JP5116346B2 - Phase difference measuring device using a spectroscope - Google Patents

Phase difference measuring device using a spectroscope Download PDF

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JP5116346B2
JP5116346B2 JP2007100363A JP2007100363A JP5116346B2 JP 5116346 B2 JP5116346 B2 JP 5116346B2 JP 2007100363 A JP2007100363 A JP 2007100363A JP 2007100363 A JP2007100363 A JP 2007100363A JP 5116346 B2 JP5116346 B2 JP 5116346B2
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phase difference
wavelength
wave plate
polarizer
measurement
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JP2008256591A (en
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一郎 網盛
史生 小畑
弘毅 高橋
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Fujifilm Corp
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01Arrangements or apparatus for facilitating the optical investigation
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41Refractivity; Phase-affecting properties, e.g. optical path length
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/60Specific applications or type of materials
    • G01N2223/605Specific applications or type of materials phases
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/01Indexing codes associated with the measuring variable
    • G01N2291/012Phase angle

Description

本発明は位相差測定装置に関し、特に小さい位相差の精度の高い決定が可能な位相差測定装置に関する。   The present invention relates to a phase difference measuring device, and more particularly to a phase difference measuring device capable of determining a small phase difference with high accuracy.

位相差測定装置は液晶ディスプレイ(LCD)用の位相差フィルム評価や、光ディスク、プラスチック等の光学素子の品質管理などで利用されてきている。従来の位相差測定装置では主に単色光を用いた測定が行われていたが、近年は特にLCDのように可視光全域に渡る特性が重要となってきたことから、位相差の波長依存性測定のニーズが高まっている。
位相差は、エリプソメトリによる偏光解析を用いて測定することにより精度よく測定することができる。しかしながら、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が必要であり、原理的に複雑で高価な方法である。さらに、単一波長での測定データを基にする方法であるため、位相差の波長分散測定が必要な場合は、モノクロメータなどで波長スキャンすることになるため高速測定ができないという問題がある。
The phase difference measuring apparatus has been used for phase difference film evaluation for a liquid crystal display (LCD), quality control of optical elements such as optical discs and plastics. Conventional phase difference measurement equipment mainly uses monochromatic light, but in recent years, characteristics over the entire visible light area, such as LCDs, have become important. The need for measurement is increasing.
The phase difference can be accurately measured by measuring using ellipsometry ellipsometry. However, ellipsometry is a mechanism for rotating a polarizer and a compensator at high speed, or a method for modulating polarization or phase such as a photoelastic modulator (PEM) or a left and right circularly polarized heterodyne interferometry, and for processing the acquired data at high speed This is a complicated and expensive method in principle. Furthermore, since this method is based on measurement data at a single wavelength, there is a problem that when wavelength dispersion measurement of a phase difference is necessary, wavelength scanning is performed with a monochromator or the like, so that high-speed measurement cannot be performed.

安価な位相差測定装置としては、例えば非特許文献1や特許文献1及び2に開示されるように、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決定する方法が知られている。この方法により必要とする波長範囲において、位相差を測定することができ、また位相差の波長分散も簡便に判断することができる。しかしながら、原理的に位相差干渉によって、測定波長域内で分光スペクトルの山と谷が観測されている必要があるこの方法は、数十nm程度以下の小さい位相差を測定するのに不向きであった。また、通常の分光光度計はモノクロメータで波長スキャンするため、測定時間も長かった。
Westら,Journal of Optical Society of America,vol.39,p.791−794(1949). 特許第3777659号 特公平5−18370号公報
As an inexpensive phase difference measurement apparatus, for example, as disclosed in Non-Patent Document 1 and Patent Documents 1 and 2, a method of determining a phase difference using a spectrum obtained by a spectrophotometer or the like is known. . By this method, the phase difference can be measured in the required wavelength range, and the wavelength dispersion of the phase difference can be easily determined. However, in principle, this method, in which peaks and valleys of the spectrum are required to be observed in the measurement wavelength range due to phase difference interference, is not suitable for measuring a small phase difference of about several tens of nanometers or less. . In addition, since a normal spectrophotometer scans a wavelength with a monochromator, the measurement time is long.
West et al., Journal of Optical Society of America, vol. 39, p. 791-794 (1949). Japanese Patent No. 3777659 Japanese Patent Publication No.5-18370

本発明は小さい位相差を簡便に精度よく測定できる位相差測定装置の提供を課題とする。   An object of the present invention is to provide a phase difference measuring apparatus that can easily and accurately measure a small phase difference.

すなわち、本発明は下記[1]〜[7]を提供するものである。
[1]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と、計算手段とを含む位相差測定装置であって、
波長板が、偏光子と検光子の間に配置されており、かつ
測定波長域内の2つ以上の波長それぞれにおいて、該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位相差測定装置。
[2] 前記分光器のFWHMで定義される分解能Fと前記の整数または半整数が取り得る最大値n1とが以下の条件(B)を満たす[1]に記載の位相差測定装置。
(B)F×n1≦50nm
That is, the present invention provides the following [1] to [7].
[1] 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 a calculation means,
A wave plate is disposed between the polarizer and the analyzer, and the retardation value of the wave plate is divided by an integer of 0.5 or more or a half integer at each of two or more wavelengths within the measurement wavelength range. A phase difference measuring device whose value matches the wavelength.
[2] The phase difference measuring apparatus according to [1], wherein the resolution F defined by the FWHM of the spectroscope and the maximum value n1 that the integer or half integer can take satisfy the following condition (B).
(B) F × n1 ≦ 50 nm

[3] 前記波長板のレターデーション値が、前記測定波長域の下限波長λminにおいて3×λmin以上である[1]または[2]に記載の位相差測定装置。
[4] 前記波長板が光軸に対して挿入と退避を行う手段を具備する[1]〜[3]のいずれか一項に記載の位相差測定装置。
[5] 前記分光器が、回折格子と1次元の受光アレイからなるマルチチャンネル分光器である[1]〜[4]のいずれか一項に記載の位相差測定装置。
[3] The retardation measuring device according to [1] or [2], wherein the retardation value of the wave plate is 3 × λ min or more at a lower limit wavelength λ min of the measurement wavelength region.
[4] The phase difference measuring apparatus according to any one of [1] to [3], wherein the wavelength plate includes means for inserting and retracting with respect to an optical axis.
[5] The phase difference measuring apparatus according to any one of [1] to [4], wherein the spectrometer is a multichannel spectrometer including a diffraction grating and a one-dimensional light receiving array.

[6]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る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、
0.5以上の整数または半整数nxとの積λxxが波長板のレターデーション値を示す波長λxが測定波長域λmin〜λmaxにおいて2つ以上存在する波長板を選択し、
該波長板を偏光子と検光子との間に配置することを含む方法。
[7] 前記波長板と試料の光学軸とを分光スペクトル測定時に一致又は直交させる[6]に記載の方法。
[6] 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,
Select the wave plate product lambda x n x is the wavelength lambda x showing a retardation value of the wavelength plate with 0.5 or more integer or half-integer n x there are two or more in the measurement wavelength range Ramudamin~ramudamax,
Placing the waveplate between a polarizer and an analyzer.
[7] The method according to [6], wherein the wavelength plate and the optical axis of the sample are made coincident or orthogonal at the time of spectral measurement.

本発明により、小さい位相差を簡便に精度よく測定することが可能な位相差測定装置が提供される。   According to the present invention, there is provided a phase difference measuring apparatus capable of easily and accurately measuring a small phase difference.

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、本発明の測定装置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 measuring apparatus 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 with respect to the arrangement of the polarizer and the analyzer without the sample. 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。

Figure 0005116346
If the transmission axis of the polarizer is the reference direction (0 degree),
The Mueller matrix Mp of the polarizer is described as in equation (1).
Figure 0005116346

同様に検光子のミューラー行列Maは式(2)のように記述される。

Figure 0005116346
Similarly, the Mueller matrix Ma of the analyzer is described as shown in Equation (2).
Figure 0005116346

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。

Figure 0005116346
The Mueller matrix Mr of the retardation film whose optical axis is inclined by 45 degrees with respect to the transmission axis of the polarizer is described as in Expression (3).
Figure 0005116346

ここで、Γは式(4)で表される値である。

Figure 0005116346
Here, Γ is a value represented by Expression (4).
Figure 0005116346

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。
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.
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).

Figure 0005116346
Figure 0005116346

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   The first component of the above formula Sout is the light transmittance. That is, the light transmittance T (λ) is expressed by the following equation (6).

Figure 0005116346
Figure 0005116346

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)の分光透過スペクトルの例を示す。
また、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 (transmittance 0%), and when Re / λ is a half integer, 1 (transmittance 100%). FIG. 1 shows an example of the spectral transmission spectrum of a sample (film) with Re = 2000 nm.
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).

Figure 0005116346
Figure 0005116346

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は、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 (transmittance 0%) when Re / λ is an integer, and 1 (transmittance 100%) when Re / λ is a half integer.
Therefore, when the polarizer, the sample, and the analyzer have any of the above arrangements, the wavelength at the valley position (transmittance 0%) and the wavelength at the peak position (transmittance 100%) in the spectral spectrum It can be seen that the value of the phase difference Re can be obtained by reading.

[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 times 400 nm, but one-fifth of 2000 nm is about 363 nm. Therefore, the peak of the mountain seen at 400 nm of the sample having this wavelength dispersion is outside the graph in FIG. The peak of the peak that should exist at 363 nm is shifted to the long wave side due to the increase in phase difference. Since the wavelength dispersion of the phase difference can be described by the Cauchy dispersion formula, it is preferable to use the Cauchy dispersion formula to obtain the phase difference by fitting from the transmission spectrum.

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)を表すのに用いられ、式(8)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 (8).

Figure 0005116346
Figure 0005116346

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(*)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 (*), as with the refractive index.

Figure 0005116346
Figure 0005116346

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。ピークが観測されていないスペクトルを用い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 is reduced in this way, neither half-integer multiple nor integer multiple is observed in the measurement wavelength range, so that no peak is seen in the spectrum. Theoretically, the phase difference can be obtained using 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. Therefore, the accuracy of the calculated phase difference is affected.

本発明の装置においては、測定波長範囲の分光スペクトルにピークが観測される状態とするため、波長板を利用する。例えば、試料の光学軸と光学軸の一致した既知の波長板を挿入することができる。
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(10)のようになる。
In the apparatus of the present invention, a wavelength plate is used in order to obtain a state in which a peak is observed in the spectrum of the measurement wavelength range. For example, it is possible to insert a known wave plate whose optical axis coincides with the optical axis of the sample.
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 (10).

Figure 0005116346
Figure 0005116346

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(11)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 (11).

Figure 0005116346
であり、Rewpは波長板の位相差を表す。
Figure 0005116346
Re wp represents the phase difference of the wave plate.

すなわち光の透過率T(λ)は下記の式(12)で表される。 That is, the light transmittance T (λ) is expressed by the following equation (12).

Figure 0005116346
Figure 0005116346

式(12)からわかるように、本発明の装置では波長板によって位相差が底上げされる。試料の位相差は、測定波長範囲においてスペクトルにピークを検出し、測定された位相差を決定後、波長板の位相差を差し引くことで算出すればよい。 As can be seen from equation (12), in the apparatus of the present invention, the phase difference is raised by the wave plate. The phase difference of the sample may be calculated by detecting a peak in the spectrum in the measurement wavelength range, determining the measured phase difference, and subtracting the phase difference of the wave plate.

[位相差測定装置]
次に本発明の位相差測定装置の概要を説明する。本発明の位相差測定装置は、光源、偏光子、試料台、検光子、分光器を含み、これらは図3に示す順で配置されていることが好ましい。また、位相差測定装置は上述の波長板を含み、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。計算手段としては、コンピュータ上でソフトウェアとして解析する方法や、メモリや演算プロセッサを搭載した専用のボードで解析する方法、あるいはピーク等の特徴的な箇所を人力で計算可能な数点ピックアップし、その値が一致するように自ら位相差を決定する手段が挙げられる。
[Phase difference measuring device]
Next, the outline of the phase difference measuring apparatus of the present invention will be described. The phase difference measuring apparatus of the present invention includes a light source, a polarizer, a sample stage, an analyzer, and a spectrometer, and these are preferably arranged in the order shown in FIG. Further, the phase difference measuring apparatus includes the above-described wave plate, and further includes an optical signal analyzing apparatus and the like as calculation means for performing the above correction, fitting and the like. As a calculation means, a method of analyzing as software on a computer, a method of analyzing with a dedicated board equipped with a memory and an arithmetic processor, or picking up several points that can be manually calculated for characteristic points such as peaks, etc. There is a means for determining the phase difference by itself so that the values match.

[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、レーザーや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 such as a laser or LED. If the measurement wavelength range is a part of the visible range, it is not always visible. It does not have to be white. 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。本発明の位相差測定装置は従来の装置に比較して、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, but a rotation mechanism about the optical axis is preferable because it allows 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 region because a spectroscope is used. Since the phase difference measuring apparatus of the present invention is less affected by the absolute value of the transmittance than the conventional apparatus, 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 polarizer as a prism polarizer, and a Grand Taylor 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 have a wider wavelength range and a required degree of polarization. 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.

[波長板]
波長板は試料台の偏光子側に配置しても(図4)、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。
前記波長板は、前記波長板は、0.5以上の整数または半整数であるnxとの積λxxが前記波長板のレターデーション値を示している波長λxを測定波長域λmin〜λmaxにおいて2つ以上有する。すなわち、波長板としては測定波長域のスペクトルにおいて少なくとも山1つおよび谷1つを有する波長板を選択する。
[Wave plate]
The wave plate may be disposed on the polarizer side of the sample stage (FIG. 4) 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.
The wave plate, the wave plate, measurement wavelength range λmin~ wavelength λx the product lambda x n x and n x is 0.5 or more integer or half-integer indicates the retardation value of the wavelength plate Two or more at λmax. That is, as the wave plate, a wave plate having at least one peak and one valley in the spectrum of the measurement wavelength region is selected.

上記の条件を満たす波長板につき、波長板の位相差(波長分散を考慮しない値であってもよい)と測定波長域とから、nxがとり得る最大値n1及び最小値n2は以下のように決めることができる。波長板の位相差をλmaxおよびλminにおいてそれぞれの波長で割った値をnmax、nminとする。n1はnminより小さくて最も近い整数または半整数である。n2はnmaxよりも大きくて最も近い整数または半整数である。これは、波長板のみの分光スペクトル、即ち本発明の位相差測定装置で空気を測定したときの分光スペクトルの測定波長範囲の両側に存在する山または谷のピークの次数(nx)と一致する。 Per above conditions are satisfied wavelength plate, a retardation wave plate (which may be a value without consideration of wavelength dispersion) and the measurement wavelength range, the maximum value n1 and the minimum value n2 which n x can take the following Can be decided. Values obtained by dividing the retardation of the wave plate by the respective wavelengths at λmax and λmin are defined as nmax and nmin. n1 is an integer or a half integer that is smaller than and smaller than nmin. n2 is an integer or half integer that is greater than nmax and is closest. This coincides with the order of peaks (n x ) of peaks or valleys existing on both sides of the spectral spectrum of the wavelength plate alone, that is, when the air is measured with the phase difference measuring device of the present invention. .

波長板のn2は0.5以上であり、1.0以上が好ましく、5以上がより好ましい。
通常波長板の位相差はλmin以上であることが好ましく、λmin×3以上であることがより好ましく、λmin×5以上であることがさらに好ましい。すなわち測定波長域が400nm〜である場合、400nm程度以上であることが好ましく、1200nm程度以上であることがより好ましく、2000nm程度以上であることがさらに好ましい。
N2 of the wave plate is 0.5 or more, preferably 1.0 or more, and more preferably 5 or more.
Usually, the retardation of the wave plate is preferably λmin or more, more preferably λmin × 3 or more, and further preferably λmin × 5 or more. That is, when the measurement wavelength region is 400 nm or more, it is preferably about 400 nm or more, more preferably about 1200 nm or more, and further preferably about 2000 nm or more.

波長板の位相差は大きすぎると逆に問題となる。クロスニコルの測定ではΓがπの偶数倍のときに谷のピークを与える。例えばΓ=2nπとするとき、Re=nλpeakとなる。つまり、ピーク位置λpeakは式(13)となる。   On the contrary, if the retardation of the wave plate is too large, a problem arises. In the crossed Nicols measurement, a valley peak is given when Γ is an even multiple of π. For example, when Γ = 2nπ, Re = nλpeak. That is, the peak position λpeak is expressed by Equation (13).

Figure 0005116346
この分光スペクトルで見られるピーク位置λpeakは、波長による位相差の変化によってシフトするが、そのシフト量は式(14)のように記述される。
Figure 0005116346
The peak position λpeak seen in this spectroscopic spectrum is shifted by the change of the phase difference depending on the wavelength, and the shift amount is described as in the equation (14).

Figure 0005116346
Figure 0005116346

式(14)から、位相差の変化によるピークシフトはnが大きくなるにつれて小さくなることが分かる。このことから、位相差が大きな波長板を使うとスペクトルのシフト量が小さくなり、測定精度が低下することが分かる。   From equation (14), it can be seen that the peak shift due to the change in phase difference decreases as n increases. From this, it can be seen that when a wave plate having a large phase difference is used, the shift amount of the spectrum is reduced and the measurement accuracy is lowered.

また、測定精度は分光器の波長分解能にも依存する。高い波長分解能の分光器ならばわずかなピークシフトでも十分な精度で検出できる。分光器の波長分解能は、通常FWHM(Full Width Half Maximum)で表し、ピーク位置検出精度としては分光器に用いられるディテクタの強度分解能にもよるがおよそ100分の1は検出可能である。従って、FWHMがFの分光器により波長板の位相差が特定の測定波長のn倍のものを用いる場合、該測定波長において測定位相差精度が±Anm必要ならば、光学系のスペックとしては式(15)を満たせばよい。
F×n≦A×200nm (15)
例えば、測定位相差精度が±0.25nm必要であれば
F×n≦50nm
を満たせばよい。
The measurement accuracy also depends on the wavelength resolution of the spectrometer. A spectroscope with high wavelength resolution can detect even a slight peak shift with sufficient accuracy. The wavelength resolution of the spectroscope is usually expressed by FWHM (Full Width Half Maximum), and the peak position detection accuracy can be detected by about 1 / 100th depending on the intensity resolution of the detector used in the spectroscope. Therefore, when using a spectroscope whose FWHM is F and the wave plate has a phase difference n times the specific measurement wavelength, if the measurement phase difference accuracy is ± A nm at the measurement wavelength, the optical system specifications are (15) may be satisfied.
F × n ≦ A × 200 nm (15)
For example, if the measurement phase difference accuracy is ± 0.25 nm, F × n ≦ 50 nm
Should be satisfied.

さらに、F×nは30nm以下がより好ましく、20nm以下が最も好ましい。
装置としては、nとしてn1を選択して上記式(15)を判断することが好ましい。
上記2点および市販の分光器のFWHMを考慮すると、n1が33以下となる波長板が好ましく、15以下となる波長板がより好ましい。しかしながら、市販の波長板の厚さなどを考慮すると、波長板の位相差は通常10000nm程度以下であることが好ましく、8000nm程度以下であることがより好ましく、6000nm程度以下であることがさらに好ましい。
波長板の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は、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。
Furthermore, F × n is more preferably 30 nm or less, and most preferably 20 nm or less.
As an apparatus, it is preferable that n1 is selected as n and the above equation (15) is determined.
In consideration of the above two points and the FWHM of a commercially available spectroscope, a wave plate with n1 of 33 or less is preferable, and a wave plate with 15 or less is more preferable. However, considering the thickness of a commercially available wave plate, the retardation of the wave plate is usually preferably about 10,000 nm or less, more preferably about 8000 nm or less, and further preferably about 6000 nm or less.
The material of the wave plate generally includes stretched polymer film, inorganic crystals such as quartz and calcite, but the wave plate directly affects the measured retardation value, so it changes depending on the environment such as temperature and humidity. Difficult things are desirable. Preferable examples of such a wave plate include quartz, calcite, and a polymer stretched film sandwiched with glass.

[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。
[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.

[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(7)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 (7). 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(11)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(11)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 wave plate, the wave plate + sample, or wave plate-sample (the polarizer and the analyzer are crossed Nicols according to the equation (11), and the transmission axis of the polarizer is used. The Stokes parameter of an optical system having a sample whose slow axis is tilted by −45 degrees and a wave plate whose slow axis is tilted by 45 degrees with respect to the transmission axis of the polarizer is obtained in the same manner as in equation (11). A phase difference 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.

吸収や散乱を有する試料の場合、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して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)を得てもよい。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位相差の影響がない分光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とができる。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 case of a sample having absorption or scattering, after the wave plate measurement, the wave plate is retracted, and the sample is rotated 360 degrees by rotating the optical axis to detect the angle at which the transmittance of the sample is minimized, and the spectrum is kept in this arrangement. May be obtained to obtain a 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 described above with the wave plate inserted, but by dividing this spectral spectrum by the spectral spectrum that is not affected by the phase difference before fitting, Transmission loss can be corrected. 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]
実際には位相差の波長分散として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し、式(16)を用いてフィッティングすることが好ましい。
[Correction and fitting means]
In practice, it is preferable to use Cauchy's equation as the wavelength dispersion of the phase difference, and to perform fitting using Equation (16), taking into account the change in transmittance due to noise in the optical system.

Figure 0005116346
Figure 0005116346

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。   Tmax (λ) and Tmin (λ) are for correcting the transmittance, and may be constants having no wavelength dependency, linear expressions (17), quadratic expressions (18), or exponential functions (19). In terms of accuracy, a linear expression is sufficient, which is preferable.

Figure 0005116346
Figure 0005116346

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, the peak position of the valley is important for the square error of 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 is important. Therefore, it is preferable to use a method such as a method of multiplying absorption / scattering spectra, or a combination thereof.

本発明の位相差測定装置は、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。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 measuring apparatus of the present invention is not limited to the above method as long as necessary measurement data can be obtained even if it is not in the above order. 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3つの水晶板を用いた。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 three quartz plates having the phase difference shown in FIG. 5 were used as wavelength plates. 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 spectrometer 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、2)
550nmにおいておよそλ/4の位相差を有する試料をn=10で測定した。550nmにおいて約10λのレターデーションを有する波長板を用いたものを実施例1、550nmにおいて約2λのレターデーションを有する波長板を用いたものを実施例2、550nmにおいて約λ/4のレターデーションを有する波長板を用いたものを比較例1とした。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。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。実施例1、2と比較例1のn1、n2およびF×n1を表1に、実施例1、2と比較例1において測定された450、550、650nmにおける位相差の平均値を表2に、標準偏差を表3に示した。
(Example 1, Comparative Examples 1 and 2)
A sample having a phase difference of approximately λ / 4 at 550 nm was measured at n = 10. Example 1 using a wave plate having a retardation of about 10λ at 550 nm Example 1 using a wave plate having a retardation of about 2λ at 550 nm Example 2 Using a wave plate having a retardation of about 2λ at 550 nm What used the wave plate which it has was made into the comparative example 1. 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. 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. N1, n2 and F × n1 of Examples 1 and 2 and Comparative Example 1 are shown in Table 1, and average values of phase differences measured at 450, 550 and 650 nm measured in Examples 1, 2 and Comparative Example 1 are shown in Table 2. Standard deviations are shown in Table 3.

Figure 0005116346
Figure 0005116346

Figure 0005116346
Figure 0005116346

Figure 0005116346
Figure 0005116346

表2より、実施例1、2は位相差が正しい値であったのに対し、比較例1の位相差は実際のサンプルの値から明らかにずれていた。しかも、表3から分かるように比較例3は測定ごとに大きく異なる結果であった。また、実施例1および2では550nm付近では同程度の繰り返し精度であるが、450および650nm付近では実施例1の方が優れた繰り返し精度であった。これは、測定される分光スペクトルのピークの数が圧倒的に実施例1の方が多いことに起因する。以上の結果より、本発明の位相差装置により、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分かる。   From Table 2, the phase differences in Examples 1 and 2 were correct values, whereas the phase difference in Comparative Example 1 was clearly deviated from the actual sample values. Moreover, as can be seen from Table 3, Comparative Example 3 had a result that varied greatly for each measurement. In Examples 1 and 2, the repetition accuracy was about the same in the vicinity of 550 nm, but in the vicinity of 450 and 650 nm, the repetition accuracy of Example 1 was superior. This is due to the fact that Example 1 has an overwhelmingly larger number of measured spectral peaks. From the above results, it can be seen that the phase difference can be accurately measured in the phase difference sample having absorption or scattering by the phase difference device of the present invention.

本発明の位相差測定における分光スペクトルの原理的な図である。It is a fundamental figure of the spectrum in the phase difference measurement of this invention. 本発明の位相差測定における小さな位相差の試料に対する分光スペクトルの原理的な図である。It is a fundamental figure of the spectral spectrum with respect to the sample of a small phase difference in the phase difference measurement of this invention. 本発明の位相差測定装置における光源、偏光子、試料台、検光子、分光器の好ましい配置を示す概略図である。It is the schematic which shows the preferable arrangement | positioning of the light source in the phase difference measuring apparatus of this invention, a polarizer, a sample stand, an analyzer, and a spectrometer. 本発明の位相差測定装置の概略図である。It is the schematic of the phase difference measuring apparatus of this invention. 本発明の実施例に用いた波長板の位相差の波長分散である。It is wavelength dispersion of the phase difference of the waveplate used for the Example of this invention.

Claims (7)

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と、計算手段とを含む位相差測定装置であって、
波長板が、偏光子と検光子の間に配置されており、
測定波長域内の2つ以上の波長それぞれにおいて、該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し、
前記波長板のレターデーション値が、前記測定波長域の下限波長λminにおいて3×λmin以上であり、かつ
前記分光器のFWHMで定義される分解能Fと前記の整数または半整数が取り得る最大値n1とが以下の条件(B)を満たす位相差測定装置:
(B)F×n1≦50nm。
A phase difference measuring device 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 a calculation means,
A wave plate is disposed between the polarizer and the analyzer,
In each of two or more wavelengths in the measurement wavelength range, the value obtained by dividing the retardation value of the wave plate by an integer of 0.5 or more or a half integer matches the wavelength ,
The retardation value of the wave plate is 3 × λ min or more at the lower limit wavelength λ min of the measurement wavelength range, and
A phase difference measuring apparatus in which the resolution F defined by the FWHM of the spectroscope and the maximum value n1 that the integer or half integer can take satisfy the following condition (B):
(B) F × n1 ≦ 50 nm.
前記測定波長域が400nm〜700nmを含み、かつ前記波長板のレターデーション値が1200nm以上10000nm以下である請求項1に記載の位相差測定装置。The phase difference measurement apparatus according to claim 1, wherein the measurement wavelength region includes 400 nm to 700 nm, and the retardation value of the wave plate is 1200 nm or more and 10,000 nm or less. 前記波長板が光軸に対して挿入と退避を行う手段を具備する請求項1または2に記載の位相差測定装置。 The phase difference measuring apparatus according to claim 1, wherein the wavelength plate includes means for inserting and retracting the optical plate with respect to the optical axis. 前記分光器が、回折格子と1次元の受光アレイからなるマルチチャンネル分光器である請求項1〜3のいずれか一項に記載の位相差測定装置。 The phase difference measuring apparatus according to any one of claims 1 to 3, wherein the spectroscope is a multi-channel spectroscope including a diffraction grating and a one-dimensional light receiving array. 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る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、
0.5以上の整数または半整数nxとの積λxxが波長板のレターデーション値を示す波長λxが測定波長域λmin〜λmaxにおいて2つ以上存在する波長板を選択し、
該波長板を偏光子と検光子との間に配置することを含み、
前記波長板のレターデーション値が、前記測定波長域の下限波長λminにおいて3×λmin以上であり、
前記分光器のFWHMで定義される分解能Fとn x が取り得る最大値n1とが以下の条件(B)を満たす方法:
(B)F×n1≦50nm。
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,
Select the wave plate product lambda x n x is the wavelength lambda x showing a retardation value of the wavelength plate with 0.5 or more integer or half-integer n x there are two or more in the measurement wavelength range Ramudamin~ramudamax,
It looks including placing a wavelength plate between the polarizer and the analyzer,
The retardation value of the wave plate is 3 × λ min or more at the lower limit wavelength λ min of the measurement wavelength range,
How the maximum value n1 resolution F and n x being defined by the spectrometer FWHM can take satisfy the following condition (B):
(B) F × n1 ≦ 50 nm.
前記測定波長域が400nm〜700nmを含み、かつ前記波長板のレターデーション値が1200nm以上10000nm以下である請求項5に記載の方法。The method according to claim 5, wherein the measurement wavelength region includes 400 nm to 700 nm, and the retardation value of the wave plate is 1200 nm or more and 10,000 nm or less. 前記波長板と試料の光学軸とを分光スペクトル測定時に一致又は直交させる請求項5または6に記載の方法。 The method according to claim 5 or 6, wherein the wavelength plate and the optical axis of the sample are made coincident or perpendicular to each other at the time of spectral measurement.
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