JP2023056722A - Method for calculating optical spectrum, and program - Google Patents

Abstract

To provide a method for calculating an optical spectrum and a program that can easily design an anti-reflection film having desired characteristics.SOLUTION: A method for calculating an optical spectrum of the present embodiment has a measurement step, a height distribution calculation step, and a spectrum calculation step. The measurement step includes preparing a plurality of sample substrates different from each other in a refractive index distribution in a thickness direction near a surface, and measuring the sample regular reflection spectra in the plurality of sample substrates. The height distribution calculation step includes calculating a height distribution function H(x) of an anti-glare surface on the basis of, the plurality of sample regular reflection spectra measured in the measurement step. The spectrum calculation step includes calculating interference of light caused by a rugged structure of the anti-glare surface on the basis of the height distribution function H(x), and determining an optical spectrum in consideration of the interference of light.SELECTED DRAWING: Figure 8

Description

The present invention relates to an optical spectrum calculation method and program.

From the viewpoint of improving the visibility of a display device, it has been proposed to impart an anti-glare effect to the surface of a transparent article such as a cover glass disposed on the display surface of the display device as an anti-glare surface. The anti-glare effect of the anti-glare surface is exhibited based on the uneven structure of the anti-glare surface.

Further, for example, Patent Literature 1 discloses applying an antireflection film made of, for example, an optical multilayer film to the surface of a transparent article. This antireflection film can improve the antiglare effect and contrast.

WO2018/179825

In the film design of the antireflection film, when the surface of the transparent article on which the antireflection film is provided is a flat surface without irregularities, the optical spectrum of the reflected light can be easily calculated, so that the desired characteristics can be obtained. It is possible to easily design the antireflection coating.

However, in order to further improve the anti-glare effect, when the surface of the transparent article is an anti-glare surface having an uneven structure and an anti-reflection film is provided on the anti-glare surface, the light reflected by the unevenness of the anti-glare surface interferes. It was difficult to calculate the optical spectrum of the reflected light due to As a result, it has been difficult to design an antireflection coating with desired properties.

SUMMARY OF THE INVENTION It is an object of the present invention to provide an optical spectrum calculation method and a program that make it possible to easily design an antireflection film having desired characteristics.

A method for calculating an optical spectrum for solving the above-mentioned problems is a method of calculating an optical spectrum of a film-coated transparent substrate provided with an anti-glare surface having an uneven structure on its surface and an anti-reflection film provided on the anti-glare surface. In a calculation method, using a plurality of sample substrates each having the anti-glare surface on the surface and having different refractive index distributions in the thickness direction near the surface, the surface of the plurality of sample substrates a measuring step of measuring a specular reflection spectrum of a sample; a height distribution calculating step of calculating a height distribution function of the anti-glare surface based on the plurality of specular reflection spectra of the sample measured in the measuring step; and a spectrum calculation step of calculating interference of light based on the height distribution function and obtaining the optical spectrum in consideration of the interference of light.

According to this aspect, the height distribution function of the antiglare surface is calculated based on the sample specular reflection spectrum of each of the plurality of sample substrates. Accordingly, it is possible to calculate the light interference due to the uneven structure of the anti-glare surface based on the calculated height distribution function of the anti-glare surface. As a result, the optical spectrum on the anti-glare surface provided with the anti-reflection film can be easily calculated in consideration of the light interference of the uneven structure of the anti-glare surface.

In the measuring step of the method for calculating the optical spectrum, it is preferable that the specular reflection spectrum of the sample is measured by reflected light of light vertically incident on the anti-glare surface of the sample substrate.

According to this aspect, it is possible to simplify the calculation formula for calculating the height distribution function in the height distribution calculation step, and as a result, it is possible to more easily calculate the optical spectrum of the film-coated transparent substrate. becomes.

In the optical spectrum calculation method, the plurality of sample substrates are a first sample substrate having no optical film on the anti-glare surface and a second sample substrate having an optical film on the anti-glare surface. , is preferably included.

According to this aspect, since it is not necessary to provide the optical film on the first sample substrate, it is possible to simplify the process.
A program for solving the above problem is a computing device for calculating an optical spectrum in a film-coated transparent substrate comprising a transparent substrate having an anti-glare surface having an uneven structure on its surface and an antireflection film provided on the anti-glare surface. a height distribution calculating step of calculating a height distribution function of the anti-glare surface based on a plurality of sample specular reflection spectra obtained as input values; calculating interference based on the height distribution function, and obtaining the optical spectrum considering the interference of the light.

According to this aspect, the height distribution function of the antiglare surface is calculated based on the sample specular reflection spectrum of each of the plurality of sample substrates. Accordingly, it is possible to calculate the light interference due to the uneven structure of the anti-glare surface based on the calculated height distribution function of the anti-glare surface. As a result, the optical spectrum on the anti-glare surface provided with the anti-reflection film can be easily calculated in consideration of the light interference of the uneven structure of the anti-glare surface.

According to the optical spectrum calculation method and program of the present invention, it is possible to easily design an antireflection film having desired characteristics.

1 is a schematic diagram showing a film-coated transparent substrate 10 that is an object of optical spectrum calculation according to an embodiment. FIG. It is a schematic diagram which shows the 1st sample base material used by the measurement step of the same form. It is a schematic diagram which shows the 2nd sample base material used by the measurement step of the same form. It is a schematic diagram which shows the measuring apparatus used by the measuring step of the same form. 10 is a graph showing a first sample specular reflectance spectrum; FIG. 4 is a graph showing a second sample specular reflectance spectrum; FIG. FIG. 4 is an explanatory diagram for explaining a method of calculating reflectance R; 4 is a graph showing a height distribution function; 4 is a graph showing simulated values and measured values of optical spectra;

An embodiment of an optical spectrum calculation method and program will be described below with reference to the drawings. In the drawings, for convenience of explanation, part of the configuration may be exaggerated or simplified. Also, the dimensional ratio of each part may differ from the actual one.

(Transparent substrate with film 10)
First, the film-coated transparent substrate 10, which is the object of calculation of the optical spectrum, will be described.
As shown in FIG. 1, the film-coated transparent substrate 10 is used, for example, by arranging it on the display surface of a display device. In this case, the film-attached transparent substrate 10 may be a member attached on the display surface of the display device. That is, the film-coated transparent substrate 10 may be a member that is attached to the display device afterward.

The film-coated transparent substrate 10 includes a transparent substrate 11 and an antireflection film 12 . The film-attached transparent substrate 10 may have other layers such as an antifouling layer.
The transparent substrate 11 has a sheet-like or plate-like shape having a pair of main surfaces facing each other. The material of the transparent substrate 11 is not particularly limited. Examples of the material of the transparent substrate 11 include glass and resin. The material of the transparent substrate 11 is preferably glass, and as the glass, known glass such as alkali-free glass, borosilicate glass, aluminosilicate glass, soda lime glass, and chemically strengthened glass can be used. . The transparent substrate 11 is preferably made of glass because the transmittance of visible light is less likely to change over time.

(Transparent substrate 11)
The transparent substrate 11 has an anti-glare surface 13 with an uneven structure on one main surface. The transparent substrate 11 of this embodiment includes, for example, a substrate body 21 and a translucent antiglare layer 22 provided on the surface of the substrate body 21 . Antiglare surface 13 is provided on antiglare layer 22 . The structure of the antiglare surface is not particularly limited. The anti-glare surface includes, for example, an anti-glare surface formed by applying a coating agent, and an anti-glare surface formed by blasting or etching. Alternatively, the anti-glare layer 22 may be omitted and the anti-glare surface 13 may be formed directly on the surface of the substrate body 21 .

(Antireflection film 12)
The antireflection film 12 is deposited on the antiglare surface 13 . The antireflection film 12 is, for example, an optical multilayer film. The optical multilayer film used as the antireflection film 12 includes, for example, a single layer or multiple layers of silicon dioxide, a single layer or multiple layers of niobium pentoxide, or the like. The number of layers, the material of each layer, and the thickness of each layer in the antireflection film 12 are set according to desired reflection characteristics. Also, the antireflection film 12 may have a single-layer film structure.

(Calculation method of optical spectrum)
Next, a method for calculating the optical spectrum of the film-coated transparent substrate 10 will be described. This calculation method is implemented by sequentially passing through a measurement step, a height distribution calculation step, and a spectrum calculation step, which will be described below.

Note that the height distribution calculation step and the spectrum calculation step among the above three steps are executed, for example, by executing a program stored in the memory of a computer as a calculation device. A computer may consist of one or more processors that operate according to computer programs (software), and such processors and application specific integrated circuits (ASICs) that perform at least some of the various types of processing. It may be configured by combining with one or more dedicated hardware circuits such as. A processor includes a CPU and memory, such as RAM and ROM, which stores program code or instructions configured to cause the CPU to perform processes. Memory or computer-readable media includes any available media that can be accessed by a general purpose or special purpose computer. Alternatively, instead of a computer including the above processor, a processing circuit configured by one or more dedicated hardware circuits that perform all of the various types of processing may be used.

(measurement step)
In the measurement step, a plurality of transparent substrates having antiglare surfaces similar to the antiglare surface 13 of the transparent substrate 11 are prepared as measurement samples. The measurement sample is manufactured through the same manufacturing process as the manufacturing process of the transparent substrate 11 . Then, in this embodiment, a first sample substrate 31 shown in FIG. 2 and a second sample substrate 32 shown in FIG. 3 are produced based on the measurement samples.

The first sample substrate 31 and the second sample substrate 32 are configured such that the refractive index distribution in the thickness direction is different from each other on the anti-glare surface 13 of the transparent substrate 11 as the measurement sample. For example, in the second sample substrate 32 , the optical film 33 is provided on the antiglare surface 13 of the transparent substrate 11 . On the other hand, in the first sample substrate 31, no optical film is provided on the antiglare surface 13 of the transparent substrate 11. FIG. Thereby, the refractive index distribution in the thickness direction of the antiglare surface 13 is made different between the first sample substrate 31 and the second sample substrate 32 . In order to eliminate the influence of reflection from the back surface of the measurement sample, it is preferable to subject the back surface of the measurement sample to blasting.

The optical film 33 of the second sample substrate 32 has a single-layer or multi-layer film structure. The optical film 33 includes, for example, a single layer or multiple layers of silicon dioxide, a single layer or multiple layers of niobium pentoxide, or the like.

Even when an optical film is provided on the anti-glare surface 13 of the first sample substrate 31, the refractive index distribution in the thickness direction can be changed from that of the first sample substrate 31 by changing the film configuration of the optical film. It is possible to make it different from the second sample substrate 32 .

In the measurement step, specular reflection spectra of each of the first sample base material 31 and the second sample base material 32 are measured using the measuring device 41 shown in FIG.
As shown in FIG. 4 , the measurement device 41 includes a light source 42 , a bifurcated optical fiber 43 , a collimator lens 44 and a spectroscope 45 . Light emitted from a light source 42 is introduced into a bifurcated optical fiber 43, converted into parallel light L by a collimator lens 44, and irradiated to a first sample substrate 31 or a second sample substrate 32 as a measurement sample. . The optical axis CL of the collimator lens 44 is set perpendicular to the antiglare surface 13 of the measurement sample. Thereby, the light emitted from the collimator lens 44 perpendicularly enters the anti-glare surface 13 of the measurement sample.

Then, only the specular reflection component of the light reflected by the antiglare surface 13 is introduced into the spectroscope 45 via the bifurcated optical fiber 43 by the collimator lens 44, and the spectroscope 45 measures the spectrum of the specular reflection component. For example, FIG. 5 shows a first sample specular reflection spectrum Sp1 obtained by spectrum measurement for the first sample substrate 31. As shown in FIG. Further, for example, FIG. 6 shows a second sample specular reflection spectrum Sp2 obtained by spectrum measurement for the second sample base material 32. As shown in FIG. The film configuration of the optical film 33 on the second sample substrate 32 is desirably set so that the peak wavelengths of the first sample specular reflection spectrum Sp1 and the second sample specular reflection spectrum Sp2 are largely different. This is for calculating an accurate height distribution function H(x) in the subsequent height distribution calculation step.

(Calculation method of reflectance R)
Next, a calculation method of the reflectance R on the main surface of the film-coated transparent substrate 10 on the antiglare surface 13 side will be described. The reflectance R can be calculated based on the following formula (1).

上記式（１）に示すように、反射率Ｒは、高さ分布関数Ｈ（ｘ）を重みとして、複素数振幅反射率ｒ（ｘ）をアンチグレア高さｘで積分することで計算される。アンチグレア高さｘは、厚方向における境界面２３からアンチグレア面１３の凹凸構造における凸部の先端までの長さである。

As shown in equation (1) above, the reflectance R is calculated by integrating the complex amplitude reflectance r(x) with the antiglare height x, weighted by the height distribution function H(x). The antiglare height x is the length from the boundary surface 23 in the thickness direction to the tips of the protrusions in the uneven structure of the antiglare surface 13 .

The formula (1) will be described below. As shown in FIG. 7, specular reflection is considered in which parallel light irradiated onto the transparent substrate 11 from the position P is reflected by the anti-glare surface 13 and returns to the position P. As shown in FIG. At this time, the reflected light L1 returning to the position P has a phase difference depending on whether the parallel light is reflected by the concave portion or the convex portion of the anti-glare surface 13 . Further, when there is a refractive index difference between the base body 21 and the anti-glare layer 22, the reflected light L1 reflected by the anti-glare surface 13 and the boundary surface 23 between the base body 21 and the anti-glare layer 22 are transmitted through the anti-glare layer 22. Consider the interference with the reflected light L2 reflected at . Based on this idea, the reflected light from the transparent base material 11 is expressed as a complex amplitude reflectance r(x) in which the amplitude reflectance and the phase change are collectively expressed as a complex number. Further, when the period of the uneven structure of the anti-glare surface 13 is sufficiently short and the distance from the anti-glare surface 13 to the position P is sufficiently long, it is assumed that the complex amplitude reflectance r(x) causes interference at the position P. . Since the antiglare height x has a density represented by the height distribution function H(x), the complex amplitude reflectance r(x) is integrated with the antiglare height x using the height distribution function H(x) as a weight. The reflectance R can be calculated with By calculating the reflectance R for each wavelength based on the height distribution function H(x), the optical spectrum on the main surface of the film-coated transparent substrate 10 on the antiglare surface 13 side can be calculated. That is, if the height distribution function H(x) is obtained, the optical spectrum of the film-coated transparent substrate 10 can be calculated.

(Height distribution calculation step)
In the height distribution calculating step, the height distribution function H(x ) is calculated. The computer that executes the program that executes the height distribution calculation step obtains the first sample specular reflection spectrum Sp1 and the second sample specular reflection spectrum Sp2 as input values.

The height distribution function H(x) is, for example, the following formula (2).

上記式（２）に示すように、高さ分布関数Ｈ（ｘ）は、３つの正規分布関数Ｇ_１，Ｇ_２，Ｇ_３と、歪みを与えるための２つのシグモイド関数Ｓ_１，Ｓ_２とを合成した関数である。上記式（２）において、ｋ_２，ｋ_３は比例定数である。

As shown in the above formula (2), the height distribution function H(x) consists of three normal distribution functions G ₁ , G ₂ , G ₃ and two sigmoid functions S ₁ , S ₂ for giving distortion. is a function that combines In the above formula (2), k ₂ and k ₃ are proportionality constants.

Each normal distribution function G ₁ , G ₂ , G ₃ is represented by the following formula (3), and each sigmoid function S ₁ , S ₂ is represented by the following formula (4).

上記式（３）において、ｄはシフト量であり、σは標準偏差である。上記式（４）において、ａはゲインであり、ｄはシフト量である。

In the above formula (3), d is the shift amount and σ is the standard deviation. In the above formula (4), a is the gain and d is the shift amount.

In the height distribution calculation step of the present embodiment, the specular reflection spectrum calculated from the reflectance R of the above equation (1) has a height corresponding to each of the first sample specular reflection spectrum Sp1 and the second sample specular reflection spectrum Sp2. Find the solution for the height distribution function H(x). That is, in the height distribution function H(x), the proportionality constants k ₂ and k ₃ , the shift amount d, the standard deviation σ, and the gain a are changed, and the first sample specular reflection spectrum Sp1 and the second sample positive A value of each parameter that matches with each of the reflection spectra Sp2 is obtained.

FIG. 8 shows an example of the height distribution function H(x). As shown in the figure, the height distribution function H(x) is expressed as a histogram showing the frequency for each height on the antiglare surface 13. FIG. The height on the horizontal axis is the height with reference to the interface 23 between the antiglare layer 22 and the substrate body 21 .

As shown in FIG. 1, the thickness from the boundary surface 23 between the antiglare layer 22 and the substrate main body 21 to the concave surface of the uneven structure of the antiglare surface 13 is defined as the antiglare film thickness t. Further, in the figure, the projection height of the projections in the uneven structure of the anti-glare surface 13 is defined as the projection height h.

As shown in FIG. 8, the height distribution function H(x) has a first peak P1 with the highest frequency when the height on the horizontal axis is the antiglare film thickness t. That is, the antiglare surface 13 has the largest distribution of portions having a height equal to the antiglare film thickness t. Also, the height distribution function H(x) has a second peak P2 corresponding to the antiglare height x of the antiglare surface 13 at a portion higher than the first peak P1. Note that FIG. 8 also shows sigmoid functions S ₁ and S ₂ included in the height distribution function H(x) of this example.

Further, each parameter in the height distribution function H(x) shown in FIG. 8 is shown in Tables 1 and 2 below.

(Spectrum calculation step)
After the height distribution calculation step, the spectrum calculation step is performed. In the spectrum calculation step, in the film-coated transparent substrate 10, the light interference in the antireflection film 12 and the light interference due to the uneven structure of the anti-glare surface 13 are calculated. Obtain 10 optical spectra. The light interference due to the uneven structure of the antiglare surface 13 is calculated based on the above formula (1). At this time, the height distribution function H(x) calculated in the height distribution calculation step is substituted for the height distribution function H(x) included in the above equation (1). Further, the interference of light in the antireflection film 12 is the interference due to reflection at each layer interface in the antireflection film 12 having an arbitrary film configuration, and the interference of light can be obtained by calculation.

FIG. 9 shows a comparison between the simulated values calculated in the spectrum calculation step and the measured values in the optical spectrum of the film-coated transparent substrate 10 . As shown in the figure, there is no significant deviation in the wavelengths at which the optical spectrum peaks between the simulated values and the measured values. Therefore, it can be said that the optical spectrum of the film-coated transparent substrate 10 can be suitably calculated by the calculation method of the present embodiment.

Effects of the present embodiment will be described.
(1) In the measurement step, a plurality of sample substrates having different refractive index distributions in the thickness direction near the surface are prepared, and sample specular reflection spectra of the plurality of sample substrates are respectively measured. In the height distribution calculating step, the height distribution function H(x) of the antiglare surface 13 is calculated based on the plurality of sample specular reflection spectra measured in the measuring step. In the spectrum calculation step, the light interference due to the uneven structure of the anti-glare surface 13 is calculated based on the height distribution function H(x), and the optical spectrum is obtained in consideration of the light interference.

According to this aspect, the height distribution function H(x) of the antiglare surface 13 is calculated based on the sample specular reflection spectrum of each of the plurality of sample substrates. Thereby, the light interference due to the uneven structure of the anti-glare surface 13 can be calculated based on the calculated height distribution function H(x) of the anti-glare surface 13 . As a result, the optical spectrum of the anti-glare surface 13 provided with the anti-reflection film 12 can be easily calculated in consideration of the light interference of the uneven structure of the anti-glare surface 13 .

(2) In the measurement step, the specular reflection spectrum of the sample is measured by the reflected light of the light vertically incident on the antiglare surface 13 of the sample substrate. According to this aspect, it is possible to simplify the calculation formula for calculating the height distribution function H(x) in the height distribution calculation step. As a result, the optical spectrum of the film-coated transparent substrate 10 can be more easily can be calculated.

(3) The plurality of sample substrates include a first sample substrate 31 with no optical film provided on the anti-glare surface 13 and a second sample substrate 32 with an optical film 33 provided on the anti-glare surface 13. . According to this aspect, since it is not necessary to provide the optical film on the first sample substrate 31, the process can be simplified.

This embodiment can be implemented with the following modifications. This embodiment and the following modified examples can be implemented in combination with each other within a technically consistent range.
- In the measurement step, the specular reflection spectrum of the sample may be measured by the specular reflection of the light incident on the antiglare surface 13 of the sample substrate at an oblique angle.

- In the first sample substrate 31 of the above embodiment, the anti-glare surface 13 is not provided with an optical film, but the present invention is not particularly limited to this. An optical film may also be provided on the anti-glare surface 13 of the first sample substrate 31 if the refractive index distribution in the thickness direction of the anti-glare surface 13 is different from that of the second sample substrate 32 .

- The embodiments and modifications disclosed this time are exemplifications in all respects, and the present invention is not limited to these exemplifications. That is, the scope of the present invention is indicated by the scope of claims, and is intended to include all changes within the meaning and scope of equivalence to the scope of claims.

DESCRIPTION OF SYMBOLS 10... Film-attached transparent base material 11... Transparent base material 12... Antireflection film 13... Anti-glare surface 21... Base material body 22... Anti-glare layer 23... Boundary surface 31... First sample base material 32... Second sample base material 33... Optical film 41 Measuring device 42 Light source 43 Bifurcated optical fiber 44 Collimator lens 45 Spectroscope Sp1 First sample regular reflection spectrum Sp2 Second sample regular reflection spectrum t Antiglare film thickness x Antiglare height

Claims (4)

A method for calculating an optical spectrum in a film-coated transparent substrate comprising a transparent substrate having an anti-glare surface having an uneven structure on its surface and an antireflection film provided on the anti-glare surface, the method comprising:
Using a plurality of sample substrates each having the anti-glare surface on the surface and having different refractive index distributions in the thickness direction near the surface, sample specular reflection spectra on the surfaces of the plurality of sample substrates are measured. a measuring step to
a height distribution calculating step of calculating a height distribution function of the anti-glare surface based on the plurality of sample specular reflection spectra measured in the measuring step;
a spectrum calculation step of calculating the light interference due to the uneven structure based on the height distribution function and obtaining the optical spectrum in consideration of the light interference;
having
How to calculate the optical spectrum. In the measuring step, the specular reflection spectrum of the sample is measured by the reflected light of the light vertically incident on the antiglare surface of the sample substrate.
The method of calculating an optical spectrum according to claim 1. The plurality of sample substrates include a first sample substrate having no optical film on the anti-glare surface and a second sample substrate having an optical film on the anti-glare surface.
The method of calculating an optical spectrum according to claim 1. A program for causing a computer to function as a computing device for calculating an optical spectrum in a film-coated transparent substrate having an anti-glare surface having an uneven structure on its surface and an anti-reflection film provided on the anti-glare surface. hand,
a height distribution calculating step of calculating a height distribution function of the anti-glare surface based on a plurality of sample specular reflection spectra obtained as input values;
a spectrum calculation step of calculating the light interference due to the uneven structure based on the height distribution function and obtaining the optical spectrum in consideration of the light interference;
having
program.

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