroscopic spectrum measured with the polarizer and the analyzer arranged in a para-Nicol arrangement or a crossed Nicol arrangement, and an angle formed by the transmission axis of the polarizer with the optical axis of the sample arranged on the sample stage being 45 degrees.
［５］光源、偏光子、試料台、検光子、及び分光器がこの順に配置されている光学系、ならびに下記（２１）により（１２）を補正する手段を含む位相差測定装置：
（２１）偏光子の透過軸と試料台上に配置された試料の光学軸と該検光子の透過軸との配置を該試料の位相差が検出されない配置として測定された分光スペクトル；
（１２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料台上に配置される試料の光学軸を偏光子の透過軸の為す角を４５度として測定される分光スペクトル。
[5] An optical system in which a light source, a polarizer, a sample stage, an analyzer, and a spectrometer are arranged in this order, and a phase difference measuring device including means for correcting (12) according to (21) below:
(21) A spectral spectrum measured by setting the arrangement of the transmission axis of the polarizer, the optical axis of the sample arranged on the sample stage, and the transmission axis of the analyzer as an arrangement where the phase difference of the sample is not detected;
(12) A spectroscopic spectrum measured with the polarizer and the analyzer arranged in a para-Nicol arrangement or a crossed Nicol arrangement, and an angle formed by the transmission axis of the polarizer with the optical axis of the sample arranged on the sample stage being 45 degrees.
［６］光源、偏光子、試料台、検光子、及び分光器がこの順に配置されている光学系、ならびに下記（３１）により（１２）を補正する手段を含む位相差測定装置：
（３１）偏光子と検光子とをパラニコル配置とし、かつ偏光子の透過軸と試料台上に配置される試料の光学軸との為す角を０または９０度として測定される分光スペクトル；
（１２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料台上に配置される試料の光学軸を偏光子の透過軸の為す角を４５度として測定される分光スペクトル。
[6] An optical system in which a light source, a polarizer, a sample stage, an analyzer, and a spectroscope are arranged in this order, and a phase difference measuring apparatus including means for correcting (12) according to (31) below:
(31) A spectroscopic spectrum measured with a polarizer and an analyzer arranged in a paranicol arrangement, and an angle formed between the transmission axis of the polarizer and the optical axis of the sample placed on the sample stage is 0 or 90 degrees;
(12) A spectroscopic spectrum measured with the polarizer and the analyzer arranged in a para-Nicol arrangement or a crossed Nicol arrangement, and an angle formed by the transmission axis of the polarizer with the optical axis of the sample arranged on the sample stage being 45 degrees.
［７］ 前記（１２）を、コーシーの分散式を用いてフィッティングする手段をさらに含む［４］〜［６］のいずれか一項に記載の位相差測定装置。
［８］ 前記光学系の偏光子と検光子の間に波長板が配置されている［４］〜［７］のいずれか一項に記載の位相差測定装置。
［９］測定波長域内の２つ以上の波長それぞれにおいて、前記波長板のレターデーション値を０．５以上の整数または半整数で除算した値が該波長と一致する［８］に記載の位相差測定装置。
[7] The phase difference measuring apparatus according to any one of [4] to [6], further including means for fitting the (12) using a Cauchy dispersion formula.
[8] The phase difference measuring apparatus according to any one of [4] to [7], wherein a wave plate is disposed between a polarizer and an analyzer of the optical system.
[9] The phase difference according to [8], wherein a value obtained by dividing the retardation value of the wave plate by an integer of 0.5 or more or a half integer matches each wavelength at two or more wavelengths in the measurement wavelength range. measuring device.
本発明により、散乱、吸収または偏光解消を示す試料の位相差を正確に測定できる位相差測定方法および装置が提供される。 The present invention provides a phase difference measurement method and apparatus capable of accurately measuring a phase difference of a sample exhibiting scattering, absorption, or depolarization.
以下、本発明を詳細に説明する。
なお、本明細書において「〜」とはその前後に記載される数値を下限値および上限値として含む意味で使用される。
本明細書において、角度について記載のある場合は、厳密な角度との誤差が±１度の範囲内であればよく、±０．１度の範囲内であることがより好ましい。
０度とは実質的に二つの軸の為す角度が平行である状態を表し、９０度とは実質的に二つの軸の為す角度が直交している状態を表す。
Hereinafter, the present invention will be described in detail.
In the present specification, “to” is used to mean that the numerical values described before and after it are included as a lower limit value and an upper limit value.
In the present specification, when an angle is described, an error from a strict angle may be within a range of ± 1 degree, and more preferably within a range of ± 0.1 degree.
0 degree represents a state in which the angles formed by the two axes are substantially parallel, and 90 degrees represents a state in which the angles formed by the two axes are substantially orthogonal.
パラニコルとは偏光子と検光子の透過軸の為す角度が０度であることを表し、クロスニコルとは偏光子と検光子の透過軸の為す角度が９０度であることを表すが、実際は後述の測定手段で示すように、本発明の測定方法で用いられる光学系において、試料がない状態での偏光子と検光子の配置につき、入射光透過率が最も小さい位置と最も大きい位置をそれぞれクロスニコル、パラニコル位置とする場合もある。
本明細書において、「分光スペクトル」とは「吸収スペクトル」、「散乱スペクトル」、及び「透過スペクトル」等を含む意味であり、「透過スペクトル」であることが好ましい。
Paranicol means that the angle formed by the transmission axis of the polarizer and the analyzer is 0 degree, and crossed Nicol means that the angle made by the transmission axis of the polarizer and the analyzer is 90 degrees. In the optical system used in the measurement method of the present invention, the position where the incident light transmittance is the smallest and the position where the greatest incident light is crossed are respectively crossed in the optical system used in the measurement method of the present invention. In some cases, the positions are Nicol and Paranicol.
In this specification, “spectral spectrum” means “absorption spectrum”, “scattering spectrum”, “transmission spectrum”, and the like, and is preferably “transmission spectrum”.
［位相差測定原理］
分光スペクトルから試料の位相差を決定する原理を以下に説明する。
偏光状態とそれに基づく透過率などの光学特性は、ジョーンズ行列やミューラー行列により記述することができるが、以下では特に偏光解消度が考慮できるミューラー行列で説明する。ミューラー行列によれば、偏光状態はストークスパラメータで記述され、位相差フィルムや偏光子、検光子などを通過するときの各素子による偏光状態の変化が、４×４のミューラー行列により記述される。
まず、偏光子と検光子とがクロスニコルであり、偏光子の透過軸に対して光学軸が４５度傾いた位相差フィルムの光の透過率につき説明する。
[Principle of phase difference measurement]
The principle of determining the phase difference of the sample from the spectroscopic spectrum will be described below.
Optical characteristics such as the polarization state and the transmittance based on the polarization state can be described by a Jones matrix or a Mueller matrix. In the following, a description will be given using a Mueller matrix that can take into account the degree of depolarization. According to the Mueller matrix, the polarization state is described by a Stokes parameter, and the change of the polarization state by each element when passing through a retardation film, a polarizer, an analyzer or the like is described by a 4 × 4 Mueller matrix.
First, the light transmittance of the retardation film in which the polarizer and the analyzer are crossed Nicols and the optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer will be described.
偏光子の透過軸を基準方向（０度）とすると、
偏光子のミューラー行列Ｍｐは式（１）のように記述される。
The Mueller matrix Mp of the polarizer is described as in Equation (1).
検光子のミューラー行列Ｍａは式（２）のように記述される。
偏光子の透過軸に対して光学軸が４５度傾いた位相差フィルムのミューラー行列Ｍｒは式（３）のように記述される。
ここで、Γは式（４）で表される値である。
式中、Reは前記位相差フィルムの位相差であり、λは測定波長である。分光スペクトル測定の際はλが変数となる。
入射光が偏光子を１００％通過する偏光であるとしたとき、言い換えると偏光子を通過した光を１００％としたとき、この偏光子→位相差フィルム→検光子を通過するストークスパラメータは式（５）のようになる。
In the formula, Re is a retardation of the retardation film, and λ is a measurement wavelength. Λ is a variable when measuring a spectrum.
When the incident light is polarized light passing through the polarizer 100%, in other words, when the light passing through the polarizer is 100%, the Stokes parameter passing through the polarizer → retardation film → analyzer It becomes like 5).
上記式Soutの第一成分が光の透過率である。すなわち、光の透過率Ｔ（λ）は以下式（６）のように表される
式（６）から、偏光子と検光子とがクロスニコルであり、偏光子の透過軸に対して光学軸が４５度傾いた位相差Reのフィルムの光の透過率Ｔ（λ）は、理論上Re/λが整数のときに０（透過率０％）となり、Re/λが半整数のときに１（透過率１００％）となることが分かる。図１にRe＝２０００ｎｍの試料（フィルム）の分光スペクトルの例を示す。
同様に偏光子と検光子とがパラニコルとして、偏光子の透過軸に対して光学軸が４５度傾いた位相差フィルムの光の透過率は、下記の式（７）で表される。
From equation (6), the polarizer T and the analyzer are crossed Nicols, and the light transmittance T (λ) of the film having a phase difference Re whose optical axis is inclined 45 degrees with respect to the transmission axis of the polarizer It can be seen that when Re / λ is an integer, 0 (
Similarly, the light transmittance of the retardation film in which the polarizer and the analyzer are paranicol and the optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer is expressed by the following formula (7).
式（７）から、理論上Re/λが整数のときに０（透過率０％）となり、Re/λが半整数のときに１（透過率１００％）となることが分かる。
したがって、偏光子、試料、および検光子が上記何れかの配置である場合に、分光スペクトルにおいて谷の位置（透過率０％）である波長及び山の位置（透過率１００％）である波長を読み取ることによって位相差Reの値を求めることができることがわかる。
From equation (7), it can be seen that, theoretically, Re / λ is 0 (
Therefore, when the polarizer, the sample, and the analyzer are arranged in any of the above, the wavelength at the valley position (
［吸収、散乱の影響］
本発明の方法は、偏光子の透過軸と該試料の光学軸と該検光子の透過軸との配置を該試料の位相差が検出される配置として測定される分光スペクトルを、該試料の位相差の影響がない該試料の分光スペクトルデータで補正することにより、試料の位相差をより正確に決定することを可能とする。
上記分光スペクトルデータから得られる試料の光透過率が波長の関数としてｔ（λ）で表されるとすると、吸収性または散乱性フィルムのミューラー行列Ｍｔは等方性の場合はスカラー量となるので、上述した偏光子と検光子とがクロスニコルであり偏光子の透過軸に対して光学軸が４５度傾いた位相差フィルムの光の透過率Ｔ（λ）は下記式（８）のように記述される。
[Influence of absorption and scattering]
According to the method of the present invention, the spectral spectrum measured by setting the arrangement of the transmission axis of the polarizer, the optical axis of the sample, and the transmission axis of the analyzer as an arrangement in which the phase difference of the sample is detected is obtained. By correcting the spectral data of the sample that is not affected by the phase difference, the phase difference of the sample can be determined more accurately.
If the light transmittance of the sample obtained from the spectral data is expressed as t (λ) as a function of wavelength, the Mueller matrix Mt of the absorptive or scattering film is a scalar quantity when it is isotropic. The light transmittance T (λ) of the retardation film in which the polarizer and the analyzer described above are crossed Nicols and the optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer is expressed by the following equation (8). Described.
式（８）からわかるように、位相差の影響がない試料の分光スペクトルデータからｔ（λ）を求めることにより、吸収／散乱項と位相差項を分離することができる。 As can be seen from Equation (8), the absorption / scattering term and the phase difference term can be separated by obtaining t (λ) from the spectral spectrum data of the sample that is not affected by the phase difference.
位相差の影響がない試料の分光スペクトルデータとしては該試料の既知のデータを用いてもよいが、位相差測定のための光学系において偏光子の透過軸と該試料の光学軸と該検光子の透過軸との配置を該試料の位相差が検出されない配置として測定された分光スペクトルデータであることが好ましい。
試料の位相差が検出されない配置としては偏光子と検光子とをパラニコル配置とし、かつ偏光子の透過軸と試料の光学軸との為す角を０または９０度とした配置が挙げられる。すなわち、例えば透過軸と試料の光学軸との為す角を０度とした場合（偏光子の透過軸と光学軸が一致している場合）について以下に説明する。
偏光子の透過軸と光学軸が一致した位相差フィルムのミューラー行列Ｍｒ２は式（９）のように記述される。
As the spectral data of the sample that is not affected by the phase difference, known data of the sample may be used. However, in the optical system for phase difference measurement, the transmission axis of the polarizer, the optical axis of the sample, and the analyzer It is preferable that the spectral spectrum data is measured as an arrangement where the phase difference of the sample is not detected.
Examples of the arrangement in which the phase difference of the sample is not detected include an arrangement in which the polarizer and the analyzer are arranged in a paranicol arrangement, and the angle between the transmission axis of the polarizer and the optical axis of the sample is 0 or 90 degrees. That is, for example, the case where the angle between the transmission axis and the optical axis of the sample is 0 degree (when the transmission axis of the polarizer and the optical axis coincide) will be described below.
The Mueller matrix Mr2 of the retardation film in which the transmission axis and the optical axis of the polarizer coincide with each other is described as in Expression (9).
これより偏光子と検光子がパラニコルのときの吸収や散乱を考慮した透過光のストークスパラメータSoutは式（１０）となる。
（１０）式からこの光学系の透過率はｔ（λ）で表されることがわかる。
位相差の影響がない試料の分光スペクトルデータにおける透過率ｔ（λ）を用いて、たとえば上記式（８）の透過率Ｔ（λ）の式を割り算により補正してやることにより、吸収や散乱の影響のないスペクトルに補正することができ、その結果として得られる位相差の精度が向上する。
From equation (10), it can be seen that the transmittance of this optical system is represented by t (λ).
By using the transmittance t (λ) in the spectral spectrum data of the sample not affected by the phase difference, for example, by correcting the equation of the transmittance T (λ) in the above equation (8) by division, the influence of absorption and scattering is obtained. It is possible to correct to a spectrum having no noise, and the accuracy of the resulting phase difference is improved.
［位相差の波長分散］
試料の位相差に波長分散がある場合は、分光スペクトルにある山と谷のピークにおける波長が上記の理論で説明される波長よりずれる。例えば図１の例で５００ｎｍにおいて位相差が２０００ｎｍならば図１の通り透過率は０％であるが、仮に４００ｎｍにおける位相差が波長分散で２２００ｎｍとなったとすると、半整数倍なので透過率は１００％となり、図１と異なる。この２２００ｎｍは４００ｎｍの５．５倍であるが、２０００ｎｍの５．５分の１は約３６３ｎｍであるから、この波長分散を有する試料の４００ｎｍに見られる山のピークは、図１においてグラフの外にある３６３ｎｍに存在するはずの山のピークが、位相差が大きくなったことによって長波側にシフトしたものであるということになる。位相差の波長分散は、コーシーの分散式によって記述することができるので、透過スペクトルからフィッティングにより位相差を求めるには、コーシーの分散式を用いることが好ましい。
[Chromatic dispersion of phase difference]
When there is chromatic dispersion in the phase difference of the sample, the wavelength at the peak of the peak and valley in the spectrum is shifted from the wavelength explained in the above theory. For example, in the example of FIG. 1, when the phase difference is 2000 nm at 500 nm, the transmittance is 0% as shown in FIG. 1. However, if the phase difference at 400 nm is 2200 nm in terms of chromatic dispersion, the transmittance is 100 because it is a half integer multiple. %, Which is different from FIG. This 2200 nm is 5.5
コーシーの分散式は、一般に屈折率の波長依存性（波長分散）を表すために用いられ、式（１１）のように記述される。 The Cauchy's dispersion formula is generally used to express the wavelength dependence (wavelength dispersion) of the refractive index, and is described as the formula (11).
レターデーションは、複屈折すなわち二つの異なる屈折率の差に試料の厚みdを乗じたものであるから、屈折率と同様に式（１２）のようにコーシーの分散式を適用することができる。 Retardation is birefringence, that is, the difference between two different refractive indexes multiplied by the thickness d of the sample. Therefore, the Cauchy's dispersion formula can be applied as in the formula (12) in the same manner as the refractive index.
コーシーの分散式は波長の４次までを用いることが多いが、よりフィッティングをより簡便かつ高速にするためには２次まででもよく、精度上必要がある場合には６次以上の偶数次まで用いてもよい。精度と速度のバランスからは４次までを用いることが好ましい。また、位相差の波長分散としてはコーシーの分散式以外にもHandbook ｏｆ ｏｐｔｉｃｓ（２ｎｄ ｅｄ．），ｖｏｌ．１（ＭｃＧｒａｗ−Ｈｉｌｌ）のｐ．３３．６１−３３．８４に記載されている任意の式もしくは任意の２つ以上の和を用いることができる。 Cauchy's dispersion formula often uses up to the 4th order of the wavelength, but in order to make fitting more simple and fast, it may be up to the 2nd order. It may be used. From the balance of accuracy and speed, it is preferable to use up to the fourth order. In addition to Cauchy's dispersion formula, the chromatic dispersion of the phase difference can be found in Handbook of optics (2nd ed.), Vol. 1 (McGraw-Hill) p. Any formula described in 33.61-33.84 or any sum of two or more can be used.
［波長板の利用］
図２にRe=１００ｎｍの試料（フィルム）の分光スペクトル例を示す。このように試料の位相差が小さくなると、測定波長範囲において半整数倍も整数倍も見られなくなるため、スペクトルにピークが見られなくなる。ピークが観測されないスペクトルによっても理論的には位相差を求めることはできるが、実際には計測系のノイズや試料の吸収、散乱、偏光解消などの影響によってスペクトルの絶対値が変化してしまい、算出される位相差の精度に影響がある。
[Use of wave plate]
FIG. 2 shows an example of a spectrum of a sample (film) with Re = 100 nm. When the phase difference of the sample is thus reduced, neither half-integer times nor integer times are seen in the measurement wavelength range, so that no peak is seen in the spectrum. Theoretically, the phase difference can be obtained from a spectrum where no peak is observed, but in reality the absolute value of the spectrum changes due to the influence of measurement system noise, sample absorption, scattering, depolarization, etc. This affects the accuracy of the calculated phase difference.
測定波長範囲においてスペクトルにピークが観測される状態とするため、位相差が小さい試料の測定には波長板を利用して、得られる値の精度を上げることができる。例えば試料の光学軸と光学軸の一致した位相差Rewpの波長板を挿入することを考える。偏光子の透過軸に対して光学軸が４５度傾いた波長板のミューラー行列Mwpは式（１３）のようになる。 Since a peak is observed in the spectrum in the measurement wavelength range, a wavelength plate can be used to measure a sample with a small phase difference, and the accuracy of the obtained value can be increased. For example, consider inserting a wave plate having a phase difference Rewp in which the optical axis of the sample coincides with the optical axis. The Mueller matrix Mwp of the wave plate whose optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer is as shown in Expression (13).
偏光子と検光子とがクロスニコルであり偏光子の透過軸に対して光学軸が４５度傾いた試料および偏光子の透過軸に対して光学軸が４５度傾いた波長板を有する光学系のストークスパラメータは、式（１４）となる。 An optical system having a sample in which the polarizer and the analyzer are crossed Nicols, the optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer, and the wave plate whose optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer. The Stokes parameter is expressed by equation (14).
すなわち光の透過率Ｔ（λ）は下記の式（１５）で表される。 That is, the light transmittance T (λ) is expressed by the following equation (15).
この式より、波長板によって位相差を底上げすることによって、測定波長範囲においてスペクトルにピークを検出することができることがわかる。このピークから測定された位相差を決定後、試料の位相差は波長板の位相差を差し引いて算出すればよい。 From this equation, it can be seen that a peak can be detected in the spectrum in the measurement wavelength range by raising the phase difference with the wave plate. After determining the phase difference measured from this peak, the phase difference of the sample may be calculated by subtracting the phase difference of the wave plate.
［位相差測定装置］
以上で説明した本発明の方法は下記で説明する位相差測定装置によって、実施することができる。
位相差測定装置は、光源、偏光子、試料台、検光子、及び分光器を含み、図３に示す順で配置されていることが好ましい。位相差測定装置はさらに上記の補正、フィッティング等を行う計算手段として光信号解析装置等を含む。
[Phase difference measuring device]
The method of the present invention described above can be implemented by a phase difference measuring apparatus described below.
The phase difference measurement apparatus includes a light source, a polarizer, a sample stage, an analyzer, and a spectrometer, and is preferably arranged in the order shown in FIG. The phase difference measuring apparatus further includes an optical signal analyzing apparatus and the like as calculation means for performing the above correction, fitting and the like.
［光源］
光源は白色光源であることが好ましい。白色光源としては、レ−ザーやＬＥＤのように狭い波長範囲でなく、測定波長範囲において出力を有していれば特に限定はなく、測定波長範囲が可視域の一部であるならば、必ずしも見た目に白色でなくともよい。そのような光源の例としては、ハロゲンランプやキセノンランプが挙げられる。また、複数色の光源を混色させて用いてもよい。光源は入力する電源や環境温度により出力が変化するため、電源点灯後２０分〜１時間程度放置した後に輝度の変化が５％／時間以下であることが好ましく、そのようにするために電源に安定化装置が用いられていることが好ましい。
[light source]
The light source is preferably a white light source. The white light source is not particularly limited as long as it has an output in the measurement wavelength range rather than a narrow wavelength range like a laser or LED, and if the measurement wavelength range is part of the visible range, it is not necessarily limited. It does not have to be white in appearance. Examples of such a light source include a halogen lamp and a xenon lamp. Further, a plurality of color light sources may be mixed and used. Since the output of the light source changes depending on the input power supply and the environmental temperature, it is preferable that the change in luminance is 5% / hour or less after leaving the power supply for about 20 minutes to 1 hour. A stabilizing device is preferably used.
［偏光子、検光子］
偏光子には回転機構は特に必要ないが、光軸中心の回転機構があると全方位角測定が可能となるので好ましい。検光子は、その透過軸を偏光子の透過軸とパラニコル又はクロスニコルにする等の必要があるため、光軸中心の回転機構があることが好ましい。
偏光子および検光子としては、分光器を用いるため広い波長域で高い偏光度を有することが望ましい。本発明の方法は、従来の方法に比較して、透過率の絶対値に影響されにくいので偏光度は９５％以上あればよい。この偏光度を有する波長域は３９０〜８００ｎｍであることが特に好ましい。この偏光度を有している限り、偏光子は吸収型偏光子でも反射型偏光子でもよいが、検光子としては吸収型偏光子が好ましい。具体的には、広い波長域で比較的高い偏光度を有するヨウ素系偏光子、二色性色素を用いた二色性色素偏光子、プリズム型偏光子としてグラントムソン型偏光子、グランテーラー型偏光子、その他の偏光子としてワイヤグリッド偏光子、誘電体偏光子等が挙げられ、波長域が広いヨウ素系偏光子とプリズム型偏光子が好ましく、より波長域が広くかつ必要とする偏光度を有するヨウ素系偏光子が特に好ましい。
[Polarizer, Analyzer]
The polarizer does not require a rotation mechanism in particular, but a rotation mechanism about the optical axis is preferable because it enables omnidirectional measurement. It is preferable that the analyzer has a rotation mechanism around the optical axis because the transmission axis of the analyzer needs to be paranicol or crossed Nicol with the transmission axis of the polarizer.
As a polarizer and an analyzer, it is desirable to have a high degree of polarization in a wide wavelength range because a spectroscope is used. Since the method of the present invention is less affected by the absolute value of the transmittance than the conventional method, the degree of polarization may be 95% or more. The wavelength region having this degree of polarization is particularly preferably 390 to 800 nm. As long as it has this degree of polarization, the polarizer may be an absorptive polarizer or a reflective polarizer, but the analyzer is preferably an absorptive polarizer. Specifically, an iodine-based polarizer having a relatively high degree of polarization in a wide wavelength range, a dichroic dye polarizer using a dichroic dye, a Glan-Thompson type polarizer as a prism type polarizer, and a Grand Taylor type polarization Examples of the polarizer and other polarizers include a wire grid polarizer and a dielectric polarizer, and iodine-type polarizers and prism-type polarizers having a wide wavelength range are preferable, and a wider wavelength range and a required degree of polarization are provided. An iodine polarizer is particularly preferred.
［試料台］
偏光子と検光子の間には試料台が配置されているが、試料台は光軸中心の回転機構があることが好ましく、さらに斜め入射時の位相差を測定するために、試料台全体が回転する機構があることが好ましい。
[Sample stand]
A sample stage is arranged between the polarizer and the analyzer, but the sample stage preferably has a rotation mechanism centered on the optical axis, and in order to measure the phase difference at oblique incidence, the entire sample stage is There is preferably a rotating mechanism.
［分光器］
分光器としては、必要な波長範囲の分光が可能で十分な光強度の分解能を有していれば特に限定はない。モノクロメータでスキャンする分光器でも回折格子で分光した光を１次元フォトディテクタアレイで計測するマルチチャンネルタイプ分光器でもよいが、測定時間が短いマルチチャンネルタイプが好ましい。分光器の強度の分解能としてはデジタルならば８ビット以上であることが好ましく、１２ビット以上であることが特に好ましい。また、波長分解能Ｆは位相差の測定精度と対応するため、ＦＷＨＭで１０ｎｍ以下が好ましく、５ｎｍ以下が特に好ましい。さらに、波長板の位相差が測定対象波長λに対してｎλとするとき、Ｆ×ｎは２００ｎｍ以下が好ましく、１００ｎｍ以下がより好ましく、５０ｎｍ以下が最も好ましい。
[Spectrometer]
The spectroscope is not particularly limited as long as it can perform spectroscopy in a necessary wavelength range and has sufficient resolution of light intensity. A spectroscope that scans with a monochromator or a multi-channel type spectroscope that measures light dispersed by a diffraction grating with a one-dimensional photodetector array may be used, but a multi-channel type with a short measurement time is preferable. The resolution of the intensity of the spectroscope is preferably 8 bits or more and particularly preferably 12 bits or more if it is digital. Further, since the wavelength resolution F corresponds to the measurement accuracy of the phase difference, the FWHM is preferably 10 nm or less, and particularly preferably 5 nm or less. Furthermore, when the retardation of the wave plate is nλ with respect to the wavelength λ to be measured, F × n is preferably 200 nm or less, more preferably 100 nm or less, and most preferably 50 nm or less.
［波長板］
位相差測定装置としては、図４のように偏光子と検光子の間に波長板が挿入されていることがさらに好ましい。波長板は試料台の偏光子側に配置しても検光子側に配置してもよい。波長板は光軸を中心とした回転機構と、光軸上から波長板を退避させるための一軸ステージがあることが好ましい。波長板によって、前述の通り小さな位相差の試料を測定することが可能となる。
さらに、光源や分光器にはわずかな偏光依存性があり、それがスペクトル測定に影響する可能性があるため、光源と偏光子の間、および検光子と分光器の間には測定波長域においてなるべく吸収を持たない偏光解消子を挿入することもできる。
[Wave plate]
As the phase difference measuring apparatus, it is more preferable that a wave plate is inserted between the polarizer and the analyzer as shown in FIG. The wave plate may be arranged on the polarizer side of the sample stage or on the analyzer side. It is preferable that the wave plate has a rotation mechanism around the optical axis and a uniaxial stage for retracting the wave plate from the optical axis. With the wave plate, it is possible to measure a sample having a small phase difference as described above.
In addition, light sources and spectrometers have a slight polarization dependence that can affect spectral measurements, so between the light source and the polarizer and between the analyzer and the spectrometer in the measurement wavelength range. It is also possible to insert a depolarizer having as little absorption as possible.
波長板としては、測定波長範囲にピークが見られれば特に限定はないが、測定波長域において０．５以上の整数または半整数との積が前記波長板のレターデーション値を示している波長を２つ以上有していることが好ましい。測定精度との関係から４００〜１００００ｎｍ波長板が好ましく、１２００〜８０００ｎｍ波長板がさらに好ましく、２０００〜６０００ｎｍ波長板が特に好ましい。材料としては一般に延伸したポリマーフィルムや水晶、カルサイトなどの無機結晶が挙げられるが、波長板は測定される位相差の値に直接影響するため、温度や湿度などの環境により変化しにくいものが望ましい。そのような波長板の好ましい例として、水晶、カルサイト、ポリマー延伸フィルムをガラスでサンドイッチしたものなどが挙げられる。 The wavelength plate is not particularly limited as long as a peak is observed in the measurement wavelength range, but the product of the integer or half integer of 0.5 or more indicates the retardation value of the wavelength plate in the measurement wavelength range. It is preferable to have two or more. A 400-10000 nm wavelength plate is preferable from a relationship with measurement accuracy, a 1200-8000 nm wavelength plate is more preferable, and a 2000-6000 nm wavelength plate is particularly preferable. In general, the materials include stretched polymer films, quartz crystals, calcite, and other inorganic crystals. However, the wavelength plate directly affects the measured retardation value, so it is difficult to change depending on the environment such as temperature and humidity. desirable. Preferred examples of such a wave plate include quartz, calcite, and a polymer stretched film sandwiched with glass.
［測定手順］
測定手順の一例を説明する。
入射偏光子は試料台全体の回転軸方向に対して４５度に透過軸を固定する。次に、光軸上に波長板と試料がない状態で検光子を３６０度回転させ、分光器で透過スペクトルを観測しながら、最も透過率の小さい位置と透過率の大きい位置をそれぞれクロスニコル、パラニコル位置として検出する。それらのときの分光スペクトルをそれぞれ、０％、１００％として光学系を較正し、透過率測定ができるようにしてから、検光子をクロスニコルもしくはパラニコルに配置する。以下、クロスニコルで説明する。次いで、標準となる波長板の位相差を測定する。波長板を光軸回転で３６０度回転させて試料の透過率が最小となる角度を検出する。次いで、最小となる角度から４５度回転させ（クロスニコル下における明光位）、分光スペクトルを測定すると図１のようなスペクトルが得られる。このスペクトルに対し、式（１４）の第一要素を用いてフィッティングすることで、位相差を求めることができる。波長板は既知のものを用いてよいので、波長板の遅相軸（屈折率の大きい方の軸で光学軸に対して平行または直交）はあらかじめ既知であるから、最初から遅相軸を４５度傾斜させた状態で分光スペクトルを測定してもよい。
[Measurement procedure]
An example of the measurement procedure will be described.
The incident polarizer fixes the transmission axis at 45 degrees with respect to the rotation axis direction of the entire sample stage. Next, the analyzer is rotated 360 degrees with no wave plate and sample on the optical axis, and the transmission spectrum is observed with a spectroscope while the position with the smallest transmittance and the position with the largest transmittance are crossed Nicols, Detect as paranicol position. The optical system is calibrated by setting the spectrums at that time to 0% and 100%, respectively, so that the transmittance can be measured, and then the analyzer is placed in crossed Nicol or para Nicol. Hereinafter, cross-Nicol will be described. Next, the phase difference of the standard wave plate is measured. The wave plate is rotated 360 degrees by rotating the optical axis, and the angle at which the transmittance of the sample is minimized is detected. Next, when the spectroscopic spectrum is measured by rotating 45 degrees from the minimum angle (bright light level under crossed Nicols), a spectrum as shown in FIG. 1 is obtained. The phase difference can be obtained by fitting the spectrum using the first element of Expression (14). Since a known wave plate may be used, the slow axis of the wave plate (the axis having the higher refractive index, which is parallel or orthogonal to the optical axis) is known in advance. The spectroscopic spectrum may be measured in a state tilted by a predetermined degree.
次いで波長板を光軸上から退避させ、試料を光軸回転で３６０度回転させて試料の透過率が最小となる角度を検出する。次いで波長板を遅相軸を４５度にして挿入し、試料を透過率が最小となる角度から±４５度に設定して２つの分光スペクトルを測定する。この分光スペクトルを波長板のときと同様にしてフィッティングすると、式（１４）に従って波長板＋試料、もしくは波長板−試料（偏光子と検光子とがクロスニコルであり偏光子の透過軸に対して遅相軸が−４５度傾いた試料および偏光子の透過軸に対して遅相軸が４５度傾いた波長板を有する光学系のストークスパラメータとして式（１４）と同様に求められる）の位相差を得ることができる。±４５度の二つの配置のうち、波長板＋試料を得る配置が波長板と試料の遅相軸が一致しているので、これにより試料の遅相軸を識別することができる。以上により、位相差の波長分散と遅相軸の方向を得ることができる。 Next, the wave plate is retracted from the optical axis, and the sample is rotated 360 degrees by rotating the optical axis, and the angle at which the transmittance of the sample is minimized is detected. Next, the wavelength plate is inserted with the slow axis set at 45 degrees, and the sample is set at ± 45 degrees from the angle at which the transmittance is minimized, and two spectrums are measured. When this spectral spectrum is fitted in the same manner as in the case of the waveplate, the waveplate + sample or waveplate-sample (the polarizer and the analyzer are crossed Nicols and the transmission axis of the polarizer is in accordance with equation (14). The phase difference of the optical system having the sample with the slow axis tilted by −45 degrees and the optical system having the wave plate with the slow axis tilted by 45 degrees with respect to the transmission axis of the polarizer is obtained in the same manner as the equation (14). Can be obtained. Of the two arrangements of ± 45 degrees, the arrangement of obtaining the waveplate and the sample has the same slow axis of the waveplate and the sample, so that the slow axis of the sample can be identified. As described above, the wavelength dispersion of the phase difference and the direction of the slow axis can be obtained.
本発明の方法においては、波長板測定後に波長板を退避させ、試料を光軸回転で３６０度回転させて試料の透過率が最小となる角度を検出した後、この配置のままでスペクトルを測定する。これが、位相差の影響がない分光スペクトル（吸収・散乱スペクトル）となる。このまま上記と同様にして波長板挿入状態で試料の±４５度での分光スペクトルを求めるが、フィッティングの前にこの分光スペクトルを吸収・散乱スペクトルで除算することにより、吸収や散乱による透過率のロスを補正する。これにより、吸収や散乱を有する試料でも、精度よく位相差を測定することができる。 In the method of the present invention, after the wave plate measurement, the wave plate is retracted, the sample is rotated 360 degrees by rotating the optical axis, the angle at which the transmittance of the sample is minimized is detected, and then the spectrum is measured in this arrangement. To do. This is a spectral spectrum (absorption / scattering spectrum) that is not affected by the phase difference. The spectral spectrum at ± 45 degrees of the sample is obtained in the same manner as above with the wave plate inserted, but the transmittance loss due to absorption or scattering is obtained by dividing this spectral spectrum by the absorption / scattering spectrum before fitting. Correct. Thereby, even for a sample having absorption or scattering, the phase difference can be accurately measured.
［補正、及びフィッティング手段］
得られたデータを基に、上記（８）式に基づいて、T(λ)をt（λ）で除算して、スペクトルの補正を行い、位相差を決定する。
実際にはt（λ）で除算して得られた補正後のスペクトルT(λ)はさらに式（１６）でフィッティングを行うことが好ましい。すなわち、位相差の波長分散として上記のコーシーの式を用い、さらに光学系のノイズ等に起因する透過率変化を考慮することが好ましい。
[Correction and fitting means]
Based on the obtained data, T (λ) is divided by t (λ) based on the above equation (8) to correct the spectrum and determine the phase difference.
In practice, it is preferable that the corrected spectrum T (λ) obtained by dividing by t (λ) is further subjected to fitting according to equation (16). That is, it is preferable to use the above Cauchy equation as the wavelength dispersion of the phase difference, and to further consider the change in transmittance due to the noise of the optical system.
Tmax(λ)、Tmin(λ)は透過率を補正するためのものであり、波長依存性のない定数でも一次式（１７）でも二次式（１８）でも指数関数（１９）でもよいが、精度上は一次式で十分であるので好ましい。
フィッティングの方法は、例えば科学計測のためのデータ処理入門，南茂夫監修、河田聡編著に記載のような非線形最適化手法や、遺伝的アルゴリズム等を用いることができる。これら手法はフィッティングの際の初期値が重要であるが、精度良くフィッティングするために、式（１６）においてＣ＝０、Tmax=1、Tmin=0として先にフィッティングしたものを初期値として、全パラメータをフィッティングすることが好ましい。フィッティングにおいては、二乗誤差を最小にするのが最もポピュラーであり好ましい。あるいは、各波長ごとの二乗誤差に対し、山谷のピーク位置が重要であるから例えば（５０−Ｔ（λ））の二乗を重み関数として乗じる方法や、吸収・散乱スペクトルの透過率が高い部分が重要であるから例えば吸収・散乱スペクトルを乗じる方法、さらにはそれらの組み合わせなどの手法を用いることが好ましい。 As a fitting method, for example, a non-linear optimization method as described in “Introduction to data processing for scientific measurement”, supervised by Shigeo Minami, edited by Kei Kawada, a genetic algorithm, or the like can be used. In these methods, the initial value at the time of fitting is important. However, in order to perform fitting with high accuracy, the initial fitting is performed using C = 0, Tmax = 1, and Tmin = 0 in Equation (16) as initial values. It is preferable to fit the parameters. In fitting, it is most popular and preferable to minimize the square error. Alternatively, since the peak position of the valley is important for the square error for each wavelength, for example, a method of multiplying the square of (50−T (λ)) as a weight function, or a portion with high transmittance of the absorption / scattering spectrum Since it is important, it is preferable to use a method such as a method of multiplying absorption / scattering spectra, or a combination thereof.
本発明の位相差の決定方法は、上記の順序でなくとも必要な測定データを得ることができれば、上記の方法に限定されない。実際、波長板がない場合でも遅相軸検出はできないが、位相差測定は可能である。また、試料や波長板の光軸上での回転は３６０度でなくとも１８０度でも可能である。さらには、偏光子を４５度以外に配置しても測定は可能であるし、偏光子と検光子がクロスニコルでなくパラニコルでも測定は可能である。 The phase difference determination method of the present invention is not limited to the above method as long as necessary measurement data can be obtained without being in the above order. In fact, even if there is no wave plate, the slow axis cannot be detected, but the phase difference can be measured. Further, the rotation of the sample and the wave plate on the optical axis can be performed at 180 degrees instead of 360 degrees. Furthermore, the measurement can be performed even if the polarizer is arranged at a position other than 45 degrees, and the measurement can be performed even if the polarizer and the analyzer are not crossed Nicols but paranicols.
以下に実施例を挙げて本発明をさらに具体的に説明する。以下の実施例は本発明の趣旨から逸脱しない限り適宜変更することができる。従って、本発明の範囲は以下の具体例に制限されるものではない。 The present invention will be described more specifically with reference to the following examples. The following embodiments can be modified as appropriate without departing from the spirit of the present invention. Therefore, the scope of the present invention is not limited to the following specific examples.
（位相差測定装置の構成）
図４に示す構成の位相差測定装置を用いた。偏光子は４５度に固定し、波長板として図５に示す位相差を有する水晶板を用いた。光源としては、ハロゲンランプ（ＥＤＩ１００ＤＨ，三菱レイヨン製）、偏光子および検光子としてはヨウ素系偏光子（ＨＣ２−８１１８，サンリッツ製）、分光器としてはファイバ型のマルチチャンネル分光器（ＵＳＢ２０００，オーシャンオプティクス社製，Ａ／Ｄ分解能１２ｂｉｔ，波長分解能（ＦＷＨＭ）１．５ｎｍ）を用いた。測定波長範囲は４００〜７００ｎｍとした。
(Configuration of phase difference measuring device)
A phase difference measuring apparatus having the configuration shown in FIG. 4 was used. The polarizer was fixed at 45 degrees, and a quartz plate having a phase difference shown in FIG. 5 was used as a wavelength plate. The light source is a halogen lamp (EDI100DH, manufactured by Mitsubishi Rayon), the polarizer and analyzer are iodine-based polarizers (HC2-8118, manufactured by Sanlitz), and the spectroscope is a fiber-type multichannel spectrometer (USB2000, Ocean Optics). A / D resolution 12 bits, wavelength resolution (FWHM) 1.5 nm). The measurement wavelength range was 400 to 700 nm.
（実施例１、比較例１、参照例１）
５５０ｎｍにおいておよそλ／４の位相差を有する試料を測定した。上述の手順に従って、偏光子と検光子の配置をクロスニコルとし、波長板と試料との遅相軸を偏光子の透過軸に対して４５度に設定して測定を行った。フィッティングとしては、式（１６）および（１７）を用い、最小二乗誤差を与えるものを解とした。実施例１においては、上記のλ／４の位相差を有する試料に緑に着色した位相差を持たないフィルタを重ねたものを試料とした。この試料を波長板のない状態で、光軸回転で３６０度回転させて試料の透過率が最小となる角度を検出した後、この配置のままでスペクトルを測定して、スペクトル補正に用いた。比較例１ではλ／４の位相差を有する試料に緑に着色した位相差を持たないフィルタを重ねたものを試料としたうえで、実施例１で行ったスペクトル補正を行わなかった。参照例１では緑のフィルタを重ねない試料を用い、実施例１で行ったスペクトル補正を行わなかった。実施例１と比較例１のスペクトルを図６に、そのときに測定された位相差の波長分散を図７に、５００、５５０、６００ｎｍにおける位相差の値を表１に示した。フィッティングには非線形最適化の一つとして高速かつ高精度であることが知られているLevenberg-Marquardtのアルゴリズムを用いてコンピュータ上で計算することにより位相差を求めた。
(Example 1, Comparative Example 1, Reference Example 1)
A sample having a phase difference of approximately λ / 4 at 550 nm was measured. According to the above procedure, the measurement was performed with the polarizer and analyzer arranged in crossed Nicols and the slow axis of the wave plate and sample set to 45 degrees with respect to the transmission axis of the polarizer. For fitting, equations (16) and (17) were used, and the solution giving the least square error was used as the solution. In Example 1, a sample in which the above-described sample having a phase difference of λ / 4 was overlapped with a green colored filter having no phase difference was used. The sample was rotated 360 degrees by rotating the optical axis in the absence of a wave plate to detect the angle at which the transmittance of the sample was minimized, and then the spectrum was measured in this arrangement and used for spectrum correction. In Comparative Example 1, a sample having a phase difference of λ / 4 and a filter that does not have a phase difference colored in green were used as a sample, and the spectrum correction performed in Example 1 was not performed. In Reference Example 1, a sample on which the green filter was not overlapped was used, and the spectrum correction performed in Example 1 was not performed. The spectra of Example 1 and Comparative Example 1 are shown in FIG. 6, the chromatic dispersion of the phase difference measured at that time is shown in FIG. 7, and the values of the phase differences at 500, 550 and 600 nm are shown in Table 1. The phase difference was obtained by calculating on the computer using the Levenberg-Marquardt algorithm, which is known to be fast and highly accurate as one of nonlinear optimization.
さらに、二乗誤差の代わりに（５０−Ｔ（λ））の二乗と吸収・散乱スペクトルを両方用いた誤差でもフィッティングを行ったが、ほぼ同様の結果であった。以上の結果より、本発明の方法により、吸収や散乱を有する位相差試料において精度よく位相差が測定できることがわかる。 Further, fitting was performed using an error using both the square of (50-T (λ)) and the absorption / scattering spectrum instead of the square error, but the results were almost the same. From the above results, it can be seen that the phase difference can be measured with high accuracy in the phase difference sample having absorption or scattering by the method of the present invention.
Claims (9)
該試料の位相差の影響がない該試料の分光スペクトルデータを用意すること、
該偏光子の透過軸と該試料の光学軸と該検光子の透過軸との配置を該試料の位相差が検出される配置として測定される少なくとも１つの分光スペクトルを測定すること、
および
前記分光スペクトルデータにより前記分光スペクトルを補正すること
を含む方法。 A method of determining a phase difference of a sample from a spectrum measured by an optical system in which a light source, a polarizer, a sample, an analyzer, and a spectrometer are arranged in this order,
Preparing spectral data of the sample not affected by the phase difference of the sample;
Measuring at least one spectroscopic spectrum measured with an arrangement of the transmission axis of the polarizer, the optical axis of the sample, and the transmission axis of the analyzer as an arrangement in which a phase difference of the sample is detected;
And correcting the spectral spectrum with the spectral data.
（１）偏光子と検光子とをパラニコル配置とし、かつ偏光子の透過軸と試料の光学軸との為す角を０または９０度として分光スペクトルを測定すること、及び
（２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料の光学軸を偏光子の透過軸の為す角を４５度として分光スペクトルを測定すること
（３）（２）で得られるスペクトルにより（１）で得られるスペクトルを補正すること
を含む方法。 A method of determining a phase difference of a sample from a spectrum measured by an optical system in which a light source, a polarizer, a sample, an analyzer, and a spectrometer are arranged in this order,
(1) Measure the spectroscopic spectrum with the polarizer and analyzer in a paranicol arrangement and the angle between the transmission axis of the polarizer and the optical axis of the sample as 0 or 90 degrees; and (2) Polarizer and analyzer. Measure the spectroscopic spectrum with the photon in the paranicol arrangement or the crossed nicol arrangement, and the angle of the optical axis of the sample made by the transmission axis of the polarizer at 45 degrees. Correcting the resulting spectrum.
（１１）試料台上に配置される試料の位相差の影響がない該試料の分光スペクトルデータ；
（１２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料台上に配置される試料の光学軸を偏光子の透過軸の為す角を４５度として測定される分光スペクトル。 An optical system in which a light source, a polarizer, a sample stage, an analyzer, and a spectrometer are arranged in this order, and a phase difference measuring device including means for correcting (12) according to (11) below:
(11) Spectral spectrum data of the sample not affected by the phase difference of the sample placed on the sample stage;
(12) A spectroscopic spectrum measured with the polarizer and the analyzer arranged in a para-Nicol arrangement or a crossed Nicol arrangement, and an angle formed by the transmission axis of the polarizer with the optical axis of the sample arranged on the sample stage being 45 degrees.
（２１）偏光子の透過軸と試料台上に配置された試料の光学軸と該検光子の透過軸との配置を該試料の位相差が検出されない配置として測定された分光スペクトル；
（１２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料台上に配置される試料の光学軸を偏光子の透過軸の為す角を４５度として測定される分光スペクトル。 An optical system in which a light source, a polarizer, a sample stage, an analyzer, and a spectrometer are arranged in this order, and a phase difference measuring device including means for correcting (12) according to (21) below:
(21) A spectral spectrum measured by setting the arrangement of the transmission axis of the polarizer, the optical axis of the sample arranged on the sample stage, and the transmission axis of the analyzer as an arrangement where the phase difference of the sample is not detected;
(12) A spectroscopic spectrum measured with the polarizer and the analyzer arranged in a para-Nicol arrangement or a crossed Nicol arrangement, and an angle formed by the transmission axis of the polarizer with the optical axis of the sample arranged on the sample stage being 45 degrees.
（３１）偏光子と検光子とをパラニコル配置とし、かつ偏光子の透過軸と試料台上に配置される試料の光学軸との為す角を０または９０度として測定される分光スペクトル；
（１２）偏光子と検光子とをパラニコル配置又はクロスニコル配置とし、かつ試料台上に配置される試料の光学軸を偏光子の透過軸の為す角を４５度として測定される分光スペクトル。 A phase difference measuring apparatus including an optical system in which a light source, a polarizer, a sample stage, an analyzer, and a spectrometer are arranged in this order, and means for correcting (12) according to the following (31):
(31) A spectroscopic spectrum measured with a polarizer and an analyzer arranged in a paranicol arrangement, and an angle formed between the transmission axis of the polarizer and the optical axis of the sample placed on the sample stage is 0 or 90 degrees;
(12) A spectroscopic spectrum measured with the polarizer and the analyzer arranged in a para-Nicol arrangement or a crossed Nicol arrangement, and an angle formed by the transmission axis of the polarizer with the optical axis of the sample arranged on the sample stage being 45 degrees.
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| JP2007100362A JP5116345B2 (en) | 2007-04-06 | 2007-04-06 | Phase difference measuring method and apparatus |
| KR1020080030796A KR101460802B1 (en) | 2007-04-06 | 2008-04-02 | Method and apparatus for measuring phase difference |
| CNA200810091808XA CN101281092A (en) | 2007-04-06 | 2008-04-03 | Phase difference measuring apparatus and method |
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Cited By (9)
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| JP2011013140A (en) * | 2009-07-03 | 2011-01-20 | Oji Keisoku Kiki Kk | On-line phase difference measuring instrument for polarizing plate |
| EP2372412A1 (en) | 2010-03-26 | 2011-10-05 | Fujifilm Corporation | Patterned birefringent product |
| EP2404763A2 (en) | 2010-07-09 | 2012-01-11 | Fujifilm Corporation | Counterfeiting prevention device having printing and birefringence pattern |
| EP2413168A1 (en) | 2010-07-28 | 2012-02-01 | Fujifilm Corporation | Birefringence pattern builder |
| WO2012067128A1 (en) | 2010-11-19 | 2012-05-24 | 富士フイルム株式会社 | Double-refraction pattern transfer foil |
| WO2013042737A1 (en) | 2011-09-21 | 2013-03-28 | 富士フイルム株式会社 | Object including latent image |
| WO2013047459A1 (en) | 2011-09-26 | 2013-04-04 | 富士フイルム株式会社 | Variable color display method using phase difference film |
| WO2013047633A1 (en) | 2011-09-28 | 2013-04-04 | 富士フイルム株式会社 | Object having latent image and latent image photography device which photographs same |
| JP2014052317A (en) * | 2012-09-07 | 2014-03-20 | Oji Holdings Corp | Method and device for measuring birefringence of uniaxially oriented article |
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| CN101738369B (en) * | 2008-11-24 | 2011-09-14 | 财团法人工业技术研究院 | Phase difference detection device |
| CN103018213B (en) * | 2011-09-26 | 2015-04-15 | 同济大学 | Method and device for measuring wide spectral transmittance in 0-70-degree incidence of optical film |
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| JPH10332533A (en) * | 1997-06-03 | 1998-12-18 | Unie Opt:Kk | Birefringence evaluation system |
| JP2001141602A (en) * | 1999-11-12 | 2001-05-25 | Unie Opt:Kk | System and method for evaluating double refraction |
| JP2001242040A (en) * | 2000-03-01 | 2001-09-07 | Stanley Electric Co Ltd | Evaluation method for liquid crystal display element |
| WO2002065053A1 (en) * | 2001-02-09 | 2002-08-22 | Otsuka Electronics Co., Ltd. | Method for measuring gap of liquid crystal cell |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2011013140A (en) * | 2009-07-03 | 2011-01-20 | Oji Keisoku Kiki Kk | On-line phase difference measuring instrument for polarizing plate |
| EP2372412A1 (en) | 2010-03-26 | 2011-10-05 | Fujifilm Corporation | Patterned birefringent product |
| EP2404763A2 (en) | 2010-07-09 | 2012-01-11 | Fujifilm Corporation | Counterfeiting prevention device having printing and birefringence pattern |
| EP2413168A1 (en) | 2010-07-28 | 2012-02-01 | Fujifilm Corporation | Birefringence pattern builder |
| WO2012067128A1 (en) | 2010-11-19 | 2012-05-24 | 富士フイルム株式会社 | Double-refraction pattern transfer foil |
| WO2013042737A1 (en) | 2011-09-21 | 2013-03-28 | 富士フイルム株式会社 | Object including latent image |
| WO2013047459A1 (en) | 2011-09-26 | 2013-04-04 | 富士フイルム株式会社 | Variable color display method using phase difference film |
| WO2013047633A1 (en) | 2011-09-28 | 2013-04-04 | 富士フイルム株式会社 | Object having latent image and latent image photography device which photographs same |
| JP2014052317A (en) * | 2012-09-07 | 2014-03-20 | Oji Holdings Corp | Method and device for measuring birefringence of uniaxially oriented article |
Also Published As
| Publication number | Publication date |
|---|---|
| JP5116345B2 (en) | 2013-01-09 |
| KR20080090994A (en) | 2008-10-09 |
| CN101281092A (en) | 2008-10-08 |
| KR101460802B1 (en) | 2014-11-11 |
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