Article having an anti-glare surface exhibiting low sparkle and minimizing color artifacts.

Abstract

Disclosed herein is an article having a scattering region configured to minimize color artifacts and provide relatively low sparkle. The scattering surface may be a portion of the surface of the article comprising a plurality of first regions located at a first height and a plurality of second regions located at a second height. The scattering surface is designed within the Fourier region, and the article has a first range of scattering angles in which the radial PSD increases with increasing scattering angles of light relative to the specular reflection direction, and a peak angle θ in which the radial PSD has a peak value. peak , and radial PSD decreases sharply with increasing scattering angle, θ peak It is constructed to show radial power spectral density including a second range of scattering angles at larger angles.

Description

Description of related applications

[0001] This application claims the benefit of priority under U.S.C. Title 35, Section 119 of U.S. Provisional Patent Application No. 63 / 420222, filed on 28 October 2022, whose contents are relied upon and are fully referenced herein. [Technical Field]

[0002] This disclosure relates to an article having an anti-glare surface exhibiting low sparkle with minimal color artifacts. [Background technology]

[0003] Transparent substrates are used to cover the displays of display devices. Examples of such display devices include smartphones, tablets, televisions, computer monitors, and in-car displays. The displays are often liquid crystal displays or organic light-emitting diodes. The substrate protects the display, while its transparency allows the user of the device to view the display. Glare is a phenomenon associated with a reduced viewing experience in the presence of bright light sources. In addition, reflected images from the surroundings, not just bright light sources, can also contribute to a reduced viewing experience of the display. For example, the user's own reflection, which is visually prominent, and light from the surrounding environment can be distracting, reduce visibility, and cause eye strain.

[0004] Several techniques exist to reduce glare, including anti-reflective coatings and anti-glare technologies. Anti-reflective coatings can reduce glare by directly reducing the overall amount of reflection. However, certain existing anti-reflective coatings may not be able to reduce such reflections to a degree sufficient to make them unnoticeable to the user across the entire visible spectrum. Anti-glare technologies attempt to reduce the peak intensity of reflections by spreading the reflection of light over a wide range of angles, making distracting reflected images less noticeable to the user. However, if the reflection angle is too large, haze can become relatively high, which can reduce the contrast of the displayed image. [Overview of the project] [Problems that the invention aims to solve]

[0005] Therefore, alternatives to existing anti-glare and anti-reflective coating technologies that allow for favorable control of the angular distribution of scattered light would be beneficial. [Means for solving the problem]

[0006] Aspect (1) of the present disclosure is a substrate having a first principal surface; a second principal surface opposite to the first principal surface; and a scattering region formed within the first principal surface, wherein within the scattering region, the first principal surface includes a plurality of first regions positioned at a first height with respect to a virtual base plane extending over the substrate, and a plurality of second regions positioned at a second height with respect to the virtual base plane, the first height being greater than the second height by an etching depth of 80 nm or more and 600 nm or less, and the scattering region having a first range of scattering angles in which the radial PSD increases with increasing scattering angle of light in the specular reflection direction, and a peak angle θ in which the radial PSD has a peak value. peak , and radial PSD decreases to 10% of its peak value at a first scattering angle of 2° or more and 15° or less with respect to the specular reflection direction, θ peak The present invention relates to an article comprising a substrate having radial PSDs including a second range of scattering angles at larger angles.

[0007] Aspect (2) of the present disclosure relates to an article according to aspect (1), wherein, within a second range of scattering angles, the radial PSD is greater than the first scattering angle and decreases to 1% of the peak value at a second scattering angle of 3.5° or more and 30° or less with respect to the specular reflection direction.

[0008] Aspect (3) of the present disclosure relates to an article according to aspect (2), wherein, within a first range of scattering angles, the radial PSD is less than 10% of the peak value at scattering angles of 0.05° or greater.

[0009] Aspect (4) of the present disclosure relates to an article according to any of aspects (2) to (3), wherein the first scattering angle is 6° or more and 13° or less with respect to the specular reflection direction, and the second scattering angle is 12.5° or more and 30.0° or less with respect to the specular reflection direction.

[0010] Aspect (5) of the present disclosure relates to an article according to any of aspects (2) to (3), wherein the first scattering angle is 2° or more and 7° or less with respect to the specular reflection direction, and the second scattering angle is 3.5° or more and 13.5° or less with respect to the specular reflection direction.

[0011] Aspect (6) of the present disclosure relates to an article according to aspect (5), wherein, within a second range of scattering angles, the radial PSD is reduced to 0.1% of the peak value at a third scattering angle of 8° or less with respect to the specular reflection direction.

[0012] Aspect (7) of the present disclosure relates to an article according to aspect (5), wherein, within a second range of scattering angles, the radial PSD is reduced to 0.01% of the peak value at a third scattering angle of 16° or less with respect to the specular reflection direction.

[0013] Aspect (8) of this disclosure is θ peak This relates to an article in any of the forms (1) to (7) wherein the angle is 0.3° or more and 0.5° or less.

[0014] Aspect (9) of the present disclosure relates to an article according to any of aspects (1) to (8), wherein, within a scattering region, a first principal surface includes a plurality of inclined transition surfaces extending between the boundaries of a plurality of first regions and a plurality of second regions, the plurality of inclined transition surfaces being inclined such that the height of the first principal surface decreases with increasing distance from the boundaries of the plurality of first regions.

[0015] Aspect (10) of the present disclosure relates to an article according to aspect (9), wherein at least some of a plurality of inclined transition surfaces extend over a lateral distance of 1.0 μm or more and 10 μm or less between a plurality of first regions and a plurality of second regions connected by the inclined transition surfaces, and the lateral distance over which the inclined transition surfaces extend is parallel to the surface normal of the inclined transition surface and is measured in a direction parallel to a virtual base plane.

[0016] Aspect (11) of the present disclosure relates to an article according to any of aspects (1) to (10), wherein the article exhibits a transmittance haze of 2.0% or less and a sparkle of 2.5% or less as measured at 140 ppi.

[0017] Aspect (12) of the present disclosure relates to an article according to any of aspects (1) to (11), wherein the first mean modulation transfer function of the article averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.55 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on a first principal surface at an incident angle of 20°.

[0018] Aspect (13) of the present disclosure relates to an article according to any of aspects (1) to (12), wherein a first average modulation transfer function is at least 0.7 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on a first principal surface at an incident angle of 20°.

[0019] Aspect (14) of the present disclosure relates to an article according to any of aspects (1) to (13), wherein the second mean modulation transfer function of the article averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.6 when the article is viewed at a field of view of 20° and light having a luminance of 45,000 lux is incident on a first principal surface at an incident angle of 45°.

[0020] Aspect (15) of the present disclosure relates to an article according to aspect (1), wherein, within a scattering region, the first principal surface includes a plurality of third regions positioned at a third height with respect to a virtual base plane, and a plurality of fourth regions positioned at a fourth height with respect to a virtual base plane, the fourth height being different from the first, second, and third heights.

[0021] Aspect(16) of the present disclosure relates to an article according to aspect(15), wherein the article exhibits a specular reflectance (Rs) of 4.0 or less and a combined image sharpness of less than 65%.

[0022] Aspect (17) of the present disclosure relates to an article according to any of aspects (1) to (16), wherein the substrate is a glass substrate, and the article further comprises a display configured to emit light through the substrate, which is positioned adjacent to a second main surface.

[0023] Aspect (18) of the present disclosure is an article having a first principal surface; a second principal surface opposite to the first principal surface; and a scattering region formed within the first principal surface, wherein within the scattering region, the first principal surface includes a plurality of first regions positioned at a first height with respect to a virtual baseline extending over a substrate, and a plurality of second regions positioned at a second height with respect to the virtual baseline, the first height being greater than the second height by an etching depth of 80 nm or more and 600 nm or less, and the scattering region having a peak angle (θ) such that the radial PSD increases with increasing scattering angle. peak The first scattering angle on the first side of θ, and the radial PSD decreases with increasing scattering angle, θ peakhaving a radial PSD that includes a second range of scattering angles on the second side of , and the bidirectional reflectance distribution function (the "BRDF") of the article is less than 10 times the peak intensity value at a scattering angle of 20° with respect to the specular reflection direction, and the BRDF is measured from light having a wavelength of 520 nm incident on the first major surface at an incident angle of 20°, for the article. -5

[0024] Aspect (19) of the present disclosure relates to an article according to aspect (18), wherein the BRDF has an amplitude less than 1.7×10 -4 sr -1 at a scattering angle of 30° with respect to the specular reflection direction.

[0025] Aspect (20) of the present disclosure relates to an article according to any one of aspects (18)-(19), wherein within the second range of scattering angles, the radial PSD decreases to 10% of the peak value at a first scattering angle of 2° or more and 15° or less with respect to the specular reflection direction. peak

[0026] Aspect (21) of the present disclosure relates to an article according to aspect (20), wherein within the second range of scattering angles, the radial PSD is greater than the first scattering angle and decreases to 1% of the peak value at a second scattering angle of 3.5° or more and 30° or less with respect to the specular reflection direction.

[0027] Aspect (22) of the present disclosure relates to an article according to aspect (21), wherein within the second range of scattering angles, the radial PSD decreases to 0.1% of the peak value at a third scattering angle of 8° or less with respect to the specular reflection direction.

[0028] Aspect (23) of the present disclosure relates to an article according to aspect (22), wherein within the second range of scattering angles, the radial PSD decreases to 0.01% of the peak value at a third scattering angle of 16° or less with respect to the specular reflection direction.

[0029] Aspect (24) of the present disclosure relates to an article according to any one of aspects (20)-(23), wherein within the first range of scattering angles, the radial PSD is less than 10% of the peak value at a scattering angle of 0.05° or more.

[0030] ​​ Aspect (25) of this disclosure is θ peak However, this relates to articles in any of the forms (18) to (24) where the angle is 0.3° or more and 0.5° or less.

[0031] Aspect (26) of the present disclosure relates to an article according to any of aspects (18) to (25), wherein, within a scattering region, a first principal surface includes a plurality of inclined transition surfaces extending between the boundaries of a plurality of first regions and a plurality of second regions, the plurality of inclined transition surfaces being inclined such that the height of the first principal surface decreases with increasing distance from the boundaries of the plurality of first regions.

[0032] Aspect (27) of the present disclosure relates to an article according to aspect (26), wherein at least some of a plurality of inclined transition surfaces extend over a lateral distance of 1.0 μm to 10 μm between a plurality of first regions and a plurality of second regions connected by the inclined transition surfaces, and the lateral distance over which the inclined transition surfaces extend is parallel to the surface normal of the inclined transition surface and measured in a direction parallel to a virtual base plane.

[0033] Aspect (28) of the present disclosure relates to an article according to any of aspects (18) to (27), wherein the article exhibits a transmittance haze of 2.0% or less and a sparkle of 2.5% or less as measured at 140 ppi.

[0034] Aspect (29) of the present disclosure is a substrate having a first principal surface; a second principal surface opposite to the first principal surface; and a scattering region formed within the first principal surface, wherein within the scattering region, the first principal surface includes a plurality of first regions positioned at a first height with respect to a virtual base plane extending over the substrate, a plurality of second regions positioned at a second height with respect to the virtual base plane, and a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions, wherein the height of the first principal surface is a distance from the boundaries of the plurality of first regions The gradient decreases with increasing θ, and at least some of the multiple gradient transition surfaces extend between regions of a plurality of first regions and a plurality of second regions connected by the gradient transition surfaces, with a lateral distance of 1.0 μm or more and 10 μm or less, the lateral distance over which the gradient transition surfaces extend is parallel to the surface normal of the gradient transition surface and measured in a direction parallel to the virtual base plane, and the scattering region has a first range of scattering angles where the radial PSD increases with increasing scattering angle of light relative to the specular reflection direction, and the peak scattering angle θ has a peak value. peak , and radial PSD decreases to 10% of its peak value at a first scattering angle of 2° or more and 15° or less with respect to the specular reflection direction, θ peak The present invention relates to an article comprising a substrate having radial PSDs including a second range of scattering angles at a larger scattering angle.

[0035] Aspect (30) of the present disclosure relates to an article according to aspect (29), wherein, within a first range of scattering angles, the radial PSD is less than 10% of the peak value at scattering angles of 0.05° or greater.

[0036] Aspect (31) of this disclosure is θ peak However, this relates to articles in any of the forms (29) to (30) where the angle is 0.3° or more and 0.5° or less.

[0037] Aspect (32) of the present disclosure relates to an article according to any of aspects (29) to (31), wherein the first scattering angle is 6° or more and 13° or less with respect to the specular reflection direction, and within a second range of scattering angles, the radial PSD is reduced to 1% of its peak value at a second scattering angle of 12.5° or more and 30.0° or less with respect to the specular reflection direction.

[0038] Aspect (33) of the present disclosure relates to an article according to any of aspects (29) to (31), wherein the first scattering angle is 2° or more and 7° or less with respect to the specular reflection direction, and within a second range of scattering angles, the radial PSD is reduced to 1% of its peak value at a second scattering angle of 3.5° or more and 13.5° or less with respect to the specular reflection direction.

[0039] Aspect (34) of the present disclosure relates to an article according to aspect (33), wherein, within a second range of scattering angles, the radial PSD is reduced to 0.1% of the peak value at a third scattering angle of 8° or less with respect to the specular reflection direction.

[0040] Aspect (35) of the present disclosure relates to an article according to aspect (34), wherein, within a second range of scattering angles, the radial PSD is reduced to 0.01% of the peak value at a third scattering angle of 16° or less with respect to the specular reflection direction.

[0041] Aspect (36) of the present disclosure relates to an article according to any of aspects (29) to (35), wherein the article exhibits a transmittance haze of 2.0% or less and a sparkle of 2.5% or less as measured at 140 ppi.

[0042] Aspect (37) of the present disclosure relates to an article according to any of aspects (29) to (36), wherein the first average modulation transfer function of the article averaged over spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.07 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 20°, and the second average modulation transfer function of the article averaged over spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.6 when the article is viewed at a field of view of 20° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 45°.

[0043] Aspect (38) of the present disclosure relates to an article according to aspect (29), wherein, within a scattering region, the first principal surface includes a plurality of third regions positioned at a third height with respect to a virtual base plane, and a plurality of fourth regions positioned at a fourth height with respect to a virtual base plane, the fourth height being different from the first, second, and third heights.

[0044] Aspect(39) of the present disclosure relates to an article according to aspect(38), wherein the article exhibits a specular reflectance (Rs) of 4.0 or less and a combined image sharpness of less than 65%.

[0045] It should be understood that both the general description above and the detailed description below are illustrative only and intended to provide an overview or framework for understanding the nature and features of the claims. The accompanying drawings are included for further understanding and constitute part of this specification. The drawings illustrate one or more embodiments and, together with the description, serve to illustrate the principles and operation of the various embodiments. [Brief explanation of the drawing]

[0046] The accompanying drawings incorporated herein and forming part thereof illustrate several aspects of the present invention and, together with the description, illustrate the principles of the present invention. [Figure 1] Perspective view of a display article according to one or more embodiments of the present disclosure [Figure 2] A schematic diagram showing a portion of the scattering area of ​​the display article in Figure 1, according to one or more embodiments of the present disclosure. [Figure 3A] A schematic diagram showing the height profile of the scattering region shown in Figure 2, according to one or more embodiments of the present disclosure. [Figure 3B] A cross-sectional view of the transition surface between two regions at different heights of the scattering region shown in Figure 2, according to one or more embodiments of the present disclosure. [Figure 4] Plots of multiple target radial power spectral densities for a scattering region according to one or more embodiments of the present disclosure. [Figure 5]Flowchart of a method for creating a phase map of a scattering region based on a target radial power spectral density ("PSD") for that scattering region, according to one or more embodiments of the present disclosure. [Figure 6A] Plots of modeled sparkle and transmission haze performance of an exemplary article as a function of the α parameter with respect to the target radial PSD used to construct the sample, according to one or more embodiments of the present disclosure. [Figure 6B] Figure 6A shows qualitative simulation color development of reflected light from a sample for various detector saturation levels with respect to α values ​​ranging from 0.1 to 1.0, according to one or more embodiments of the present disclosure. [Figure 6C] Figure 6A shows qualitative simulation color development of reflected light from a sample for various detector saturation levels with respect to α values ​​ranging from 1.0 to 10.0, according to one or more embodiments of the present disclosure. [Figure 6D] Plots of both pre- and post-target radial PSDs improved by phase thresholding to provide a binary phase mask, according to one or more embodiments of the present disclosure. [Figure 6E] A diagram showing a block of a phase map after phase thresholding according to one or more embodiments of the present disclosure. [Figure 6F] Plots of both pre- and post-improvement radial PSDs to achieve a 50% local fill ratio for each phase after phase thresholding according to one or more embodiments of the present disclosure. [Figure 7] Flowchart of a method for manufacturing an article having a scattering region by performing one or more etching steps on the surface of the article according to one or more embodiments of the present disclosure. [Figure 8] A schematic diagram showing an apparatus for measuring the washout performance of an article, according to one or more embodiments of the present disclosure. [Figure 9] A schematic diagram showing a vehicle interior equipped with a display, and an ambient light source that emits light incident on the display and scattered therefrom, according to one or more embodiments of the present disclosure. [Figure 10A]Images of multiple patterns emitted through a sample having an existing anti-glare surface treatment when illuminated under certain conditions by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 10B] Images of multiple patterns emitted through a sample having an existing anti-glare surface treatment when illuminated under certain conditions by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 10C] Images of multiple patterns emitted through a sample having an existing anti-glare surface treatment when illuminated under certain conditions by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 10D] Images of multiple patterns emitted through a sample having an existing anti-glare surface treatment when illuminated under certain conditions by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 10E] Images of multiple patterns emitted through a sample having an existing anti-glare surface treatment when illuminated under certain conditions by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 10F] Images of multiple patterns emitted through a sample having an existing anti-glare surface treatment when illuminated under certain conditions by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 11] Plots of measured modulation transfer functions from images shown in Figures 10A to 10F according to one or more embodiments of the present disclosure. [Figure 12] Plots of measured modulation transfer functions from images shown in Figures 10A to 10F according to one or more embodiments of the present disclosure. [Figure 13A] Images of multiple patterns emitted through a sample having a scattering region formed from a target radial PSD described herein, when illuminated under certain conditions, by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 13B]Images of multiple patterns emitted through a sample having a scattering region formed from a target radial PSD described herein, when illuminated under certain conditions, by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 13C] Images of multiple patterns emitted through a sample having a scattering region formed from a target radial PSD described herein, when illuminated under certain conditions, by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 13D] Images of multiple patterns emitted through a sample having a scattering region formed from a target radial PSD described herein, when illuminated under certain conditions, by the apparatus shown in Figure 8, according to one or more embodiments of the present disclosure. [Figure 14] Plots of specular reflectance (Rs) measurements as a function of sparkle measurements for a first set of examples manufactured by the methods shown in Figures 5 and 7 according to one or more embodiments of the present disclosure. [Figure 15A] A schematic diagram showing a portion of a modeled surface having a first region positioned at a first height, a second region positioned at a second height, and a transition surface extending between the first and second regions, according to one or more embodiments of the present disclosure. [Figure 15B] Cross-sectional view of the modeled surface shown in Figure 15A along line 1504 shown in Figure 15A, according to one or more embodiments of the present disclosure. [Figure 15C] Plot of surface height measurements along line 1504 across the transition plane of the modeled surface shown in Figure 15A, according to one or more embodiments of the present disclosure. [Figure 15D] Plot of the modeled specular reflection reduction spectrum of the modeled surface shown in Figure 15A according to one or more embodiments of the present disclosure. [Figure 16A] A schematic diagram showing a portion of a modeled surface, which is an improved version of the modeled surface shown in Figure 15A, according to one or more embodiments of the present disclosure, including feature rounding so that the gradient of the improved surface transitions more gradually between the first region and the transition surface. [Figure 16B]Cross-sectional view of the modeled surface shown in Figure 16A along line 1504 shown in Figure 16A, according to one or more embodiments of the present disclosure. [Figure 16C] Plot of surface height measurements along line 1504 across the transition plane of the modeled surface shown in Figure 16A, according to one or more embodiments of the present disclosure. [Figure 16D] Plot of the modeled specular reflection reduction spectrum of the modeled surface shown in Figure 16A according to one or more embodiments of the present disclosure. [Figure 17] Plots of modeled radial PSDs for multiple modeled surfaces with different degrees of feature rounding according to one or more embodiments of the present disclosure. [Figure 18A] Plan view images of a first article manufactured by the method shown in Figures 5 and 7, without feature rounding, according to one or more embodiments of the present disclosure. [Figure 18B] Perspective view images of a first article manufactured by the method shown in Figures 5 and 7, without feature rounding, according to one or more embodiments of the present disclosure. [Figure 18C] Plan view images of a second article manufactured by the method shown in Figures 5 and 7, characterized by rounded edges, according to one or more embodiments of the present disclosure. [Figure 18D] Perspective view images of a second article manufactured by the method shown in Figures 5 and 7, with feature rounding, according to one or more embodiments of the present disclosure. [Figure 18E] Plots of radial PSD measured from the surfaces of the first and second articles shown in Figures 18A-18D according to one or more embodiments of the present disclosure. [Figure 19] Plots of bidirectional reflectance distribution functions measured from multiple samples, both with and without feature rounding, manufactured by the methods shown in Figures 5 and 7, with different target radial PSDs, according to one or more embodiments of the present disclosure. [Modes for carrying out the invention]

[0047] Broadly speaking with reference to the drawings, articles are described herein having a surface having a scattering region designed to provide a preferred combination of anti-glare ("AG") performance attributes. The scattering region is designed in a spatial frequency domain based on a target radial power spectral density ("PSD") of the article, and the target radial PSD is converted into a phase profile (or "phase map") used to form multiple surface features in the scattering region. The surface features may include multiple regions of the surface positioned at different heights with respect to a virtual baseline extending across the article, and transition planes extending between those regions. The surface features are such that the scattering region has a first range of scattering angles in which the radial PSD increases with increasing scattering angle relative to the specular reflection direction, and a peak scattering angle θ in which the radial PSD has a peak value. peak The method for forming multiple surface features described herein facilitates a rapid decrease in radial PSD with increasing scattering angles within a second range of scattering angles, so that within the second range of scattering angles, the PSD decreases to 10% of the peak value at a first scattering angle of 15° or less with respect to the specular reflection direction, and to 1% of the peak value at a second scattering angle of 30° or less with respect to the specular reflection direction. Such a rapid decrease within the second range of scattering angles facilitates the minimization of observable color artifacts while exhibiting a preferred combination of AG performance attributes for various applications.

[0048] To achieve the radial PSD described herein, which decreases rapidly within a second range of scattering angles, the boundaries of multiple regions of a surface located at different heights may be rounded such that the transition of the gradient of the first principal surface (e.g., between a region located at one of the heights and the transition surface) is more gradual than that of a surface not characterized by the rounding method described herein. As a result, within the scattering region, adjacent regions of the first principal surface located at different heights with respect to the virtual base plane may be separated by a lateral distance of 1.0 μm or more (e.g., 1.0 μm or more and 10 μm or less, 1.0 μm or more and 9.0 μm or less, 1.0 μm or more and 8.0 μm or less, 1.0 μm or more and 7.0 μm or less, 1.0 μm or more and 6.0 μm or less, 1.0 μm or more and 5.0 μm or less, 2.0 μm or more and 5.0 μm or less) measured in a direction parallel to the surface normal of the transition surface and parallel to the virtual base plane. Such a gradual surface height transition can be achieved by controlling the surface energy between the resist and the article during the etching process that forms the scattering region described herein. The lack of sharpness in the surface height transition reduces radial PSD at high scattering angles, which contributes to desirable washout and transmission haze performance.

[0049] The context in which the articles described herein would be particularly useful is the context of in-cabin displays. An in-cabin may be equipped with one or more displays (e.g., a center console display, a dashboard display, a pillar display, a seatback display, etc.). Such displays will have a fixed orientation toward the driver. While driving, the vehicle is exposed to ambient light conditions that can produce relatively severe glare. For example, sunlight entering the in-cabin through the side windows or windshield may reflect or scatter off the displays, producing bright glare that can distract the driver and degrade the performance of the displays through washout. The articles described herein can reduce such washout from ambient light conditions normally encountered by a sharp reduction in radial PSD achieved within a second range of scattering angles. Such desirable washout performance can be achieved while also providing desirable sparkle performance and transmittance haze performance.

[0050] As used herein, the term “radial PSD” refers to a profile calculated from a surface height profile measured from a surface, when used to describe the surface of a particular article. In particular, the surface height profile of a 1x1 mm area of ​​the surface is measured using white light interferometry. The data array of the surface height profile is input into the Gwyddion data analysis program to calculate the radial power spectral density. The term “radial PSD” should be distinguished from the term “target radial PSD.” The target radial PSD is not calculated from the measured surface height profile of a surface, but rather mathematically calculated from the desired far-field scattering pattern of that surface.

[0051] As used herein, "specular reflectance (Rs)" or "Rs" is defined as the peak intensity of light reflected from the first surface of a substrate within a cone at an angle of ±0.1°. Specular reflectance can be measured using a Rhopoint IQ meter, which reports the Rs value in gross units.

[0052] Articles described herein can be characterized by their image clarity values. Terms such as “Reflected Image Clarity,” “Image Clarity,” and “DOI” are defined by Method A of ASTM Procedure D5767 (ASTM 5767), entitled “Standard Test Methods for Instrumental Measurements of Distinctness-of-Image Gloss of Coating Surfaces.” According to Method A of ASTM 5767, glass reflectance coefficient measurements are performed at the specular viewing angle and at least one rough surface of the glass article at an angle slightly outside the specular viewing angle (0.2° to 0.4° away from the specular direction). Such measurements can be performed using an orientation measuring instrument (Rhopoint IQ (Goniophotometer) 20° / 60° / 85°, Rhopoint Instruments) calibrated against an accredited black glass standard, as specified in ASTM Procedures D523 and D5767.

[0053] As used herein, the terms “haze” or “transmitted haze” refer to the percentage of transmitted light scattered outside a pyramidal area of ​​approximately ±2.5°, as defined in ASTM D1003, “Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics,” the content of which is fully cited herein. Note that although the title of ASTM D1003 refers to plastics, its standards also apply to substrates made from glass materials. For optically smooth surfaces, transmitted haze is generally close to zero.

[0054] As used herein, the terms “sparkle,” “sparkle contrast,” “display sparkle,” “pixel power deviation,” and “PPD,” and similar terms, refer to the visual phenomena that occur when a textured transparent surface is combined with a pixelated display. Generally, the quantification of sparkle involves imaging an illuminated or simulated display on a textured surface within the field of view. The calculation of sparkle in region P is equal to σ(P) / μ(P), where σ(P) is the standard deviation of the distribution of integrated intensity for each display pixel contained within region P, divided by the average intensity μ(P). (1) J. Gollier et al., "Apparatus and method for determining sparkle," U.S. Patent No. 941180B2, U.S. Patent and Trademark Office, July 20, 2016; (2) A. Stillwell et al., "Perception of Sparkle in Anti-Glare Display Screens," JSID 22(2), pp. 129-136 (2014); and (3) C. Cecala et al., "Fourier Optics Modeling of Display Sparkle from Anti-Glare Cover Glass: Comparison to Experimental Data," Optical Society of America Imaging and Applied Optics Congress, JW5B.8 (2020). Following these instructions, a person skilled in the art can construct an imaging system for quantifying sparkle. Alternatively, a commercially available system (e.g., SMS-1000, Display Messtechnik & Systeme GmbH & Co.Kg, Germany) can be used. Unless otherwise specified, sparkle is measured on a 140 PPI display using the following procedure.Only the green subpixels are illuminated (R=0, B=0, G=255), and a 140 PPI display (e.g., Z50, Lenovo Group Limited, Hong Kong) is imaged using a lens / machine vision camera combination with f=50mm (e.g., C220503 1:2.8 50mm Φ30.5, Tamron, Japan, and Stingray F-125 B, Allied Vision Technologies GmbH, Germany). The lens settings are aperture=5.6, depth of field=0.3, working distance=approximately 290mm; with these settings, the display pixel to camera pixel ratio is approximately 1:9. The field of view for analysis includes approximately 7500 display pixels. In the camera settings, gain and gamma correction were turned off. Periodic intensity fluctuations from the display, and non-periodic intensity fluctuations, such as dead pixels, are removed during the analysis before sparkle calculation.

[0055] Anti-glare performance can be measured with no material bonded to the surface (described as "unbonded" in this specification) or with a black absorber bonded to the back surface of the glass (described as "bonded" in this specification).

[0056] Referring now to Figure 1, an article 10 according to an exemplary embodiment is shown. Article 10 includes a substrate 12. In the illustrated embodiment, article 10 is a display article (e.g., a display cover article) and further includes a housing 14 to which the substrate 12 is coupled and a display 16 within the housing 14. In such an embodiment, the substrate 12 at least partially covers the display 16 so that light emitted by the display 16 can pass through the substrate 12.

[0057] The substrate 12 may be made of various materials depending on the mounting configuration. For example, in embodiments such as the one shown in Figure 1, the substrate 12 is a glass or glass-ceramic substrate. Various properties and examples of such glass or glass-ceramic substrates are described in more detail herein. In embodiments, the substrate 12 may be made from a material other than glass, such as paper, plastic, or other suitable polymer material. In embodiments, the substrate 12 may include a combination of glass and polymer material. In one example, the scattering region 20 described herein is formed within a layer of polymer material formed on a glass substrate. In embodiments, the substrate 12 is transparent or exhibits an average transmittance of 70% or more (e.g., 80% or more, 85% or more, 90% or more, 92% or more, 92.5% or more, 93% or more) for light incident on the substrate 12 in the wavelength range of 400 nm to 700 nm. In embodiments, the substrate 12 is opaque or exhibits an average transmittance of 30% or less for light incident on the substrate in the wavelength range of 400 nm to 700 nm. In this embodiment, the substrate 12 is colored such that it exhibits a colored appearance under ambient lighting (for example, sunlight).

[0058] The substrate 12 has a first principal surface 18, a second principal surface 19, a scattering region 20 defined on the first principal surface 18, and a thickness 21 that partially borders the first principal surface 18 (for example, representing the minimum distance between the first principal surface 18 and the second principal surface 19 at a particular point on the first principal surface 18). In the illustrated embodiments, the substrate 12 is substantially planar in shape such that the first principal surface 18 and the second principal surface 19 are generally flat (except for a number of surface features formed on the first principal surface 18 as described herein). Embodiments in which the substrate 12 includes a curved shape (for example, by appropriate heat-forming and cold-forming techniques) are also conceivable and are within the scope of this disclosure. In such embodiments, the reference herein to “surface normal” (shown as surface normal 33 in Figure 1) refers to a local surface normal at a point where light from the external environment 24 is incident on the first principal surface 18. In the illustrated embodiment, the first main surface 18 generally faces the external environment 24 surrounding the article 10 and has its back to the display 16. In the embodiment, the display 16 emits visible light that passes through the thickness 21 of the substrate 12, exits the first main surface 18, and enters the external environment 24.

[0059] As shown in Figure 1, the light from the external environment 24, represented by the incident light ray 22, has an incident angle θ i The incident ray 22 may be incident on the first principal surface 18 at a zenith angle extending with respect to the surface normal 33 of the first principal surface 18, which is shown as the z-direction in Figure 1. The incident ray 22 can represent light from a number of different light sources outside the article 10. For example, the incident ray 22 may represent sunlight incident on the first principal surface 18, or light from another external light source (e.g., light reflected or scattered by an external object, or light produced by another light source). The scattering region 20 scatters the light represented by the incident ray 22 in the scattering direction represented by the scattered ray 25. The light is incident at an angle θ with respect to the surface normal 33. i and scattering angle θ s The light is scattered in a specific direction with a scattering amplitude that depends on the ray. As shown in the figure, when the scattered ray 25 is projected onto the plane of the first principal surface 18 that extends perpendicular to the surface normal 33, it is scattered in a scattering direction that extends at an azimuthal angle Φ with respect to the first direction (the x-direction shown in Figure 1).

[0060] As described herein, the scattering region 20 is designed based on the target radial PSD. The target radial PSD is azimuthally averaged with respect to the azimuthal angle Φ such that the PSD is statistically isotropic with respect to the azimuthal angle. The target radial PSD follows the same functional relationship as the zenith angle θ, regardless of the azimuthal angle Φ. s It changes along with. Such a target radial PSD beneficially minimizes the effect of the rotational orientation of article 10 in the external environment 24 on AG performance.

[0061] Figure 2 schematically shows a plan view of region II of the scattering region 20 of the article 10 shown in Figure 1, according to an exemplary embodiment of the present disclosure. As shown in the figure, the scattering region 20 includes a plurality of surface features 26. The plurality of surface features 26 are designed based on a target radial PSD in the Fourier region, as described herein. In the illustrated example, the plurality of surface features 26 include a plurality of first regions 28 and a plurality of second regions 30 of the first principal surface 18. The plurality of first regions 28 and the plurality of second regions 30 are generally regions of the first principal surface 18 arranged at different heights. In the embodiment, the plurality of first regions 28 and the plurality of second regions 30 can be characterized as planar in the sense that the surface heights of the first principal surface 18 are substantially the same within each of the regions. For example, in these embodiments, within a particular region of a plurality of first regions 28 or within one region of a plurality of second regions 30, the variation in surface height (or roughness) may be less than 50 nm (or less than 20 nm RMS, or less than 10 nm RMS) with respect to the variation in root mean square (RMS). For example, in these embodiments, each of the plurality of first regions 28 and the plurality of second regions 30 can be characterized by a variation in surface height ranging from 0.1 nm RMS to 50 nm RMS, 0.1 nm RMS to 20 nm RMS, 0.1 nm RMS to 10 nm RMS, or 0.1 nm RMS to 1 nm RMS.

[0062] In the embodiment, at least some of the plurality of first regions 28 and the plurality of second regions 30 may have a curved surface that is not planar and extends to a non-constant height. In such an embodiment, the plurality of first regions 28 and the plurality of second regions 30 may be approximated as a plane and an average height. For example, each of the plurality of first regions 28 can be considered as an area of ​​a first main surface 18 located at a first average height, and the plurality of second regions 30 can be considered as an area of ​​the first main surface 18 located at a second average height, where the first average height differs from the second average height by at least 100 nm.

[0063] The multiple surface features 26 generally differ in size and surrounding shape and have longitudinal axes extending in multiple different directions in a plane parallel to the virtual base plane 35 (see Figure 3A). However, the randomness in the structure of the multiple surface features 26 differs from the randomness in certain existing AG surfaces (e.g., resulting from sandblasting) in that the arrangement of the multiple surface features 26 is reproducible (within manufacturing tolerances) by the methods described herein.

[0064] Referring to Figures 2-3A, in the illustrated example, the plurality of first regions 28 are positioned at a first height h1 relative to a virtual base plane 35 extending across the substrate 12, and the plurality of second regions 30 are positioned at a second height h2 relative to the virtual base plane 35. In the illustrated example, the plurality of surface features 26 are regions of constant height on the first main surface 18 (with the understanding that the actual structure of the plurality of surface features 26 may include deviations in surface height related to the roughness of the first main surface 18, and may not extend precisely in the xy plane due to the action of processes that form the plurality of surface features 26, such as the etching process described herein). The plurality of surface features 26 may also include closed microstructures (where the boundaries associated with a particular surface feature are closed contours). Furthermore, a particular region of the plurality of first regions 28 is completely surrounded by a region within the plurality of second regions 30, and vice versa.

[0065] As shown in Figure 3A, the multiple first regions 28 and the multiple second regions 30 are separated from each other by transition surfaces 40 of the first main surface. The transition surfaces 40 represent segments of the first main surface 18 in which the height of the first main surface 18 varies to the extent that it is greater than the height in the multiple first regions 28 and the multiple second regions 30. The average gradient of the first main surface 18 within the transition surfaces 40 will be greater than the average gradient within the multiple first regions 28 and the multiple second regions 30. In this embodiment, the transition surface 40 includes a region of the first main surface 18 where the surface height differs by 50 nm or more per 1 μm straight distance (for example, 100 nm or more per 1 μm straight distance, 200 nm or more per 1 μm straight distance, 300 nm or more per 1 μm straight distance, 400 nm or more per 1 μm straight distance, 500 nm or more per 1 μm straight distance, and 500 nm or more per 1 μm straight distance), where the straight distance is measured in a plane parallel to the virtual base plane 35.

[0066] Referring to Figure 3B, in this embodiment, each of the transition surfaces 40 includes a first edge 42 positioned adjacent to one of a plurality of first regions 28 and a second edge 44 positioned adjacent to one of a plurality of second regions 30. The first edge 42 may represent the outer boundary of one of the plurality of first regions 28, and the second edge 44 may represent the outer boundary of adjacent regions of the plurality of second regions 30. As shown in Figure 3B, the transition surface 40 may have a width w. The width w is measured as the transverse distance in a plane parallel to the virtual base plane 35 (the xy plane shown in Figures 1-2) between the first edge 42 and the second edge 44. The transverse distance is also measured in the direction extending parallel to the projection of the surface normal 46 of the transition surface 40 into the xy plane. In the embodiment, the width w is between 1.0 μm and 10.0 μm (e.g., 1.0 μm and 9.0 μm, 1.0 μm and 8.0 μm, 1.0 μm and 7.0 μm, 1.0 μm and 6.0 μm, 1.5 μm and 6.0 μm, 2.0 μm and 6.0 μm). Widths within such a range indicate a lack of sharpness in the gradient transition of the first main surface 18. The first main surface 18 transitions gradually between gradients (e.g., rounded corners) rather than at relatively sharp corners at the first and second edges 42 and 44. As described in more detail herein, the rounding of such features helps to reduce high spatial frequency components in the radial PSD of the scattering region 20, thereby providing desirable washout performance. Unless otherwise specified, the width w is the maximum measurement with respect to the lateral distance across a particular transition surface.

[0067] The width w can be measured using various different techniques. For example, the width w can be measured physically by creating a line profile of the first main surface 18. The line profile can be created by measuring the surface height of the first main surface 18 using white light interferometry. The line profile can also be obtained by cutting a cross-section of the substrate 12 in a direction extending perpendicular to the transition surface 40 and obtaining an image of the cross-section (for example, using a scanning electron microscope or atomic force microscope). The image is sampled in a direction extending perpendicular to the transition surface 40 at the point where the width w is being measured (in a direction extending parallel to the projection of the surface normal 46 onto the xy plane, the surface normal being located at the first edge 42). The width w at a particular point on the transition surface 40 is calculated as the minimum lateral distance between points located at heights that differ from each other by no more than 10% of the difference between h1 and h2 (the difference between h1 and h2 represents the etching depth used in the manufacture of the article 10). The specific modality used to image the first principal surface 18 in measuring the width w may vary depending on the size of the width w. If the width is less than 2.0 μm, an atomic force microscope can be used to image the first principal surface 18. If the width w is 2.0 μm or greater, the line contour can be extracted from white light interferometer data acquired with an azimuthal resolution of less than 0.2 nm. The resulting width w can be measured as the minimum lateral distance between points located at heights that differ from each other by no more than 10% of the difference between h1 and h2.

[0068] Referring again to Figure 3A, the physical structure of the multiple surface features 26 can be determined using Fourier analysis of diffraction. As shown in Figure 3A, the incident rays from the external environment 24 are

[0069]

number

[0070] It can be approximated as a uniform plane wave expressed as, where I o k represents the uniform intensity of the incident line, xo and k yoThis represents the wave vector component related to the wavelength and angle of incidence of the incident line to the first principal plane 18 (for example, the angle of incidence can be separated into xz-plane and yz-plane components as shown in Figure 1). In such a case, the scalar near-field with respect to the exit line (after interaction with the first principal plane 18) is:

[0071]

number

[0072] It can be approximated as follows, where ρ is the Fresnel coefficient of the interface, TIFF2026510089000004.tif10114

[0073] H(x,y) is the local phase accumulated by passing through the distance to the first main surface 18 twice, and H(x,y) represents a pattern formed by multiple surface features 26. In this example, the incident line is approximated to have a uniform intensity distribution, and the interface between the substrate 12 and the external environment 24 is approximated to apply only a spatially varying phase so that the near-field exit line also has a uniform intensity distribution.

[0074] In this example shown in Figure 3, the non-near-field scattering pattern associated with the emission line can be represented in spatial frequency (k) space, and the near-field u can be calculated using Equation 3 by the Fourier transform. near Associated with (x,y),

[0075]

number

[0076] It is expressed as, in the formula, k x and k y This represents the scattering vector component (k x =|k| * cos(Φ), k y =|k| * sin(Φ), where k is...

[0077]

number

[0078] It is expressed as follows, where Φ is the azimuth angle shown in Figure 3, and λ is the wavelength of the scattered rays. As used here, the "PSD" of the scattering region 20 is,

[0079]

number

[0080] It is expressed as follows, where A is the area of ​​the scattering region 20. As used here, the term “target radial PSD” refers to Equation 5 when averaged over the entire range of the azimuth angle Φ. The target radial PSD is given by the following equation:

[0081]

number

[0082] Using azimuthally averaged PSD( <psd> Φ It is expressed as ). Therefore, the target radial PSD depends only on the magnitude of the spatial frequency and wavelength of the scattered radiation. Unless otherwise specified, the radial PSD is expressed assuming a wavelength of 550 nm. The term "target radial PSD" refers to the result calculated from Equation 6. Both plots of the target radial PSD and the PSDs described herein can be expressed as a function of either the scattering angle (Φs) or the spatial frequency k, with the understanding that such values ​​can be transformed using Equation 4, assuming a wavelength of 550 nm.

[0083] In the embodiment, the multiple surface features 26 are constructed such that when H(x,y) is input to Equation 6, they substantially coincide with the target radial PSD. An example group of target radial PSDs that can be used to design the scattering region 20 is shown in the second range of scattering angles 404 (see Figure 4),

[0084]

number

[0085] It can be expressed as follows, where α is the exponential decay parameter, and k max This is the non-zero scattering angle θ where the target radial PSD is equal to zero. max The spatial frequency associated with k peak The peak angle θ at which the target radial PSD has its peak value is peak This is the spatial frequency related to [the phenomenon]. Assuming a wavelength of 550 nm, the parameters α and θ are [parameters]. max , and θ peak By using different values, you can generate target radial PSDs that provide different performance attributes.

[0086] Figure 4 shows θ max =12.0° and θ peak The image shows plots of multiple target radial PSDs created using multiple different values ​​for α at =0.3°. The target radial PSDs include a first range of scattering angles 402 where the target radial PSD increases nearly linearly in proportion to the scattering angle. The first range of scattering angles 402 is the peak angle θ at which the target radial PSD has a peak value. peak It extends to θ. The target radial PSD decreases according to Equation 6 at a rate determined by α, θ peak This also includes a second range of scattering angles, 404, at larger scattering angles. Radial PSDs with lower α values ​​(less than 1) generally exhibit greater sparkle performance at higher spatial frequencies (or scattering angles) than radial PSDs with higher α values ​​(greater than 1). Consequently, lower α values ​​generally provide better sparkle performance than radial PSDs with higher α values. However, lower α values ​​result in more noticeable color artifacts, where visible color separation can be introduced into the light by scattering. Selecting the appropriate target radial PSD for a given application involves trade-offs between various performance attributes, as will be described in more detail herein.

[0087] Once a suitable target radial PSD has been identified, the phase distribution with respect to the first main surface 18 is determined using the method described herein, with respect to that target radial PSD. TIFF2026510089000010.tif10114

[0088] This can be determined. Figure 5 shows a flowchart of an exemplary method 500 for determining the pattern of multiple surface features 26 of the scattering region 20. The various components shown in Figures 1-4 are mentioned to help explain method 500. Any number of anti-glare surfaces may be formed using method 500, and the illustrated scattering region 20 may be formed by alternative methods.

[0089] In block 502, the target radial PSD of the scattering region 20 is selected. The target radial PSD is determined by parameters α and θ based on performance attributes desired for a specific application. max , and θ peak This can be created by selecting a value for α. For example, Figure 6A shows a plot of modeled transmission haze and sparkle performance for an article manufactured to have the radial PSD shown in Figure 4, given an etching depth of 140 nm. As shown in the figure, generally, as the α value increases, the predicted sparkle increases, while the transmission haze decreases. Therefore, for applications requiring relatively low levels of haze, an α value greater than 1 will be required. This is based on the understanding that such high α values ​​will generally result in more than 1.0% sparkle. Another consideration for parameter selection is color artifact performance. Figures 6B and 6C show qualitative simulated color development of reflected light for various levels of detector saturation. In the various plots in Figures 6B and 6C, the x and y axes are θ according to the azimuth angle Φ. x Components and θ y These are the scattering angles separated into components (see Figure 1). Figure 6B shows the simulated color development for α values ​​ranging from 0.1 to 1, and Figure 6C shows the simulated color development for α values ​​ranging from 1.0 to 10.0. As shown in the figures, surfaces with low α values ​​exhibit a pronounced color boundary that becomes less visible as α increases. For α values ​​greater than 4, the appearance does not change significantly. Therefore, for applications where the reflected light appearance of article 10 is an important consideration, an α value of 4 or 5 would provide a favorable balance between color artifacts and sparkle performance (showing less than 1.5% or less sparkle, or less than 1.4% sparkle).

[0090] parameter θ max This generally determines the size of the target radial PSD at relatively large scattering angles. As described herein with respect to examples, θ max For a high value (greater than 10), the target radial PSD is θ max Compared to target radial PSDs with low values ​​(less than 10), superior sparkle performance can be associated with inferior washout performance. If superior sparkle performance is desired (for example, if the washout index under any of the lighting conditions described herein is 0.6 or greater, 0.65 or greater, 0.7 or greater, or even 0.75 or greater), then θ between 2 and 5. max You can select a value, on the other hand, if the reduction in specular reflectance is the main concern, then θ greater than 20 max You can select a value for θ less than 1° (for example, 0.2° or more and 0.8° or less, or 0.3° or more and 0.5° or less). max The value was found to provide favorable haze performance without significantly affecting other performance attributes.

[0091] Returning to Figure 5, after the target radial PSD is created, in block 504, a phase map relating to the scattering region 20 is created based on the target radial PSD. In the embodiment, the phase map can be created using the inverse Fourier transform of the target radial PSD. Such a method can generally produce a complex-value phase map that is non-duplex (and therefore does not coincide with a surface having multiple first regions 28 and multiple second regions 30 shown in Figure 3). Non-duplex phases are problematic in that certain existing manufacturing processes, such as the etching method described herein, cannot manufacture such structures. Therefore, in block 506, a threshold is applied to the phase map such that the discrete regions ("pixels") of the phase map form a discrete distribution of phases. The threshold can be applied to real values ​​such that virtual terms of the created phases can be discarded and a first phase (e.g., π / 2) is assigned to pixels with a mean value below the threshold, and a second phase (e.g., -π / 2) is assigned to pixels with a mean value above the threshold. In the embodiment, the threshold value is selected such that an equal number of pixels are calculated to have a first phase and a second phase (for example, each phase occupies 50% of the surface area of ​​the scattering region). The pixel size can be selected based on the estimated minimum feature size achievable by the etching process described herein. In the embodiment, the pixel size is 20 nm or larger (for example, 300 nm or larger, 400 nm or larger, 500 nm or larger, 600 nm or larger, 700 nm or larger, 800 nm or larger, 900 nm or larger, 1000 nm or larger).

[0092] The problem arising from such thresholding to create a discrete phase distribution suitable for the etching process is that the spatial frequency components of the radial PSD change during the thresholding operation. Figure 6D shows a plot of the target radial PSD 620 before thresholding and the second radial PSD 621 calculated from the phase distribution after thresholding. As shown in the figure, the second radial PSD 621 includes a first rising segment 622 and a second rising segment 624, where the second radial PSD 621 is higher than the target radial PSD 620. The ability to correct the second rising segment 624 is limited by the step-like shape of the feature. However, the first rising segment 622 can be corrected using a high-pass filtering operation.

[0093] The first ascending segment 622 can be considered to be corrected at least partially by ensuring that a subregion of the phase map has a phase filling ratio that matches that of the entire scattering region 20. Thus, referring again to Figure 5, in blocks 508 and 510, subregions of the phase map where each phase does not constitute a desired filling ratio are identified, and then, in each of the identified subregions, the subregions are modified so that each phase constitutes a desired filling ratio. To illustrate, in the example where the scattering region 20 contains two phases, each having a 50% filling ratio, the phase map can be corrected by ensuring that the subregions also have a 50% filling ratio for each phase. Such a local 50% filling ratio for each phase in each subregion can be achieved by inverting the phase of a particular pixel (e.g., from the first phase to the second phase, or vice versa) to reduce the continuity of the subregion. The basis of such an operation can be understood based on the Hadamard transform, which is an orthogonal expansion with respect to the orthogonal Walsh function. Hadamard transform of vector ν TIFF2026510089000011.tif5114

[0094] This is the Walsh function (W(N,p) n ):

[0095]

number

[0096] This is a development concerning the following. For a given N, the Walsh functions are arranged in order of the number of times the function's value changes from +1 to -1. Value p = 2 m The Walsh function with m being greater than 0 is given by 0 to 2 N When plotted over a range of values ​​up to 2 |N-m| It alternates with half a period (therefore, 2 |N-m| (It has "continuity"). The Walsh function for p=1 is a constant and has only zero-frequency components. These Walsh functions are orthogonal in the frequency domain. This means that p=2 m Therefore, the Walsh function for m>0 means that it has no zero-frequency components. In fact, p=2 m Therefore, each Walsh function for m>0 is 2 m-1 It can be shown that it does not have frequency components below a certain value. That is, p=2 m Therefore, a subset of Walsh functions for m>0 has an increasing lower bound on frequency. Considering this, 2 m-1 Images with an Adamard transform that does not include frequencies below 1, 2, 4, 8, ... 2 m We can conclude that the Walsh function is also not included. That is, for a given image, W(N,2) in the Hadamard transform of the image m The absence of any subsets in the Walsh function is necessary, but insufficient, with respect to the absence of low-frequency components. This forms the theoretical basis for the pixel phase inversion operation described herein.

[0097] In view of the foregoing, the applicant believes that the first rising segment 622 can be corrected at least partially by inverting the image to achieve a local fill ratio of 50% in various subregions of the pixel map in a manner that reduces the continuity of the phase map. This operation can be performed by an algorithm that scans the pixel map generated by random phase generation and thresholds it to a predetermined block size (e.g., containing a predetermined array of x × y pixels). The block size can be determined by starting at an initial position on the phase map (e.g., so that the corners of the block are aligned with the corners of the phase map), analyzing the pixels contained within the block to determine the fill ratio of each block, and comparing the local fill ratio of the block to the value for the entire scattering region 20 (which is 50%). If the local fill ratio matches the fill ratio for the entire scattering region 20, the algorithm can analyze a new block (e.g., by moving the block of analysis by one pixel in the x or y direction as shown in Figure 2).

[0098] If the local packing ratio does not match the packing ratio associated with the entire scattering region 20, the algorithm identifies a subarray of pixels within the block that does not conform to the desired packing ratio for that block, and inverts the phase values ​​of one or more pixels in at least one of the subarrays so that the block has the desired packing ratio. Pixels are inverted within a given subarray only if doing so would tend to reduce local continuity within the block. An example is shown in Figure 6E, which shows block 630 of the phase map created by iterative phase retrieval and thresholding. Block 630 contains an 8x8 array of pixels 632. The size of block 630 is selected based on the Hadamard transform analysis described above. As previously mentioned, the Walsh function W(N,2 m ) has a length of 2 N-m It is constant across adjacent blocks (in one dimension). Assuming this, if the local filling ratio of all blocks of this length is 50%, then this image is the Walsh function W(N,2 m ), or any Walsh function of lower continuity (i.e., from the Walsh function W(N,1) to W(N,2) m-1 It cannot contain either of the following. In other words, achieving a 50% local filling ratio on a particular scale means that the pattern must have variations with periods smaller than that scale. When the block size is relatively small, the phase map tends to vary with smaller periods (having larger high-frequency components) and scatter more light at larger scattering angles. When the block size is very large, this condition has been found not to reduce the radial PSD at low scattering angles to a considerable extent. In the embodiment, the block size is about 60 μm × 60 μm (e.g., 25 μm × 25 μm to 125 μm × 125 μm). This size is a result of the correction of the local phase map, θ max It was found to be small enough to reduce the low-frequency components in the radial PSD without significantly altering the other parameters.

[0099] In block 630, pixels 632a assigned to have a first phase value are marked with "+", and pixels 632b assigned to have a second phase value are marked with "-". Analyzing the phase values ​​within block 630 reveals that the block has two more pixels 632b than pixels 632a. Therefore, in order to achieve the desired 50% local filling ratio for block 630, one of the pixels 632b needs to be converted to a pixel 632a. The pixel 632b to be converted is selected to avoid increasing the high-frequency components of the phase map. To illustrate, the first subarray 634 of block 630 contains four pixels 632b with a second phase value, and the second subarray 636 contains three pixels 632a and one pixel 632b with a first phase value. Converting one of the pixels 632b in the first subarray 634 will decrease the area where the phase map has a constant value, thus tending to increase the high-frequency components of the phase map. Transforming a pixel 632b in a second subarray 636 into a single pixel 632a would likely reduce high-frequency components by increasing the area where the phase map is constant. Therefore, in this embodiment, the algorithm can transform the phase value of a pixel by identifying a 2x2 subarray containing only one pixel having the phase to be transformed (the second phase value in the example shown in Figure 6A), ensuring a 50% local filling ratio within the block, and then transforming the phase value associated with that single pixel.

[0100] Figure 6F shows plots of the unimproved radial PSD638 and the improved radial PSD640 after thresholding. The PSDs shown are α=4, θ peak =0.3°, and θ max It was created based on Equation 7, where =12°. To create the unmodified radial PSD638, a phase map was created to be thresholded to achieve a two-phase phase map with a 50% fill ratio in terms of phase. To create the improved radial PSD640, the phase map used to create the unmodified radial PSD638 was improved to achieve local 50% over a 96 μm × 96 μm block (representing 8 × 8 pixels) according to the method described herein. As shown in the figure, the improved radial PSD640 has a smaller scattering angle than the unmodified radial PSD638, particularly at scattering angles less than 0.1°. For example, as shown in the figure, the improved radial PSD640 has a smaller scattering angle than θ at scattering angles greater than 0.05° (approximately 0.07°). peak The peak value is 10% at θ, where the unimproved radial PSD638 is 10% of the peak value at scattering angles less than 0.05°. The improved radial PSD640 is approximately 2% of the peak value at the reflection angle, while the unimproved radial PSD638 has a minimum value of approximately 6.5% of the peak value at the reflection angle. In addition, even with improvements to the phase mask, θ peak At larger scattering angles, the radial PSD appears to remain substantially unchanged. Such results demonstrate the effectiveness of the phase mask improvement methods described herein and also demonstrate that such improvements result in a reduction at smaller scattering angles.

[0101] Figure 7 shows a flowchart of an exemplary method 700 for manufacturing an article 10 according to an exemplary embodiment of the present disclosure. Various components and processes shown in Figures 1-6F are mentioned for the purpose of illustrating method 700. The method used to form the article 10 is not particularly limited, and any suitable method may be used. In block 702, a pattern of several surface features 26 is determined. In the embodiment, the pattern is determined by performing method 500 as described herein with respect to Figure 5, by selecting a target radial PSD, creating a phase map based on the target radial PSD, thresholding the resulting phase map, and refining the phase map to provide a local fill ratio for the phase in a subregion of the phase map.

[0102] In block 704, a resist is deposited and patterned on the first main surface 18. The properties of resist deposition and patterning will vary depending on the manufacturing technique used. In the embodiment, various nanoimprint or photolithography techniques can be used to deposit and pattern the resist layer. In such an embodiment, in order to facilitate the use of existing resist application and patterning techniques, the minimum feature size (e.g., minimum line dimension) associated with the multiple surface features 26 can be set to at least 400 nm (e.g., 500 nm or more, 600 nm or more, 700 nm or more, 800 nm or more, 900 nm or more, 1.0 μm or more, 1.5 μm or more, 2.0 μm or more, 2.5 μm or more, 5.0 μm or more). In the embodiment, for example, the resist can be formed using thermoplastic nanoimprint lithography, and the resist can be formed from a thermoplastic polymer that is rotationally coated onto a substrate 12 and then imprinted by a mold to form a first pattern that at least partially corresponds to a pattern of a plurality of surface features 26 on a first main surface 18. The resist can then be thermocured to form an etching mask. Other methods for forming the resist (e.g., gravure offset printing, other printing techniques) are also possible and are included in the scope of this disclosure.

[0103] Photolithography techniques (e.g., photoimprint nanolithography, optical photolithography) can also be used, and the resist can be deposited on the first main surface 18 by a suitable application method (e.g., rotary coating). In such embodiments, a mask constituting a first pattern that at least partially corresponds to a determined pattern for a plurality of surface features 26 is aligned on the first main surface 18, and the resist can be exposed to radiation from a suitable light source (e.g., ultraviolet light) to cure the resist and form an etching mask. Subsequently, the resist can be developed such that a portion of the first main surface 18 remains exposed through the cured resist. Any suitable photolithography technique may be used to pattern the resist.

[0104] In block 706, during the deposition of resist on the first main surface 18, the adhesion between the resist and the first main surface 18 is controlled to facilitate feature rounding during etching. Such adhesion can control undercuts in the etching process, thereby altering the shape of the edges of multiple surface features 26. More specifically, such adhesion control increases the width w of the transition surface 40 described herein with respect to Figure 3B to more than 1.0 μm, θ peak This can help reduce radial PSD at larger, relatively high scattering angles. In embodiments, an adhesion promoter (e.g., hexamethyldisilazane (HDMS) or N,N-dimethyl-N-(3-(trimethoxysilyl)propyl)octadecane-1-ammonium chloride, YSAM C18) is applied to the first main surface 18 before the resist is applied. By controlling the chemical properties of the adhesion promoter (with respect to hydrophobic groups), some control over undercuts during etching and feature rounding can be provided. In addition to, or instead of, the amount of adhesion promoter applied to the surface may also affect the amount of adhesion. The adhesion promoter may also be removed from the first main surface 18 before the resist is applied thereto in order to alter the adhesion of the resist. The applicant has found that any process that alters the interfacial chemistry and water contact angle of the first main surface 18 may alter the adhesion with the resist and thus affect the amount of feature rounding. Any suitable technique may be used to reduce the adhesion between the resist and the first main surface 18 to result in feature rounding. In the embodiment, any of the adhesion promoters described in U.S. Patent No. 9,884,782, filed on April 1, 2015, and fully referenced herein, may be applied to the glass before the deposition of the resist, so that the substrate 12 exhibits a water contact angle of 40° or more and 70° or less (e.g., 45° or more and 60° or less, or 48° or more and 52° or less) after the application of the adhesion promoter. Such a water contact angle has been found to be associated with an appropriate amount of feature rounding.

[0105] In block 708, the exposed areas of the first main surface 18 (through the cured and patterned resist) are exposed to a suitable etching solution for an appropriate etching period determined based on the target etching depth. Each area of ​​the first main surface 18 exposed through the patterned resist formed in block 504 can come into direct contact with the etching solution, thereby decomposing the substrate 12 and removing material therefrom, forming areas on the first main surface 18 that are located at a reduced height relative to the virtual base plane 35 compared to the areas of the first main surface 18 covered with the patterned resist. In the embodiment, the etching solution in contact with the first main surface 18 is an HF / HNO3 etching solution. In the embodiment, the etching solution consists of a combination of hydrofluoric acid (HF, 49 w / w%) and nitric acid (HNO3, 69 w / w%), where HF is 0.1 to 5 v / v% and HNO3 is 0.1 to 5 v / v%. Typical concentrations used to achieve the etching depths described herein are solutions of 0.1 v / v% HF / 1 v / v% HNO3 to 0.5 v / v% HF / 1 v / v% HNO3. In embodiments, etching can be carried out at room temperature to 45°C using immersion or spray etching processes.

[0106] Block 710 is a determination block that determines whether the scattering region 20 includes three or more heights. With respect to Figure 3A, in the embodiment, the multiple surface features 26 may include a plurality of third regions 32 located at a third height h3 with respect to the virtual base plane 35 and a plurality of fourth regions 34 located at a fourth height h4 with respect to the virtual base plane 35. The third height h3 may be the same as the etching depth that distinguishes h1 from h2, or it may differ from the fourth height h4 by a second etching depth. Including the plurality of third regions 32 and the plurality of fourth regions 34 can provide certain performance improvements over a single etching design, such as improved specular reflectance reduction and reduced DOI. Multileveling enables coherent suppression of specular reflection over a wide range of optical wavelengths. The performance attributes of multilevel designs are described in more detail herein with respect to examples.

[0107] If multileveling is desired, method 700 can return to block 702 to determine the pattern for the additional etching step. In the embodiment, the same target radial PSD can be used to create the pattern for the second etching as used for the first etching step. However, when the resist is placed on the first main surface 18, the substrate 12 can be rotated by a certain angle (e.g., 90°, 180°, or any other angle) so that its pattern is applied to the first main surface 18 in a different orientation in the second etching compared to the first etching. In the embodiment, a different target radial PSD can be used to create the pattern for the second etching which is not used for the first etching.

[0108] Properties of the substrate Here, we will describe the various properties of the substrate 12 according to the embodiments of this disclosure.

[0109] In the embodiments, the substrate 12 is a glass substrate or a glass-ceramic substrate. In the embodiments, the substrate 12 is a multi-component glass composition having about 40 mol% to 80 mol% silica and the remaining amount of one or more other components, such as alumina, calcium oxide, sodium oxide, or boron oxide. In some embodiments, the bulk composition of the substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, and phosphate silicate glass. In other embodiments, the bulk composition of the substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, phosphate silicate glass, soda-lime glass, alkali aluminosilicate glass, and alkali aluminoborosilicate glass. In further embodiments, the substrate 12 is a glass-based substrate comprising a glass-ceramic material containing about 90% by mass or more of glass and ceramic components, but is not limited to the following. In other embodiments of Article 10, the substrate 12 may be a polymer material having durable and mechanical properties suitable for generating and maintaining the scattering region 20.

[0110] In the embodiments, the substrate 12 has a bulk composition constituting an alkali aluminosilicate glass, comprising alumina, at least one alkali metal, and, in some embodiments, more than 50 mol% SiO2, in other embodiments, at least 58 mol% SiO2, and in yet another embodiment, at least 60 mol% SiO2, with a ratio of (Al2O3 (mol%) + B2O3 (mol%)) / Σ alkali metal modifier (mol%) > 1, where the modifier is an alkali metal oxide. In a particular embodiment, this glass substantially consists of or comprises about 58 mol% to about 72 mol% SiO2, about 9 mol% to about 17 mol% Al2O3, about 2 mol% to about 12 mol% B2O3, about 8 mol% to about 16 mol% Na2O, and 0 mol% to about 4 mol% K2O, with a ratio of (Al2O3 (mol%) + B2O3 (mol%)) / Σ alkali metal modifier (mol%) > 1, where the modifier is an alkali metal oxide.

[0111] In the embodiment, the substrate 12 has a bulk composition that constitutes an alkali aluminosilicate glass substantially consisting of or comprising about 61 mol% to about 75 mol% SiO2, about 7 mol% to about 15 mol% Al2O3, 0 mol% to about 12 mol% B2O3, about 9 mol% to about 21 mol% Na2O, 0 mol% to about 4 mol% K2O, 0 mol% to about 7 mol% MgO, and 0 mol% to about 3 mol% CaO.

[0112] In this embodiment, the substrate 12 contains approximately 60 mol% to approximately 70 mol% SiO2, approximately 6 mol% to approximately 14 mol% Al2O3, 0 mol% to approximately 15 mol% B2O3, 0 mol% to approximately 15 mol% Li2O, 0 mol% to approximately 20 mol% Na2O, 0 mol% to approximately 10 mol% K2O, 0 mol% to approximately 8 mol% MgO, 0 mol% to approximately 10 mol% CaO, and 0 mol% to approximately 5 mol% The bulk composition of the alkali aluminosilicate glass comprises ZrO2, 0 mol% to about 1 mol% of SnO2, 0 mol% to about 1 mol% of CeO2, less than about 50 ppm of As2O3, and less than about 50 ppm of Sb2O3, and is substantially composed of or consists of 12 mol% ≤ Li2O + Na2O + K2O ≤ 20 mol%, and 0 mol% ≤ MgO + Ca ≤ 10 mol%.

[0113] In the embodiment, the substrate 12 substantially consists of or comprises about 64 mol% to about 68 mol% SiO2, about 12 mol% to about 16 mol% Na2O, about 8 mol% to about 12 mol% Al2O3, 0 mol% to about 3 mol% B2O3, about 2 mol% to about 5 mol% K2O, about 4 mol% to about 6 mol% MgO, and 0 mol% to about 5 mol% CaO, with 66 mol% ≤ SiO2+ It has a bulk composition that constitutes alkali aluminosilicate glass, with B2O3 + CaO ≤ 69 mol%, Na2O + K2O + B2O3 + MgO + CaO + SrO > 10 mol%, 5 mol% ≤ MgO + CaO + SrO ≤ 8 mol%, (Na2O + B2O3)-Al2O3 ≤ 2 mol%, 2 mol% ≤ Na2O-Al2O3 ≤ 6 mol%, and 4 mol% ≤ (Na2O + K2O)-Al2O3 ≤ 10 mol%.

[0114] In the embodiment, the substrate 12 has a bulk composition containing SiO2, Al2O3, P2O5, and at least one alkali metal oxide (R2O), where 0.75 > [(P2O5 (mol%) + R2O (mol%)) / M2O3 (mol%)] ≤ 1.2, and where M2O3 = Al2O3 + B2O3. In the embodiment, [(P2O5 (mol%) + R2O (mol%)) / M2O3 (mol%)] = 1, and in the embodiment, the glass does not contain B2O3, and M2O3 = Al2O3. In the embodiment, the substrate 12 contains about 40 to about 70 mol% SiO2, 0 to about 28 mol% B2O3, about 0 to about 28 mol% Al2O3, about 1 to about 14 mol% P2O5, and about 12 to about 16 mol% R2O. In some embodiments, the glass substrate contains about 40 to about 64 mol% SiO2, 0 to about 8 mol% B2O3, about 16 to about 28 mol% Al2O3, about 2 to about 12 mol% P2O5, and about 12 to about 16 mol% R2O. The substrate 12 may further contain at least one alkaline earth metal oxide, such as MgO or CaO, but is not limited to the following.

[0115] In some embodiments, the substrate 12 has a bulk composition that is substantially lithium-free, i.e., its glass contains less than 1 mol% Li2O, in other embodiments less than 0.1 mol% Li2O, in other embodiments 0.01 mol% Li2O, and in yet other embodiments 0 mol% Li2O. In some embodiments, such glass does not contain at least one of arsenic, antimony, and barium, i.e., its glass contains less than 1 mol%, in other embodiments less than 0.1 mol%, and in yet other embodiments 0 mol% As2O3, Sb2O3, and / or BaO.

[0116] In this embodiment, the substrate 12 has a bulk composition that is substantially composed of or consists of a glass composition such as Corning® Eagle XG® glass, Corning® Gorilla® glass, Corning® Gorilla® Glass 2, Corning® Gorilla® Glass 3, Corning® Gorilla® Glass 4, or Corning® Gorilla® Glass 5.

[0117] In the embodiment, the substrate 12 has an ion-exchangeable glass composition that is strengthened by any chemical or thermal means known in the art. In the embodiment, the substrate 12 is chemically strengthened by ion exchange. In the process, metal ions on or near the first main surface 18 of the substrate 12 are exchanged for larger metal ions in the glass substrate that have the same valence as those metal ions. This exchange is generally carried out by bringing the substrate 12 into contact with an ion exchange medium, such as a molten salt bath containing larger metal ions. The metal ions are typically monovalent metal ions, such as alkali metal ions. In a non-limiting example, chemical strengthening by ion exchange of a substrate 12 containing sodium ions is carried out by immersing the substrate 12 in an ion exchange bath containing a molten potassium salt, such as potassium nitrate (KNO3). In one particular embodiment, ions in the surface layer of the substrate 12 adjacent to the first main surface 18 and larger ions are exchanged with Li + (If present in glass), Na + , K + , Rb + , and Cs + These are monovalent alkali metal ions. Alternatively, the monovalent cation in the surface layer of the substrate 12 is Ag + These ions may be substituted with monovalent cations other than alkali metal ions.

[0118] In such embodiments, the substitution of smaller metal ions with larger metal ions in the ion exchange process creates a compressive stress region in the substrate 12 that extends from the first main surface 18 to a depth under compressive stress (referred to as the "depth of the layer"). This compressive stress in the substrate 12 is balanced by an internal tensile stress (also referred to as the "central tension"). In some embodiments, the first main surface 18 of the substrate 12 described herein, when strengthened by ion exchange, has a compressive stress of at least 350 MPa, and the region under compressive stress extends from below the first main surface 18 to a depth of at least 15 μm in thickness 21, i.e., the depth of the layer.

[0119] The ion exchange process is typically carried out by immersing the substrate 12 in a molten salt bath containing larger ions to be exchanged for smaller ions in the glass. Those skilled in the art will recognize that the parameters of the ion exchange process, including but not limited to the bath composition and temperature, immersion time, the number of times the glass is immersed in the salt bath (or multiple baths), the use of multiple salt baths, slow cooling, and additional steps such as washing, are generally determined by the glass composition and the desired layer depth and compressive stress of the glass as a result of strengthening operations. As an example, ion exchange of alkali metal-containing glass can be carried out by immersion in at least one molten bath containing salts such as nitrates, sulfates, and chlorides of larger alkali metal ions, but not limited to those mentioned above. The temperature of the molten salt bath is typically in the range of about 380°C to about 450°C, while the immersion time ranges from about 15 minutes to about 16 hours. However, different temperatures and immersion times than those described above may be used. When such ion exchange treatment is applied to a substrate 12 having an alkali aluminosilicate glass composition, it results in a compressive stress region with a depth (layer depth) ranging from approximately 10 μm to at least 50 μm, with compressive stress ranging from approximately 200 MPa to approximately 800 MPa, and a central tension of less than approximately 100 MPa.

[0120] An etching process that can be used to create a scattering region 20 on the substrate 12 can remove alkali metal ions from the substrate 12 that would otherwise be replaced by larger alkali metal ions in the ion exchange process, thus giving priority to creating a compressive stress region in the article 10 after the formation and generation of the scattering region 20. [Examples]

[0121] Embodiments of this disclosure will be further understood by considering the following examples.

[0122] A first set of embodiments was constructed by carrying out methods 500 and 700 as described herein with respect to Figures 5 and 7. Specifically, the α values ​​of 4 and 5, and the θ values ​​of 0.3 and 0.5. peak The values ​​of θ for 4, 8, 12, 16, and 32. max The target radial PSD was created using the values. The examples were formed on 0.7 mm thick Corning AutoGrade® Glass. Method 500 was performed on each example to determine the resist deposition pattern (using a 50% fill ratio for each height). The samples were etched through the resist to various etching depths according to Method 700 (etching depth was measured with a 2D tactile surface shape analyzer and then confirmed with a white light interferometer over a 1 × 1 mm area). The target radial PSD and etching depth are summarized in Table 1 below (" * Examples marked with '' include feature rounding by block 706 of Method 700). DOI values ​​are reported in gloss units according to ASTM E430.

[0123] [Table 1]

[0124] As shown in Table 1, several performance attributes of the sample were measured, including transmitted haze, sparkle (PPD), combined image sharpness, specular reflectance (Rs), and washout index in two different configurations. The washout index relates to how the scattering region 20 affects the black level contrast of the display in the presence of an external light source. A high value of the washout index is associated with superior performance. Samples with rounded characteristics exhibit higher washout index performance of 0.68 or higher (in some cases, 0.70 or higher, 0.75 or higher, and even 0.80 or higher). Details regarding the measurement and calculation of the washout index are given in more detail in this specification. A range of performance attributes achieved in a subset of the first set of examples is given in Table 2 below.

[0125] [Table 2]

[0126] As shown in Table 2, a relatively low θ max Value (for example, θ) max Samples prepared using a target radial PSD with a θ of 4° tended to exhibit excellent transmission haze performance (in some cases providing transmission haze values ​​of ≤3.0%, ≤2.75%, ≤2.5%, ≤2.0%, ≤1.75%, ≤1.50%, ≤1.25%, ≤1.0%, and even ≤0.75%). However, relatively high θ max Value (for example, θ) max Samples prepared using a target radial PSD with a 32° (=32°) tended to exhibit superior sparkle performance (in some cases, less than 1.0%, less than 0.9%, less than 0.8%, less than 0.7%, less than 0.6%, and even less than 0.55%). The last row of Table 2 includes several samples with rounded features, which generally resulted in superior washout and haze performance compared to samples without rounded features but formed using the same target radial PSD.

[0127] The “washout” indices included in Tables 1 and 2 were developed to quantify the effect of glare events (e.g., exposure to sunlight) on the contrast and resolution of the embedded display. Such indices are useful for testing the performance of cover materials for applications that may be exposed to light from external light sources (e.g., in-cabin displays, outdoor displays). To quantify “washout,” the modulation transfer function (MTF) of the anti-glare surface was measured under various lighting conditions, and the average value of the MTF over numerous spatial frequencies was used to evaluate the effect of lighting conditions on display performance. The MTF at a specific spatial frequency f is

[0128]

number

[0129] It can be expressed as follows, and in the formula,

[0130]

number

[0131] And I(f) max and I(f) min These are the maximum and minimum intensities of the input and output modulated images at spatial frequency f. In this equation, MF in This represents the MF value associated with the input pattern emitted through the sample cover material. out The value represents the MTF value when the cover material is placed under the tested lighting conditions across the input pattern (e.g., from the display). A higher MTF value generally means that the lighting conditions have little impact on the display performance (thus, the performance of the scattering region of the cover material is good). In embodiments, an MTF value of 0.60 or greater (e.g., 0.65 or greater, 0.70 or greater, 0.75 or greater, 0.76 or greater, 0.77 or greater, 0.78 or greater, 0.79 or greater, 0.80 or greater, 0.81 or greater, 0.82 or greater, 0.83 or greater, 0.84 or greater, 0.85 or greater, 0.86 or greater, 0.87 or greater, 0.88 or greater, 0.89 or greater, 0.90 or greater, 0.91 or greater, 0.92 or greater, 0.93 or greater, 0.94 or greater, and 0.95 or greater) is preferred for a given lighting condition and indicates a minimal reduction in display performance caused by exposure to external light.

[0132] FIG. 8 schematically shows an apparatus 800 for measuring the washout effect. As shown in the figure, a sample 802 (e.g., corresponding to the substrate 12 described herein) is placed on top of a display 804. The sample 802 is positioned such that the scattering region faces outward (not towards the display 804). As shown in the enclosure 805 (showing a front view of the sample 802 and the display 804), the display 804 generates a plurality of target patterns 806 in which the intensity of the light emitted by the display 804 varies with a specific spatial frequency f i A plurality of first light sources 808 are distributed around the sample 802. The plurality of first light sources 808 (e.g., room lamps) are configured to emit relatively low-intensity light to simulate the sample 802 encountered under normal ambient conditions (e.g., room lamps). As reported herein, the plurality of first light sources 808 were configured to emit white light having a color temperature of 130 lux and 2100K. The projection light source 810 is configured to emit relatively high-intensity light to simulate sunlight illumination. The projection light source 810 is positioned such that the light emitted thereby is incident on the sample at an incident angle θ i In embodiments, the projection light source 810 has an incident angle θ i It is movable to change or otherwise adjustable. In the embodiment, the projection light source 810 emits light over a certain emission area, and thus the light emitted by the projection light source 810 is at an incident angle θ within a certain range. i Then, it is directed onto sample 802.

[0133] Camera 812 is positioned to receive light scattered from sample 802. The camera receives light scattered from sample 802 at a field of view angle θ. v It is positioned so that it enters the camera 812 within a certain field of view (or a certain range of field of view). In this embodiment, the camera 812 is positioned within a field of view θ v It is movable to change or otherwise adjustable. The computing system 814 receives the image generated by the camera 812, analyzes the image, and calculates multiple MTF values ​​for each of the multiple target patterns 806 emitted by the display 804. For each of the target patterns 806, the computing system 814 uses equations 9 and 10 to calculate the MTF value and generates an output that measures the dependence of the MTF value on spatial frequency. Multiple first light sources 808 and projection light sources 810 allow the MTF values ​​to be measured under multiple different lighting conditions to determine the effectiveness of the pattern on the sample 802 without reducing washout. If only the first light sources 808 emit light, a "room lamp washout" effect can be measured. If both the first light sources 808 and projection light sources 810 emit light, a "sunlight washout" effect can be measured.

[0134] Such washout measurements would be particularly useful in evaluating the performance of cover materials for interior displays. Figure 9 shows an interior 1000 with three different interior systems 100, 200, and 300 according to exemplary embodiments. Interior system 100 includes a center console base 110 having a surface 120 with a display 130. Interior system 200 includes a dashboard base 210 having a surface 220 with a display 230. The dashboard base 210 typically includes an instrument panel 215, which may also include a display 216. Interior system 300 includes a dashboard handle base 310 having a surface 320 and a display 330. In one or more embodiments, an interior system may include a base which is any part of the interior of the vehicle, including armrests, pillars, seatbacks, floorboards, headrests, door panels, or surfaces. In embodiments, the displays 130, 230, and 330 are flat and include a cover glass with a planar main surface. In the embodiments, one or more of the displays 130, 230, and 330 are curved, and the curved display may include a curved cover glass that would have been heat-formed or cold-formed to have such curvature. For example, such embodiments may incorporate an opaque layer formed from a photocurable ink described herein, disposed on a cold-formed glass substrate.Such cold forming may include any of the techniques described in the specifications of U.S. Patent Application Publication No. 2019 / 0329531A1, titled "Laminating thin strengthened glass to curved molded plastic surface for decorative and display cover application", which is incorporated herein by reference in its entirety; U.S. Patent Application Publication No. 2019 / 0315648A1, titled "Cold-formed glass article and assembly process thereof"; U.S. Patent Application Publication No. 2019 / 0012033A1, titled "Vehicle interior systems having a curved cover glass and a display or touch panel and methods for forming the same"; and U.S. Patent Application No. 17 / 214124, titled "Curved glass constructions and methods for forming same".

[0135] Various components of the passenger compartment 1000 may be exposed to illumination from various light sources. For example, as shown in FIG. 9, a first ambient light source 900 can emit light that passes through the first side window of the vehicle and is incident on the display 216 at an incident angle θ i1 The display 216 may scatter light at a specific scattering angle θ v1 such that the scattered light enters the driver's field of view and may be directed to distract the driver. A second ambient light source 902 can emit light that passes through the second side window of the vehicle and is incident on the display 130 at an incident angle θ i2 The display 130 may scatter light at a specific scattering angle θ v2 The scattered light may enter the driver's field of vision and be directed in a way that distracts the driver. The first and second ambient light sources 900 and 902 can represent sunlight at various points in time. In fact, the ISO 15002 / SA 1757 standard defines a first condition (i.e., related to the “washout 1” index herein) where 45k lux light (direct sunlight) is incident on the display 216 at an angle of 20° and scattered towards the driver at a scattering angle of 0°. i1 =20° and θ v1 A second condition (i.e., θ = 0°), where 45k lux light (direct sunlight) is incident on the display 130 at an angle of 45° and scattered towards the driver at a scattering angle of 20° (i.e., related to the “washout 2” index herein). i2 =45° and θ v2 The angle specified is 20°. The apparatus 800 shown in Figure 8 can be used to test for washout under such conditions by changing the orientation of the sample 802 and adjusting the projection light source 810.

[0136] Using the apparatus 800 shown in Figure 8, samples constructed according to the method described herein were tested by applying the two criteria of ISO 15002 / SA 1757 described herein. An Apple® mini-iPad® 4 was used as the display 804. A Pixelink 3.1 MP PL-B776 was used as the camera 812. A parallel LED light source (emitting 45,000 lux of white light) was used as the projection light source 810 (model LCS-6500-65-22 manufactured by Mightex Systems). Multiple projection light sources were used and positioned to emit light incident on sample 802 at incidence angles of 20° and 45°. Sample 802 and camera 812 also had a field of view angle θ v and the angle of incidence θ i It was mounted on a rotating stage so that it could be adjusted to two conditions. The laboratory room lamp was used as the first light source 808 and was measured to have a luminance of 132 lux.

[0137] In the first set of measurements, sample 802 had a standard AG surface treatment (referred to herein as "counterexample 1," by sandblasting the first main surface 18). The results are shown in Figures 10A to 10F. Figures 10A to 10C show the results under the first conditions described herein (i.e., θ i1 =20° and θ v1 The images show patterns captured at θ = 0°. Figure 10A shows image 1002 where the display 804 is not covered with sample 802 in a darkroom. Figure 10B shows image 1004 where the display 804 is covered with sample 802 when only the first light source 808 is emitting light (laboratory lamp is on). Figure 10C shows image 1006 where the display 804 is covered with sample 802 and both the first light source 808 and the projection light source 810 are emitting light. Figures 10D-10F show images under the second condition described herein (i.e., θ = 0°). i2 =45° and θ v2 The images show patterns captured at an angle of 20°. Figure 10D shows image 1008 where the display 804 is not covered with sample 802 in a darkroom. Figure 10E shows image 1010 where the display 804 is covered with sample 802 when only the first light source 808 is emitting light (laboratory lamp is turned on). Figure 10F shows image 1012 where the display 804 is covered with sample 802 and both the first light source 808 and the projection light source 810 are emitting light.

[0138] Figures 11 and 12 are plots 1102 and 1104 of MTF values ​​obtained from the images shown in Figures 10A to 10F. Figure 11 includes a first series 1106 representing various MTF values ​​obtained from image 1004 shown in Figure 10B (for a first condition in which only the first light source 808 is turned on). Figure 11 also includes a second series 1108 representing various MTF values ​​obtained from image 1006 shown in Figure 10C (for a first condition in which both the first light source 808 and the projection light source 810 are operated). Figure 12 includes a first series 1110 representing various MTF values ​​obtained from image 1010 shown in Figure 10E (for a second condition in which only the first light source 808 is turned on). Figure 12 also includes a second series 1112 representing various MTF values ​​obtained from image 1012 shown in Figure 10F (for a second condition in which both the first light source 808 and the projection light source 810 were in operation). These experimental results show that (1) very small drops caused by room lamp conditions can be resolved in this setting, indicating high sensitivity of the measurement setting; (2) sample 802 only resulted in a decrease in image contrast and did not affect the display resolution; (3) this setting can identify the influence of different group effects on display performance; and (4) this setting can characterize the "washout effect" from different angles.

[0139] To quantitatively evaluate the effect of sample 802, the MTF values ​​at spatial frequencies associated with points 1114, 1116, 1118, 1120, and 1122 in the first series 1106 were averaged (MTF values ​​at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm were averaged for each of the series 1106, 1108, 1110, and 1112). The “washout” index described herein was the average value of the MTF values ​​across these spatial frequencies for each condition.

[0140] A series of measurements similar to those described herein were performed on samples having a scattering region designed based on the target radial PSD according to Equation 7, with respect to Figures 10A-12 (Examples 22 and 5). Specifically, α=4, θ peak =0.3°, and θ max The first sample (Example 22) was constructed based on a target radial PSD of 4°, and α=4, θ peak =0.5°, and θ max Another test was performed using two different samples of the second sample (Example 5, see Table 1) constructed based on a target radial PSD of θ = 4°. For substantially these samples, the etching depth was 150 nm. The second sample was feature-rounded by performing block 706 of method 700 shown in Figure 7. The previously described conditions (θ i1 =20° and θ v1 =0°; and θ i2 =45° and θ v2 Each sample was tested at each of the following angles (=20°). Figure 13A shows image 1300 with the projection light source 810 illuminating the first sample under the first condition. Figure 13B shows image 1302 with the projection light source 810 illuminating the first sample under the second condition. Figure 13C shows image 1304 with the projection light source 810 illuminating the second sample under the first condition. Figure 13D shows image 1306 with the projection light source 810 illuminating the second sample under the second condition. Counterexamples of conventional AG (shown in Figures 10A-12) and the results for the first and second samples are summarized in Table 3 below.

[0141] [Table 3]

[0142] As shown in Table 3, Example 22 (without feature rounding) yielded the best results with respect to specular reflectance reduction (coupled specular reflectance (Rs) value less than 9) and coupled DOI (coupled DOI less than 55%), whereas Example 5 provided very good washout performance, with a washout index of 0.80 or higher under the first condition and a washout index of 0.70 or higher under the second condition. While achieving such washout performance, it still provided improved haze, coupled DOI, and specular reflectance performance compared to counterexample 1. These examples demonstrate the ability of the articles described herein to achieve a unique combination of performance attributes: transmitted haze of less than 2.0% (and even less than 1.5% or 1.25%), coupled Rs of less than 15, sparkle of less than 2.5% (measured at 140 ppi), a washout index of 0.7 or higher under the first condition, and a washout index of 0.55 or higher under the second condition. Articles constructed by the methods described herein, with their characteristic rounding, exhibit consistent display performance across a wide range of ambient lighting conditions, making them particularly well suited for automotive applications.

[0143] Figure 14 shows plots 1400 of sparkle and specular reflectance (Rs) measurements for the first set of examples (including the samples given in Table 1, etc.). The Rs and sparkle results were plotted relative to each other to form plot 1400. The results are the same θ max Different curves were fitted for each subset of the examples formed by the target radial PSD having a value (but a different alpha value). Curve 1402 is θ max The results were fitted using a target radial PSD with =32°. Curve 1404 is θ max The results were fitted using a target radial PSD with =16°. Curve 1406 is θ max The results were fitted using a target radial PSD with =12°. Curve 1408 is θ max The results were fitted using a target radial PSD with =8°. Curve 1410 is θ max =4°, and θ peak The results were fitted using a target radial PSD with =0.5°. Curve 1412 is θ max =4°, and θ peak The results formed using a target radial PSD with =0.3° were fitted. As shown in the figure, θ max Examples formed using a target radial PSD with =32° yielded the most preferred combination of results regarding sparkle and Rs, with numerous samples giving less than 1% sparkle and less than 10 Rs.

[0144] Of note in plot 1400 is that curves 1402, 1404, 1406, 1408, 1410, and 1412 each suggest similar minimum Rs values ​​for each subset of the examples, ranging from approximately 5 to approximately 9. Each example in the first set of examples shown in plot 1400 was formed as a binary surface (a first principal surface 18 within the scattering region 20 containing multiple first regions 28 and multiple second regions 30, where the multiple first regions 28 occupy approximately 50% of the surface area within the scattering region 20, and the multiple second regions 30 occupy the other 50%). Although not intended to be theoretically restrictive, for incident plane waves (as shown in Figure 3), specular reflection from a binary image (related to the height profile H(x,y) within the scattering region 20) is thought to depend only on the filling ratio of the binary image, and not on the image itself. Considering this, it is not surprising that curves 1402, 1404, 1406, 1408, 1410, and 1412 each suggest a similar lower limit (floor) of Rs. The variation in the measured Rs would be explained by the variation from the light source used to measure specular reflectance from a uniform plane wave.

[0145] The previous embodiment described in Figure 14 was a binary surface with a filling ratio of approximately 50% related to each surface height, but this filling ratio can vary, and it is still considered that an acceptable specular reflectance result can be obtained. When a binary surface is used, the assumed surface area ratio at each height is 40% or more and 60% or less (for example, 42.5% or more and 57.5% or less, 45% or more and 55% or less, 47.5% or more and 52.5% or less), and even then, it gives an acceptable reduction in specular reflectance (compared to a smooth substrate 12 without scattering regions). Referring to Figure 2 for explanation, one of the multiple first regions 28 and the multiple second regions 30 may have a total surface area that constitutes more than 50% (e.g., more than 50% and 60% or less) of the total surface area of ​​the scattering region 20, while the other of the multiple first regions 28 and the multiple second regions 30 may have a total surface area that occupies less than 50% (e.g., less than 50% and 40% or more) of the total surface area of ​​the scattering region 20, and still provide acceptable specular reflectance performance.

[0146] To investigate the effect of feature rounding on optical performance, a different model was created. Figure 15A shows a portion of the modeled surface 1500. This surface is θ max =4°, θ peak It was fabricated using a target radial PSD with α=0.5° and α=4. As shown in Figure 15A, surface 1500 includes a first region 28 located at a first height and a second region 30 located at a second height, the first height differing from the second height by approximately 130 nm. The transition surface 1506 is the surface through which surface 1500 transitions between the first and second heights. In this example, it was assumed that within the transition surface 1506, surface 1500 extends perpendicular to the direction in which the surface extends into the first region 28 and the second region 30. Figure 15B shows a cross-sectional view of surface 1500 through line 1504 shown in Figure 15A. As shown in the figure, line 1504 extends parallel to the surface normal of transition surface 1506. Transition surface 1506 is shown to have an undefined gradient. Figure 15C shows a plot of the number of occurrences of surface height measurements across surface 1504. As shown in the figure, the number of height occurrences in the first group at the second height 1510 accounts for 50% of the measured number of height occurrences, and the number of height occurrences in the second group at the first height 1512 accounts for 50% of the other 50% of the measured number of height occurrences. This indicates that there is no measured height between the first and second heights, which is consistent with the undefined gradient of the transition surface 1506. Figure 15D shows a plot 1514 of the predicted decrease in specular reflectance as a function of wavelength. As shown in the figure, the minimum specular reflectance for this design occurs at approximately 525 nm.

[0147] To predict the effect of feature rounding, surface 1500 was modified so that the gradient transitions from the first and second regions 28 and 30 to the transition surface 1506. Specifically, corners 1518 and 1520 (see Figure 15B) were rounded by applying a Gaussian blur filter (the Matlab® imgaussfilt image filter was used to define the amount of feature rounding). Figure 16B shows a portion of the modified surface 1600. As a result of feature rounding, the modified surface 1600 includes a transition surface 1602 between regions 28 and 30 with a finite gradient (in this example, the gradient extended such that the transition surface 1602 extends in a plane that extends at 3° with respect to the direction of the first region 28). Figure 16B shows a cross-sectional view of the modified surface 1600 through line 1504 shown in Figure 16A. As shown in the figure, the gradient of the improved surface 1600 transitions more gradually at angles 1605 and 1607 between the values ​​in regions 28 and 30 and the values ​​within the transition surface 1602 than at angles 1518 and 1520 shown in Figure 15B. That is, on the improved surface 1600, the gradient has a smoother transition than on surface 1500. Figure 16C shows a plot 1604 of the number of surface height measurements occurring across the improved surface 1600. As shown in the figure, the first group of height measurements 1606 at the second height account for approximately 30% of the measured height measurements, and the second group of height measurements 1608 at the first height account for approximately 30% of the measured height measurements. This indicates that approximately 40% of the height measurements occur at heights other than the first and second heights, which is consistent with the finite gradient of the transition surface 1602. In this case, the lateral distance between the first region 28 and the second region 30 (along line 1504, see Figure 16A) was approximately 2.3 μm (corresponding to the width w shown in Figure 3B). Furthermore, the probability count curve had a slope of 170% / μm. Figure 16D is plot 1610, which includes curves 1612 and 1614 of the modeled specular reflectance of the improved surface 1600. Curve 1612 represents the modeled specular reflectance when the improved surface 1600 has the same etching depth as the example shown in Figure 15B, while curve 1614 represents the modeled specular reflectance when the etching depth of the improved surface 1600 is increased by 15%, with a minimum value of approximately 525 nm.As shown in the figure, the smoother transition associated with the improved surface 1600 is not expected to decrease the minimum specular reflectance, but rather shifts the wavelength at which the specular reflectance is lowest. This wavelength shift can be corrected by adjusting the etching depth.

[0148] Figure 17 shows plots of modeled radial PSD for four surfaces with varying degrees of feature rounding. As shown in the figure, the value d in the legend represents the lateral distance between the edges of the first region 28 and the second region 30 (measured perpendicular to their respective transition surfaces) (corresponding to the width w shown in Figure 3B). As shown in the figure, the radial PSD decreases for examples where the value of d is larger. Samples with a greater amount of feature rounding (such that the gradient of the first principal surface 18 transitions from minimum to maximum over a larger lateral distance) are predicted to have lower PSDs at relatively large scattering angles of 7° or more. These lower PSDs for samples with a greater amount of feature rounding are thought to provide superior washout performance compared to unrounded samples by offering lower scattering amplitudes at high scattering angles.

[0149] Radial PSD was measured from two different samples to confirm the results of the modeling described in Figures 16A-17. These samples were θ max =4, α=4, and θ peak The surface was fabricated using a target radial PSD with a radius of 0.5. Figures 18A and 18B are plan and perspective views, respectively, of surface 1800, which was formed without feature rounding (adhesion between resist and substrate was not controlled). These images were created from white light interferometry measurements of surface 1800. As shown in the figure, surface 1800 included a first region 28 located at a first height, a second region 30 located at a second height, and a transition surface 1802 extending between the first region 28 and the second region 30. Figures 18C and 18D are plan and perspective views, respectively, of surface 1804, which was formed with feature rounding (adhesion between resist and substrate was controlled). These images were created from white light interferometry measurements of surface 1804. As shown in the figure, surface 1804 included a first region 28 located at a first height, a second region 30 located at a second height, and a transition surface 1806 extending between the first region 28 and the second region 30. As a result of feature rounding, the transition surface 1806 has a smaller slope than the transition surface 1802 shown in Figures 18A-18B. The width w (see Figure 3B) of the transition in height of surface 1804 from the first height to the second height was measured to be between 2.0 μm and 10.0 μm.

[0150] Figure 18E shows plots of radial PSDs 1810 and 1812 measured from surfaces 1800 and 1804 shown in Figures 18A-18D, respectively. Radial PSDs 1810 and 1812 were plotted in Gwyddion from white light interferometry data shown in Figures 18A-18D. Radial PSDs 1810 and 1812 were created from white light interferometry data (approximately 360 nm lateral resolution) from 1 × 1 mm areas of each surface. Radial PSDs 1810 and 1812 were created from the entire 1 × 1 mm area, but the images in Figures 18A-18D represent subdivisions of the imaging area. It was found that the specific 1 × 1 mm area used did not affect the resulting radial PSDs. As shown in the figure, radial PSD1810 associated with surface 1800 is significantly higher than radial PSD1812 associated with surface 1804 at scattering angles greater than 5°. In fact, radial PSD1812 decreases to 0.1% of its peak value at scattering angles of 8° or less relative to the specular reflection direction. Radial PSD1812 decreases to 0.01% of its peak value at a third scattering angle of 16° or less relative to the specular reflection direction. Radial PSD1810, in contrast, decreases to 10% of its peak value at a scattering angle of 10°. -3 It is greater than twice. Such lower measured radial PSDs, given by feature rounding, demonstrate the effectiveness of feature rounding performed by the method described herein.

[0151] Bidirectional reflection distribution function (BRDF) measurements were performed on five different samples prepared according to the method described herein. The first sample was not feature-rounded, and θ max =4°, α=4, and θ peak The second sample was formed based on a target radial PSD of =0.3°. The second sample was not characterized by rounding, and θ max =4°, α=4, and θ peak It was formed based on a target radial PSD of =0.5°. The third sample was characterized by rounding and θ max =8°, α=5, and θ peak It was formed based on a target radial PSD of =0.3°. The fourth sample was characterized by rounding, θ max =8°, α=5, and θ peak It was formed based on a target radial PSD of =0.3°. The fifth sample was not characterized by rounding, and θ max =8°, α=4, and θ peak The samples were formed based on a target radial PSD of 0.3°. Measurements were performed in reflection mode using a REFLET 180S system from Synopsys, Inc. Figure 19 shows a plot of the results measured at 520 nm with an incident angle of 20°. As shown in the figure, the feature-rounded samples showed lower scattering intensities at scattering angles greater than 20° relative to the specular reflection direction. When normalized with respect to the specular reflection peak, the effectiveness of feature rounding in reducing scattering amplitude at relatively high scattering angles is even more pronounced. At a scattering angle of 20° relative to the specular reflection direction, the third and fourth samples (feature-rounded) showed 10 times the intensity measured at their specular reflection peaks. -6 It showed a scattering intensity of less than twice that of sample 4 (10 times the intensity at its specular reflection peak). -7 (The values ​​were less than double). All samples that had not undergone feature rounding showed, in contrast, a 10% specular reflection peak at a scattering angle of 20°. -5 The BRDF amplitude was more than doubled. Regarding the actual (unnormalized) BRDF amplitude, each of the feature-rounded samples showed 1.7e-4sr at a scattering angle of 30°. -1 BRDF amplitude less than 1.5e-4sr at a scattering angle of 40° -1 The sample exhibited a BRDF amplitude of less than 1.5°. Such a relatively low BRDF amplitude at a high scattering angle, achieved by the feature-rounded sample, demonstrates the excellent washout performance of such sample.

[0152] Additional sets of samples were prepared using multiple etching processes. The parameters associated with each process, including the target radial PSD and etching depth for each etching, as well as the results of optical performance measurements, are given in Table 4 below.

[0153] [Table 4]

[0154] For samples that underwent multiple etching processes, additional measurements were performed, and the sets of performance attributes predicted to be achieved with various etching sequences are summarized in Table 5 below.

[0155] [Table 5]

[0156] As demonstrated by the comparison between Tables 1 and 2 and Tables 4 and 5, samples produced by multiple etching steps tend to have increased sparkle and haze compared to those produced using a single etching step. However, multiple etching designs can significantly reduce the sharpness of specular reflection and the combined image. The presence of multiple heights allows for interference suppression of specular reflection over a wide optical bandwidth. As shown in Table 4, the Rs values ​​obtained with multiple etching designs were generally less than 4.0, in some cases less than 3.0, and even less than 2.0. Single etching designs, in contrast, had much higher Rs values. The sharpness values ​​of the combined image achieved with multiple etching designs were generally less than 65%, in some cases less than 55%, and in one example even less than 30%. Generally, the design used will be determined by the performance attributes designed for the specific application. Single-etched designs would be desirable for applications where low haze, sparkle, and excellent washout performance (such as in automotive displays) are required, while multi-etched designs would be more suitable for applications requiring superior specular reflectance reduction and / or DOI.

[0157] Unless otherwise specified, none of the methods described herein are intended to be construed as requiring their steps to be performed in a particular order. Therefore, if a claim for a method does not actually enumerate the order in which its steps should be performed, or if it is not otherwise stated in the claims or description that the steps should be limited to a particular order, no particular order is implied. Furthermore, as used herein, nouns are intended to refer to one or more components or elements, and not to be construed as referring to only one.

[0158] It will be apparent to those skilled in the art that various modifications and alterations can be made without departing from the spirit or scope of the disclosed embodiments. Since modifications, combinations, partial combinations and alterations of the disclosed embodiments, including the spirit and substance of the embodiments, will be conjured to those skilled in the art, the disclosed embodiments should be construed to encompass the entirety of the claims and their equivalents.

[0159] Preferred embodiments of the present invention are described below in separate sections.

[0160] Embodiment 1 It is a substrate, First main surface, A second principal surface opposite to the first principal surface, and Scattering region formed within the first main surface, It has, Within the scattering region, the first principal surface is A plurality of first regions positioned at a first height with respect to a virtual base plane extending across the substrate, A plurality of second regions positioned at a second height with respect to the virtual base plane, Includes, The first height is greater than the second height by an etching depth of 80 nm or more and 600 nm or less. The aforementioned scattering region is a radial PSD, The radial PSD increases with increasing light scattering angle relative to the specular reflection direction, in a first range of scattering angles, The radial PSD has a peak value, and the peak angle θ peak , and The radial PSD decreases to 10% of the peak value at a first scattering angle of 2° or more and 15° or less with respect to the specular reflection direction, θ peak Second range of scattering angles at larger angles, A substrate having radial PSDs, An article equipped with.

[0161] Embodiment 2 The article according to Embodiment 1, wherein, within the second range of the scattering angles, the radial PSD decreases to 1% of the peak value at a second scattering angle that is greater than the first scattering angle and is 3.5° or more and 30° or less with respect to the specular reflection direction.

[0162] Embodiment 3 The article according to Embodiment 2, wherein, within the first range of scattering angles, the radial PSD is less than 10% of the peak value at a scattering angle of 0.05° or more.

[0163] Embodiment 4 The first scattering angle is 6° or more and 13° or less with respect to the specular reflection direction, The article according to Embodiment 2 or 3, wherein the second scattering angle is 12.5° or more and 30.0° or less with respect to the specular reflection direction.

[0164] Embodiment 5 The first scattering angle is 2° or more and 7° or less with respect to the specular reflection direction, The article according to Embodiment 2 or 3, wherein the second scattering angle is 3.5° or more and 13.5° or less with respect to the specular reflection direction.

[0165] Embodiment 6 The article according to Embodiment 5, wherein, within the second range of the scattering angles, the radial PSD decreases to 0.1% of the peak value at a third scattering angle of 8° or less with respect to the specular reflection direction.

[0166] Embodiment 7 The article according to Embodiment 5, wherein, within the second range of the scattering angles, the radial PSD decreases to 0.01% of the peak value at a third scattering angle of 16° or less with respect to the specular reflection direction.

[0167] Embodiment 8 θ peak An article according to any one of Embodiments 1 to 7, wherein the angle is 0.3° or more and 0.5° or less.

[0168] Embodiment 9 Within the scattering region, the first principal surface includes a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions. The article according to any one of embodiments 1 to 8, wherein the plurality of inclined transition surfaces are inclined such that the height of the first main surface decreases with increasing distance from the boundary of the plurality of first regions.

[0169] Embodiment 10 The article according to Embodiment 9, wherein at least some of the plurality of inclined transition surfaces extend over a lateral distance of 1.0 μm or more and 10 μm or less between regions of the plurality of first regions and the plurality of second regions connected by the inclined transition surfaces, and the lateral distance over which the inclined transition surfaces extend is parallel to the surface normal of the inclined transition surface and measured in a direction parallel to the virtual base plane.

[0170] Embodiment 11 The aforementioned article, Transmitted haze of 2.0% or less, and Sparkle of 2.5% or less when measured at 140ppi. An article according to any one of embodiments 1 to 10, which shows the following.

[0171] Embodiment 12 An article according to any one of embodiments 1 to 11, wherein the first average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, is at least 0.55 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 20°.

[0172] Embodiment 13 The article according to Embodiment 12, wherein the first average modulation transfer function is at least 0.7 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 20°.

[0173] Embodiment 14 An article according to any one of embodiments 1 to 13, wherein the second average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, is at least 0.6 when the article is viewed at a field of view of 20° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 45°.

[0174] Embodiment 15 Within the scattering region, the first principal surface is A plurality of third regions positioned at a third height relative to the virtual base plane, and A plurality of fourth regions positioned at a fourth height relative to the virtual base plane, Includes, The article according to Embodiment 1, wherein the fourth height is different from the first height, the second height, and the third height.

[0175] Embodiment 16 The aforementioned article, Specular reflectance (Rs) of 4.0 or less, and Sharpness of combined images less than 65%, An article as described in Embodiment 15, which shows the following.

[0176] Embodiment 17 The article according to any one of Embodiments 1 to 16, wherein the substrate is a glass substrate, and the article further includes a display configured to emit light through the substrate and disposed adjacent to the second main surface.

[0177] Embodiment 18 The first main surface, a second main surface opposite to the first main surface, and a scattering region formed within the first main surface, An article having: Within the scattering region, the first main surface is a plurality of first regions disposed at a first height with respect to a virtual base plane extending to the substrate, and a plurality of second regions disposed at a second height with respect to the virtual; said virtual base plane, and including: The first height is greater than the second height by an etching depth of 80 nm or more and 600 nm or less, The scattering region is a radial PSD, and has a radial PSD including a first range of scattering angles on a first side of a peak angle (θ peak ) where the radial PSD increases as the scattering angle increases, and a second range of scattering angles on a second side of θ peak where the radial PSD decreases as the scattering angle increases, The bidirectional reflectance distribution function ( "BRDF") of the article is less than 10 times the peak intensity value at a scattering angle of 20° with respect to the specular reflection direction, -5 times, The BRDF is measured from light having a wavelength of 520 nm incident on the first main surface at an incident angle of 20°. An article.

[0178] Embodiment 19 The article according to Embodiment 18, wherein the BRDF has an amplitude less than 1.7×10 -4 sr -1 at a scattering angle of 30° with respect to the specular reflection direction.

[0179] Embodiment 20 Within the second range of the scattering angles, the radial PSD has a first scattering angle of θ of 2° or more and 15° or less with respect to the specular reflection direction. peak The article according to embodiment 18 or 19, which is reduced to 10% of the peak value.

[0180] Embodiment 21 The article according to Embodiment 20, wherein, within the second range of the scattering angle, the radial PSD decreases to 1% of the peak value at a second scattering angle that is greater than the first scattering angle and is 3.5° or more and 30° or less with respect to the specular reflection direction.

[0181] Embodiment 22 The article according to Embodiment 21, wherein, within the second range of the scattering angles, the radial PSD decreases to 0.1% of the peak value at a third scattering angle of 8° or less with respect to the specular reflection direction.

[0182] Embodiment 23 The article according to Embodiment 22, wherein, within the second range of the scattering angles, the radial PSD decreases to 0.01% of the peak value at a third scattering angle of 16° or less with respect to the specular reflection direction.

[0183] Embodiment 24 The article according to any one of embodiments 20 to 23, wherein, within the first range of the scattering angles, the radial PSD is less than 10% of the peak value at a scattering angle of 0.05° or more.

[0184] Embodiment 25 θ peak The article according to any one of embodiments 18 to 24, wherein the angle is 0.3° or greater and 0.5° or less.

[0185] Embodiment 26 Within the scattering region, the first principal surface includes a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions. The article according to any one of Embodiments 18 to 25, wherein the plurality of inclined transition surfaces are inclined such that the height of the first main surface decreases as the distance from the boundary of the plurality of first regions increases.

[0186] Embodiment 27 The article according to Embodiment 26, wherein at least some of the plurality of inclined transition surfaces extend in a lateral direction of 1.0 μm or more and 10 μm or less between regions among the plurality of first regions and the plurality of second regions connected by the inclined transition surface, and the lateral distance in which the inclined transition surface extends is parallel to the surface normal of the inclined transition surface and is measured in a direction parallel to the virtual base plane.

[0187] Embodiment 28 The article has a transmission haze of 2.0% or less, and sparkle of 2.5% or less measured at 140 ppi, and is the article according to any one of Embodiments 18 to 27.

[0188] Embodiment 29 A substrate, having a first main surface, a second main surface opposite to the first main surface, and a scattering region formed in the first main surface, and including: within the scattering region, the first main surface includes a plurality of first regions arranged at a first height with respect to a virtual base plane extending on the substrate, a plurality of second regions arranged at a second height with respect to the virtual base plane, and a plurality of inclined transition surfaces extending between boundaries of the plurality of first regions and the plurality of second regions, and the plurality of inclined transition surfaces are inclined such that the height of the first main surface decreases as the distance from the boundary of the plurality of first regions increases. At least some of the plurality of inclined transition surfaces extend over a lateral distance of 1.0 μm or more and 10 μm or less between the regions of the plurality of first regions and the plurality of second regions connected by the inclined transition surfaces, and the lateral distance over which the inclined transition surfaces extend is measured in a direction parallel to the surface normal of the inclined transition surface and parallel to the virtual base plane. The aforementioned scattering region is a radial PSD, The radial PSD increases with increasing light scattering angle relative to the specular reflection direction, in a first range of scattering angles, The radial PSD has a peak value, and the peak scattering angle θ peak , and The radial PSD decreases to 10% of the peak value at a first scattering angle of 2° or more and 15° or less with respect to the specular reflection direction, θ peak For larger scattering angles, a second range of scattering angles, An article comprising a substrate having radial PSDs.

[0189] Embodiment 30 The article according to Embodiment 29, wherein, within the first range of scattering angles, the radial PSD is less than 10% of the peak value at a scattering angle of 0.05° or more.

[0190] Embodiment 31 θ peak The article according to Embodiment 29 or 30, wherein the angle is 0.3° or greater and 0.5° or less.

[0191] Embodiment 32 The first scattering angle is 6° or more and 13° or less with respect to the specular reflection direction, The article according to any one of embodiments 29 to 31, wherein, within the second range of the scattering angles, the radial PSD is reduced to 1% of the peak value at a second scattering angle that is 12.5° or more and 30.0° or less with respect to the specular reflection direction.

[0192] Embodiment 33 The first scattering angle is 2° or more and 7° or less with respect to the specular reflection direction, The article according to any one of embodiments 29 to 31, wherein, within the second range of the scattering angles, the radial PSD is reduced to 1% of the peak value at a second scattering angle that is 3.5° or more and 13.5° or less with respect to the specular reflection direction.

[0193] Embodiment 34 The article according to Embodiment 33, wherein, within the second range of the scattering angles, the radial PSD decreases to 0.1% of the peak value at a third scattering angle of 8° or less with respect to the specular reflection direction.

[0194] Embodiment 35 The article according to embodiment 34, wherein, within the second range of the scattering angles, the radial PSD decreases to 0.01% of the peak value at a third scattering angle of 16° or less with respect to the specular reflection direction.

[0195] Embodiment 36 The aforementioned article, Transmitted haze of 2.0% or less, and Sparkle of 2.5% or less when measured at 140ppi. An article according to any one of embodiments 29 to 35, showing the following.

[0196] Embodiment 37 The first average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, is at least 0.07 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 20°. An article according to any one of embodiments 29 to 36, wherein the second average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, is at least 0.6 when the article is viewed at a field of view of 20° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 45°.

[0197] Embodiment 38 Within the scattering region, the first principal surface is A plurality of third regions positioned at a third height relative to the virtual base plane, and A plurality of fourth regions positioned at a fourth height relative to the virtual base plane, Includes, The article according to Embodiment 29, wherein the fourth height is different from the first height, the second height, and the third height.

[0198] Embodiment 39 The aforementioned article, Specular reflectance (Rs) of 4.0 or less, and Sharpness of combined images less than 65%, An article as described in Embodiment 38, which shows the following. [Explanation of Symbols]

[0199] 10 Goods 12 circuit boards 14 cabinets 16 displays 18. First main surface 19 Second main surface 20 scattering area 22 Incident ray 24 External environment 25 Scattered rays 26, 46 Surface Features 28. First Domain 30 Second Domain 32 The Third Domain 33 Surface Normal 34. The Fourth Domain 35 Virtual Baseline 40 Transition Surface 42 First Edge 44 The second edge 100, 200, 300 Car Compartment System 110 Center Console Base 120, 220, 320 surface 130, 230, 330 displays 210 Dashboard Base 215 Instrument Panel 310 Dashboard Handle Base 802 Samples 804 Display 806 Target Patterns 808 First light source 810 Projection light source 812 Camera 814 Computing systems, computers 900 First ambient light source 902 Second ambient light source 1000 cabin< / psd>

Claims

1. It is a substrate, First main surface, A second principal surface opposite to the first principal surface, and Scattering region formed within the first main surface, It has, Within the scattering region, the first main surface is A plurality of first regions positioned at a first height with respect to a virtual base plane extending across the substrate, A plurality of second regions positioned at a second height with respect to the virtual base plane, Includes, The first height is greater than the second height by an etching depth of 80 nm or more and 600 nm or less. The scattering region is a radial PSD, The radial PSD increases with increasing light scattering angle relative to the specular reflection direction, in a first range of scattering angles, The radial PSD has a peak value, and the peak angle θ ｐｅａｋ , and The radial PSD decreases to 10% of the peak value at a first scattering angle of 2° or more and 15° or less with respect to the specular reflection direction, θ ｐｅａｋ Second range of scattering angles at larger angles, A substrate having radial PSDs, An article equipped with.

2. The article according to claim 1, wherein, within the second range of the scattering angles, the radial PSD decreases to 1% of the peak value at a second scattering angle that is greater than the first scattering angle and is 3.5° or more and 30° or less with respect to the specular reflection direction.

3. The article according to claim 2, wherein, within the first range of scattering angles, the radial PSD is less than 10% of the peak value at a scattering angle of 0.05° or more.

4. (a) The first scattering angle is 6° or more and 13° or less with respect to the specular reflection direction, and the second scattering angle is 12.5° or more and 30.0° or less with respect to the specular reflection direction, or (b) The first scattering angle is 2° or more and 7° or less with respect to the specular reflection direction, and the second scattering angle is 3.5° or more and 13.5° or less with respect to the specular reflection direction. The article according to claim 2 or 3.

5. θ ｐｅａｋ An article according to any one of claims 1 to 3, wherein the angle is 0.3° or more and 0.5° or less.

6. Within the scattering region, the first main surface includes a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions. The article according to any one of claims 1 to 3, wherein the plurality of inclined transition surfaces are inclined such that the height of the first main surface decreases with increasing distance from the boundary of the plurality of first regions.

7. The article according to claim 6, wherein at least some of the plurality of inclined transition surfaces extend over a lateral distance of 1.0 μm or more and 10 μm or less between regions of the plurality of first regions and the plurality of second regions connected by the inclined transition surfaces, and the lateral distance over which the inclined transition surfaces extend is parallel to the surface normal of the inclined transition surface and is measured in a direction parallel to the virtual base plane.

8. The aforementioned article, Transmitted haze of 2.0% or less, and Sparkle of 2.5% or less when measured at 140 ppi. An article according to any one of claims 1 to 3, which shows the following.

9. (a) The first average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, is at least 0.55 when the article is viewed at a field of view of 0° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 20°, and (b) The second average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, is at least 0.6 when the article is viewed at a field of view of 20° and light having a luminance of 45,000 lux is incident on the first principal surface at an incident angle of 45°. An article according to any one of claims 1 to 3, wherein at least one of the following conditions is met.

10. Within the scattering region, the first main surface is A plurality of third regions positioned at a third height with respect to the virtual base plane, and A plurality of fourth regions positioned at a fourth height with respect to the virtual base plane, Includes, The fourth height is different from the first height, the second height, and the third height. The aforementioned article, Specular reflectance (Rs) of 4.0 or less, and Sharpness of combined images less than 65%, The article according to claim 1, which shows the following.

Images