JP4923255B2 - Method for measuring diameter of cylindrical body, refractive index, distance between central axes, and angle formed between incident optical axis and apparatus using the same - Google Patents

Description

  The present invention relates to a nanocarbon tube, an optical fiber, a plated wire, a vapor deposition wire, a string of straws, etc., in which a plurality of small-diameter cylinders are arranged in parallel or coaxially. The present invention relates to a measuring method for simultaneously measuring the distance between the central axes and the angle formed between the incident optical axis and an apparatus using the measuring method.

As a method for obtaining the diameter of the thin cylindrical body, it is possible to measure a fiber having an outer diameter of about 10 μm in Patent Document 1 by measuring the outer diameter during fiber production based on the ratio of the diffraction intensity of laser light. It is shown.
Patent Documents 2 and 3 disclose that a thin line having an outer diameter of 17.5 μm can be measured by a method of calculating the outer diameter from the diffraction pattern of the Fraunhofer diffraction image of the thin line to be measured by laser light. Yes.

However, there was no effective measurement method when measuring the outer diameter of a small-diameter cylindrical body on the order of nm.
Therefore, as shown in Non-Patent Document 1, the present inventors use a laser beam obtained by polarizing a laser beam vertically or horizontally with respect to the object to be measured, and measure the scattering intensity by the object to be measured. We developed a method to measure the outer diameter and refractive index from the deviation from the calculated value based on the base. According to this method, it was shown that a thin cylindrical body having an outer diameter of about 240 nm can be measured.

  Furthermore, the present inventors have proposed the measuring method and measuring apparatus shown in Patent Document 4 as a method for measuring the outer diameter and refractive index of a nanofiber having a smaller diameter. By using this method, it is possible to measure the outer diameter of nanofibers as thin as about 90 nm.

JP-A-5-45130 JP-A-6-288723 JP-A-6-241733 Fumiaki Tajima, Yoshiro Nishiyama, “Examination of the possibility of measuring the thickness and refractive index of a spider thread with a thickness of about 120 nm”, Proceedings of the 64th Annual Meeting of the Japan Society of Applied Physics, Japan Society of Applied Physics, March 2004 JP 2006-242591 A

In the outer diameter measuring method proposed in Patent Document 4 by the present inventors, the outer diameter measurement of a nanofiber having a smaller diameter is performed as compared with the measuring methods shown in Patent Document 1 to Patent Document 3 and Non-Patent Document 1. Is possible.
However, tube-shaped cylinders such as nanocarbon tubes know their inner diameter, and coaxial cylinders such as optical fibers that have a core and a clad disposed on the outer periphery of the core have a diameter and light of the core. Controlling the diameter of the fiber itself, the eccentricity of the core, the individual refractive index, and the like are important factors for improving the characteristics, and it is necessary to know these values.
In addition, it is possible to know the dimensions, refractive index, etc. in the method of directly knowing the thickness of the coating layer of a cylindrical body having a coating layer on the outer periphery of a plated wire, etc., and in the elucidation of biological structures such as nerve fibers taking a composite structure. It is desired.
Therefore, the present invention provides a measuring method for measuring these with high accuracy and efficiency, and an apparatus using the measuring method.

Measuring method according to the present invention, the parallel-polarized light polarized parallel to the length direction of the plurality of cylindrical bodies central axis has a parallel relationship projected on the plurality of cylindrical bodies, each of said plurality of cylinder The scattering angle and scattered light intensity of the scattered light generated by reflecting a part of the parallel polarized light are measured at a plurality of observation points arranged on the circumference around the plurality of cylindrical bodies. A plurality of calculations based on an equation considering multiple scattering between cylinders from the distance from the observation point to the center of the cylinder and the scattering angle for each cylinder when the scattering intensity is measured The scattered light intensity is calculated, and from the plurality of measured scattered light intensities obtained by the measurement and the calculated plurality of calculated scattered light intensities, the individual diameters, refractive indexes, central axis distances and Calculate the deviation index expressed as a function of the angle between the incident optical axis and the interval. Deriving individual diameters, refractive indices, central axis distances and angles formed by the intervals between the incident optical axes and the individual cylinder diameters and refractions to minimize the deviation index. rate, determine the angle between the center axis distance and the incident optical axis and the distance, the diameter of the cylindrical body, the refractive index, a method for measuring the angle of the central axis between the distance and the incident optical axis and distance.

Another measuring method according to the present invention is to project the parallel-polarized light polarized parallel to the length direction of the plurality of cylindrical bodies having the same central axis in said plurality of cylinder, said plurality of cylinder The scattering angle and the scattered light intensity of the scattered light generated by reflecting a part of the parallel polarized light individually are measured at a plurality of observation points arranged on the circumference around the plurality of cylindrical bodies, When measuring the measured scattering intensity, from the distance from the observation point for each cylindrical body to the center of the cylindrical body and the scattering angle for each cylindrical body, a plurality of formulas based on the multiple scattering between the cylindrical bodies are considered. The calculated scattered light intensity is calculated, and from the plurality of measured scattered light intensities obtained by the measurement and the calculated calculated scattered light intensities, the individual diameter, refractive index, and center axis distance of the plurality of cylindrical bodies And a deviation index expressed as a function of the angle between the incident optical axis and the interval is calculated. Deriving individual diameters, refractive indices, central axis distances and angles formed by the intervals between the incident optical axes and the individual cylinder diameters and refractions to minimize the deviation index. rate, determine the angle between the center axis distance and the incident optical axis and the distance, the diameter of the cylindrical body, the refractive index, a method for measuring the angle of the central axis between the distance and the incident optical axis and distance.

In the above three measurement methods, vertically polarized light can be used instead of the parallel polarized light.

An apparatus according to the present invention is an apparatus using the measurement method according to any one of claims 1 to 4 .

  According to the present invention, the diameter, refractive index, and central axis of the object to be measured based on the scattered light intensity and the scattering angle of the scattered light caused by the scattering of the projected laser light by the plurality of cylindrical bodies that are the object to be measured. By calculating and optimizing a deviation index that is a function of the distance between and the angle between the incident optical axis and the angle, the diameter, refractive index and the distance between the central axes, and the angle between the incident optical axis Can be obtained efficiently and accurately at the same time, and has an industrially significant effect.

The form of the object to be measured used for the measurement of the present invention is shown in FIG.
FIG. 1A shows an example in which the central axes have a parallel relationship, and a-1 and a-2 are examples in which two cylindrical bodies having different distances L between the central axes are formed, a-3 Is an example of two cylindrical bodies having a cylindrical body inside at a distance L between the central axes. FIG. 1B is an example of a coaxial cylindrical body having the same central axis, and b-1 and b-4 are solid multi-cylindrical bodies, and an optical fiber and a plating wire provided with a coating layer on the outer surface. It is an example. b-2 and b-3 are examples of hollow cylindrical bodies (cylindrical bodies), and b-3 is a coaxial cylindrical body arranged in the hollow of b-1. FIG. 1 (c) shows an example in which a cylindrical body having a central axis in parallel and a coaxial cylindrical body exist, and c-1 is another cylindrical body having an eccentric axis in a coaxial cylindrical body such as b-1. C-2 is an example of a state in which the central axis of the inner cylindrical body of b-4 is eccentric. As described above, some examples of the object to be measured are shown. However, the form of the object to be measured used in the present invention is not limited to FIG. 1 as long as the requirements of the present invention are satisfied.

The method for measuring the diameter and refractive index of the present invention and the angle between the central axis and the angle between the incident optical axis and the object to be measured (consisting of a plurality of cylindrical bodies) shown in FIG. 1 is shown in the flowchart of FIG. Do along.
In order to measure the scattered light intensity I _i in FIG. 2, the laser beam 3a having the wavelength λ nm (446.1 nm) is emitted from the light source 3 to the object to be measured 2 with the diameter / refractive index measuring apparatus 1 shown in FIG. The light is emitted, and the laser beam 3a is made vertically or horizontally polarized with respect to the object to be measured by the deflecting device 4 and projected onto the object to be measured 2 supported on the upper surface of the detection unit 5 by the support base 5b. A part of the laser beam 3a is reflected by the object to be measured 2, and the measured scattered light intensity I is measured by the detector 6 disposed at the scattering angle θ with respect to the optical axis of the laser beam 3a. In this procedure, the scattering angle θ _i (i = 0... N) is changed, and the measured scattered light intensity I _i (i = 0... N) at that time is sequentially measured.
Alternatively, as shown in FIG. 4, a plurality of detectors 6 (28 in the case of FIG. 4) are arranged on the circumference of the support base 5 b that supports the DUT 2, and the scattering angle θ of each detector 6. _i in may be to measure the measuring scattered light intensity I _i.

These measured scattering angle θ _i and measured scattered light intensity I _i are the same as those of a personal computer equipped with the simultaneous analysis program for the diameter, refractive index, distance between the central axes and the angle between the incident optical axis and the distance shown in FIG. To the operation unit 7.
The calculated scattered light intensity σ _i is calculated in the calculation unit 7.
In the present invention, the calculated scattered light intensity σ _i is obtained by using the equation expressed by Equation 1 when the number of cylindrical bodies is two. Since accurate values can be obtained in the subsequent calculation of the diameter, refractive index, distance between the central axes, and the angle between the incident optical axis and this expression, this expression is expressed using the first and third kind Bessel functions. ing. When calculating the calculated scattered light intensity σ _i , if it is scattered by vertically polarized light, it is calculated using the subscript 式 equation, and if it is scattered horizontally polarized light, it is calculated using the subscript 添 equation. .

ここで、図５は数１における幾何学関係を示し、添字‖は水平偏光によるものを表し添字⊥は垂直偏光によるものを表す、ｋは波数、ｒ_１０、ｒ_２０は被測定物の半径（Ｄ_１０／２、Ｄ_２０／２）、Ｊ_ｍ（ｘ）は第一種ベッセル関数、Ｈ_ｍ ^（１）（＝Ｊ_ｍ（ｘ）+ｉＹ_ｍ（ｘ））は第三種ベッセル関数を表し、ｍは次数である。

Here, FIG. 5 shows the geometrical relationship in equation (1), where the subscript ‖ indicates horizontal polarization and the subscript ⊥ indicates vertical polarization, k is the wave number, r ₁₀ and r ₂₀ are the radii of the object to be measured ( _{D 10/2, D 20/} 2), J m (x) is the first kind Bessel ^{_{function, H m (1) (=}} J m (x) + iY m (x)) represents a third kind Bessel function , M is the order.

By the way, as the formula of the calculated scattered light intensity shown in Equation 1, an appropriate formula is selected according to the form of the object to be measured as shown in FIG. For example, in the case where the cylindrical body is eccentric in a cylindrical shape, a more accurate result can be obtained by changing the formula shown in Formula 1 to the formula of Formula 2, and the number of column bodies is 3 or more. In this case, the diameter, the refractive index, the distance between the central axes, and the angle formed between the incident optical axes can be calculated by expanding the expression shown in Equation 1 as appropriate.
In addition, the formula (1) is effective for measuring highly transparent materials such as fiber knitting fabrics and cocoon threads, but in the case of highly reflective metals such as metallic superconducting wires, carbon nanotubes, etc. For hollow samples like this, the calculated scattered light intensity formula can be changed to a more suitable formula to simultaneously measure the diameter, refractive index, central axis distance, and angle between the incident optical axis and the present invention. Can do.

ただし、ｊ＝１、２。上記Ｈ_{ｊ（ｑ）ｃ/ｓ}については、ＥをＨに読み替える。図６は数２における幾何学関係を示している。

However, j = 1,2. For H _{j (q) c / s} , replace E with H. FIG. 6 shows the geometric relationship in equation (2).

Next, using the calculated scattered light intensity σ _i calculated from the measured measured scattered light intensity I _i and the measured angle θ _i , the diameter D _j , the refractive index n _j , the center-to-axis distance L, and the incident light shown in Equation 3 A deviation index U (n ₁ , D ₁ , n ₂ , D ₂ , L, ψ) of a form including an angle ψ formed by an axis and an interval is created. As a function of the deviation index as a function of the diameters D ₁ and D ₂ , the refractive indexes n ₁ and n ₂ and the distance L between the central axes, the point at which the deviation index is minimum (n ₁₀ , D ₁₀ , n ₂₀ , D ₂₀ , L ₀ , Ψ ₀ ), and the combination of the diameter D ₁ , D ₂ , the refractive index n ₁ , n ₂ , the distance L between the central axes, and the angle ψ formed by the interval between the incident optical axis and the refractive index of the object to be measured. And the distance between the central axes.

First, in this calculation, when the deviation index is the diameter D ₁₀ , D ₂₀ , the refractive index n ₁₀ , n ₂₀ , and the center axis distance L ₀ , I _i ^(opt) = bσ _i (n ₁₀ , D ₁₀ , n ₂₀ , D ₂₀ , L ₀ , ψ ₀ ), the optimum distribution is shown, and the optimum deviation index U _T ^(opt) (n ₁ , D ₁ , n ₂ , D ₂ , L, ψ) in this optimum distribution is expressed by the following _equation (3). It expresses like this.

ここで、Ｎは測定数、ｂは入射波強度を表す。

Here, N represents the number of measurements, and b represents the incident wave intensity.

Next, a set G of deviation indexes as a function of the diameters D ₁ and D ₂ , the refractive indexes n ₁ and n ₂ , and the center axis distance L is expressed as G = {n ₁ , D ₁ , n ₂ , D ₂ , L, ψ | U _T ^(opt) (n ₁ , D ₁ , n ₂ , D ₂ , L, ψ) ≦ U _T (n ₁₀ , D ₁₀ , n ₂₀ , D ₂₀ , L ₀ , ψ ₀ )} Within the range, n _min , n _max , D _min , D _max , L _min , and L _max are obtained.
Next, regarding each of the obtained values and the difference between n ₁₀ , D ₁₀ , n ₂₀ , D ₂₀ , and L ₀ and the diameter, (D _min −D ₁₀ , D _max −D ₁₀ ), (D _min −D ₂₀ , D _max −D ₂₀ ), (n _min −n ₁₀ , n _max −n ₁₀ ) regarding the refractive index, (n _min −n ₂₀ , n _max −n ₂₀ ), and (L _min −L ₂₀ ) regarding the distance between the central axes. ₁₀ , L _max −L ₁₀ ) and (L _min −L ₂₀ , L _max −L ₂₀ ) are defined as uncertainties, and a point (n ₁₀ , D ₁₀ , n ₂₀ , D ₂₀ , L) that minimizes this value is defined. ₀ , ψ ₀ ), the diameter of the object to be measured, the refractive index, the distance between the central axes, and the angle formed by the incident optical axis are calculated.

Hereinafter, the present invention will be described using examples.
As an object to be measured, sample A (corresponding to a-1 in FIG. 1 (a)) having a central axis in parallel and a large distance between the central axes and samples B and C having a small distance between the central axes (FIG. 1 (a)). These samples using a-2) are set on the support 5b of the diameter / refractive index measuring apparatus 1 in FIG. 2, and a laser beam having a wavelength λ = 441.6 nm is projected, and the scattering angle θ _{i is set} to 0. Then, the scattering intensity was measured in order of 2 degrees between 150 degrees and 150 degrees, and the scattering intensity was measured to obtain the measured scattered light intensity I _i .

Next, the previous scattering angle θ _i and the measured scattered light intensity I _i are input to a personal computer, the calculated scattered light intensity σ _i is obtained from the scattered angle θ _i, and the calculated scattered light intensity I _i is obtained as the calculated scattered light intensity σ. deviation index from _{i U I (n 1, D} 1, n 2, D 2, L, ψ) was _calculated, and _{U I (n 1, D 1} , n 2, D 2, L, ψ) and the minimum The values were determined as optimum values, and D ₁ , n ₁ , D ₂ , n ₂ , and L at that time were taken as the diameter, the refractive index, and the distance between the central axes, respectively. The results are shown in Table 1.
The measurement is performed with both vertically polarized light and horizontally polarized light.

As is clear from Table 1, in the samples A, B, and C (form shown in FIG. 1 (a)) having two cylindrical bodies whose central axes have a parallel relationship, even if the distance between the central axes is on the order of nm, it is on the order of μm. It can be seen that the diameter and the refractive index of each cylindrical body are accurately obtained even if they are separated from each other.
It can also be seen that there is no significant difference in the accuracy obtained when using vertically polarized light and when using horizontally polarized light.

It is a schematic diagram which shows the form example of a to-be-measured object. It is a measuring method flowchart concerning the present invention. It is a figure which shows an example of a diameter / refractive index / center distance measuring apparatus. It is a figure which shows another example of a diameter / refractive index / center distance measuring apparatus. It is explanatory drawing which shows the geometric display of Numerical formula 1. It is explanatory drawing which shows the geometric display of Numerical formula 2.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Measuring apparatus 2 Measured object 3 Light source 3a Laser light 3b Scattered light 4 Deflector 5a Detection part 5b Support base 6 Detector 7 Arithmetic part θ _i Scattering angle I _i Measurement light scattering intensity σ _i Calculated scattered light intensity D ₁ , D ₂ Diameter n ₁ , n ₂ Refractive index L Center axis distance ψ Angle formed by incident optical axis and distance L

Claims (5)

Projecting parallel polarized light, which is polarized parallel to the length direction of the plurality of cylindrical bodies having a parallel relationship with the central axis, onto the plurality of cylindrical bodies ,
A plurality of observations arranged on a circumference around the plurality of cylindrical bodies, and a scattering angle and a scattered light intensity of scattered light generated by reflection of a part of the parallel polarized light by each of the plurality of cylindrical bodies. Measure at point,
Based on an equation considering multiple scattering between cylinders from the distance from the observation point for each cylinder to the center of the cylinder and the scattering angle for each cylinder when the measured scattering intensity is measured calculating the calculated scattered light intensity,
Based on the plurality of measured scattered light intensities obtained by the measurement and the calculated plurality of calculated scattered light intensities, the individual diameters, refractive indexes, distances between the central axes, and intervals between the incident optical axes of the plurality of cylindrical bodies are formed. Calculate the deviation index expressed as a function of angle,
Deriving individual diameters, refractive indices, central axis distances and angle combinations between the incident optical axes and the intervals of the plurality of cylindrical bodies that minimize the deviation index,
Finding the individual diameter, refractive index, center axis distance and angle between the incident optical axis of the plurality of cylindrical bodies ,
A method of measuring the diameter, refractive index, distance between central axes, and the angle between the incident optical axis and the cylinder. Parallel-polarized light polarized parallel to the length direction of the plurality of cylindrical bodies having the same central axis projected on the plurality of cylindrical bodies,
A plurality of observations arranged on a circumference around the plurality of cylindrical bodies, and a scattering angle and a scattered light intensity of scattered light generated by reflection of a part of the parallel polarized light by each of the plurality of cylindrical bodies. Measure at point,
Based on an equation considering multiple scattering between cylinders from the distance from the observation point for each cylinder to the center of the cylinder and the scattering angle for each cylinder when the measured scattering intensity is measured calculating the calculated scattered light intensity,
Based on the plurality of measured scattered light intensities obtained by the measurement and the calculated plurality of calculated scattered light intensities, the individual diameters, refractive indexes, distances between the central axes, and intervals between the incident optical axes of the plurality of cylindrical bodies are formed. Calculate the deviation index expressed as a function of angle,
Deriving individual diameters, refractive indices, central axis distances and angle combinations between the incident optical axes and the intervals of the plurality of cylindrical bodies that minimize the deviation index,
Finding the individual diameter, refractive index, center axis distance and angle between the incident optical axis of the plurality of cylindrical bodies ,
A method of measuring the diameter, refractive index, distance between central axes, and the angle between the incident optical axis and the cylinder. Projecting vertically polarized light polarized in a direction orthogonal to the length direction of a plurality of cylindrical bodies having a parallel relationship with the central axis onto the plurality of cylindrical bodies ,
A plurality of observations in which a scattering angle and a scattered light intensity of scattered light generated by reflection of a part of the vertically polarized light by each of the plurality of cylindrical bodies are arranged on the circumference around the plurality of cylindrical bodies. Measure at point,
Based on an equation considering multiple scattering between cylinders from the distance from the observation point for each cylinder to the center of the cylinder and the scattering angle for each cylinder when the measured scattering intensity is measured calculating the calculated scattered light intensity,
Based on the plurality of measured scattered light intensities obtained by the measurement and the calculated plurality of calculated scattered light intensities, the individual diameters, refractive indexes, distances between the central axes, and intervals between the incident optical axes of the plurality of cylindrical bodies are formed. Calculate the deviation index expressed as a function of angle,
Deriving individual diameters, refractive indices, central axis distances and angle combinations between the incident optical axes and the intervals of the plurality of cylindrical bodies that minimize the deviation index,
Finding the individual diameter, refractive index, center axis distance and angle between the incident optical axis of the plurality of cylindrical bodies ,
A method of measuring the diameter, refractive index, distance between central axes, and the angle between the incident optical axis and the cylinder. Projecting vertically polarized light polarized in a direction orthogonal to the length direction of a plurality of cylinders having the same central axis onto the plurality of cylinders ,
A plurality of observations in which a scattering angle and a scattered light intensity of scattered light generated by reflection of a part of the vertically polarized light by each of the plurality of cylindrical bodies are arranged on the circumference around the plurality of cylindrical bodies. Measure at point,
Based on an equation considering multiple scattering between cylinders from the distance from the observation point for each cylinder to the center of the cylinder and the scattering angle for each cylinder when the measured scattering intensity is measured calculating the calculated scattered light intensity,
Based on the plurality of measured scattered light intensities obtained by the measurement and the calculated plurality of calculated scattered light intensities, the individual diameters, refractive indexes, distances between the central axes, and intervals between the incident optical axes of the plurality of cylindrical bodies are formed. Calculate the deviation index expressed as a function of angle,
Deriving individual diameters, refractive indices, central axis distances and angle combinations between the incident optical axes and the intervals of the plurality of cylindrical bodies that minimize the deviation index,
Finding the individual diameter, refractive index, center axis distance and angle between the incident optical axis of the plurality of cylindrical bodies ,
A method of measuring the diameter, refractive index, distance between central axes, and the angle between the incident optical axis and the cylinder. Device using any of the measuring method of claims 1 to 4.

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