Anti-glare textured surfaces and related methods

Abstract

Described herein is a display article having a diffractive surface region formed on a primary surface. In the diffractive surface region, the primary surface has a plurality of regions disposed at a plurality of heights measured from an imaginary reference plane extending through the display article, the heights forming a discrete height distribution. The plurality of regions are arranged to define a range of angles of incidence on the first primary surface, [Θ min ,Θ max ], the target wavelength range [λ min ,λ max ] such that the specular reflectance of light incident on the first major surface is reduced by at least a factor of 10 compared to when the first major surface is an untextured surface that does not include a diffractive surface region. The difference between heights in the discrete height distribution is within ±5% of an integer multiple of one-quarter of Equation (9), where λ' min = λ min / cosθ min and λ' max = λ max / cosθ max It is.

Description

Priority

[0001] This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Patent Application No. 63 / 325,280, filed March 30, 2022, the entire disclosure of which is incorporated herein by reference. [Technical field]

[0002] The present disclosure relates to anti-glare articles, and more particularly to display articles comprising a surface having a diffractive surface region that includes a plurality of regions arranged in a discrete height distribution in a pattern based on a target scattering pattern. [Background technology]

[0003] Substrates transparent to visible light are used to cover the displays of display articles. Examples of such display articles include smartphones, tablet devices, televisions, computer monitors, and in-car displays. Liquid crystal displays and organic light-emitting diode displays are particularly popular displays. The substrate protects the display and, at the same time, the transparency of the substrate allows the device user to view the display. Glare is a phenomenon that reduces the viewing experience in the presence of a bright light source. In addition, reflected images from the surrounding environment other than the bright light source can also reduce the visibility of the display. For example, if the user's own reflected image or light from the surrounding environment is visible to the eye, it may be distracting, reduce visibility, or cause visual fatigue.

[0004] There are already several technologies to reduce glare, such as anti-reflective coatings and anti-glare technologies. Anti-reflective coatings directly reduce the total amount of reflection, thereby reducing glare. However, some existing anti-reflective coatings are unable to reduce reflections sufficiently across the entire visible spectrum to make them invisible to the user. On the other hand, anti-glare technologies aim to reduce the peak intensity of reflections by spreading the light reflection over a wide range of angles, making the reflections less noticeable and distracting to the user. However, if the reflection angle becomes too large, the reflections can cause a relatively large haze, which can reduce the contrast of the displayed image. Summary of the Invention [Problem to be solved by the invention]

[0005] Therefore, it would be beneficial to have an alternative to existing anti-glare and anti-reflective coating technologies that provides better control over the angular distribution of scattered light. [Means for solving the problem]

[0006] Aspect (1) of the present disclosure relates to a display article comprising a first principal surface, a second principal surface opposite to the first principal surface, and a diffractive surface region formed on the first principal surface. The first principal surface has a plurality of regions provided at a plurality of heights forming a discrete height distribution within the diffractive surface region. Each height included in the discrete height distribution is a relative height measured from an imaginary reference plane that extends through the display article and parallel to the first principal surface. The plurality of regions are arranged to define a range of angles of incidence on the first principal surface from a minimum incidence angle Θ min From the maximum incidence angle Θ max When the range is set to , the minimum wavelength λ min Maximum wavelength λ max The first major surface is arranged such that the specular reflectance of light incident on the first major surface is reduced by a factor of at least 10 compared to a non-textured surface not including a diffractive surface region within a wavelength range of interest of: Within ±5% of an integer multiple of TIFF2025510549000002.tif6114, where TIFF2025510549000003.tif14114,λ' min = λ min / cosθ min , and λ' max = λ max / cosθ max It is.

[0007] Aspect (2) of the present disclosure relates to a display article according to aspect (1), wherein the diffractive surface region scatters light in a far-field scattering pattern having a peak scattering angle of 1.5° or less in the wavelength range of interest.

[0008] A third aspect of the present disclosure relates to a display article according to the second aspect, wherein the scattering angle of the peak point in at least a portion of the wavelength range of interest is 0.5° or less.

[0009] A fourth aspect of the present disclosure relates to a display article according to the second aspect, wherein the far-field scattering pattern approximates a Laguerre-Gaussian mode.

[0010] The fifth aspect of the present disclosure is min is 380 nm or more and λ max is 1200 nm or less, and Θ min is 0° or more and Θ max is 75° or less.

[0011] The sixth aspect of the present disclosure is min = 400 nm and λ max = 800 nm.

[0012] A seventh aspect of the present disclosure relates to a display article according to any one of the first to sixth aspects, in which the specular reflectance is reduced by at least 100 times compared to when the first main surface is a non-textured surface.

[0013] An embodiment (8) of the present disclosure relates to the display article according to any one of the embodiments (1) to (7), wherein the minimum feature size of the multiple regions is 1 μm or more.

[0014] An aspect (9) of the present disclosure relates to the display article according to any one of aspects (1) to (8), in which the multiple regions are arranged in a pattern having periodicity in two directions perpendicular to each other.

[0015] Aspect (10) of the present disclosure relates to a display article according to aspect (9), wherein the pattern has at least one surrounding area, the surrounding area being completely surrounded by an area having a different height from an imaginary reference plane than the surrounding area.

[0016] An embodiment (11) of the present disclosure relates to a display article according to any one of the embodiments (1) to (10), in which the transmission haze of light incident on the first main surface is 4% or less over the entire wavelength range of 400 nm to 800 nm.

[0017] An aspect (12) of the present disclosure relates to a display article according to any one of aspects (1) to (11), wherein the total surface area ratio (%) of the diffractive surface area occupied by the areas provided at each height included in the discrete height distribution among the plurality of areas is a predetermined total surface area ratio (%) that is determined in advance so as to minimize the specular reflectance.

[0018] A thirteenth aspect of the present disclosure relates to a display article according to the twelfth aspect, wherein the discrete height distribution comprises three or more heights.

[0019] An embodiment (14) of the present disclosure is a method for forming a discrete height distribution, the discrete height distribution including at least four heights, the at least four heights being greater than or equal to a minimum height h min and, a second height that is within ±5% of TIFF2025510549000004.tif6114; and a third height that is within ±5% of TIFF2025510549000005.tif6114; and and a fourth height that is within ±5% of TIFF2025510549000006.tif6114.

[0020] Aspect (15) of the present disclosure relates to a display article according to aspect (14), wherein a first plurality of regions having a minimum height occupy a first total surface area percentage (%) relative to the diffractive surface area, and a second plurality of regions having a second height occupy a second total surface area percentage (%) relative to the diffractive surface area, the first total surface area percentage (%) being smaller than the second total surface area percentage (%).

[0021] A sixteenth aspect of the present disclosure relates to a display article according to aspect (15), wherein a third plurality of regions having a third height occupy a third total surface area percentage (%) relative to the diffractive surface area, a fourth plurality of regions having a fourth height occupy a fourth total surface area percentage (%) relative to the diffractive surface area, the first total surface area percentage (%) being within ±5% of the fourth total surface area percentage (%), and the second total surface area percentage (%) being within ±5% of the third total surface area percentage (%).

[0022] A seventeenth aspect of the present disclosure relates to a display article according to the thirteenth aspect, wherein the total surface area percentage of each height is 40% or less.

[0023] An aspect (18) of the present disclosure relates to a glass display article comprising a first major surface, a second major surface opposite the first major surface, and a diffractive surface region formed on the first major surface. The first major surface has a first plurality of regions having a first plurality of heights and a second plurality of regions having a second plurality of heights within the diffractive surface region. The first plurality of heights are measured from an imaginary reference plane that extends through the glass display article parallel to the first major surface, and the maximum height h is the average of the first plurality of heights. max The first plurality of regions occupy a first total surface area percentage relative to the diffractive surface area. The second plurality of heights are measured from a virtual reference plane and have a minimum height h minThe second plurality of regions occupies a second total surface area percentage (%) of the diffractive surface area. The first plurality of regions and the second plurality of regions define a range of angles of incidence on the first major surface that is less than or equal to a minimum angle of incidence Θ min From the maximum incidence angle Θ max When the range is set to , the minimum wavelength λ min Maximum wavelength λ max are arranged in a predetermined pattern that is determined based on the expected specular reflectance of light incident on the first major surface within a wavelength range of interest of h max -h min teeth, Within ±5% of an integer multiple of TIFF2025510549000007.tif6114, where TIFF2025510549000008.tif14114,λ' min = λ min / cosθ min , and λ' max = λ max / cosθ max The average measured specular reflectance of the first major surface over the range of angles of incidence and in the wavelength range of interest is less than or equal to 2.5%.

[0024] Aspect (19) of the present disclosure relates to a glass display article according to aspect (18), wherein the diffractive surface region scatters light in a far-field scattering pattern having a peak scattering angle of 1.5° or less in the wavelength range of interest.

[0025] Aspect (20) of the present disclosure relates to a glass display article according to aspect (19), wherein the scattering angle of the peak point in the wavelength range of interest is 0.5° or less.

[0026] Aspect (21) of the present disclosure relates to a glass display article according to aspect (19) or (20), wherein the far-field scattering pattern approximates a Laguerre-Gaussian mode.

[0027] The embodiment (22) of the present disclosure is min is 380 nm or more and λ max is 1200 nm or less, and Θ min is 0° or more and Θmax is 75° or less.

[0028] In an embodiment (23) of the present disclosure, the first main surface has a third plurality of regions having a third plurality of heights within the diffractive surface region, and the third plurality of heights are heights measured from a virtual reference plane, and a height h 1 and the third plurality of regions occupy a third total surface area percentage (%) of the diffractive surface area, and the height h 1 but, The present invention relates to a glass display article according to any one of aspects (18) to (22), wherein the color difference between the transparent and transparent portions of the glass display article and the transparent portions of the glass display article is within ±5% of TIFF2025510549000009.tif6114.

[0029] In an embodiment (24) of the present disclosure, the first main surface has a fourth plurality of regions having a fourth plurality of heights within the diffractive surface region, the fourth plurality of heights being heights measured from a virtual reference plane, and a height h 2 and a fourth plurality of regions occupying a fourth total surface area percentage (%) of the diffractive surface area, and a height h 2 but, The glass display article of claim 23, wherein the chromaticity is within ±5% of TIFF2025510549000010.tif6114.

[0030] Aspect (25) of the present disclosure relates to a glass display article according to aspect (24), wherein the first total surface area ratio (%) is within ±5% of the second total surface area ratio (%) and the third total surface area ratio (%) is within ±5% of the fourth total surface area ratio (%).

[0031] Aspect (26) of the present disclosure relates to a glass display article according to aspect (24), wherein the first total surface area percentage (%), the second total surface area percentage (%), the third total surface area percentage (%), and the fourth total surface area percentage (%) are all 40% or less.

[0032] An aspect (27) of the present disclosure relates to the glass display article according to any one of aspects (18) to (26), wherein the first plurality of regions and the second plurality of regions have a feature size of 1 μm or more.

[0033] An aspect (28) of the present disclosure relates to a glass display article according to any one of aspects (18) to (27), wherein the predetermined pattern has periodicity in two directions perpendicular to each other.

[0034] An aspect (29) of the present disclosure relates to a glass display article according to any one of aspects (18) to (28), wherein the predetermined pattern has at least one surrounding area, the surrounding area being an area completely surrounded by an area having a different height from a virtual reference plane than the surrounding area.

[0035] An aspect (30) of the present disclosure relates to a glass display article according to any one of the aspects (18) to (29), in which the transmission haze of light incident on the first main surface is 4% or less over the entire wavelength range of 400 nm to 800 nm.

[0036] Aspect (31) of the present disclosure relates to a method for forming diffractive surface regions on a substrate for a display article, the method comprising: determining a pattern of a plurality of regions on a first major surface of the substrate, each region of the plurality of regions having a surface area at a height measured from an imaginary reference plane extending through the display article parallel to the first major surface, the plurality of regions having a discrete height distribution; placing one or more etching masks on the first major surface to allow etching to occur only on selected regions of the first major surface to form at least some of the plurality of regions; and contacting the display article with an etching solution for a period of time after placing each of the one or more etching masks on the first major surface. The step of contacting with the etching solution is performed such that the difference between the heights in the discrete height distribution is: The height distribution is determined so that a plurality of regions having a discrete height distribution are formed on the substrate so that the height distribution is within ±5% of an integer multiple of TIFF2025510549000011.tif6114. TIFF2025510549000012.tif14114, lambda min is the minimum wavelength in the wavelength range of interest, λ max is the maximum wavelength in the wavelength range of interest, and [Θ min ,Θ max ] defines the range of incidence angles over which it is desired to minimize the specular reflectance of the display article, and λ' min = λ min / cosθ min And λ' max = λ max / cosθ max It is.

[0037] In an aspect (32) of the present disclosure, the step of determining a pattern of the plurality of regions is based on the following formula: FA=1 where A is a vector having N components, N corresponds to the number of heights in the discrete height distribution, 1 is a unit column vector having N components, F is an N×N matrix, and the value of each component of F is F ij is the following formula:

number

[0038] An aspect (33) of the present disclosure is a method for determining a pattern of a plurality of regions, the method comprising: generating an initial pattern of a plurality of regions; approximating the incident light by a uniform electric field and approximating the diffractive surface regions as causing only a phase shift in the reflected light, thereby generating an estimated far-field scattering pattern; TIFF2025510549000014.tif6114, and using an optimization algorithm to calculate and updating the initial pattern to reduce the difference between TIFF2025510549000015.tif6114 and the target scattering pattern u(λ).

[0039] An aspect (34) of the present disclosure is that the optimization algorithm solves the following objective function for pattern P:

number

[0040] Aspect (35) of the present disclosure is a method according to aspect (33), wherein the target scattering pattern approximates a Laguerre-Gaussian mode.

[0041] An aspect (36) of the present disclosure relates to a method according to any one of aspects (33) to (35), wherein the scattering angle of the peak point in the target wavelength range of the target scattering pattern is 1.5° or less.

[0042] An aspect (37) of the present disclosure relates to the method according to any one of aspects (33) to (36), wherein the scattering angle of the peak point in the target wavelength range is 0.5° or less.

[0043] An aspect (38) of the present disclosure relates to a method according to any of aspects (31) to (37), wherein the one or more etching masks include at least two etching masks configured such that the discrete height distribution includes at least four heights.

[0044] Aspect (39) of the present disclosure relates to a method according to aspect (38), wherein the at least two etching masks include a first etching mask and a second etching mask, and after exposing the substrate to an etching solution through the first etching mask, a second etching mask is disposed on the first principal surface, and the second etching mask is configured to expose a portion of the first principal surface that has been etched through the first etching mask, thereby causing the portion to be subjected to both etching through the first etching mask and etching through the second etching mask.

[0045] An embodiment (40) of the present disclosure relates to the method according to any one of the embodiments (31) to (39), wherein the minimum processing dimension of the pattern is 1 μm or more.

[0046] An embodiment (41) of the present disclosure relates to a method according to any one of embodiments (31) to (40), wherein the pattern has periodicity in at least two directions perpendicular to each other.

[0047] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary and are intended to provide an overview or framework for understanding the nature and features of the claimed invention. The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiments and, together with the following detailed description, serve to explain the principles and operation of various embodiments. [Brief description of the drawings]

[0048] The accompanying drawings, which are incorporated in and constitute a part of this specification, serve to explain the principles of the invention together with the following detailed description. [Figure 1] FIG. 1 is a perspective view of a display article according to one or more embodiments of the present disclosure. [Diagram 2] FIG. 2 is a schematic illustrating multiple regions in a diffractive surface region of the display article shown in FIG. 1 in accordance with one or more embodiments of the present disclosure. [Diagram 3] FIG. 3 is a schematic illustrating a height profile of the diffractive surface region shown in FIG. 2 in accordance with one or more embodiments of the present disclosure. [Figure 4A] FIG. 1 illustrates a two-dimensional intensity map of a Laguerre-Gaussian mode in accordance with one or more embodiments of the present disclosure. [Figure 4B] FIG. 4B illustrates a one-dimensional intensity plot of the Laguerre-Gaussian mode shown in FIG. 4A in accordance with one or more embodiments of the present disclosure. [Figure 5A] FIG. 1 illustrates the calculated optimal specular suppression width as a function of the number of heights in the discrete height distribution for a pattern with multiple regions at multiple heights in accordance with one or more embodiments of the present disclosure. [Figure 5B] FIG. 13 illustrates the calculated optimum specular suppression width as a function of optical bandwidth for each of a number of discrete height distributions for a pattern of multiple regions at multiple heights in accordance with one or more embodiments of the present disclosure. [Figure 5C] FIG. 1 illustrates the calculated specular reflectance as a function of optical bandwidth for each of a number of discrete height distributions for a pattern of multiple regions at multiple heights in accordance with one or more embodiments of the present disclosure. [Figure 6A] 1 is a flow diagram of a method for determining a pattern of multiple regions in a diffractive surface region, in accordance with one or more embodiments of the present disclosure. [Figure 6B] FIG. 6B is a schematic diagram illustrating a computing system that may be used to perform the method illustrated in FIG. 6A, in accordance with one or more embodiments of the present disclosure. [Figure 7] FIG. 1 is a flow diagram of an exemplary method for making a diffractive surface region of a display article in accordance with one or more embodiments of the present disclosure. [Figure 8A] FIG. 2 is a schematic illustrating a pattern of a first etch mask for forming multiple regions in a diffractive surface region, in accordance with one or more embodiments of the present disclosure. [Figure 8B] 1 is a schematic illustrating a pattern of a second etch mask for forming multiple regions in a diffractive surface region, in accordance with one or more embodiments of the present disclosure. [Figure 9]8B shows a number of calculated far-field scattering patterns for a diffractive region formed using a first mask shown in FIG. 8A and a second mask shown in FIG. 8B in accordance with one or more embodiments of the present disclosure. [Figure 10A] FIG. 8B illustrates a histogram of surface heights for a diffractive surface region formed using a first mask shown in FIG. 8A and a second mask shown in FIG. 8B in accordance with one or more embodiments of the present disclosure. [Figure 10B] 8B is a graph showing calculated reflectance and haze performance for a diffractive region formed using a first mask shown in FIG. 8A and a second mask shown in FIG. 8B in accordance with one or more embodiments of the present disclosure. [Figure 11A] FIG. 1 shows far-field scattering pattern measurements for an article of Example 2 having diffractive surface regions in accordance with one or more embodiments of the present disclosure. [Figure 11B] FIG. 13 is a graph showing reflected intensity measurements for the article of Example 2 according to one or more embodiments of the present disclosure. [Figure 11C] FIG. 13 is a graph showing the azimuth-averaged scattering intensity of the article of Example 2 at multiple wavelengths, according to one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0049] With general reference to the drawings, the present specification describes a display article with a diffractive region designed to significantly reduce specular reflections across the wavelength range of interest while providing relatively low scattering intensities at large scattering angles. Such a diffractive surface region has the advantage of preventing reflected images from being noticeable to the user and disrupting the display viewing experience while maintaining good image contrast characteristics. The diffractive surface region provides the above-mentioned good performance by providing a plurality of regions on a main surface of the display article, the portions of the main surface being at a certain height from a virtual reference plane, and the plurality of regions are structured such that the heights of the regions form a discrete height distribution. The difference between the heights in the discrete height distribution is: The size is within ±5% of an integer multiple of TIFF2025510549000018.tif6114. Here, TIFF2025510549000019.tif5114 shows the range of incidence angles (Θ min From Θ max ) and target wavelength range (λ min From λ max (up to) and is defined according to TIFF2025510549000020.tif14114, where λ′ min = λ min / cosθ min , λ' max = λ max / cosθ max The regions are arranged in a pattern determined based on a target far-field scattering pattern that provides a relatively low amplitude of scattering at scattering angles greater than 2°. Arranging the regions of the diffractive surface region in such a height distribution has been found to reduce specular reflectance by at least a factor of 10 (e.g., at least a factor of 100, at least a factor of 1000) compared to a non-textured article not having a diffractive surface region, while providing good haze performance.

[0050] As used herein, the term "specular reflectance" refers to the percentage of light reflected from an article at an angle of reflection equal to the angle of incidence of the light.

[0051] As used herein, the term "haze" or "transmission haze" refers to the percentage of transmitted light scattered outside an angular cone of approximately ±2.5° according to ASTM Standard D1003 "Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics." The entire contents of ASTM Standard D1003 are incorporated herein by reference. Although the name of ASTM Standard D1003 includes the term "plastic," this standard also applies to substrates including glass materials. Typically, the transmission haze of an optically smooth surface is close to zero.

[0052] 1, an exemplary embodiment of a display article 10 is shown. Display article 10 includes a substrate 12. In some embodiments, display article 10 further includes a housing 14 to which substrate 12 is coupled, and a display 16 within housing 14. In such embodiments, substrate 12 covers at least a portion of display 16 such that light emitted from display 16 can be transmitted through substrate 12.

[0053] Substrate 12 has a first major surface 18, a second major surface 19, a diffractive surface region 20 defined on first major surface 18, and a thickness 21, with thickness 21 being bounded in part by first major surface 18 (e.g., thickness 21 represents the minimum distance between first major surface 18 and second major surface 19 at a particular point on first major surface 18). In the illustrated embodiment, substrate 12 is substantially flat in shape, with first major surface 18 and second major surface 19 being generally planar (except for a height transition in first major surface 18 as described herein). Also contemplated and within the scope of the present disclosure are embodiments in which substrate 12 has a curved shape (e.g., by suitable hot and cold forming techniques). Typically, first major surface 18 faces toward an external environment 24 surrounding display article 10 and distal to display 16. In embodiments, visible light emitted by display 16 is transmitted through a thickness 21 of substrate 12 and exits from first major surface 18 to an external environment 24 .

[0054] The diffractive surface region 20 is structured to scatter light from the external environment 24 in a scattering pattern designed to suppress specular reflectance while maintaining a relatively low amplitude of scattering at scattering angles (Θ) of 2.0° or greater (e.g., 2.5° or greater, 3.0° or greater). In some embodiments, the diffractive surface region 20 scatters ... i ) over the wavelength range of interest [λ min ,λ max ] is constructed to have a far-field scattering pattern with a maximum scattering amplitude at scattering angles of 2.0° or less (e.g., 1.5° or less, 1.0° or less, 0.9° or less, 0.8° or less, 0.7° or less, 0.6° or less, 0.5° or less) throughout the entire region. In some embodiments, diffractive surface region 20 is constructed to reduce specular reflectance by at least a factor of 10 (e.g., at least a factor of 100, at least a factor of 1000, at least a factor of 1000) compared to a smooth, non-textured first major surface 18. Diffractive surface region 20 is constructed to reduce specular reflectance of substrate 12 while controlling scattering amplitude at relatively large scattering angles, thereby providing better anti-glare and haze performance than certain existing display articles.

[0055] In this specification, when the term "untextured version" is used in describing the specular reflectance performance of the article described herein, it refers to the specular reflectance predicted using Fresnel coefficients when the material constituting the substrate 12 is an optically smooth surface. For example, when the substrate 12 has a refractive index n 1 (e.g., glass or a suitable polymeric material) and the external environment has a refractive index of n 2 (e.g., the refractive index of air), the specular reflectance of a non-textured substrate 12 can be calculated using the following formula:

number

[0056] FIG. 2 is a schematic plan view of region II of the diffractive surface region 20 of the display article 10 shown in FIG. 1 according to an exemplary embodiment of the present disclosure. In some embodiments, in the diffractive surface region 20, the first major surface 18 has an uneven structure with a variation in relative surface height measured from a virtual reference plane, and this variation is larger than the maximum surface roughness value (e.g., Sa value) of the portion of the first major surface 18 extending within ±2° in a direction parallel to the second major surface 19. The variation in surface height of the first major surface 18 exceeds the range of surface height variation associated with the inherent roughness of the material forming the substrate 12. In the diffractive surface region 20, as a result of such variation in surface height, a plurality of regions 22 are provided on the first major surface 18. Each of the plurality of regions 22 constitutes a part of the first major surface 18 and extends generally parallel to the second major surface 19. However, it should be understood that as a result of the process for forming the plurality of regions 22 described herein, each of the plurality of regions 22 may be inclined with respect to the second major surface 19. In some embodiments, each of the plurality of regions 22 corresponds to a continuous portion of the first major surface 18, and the variation in surface height in this portion does not exceed the range of the variation in surface height associated with the surface roughness of the first major surface 18. Each of the plurality of regions 22 constitutes a portion of the first major surface 18 that is provided at a common height (e.g., a height within the tolerance of the molding process) from an imaginary reference plane that extends through the substrate 12. Each of the plurality of regions 22 is adjacent to at least one other of the plurality of regions 22, and the height of each region from the imaginary reference plane is different from the height from the imaginary reference plane at which the portion of the first major surface 18 that the adjacent region constitutes is provided. The regions of the plurality of regions 22 that are at the same height from the imaginary reference plane may be separated from each other by at least one other region that is provided at a different height from the imaginary reference plane. The boundaries of each of the plurality of regions 22 are defined by lines connecting points on the first major surface 18 where an abrupt change in surface height (eg, a change of more than 50 nm) is observed.

[0057] As described herein, the regions 22 forming the diffractive surface region 20 are arranged in a predetermined pattern calculated based on a target far-field scattering pattern. The target far-field scattering pattern is a pattern that has a low amplitude of specular reflectance for light incident on the first major surface 18 from the external environment 24, and a low amplitude of scattering at scattering angles greater than 2° (e.g., greater than 5°, greater than 10°). The predetermined pattern is a pattern that is not typically discernible by observation with the naked eye, but is identified using an optimization algorithm according to the method described herein. The size and shape of the regions 22 may vary substantially within the diffractive surface region 20. For example, in some embodiments, the maximum linear dimension of the regions 22 (the length of the longest line segment connecting one portion of the perimeter of the region to another portion of the perimeter without intersecting with other portions of the perimeter) may vary from tens of micrometers to hundreds of micrometers.

[0058] FIG. 3 is a schematic diagram showing a simplified cross section of the diffractive surface region 20 passing through the line III-III shown in FIG. 2. Note that the cross section shown in FIG. 3 is a simplified conceptual diagram for the purpose of explanation, and does not correspond to the actual pattern shown in FIG. 2. As shown in FIG. 3, the multiple regions 22 are composed of multiple parts provided on the first main surface 18 such that the heights measured from a virtual reference plane 25 extending parallel to the first main surface 18 through the substrate 12 are distributed in a discrete height distribution (each region is composed of a part of the first main surface 18 extending generally parallel to the virtual reference plane 25 within a range allowed by manufacturing tolerances). In several embodiments, the multiple regions 22 have a maximum height h max The first plurality of regions 22a, in which the first main surface 18 is provided, and the minimum height h minand a second plurality of regions 22b in which the first major surface 18 is provided. It should be noted that the virtual reference plane 25 is not a physical component of the substrate 12, but is a virtual reference plane that extends through the substrate 12. In some embodiments, the virtual reference plane 25 extends through the geometric center of the substrate 12. In the illustrated embodiment, the first plurality of regions 22a of the first major surface 18 represent points on the first major surface 18 that are located at positions that are the greatest distance from the virtual reference plane 25, and thus the thickness 21 is at a maximum value when measured within the first plurality of regions 22a. However, the exact height of each of the first plurality of regions 22a is determined by the following formula: max In some embodiments, h max indicates the average height measurement of the first plurality of regions 22a, and the height of each region of the first plurality of regions 22a is h max The same is true for the other heights in the discrete height distribution.

[0059] In some embodiments, the discrete distribution of heights (heights from the imaginary reference plane 25) at which the first principal surface 18 is located can include any number of heights (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, or even more heights). In some embodiments, the regions 22 are spaced apart from the imaginary reference plane 25 by a height h 1 a third plurality of regions 22c in which the first main surface 18 is provided, and a height h 2 and a fourth plurality of regions 22d in which the first main surface 18 is provided. The heights included in the discrete height distribution are equally spaced, and the difference between adjacent heights is within ±5% of the spacing constant (for example, h max -h 2 =h 2 -h 1 =h 1 -h min ). The difference between heights in the discrete height distribution can be an integer multiple of the spacing constant. The values ​​of the spacing constant that can be employed to achieve good anti-glare and haze performance attributes are described in more detail herein.

[0060] As shown in FIG. 3, the multiple regions 22 of the first major surface 18 are separated from each other by transition surfaces 26 of the substrate 12. The transition surfaces 26 refer to sections of the outer surface of the substrate 12 that extend at a fairly large angle (e.g., an angle of more than 20°) with respect to the imaginary reference plane 25. The transition surfaces 26 indicate points at which the surface height of the first major surface 18 exceeds the range of surface height variations associated with the surface roughness of the first major surface 18. The length of each transition surface 26 depends on the pattern of the multiple regions 22 (i.e., which heights of the discrete height distribution are adjacent to each other). In some embodiments, at least some of the multiple transition surfaces 26 extend perpendicular to the imaginary reference plane 25 (or in a direction within ±10° of the perpendicular direction). The transition surfaces 26 that extend perpendicular to the imaginary reference plane 25 in this manner are less likely to cause a difference in height (e.g., h max -h min , h max -h 2 , h max -h 1 ) may have a length corresponding to

[0061] Of course, due to manufacturing tolerances, each region of the first plurality of regions 22a may have a width of h max Each of the second plurality of regions 22b may be provided at a height slightly different from h min Each of the third plurality of regions 22c may be provided at a height slightly different from h 1 Each of the fourth plurality of regions 22d may be provided at a height slightly different from that of the first plurality of regions 22a. 2 Therefore, the height h max , h min , h 1 , h 2may represent a manufacturing target for forming diffractive surface region 20 using any of the methods described herein. In some embodiments, each of first plurality of regions 22a, second plurality of regions 22b, third plurality of regions 22c, and fourth plurality of regions 22d is provided at a height that is within ±5% of its target value. In some embodiments, if the average surface height of each of first plurality of regions 22a, second plurality of regions 22b, third plurality of regions 22c, and fourth plurality of regions 22d is measured and averaged for each set of average surface height values ​​corresponding to each height in the discrete height distribution, the average value for each set can be within ±5% of the manufacturing target value. In some embodiments, a difference can be provided between the average values ​​for each of such sets, and such difference can be within ±5% of an integer multiple of a spacing constant that defines the height spacing described herein.

[0062] In some embodiments, the total area of ​​the regions 22 at each height included in the discrete height distribution occupies a predetermined total surface area ratio (%) in the diffractive surface region 20. In the illustrated example, the first plurality of regions 22a occupies a first total surface area ratio (%) in the diffractive surface region 20, the second plurality of regions 22b occupies a second total surface area ratio (%) in the diffractive surface region 20, the third plurality of regions 22c occupies a third total surface area ratio (%) in the diffractive surface region 20, and the fourth plurality of regions 22d occupies a fourth total surface area ratio (%) in the diffractive surface region 20. In some embodiments, the first total surface area ratio (%) is within ±5% of the second total surface area ratio (%), and the third total surface area ratio (%) is within ±5% of the fourth total surface area ratio (%). In some embodiments, the second total surface area ratio (%) and the third total surface area ratio (%) are larger than the first total surface area ratio (%) and the second total surface area ratio (%). In several embodiments, the first total surface area percentage, the second total surface area percentage, the third total surface area percentage, and the fourth total surface area percentage are all less than 40%.

[0063] The arrangement pattern of the regions 22 and the percentage of total surface area per height included in the discrete height distribution can be determined using scalar diffraction theory and appropriate optimization algorithms as described herein. As shown in Figure 3, the radiation incident from the external environment 24 can be approximated by a uniform plane wave that is approximated as follows:

number

number

[0064] In the example shown in FIG. 3, the far-field scattering pattern for the outgoing radiation is expressed in reciprocal space (k-space), and the near-field u near From (x, y), the Fourier transform is expressed as follows.

number

number

[0065] Examples of the scattering distribution of the LG mode when the azimuthal index l is 2 are shown in Figures 4A and 4B. Figure 4A shows the two-dimensional scattering function, and Figure 4B shows the distribution of the scattering function along the line k y / k 0 Scattering amplitude through k = 0 (a graph showing scattering amplitudes for various angles of incidence of incident radiation at a single plane of incidence). As shown, the specular reflection in this scattering pattern is very small, with only a small scattering angle of k corresponding to a maximum scattering angle of 0.5 degrees. x / k 0= 0.008, the scattering is at a maximum. It should be understood that while the LG mode is one possible target far-field scattering distribution, various target far-field scattering distributions can be contemplated and are within the scope of the present disclosure. As described herein, the target far-field scattering distribution can be used in a suitable optimization algorithm to determine a pattern of the plurality of regions 22.

[0066] In some embodiments, the goal of reducing specular reflection is to reduce the minimum wavelength of interest, λ min Maximum target wavelength λ max This applies over the following wavelength range: min and λ max may vary depending on the application. For example, in one application, the goal may be to minimize specular reflectance across the visible to near infrared range, in which case λ min = 380 nm, λ max In another example, it may be desired to only suppress specular reflectance across the visible spectrum, in which case λ min = 380 nm, λ max = 730 nm. Any suitable wavelength range can be the wavelength range of interest.

[0067] In some embodiments, the goal of reducing specular reflection is to reduce the incidence angle Θ i (see Figure 3). That is, for certain display applications, the reflective surface is applied over a wide range of incidence angles Θ to prevent the user from seeing reflected images from different angles. i In some embodiments, it may be advantageous to provide anti-glare functionality over a range of, for example, Θ min From Θ max It may be desirable to minimize specular reflections at angles of incidence ranging from Θ min =0°, Θ min = 5°, Θ min = 10°, or Θ min = 20°. In some embodiments, Θ max = 70°, Θ max = 60°, Θmax = 50°, Θ max = 45°, Θ max = 40°, Θ max = 35°, or Θ max = 30°. Therefore, the objective of reducing specular reflection is to reduce the wavelength range of interest [λ min ,λ max ] over the range [Θ min ,Θ max It will be understood that the objective of this paper is to minimize specular reflection at angles of incidence within the range k' min From k' max This can be expressed simply as minimizing the specular reflection for wave vectors k up to k' min From k' max It will be understood that this refers to minimizing the specular reflectance up to the The file is TIFF2025510549000027.tif9114.

[0068] Referring to FIG. 3, the height h i The total surface area ratio (%) for each j (j is an integer reference number). In addition, in order to make the multiple regions 22 occupy 100% of the surface area of ​​the first main surface 18 in the diffractive surface region 20, TIFF2025510549000028.tif7114. In this case, taking into account equations (3) to (5), the objective of minimizing the specular reflectance can be mathematically expressed as minimizing a function proportional to f(A,h) as follows:

number

number

number

[0069] Referring to equations (7) to (9), each height h j Ideal total surface area ratio (%) A jsatisfies a set of linear equations, expressed as the following matrix equation: FA=1 (10) In the formula, A is the ideal area A j where 1 is a unit column vector with N components (N corresponds to the number of heights included in the discrete height distribution (hereinafter also referred to as discrete heights)), F is an N×N matrix, and each component of F is calculated by the following formula:

number

[0070] Using equations (10) and (11), each height h calculated using equation (9) j Ideal total surface area ratio (%) A j By calculating min , λ max , Θ min , Θ max For the value of min ,λ max ] and the incidence angle range [Θ min ,Θ max Optimal local phase accumulation function that minimizes specular reflection at TIFF2025510549000037.tif8114 can be calculated (using equations (4) and (5)). min = 400 nm, λ max = 800 nm, Θ min =0°, Θ max In the example of =60°, λ' min , λ' max By calculating the value of and substituting it into equation (9), The value of TIFF2025510549000038.tif6114 can be calculated as 150 nm. By inserting the values ​​of TIFF2025510549000039.tif5114 into formula (11), the area vector A is calculated as (0.178, 0.322, 0.322, 0.178). In the vector, the first value is the height h min The second value is the total surface area ratio (%) at height h 1The third value is the total surface area ratio (%) at height h 2 The total surface area ratio (%) at max The total surface area ratio (%) is shown.

[0071] 5A, 5B, and 5C show a number of different wavelength ranges of interest (octave = log 2 (λ max / λ min 5B shows the ideal specular reflection calculated for multiple distributions of heights of multiple regions 22 (each distribution has a different number of heights) in the 3D space (expressed in units of 3D space). As shown in FIG. 5B, when the target wavelength range is 400 nm to 800 nm (corresponding to one octave), the specular reflection is reduced by about 10 dB compared to the case of a non-textured surface when the number of discrete heights is two, and by about 30 dB when the number of discrete heights is four. As shown in FIG. 5C, in the target wavelength range of 400 nm to 800 nm, the specular reflectance is slightly less than 1% when the number of discrete heights is two, and is less than 0.01% when the number of discrete heights is four. The analysis results are summarized in Table 1 below. The table shows the reduction in specular reflectance (in dB) for various wavelength ranges of interest compared to a non-textured first major surface 18 (each value represents the average reduction over the wavelength range of interest). [Table 1]

[0072] Table 1 can provide guidance in identifying the number of heights required for a particular application, depending on the required reduction in specular reflectance and the relevant wavelength range of interest. Generally, the greater the bandwidth of the wavelength range of interest, the greater the number of heights required to achieve a particular reduction in reflectance from that from a non-textured surface.

[0073] FIG. 6A illustrates a flow diagram of a method 600 for determining a pattern of a plurality of regions in a diffractive surface region according to an exemplary embodiment of the present disclosure. The method 600 can be executed on a computer system 1000 illustrated in FIG. 6B. In some embodiments, the computer system 1000 includes a processing circuit or processor 1002, a main memory 1004 (e.g., read only memory (ROM), flash memory, dynamic random access memory (DRAM) (e.g., synchronous DRAM (SDRAM)), etc.), and a static memory 1006 (e.g., flash memory, static random access memory (SRAM), etc.), which can communicate with each other via a data bus 1008. Alternatively, the processor 1002 can be connected to the main memory 1004 and / or the static memory 1006 directly or via other connection means. The computer system 1000 can further include a network interface device 1010. The computer system 1000 can also include an input unit 1012. The input 1012 is configured to receive inputs and selections that are communicated to the computer system 1000 in executing the instructions. The computer system 1000 may also include an output 1014, including, but not limited to, a display, a video display (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device (e.g., a keyboard), and / or a cursor control device (e.g., a mouse). The computer system 1000 may also include instructions 1016. The instructions 1016 may be stored on a computer-readable medium 1018 and may additionally or alternatively remain in the main memory 1004 and / or in the processor 1002 during execution of the instructions 1016 by the computer system 1000. The main memory 1004 and the processor 1002 also constitute computer-readable media.Additionally, instructions 1016 may be sent or received from the network interface device 1010 over the network 1020. A user may use the computer system 1000 to execute the method 600 by providing inputs at the input 1012 to cause the processor 1002 to execute the following process steps encoded in the instructions 1016:

[0074] In embodiments, method 600 can be used to design a variety of display articles. For example, method 600 can be used to design diffractive surface region 20 of display article 10 described herein in the description of Figures 1-3. Thus, although method 600 will be described with reference to various features shown in Figures 1-3, it should be understood that method 600 can be used to design other display articles.

[0075] 6A, at block 602, a discrete height distribution of diffractive surface regions 20 is identified. In some embodiments, for example, a user may determine a suitable wavelength range of interest [λ] for which specular reflectance is to be minimized. min ,λ max ] and the incidence angle range [Θ min ,Θ max ] can be specified. Such values ​​may vary depending on the application. For example, a display article 10 implemented in a television or computer monitor may require reduced specular reflectance over a different range of incidence angles than a display article 10 implemented in an interior display of an automobile. The specified wavelength range of interest [λ min ,λ max ] and the incidence angle range [Θ min ,Θ max ] is input to the computer system 1000 (e.g., via input 1012), the computer system 1000 executes instructions 1016 to calculate a number of graphs, such as those shown in FIGS. 5A-5C herein, for a given wavelength range of interest [λ min ,λ max ] and the incidence angle range [Θ min ,Θmax ] displays how much specular reflectance may be reduced by various height distributions. In some embodiments, a user may select the number of heights to include in the distribution based on the displayed specular reflectance reduction performance. Also, in some embodiments, instructions 1016 automatically cause processor 1002 to select the number of heights to include in the distribution based on specular reflectance performance requirements entered by the user (e.g., the user may specify a maximum allowable specular reflectance). The heights to include in the discrete height distribution are determined by equations (7)-(9) described herein.

[0076] At block 604, an ideal surface area percentage for each height in the discrete height distribution is identified. The ideal surface area percentage may be calculated using equations (10) and (11) described herein. Then, at block 606, an ideal target scattering pattern is identified. In embodiments, the ideal target scattering pattern may vary depending on the application, and the ideal target scattering pattern may be determined by the application. For example, the user may select the azimuth indices l and k mentioned in the description of equation (6) in this specification. max By specifying the parameters with appropriate values, a suitable LG mode can be defined, although any other suitable ideal scattering pattern can also be used.

[0077] At block 608, an initial pattern of the multiple regions 22 is generated. In some embodiments, instructions 1016 start the optimization algorithm by inputting a pre-stored initial pattern. Any suitable random pattern can be used as the initial pattern of the multiple regions 22, as it has been determined that the initial pattern does not significantly affect the final optimization result. Once the initial pattern is generated, instructions 1016 can cause the processor 1002 to estimate a far-field scattering pattern u(λ) for the initial pattern. For example, the initial pattern can be used to calculate the local phase accumulation function u(λ) of equations (4) and (5): TIFF2025510549000042.tif8114 can be defined and the estimated far-field scattering pattern u(λ) can be calculated.

[0078] The initial pattern is then updated using an optimization algorithm to minimize a suitable objective function in block 610. As described herein, the discrete height distribution and the ideal surface area percentage per height are determined over the wavelength range of interest [λ min ,λ max ] and the incidence angle range [Θ min ,Θ max The objective of keeping the scattering intensity relatively low at large scattering angles (e.g., scattering angles of 2.0° or more, 2.5° or more, 3.0° or more, 3.5° or more, 4.0° or more, 4.5° or more, 5.0° or more, or more) can be determined based on the estimated far-field scattering pattern u(λ) and the ideal target scattering pattern The method can be implemented by comparing the estimated far-field scattering pattern u(λ) with the ideal target scattering pattern u(λ). TIFF2025510549000044.tif6114, and in the area term, the actual total surface area ratio (%) for each height included in the initial pattern is compared with the ideal value A calculated using equations (10) and (11) in this specification. j A comparison can be made with.

[0079] In embodiments, a suitable objective function can be expressed as:

number

[0080] The initial pattern can be updated using a suitable nonlinear function optimization algorithm, where the estimated far-field scattering pattern u(λ) is calculated by iteratively computing a converged solution that minimizes an objective function, and comparing the objective function values ​​of each loop with each other, thereby optimizing the estimated far-field scattering pattern u(λ) to the ideal target far-field scattering pattern u(λ). TIFF2025510549000047.tif6114 and the percentage of total surface area per height in the discrete height distribution is made to approach the ideal value calculated using equations (10) and (11). However, any suitable optimization algorithm can be used, including Newton Conjugate Gradient (Newton-CG), Broyden-Fletcher-Goldfarb-Shanno (BFGS), Sequential Least Squares Programming (SLSQP), etc.

[0081] 1-3, the plurality of regions 22 on the first major surface 18 may be formed using any suitable technique. Figure 7 shows a flow diagram of an exemplary method 700 of making a display article 10 in accordance with an exemplary embodiment of the present disclosure. Method 700 will now be described with reference to the various components shown in Figures 1-3. However, it should be understood that the method of forming the diffractive surface regions 20 is not particularly limited to this particular method, and any suitable method may be used.

[0082] At block 702, a pattern of the plurality of regions 22 is determined. In some embodiments, the pattern can be determined by method 600 described herein with respect to FIG. 6A. At block 704, a resist is deposited and patterned on the first major surface 18. How the resist is deposited and patterned can vary depending on the fabrication technique used. In some embodiments, a variety of nanoimprinting or photolithography techniques can be used to deposit and pattern the resist layer. In such embodiments, the minimum feature size (e.g., minimum linear dimension) of the plurality of regions 22 can be set to at least 1 μm (e.g., 1.5 μm or more, 2.0 μm or more, 2.5 μm or more, 5.0 μm or more, 10 μm or more) to allow for the use of existing resist application and patterning techniques. In some embodiments, the resist can be formed using, for example, thermoplastic nanoimprint lithography, where the resist can be formed of a thermoplastic polymer. A thermoplastic polymer is spin-coated onto substrate 12 and then mold-imprinted to form a first pattern on first major surface 18 that corresponds at least in part to the pattern of regions 22. The resist may then be thermally cured to form an etch mask. Other methods of forming the resist (e.g., other printing techniques such as gravure offset printing) are contemplated and are within the scope of the present disclosure.

[0083] Photolithography (e.g., nanoimprint photolithography, optical photolithography) techniques can also be used, and the resist can be deposited on the first major surface 18 by a suitable application method (e.g., spin coating). In such an embodiment, a mask having a first pattern corresponding at least in part to the determined pattern of the plurality of regions 22 can be aligned with the first major surface 18, and the resist can be hardened to form an etching mask by exposing the resist to radiation (e.g., ultraviolet light) from a suitable light source. The resist can then be developed to leave portions of the first major surface 18 exposed through the hardened resist. However, any suitable photolithography technique can be used to pattern the resist. In some embodiments, the portions of the first major surface 18 covered by the resist extend beyond the first major surface 18 by a height h max The resist may be patterned to form at least some of the first plurality of regions 22a (described in the description of FIG. 3) provided in the first region.

[0084] At block 706, the exposed portions of first surface 18 (from the cured and patterned resist) are exposed to a suitable etchant for an appropriate etching duration, determined based on the target etch depth. Each portion of first surface 18 exposed from the resist pattern formed at block 704 may be directly contacted with the etchant. The etchant may etch the substrate and remove material from the substrate to form regions on first surface 18 that are lower above virtual reference plane 25 than the portions of first surface 18 covered by the resist pattern. In some embodiments, the etchant contacting first surface 18 may be HF / HNO 3 In some embodiments, the etching solution is a mixture of hydrofluoric acid (HF, 49% by weight) and nitric acid (HNO 3 , 69% by mass), HF is 0.1 to 5% by volume, HNO 3The typical concentration used to achieve the etch depths described herein is 0.1% HF / 1% HNO 3 ~0.5% HF / 1% HNO 3 In embodiments, the etching can be performed at temperatures from room temperature to about 45° C. by a dip etching process or a spray etching process.

[0085] At decision block 708, it is determined whether the desired height distribution has been achieved. It will be appreciated that it may be desirable to have the number of heights (heights from the virtual reference plane 25) at which the regions 22 are provided be two or more. In some embodiments, the step of forming the diffractive surface region 20 so that the number of heights (heights from the virtual reference plane 25) at which the regions are provided is two or more may include multiple etching steps with different etching masks and etching durations. For example, in some embodiments, a first etching step is performed for a first etching duration using a first etching mask. The first etching duration is performed to etch a portion of the first major surface 18. TIFF2025510549000048.tif5114. After such etching steps (and additional steps such as cleaning), a second resist may be placed on first major surface 18, patterned, and etched for a second etching period. Portions of first major surface 18 that were etched in the first etching step may be left exposed from the second resist. Also, portions of first major surface 18 that were not etched in the first etching step (because they were covered by the first etching mask) may be left exposed from the second resist. The second etching period may be a period during which the etching depth is As a result, the portion of the first main surface 18 that comes into contact with the etching solution in both etching steps has a total height of TIFF2025510549000050.tif5114, and the part that comes into contact with the etching solution only in the first etching step The part that is etched to the height of TIFF2025510549000051.tif5114 and comes into contact with the etching solution only in the second etching step. TIFF2025510549000052.tif6114, and the portions of first main surface 18 that were covered with resist in both the first and second etching steps are not processed. This example is one way of achieving a number of discrete heights of first main surface 18 of four. Performing the etching steps in any suitable combination and in a variety of different sequences is contemplated and is within the scope of the present disclosure.

[0086] Thus, the resist deposited and patterned on the first major surface 18 in method 700 may not (individually) correspond exactly to the desired final pattern of the regions. Rather, each resist pattern may be an intermediate pattern designed to combine with other etch mask patterns that may be formed on the substrate 12 to form the final pattern determined by the method 600 described herein. Blocks 704, 706, and 708 may be repeated until the desired number of heights is included in the discrete height distribution. At this point, method 700 may end, or the substrate 12 may be subjected to additional processing steps (e.g., chemical strengthening).

[0087] Substrate Characteristics Various characteristics of the substrate 12, according to embodiments of the present disclosure, will now be described.

[0088] In some embodiments, substrate 12 is a glass substrate or a glass-ceramic substrate. In some embodiments, substrate 12 is a multi-component glass composition comprising about 40 mol % to 80 mol % silica, with the balance being one or more other components (e.g., alumina, calcium oxide, sodium oxide, boron oxide, etc.). In some embodiments, the bulk composition of substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, and phosphosilicate glass. In other embodiments, the bulk composition of substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, phosphosilicate glass, soda-lime glass, alkali aluminosilicate glass, and alkali aluminoborosilicate glass. In further embodiments, substrate 12 is a glass-based substrate, including, but not limited to, glass-ceramic materials comprising about 90% or more by weight of glass and ceramic components. In other embodiments of display article 10, substrate 12 can be a polymeric material having suitable durability and mechanical properties for the growth and retention of diffractive surface regions 20.

[0089] In some embodiments, the bulk composition of substrate 12 is alumina, at least one alkali metal, and SiO 2 and, in some embodiments, the glass comprises more than 50 mol % SiO 2 In other embodiments, at least 58 mol % SiO 2 and in yet other embodiments, at least 60 mol % SiO 2 Including the ratio (Al 2 O 3 (mol%)+B 2 O 3 (mol%) / ΣAlkali Metal Modifier (mol%)>1, where the alkali metal modifier is an alkali metal oxide. In certain embodiments, the glass has about 58 mol% to about 72 mol% SiO 2 , about 9 mol% to about 17 mol% Al 2 O 3 , about 2 mol % to about 12 mol % B 2 O 3 , about 8 mol % to about 16 mol % Na2 O, and 0 mol% to about 4 mol% K 2 O, or consisting essentially of them, and the ratio (Al 2 O 3 (mol%)+B 2 O 3 (mol %) / Σalkali metal modifier (mol %)>1, where the alkali metal modifier is an alkali metal oxide.

[0090] In some embodiments, the bulk composition of substrate 12 is about 61 mol % to about 75 mol % SiO 2 , about 7 mol% to about 15 mol% Al 2 O 3 , 0 mol% to about 12 mol% B 2 O 3 , about 9 mol % to about 21 mol % Na 2 O, 0 mol% to about 4 mol% K 2 % to about 3 mol % CaO.

[0091] In some embodiments, the bulk composition of substrate 12 is about 60 mol % to about 70 mol % SiO2 and about 6 mol % to about 14 mol % Al. 2 O 3 , 0 mol % to about 15 mol % B 2 O 3 , 0 mol % to about 15 mol % Li 2 O, 0 mol% to about 20 mol% Na 2 O, 0 mol% to about 10 mol% K 2 O, 0 mol% to about 8 mol% MgO, 0 mol% to about 10 mol% CaO, 0 mol% to about 5 mol% ZrO 2 , 0 mol% to about 1 mol% SnO 2 , 0 mol% to about 1 mol% CeO 2 , less than about 50 ppm As 2 O 3 , and less than about 50 ppm Sb 2 O 3and 12 mol % or less Li 2 O+Na 2 O+K 2 %. O≦20 mol %, and 0 mol %≦MgO+Ca≦10 mol %.

[0092] The bulk composition of the substrate 12 is about 64 mol % to about 68 mol % SiO 2 , about 12 mol % to about 16 mol % Na 2 O, about 8 mol% to about 12 mol% Al 2 O 3 , 0 mol% to about 3 mol% B 2 O 3 , about 2 mol % to about 5 mol % K 2 0, about 4 mol% to about 6 mol% MgO, and 0 mol% to about 5 mol% CaO; and 2 +B 2 O 3 +CaO≦69mol%, Na 2 O+K 2 O+B 2 O 3 + MgO + CaO + SrO > 10 mol%, 5 mol% ≦ MgO + CaO + SrO ≦ 8 mol%, (Na 2 O+B 2 O 3 )-Al 2 O 3 ≦2mol%, 2mol%≦Na 2 O-Al 2 O 3 ≦6 mol%, and 4 mol%≦(Na 2 O+K 2 O)-Al 2 O 3 ≦10 mol % of the alkali aluminosilicate glass.

[0093] In some embodiments, the bulk composition of the substrate 12 is SiO 2 , Al 2 O 3 , P 2 O 5 and at least one alkali metal oxide (R2 O), 0.75>[(P 2 O 5 (mol%)+R 2 O (mol%) / M 2 O 3 (mol%)≦1.2, and M 2 O 3 =Al 2 O 3 +B 2 O 3 In some embodiments, [(P 2 O 5 (mol%)+R 2 O (mol%) / M 2 O 3 (mol %)]=1, and in some embodiments the glass is 2 O 3 Not including M 2 O 3 =Al 2 O 3 In some embodiments, the substrate 12 is about 40 to about 70 mol % SiO 2 , 0 to about 28 mol % B 2 O 3 , about 0 to about 28 mol % Al 2 O 3 , about 1 to about 14 mol % P 2 O 5 and about 12 to about 16 mol % of R 2 In some embodiments, the glass substrate comprises about 40 to about 64 mol % SiO 2 , 0 to about 8 mol% B 2 O 3 , about 16 to about 28 mol % Al 2 O 3 , about 2 to about 12 mol % P 2 O 5 and about 12 to about 16 mol % of R 2 O. Substrate 12 may also further include at least one alkaline earth metal oxide, such as, but not limited to, MgO or CaO.

[0094] In some embodiments, the substrate 12 has a bulk composition that is substantially free of lithium. 2 In another embodiment, the glass contains Li 2 In another embodiment, the glass contains less than 0.1 mol % Li 2 In yet another embodiment, the glass contains Li 2 In some embodiments, the glass is free of at least one of arsenic, antimony, and barium. 2 O 3 , Sb 2 O 3 and / or BaO is less than 1 mol %, in other embodiments less than 0.1 mol %, and in yet other embodiments 0 mol %.

[0095] In several embodiments, the bulk composition of substrate 12 comprises (or consists essentially of, or consists of) Corning® Eagle XG® glass, Corning Gorilla® glass, Corning Gorilla glass 2, Corning Gorilla glass 3, Corning Gorilla glass 4, or Corning Gorilla glass 5.

[0096] In embodiments, the substrate 12 has an ion-exchanged glass composition that has been strengthened by either chemical or thermal means known in the art. In embodiments, the substrate 12 is chemically strengthened by ion exchange. In this process, metal ions at or near the first major surface 18 of the substrate 12 are exchanged with larger metal ions of equal valence to the metal ions in the substrate 12. Generally, ion exchange is accomplished by contacting the substrate 12 with an ion exchange medium (e.g., a molten salt bath, etc.) that contains the larger metal ions. The metal ions are typically monovalent metal ions, such as alkali metal ions. By way of non-limiting example, when chemically strengthening a substrate 12 containing sodium ions by ion exchange, the strengthening of the substrate 12 is accomplished by contacting the substrate 12 with potassium nitrate (KNO 3 In one particular embodiment, the surface ions adjacent to the first major surface 18 of the substrate 12 and larger ions are Li + (when located in glass) or Na + , K + , Rb + , Cs + Alternatively, the monovalent cations in the surface layer of the substrate 12 may be Ag. + The cations may also be substituted with monovalent cations other than the alkali metal cations, such as:

[0097] In such embodiments, the ion exchange process replaces smaller metal ions with larger metal ions to create a compressive stress region in substrate 12 that extends from first major surface 18 to a depth (referred to as the "depth of layer") where the compressive stress is balanced by a tensile stress (also known as the "central tension") within substrate 12. In some embodiments, first major surface 18 of substrate 12 described herein is strengthened by ion exchange to have a compressive stress of at least 350 MPa, with the compressive stress region extending at least 15 μm into thickness 21 below first major surface 18 (i.e., the depth of layer).

[0098] The ion exchange process is typically performed by immersing the substrate 12 in a molten salt bath containing larger ions that will replace the smaller ions in the glass. Parameters of the ion exchange process include, but are not limited to, the composition and temperature of the bath, the time of immersion, the number of times the glass is immersed in the salt bath(s), the use of multiple salt baths, and additional steps such as annealing and washing steps. Those skilled in the art will appreciate that the parameters of such an ion exchange process are typically determined by the composition of the glass, as well as the depth and compressive stress of the glass that is desired as a result of the strengthening process. By way of example, ion exchange of an alkali metal-containing glass can be performed by immersion in at least one molten bath containing salts of larger alkali metal ions (e.g., but not limited to, nitrates, sulfates, chlorides, etc.). The temperature of the molten salt bath typically ranges from about 380° C. to about 450° C., and the immersion time ranges from about 15 minutes to about 16 hours. However, other temperatures and immersion times can be used. When such an ion exchange treatment is performed on a substrate 12 having an alkali aluminosilicate glass composition, a compressive stress region is obtained having a depth (layer depth) in the range of about 10 μm to at least 50 μm, a compressive stress in the range of about 200 MPa to about 800 MPa, and a central tension of less than about 100 MPa.

[0099] It should be noted that the diffractive surface regions 20 of the substrate 12 can be formed using an etching process, however, the etching process may remove alkali metal ions in the substrate 12 that would otherwise be replaced by larger alkali metal ions during the ion exchange process. For this reason, it is preferred to grow the compressive stress regions in the display article 10 after the diffractive surface regions 20 are formed and grown. EXAMPLES

[0100] Embodiments of the present disclosure can be further understood in light of the following examples.

[0101] In Example 1, the process described in the description of FIG. 6A herein was carried out on a 2.048 mm×2.048 mm sample with four discrete heights within the design wavelength range of 400 nm to 800 nm. In this example, only the normal incidence angle was considered. The etching depth was determined using equations (8) and (9) herein, and the ideal total surface area ratio (%) was determined using equations (10) and (11). Then, an appropriate optimization algorithm was used to minimize equation (12). The target scattering pattern was taken as the LG mode with l=2, and the weighting parameter w was set to 10.

[0102] 8A and 8B are diagrams showing etching mask patterns. In each diagram, the etching depth used in that pattern is indicated. FIG. 8A is a plan view of a first etching mask 800 in this embodiment. The first etching depth used in the first etching mask 800 is: TIFF2025510549000053.tif6114=133.3 nm. FIG. 8B is a plan view of the second etching mask 802. The second etching depth used in the second etching mask 802 is TIFF2025510549000054.tif5114=266.7 nm. As shown, both the first etching mask 800 and the second etching mask 802 have a wormhole-like structure in which regions of the same height form relatively large continuous regions (e.g., regions with a maximum length dimension on the order of hundreds of micrometers). In addition, both the first etching mask 800 and the second etching mask 802 include surrounding regions 804, 806, 808, 810, which are relatively small regions (regions with a maximum length dimension on the order of tens of micrometers) that are completely surrounded by regions etched to different depths. The light-colored regions in one of the first etching mask 800 and the second etching mask 802 (which correspond to substrate regions that are not etched in the etching step using that mask) overlap with the light-colored regions in the other etching mask to form a maximum height h from the virtual reference plane. max In some cases, the dark areas of the other etching mask can be overlapped to form a region with a height of h 1 The area and height h 2 In some cases, the dark areas in one of the first and second etching masks 800 and 802 (which correspond to the substrate areas to be etched in the etching step using that mask) may overlap with the dark areas in the other etching mask to form a minimum height h min In some cases, it may be possible to form a region of

[0103] The methods described herein can generate periodic etch patterns (in both x and y directions) that tile the patterns shown in Figures 8A and 8B so that they can be spread over larger areas. In some embodiments, the minimum tile dimension of the etch mask can be 2 mm to 500 μm to avoid noticeable variations in scattering intensity due to the periodicity of the pattern while allowing design flexibility to derive a suitable pattern.

[0104] Figure 9 shows the far-field scattering patterns of this example calculated for several wavelengths in the wavelength range of interest. All scattering patterns show a characteristic "donut shape" and are very similar to the LG mode with l=2. The scattering angle of the peak point of these scattering patterns was 0.25°. This indicates that these scattering patterns can suppress the haze to a relatively low level.

[0105] FIG. 10A shows a histogram of the etch depth (for each height h j The ratio of the frequencies of each height is in excellent agreement with the ideal ratio of 0.147:0.353:0.353:0.147. That is, in several embodiments, the height h max A first total surface area ratio (%) of the first plurality of regions 22a provided in 1 ) to the height h min A second total surface area ratio (%) of the second plurality of regions 22b provided in 2 ) (for example, A 2 3. In some embodiments, the height h 1 A third total surface area ratio (%) of the third plurality of regions 22c provided in 3 ) to the height h 2 A fourth total surface area ratio (%) of the fourth plurality of regions 22d provided in 4 ) (for example, A 4 Within ±5% of the above (see FIG. 3).4 >A 1 In some embodiments, A 4 >A 2 In some embodiments, A 3 >A 1 In some embodiments, A 3 >A 2 In some embodiments, A 1 and A 2 A 3 and A 4 In some embodiments, A 1 +A 2 3 In some embodiments, A 1 +A 2 4 In some embodiments, when the number of heights included in the discrete height distribution is four, A 1 , A 2 , A 3 , A 4 In an embodiment in which the number of heights included in the discrete height distribution is two, A 1 (h max ) and A 2 ( TIFF2025510549000055.tif5114) are all 50%. min h max is at least 100 nm (e.g., at least 105 nm, at least 110 nm, at least 115 nm, at least 120 nm, at least 125 nm, at least 130 nm, at least 135 nm, at least 140 nm, at least 145 nm, at least 150 nm, at least 200 nm, at least 250 nm, at least 300 nm, at least 350 nm, at least 400 nm, at least 450 nm, at least 500 nm, or even greater than 500 nm) smaller than

[0106] ​​Graph 900, shown in FIG. 10B, includes a first plot 902 showing the calculated normalized reflectance (calculated based on a reflectance of 1 for a non-textured surface) and a second plot 904 showing the calculated transmitted haze. As shown in plot 902, the specular reflectance is significantly reduced compared to a non-textured surface, with the maximum specular reflectance at both ends of the wavelength range of interest being 0.0035 times, i.e., 0.35% of the specular reflectance for a non-textured surface. Also, as shown in plot 904, a maximum haze of about 3.7% was observed at a wavelength of 400 nm, with an average of about 2.5% for the wavelength range of interest. These results demonstrate the ability of the patterns generated by the methods described herein to provide the benefit of reduced specular reflectance while maintaining relatively low haze.

[0107] Also, Example 2 was fabricated by the method 700 described in the description of FIG. 7 of this specification. In the diffractive surface region included in Example 2, the number of heights (heights from the virtual reference plane) at which the multiple regions are provided was two. The pattern was determined in a target wavelength range of 400 nm to 800 nm for normal incidence. The pattern of the multiple regions was determined by the method 600 described in the description of FIG. 6A of this specification. One etching mask was placed on the sample. The sample was a 4-inch wafer of "Gorilla" glass manufactured by "Corning" with a thickness of 0.7 mm. After resist deposition and patterning, the wafer was immersed in an etching solution (0.15% HF / 1% HFNO) for 175 seconds until the etching depth measured with a stylus was 156.5 nm. 3The substrate was exposed to a 3000 .mu.m (1000 .mu.m) solution. A typical sequence of processing steps for a standard photolithography process applicable to Example 2 includes, in order, substrate preparation (cleaning and dehydration followed by application of a spin-coatable adhesion promoter for resist (e.g., hexamethyldisilazane (HMDS)), spin-coating of photoresist, pre-baking, exposure (e.g., exposure to UV light or high temperature), development, and a wet etch process to transfer the binary image onto the glass. Resist stripping is performed at the final stage of the lithography process (e.g., by exposure to a suitable solvent) after transfer of the resist pattern to the layer below. In some cases, post-baking and post-exposure bake steps may be required to ensure adhesion of the resist during the wet etch process.

[0108] Light from a supercontinuum source was then directed through a beam splitter onto the diffractive surface area of ​​the sample, and specular reflectance and scattering measurements were performed at multiple wavelengths. The reflected and scattered light was directed through a beam splitter to a camera, and the relative intensity at various scattering angles was measured. Figure 11A shows the intensity map corresponding to the imaged scattering pattern. As shown, the scattering pattern resembles the LG mode, but the dot in the center indicates that visible specular reflection remains. Figure 11B shows a graph of the measured and calculated spectral reflectance intensity. As shown, the results are in good agreement with the theoretical values. Compared to the non-textured sample, a reduction of up to 25 dB (corresponding to a measured specular reflectance of 0.01% at a wavelength of approximately 620 nm) was achieved. It was also observed that the specular reflectance was suppressed to less than 4% over the entire wavelength range from 400 nm to 840 nm.

[0109] The azimuth-averaged scattering intensity at various scattering angles was also calculated. The results are shown in FIG. 11C. The dashed line 910 in FIG. 11C shows the scattering pattern of the LG mode target scattering distribution, which has a maximum intensity at a scattering angle of about 0.5°. As shown, the wavelengths around 600 nm are very close to the target scattering distribution, the scattering angle of the peak point is less than 0.5° at the lower end of the wavelength range, and the scattering angle of the peak point is greater than 0.5° at wavelengths 700 nm and above, but still less than 2.5°. These results demonstrate that the articles described herein have the ability to exhibit good specular reflection performance while suppressing haze to a low level.

[0110] It is to be understood that, unless expressly stated otherwise, no method described herein is intended to be construed as requiring the steps to be performed in a particular order. Thus, no particular order is intended to be inferred for the order of steps unless a method claim actually recites the order of steps, or unless other statements that limit the steps to a particular order are clearly made in the claims or detailed description of the invention. Furthermore, in this specification, the article "a" is intended to include one or more components or elements, and is not intended to be construed as meaning "only one."

[0111] It will be apparent to those skilled in the art that various modifications and changes can be made without departing from the spirit and scope of the embodiments of the present disclosure. Since those skilled in the art can think of modifications, combinations, partial combinations, and modifications of these embodiments while incorporating the intent and spirit of the embodiments of the present disclosure, the embodiments of the present disclosure should be interpreted as including all within the scope of the appended claims and their equivalents.

[0112] Preferred embodiments of the present invention will be described below in detail.

[0113] EMBODIMENT 1 A first major surface; a second main surface opposite the first main surface; and a diffractive surface area formed on the first major surface; A display article comprising: the first major surface has a plurality of regions within the diffractive surface region at a plurality of heights forming a discrete height distribution, each height in the discrete height distribution being a relative height measured from an imaginary reference plane extending through the display article and parallel to the first major surface; The plurality of regions define a range of angles of incidence on the first principal surface from a minimum angle of incidence Θ min From the maximum incidence angle Θ max When the range is set to , the minimum wavelength λ min Maximum wavelength λ max arranged such that a specular reflectance of light incident on the first principal surface is reduced by a factor of at least 10 relative to a non-textured surface not including the diffractive surface region within a wavelength range of interest: The difference between the heights included in the discrete height distribution is Within ±5% of an integer multiple of TIFF2025510549000056.tif6114, where TIFF2025510549000057.tif14114,λ' min = λ min / cosθ min , and λ' max = λ max / cosθ max A display item.

[0114] EMBODIMENT 2 2. The display article of embodiment 1, wherein the diffractive surface region scatters the light in a far-field scattering pattern having a peak point scattering angle of 1.5° or less in the wavelength range of interest.

[0115] EMBODIMENT 3 3. The display article of embodiment 2, wherein the scattering angle of the peak point in at least a portion of the wavelength range of interest is 0.5° or less.

[0116] EMBODIMENT 4 3. The display article of embodiment 2, wherein the far-field scattering pattern approximates a Laguerre-Gaussian mode.

[0117] EMBODIMENT 5 λ min is 380 nm or more and λ max is 1200 nm or less, Θ min is 0° or more and Θ max The display article according to any one of embodiments 1 to 4, wherein the angle is 75° or less.

[0118] EMBODIMENT 6 λ min = 400 nm and λ max = 800 nm.

[0119] EMBODIMENT 7 7. The display article of any one of embodiments 1 to 6, wherein the specular reflectance is reduced by at least a factor of 100 compared to when the first main surface is the non-textured surface.

[0120] EMBODIMENT 8 8. The display article according to any one of embodiments 1 to 7, wherein the minimum feature size of the plurality of regions is 1 μm or more.

[0121] EMBODIMENT 9 9. The display article according to any one of embodiments 1 to 8, wherein the multiple regions are arranged in a pattern having periodicity in two directions perpendicular to each other.

[0122] EMBODIMENT 10 the pattern has at least one enclosed area; 10. The display article of embodiment 9, wherein the surrounding area is a region that is completely surrounded by an area whose height from the virtual reference plane is different from that of the surrounding area.

[0123] EMBODIMENT 11 11. The display article according to any one of embodiments 1 to 10, wherein the transmission haze of the light incident on the first main surface is 4% or less over the entire wavelength range of 400 nm to 800 nm.

[0124] EMBODIMENT 12 A display article according to any one of embodiments 1 to 11, wherein the total surface area ratio (%) of the diffractive surface area occupied by the regions among the plurality of regions that are provided at each height included in the discrete height distribution is a predetermined total surface area ratio (%) that is determined in advance so as to minimize the specular reflectance.

[0125] EMBODIMENT 13 13. The display article of embodiment 12, wherein the discrete height distribution comprises three or more heights.

[0126] EMBODIMENT 14 the discrete height distribution includes at least four heights; The at least four heights have a minimum height h min and, a second height that is within ±5% of TIFF2025510549000058.tif6114; and a third height that is within ±5% of TIFF2025510549000059.tif6114; and and a fourth height that is within ±5% of TIFF2025510549000060.tif6114.

[0127] EMBODIMENT 15 a first plurality of regions having the minimum height occupy a first total surface area percentage of the diffractive surface area; a second plurality of regions having the second height occupying a second total surface area percentage of the diffractive surface area; 15. The display article of embodiment 14, wherein the first total surface area percentage is less than the second total surface area percentage.

[0128] EMBODIMENT 16 a third plurality of regions having the third height occupying a third total surface area percentage of the diffractive surface area; a fourth plurality of regions having the fourth height occupying a fourth total surface area percentage of the diffractive surface area; The first total surface area ratio (%) is within ±5% of the fourth total surface area ratio (%); 16. The display article of embodiment 15, wherein the second total surface area percentage is within ±5% of the third total surface area percentage.

[0129] EMBODIMENT 17 14. The display article of embodiment 13, wherein the total surface area percentage of each height is 40% or less.

[0130] EMBODIMENT 18 A first major surface; a second main surface opposite the first main surface; and a diffractive surface area formed on the first major surface; 1. A glass display article comprising: The first principal surface has, within the diffractive surface region, a first plurality of regions having a first plurality of heights; a second plurality of regions having a second plurality of heights; It has The first plurality of heights are measured from an imaginary reference plane that extends through the glass display article and parallel to the first major surface, and a maximum height h is an average of the first plurality of heights. max Within ±5% of the first plurality of regions occupying a first total surface area percentage of the diffractive surface area; The second plurality of heights are heights measured from the virtual reference plane, and a minimum height h min Within ±5% of the second plurality of regions occupying a second total surface area percentage of the diffractive surface area; The first and second regions define a range of angles of incidence on the first principal surface from a minimum angle of incidence Θ min From the maximum incidence angle Θ max When the range is set to , the minimum wavelength λ min Maximum wavelength λ max are arranged in a predetermined pattern that is determined based on the expected specular reflectance of light incident on the first principal surface within the following target wavelength range: h max -h min teeth, Within ±5% of an integer multiple of TIFF2025510549000061.tif6114, where TIFF2025510549000062.tif14114,λ' min = λ min / cosθ min , and λ' max = λ max / cosθ max and A glass display article, wherein the average measured specular reflectance of said first major surface in said wavelength range of interest within said range of incidence angles is 2.5% or less.

[0131] EMBODIMENT 19 19. The glass display article of embodiment 18, wherein the diffractive surface region scatters the light in a far-field scattering pattern having a peak point scattering angle of 1.5° or less in the wavelength range of interest.

[0132] EMBODIMENT 20 20. The glass display article of embodiment 19, wherein the scattering angle of the peak point in the wavelength range of interest is 0.5° or less.

[0133] EMBODIMENT 21 20. The glass display article of embodiment 19, wherein the far-field scattering pattern approximates a Laguerre-Gaussian mode.

[0134] EMBODIMENT 22 λ min is 380 nm or more and λ max is 1200 nm or less, Θ min is 0° or more and Θ max 22. The glass display article of any one of embodiments 18 to 21, wherein the angle is 75° or less.

[0135] EMBODIMENT 23 the first major surface has a third plurality of regions having a third plurality of heights within the diffractive surface region; The third plurality of heights are heights measured from the virtual reference plane, and a height h 1 Within ±5% of the third plurality of regions occupying a third total surface area percentage of the diffractive surface area; The height h 1 but, 23. The glass display article of any one of embodiments 18 to 22, wherein the color is within ±5% of TIFF2025510549000063.tif6114.

[0136] EMBODIMENT 24 the first major surface has a fourth plurality of regions having a fourth plurality of heights within the diffractive surface region; The fourth plurality of heights are heights measured from the virtual reference plane, and a height h 2 Within ±5% of the fourth plurality of regions occupying a fourth total surface area percentage of the diffractive surface area; The height h 2 but, 24. The glass display article of embodiment 23, wherein the chromaticity is within ±5% of TIFF2025510549000064.tif6114.

[0137] EMBODIMENT 25 The first total surface area ratio (%) is within ±5% of the second total surface area ratio (%), 25. The glass display article of embodiment 24, wherein the third total surface area percentage is within ±5% of the fourth total surface area percentage.

[0138] EMBODIMENT 26 25. The glass display article of embodiment 24, wherein the first total surface area ratio (%), the second total surface area ratio (%), the third total surface area ratio (%), and the fourth total surface area ratio (%) are all 40% or less.

[0139] EMBODIMENT 27 27. The glass display article according to any one of embodiments 18 to 26, wherein the first plurality of regions and the second plurality of regions have a feature size of 1 μm or more.

[0140] EMBODIMENT 28 28. The glass display article according to any one of embodiments 18 to 27, wherein the predetermined pattern has periodicity in two directions perpendicular to each other.

[0141] EMBODIMENT 29 the predetermined pattern has at least one enclosed area; 29. The glass display article according to any one of embodiments 18 to 28, wherein the surrounding area is a area completely surrounded by an area having a different height from the virtual reference plane than the surrounding area.

[0142] EMBODIMENT 30 30. The glass display article according to any one of embodiments 18 to 29, wherein the transmission haze of the light incident on the first main surface is 4% or less over the entire wavelength range of 400 nm to 800 nm.

[0143] EMBODIMENT 31 1. A method for forming a diffractive surface region on a substrate for a display article, the method comprising: Determining a pattern of a plurality of regions on a first major surface of the substrate, comprising: each of the plurality of regions having a surface area disposed at a height measured from an imaginary reference plane extending through the display article and parallel to the first major surface; determining a pattern, the plurality of regions having a discrete height distribution; disposing one or more etch masks on the first major surface that allow etching to occur only on selected areas of the first major surface to form at least some of the regions; contacting the display article with an etching solution for a period of time after disposing each etching mask of the one or more etching masks on the first major surface; Including, The step of contacting with the etching solution is such that the difference between heights in the discrete height distribution is: The method includes forming a plurality of regions on the substrate having the discrete height distribution such that the discrete height distribution is within ±5% of an integer multiple of TIFF2025510549000065.tif6114, TIFF2025510549000066.tif14114, lambda min is the minimum wavelength in the wavelength range of interest, λ max is the maximum wavelength in the target wavelength range, and [Θ min ,Θ max ] defines the range of incidence angles over which it is desired to minimize the specular reflectance of the display article; and λ' min = λ min / cosθ min And λ' max = λ max / cosθ max That is, the method.

[0144] EMBODIMENT 32 The step of determining the pattern of the plurality of regions comprises: FA=1 determining an ideal total surface area ratio (%) for each height included in the discrete height distribution using where A is a vector with N elements, N corresponds to the number of heights included in the discrete height distribution, 1 is a unit column vector with N elements, F is an N×N matrix, and the value of each element of F is F ij is the following formula:

number

[0145] EMBODIMENT 33 said step of determining said pattern of said plurality of regions further comprising: generating an initial pattern of the plurality of regions; The estimated far-field scattering pattern is calculated by approximating the incident light by a uniform electric field and the diffractive surface area as only inducing a phase shift in the reflected light. calculating TIFF2025510549000068.tif6114; Using an optimization algorithm, updating the initial pattern to reduce a difference between TIFF2025510549000069.tif6114 and a target scattering pattern u(λ); 33. The method of embodiment 32, comprising:

[0146] EMBODIMENT 34 The optimization algorithm solves the following objective function for the pattern P:

number

[0147] EMBODIMENT 35 35. The method of embodiment 33 or 34, wherein the target scattering pattern approximates a Laguerre-Gaussian mode.

[0148] EMBODIMENT 36 36. The method of any one of embodiments 33 to 35, wherein the target scattering pattern has a scattering angle of a peak point in the wavelength range of interest of 1.5° or less.

[0149] EMBODIMENT 37 37. The method of embodiment 36, wherein the scattering angle of the peak point in the wavelength range of interest is 0.5° or less.

[0150] EMBODIMENT 38 38. The method of any one of embodiments 31-37, wherein the one or more etching masks include at least two etching masks configured such that the discrete height distribution includes at least four heights.

[0151] EMBODIMENT 39 the at least two etching masks include a first etching mask and a second etching mask, and the second etching mask is disposed on the first main surface after exposing the substrate to an etching solution through the first etching mask; 39. The method of claim 38, wherein the second etch mask is configured to expose a portion of the first major surface that is etched through the first etch mask, thereby allowing the portion to be etched both through the first etch mask and through the second etch mask.

[0152] EMBODIMENT 40 40. The method according to any one of embodiments 31 to 39, wherein the minimum feature size of the pattern is 1 μm or more.

[0153] EMBODIMENT 41 41. The method according to any one of embodiments 31 to 40, wherein the pattern has periodicity in at least two mutually orthogonal directions. [Explanation of symbols]

[0154] 10 Display items 12 Substrate 14. Chassis 16 Display 18 First main surface 19 Second main surface 20 Diffractive Surface Area 21 Thickness 22 Multiple Areas 22a First several areas 22b Second Multiple Areas 22c Third Multiple Areas 22d Fourth Multiple Regions 24 External environment 25 Virtual Reference Plane 26 Transition plane 28 Virtual Plane 800 First Etching Mask 802 Second Etching Mask 804, 806, 808, 810 Enclosing Area 1000 Computer Systems 1002 Processor 1004 Main memory 1006 Static Memory 1008 Data Bus 1010 Network Interface Device 1012 Input section 1014 Output section 1016 Instructions 1018 Computer-readable medium 1020 Network

Claims

1. A first major surface; a second main surface opposite the first main surface; and a diffractive surface region formed on the first major surface; A display article comprising: the first major surface has a plurality of regions within the diffractive surface region at a plurality of heights forming a discrete height distribution, each height in the discrete height distribution being a relative height measured from an imaginary reference plane extending through the display article and parallel to the first major surface; The plurality of regions define a range of angles of incidence on the first principal surface from a minimum angle of incidence Θ min From the maximum incidence angle Θ max When the range is set to , the minimum wavelength λ min Maximum wavelength λ max wherein the first principal surface has a specular reflectance that is reduced by a factor of at least 10 relative to a non-textured surface that does not include the diffractive surface region within a wavelength range of interest that is: The difference between the heights included in the discrete height distribution is Within ±5% of an integer multiple of , λ' min = λ min / cosθ min , and λ' max = λ max / cosθ max A display item.

2. 10. The display article of claim 1, wherein the diffractive surface region scatters the light in a far-field scattering pattern having a peak point scattering angle of 1.5 degrees or less in the wavelength range of interest.

3. λ min is 380 nm or more and λ max is 1200 nm or less, Θ min is 0° or more and Θ max The display article of claim 1 or 2, wherein the angle is 75° or less.

4. λ min = 400 nm and λ max 3. The display article of claim 1 or 2, wherein:

5. 3. The display article of claim 1 or 2, wherein the specular reflectance is reduced by a factor of at least 100 compared to when the first major surface is the non-textured surface.

6. the plurality of regions are arranged in a pattern having periodicity in two directions perpendicular to each other, the pattern has at least one surrounding region, the surrounding region being completely surrounded by a region having a height from the virtual reference plane different from that of the surrounding region; The display article according to claim 1 or 2, wherein the minimum feature size of the plurality of regions is 1 μm or more.

7. 3. The display article according to claim 1, wherein the transmission haze of the light incident on the first main surface is 4% or less over the entire wavelength range of 400 nm to 800 nm.

8. a total surface area ratio (%) of the plurality of regions provided at each height included in the discrete height distribution to the diffractive surface region is a predetermined total surface area ratio (%) that is determined in advance so as to minimize the specular reflectance; the discrete height distribution includes three or more heights; the discrete height distribution includes at least four heights; The at least four heights are equal to or greater than a minimum height h min and, a second height that is within ±5% of a third height that is within ±5% of and a fourth height that is within ±5% of a first plurality of regions having the minimum height occupy a first total surface area percentage of the diffractive surface area; a second plurality of regions having the second height occupying a second total surface area percentage of the diffractive surface area; The first total surface area ratio (%) is smaller than the second total surface area ratio (%), a third plurality of regions having the third height occupying a third total surface area percentage of the diffractive surface area; a fourth plurality of regions having the fourth height occupying a fourth total surface area percentage of the diffractive surface area; The first total surface area ratio (%) is within ±5% of the fourth total surface area ratio (%), The second total surface area ratio (%) is within ±5% of the third total surface area ratio (%), 2. The display article of claim 1, wherein the total surface area percentage of each height is 40% or less.

9. 1. A method for forming a diffractive surface region on a substrate for a display article, the method comprising: Determining a pattern of a plurality of regions on a first major surface of the substrate, comprising: each region of the plurality of regions having a surface area disposed at a height measured from an imaginary reference plane extending through the display article and parallel to the first major surface; determining a pattern, the plurality of regions having a discrete height distribution; disposing one or more etch masks on the first major surface that allow etching to occur only on selected areas of the first major surface to form at least some of the regions; contacting the display article with an etching solution for a period of time after disposing each etching mask of the one or more etching masks on the first major surface; Including, The step of contacting with the etching solution is such that the difference between heights in the discrete height distribution is: The method is performed to form a plurality of regions having the discrete height distribution on the substrate such that the discrete height distribution is within ±5% of an integer multiple of and λ min is the minimum wavelength in the wavelength range of interest, λ max is the maximum wavelength in the target wavelength range, and [Θ min , Θ max ] defines the range of incidence angles over which it is desired to minimize the specular reflectance of the display article; and λ' min = λ min / cosθ min And λ' max = λ max / cosθ max That is, the method.

10. The step of determining the pattern of the plurality of regions comprises: F A = ​​1 determining an ideal total surface area percentage for each height included in the discrete height distribution using In the formula, A is a vector having N components, N corresponds to the number of heights included in the discrete height distribution, 1 is a unit column vector having N components, F is an N×N matrix, and the value of each component of F is F ｉｊ is expressed by the following formula: [0010] The method of claim 9, wherein the calculated value is:

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