Articles with textured regions comprising rounded surface features and associated methods

Abstract

An article comprises a substrate with a first major surface with a textured region formed therein and a second major surface. Within the textured region, the first major surface comprises a plurality of surface features that are depressions in the first major surface. The textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, and the surface angle distribution decreases to 90% of the peak at an angle within 1.8° of the peak angle on at least one side of the peak angle. The textured region exhibits a Sq value that is greater than or equal to 0.1 µm and less than or equal to 0.6 µm and a Rsm value that is greater than or equal to 5 µm and less than or equal to 100 µm.

Description

Attorney Docket No.: SP24-234ARTICLES WITH TEXTURED REGIONS COMPRISING ROUNDED SURFACE FEATURES AND ASSOCIATED METHODSCross-reference to Related Applications

[0001] This application claims the benefit of priority of U.S. Provisional Application Serial No. 63 / 844,405, filed on July 15, 2025 and U.S. Provisional Application Serial No. 63 / 690,071, filed on September 03, 2024, the content of which is relied upon and incorporated herein by reference in its entirety.FIELD

[0002] The disclosure relates to articles with textured regions with rounded surface features and methods for fabricating the same. The textured regions function to provide anti-glare performance attributes.BACKGROUND

[0003] Substrates transparent to visible light can be utilized to cover displays of display articles, or for other applications. For example, display articles may include smart phones, tablets, televisions, computer monitors, vehicle interior displays and the like. The displays are often liquid crystal displays and organic light emitting diodes, among others. The substrate protects the display, while the transparency of the substrate allows the user of the device to view the display. Glare is the phenomena associated with a degraded viewing experience in the presence of bright light sources. In addition, reflected images not from a bright light source but from the ambient can also contribute to a degraded viewing in displays. For example, a visually distinctive user’s own reflected image, or light from the surrounding environment, can result in distraction, reduction in legibility, as well as visual fatigue.

[0004] Several techniques exist to reduce glare, including anti-reflective coatings and antiglare technologies. An anti -reflection coating can reduce glare by directly reducing the total amount of reflection. However, certain existing anti-reflection coatings may fail to diminish reflections to a great enough extent throughout the visible spectrum to render such reflections unnoticed by users, and they also cannot address the reflections from the other layers of a display panel. Anti -glare technologies attempt to spread reflection of light to a large range of angles to reduce the peak intensity of the reflection and render distracting reflected images lessAtorney Docket No.: SP24-234 distinct to the user. However, reflection at angles that are too large can result in relatively high haze that can reduce the contrast of the displayed images.

[0005] Accordingly, an alternative to existing anti-glare and anti-reflective coating technologies that allows favorable control of the angular distribution of scatered light would be beneficial.SUMMARY

[0006] An aspect (1) of the present disclosure pertains to an article comprising: a substrate comprising: a first major surface; and a second major surface opposing the first major surface, a textured region formed in the first major surface, wherein, within the textured region, the first major surface comprises a plurality of surface features that are depressions in the first major surface where a height of the first major surface decreases with lateral distance from local peaks in the first major surface, wherein: the textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, the surface angle distribution decreases to 90% of the peak at an angle within 1.8° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 pm, and the textured region exhibits a Rsm value that is greater than or equal to 5 pm and less than or equal to 100 pm.

[0007] An aspect (2) of the present disclosure pertains to an article according to the aspect (1), wherein the surface angle distribution exhibits an average surface angle that is greater than or equal to 1.5°.

[0008] An aspect (3) of the present disclosure pertains to an article according to any of the aspects (l)-(2), wherein the surface angle distribution exhibits a maximum surface angle that is greater than or equal to 5°.

[0009] An aspect (4) of the present disclosure pertains to an article according to any of the aspects (l)-(3), wherein the textured surface region exhibits a PPDuo that is less than or equal to 3.0%.

[0010] An aspect (5) of the present disclosure pertains to an article according to any of the aspects ( 1 )-(4), wherein the textured surface region exhibits a coupled specular reflectance that is less than or equal to 6 GU.

[0011] An aspect (6) of the present disclosure pertains to an article according to any of the aspects (l)-(5), wherein the textured surface region exhibits corrected color shifts ^Cxcorrectedand AC ^Vcorrecfted . that are each respectively . within a rang oe of 0.0 to 0.5.Atorney Docket No.: SP24-234

[0012] An aspect (7) of the present disclosure pertains to an article according to any of the aspects ( 1 )-(6), wherein the plurality of surface features each comprise contours of constant surface height that exhibit at least one of a circular shape, a square shape, a polygon shape, a hexagonal shape, and an elliptical shape, in a plan view of the first major surface.

[0013] An aspect (8) of the present disclosure pertains to an article according to the aspect (7), wherein all of the plurality of surface features comprise contours having a circular shape.

[0014] An aspect (9) of the present disclosure pertains to an article according to the aspect (7), wherein different ones of the plurality of surface features comprise contours exhibiting different shapes.

[0015] An aspect (10) of the present disclosure pertains to an article according to the aspect (9), wherein a first portion of the plurality of surface features comprise contours exhibiting a circular shape and a second portion of the plurality of surface features comprise contours exhibiting an elliptical shape.

[0016] An aspect (11) of the present disclosure pertains to an article according to any of the aspects ( l)-( 10), wherein geometric centers of the plurality of surface features exhibit a random distribution throughout the textured region.

[0017] An aspect (12) of the present disclosure pertains to an article according to any of the aspects (l)-(l 1), wherein the textured region is devoid of planar portions at a constant surface height.

[0018] An aspect (13) of the present disclosure pertains to an article according to any of the aspects (l)-(l 1), wherein the textured region comprises planar portions separating at least some of the plurality of surface features.

[0019] An aspect (14) of the present disclosure pertains to an article according to the aspect (13), wherein the planar portions make up less than 10% of a surface area of the textured region.

[0020] An aspect (15) of the present disclosure pertains to an article according to any of the aspects ( l)-( 14), wherein: the surface angle distribution exhibits an average surface angle that is greater than or equal to 3'°, the textured region exhibits a Sq value that is greater than or equal to 0.2, and the textured region exhibits a coupled specular reflectance that is less than or equal to 2 GU.

[0021] An aspect (16) of the present disclosure pertains to an article according to the aspect (15), wherein a washout index calculated via a first average modulation transfer function of the textured region that is 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 less than 0.6 when the article is viewedAtorney Docket No.: SP24-234 at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an angle of incidence of 20°.

[0022] An aspect (17) of the present disclosure pertains to an article according to the aspect (16), wherein the textured region exhibits a reflected image visibility factor that is less than or equal to 0.5, the reflected image visibility factors being computed asRIVF = 0.33 * (MTF0 355+ (1 - 0.33) ST Fr)0381where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image patern is directed towards the textured region, the square wave image patern having a period of 26 mm.

[0023] An aspect (18) of the present disclosure pertains to an article according to the aspect (15), wherein the textured region exhibits a transmission haze that is greater than or equal to 7.5% and less than or equal to 55%.

[0024] An aspect (19) of the present disclosure pertains to an article according to the aspect (18), wherein: the transmission haze is greater than or equal to 10% and less than or equal to 30%, and the textured region exhibits a coupled DOI that is less than or equal to 40%.

[0025] An aspect (20) of the present disclosure pertains to an article according to any of the aspects ( 15)-( 19), wherein the surface angle distribution exhibits amaximum surface angle that is greater than or equal to 7.0°.

[0026] An aspect (21) of the present disclosure pertains to an article according to any of the aspects ( l)-( 14), wherein: the surface angle distribution decreases to 90% of the peak at an angle within 1.5° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sdq value that is greater than or equal to 0.01 and less than or equal to 0.15, a washout index calculated via a first average modulation transfer function of the textured region that is 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 less than 0.5 when the article is viewed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an angle of incidence of 20°, and the textured region exhibits a reflected image visibility factor that is less than or equal to 0.5, the reflected image visibility factor being computed as RIVF = 0.33 * (MTFr)0 355+ (1 - 0.33) ST Fr)0381where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image patern is directed towards the textured region, the square wave image patern having a period of 26 mm.Atorney Docket No.: SP24-234

[0027] An aspect (22) of the present disclosure pertains to an article according to the aspect (21), wherein the surface angle distribution exhibits an average surface angle that is greater than or equal to 1.5° and less than or equal to 5°.

[0028] An aspect (23) of the present disclosure pertains to an article according to any of the aspects (21)-(22), wherein the textured region exhibits a transmission haze that is greater than or equal to 1% and less than or equal to 10%.

[0029] An aspect (24) of the present disclosure pertains to an article comprising: a substrate comprising: a first major surface; a second major surface opposing the first major surface; and a textured region formed in the first major surface, wherein, within the textured region, the first major surface comprises a plurality of surface features that are depressions in the first major surface where a height of the first major surface decreases with lateral distance from local peaks in the first major surface, wherein: the textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, the surface angle distribution decreases to 90% of the peak at an angle within 1.5° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 pm, the textured region exhibits a Rsm value that is greater than or equal to 5 pm and less than or equal to 100 pm, the textured region exhibits a Sdq value that is greater than or equal to 0.01 and less than or equal to 0.15, a washout index calculated via a first average modulation transfer function of the textured region that is 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 less than 0.5 when the article is viewed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an angle of incidence of 20°, and the textured region exhibits a reflected image visibility factor that is less than or equal to 0.5, the reflected image visibility factor being computed as RIVF = 0.33 * MTFr)0355+ (1 — 0.33)(STFr)°'381, where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image patern is directed towards the textured region, the square wave image patern having a period of 26 mm.

[0030] An aspect (25) of the present disclosure pertains to an article according to the aspect (24), wherein the surface angle distribution exhibits an average surface angle that is greater than or equal to 1.5°.Atorney Docket No.: SP24-234

[0031] An aspect (26) of the present disclosure pertains to an article according to any of the aspects (24)-(25), wherein the surface angle distribution exhibits a maximum surface angle that is greater than or equal to 5°.

[0032] An aspect (27) of the present disclosure pertains to an article according to any of the aspects (24)-(26), wherein the textured surface region exhibits a PPDuo that is less than or equal to 3.0%.

[0033] An aspect (28) of the present disclosure pertains to an article according to any of the aspects (24)-(27), wherein the textured surface region exhibits a coupled specular reflectance that is less than or equal to 10 GU.

[0034] An aspect (29) of the present disclosure pertains to an article according to any of the aspects (24)-(28), wherein the textured surface region exhibits corrected color shifts AC ■r^correcfted . and AC yVcorrecfted . that are each resp rectively within a rang oe of 0.0 to 0.5.

[0035] An aspect (30) of the present disclosure pertains to an article according to any of the aspects (24)-(29), wherein the plurality of surface features each comprise contours of constant surface height that exhibit at least one of a circular shape, a square shape, a hexagonal shape, a polygon shape, and an elliptical shape, in a plan view of the first major surface.

[0036] An aspect (31) of the present disclosure pertains to an article according to the aspect (30), wherein all of the plurality of surface features comprise contours having a circular shape.

[0037] An aspect (32) of the present disclosure pertains to an article according to the aspect (30), wherein different ones of the plurality of surface features comprise contours exhibiting different shapes.

[0038] An aspect (33) of the present disclosure pertains to an article according to the aspect (32), wherein a first portion of the plurality of surface features comprise contours exhibiting a circular shape and a second portion of the plurality of surface features comprise contours exhibiting an elliptical shape.

[0039] An aspect (34) of the present disclosure pertains to an article according to any of the aspects (24)-(33), wherein geometric centers of the plurality of surface features exhibit a random distribution throughout the textured region.

[0040] An aspect (35) of the present disclosure pertains to an article according to any of the aspects (24) -(34) , wherein the textured region is devoid of planar portions at a constant surface height.Atorney Docket No.: SP24-234

[0041] An aspect (36) of the present disclosure pertains to an article according to any of the aspects (24)-(34), wherein the textured region comprises planar portions separating at least some of the plurality of surface features.

[0042] An aspect (37) of the present disclosure pertains to an article according to the aspect (36), wherein the planar portions make up less than 10% of a surface area of the textured region.

[0043] An aspect (38) of the present disclosure pertains to an article according to any of the aspects (24)-(37), wherein the surface angle distribution exhibits an average surface angle that is greater than or equal to 1.5° and less than or equal to 5°.

[0044] An aspect (39) of the present disclosure pertains to an article according to any of the aspects (24)-(38), wherein the textured region exhibits a transmission haze that is greater than or equal to 1% and less than or equal to 10%.

[0045] An aspect (40) of the present disclosure pertains to a method of forming a textured region on a first major surface of a substrate for an article, the method comprising: determining a patern for a plurality of pinhole features, wherein the plurality of pinhole features in the patern exhibit a maximum feature size that is less than 2 pm and a pinhole feature fill fraction that is less than or equal to 5% of a surface area of the textured region, disposing one or more etching masks on the first major surface that allow etching only on select regions of the first major surface for forming the plurality of pinhole features, performing a primary etching step using one or more etchants to form the plurality of pinhole features in the first major surfaces based on the patern, wherein the plurality of pinhole features have a depth D of at least 1 pm following the primary etching step; and performing a secondary etching step by applying a secondary etchant to an entirety of the textured region to form a plurality of surface features in the textured region, wherein, after the secondary etching step: the textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, the surface angle distribution decreases to 90% of the peak at an angle within 1.8° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 pm, and the textured region exhibits a Rsm value that is greater than or equal to 5 pm and less than or equal to 100 pm.

[0046] An aspect (41) of the present disclosure pertains to a method according to the aspect (40), wherein the secondary etching step is performed so as to remove at least 5 pm of the material substrate from the first major surface within the textured region.

[0047] An aspect (42) of the present disclosure pertains to a method according to the aspects (40)-(41), wherein the maximum feature size is in a range from 0.5 pm to 1.5 pm.Atorney Docket No.: SP24-234

[0048] An aspect (43) of the present disclosure pertains to a method according to any of the aspects (40)-(42), wherein determining the patern comprises calculating positions of geometric centers of the plurality of pinhole features using a spacing distribution algorithm to randomly distribute the plurality of pinhole features throughout the textured region.

[0049] An aspect (44) of the present disclosure pertains to a method according to any of the aspects (40)-(43), wherein, in the patern, each of the plurality of pinhole features comprise the same peripheral shape and size.

[0050] An aspect (45) of the present disclosure pertains to a method according to any of the aspects (40)-(44), wherein, in the patern, the plurality of pinhole features differ from one another in at least one of size and peripheral shape.

[0051] An aspect (46) of the present disclosure pertains to a method according to any of the aspects (40)-(45), wherein at least one of the primary etching step and secondary etching step employs an etching solution comprising HF.

[0052] An aspect (47) of the present disclosure pertains to a method according to any of the aspects (40)-(45), wherein at least one of the primary etching step and secondary etching step employs a metal hydroxide and not HF.

[0053] An aspect (48) of the present disclosure pertains to a method according to any of the aspects (40)-(47), wherein: in the patern, the plurality of pinhole features exhibit a pitch P that is a lateral distance between geometric centers of adjacent ones of the plurality of pinhole features, and an average value of the pitch is greater than or equal to 5 pm and less than or equal to 50 pm.

[0054] An aspect (49) of the present disclosure pertains to a method according to the aspect (48), wherein: the secondary etch step is performed so that a removal depth R of material is removed from the first major surface, for at least some of the plurality of features, 2*R is within 10% of the quantity (P - D).

[0055] An aspect (50) of the present disclosure pertains to an article according to any of the aspects (l)-(39), , wherein less than 3% of the textured region exhibits a surface angle that is less than 0.5°.

[0056] An aspect (51) of the present disclosure pertains to an article article comprising: a substrate comprising: a first major surface; a second major surface opposing the first major surface; and a textured region formed in the first major surface, wherein, within the textured region, the first major surface comprises a plurality of surface features that are depressions in the first major surface where a height of the first major surface decreases with lateral distance from local peaks in the first major surface, wherein:, less than 3% of the textured region exhibitsAtorney Docket No.: SP24-234 a surface angle that is less than 0.5°, the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 qm. the textured region exhibits a Rsm value that is greater than or equal to 5 qm and less than or equal to 100 qm, the textured region exhibits a reflected image visibility factor that is less than or equal to 0.25, the reflected image visibility factor being computed as RIVF = 0.33 * MTFr')°355+ (1 — 0.33)(STFr)°'381, where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image patern is directed towards the textured region, the square wave image patern having a period of 26 mm, and the textured region exhibits a coupled specular reflectance that is less than or equal to 2 GU.

[0057] An aspect (52) of the present disclosure pertains to an article according to any of the aspects (l)-(39) and (50)-(51), wherein the textured region exhibits histograms of 2-fold, 3- fold, 4-fold, 5-fold, and 6-fold ordering parameters, wherein none of the histograms of 2-fold, 3 -fold, 4-fold, 5 -fold, and 6-fold ordering parameters exhibits a distinct peak at an ordering parameter value above 0.7.

[0058] An aspect (53) of the present disclosure pertains to an article according to any of the aspects (l)-(39) and (50)-(52), wherein at least one of: textured region exhibits a histogram of 2-fold ordering parameters exhibiting a peak at a value of less than 0.5, the textured region exhibits a histogram of 3 -fold ordering parameters exhibiting a ordering peak at a 3 -fold ordering peak value between 0.2 and 0.4, wherein the histogram drops to less than 50% of the ordering peak at values within 0.05 of the 3-fold ordering peak value, the textured region exhibits a histogram of 4-fold ordering parameters exhibiting a ordering peak at a 4-fold ordering peak value between 0.2 and 0.4, the textured region exhibits a histogram of 5-fold ordering parameters exhibiting a higher average over a first range of 5 -fold ordering parameters from 0.5 to 0.8 than a second range of 5-fold ordering parameters from 0.2 to 0.5, and the textured region exhibits a histogram of 6-fold ordering parameters indicating that a majority of the textured region exhibits a 6-fold ordering parameter above 0.4.

[0059] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understanding the nature and character of the claims. The accompanying drawings are comprised to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the description serve to explain principles and operation of the various aspects.Attorney Docket No.: SP24-234BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings incorporated in and forming a part of the specification illustrate several aspects of the present invention and, together with the description, explain the principles of the invention. In the drawings:

[0061] FIG. 1 depicts a perspective view of a display article, according to one or more aspects of the present disclosure;

[0062] FIG. 2 schematically depicts a portion of a textured region of the display article of FIG. 1, according to one or more aspects of the present disclosure;

[0063] FIG. 3 schematically depicts a surface height profile of the textured region depicted in FIG. 2, according to one or more aspects of the present disclosure;

[0064] FIG. 4 is a flow diagram of a method of fabricating a display article including a textured region with rounded surface features, according to one or more aspects of the present disclosure;

[0065] FIGS. 5 A, 5B, and 5C are schematic depictions of different patterns that can be used to form pinhole features in an article, according to one or more aspects of the present disclosure;

[0066] FIG. 6 is a graphical representation of secondary etching of pinhole features to form a textured region with rounded features exhibiting relatively high surface angles, according to one or more aspects of the present disclosure;

[0067] FIGS. 7A and 7B are modelled surface height profiles and surface angle distributions associated with an example undergoing different amounts of secondary etching, according to one or more aspects of the present disclosure;

[0068] FIG. 8 schematically depicts an apparatus for measuring a washout index value for an article, according to one or more aspects of the present disclosure;

[0069] FIG. 9 schematically depicts a vehicle interior comprising displays and ambient light sources emitting light that is incident on and scattered from the displays, according to one or more aspects of the present disclosure;

[0070] FIG. 10 schematically depicts an apparatus for measuring a reflected image visibility factor for an article, according to one or more aspects of the present disclosure;

[0071] FIGS. 11A, 11B, 11C, and 11D are surface height profdes and associated histograms of textured regions of Examples 1 -4, according to one or more aspects of the present disclosure;

[0072] FIG. 12A and 12B are surface height profdes and associated histograms of textured regions of Examples 5-6, according to one or more aspects of the present disclosure;

[0073] FIG. 13 is a surface height profde and associated histogram of a textured region of Example 7, according to one or more aspects of the present disclosure;Atorney Docket No.: SP24-234

[0074] FIGSs 14A, 14B, 14C, and 14D are surface angle distributions for Examples 1-4, according to one or more aspects of the present disclosure;

[0075] FIGS. 15A and 15B are surface angle distributions for Examples 5-6, according to one or more aspects of the present disclosure;

[0076] FIG. 16 is a surface angle distribution for Example 7, according to one or more aspects of the present disclosure;

[0077] FIGS. 17A, 17B, 17C, 17D, 17E, 17F, 17G, 17H, 171, 17 J, 17K, 17L, and 17M are surface angle distributions for Examples 8-20, according to one or more aspects of the present disclosure;

[0078] FIGS. 18A, 18B, 18C, 18D, 18E, and 18F are surface angle distributions for Comparative Examples 1-6, according to one or more aspects of the present disclosure;

[0079] FIG. 19 is a plot of washout index as a function of reflected image visibility factor for various Examples and Counter Examples, according to one or more aspects of the present disclosure;

[0080] FIG. 20 is a plot of BSDF200as a function of washout index for various Examples and Counter Examples, according to one or more aspects of the present disclosure; and

[0081] FIGS 21A-21E are plots of histograms for 2-fold, 3-fold, 4-fold, 5-fold, and 6-fold ordering parameters measured for samples fabricated in accordance with the present disclosure and a counterexample, according to one or more embodiments of the present disclosure.DETAILED DESCRIPTION

[0082] Referring generally to the figures, described herein are articles comprising a major surface with a textured region comprising a plurality of surface features. The surface features are depressions in the surface where the height of the surface decreases with lateral distance from a local peak in the surface. The surface features are bound at least in part by inclined portions exhibiting a curvature when a cross-section of the article taken in a plane perpendicular to the major surface is viewed in a magnified scanning electron microscope image. The curvature of the inclined portions is positioned such that, proximal to the local peaks, the inclined portions form relatively high surface angles. At least some of the plurality of surface features may exhibit a maximum surface angle (amax) that is greater than 2°. For example, in aspects, surface features of the textured region each exhibit a maximum surface angle that is greater than 2°, greater than or equal to 3°, greater than or equal to 4°, greater than or equal to 5°, greater than or equal to 6°, greater than or equal to 7°, greater than or equal to 8°, greater than or equal to 9°, or even greater than or equal to 10°. Such surface angles indicateAtorney Docket No.: SP24-234 a relatively high degree of feature rounding, where portions of the major surface that are planar in shape (e.g., portions of the surface having relatively constant surface height, as described herein), if present, are separated from one another to a great enough extent to at least partially reduce diffraction caused by the textured region in comparison to a surface with a discrete, non-continuous height distribution. Reducing the diffraction caused by the textured region enables the articles described herein to have less dependance on wavelength and coherence of the incident light, thereby reducing Moire fringe interference and reflection color artifacts compared to certain existing articles with discrete height distributions.

[0083] In other aspects, the surface features described herein can be fabricated using a multi- step etching process that facilitates deterministic feature placement (i.e., controlled, repeatable surfaces, where the same pattern of surface features can be fabricated from part-to-part). This allows the spatial frequency content of the textured region to be controlled to provide favorable combinations of anti-glare (AG) performance atributes. Existing methods for providing AG surfaces, like sand blasting-based methods, provide random surface roughness profiles that are not controlled, which can result in undesirable effects such as high transmission haze and display sparkle. The methods described herein facilitate control of the spatial frequency content and allow the articles described herein to exhibit relatively low specular reflectance, transmission haze, and sparkle, all while exhibiting relatively low reflection color artifacts.

[0084] In aspects, controlling the spatial frequency content and the degree of feature rounding via the multi-step etching process described herein enables various combinations of AG performance atributes that are suitable for various applications to be achieved. The multi- step etching process described herein generally includes an initial etching step to form a patern of pinhole features in a surface of a substrate; and a secondary etching step where material is removed from the entire area associated with the textured region to be formed. Controlling characteristics (e.g., feature spacing, feature shape, feature size, feature depth) of the patern of pinhole features facilitates control of the spatial frequency content and roughness characteristics (e.g., Sq, Sdq, and Rsm values, feature surface angles) of the final textured region in the article. Roughness and slope characteristics of the textured region (e.g., feature surface angle, Sq) can also be controlled by the extent of material removal during the secondary etching step. Different combination of surface roughness characteristics can therefore be achieved by configuring the multi-step etching process described herein. For example, as described in greater detail herein, a relatively low amount of material removal during the secondary etching step (25 pm or less) can be used to facilitate the surface features in the textured surface region have, on average, relatively high average surface angle (aaVe) valuesAtorney Docket No.: SP24-234 (greater than or equal to 3.5° or preferably greater than or equal to 5°). Such aspects with such high feature surface angles may exhibit low values for coupled specular reflectance of less than or equal to 2 GU (the units “GU” are described in greater detail herein). Other implementations where more material is removed during the secondary etching step (e.g., greater than 25 pm, such as greater than or equal to 30 pm, greater than or equal to 40 pm, or even greater than or equal to 50 pm) can result in reduced average surface feature angles and higher specular reflectance, but result in relatively low haze (less than or equal to 10% or even less than or equal to 5%) and low washout (quantified as a washout index herein), even if the same patern of pinhole features is used. Either of such aspects, as described herein, can exhibit relatively low sparkle (e.g., less than or equal to 3% or preferably less than or equal to 2%), relatively low reflected image visibility, minimal color artifacts, and various ranges of distinctness of image (DOI) to provide performance atributes for a variety of applications.

[0085] A context where the articles described herein may be particularly useful is in the context of vehicle interior displays. Vehicle interiors may include one or more displays (e.g., center counsel displays, dashboard displays, pillar displays, seatback displays, and others). Such displays may be fixed in orientation relative to the driver or viewer. When in operation, vehicles are subject to ambient light conditions that can cause relatively severe glare. For example, sunlight can enter the vehicle interior through a side window or windshield and reflect or scater off of the displays, causing bright glare that can distract the driver and degrade performance of the display due to washout. The articles described herein may reduce such washout from commonly encountered ambient light conditions. Such favorable washout performance may be achieved while also providing favorable sparkle and transmission haze performance.

[0086] As used herein, “Sq,” “Sdq,” and “RSm” are structural properties of a surface. Sq, and Sdq, Rsm, are measured according to ISO (International Organization for Standards) 25178- 2:2012. Unless otherwise stated, all such values reported herein are measured by analyzing the surface with a Bruker Contour GT-X surface profiler and are calculated using MountainsMap™ software, though any commercially available surface profilers and software are capable of measuring and calculating these parameters.

[0087] “Sq” is the “root mean square height of the surface” and generally is a commonly used parameter describing the heights or amplitudes of the surface. It can help to represent an overall measure of the texture on a surface, and is equivalent to the standard deviation of the height distribution of the surface. “Sdq” is the “root mean square gradient” of the surface. “Rsm” is a “mean length of profiling elements” and is used to evaluate the lateral size of surface features.Atorney Docket No.: SP24-234

[0088] As used herein, “specular reflectance” is defined as the peak intensity of light reflected from a first surface of a substrate within a cone of angles of + / - 0. 1°. Unless otherwise noted herein, specular reflectance is measured using a Rhopoint IQ meter, which reports an Rspec, Rs value that is in gloss units (GU) at 20°. Values in GU reported herein can be converted to a percentage (to an absolute specular reflectance %R) by multiplying by a factor depending on the refractive index of the glass standard used for the measurement. The instrument used for the measurements provided herein use a glass standard having a refractive index n= 1.567, so the factor is 4.91 / 100, which corresponds to Fresnel reflection 4.91% at 20 deg. A glass substrate having an optically smooth surface typically exhibits an average spectral reflectance of 4.03% at 20°. As such, such a glass substrate typically exhibits a spectral reflectance of 4.03% / 4.91% * 100 = 82 GU.

[0089] Articles described herein may be characterized by a distinctness-of-image value. “Distinctness-of-reflected image,” “distinctness-of-image,” “DOI” or like term is 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.” In accordance with method A of ASTM 5767, glass reflectance factor measurements are made on at least one roughened surface of the glass article at the specular viewing angle and at an angle slightly off the specular viewing angles (from 0.2° to 0.4° away from specular). Such measurements can be made using a goniophotometer (Rhopoint IQ (Goniophotometer) 20° / 60° / 85°, Rhopoint Instruments) that is calibrated to a certified black glass standard, as specified in ASTM procedures D523 and D5767. Unless otherwise noted herein the DOI values provided herein are measured at a 20° angle of incidence.

[0090] As used, herein, the term “haze” or “transmission haze” refers to the percentage of transmited light scatered outside an angular cone of about ±2.5° in accordance with ASTM DI 003, entitled “Standard Test Method for Haze and Uuminous Transmitance of Transparent Plastics,” the contents of which are incorporated by reference herein in their entirety. Note that although the title of ASTM DI 003 refers to plastics, the standard has been applied to substrates comprising a glass material as well. For an optically smooth surface, transmission haze is generally close to zero.

[0091] As used herein, the terms “sparkle,” “sparkle contrast,” “display sparkle,” “pixel power deviation,” “PPD”, or like terms refers to the visual phenomenon that occurs when a textured transparent surface is combined with a pixelated display. Generally speaking, quantification of sparkle involves imaging a lit display or simulated display with the textured surface in the field of view. The calculation of sparkle for an area P is equal to o(P) / p(P), where o(P) is the standardAtorney Docket No.: SP24-234 deviation of the distribution of integrated intensity for each display pixel contained within area P divided by the mean intensity p(P). Following the guidance in: (1) J. Gollier, et al., “Apparatus and method for determining sparkle,” US9411180B2, 20 July 2016; (2) A. Stillwell, et al., “Perception of Sparkle in Anti-Glare Display Screens,” JSID 22(2), 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); one skilled in the art can build an imaging system to quantify sparkle. Alternatively, a commercially available system (e.g. the SMS-1000, Display Messtechnik & Systeme GmbH & Co. KG, Germany) can also be used. Unless described otherwise, sparkle is measured with a 140 PPI display using the following procedure. A 140 PPI display (e.g. Z50, Lenovo Group Limited, Hong Kong) with only the green subpixels lit (R = 0, B = 0, G = 255), at full display brightness is imaged using a f = 50 mm lens / machine vision camera combination (e.g. C220503 1:2.8 50 mm 030.5, Tamron, Japan) and Stingray F-125 B, Allied Vision Technologies GmbH, Germany). The lens setings are aperture = 5.6, depth of field = 0.3, working distance = about 290 mm; with these setings, the ratio of display pixels to camera pixels is approximately 1 to 9. The field of view for analysis contains approximately 7500 display pixels. Camera setings have the gain and gamma correction turned off. Periodic intensity variations from, e.g. the display, and non-periodic intensity variations, e.g. dead pixels, are removed during analysis prior to the calculation of sparkle.

[0092] Anti -glare performance (in terms of DOI, Rs, and gloss measurements) can be measured as a two surface measurement with nothing coupled to rear surface (herein described as “uncoupled”) or with an index matching fluid being used to couple to a rear surface of the substrate and / or to a display of choice (herein described as “coupled”). Unless otherwise noted, coupled values for DOI, Rs, and gloss measurements are reported herein.

[0093] Referring now to FIG. 1, an article 10 is depicted, according to an example embodiment. The article 10 comprises a substrate 12. In the depicted embodiment, the 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 aspects, the substrate 12 at least partially covers the display 16 such that light that the display 16 emits can transmit through the substrate 12.

[0094] The substrate 12 may be a variety of materials depending on the implementation. For example, in aspects, such as in the embodiment depicted in FIG. 1, the substrate 12 is a glass or glass-ceramic substrate. In aspects, the substrate 12 may be constructed of a material other than glass such as paper, plastic or other suitable polymeric material. In aspects, the substrateAtorney Docket No.: SP24-234 12 can include a combination of glass and polymeric materials. In an example, the textured region 20 described herein is formed in a layer of polymeric material formed on a glass substrate. In aspects, the substrate 12 is transparent, or exhibits an average transmitance for light normally incident on the substrate 12 that is in a wavelength range of 400 nm to 700 nm ofgreaterthan or equal to 70% (e.g., greater than or equal to 80%, greater than or equal to 85%, greater than or equal to 90%, greater than or equal to 92%, greater than or equal to 92.5%, greater than or equal to 93%). In aspects, the substrate 12 is opaque or exhibits an average transmitance for light normally incident on the substrate that is in a wavelength range of 400 nm to 700 nm that is less than or equal to 30%. In aspects, the substrate 12 is tinted to exhibit a colored appearance under ambient illumination (e.g., from sunlight).

[0095] In aspects, the substrate 12 is a glass substrate or a glass-ceramic substrate. In aspects, the substrate 12 is a multi-component glass composition having about 40 mol % to 80 mol % silica and a balance of one or more other constituents, e.g., alumina, calcium oxide, sodium oxide, boron oxide, etc. In some implementations, the bulk composition of the substrate 12 is selected from the group consisting of aluminosilicate glass, a borosilicate glass, and a phosphosilicate glass. In other implementations, the bulk composition of the substrate 12 is selected from the group consisting of aluminosilicate glass, a borosilicate glass, a phosphosilicate glass, a soda lime glass, an alkali aluminosilicate glass, and an alkali aluminoboro silicate glass. In further implementations, the substrate 12 is a glass-based substrate, including, but not limited to, glass-ceramic materials that comprise a glass component at about 90% or greater by weight and a ceramic component. In other implementations of the article 10, the substrate 12 can be a polymer material, with durability and mechanical properties suitable for the development and retention of the textured region 20.

[0096] In aspects, the substrate 12 has a bulk composition that comprises, consists essentially of or consists of a glass composition, such as Coming® Eagle XG® glass, Coming® Gorilla® glass, Coming® Gorilla® Glass 2, Coming® Gorilla® Glass 3, Coming® Gorilla® Glass 4, or Coming® Gorilla® Glass 5. In aspects, the substrate 12 has an ion-exchangeable glass composition that is strengthened by either chemical or thermal means that are known in the art. In aspects, the substrate 12 is chemically strengthened by ion exchange.

[0097] The substrate 12 includes a first major surface 18, a second major surface 19, a textured region 20 defined on the first major surface 18, and a thickness 21 that the first major surface 18 bounds in part (e.g., representing a minimum distance between the first major surface 18 and the second major surface 19 at a particular point on the first major surface 18). In the depicted embodiment, the substrate 12 is substantially planar in shape such that the first majorAtorney Docket No.: SP24-234 surface 18 and the second major surface 19 are generally flat (with the exception of plurality of surface features formed in the first major surface 18 in the textured region 20, as described herein). Aspects where the substrate 12 comprises a curved shape (e.g., via suitable hot- forming and cold-forming techniques) are also contemplated and within the scope of the present disclosure. In the depicted embodiment, the first major surface 18 generally faces toward the external environment 24 surrounding the article 10 and away from the display 16. In aspects, the display 16 emits visible light that transmits through the thickness 21 of the substrate 12, out the first major surface 18, and into the external environment 24.

[0098] As depicted in FIG. 1, light from the external environment 24, represented by incoming light ray 22, may be incident on the first major surface 18 at an angle of incidence 6i (representing a zenith angle that the incoming light ray 22 extends relative to the surface normal 33 of the first major surface 18, depicted as the z-direction in FIG. 1). The incoming light ray 22 may represent light from a number of different sources from outside of the article 10. For example, the incoming light ray 22 may represent sunlight that is incident on the first major surface 18 or light from another external light source (e.g., light reflected or scatered from an external object, light generated by another source). The textured region 20 may scater and / or reflect the light represented by the incoming light ray 22 in a scatering direction, represented by the scatered light ray 25. Light is scatered in a particular direction with a scatering amplitude that depends on the angle of incidence 6i and a scatering angle 6Srelative to the surface normal 33.

[0099] FIG. 2 schematically depicts a plan view of the region II of the textured region 20 of the article 10 depicted in FIG. 1, according to an example embodiment of the present disclosure. As shown, the textured region 20 comprises a plurality of surface features 26. The plurality of surface featuresaare negative surface features (i.e., depressions) where the height of the first major surface 18 decreases with increasing lateral distance from local peaks in surface height. The plurality of surface features 26 generally include areas where the surface height of the first major surface 18 is below an average surface height of the first major surface 18 within the textured region 20. The circular outlines in FIG. 2 represent contours of constant surface height within each of the plurality of surface features 26. While FIG. 2 depicts each of the plurality of surface features 26 as having a circular contour shape, the particular shape that the contours of constant surface height take is not particularly limiting. As described in greater detail herein, the shape of the contours may be determined at least in part based on a peripheral shape of pinhole features formed in the first major surface 18 during a primary etching step in the process of forming the textured region 20. A variety of peripheral shapes for such pinholeAtorney Docket No.: SP24-234 features are possible. For example, in aspects, the pinhole features exhibit at least one of a circular shape, a square shape, a hexagonal shape, an elliptical shapes, or other suitable shape. In aspects, different ones of the plurality of surface features 26 have different contour shapes. For example, a first subset of the plurality of surface features 26 could have a first contour shape (e.g., circular) and a second subset of the plurality of surface features 26 could have a second contour shape (e.g., elliptical). External boundaries of the plurality of surface features 26 are generally delineated by the top of sloped portions of the first major surface 18 that are sloped downward from local peaks in the first major surface. The peripheral boundary of a particular one of the plurality surface features 26 may not all be disposed at the same surface height.

[0100] Referring now to FIGS. 2-3, the plurality of surface features 26 can generally be characterized by a feature size 28, a separation distance 30, and a depth 32. The feature size 28 generally quantifies a maximum linear dimension of a peripheral boundary associated with a particular one of the plurality of surface features 26, measured in a direction parallel to X-Y plane. In FIGS. 1-3, the X-Y plane is a plane extending parallel to the second major surface 19 at a peak height associated with the first major surface 18. When the referenced surface feature has a circular peripheral boundary, for example, the feature size is a diameter of that boundary. In aspects, the plurality of surface features 26 can be characterized as having a relatively tight distribution of features sizes, such as when the pinhole features described herein are each formed with the same size and shape. In aspects, the plurality of surface features 26 can be characterizing has having a multimodal distribution of feature sizes, such as where the pinhole features described herein have multiple sizes and / or shapes prior to secondary etching. In aspects, the plurality of surface features 26 can have an average feature size (pm) that is at least: 5, 10, 15, 20, 25, 30, 35, 40, 45, or 50; alternatively, or additionally, the average maximum lateral dimension (pm) can be: 50, 45, 40, 35, 30, 25, 20, 15, 10, or 5 or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the average maximum lateral dimension (pm) can be 5-50, 5- 45, 5-40, 5-35, 5-30, 5-25, 5-20, 5-15, 5-10, 10-50, 10-45, 10-40, 10-35, 10-30, 10-25, 10-20, 10-15, 15-50, 15-45, 15-40, 15-35, 15-30, 15-25, 15-20, 20-50, 20-45, 20-40, 20-35, 20-30, 20- 25, 25-50, 25-45, 25-40, 25-35, 25-30, 30-50, 30-45, 30-40, 30-35, 35-50, 35-45, 35-40, 40-50, 40-45, or 45-50.

[0101] The separation distance 30 may represent a lateral distance between geometric centers of adjacent surface features in a direction parallel the x-y plane. An average value of the separation distance 30 may be determined based on a pitch and arrangement of the pinholeAtorney Docket No.: SP24-234 features formed during the primary etching step described herein. The separation distance 30 may be correlated with an Rsm value associated with the textured region 20. In some aspects, the Rsm value (pm) can be at least: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 75 or 100; alternatively, or additionally, the Rsm can be: 100, 75, 50, 45, 40, 35, 30, 25, 20, 15, 10, or 5 or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the Rsm (pm) can be 5-100, 5-75, 5-50, 5-45, 5-40, 5-35, 5-30, 5-25, 5-20, 5-15, 5-10, 10-50, 10-45, 10-40, 10-35, 10-30, 10-25, 10-20, 10-15, 15-50, 15-45, 15-40, 15-35, 15-30, 15-25, 15-20, 20-50, 20-45, 20-40, 20-35, 20-30, 20-25, 25-50, 25-45, 25- 40, 25-35, 25-30, 30-50, 30-45, 30-40, 30-35, 35-50, 35-45, 35-40, 40-50, 40-45, or 45-50.

[0102] The depth 32 represents a maximum dimension of the feature in the Z-direction (e.g., a distance perpendicular to the x-y plane between a peak height and a minimum height associated with a particular feature). As described in greater detail herein, an average value for the depth 32 of the plurality of surface features 26 may be determined at least in part a depth of the pinhole features formed during the primary etching step. In aspects, an average value of the depth 32 (nm) can be at least: 100, 150, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1200, 1400, 1600, 1800, 2000, 2200, 2400, or 2500; alternatively, or additionally, the average maximum depth (nm) can be: 2500, 2400, 2200, 2000, 1800, 1600, 1400, 1200, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 150, or 100 or less. For clarity, any two of the foregoing open- ended ranges can be combined to form a closed range.

[0103] In aspects, the plurality of surface features 26 may be randomly distributed throughout the textured region 20. For example, geometric centers of the plurality of surface features 26 can have a random distribution throughout the textured region 20 in a plane parallel to the x-y plane. The term “random distribution,” as used herein, refers to a patern with no long range order over a distance greater than the average separation distance (as opposed to a recurring period over a cut-through line in the article 10). In aspects, the arrangement of the geometric centers may be determined by a spacing distribution algorithm (e.g., Poisson disk sampling, maxi-min spacing, and hard-sphere distribution) subjected to certain constraints (e.g., a minimum value for the separation distance 30, the area of the textured region 20, and other parameters, as described in greater detail herein). A reason to avoid arranging the plurality of surface features 26 not in a patern is to avoid the textured region 20 reflecting ambient light with Moire fringe interference paterns and reflected color separation. When the primary surface features 26 form a patern, a possible consequence is the generation of Moire fringe interference paterns upon reflection of ambient light.Atorney Docket No.: SP24-234

[0104] In aspects, at least two of the plurality of surface features 26 can share a local peak. As described herein, the secondary etching step can be conducted until at least two of the plurality of features coalesce such that no portion of the first major surface 18 disposed at the maximum height of the first major surface 18 separates the coalesced features. To illustrate, FIG. 2 depicts a surface feature 26a that is coalesced with a surface feature 26b as a result of the secondary etching. As shown, the contours defining the surface features 26a and 26b merge to form a localized peak therebetween that is not disposed at a maximum height associated with the first major surface 18. Coalescing of features removes sharp comers from the textured region 20, which is believed to improve the washout and color artifact performance of the articles described herein.

[0105] FIG. 3 depicts a cross-sectional view of the textured region 20 depicted in FIG. 2. As shown, the article 10 includes a base plane 35 representing the portions of the first major surface 18 that are disposed most proximate to the second major surface 19. Unless otherwise noted, the base plane 35 extends parallel to the x-y plane. The base plane 35 generally represents the portion of the first major surface 18 that contacts one or more etchants of a primary etching step described herein. The base plane 35 represents areas where the most material of the substrate 12 is removed during the primary etching step. For example, the base plane 35 can represent areas of the first major surface 18 that were uncovered by an etching mask during the primary etching step.

[0106] In the depicted example, the first major surface 18 includes portions 34 disposed at a maximum height (hi in FIG. 3) relative to the base plane 35. In aspects, the portions 34 separate adjacent ones of the plurality of surface features 26 that do not coalesce as a result of the secondary etching step described herein. In such aspects, the portions 34 may be planar in shape. As used herein, the term “planar,” when used to refer to a particular area of a surface in a textured region of a substrate, refers to an area as having a height variation (or roughness) that less than 50 nm, in terms of root-mean-square (RMS) variation. For example, the portions 34, when planar, can be characterized by a surface height variation from 0.1 nm RMS to 50 nm RMS, from 0.1 nm RMS to 20 nm RMS, from 0.1 nm RMS to 10 nm RMS, or from 0.1 nm RMS to 1 nm RMS. Such RMS variation values correspond with an Sq value, unless otherwise noted herein. It is believed that the presence the portions 34, when planar, aid in lowering a specular reflectance exhibited by the article 10 by facilitating light undergoing diffractive scatering when incident on the textured region 20. As described herein, certain implementations may not include planar portions at the maximum height hi due to an elongated secondary etching step. Such aspects without planar portions at the peak height may causeAtorney Docket No.: SP24-234 light to undergo a reduced amount of diffractive scatering as compared to the aspects with the planar portions and, as a result, the aspects without the planar portions may exhibit beter washout and haze performance, but exhibit higher specular reflectance values than the aspects with the planar portions. In aspects, the planar portions of the first major surface 18, when present, make up less than 10% of a surface are of the textured surface regions as a result of the plurality of surface features being rounded to take up a majority of the first major surface 18 within the textured region 20.

[0107] Each of the plurality of surface features 26 includes a minimum height portion 36 and a sloped interior surface 38. The minimum height portion 36 is the portion of a particular feature disposed closest to the second major surface 19. The minimum height portion 36 may lie in the base plane 35. If a particular feature has multiple portions disposed at a minimum height (or an area lying at such a minimum height), the minimum height portion 36 is at a location most proximate to a geometric center of the surface feature in the x-y plane. The sloped interior surface 38 is a segment of each surface feature that has a positive gradient (in the z-direction) with increasing distance from the minimum height portion 36. Each sloped interior surface 38 extends between the minimum height portion 36 of a particular surface feature and a local peak of the first major surface 18. For example, the surface feature 26b is depicted to include a sloped interior surface 38 that extends from a minimum height portion 36 to a first local peak 40a of the first major surface 18. A feature 26c is depicted to include a sloped interior surface 38 that extends from a minimum height portion 36 to a second local peak 40b of the first major surface 18.

[0108] The local peaks of the first major surface 18 can differ from another in surface shape and height. As shown, the first local peak 40a is disposed at a maximum height I12 that is less than the maximum height hi of the first major surface 18. Moreover, the portion of the first major surface 18 immediately proximate the first local peak 40a is not planar, but rather possess a rounded profile. Such rounding results from the coalescing of adjacent features caused by the secondary etching step described herein. The second local peak 40b contrasts with the first local peak 40a in that the second local peak 40b is disposed at the maximum height hi and generally includes a planar area of the first major surface 18. A sloped interior surface 38 associated with a particular surface feature can extend to local peaks disposed at different heights and having different shapes. The surface feature 26a is depicted to include a sloped interior surface 38 that extends to both the first local peak 40a and the second local peak 40b as a result of not coalescing with the feature 26c but coalescing with the surface feature 26b during the etching process described herein.Atorney Docket No.: SP24-234

[0109] Each point of the first major surface 18 within the textured region 20 can also be characterized by a surface angle a. The surface angle a is an angle between a line tangent to the first major surface 18 at the referenced point and the x-y plane. Points within the textured region 20 that are relatively flat and parallel to the second major surface will have lower a values, while relatively steep portions of the textured region 20 (e.g., just inward of peripheral boundaries of each of the plurality of surface features 26) will have higher a values. Each surface feature can also be characterized by a maximum surface angle amax, which, as depicted in FIG. 3, can be represented by an angle between a tangent line 42 of the steepest portion of the sloped interior surface 38 and the plane of the second major surface 19. The maximum surface angle amaxrepresents a maximum value of the surface angle a within a particular surface feature. As described in greater detail herein, the patern of the plurality of surface features 26 and the length of the secondary etching step may be used to at least partially determine amax. Values of amaxprovided herein are for a maximum amaxvalue (i.e., the highest surface angle within the textured region 20). In aspects, the maximum amax(°) for the textured region 20 can be at least: 5, 10, 15, 20, 25, 30, 35, 40, 45, or 50; alternatively, or additionally, the amaxcan be: 50, 45, 40, 35, 30, 25, 20, 15, 10, or 5 or less. For clarity, any two of the foregoing open- ended ranges can be combined to form a closed range. For example, in some aspects, the amax(°) can be 5-50, 5-45, 5-40, 5-35, 5-30, 5-25, 5-20, 5-15, 5-10, 10-50, 10-45, 10-40, 10-35, 10- 30, 10-25, 10-20, 10-15, 15-50, 15-45, 15-40, 15-35, 15-30, 15-25, 15-20, 20-50, 20-45, 20-40, 20-35, 20-30, 20-25, 25-50, 25-45, 25-40, 25-35, 25-30, 30-50, 30-45, 30-40, 30-35, 35-50, 35- 45, 35-40, 40-50, 40-45, or 45-50

[0110] A distribution of surface angles a can be measured for the textured region 20 using white light interferometry. The distribution of surface angles a is a histogram of pixel counts associated with a particular range of surface angles for a particular bin. White light interferometry can be used to generate a distribution of surface heights within the textured region 20, which can be used to calculate the distribution for a. The angle a is approximated by an angle between a local surface normal (at the referenced point) and the z-axis (the direction which the surface height is measured). Unless otherwise noted herein, surface angle distributions are measured by measuring using a Bruker Contour GT-X surface profiler with a 50x objective and 0.55x zoom lens. The resulting surfaces have a lateral resolution of 230 nm by 170 nm and a vertical resolution of 0.1 nm. The slope / surface angles were calculated over a 1 mm by 1 mm field of view by calculating the slope between adjacent pixels. In aspects, the textured region 20 exhibits an average surface angle aavethat is greater than or equal to 1.5° and less than or equal to 20°. For example aave(°) can be at least: 1.5, 2, 3, 4, 5, 7, 9, 10, 12,Atorney Docket No.: SP24-234 15, 17, or 20; alternatively, or additionally, the separation distance can be: 20, 17, 15, 12, 10, 7, 5, 4, 3, 2, 1.5 or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the aavg(°) can be 1.2-20, 2- 20, 3-20, 20, 4-20, 5-20, 7-20, 10-20, 12-20, 15-20, 17-20, 2-17, 3-17, 4-17, 5-17, 7-17, 10-17, 12-17, 15-17, 2-15, 3-15, 4-15, 5-15, 7-15, 10-15, 12-15, 2-12, 3-12, 4-12, 5-12, 7-12, 10-12, 1.5-10, 2-10, 3-10, 4-10, 5-10, 7-10, 2-7, 3-7, 4-7, 5-7, 2-5, 3-5, 4-5, 2-4, 3-4, or 2-3.

[0111] As described in greater detail herein with respect to the Examples, higher aavevalues may generally be associated with a certain degree of feature rounding caused by the secondary etching step, and aspects exhibiting higher aave values (e.g., at least 3° in any of the preceding ranges) may tend to exhibit relatively low Rs values (e.g., less than or equal to 2 GU) but higher transmitance haze than certain other aspects. Lower aavevalues (e.g., less than 3° in any of the preceding ranges) may generally be associated with a high convergence of features caused in the secondary etching step, and such aspects may tend to exhibit relatively low haze and superior washout performance than aspects exhibiting higher aavevalues. Lower aavevalues may also be associated with a textured region 20 that comprises planar regions either between the plurality of surface features 26 or within the plurality of surface features 26, and such aspects may tend to exhibit relatively low specular reflectance.

[0112] The surface angle distribution of the textured region 20 may exhibit certain characteristics as a result of the multi-step etching process described herein. In aspects, the surface angle distribution of the textured region may exhibit a peak at a peak angle greater than 2°. The peak may be a local maximum in the surface angle distribution or a mode of the distribution. Peak angles over 2° indicate feature rounding caused via the secondary etching step described herein. Such peaks may be further characterized in having relatively narrow widths. In aspects, the surface angle distribution decreases to 90% of the peak value at an angle that is no more than 1.8° from the peak angle. Put differently, the surface angle distribution count drops 10% from the peak value at an angle within 1.8° of the peak angle. In some aspects, the surface angle distribution count drops 10% from the peak value at an angle within 1.5° of the peak angle. To illustrate, an example surface angle distribution for the textured region 20 may exhibit a peak at a bin associated with 5°. The surface angle distribution may drop to 90% of the value (pixel count) at 5° over the angular range from 3.2° to 6.8° or 3.5° to 6.5°. Such a sharp drop off is believed to indicate a consistent degree of feature rounding from feature-to- feature, representing the degree of control over the shape of the textured region 20 provided by the method described herein. This contrasts with certain existing anti-glare surfaces formed by sandblasting processes, which tend to exhibit broader peaks that do not drop off as quickly asAtorney Docket No.: SP24-234 those made by the method described herein. Such control over the shape of the textured region 20 facilitates providing a variety of samples having different optical performance, as described in greater detail herein.

[0113] In aspects, as a result of the plurality of structural features 26, the textured region 20 can exhibit an Sdq value (pm) that is greater than 0.01 and less than or equal to 0.4. In some aspects, the Sdq can be at least: 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.06, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0. 15, 0.20, 0.25, 0.30, 0.35, 0.4 or more; alternatively, or additionally, the Sdq can be: 0.4, 0.35, 0.30, 0.25, 0.2 0.15, 0.14, 0.13, 0.12, 0.11, 0.1, 0.09, 0.08, 0.07, 0.06, 0.05, 0.04, 0.03, 0.02, 0.01, 0.005, or 0.0045 or less. For clarity, any two of the foregoing open- ended ranges can be combined to form a closed range. For example, in some aspects, the Sdq can be 0.01-0.40, 0.01-0.35, 0.01-0.30, 0.01-0.30, 0.01-0.20, 0.01-0.15, 0.01-0.14, 0.01-0.13, 0.01-0.12, 0.01-0.11, 0.01-0.1, 0.01-0.09, 0.01-0.08, 0.01-0.07, 0.01-0.06, 0.01-0.05, 0.01-0.04, 0.01-0.03, 0.01-0.02, 0.02-0.15, 0.02-0.1, 0.02-0.09, 0.02-0.08, 0.02-.07, 0.02-0.06, 0.02-0.05, 0.02-0.04, 0.02-0.03, 0.03-0.15, 0.03-0.14, 0.03-0.13, 0.03-0.12, 0.03-0.11, 0.03-0.1, 0.03-0.09, 0.03-0.08, 0.03-0.07, 0.03-0.06, 0.03-0.05, 0.03-0.04, 0.04-0.40, 0.04-0.35, 0.04-0.30, 0.04- 0.25, 0.04-0.20, 0.04-0.15, 0.04-0.14, 0.04-0.13, 0.04-0.12, 0.04-0.11, 0.04-0.1, 0.04-0.09, 0.04-0.08, 0.04-0.07, 0.04-0.06, 0.04-0.05, 0.05-0. 15, 0.05-0.1, 0.05-0.09, 0.05-0.08, 0.05-0.07, 0.05-0.06, 0.06-0.15, 0.06-0.1, 0.06-0.09, 0.06-0.08, 0.06-0.07, 0.07-0.15, 0.07-0.1, 0.07-0.09, 0.07-0.08, 0.08-0.15, 0.08-0.1, 0.08-0.09, 0.09-1, 0.09-0.8, 0.09-0.6, 0.09-0.15, 0.09-0.14, 0.09-0.13, 0.09-0.12, 0.09-0.11, 0.09-0.1, 0.1-0.11, 0.1-0.12, 0.1-0.13, 0.1-0.14, 0.1-0.15, 0.1- 0.20, 0.1-0.25, 0. 1-0.30, 0.1-0.35, or 0. 1-0.4. The Sdq may be correlated with the aave exhibited by a particular textured region 20. Accordingly, articles exhibiting higher Sdq values (greater than 0. 1 in any of the preceding ranges) may tend to exhibit lower specular reflectance values than aspects with lower Sdq values, while aspects with lower Sdq values may tend to exhibit lower haze and superior washout performance. Articles exhibiting Sdq values less than 0.15 have been found to exhibit particularly favorable combinations of RIVF and WI values (both less than 0.5), particularly when combined with a surface angle distribution having a peak at a peak angle greater than 2°, as described in greater detail herein.

[0114] In aspects, as a result of the plurality of structural features 26, the textured region can exhibit a Sq value (pm) that is greater than 0. 1 and less than or equal to 0.6. In some aspects, the Sq value can be at least: 0.1, 0.12, 0.15, 0.2, 0.22, 0.25, 0.28, 0.3, 0.32, 0.35, 0.38, 0.4, 0.42, 0.45, 0.48, 0.5, 0.6 or more; alternatively, or additionally, the Sq can be: 0.6, 0.5, 0.48, 0.45, 0.42, 0.4, 0.38, 0.35, 0.32, 0.3, 0.28, 0.25, 0.22, 0.2, 0.15, 0.12, 0.1, or less. For clarity, anyAtorney Docket No.: SP24-234 two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the Sq value can be 0.1-0.12, 0.1-0.15, 0.1-0.18, 0.1-0.2, 0.1-0.22, 0.1-0.25, 0.1-0.28, 0.1-0.3, 0.1-0.32, 0.1-0.35, 0.1-0.38, 0.1-0.4, 0.1-0.42, 0.1-0.45, 0.1-0.48, 0.1-0.5, 0.1-0.6, 0.12-0.15, 0.12-0.2, 0.12-0.22, 0.12-0.25, 0.12-0.28, 0.12-0.3, 0.12-0.32, 0.12-0.35, 0.12-0.38, 0.12-0.4, 0.12-0.42, 0.12-0.45, 0.12-0.48, 0.12-0.5, 0.12-0.6, 0.15-0.18, 0.15-0.2, 0.15-0.22, 0.15-0.25, 0.15-0.28, 0.15-0.3, 0.15-0.32, 0.15-0.35, 0.15-0.38, 0.15-0.4, 0.15-0.42, 0.15-0.45, 0.15-0.48, 0.15-0.5, 0.15-0.6, 0.18-0.2, 0.18-0.22, 0.18-0.25, 0.18-0.28, 0.18-0.3, 0.18-0.32, 0.18-0.35, 0.18-0.38, 0.18-0.4, 0.18-0.42, 0.18-0.45, 0.18-0.48, 0.18-0.5, 0.18-0.6, 0.2-0.22, 0.2-0.25, 0.2-0.28, 0.2-0.3, 0.2-0.32, 0.2-0.35, 0.2-0.38, 0.2-0.4, 0.2-0.42, 0.2-0.45, 0.2-0.48, 0.2-0.5, 0.2-0.6, 0.22-0.25, 0.22-0.28, 0.22-0.3, 0.22-0.32, 0.22-0.35, 0.22-0.38, 0.22- 0.4, 0.22-0.42, 0.22-0.45, 0.22-0.48, 0.22-0.5, 0.22-0.6, 0.25-0.3, 0.25-0.32, 0.25-0.35, 0.25- 0.38, 0.25-0.4, 0.25-0.42, 0.25-0.45, 0.25-0.48, 0.25-0.5, 0.25-0.6, 0.3-0.32, 0.3-0.35, 0.3-0.38, 0.3-0.4, 0.3-0.42, 0.3-0.45, 0.3-0.48, 0.3-0.5, 0.3-0.6, 0.32-0.35, 0.32-0.38, 0.32-0.4, 0.32-0.42, 0.32-0.45, 0.32-0.48, 0.32-0.5, 0.32-0.60.32-0.38, 0.32-0.4, 0.32-0.42, 0.32-0.45, 0.32-0.48, 0.32-0.5, 0.32-0.6, 0.35-0.38, 0.35-0.4, 0.35-0.42, 0.35-0.45, 0.35-0.48, 0.35-0.5, 0.35-0.6, 0.4- 0.42, 0.4-0.45, 0.4-0.48, 0.4-0.5, or 0.4-0.6. As described in greater detail herein, the Sq value of a particular embodiment can be controlled via the primary and secondary etching steps. Greater depth of the pinhole features and or / or shorter secondary etching steps will generally be associated with higher Sq values. Aspects exhibiting higher Sq values (at least 0.2 in any of the preceding ranges) may tend to exhibit lower specular reflectance, but higher haze and washout than aspects exhibiting lower Sq values.

[0115] In some aspects, a textured region 20 can exhibit PPDuo as measured at an incident angle of 0 degrees. In some aspects, the PPDuo (%) can be at least: 0.1, 0.5, 1, 1.5, 2, 2.5, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.5, 5, 5.5, 6, 6.5, or 7; alternatively, or additionally, the PPDuo (%) can be: 7, 6.5, 6, 5.5, 5, 4.5, 4, 3.9, 3.8, 3.7, 3.6, 3.5, 3.4, 3.3, 3.2, 3.1, 3, 2.5, 2, 1.5, 1, 0.5, or 0.1 or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the PPDuo (%) can be 0.1-7, 0.1-6, 0.1-5, 0.1-4.5, 0.1-4, 0.1-3.9, 0.1-3.8, 0.1-3.7, 0.1-3.6, 0.1-3.5, 0.1-3.4, 0.1-3.3, 0.1-3.2, 0.1-3. 1, 0.1-3, 0.1-2.8, 0.1-2.6, 0.1-2.5, 0.1-2.4, 0.1-2.2, 0.1-2, 0.1-1.5, 0.1-1, 0.1-0.5, 0.5-7, 0.5-6, 0.5-5, 0.5-4.5, 0.5-4, 0.5-3.9, 0.5-3.8, 0.5-3.7, 0.5-3.6, 0.5-3.5, 0.5-3.4, 0.5-3.3, 0.5-3.2, 0.5-3. 1, 0.5-3, 0.5-2.8, 0.5-2.6, 0.5-2.5, 0.5-2.4, 0.5-2.2, 0.5-2, 0.5-1.5, 0.5-1, 1-7, 1-6, 1-5, 1- 4.5, 1-4, 1-3.9, 1-3.8, 1-3.7, 1-3.6, 1-3.5, 1-3.4, 1-3.3, 1-3.2, 1-3.1, 1-3, 1-2.8, 1-2.6, 1-2.5, 1-2.4, 1-2.2, 1-2, 1-1.5, 1.5-7, 1.5-6, 1.5-5, 1.5-4.5, 1.5-4, 1.5-3.9, 1.5-3.8, 1.5-3.7, 1.5-3.6, 1.5-3.5, 1.5-3.4, 1.5-3.3, 1.5-3.2, 1.5-3. 1, 1.5-3, 1.5-2.8, 1.5-2.6, 1.5-2.5, 1.5-2.4, 1.5-2.2, 1.5-2, 2-Atorney Docket No.: SP24-234 7, 2-6, 2-5, 2-4.5, 2-4, 2-3.9, 2-3.8, 2-3.7, 2-3.6, 2-3.5, 2-3.4, 2-3.3, 2-3.2, 2-3.1, 2-3, 2-2.8, 2- 2.6, 2-2.5, 2-2.4, 2-2.2, 2.2-7, 2.2-6, 2.2-5, 2.2-4.5, 2.2-4, 2.2-3.9, 2.2-3.8, 2.2-3.7, 2.2-3.6, 2.2-3.5, 2.2-3.4, 2.2-3.3, 2.2-3.2, 2.2-3. 1, 2.2-3, 2.2-2.8, 2.2-2.6, 2.2-2.5, 2.2-2.4, 2.4-7, 2.4-6, 2.4- 5, 2.4-4.5, 2.4-4, 2.4-3.9, 2.4-3.8, 2.4-3.7, 2.4-3.6, 2.4-3.5, 2.4-3.4, 2.4-3.3, 2.4-3.2, 2.4-3.1,2.4-3, 2.4-2.8, 2.4-2.6, 2.4-2.5, 2.5-7, 2.5-6, 2.5-5, 2.5-4.5, 2.5-4, 2.5-3.9, 2.5-3.8, 2.5-3.' 7, 2.5-3.6, 2.5-3.5, 2.5-3.4, 2.5-3.3, 2.5-3.2, 2.5-3.1, 2.5-3, 2.5-2.8, 2.5-2.6, 2.6-7, 2.6-6, 2.6-5, 2.6- 4.5, 2.6-4, 2.6-3.9, 2.6-3.8, 2.6-3.7, 2.6-3.6, 2.6-3.5, 2.6-3.4, 2.6-3.3, 2.6-3.2, 2.6-3.1, 2.6-3, 2.6-2.8, 2.8-7, 2.8-6, 2.8-5, 2.8-4.5, 2.8-4, 2.8-3.9, 2.8-3.8, 2.8-3.7, 2.8-3.6, 2.8-3.5, 2.8-3.4,2.8-3.3, 2.8-3.2, 2.8-3. 1, 2.8-3, 3-7, 3-6, 3-5, 3-4.5, 3-4, 3-3.9, 3-3.8, 3-3.7, 3-3.6, 3-3.5, 3-3.4,3-3.3, 3-3.2, 3-3.1, 3.1-7, 3.1-6, 3.1-5, 3. 1-4.5, 3.1-4, 3. 1-3.9, 3. 1-3.8, 3. 1-3.7, 3. 1-3.6, 3. 1-3.5,3. 1-3.4, 3.1-3.3, 3. 1-3.2, 3.2-7, 3.2-6, 3.2-5, 3.2-4.5, 3.2-4, 3.2-3.9, 3.2-3.8, 3.2-3.7, 3.2-3.6,3.2-3.5, 3.2-3.4, 3.2-3.3, 3.3-7, 3.3-6, 3.3-5, 3.3-4.5, 3.3-4, 3.3-3.9, 3.3-3.8, 3.3-3.7, 3.3-3.6,3.3-3.5, 3.3-3.4, 3.4-7, 3.4-6, 3.4-5, 3.4-4.5, 3.4-4, 3.4-3.9, 3.4-3.8, 3.4-3.7, 3.4-3.6, 3.4-3.5,3.5-7, 3.5-6, 3.5-5, 3.5-4.5, 3.5-4, 3.5-3.9, 3.5-3.8, 3.5-3.7, 3.5-3.6, 3.6-7, 3.6-6, 3.6-5, 3.6-4.5,3.6-4, 3.6-3.9, 3.6-3.8, 3.6-3.7, 3.7-7, 3.7-6, 3.7-5, 3.7-4.5, 3.7-4, 3.7-3.9, 3.7-3.8, 3.8-7, 3.8-6,3.8-5, 3.8-4.5, 3.8-4, 3.8-3.9, 3.9-7, 3.9-6, 3.9-5, 3.9-4.5, 3.9-4, 4-7, 4-6, 4-5, 4-4.5, 4.5-5, 5-7, 5-6.5, 5-6, 6-7, 6-6.5, or 6.5-7.

[0116] In some aspects, a textured region 20 can exhibit any suitable coupled DOI. In some aspects, the coupled DOI (%) can be at least: 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, or 95; alternatively, or additionally, the coupled DOI (%) can be: 100, 95, 90 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, or 25 or less. For clarity, any two of the foregoing open- ended ranges can be combined to form a closed range. For example, in some aspects, the coupled DOI (%) can be 20-100, 20-95, 20-90, 20-85, 20-80, 20-75, 20-70, 20-65, 20-60, 20- 55, 20-50, 20-45, 20-40, 20-35, 20-30, 20-25, 25-100, 25-95, 25-90, 25-85, 25-80, 25-75, 25- 70, 25-65, 25-60, 25-55, 25-50, 25-45, 25-40, 25-35, 25-30, 30-100, 30-95, 30-90, 30-85, 30-80, 30-75, 30-70, 30-65, 30-60, 30-55, 30-50, 30-45, 30-40, 30-35, 35-100, 35-95, 35-90, 35-85, 35-80, 35-75, 35-70, 35-65, 35-60, 35-55, 35-50, 35-45, 35-40, 40-100, 40-95, 40-90, 40-85, 40-80, 40-75, 40-70, 40-65, 40-60, 40-55, 40-50, 40-45, 45-100, 45-95, 45-90, 45-85, 45-80, 45-75, 45-70, 45-65, 45-60, 45-55, 45-50, 50-100, 50-95, 50-90, 50-85, 50-80, 50-75, 50- 70, 50-65, 50-60, 50-55, 55-100, 55-95, 55-90, 55-85, 55-80, 55-75, 55-70, 55-65, 55-60, 60- 100, 60-95, 60-90, 60-85, 60-80, 60-75, 60-70, 60-65, 65-100, 65-95, 65-90, 65-85, 65-80, 65- 75, 65-70, 70-100, 70-95, 70-90, 70-85, 70-80, 70-75, 75-100, 75-95, 75-90, 75-85, 75-80, 80- 100, 80-95, 80-90, 80-85, 85-100, 85-95, 85-90, 90-95, or 95-100. As described herein, DOI can be controlled to a certain extent based on an average size of the plurality of surface featuresAtorney Docket No.: SP24-234 26. When greater spacing between pinhole features is utilized, such that the textured region 20 exhibits a relatively high Rsm value (e.g., greater than or equal to 25 pm, greater than or equal to 30 pm, or even greater than or equal to 40 pm, or even greater than or equal to 50 pm), the textured region 20 may exhibit relatively low coupled DOI (e.g., less than or equal to 80%, less than or equal to 70%, or even less than or equal to 40%). Other articles with textured regions exhibiting lower Rsm values may tend to exhibit higher coupled DOI values.

[0117] In some aspects, the textured region 20 can exhibit any suitable haze. In some aspects, the haze (%) can be at least: 2, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, or 80; alternatively, or additionally, the haze (%) can be: 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, or 2 or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the haze (%) can be 2-80, 2- 75, 2-70, 2-65, 2-60, 2-55, 2-50, 2-45, 2-40, 2-35, 2-30, 2-25, 20, 2-15, 2-10, 2-5, 5-80, 5-75, 5-70, 5-65, 5-60, 5-55, 5-50, 5-45, 5-40, 5-35, 5-30, 5-25, 5-20, 5-15, 5-10, 10-80, 10-75, 10- 70, 10-65, 10-60, 10-55, 10-50, 10-45, 10-40, 10-35, 10-30, 10-25, 10-20, 10-15, 15-80, 15-75, 15-70, 15-65, 15-60, 15-55, 15-50, 15-45, 15-40, 15-35, 15-30, 15-25, 15-20, 20-80, 20-75, 20- 70, 20-65, 20-60, 20-55, 20-50, 20-45, 20-40, 20-35, 20-30, 20-25, 25-80, 25-75, 25-70, 25-65, 25-60, 25-55, 25-50, 25-45, 25-40, 25-35, 25-30, 30-80, 30-75, 30-70, 30-65, 30-60, 30-55, SOSO, 30-45, 30-40, 30-35, 35-80, 35-75, 35-70, 35-65, 35-60, 35-55, 35-50, 35-45, 35-40, 40-80, 40-75, 40-70, 40-65, 40-60, 40-55, 40-50, 40-45, 45-80, 45-75, 45-70, 45-65, 45-60, 45-55, 45- 50, 50-80, 50-75, 50-70, 50-65, 50-60, 50-55, 55-80, 55-75, 55-70, 55-65, 55-60, 60-80, 60-75, 60-70, 60-65, 65-80, 65-75, 65-70, 70-80, 70-75, or 75-80.

[0118] In some aspects, the textured region 20 can exhibit any suitable specular reflectance. In some aspects, the specular reflectance (GU) can be at least: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.1, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0,6.5, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0 or more; alternatively, or additionally, the specular reflectance (GU) can be 15.0, 14.0, 13.0, 12.0, 11.0, 10.0, 9.0, 8.0, 7.0, 6.5, 6.0, 5.5, 5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the specular reflectance can be 0.1-0.2, 0.1-0.3, 0.1-0.4, 0.1-0.5, 0.1-0.5, 0.1-0.6, 0.1-0.7, 0.1-0.8, 0.1-0.9, 0.1-1.0, 0.1-1.1, 0. 1-1.2, 0.1-1.3, 0. 1-1.4, 0. 1-1.5, 0.1-1.6, 0. 1-1.7, 0.1-1.8, 0. 1-1.9, 0. 1-2.0, 0.1-2.5, 0.1-3.0, 0.1-3.5, 0.1-4.0, 0.1-4.5, 0.1-5.0, 0.1-5.5, 0.1-6.0, 0.1-.6.5, 0.1-7.0, 0.1-8.0, 0.1-9.0, 0.1-10.0, 0.1- 11.0, 0.1-12.0, 0.1-13.0, 0.1-14.0, 0.1-15.0, 0.2-0.3, 0.2-0.4, 0.2-0.5, 0.2-0.5, 0.2-0.6, 0.2-0.7, 0.2-0.8, 0.2-0.9, 0.2-1.0, 0.2-1.1, 0.2-1.2, 0.2-1.3, 0.2-1.2, 0.2-1.5, 0.2-1.6, 0.2-1.7, 0.2-1.8, 0.2-Atorney Docket No.: SP24-234 1.9, 0.2-2.0, 0.2-2.5, 0.2-3.0, 0.2-3.5, 0.2-4.0, 0.2-4.5, 0.2-5.0, 0.2-5.5, 0.2-6.0, 0.2-.6.5, 0.2- 7.0, 0.2-8.0, 0.2-9.0, 0.2-10.0, 0.2-11.0, 0.2-12.0, 0.2-13.0, 0.2-14.0, 0.2-15.0, 0.3-0.4, 0.3-0.5, 0.3-0.5, 0.3-0.6, 0.3-0.7, 0.3-0.8, 0.3-0.9, 0.3-1.0, 0.3-1. 1, 0.3-1.2, 0.3-1.3, 0.3-1.2, 0.3-1.5, 0.3-1.6, 0.3-1.7, 0.3-1.8, 0.3-1.9, 0.3-2.0, 0.3-2.5, 0.3-3.0, 0.3-3.5, 0.3-4.0, 0.3-4.5, 0.3-5.0, 0.3-5.5, 0.3-6.0, 0.3-.6.5, 0.3-7.0, 0.3-8.0, 0.3-9.0, 0.3-10.0, 0.3-11.0, 0.3-12.0, 0.3-13.0, 0.3-14.0, 0.3- 15.0, 0.4-0.5, 0.4-0.4, 0.4-0.6, 0.4-0.7, 0.4-0.8, 0.4-0.9, 0.4-1.0, 0.4-1. 1, 0.4-1.2, 0.4-1.3, 0.4- 1.2, 0.4-1.5, 0.4-1.6, 0.4-1.7, 0.4-1.8, 0.4-1.9, 0.4-2.0, 0.4-2.5, 0.4-3.0, 0.4-3.5, 0.4-4.0, 0.4-4.5, 0.4-5.0, 0.4-5.5, 0.4-6.0, 0.4-.6.5, 0.4-7.0, 0.4-8.0, 0.4-9.0, 0.4-10.0, 0.4-11.0, 0.4-12.0, 0.4- 13.0, 0.4-14.0, 0.4-15.0, 0.5-0.6, 0.5-0.7, 0.5-0.8, 0.5-0.9, 0.5-1.0, 0.5-1. 1, 0.5-1.2, 0.5-1.3, 0.5- 1.2, 0.5-1.5, 0.5-1.6, 0.5-1.7, 0.5-1.8, 0.5-1.9, 0.5-2.0, 0.5-2.5, 0.5-3.0, 0.5-3.5, 0.5-4.0, 0.5-4.5, 0.5-5.0, 0.5-5.5, 0.5-6.0, 0.5-.6.5, 0.5-7.0, 0.5-8.0, 0.5-9.0, 0.5-10.0, 0.5-11.0, 0.5-12.0, 0.5- 13.0, 0.5-14.0, 0.5-15.0, 0.6-0.7, 0.6-0.8, 0.6-0.9, 0.6-1.0, 0.6-1.1, 0.6-1.2, 0.6-1.3, 0.6-1.2, 0.6-1.5, 0.6-1.6, 0.6-1.7, 0.6-1.8, 0.6-1.9, 0.6-2.0, 0.6-2.5, 0.6-3.0, 0.6-3.5, 0.6-4.0, 0.6-4.5, 0.6-5.0, 0.6-5.5, 0.6-6.0, 0.6-.6.5, 0.6-7.0, 0.6-8.0, 0.6-9.0, 0.6-10.0, 0.6-11.0, 0.6-12.0, 0.6-13.0, 0.6- 14.0, 0.6-15.0, 0.8-0.8, 0.8-0.9, 0.8-1.0, 0.8-1. 1, 0.8-1.2, 0.8-1.3, 0.8-1.2, 0.8-1.5, 0.8-1.6, 0.8-1.7, 0.8-1.8, 0.8-1.9, 0.8-2.0, 0.8-2.5, 0.8-3.0, 0.8-3.5, 0.8-4.0, 0.8-4.5, 0.8-5.0, 0.8-5.5, 0.8-6.0, 0.8-.6.5, 0.8-7.0, 0.8-8.0, 0.8-9.0, 0.8-10.0, 0.8-11.0, 0.8-12.0, 0.8-13.0, 0.8-14.0, 0.8-15.0, 0.9- 1.0, 0.9-1. 1, 0.9-1.2, 0.9-1.3, 0.9-1.2, 0.9-1.5, 0.9-1.6, 0.9-1.7, 0.9-1.8, 0.9-1.9, 0.9-2.0, 0.9-2.5, 0.9-3.0, 0.9-3.5, 0.9-4.0, 0.9-4.5, 0.9-5.0, 0.9-5.5, 0.9-6.0, 0.9-.6.5, 0.9-7.0, 0.9-8.0, 0.9-9.0, 0.9-10.0, 0.9-11.0, 0.9-12.0, 0.9-13.0, 0.9-14.0, 0.9-15.0, 1.0-1. 1, 1.0-1.2, 1.0-1.3, 1.0-1.2, 1.0-1.5, 1.0-1.6, 1.0-1.7, 1.0-1.8, 1 .0-1.9, 1.0-2.0, 1.0-2.5, 1.0-3.0, 1.0-3.5, 1.0-4.0, 1.0-4.5, 1.0-5.0, 1.0-5.5, 1.0-6.0, 1.0-.6.5, 1.0-7.0, 1.0-8.0, 1.0-9.0, 1.0-10.0, 1.0-11.0, 1.0-12.0, 1.0-13.0, 1.0- 14.0, 1.0-15.0, 1.5-1.6, 1.5-1.7, 1.5-1.8, 1.5-1.9, 1.5-2.0, 1.5-2.5, 1.5-3.0, 1.5-3.5, 1.5-4.0, 1.5-4.5, 1.5-5.0, 1.5-5.5, 1.5-6.0, 1.5-.6.5, 1.5-7.0, 1.5-8.0, 1.5-9.0, 1.5-10.0, 1.5-11.0, 1.5-12.0, 1.5-13.0, 1.5-14.0, 1.5-15.0, 1.7-1.8, 1.7-1.9, 1.7-2.0, 1.7-2.5, 1.7-3.0, 1.7-3.5, 1.7-4.0, 1.7-4.5, 1.7-5.0, 1.7-5.5, 1.7-6.0, 1.7-.6.5, 1.7-7.0, 1.7-8.0, 1.7-9.0, 1.7-10.0, 1.7-11.0, 1.7-12.0, 1.7- 13.0, 1.7-14.0, 1.7-15.0, 4.0-4.5, 4.0-5.0, 4.0-5.5, 4.0-6.0, 4.0-.6.5, 4.0-7.0, 4.0-8.0, 4.0-9.0, 4.0-10.0, 4.0-11.0, 4.0-12.0, 4.0-13.0, 4.0-14.0, 4.0-15.0, 7.0-8.0, 7.0-9.0, 7.0-10.0, 7.0-11.0, 7.0-12.0, 7.0-13.0, 7.0-14.0, 7.0-15.0, 10.0-11.0, 10.0-12.0, 10.0-13.0, 10.0-14.0, or 10.0-15.0.

[0119] In aspects, the textured region 20 exhibits a suitable washout index value (“WI”). The washout index value is a measure of a degradation of a contrast and resolution of an underlying display (that the article 10 is disposed over) when exposed to strong ambient light, such as sunlight. A measurement technique for WI is provided in greater detail herein with respect to FIG. 8. In aspects, WI can be 0, 0. 1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95 or more;Atorney Docket No.: SP24-234 alternatively, or additionally, WI can be 0.95, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects WI can be 0.1-0.95, 0. 1-0.9, 0. 1-0.8, 0. 1-0.7, 0. 1-0.6, 0. 1- 0.5, 0. 1-0.4, 0.1-0.3, 0.1-0.2, 0.2-0.9, 0.2-0.8, 0.2-0.7, 0.2-0.6, 0.2-0.5, 0.2-0.4, 0.2-0.3, 0.3-0.9, 0.3-0.8, 0.3-0.7, 0.3-0.6, 0.3-0.5, 0.3-0.4, 0.4-0.9, 0.4-0.8, 0.4-0.7, 0.4-0.6, 0.4-0.5, 0.5-0.95, 0.5-0.9, 0.5-0.8, 0.5-0.7, 0.5-0.6, 0.6-0.95, or 0.7-0.95.

[0120] In aspects, the textured region 20 exhibits a suitable reflected image visibility factor (“RIVF”). RIVF is a measure of the extent an image in reflection is degraded by the textured region 20 (e.g., a degradation of a user’s own reflection caused by interaction with the textured region 20). A measurement technique for RIVF is provided in greater detail herein. In aspects, RIVF can be 0, 0.1, 0.2, 0.3, 0.4, 0.48, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95 or more; alternatively, or additionally, the RIVF can be 0.95, 0.9, 0.8, 0.7, 0.6, 0.5, 0.48, 0.4, 0.3, 0.2, 0.1, or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects RIVF can be 0. 1-0.95, 0. 1-0.9, 0.1 -0.8, 0.1-0.7, 0. 1-0.6, 0. 1-0.5, 0. 1-0.4, 0.1-0.3, 0. 1-0.2, 0.2-0.9, 0.2-0.8, 0.2-0.7, 0.2-0.6, 0.2-0.5, 0.2-0.4, 0.2-0.3, 0.3-0.9, 0.3- 0.8, 0.3-0.7, 0.3-0.6, 0.3-0.5, 0.3-0.4, 0.4-0.9, 0.4-0.8, 0.4-0.7, 0.4-0.6, 0.4-0.5, 0.5-0.95, 0.5- 0.9, 0.5-0.8, 0.5-0.7, 0.5-0.6, 0.6-0.95, or 0.7-0.95.

[0121] In aspects, the textured region 20 exhibits a suitable corrected color shift. As used herein, “corrected color shift” is a measure of the amount of reflection color artifacts that the substrate 12 generates while reflecting ambient light off of the textured region 20. To determine the corrected color shift, the substrate 12 with the textured region 20 to be tested is placed over a display, with oil disposed between the substrate 12 and the display 16 to suppress the light reflections off the back surface of the substrate 12 and the surface of the display (the oil has a refractive index matching a refractive index of the substrate 12). A white light source (D65 light source) illuminates the substrate 12. Since any reflection color artifacts that the substrate 12 generates is more easily observed and is more accurately measured when the display is turned off, the display is switched-off when color separation measurements are conducted. The textured region 20 reflects a portion of the light that the white light source emits as a scatered light patern and a color CCD camera captures an image of the scatered light patern. The image is then digitally processed, and chromaticity coefficients (Cxand Cy) along a selected straight line through the locations with maximum Cx (or Cy) and minimum Cx (or Cy) are calculated. Here, chromaticity coefficients Cxand Cyare defined as Cx= PR / PR + PG + PB) and Cy= PG / (PR + PG + PB) respectively, in which PR. PG, PBare theAtorney Docket No.: SP24-234 powers (or intensities) of red, green, and blue light, respectively, at a location of the scatered light patern detected by the color CCD camera. Chromaticity is an objective specification of the quality of a color regardless of its luminance. The color shifts along the selected line, A and ACy. are calculated as the difference between the maximum Cxand the minimum Cxfor A Cy, and the difference the maximum C,, and the minimum C,, for AC,,. The color shifts ACyand ACyare then corrected to account for the fact that the visibility of color change that human eyes see is relative to not only the color shifts (ACyand ACy) but also an angle separation between the locations of the maximum and minimum Cx(for ACy) and the maximum and minimum Cy(for ACy). These corrected colors shifts are defined asThe d0ris reference angle separation arbitrarily set at d0r= 0.84 degrees. This reference angle is chosen from the angle between two adjacent measurement points of 455 point color and luminance measurement of a 300x110mm display viewed at 500mm distance. The d0xand d0yare the angle separations in degree between the locations of maximum and minimum for Cyand Cyrespectively. When the corrected color shifts CCXcorrected and ^Cy_corrected are each less than 0.3, it is assumed that it is difficult for human eyes perceive any reflection color artifacts that the substrate 12 is producing in some typical use environments. In aspects, the substrate 12 exhibits a corrected color shifts Cx correctedand CCycorrected of 0.001, 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.5, 3.0, 3.5, or 4.0, or within any range bounded by any two of those values (0.01 to 0.3, 0.05 to 1.0, and so on).

[0122] The multistep etching method described herein provides various parameters (e.g., feature patern, feature size, feature spacing, feature depth, and degree of feature rounding) that can be controlled in order to provide a variety of different optical performance (in terms of specular reflectance, WI, RIVF, DOI, haze, sparkle, and corrected color shift). For certain application, such as when the article 10 is utilized as a display cover for automotive interior displays, it may be desirable to have relatively low sparkle (e.g., less than or equal to 3.0%, less than or equal to 2.0%, less than or equal to 1.5%), low haze (e.g., less than 10%, less than or equal to 9%, less than or equal to 5%), low WI (e.g., less than or equal to 0.5, less than or equal to 0.48, less than or equal to 0.45, less than or equal to 0.4), low RIVF (e.g., less than orAtorney Docket No.: SP24-234 equal to 0.5, less than or equal to 0.48, less than or equal to 0.45, less than or equal to 0.4), and low specular reflectance (e.g., less than or equal to 6 GU, less than or equal to 3 GU, less than or equal to 2 GU, less than or equal to 1 GU), with litle regard for DOI. Other applications, such as for cover glass in consumer mobile electronic display covers, may require low sparkle (e.g., less than or equal to 3%, less than or equal to 2.5%) and particularly low specular reflectance (e.g., less than or equal to 6 GU, less than or equal to 3 GU, less than or equal to 2 GU, less than or equal to 1.5 GU, less than or equal to 1.0 GU, less than or equal to 0.5 GU), and low RIVF (e.g., less than or equal to 0.2) without regard to haze or WI. Other applications, may require low DOI (e.g., less than or equal to 40%, less than or equal to 35%, less than or equal to 30%, less than or equal to 20%), low sparkle (less than or equal to 3.0%, less than or equal to 2.0%, less than or equal to 1.5%), low specular reflectance (e.g., less than or equal to 6 GU, less than or equal to 3 GU, less than or equal to 2 GU, less than or equal to 1 GU), higher haze (e.g., greater than or equal to 10% and less than or equal to 30%), without regard for RIVF or WI. As will be appreciated after the description of the Examples described herein, the article 10 can be configured to exhibit each of these combinations of performance atributes via the method described herein.

[0123] FIG. 4 depicts a flow diagram of a method 400 of fabricating the article 10, according to an example embodiment of the present disclosure. Reference to various components and processes depicted in FIGS. 1-3 will be made to aid in describing the method 400. At block 402, a patern for the plurality of pinhole features is determined. The patern for the plurality of pinhole features may determine a distribution of pinhole features that is formed in the substrate 12 during a primary etching step. The patern of pinhole features may include a shape of the plurality of pinhole features, a size of the plurality of pinhole features, and a distribution of the plurality of pinhole features.

[0124] Referring now to FIG. 5A, and example patern for a plurality of pinhole features 500 is shown, according to an example embodiment. In the depicted example, the plurality of pinhole features 500 have a circular shape and comprise a feature size 502 (maximum linear dimension, or diameter in this example). In aspects, the feature size 502 may be greater than or equal to 0.5 pm and less than or equal to 5.0 pm. For example the feature size 502 can be 0.5 pm, 0.6 pm, 0.7 pm, 0.8 pm, 0.9 pm, 1.1 pm, 1.2 pm, 1.3 pm, 1.4 pm, 1.5 pm, 1.6 pm 1.7 pm 2.0 pm, 2.5 pm, 3.0 pm, 3.5 pm 4.0 pm, 4.5 pm, 5.0 pm, or anywhere in ranges bounded by any combination of such values. It has been found that feature sizes of less than or equal to 1.0 pm are preferred for providing the surface angle distributions described herein by facilitating generating pinhole features of a suitable aspect ratio.Atorney Docket No.: SP24-234

[0125] The patern may also have a minimum center-to-center separation distance 506, which may represent a minimum lateral distance separating adjacent ones of the plurality of pinhole features 500. In aspects, the minimum center-to-center separation distance 506 is greater than or equal to 5 pm, greater than or equal to 6 pm, greater than or equal to 7 pm, greater than or equal to 8 pm, greater than or equal to 9 pm, greater than or equal to 10 pm, greater than or equal to 15 pm, greater than or equal to 20 pm, greater than or equal to 25 pm, greater than or equal to 30 pm, greater than or equal to 40 pm, greater than or equal to 50 pm. In aspects, the minimum center-to-center separation distance is less than or equal to 100 pm, less than or equal to 75 pm, less than or equal to 50 pm, less than or equal to 40 pm, or less than or equal to 30 pm. For example, the minimum center-to-center separation distance 506 may be greater than or equal to 5 pm and less than or equal to 100 pm, greater than or equal to 10 pm and less than or equal to 50 pm, or greater than or equal to 20 pm and less than or equal to 40 pm.

[0126] As shown, the patern covers a geometric area 504 (e.g., associated area of the textured region 20) with the plurality of pinhole features 500. In aspects, a number of pinhole features in the patern can be determined based on the geometric area 504, the area of each individual pinhole feature, and a desired fill fraction for the plurality of pinhole features 500. In aspects, the fill fraction may be greater than or equal to 0.5%, greater than or equal to 1% and less than or equal to 10%, or greater than or equal to 1% and less than or equal to 5%, or greater than or equal to 2.5% and less than or equal to 5.0%.

[0127] To determine the arrangement, a spacing distribution algorithm can be utilized to determine the specific placement of the surface features according to a random distribution. The spacing distribution algorithm can be run to distribute geometric centers of each feature throughout the geometric area 504, subject to certain constraints. For example, the geometric area 504, feature size 502, number of features, and minimum center-to-center separation distance 506 can be used as constraints for the spacing distribution algorithm. Example spacing distribution algorithms include Poisson disk sampling, maxi-min spacing, and hard-sphere distribution. Poisson disk sampling inserts a first pinhole feature in the geometric area 504 and then inserts a second feature within the geometric area, placing the center at a random point. If the placement of the second feature satisfies the minimum center-to-center separation distance 506 from the first feature, then the second feature stays. The algorithm then repeats this process until no more such objects can be placed within the geometric area 504 that satisfies the minimum center-to-center separation distance 506. The result is a random distribution, but specific placement, of the features. The maxi-min spacing algorithm is so named because itAtorney Docket No.: SP24-234 atempts to maximize the minimum nearest-neighbor center-to-center separation distance 506 of a point distribution. Because it proceeds iteratively, moving each object to another place where it is further from any neighbors, the algorithm usually does not achieve a perfect hexagonal latice. It produces a random distribution with a relatively high degree of mean hexagonality, often exceeding 90%. The hard-sphere distribution algorithm is a molecular dynamics simulation performed at finite temperature. The result is a placement of objects that differ from a hexagonal lattice. However, again, there is a higher degree of hexagonality than would result from a Poisson disk algorithm. More information on the patern depicted in FIG. 4A can be found in U.S. Patent No. 11,940,593, which is entitled “Display Articles with Diffractive Anti-Glare Surfaces and Methods of Marking the Same,” and is hereby incorporated by reference in its entirety. While the features depicted in FIG. 5A are circular in shape, it should be appreciated that other peripheral feature shapes (e.g., hexagonal, rectangular, elliptical) in similar paterns are also contemplated.

[0128] FIG. 5B depicts another example patern of pinhole features. The pinhole features may have the same size, shape, and fill fraction associated with the features of the patern described with respect to FIG. 5A. The patern in FIG. 5B can be generated using the method described above with respect to FIG. 5A as a starting point to generate an initial patern. The initial patern may have a first minimum center-to-center separation distance 510. After formation of the initial patern, circular regions of exclusion 512 are drawn around each of the features in the initial patern, with each circular region of exclusion 512 having a diameter less than the first minimum center-to-center separation distance 510. A second patern for a second plurality of pinhole features is then calculated using a spacing distribution algorithm (e.g., Poisson Disk), with the circular regions of exclusion 512 not including the any pinhole features in the second patern. The second patern has a scale (minimum center-to-center separation distance) that is smaller than that of the initial patern. Such a process could repeat (e.g., with another set of exclusion regions being drawn around the second patern and another patern being formed outside of the exclusion regions) any suitable number of times until a desired fill fraction for a geometric area 514 is reached. Features of the same size can be placed at each point generated by such a patern. Details on forming the initial patern can be found in U.S. Patent Application No. 17 / 852,467, entitled “Anti-Glare Substrate For a Display Article with a Textured Region Including One or More Surfaces at Two, Three, or Four, Elevations, and Surface Features Providing at Eeast a Portion of the One or More Surfaces, and Method of Making the Same,” filed on June, 29, 2022, and hereby incorporated by reference in its entirety. As will be apparent, the paterns described in this previous patent application do not utilizeAtorney Docket No.: SP24-234 regions of exclusion, but instead form features of different radii surrounding the initial and subsequent paterns. It is believed that the additional groupings of features provided by the patern depicted in FIG. 5B facilitates lowering the sparkle exhibited by the resultant article 10.

[0129] FIG. 5C depicts another example patern for the plurality of pinhole features. The pinhole features in the patern depicted in FIG. 5C include a plurality of groupings of pinhole features, with the pinhole features in each grouping having a different cross-sectional shape (in terms of at least one of maximum dimension, peripheral shape, and / or contour shape of the resultant surface features). In aspects, the features in each grouping may be elliptical in shape and the ellipses in each grouping may have different dimensions. The major axis of each ellipse may be within the ranges provided herein with respect to the feature size 502 shown in FIG. 5 A. In aspects, at least two of the groupings differ from one another in peripheral feature shape (e.g., a first grouping can have features with an elliptical shape, while a second grouping can have features with a circular shape). Each grouping of features may be successively placed in a geometric area 516 using any of the spacing distribution algorithms described herein, while ensuring that the features do not overlap and an overall minimum center-to-center separation distance is observed. When elliptical features are used, the orientations of the ellipses (in terms of directionality of major axis) can also be randomized, along with the center locations and sizes of the ellipses. The features may occupy a fill fraction of the geometric area 516 that is in any of the ranges described with respect to the patern in FIG. 5A. More information regarding ways to generate the random patern of ellipses depicted in FIG. 5C may be found in U.S. Patent Application No. 17 / 369,315, entitled “Textured Region of a Substrate to Reduce Specular Reflectance Incorporating Surface Features with an Elliptical Perimeter or Segments Thereof, and Method of Making the Same,” filed on July 7, 2021, hereby incorporated by reference in its entirety. The triangulation methods described in U.S. Patent Application No. 17 / 369,315 may be used to generate a random distribution of ellipses that is scaled down to provide a desired fill fraction for the plurality of pinhole features. Utilizing elliptical features is believed to favorably reduce color separation effects compared to circular features.

[0130] Referring again to FIG. 4, at block 404, one or more etching masks is disposed on the substrate 12 and a primary etching step is performed using one or more etchants to form pinhole features in the textured region 20 based on the patern determined at the block 402, with the pinhole features having a depth of at least 1 pm. For example, to form a first one of the one or more etching masks, a stop layer and / or photoresist layer can be deposited on the substrate 12 and subsequently patterned. The stop layer may comprise any material known in the art that is resistant to the method of removing the substrate (or primary surface thereof)Atorney Docket No.: SP24-234 through the holes of the stop layer. In other words, the stop layer should sufficiently survive the conditions that result in the primary surface of the substrate being removed through the stop layer holes so the stop layer can perform its function as a stop layer. For example, in some aspects the stop layer comprises molybdenum, silicon carbide, silicon nitride, titanium, titanium nitride, aluminum, aluminum nitride, chromium, chromium oxynitride, zirconium, niobium, tungsten, copper, nickel, chromium plus titanium, or any combination thereof. The stop layer can be formed by sputering so that the stop layer has a thickness a range from 200 nm to 3 pm.

[0131] After deposition of the stop layer on the substrate 12, the stop layer is paterned using a photomask formed of a resist layer. The nature of the deposition and paterning of the resist layer may vary depending on the fabrication technique used. In aspects, various nanoimprint or photolithographic techniques may be used to deposit and patern the resist layer. In aspects, for example, the resist may be formed using thermoplastic nanoimprint lithography, and the resist may be formed of a thermoplastic polymer that is spin-coated onto the substrate 12 and subsequently imprinted via a mold to form a first patern that at least partially corresponds to the patern for the pinhole features. The resist may be subsequently thermally cured to form an etching mask, which is etched to transfer the etching mask patern to the stop layer.

[0132] Photolithography (e.g., photo imprint nanolithography, optical photolithography) techniques may also be used to form the resist layer. In such aspects, a mask comprising a first patern at least partially corresponding to the pattern determined for the plurality of pinhole features is aligned with the first major surface 18, and the resist may be exposed to radiation from a suitable light source (e.g., UV radiation) to cause the resist to cure and form an etching mask. The etching step can then then be used in a paterning etch step to transfer the patern to the stop layer. Any suitable photolithographic technique may be used to patern the resist. Aspects are also envisioned where only the photoresist is used (i.e., the stop layer may be omitted in some aspects).

[0133] In aspects, an adhesion promoter (e.g., HexaMethylDiSilazane (HDMS) or N,N- dimethyl-N-(3-(trimethoxysilyl)propyl)octadecan-l-ammonium chloride, YSAM C18) is applied to the first major surface 18 or stop layer prior to the resist layer being deposited. In aspects, any of the adhesion promoters described in U.S. Patent No. 9,884,782, filed on April 1, 2015, and hereby incorporated by reference in its entirety, can be applied to aid in the stop layer and / or resist layer adhering to the substrate 12. Such adhesion promoters generally exhibit a dual adhesive or attractive functionality where one portion of the agent is atractive to the substrate 12 and another portion of the agent is atracted to the photoresist material. ForAtorney Docket No.: SP24-234 certain articles described herein, it has been found that providing an adhesion promoter on the first major surface 18 that exhibits a water contact angle (after deposition) that is greater than or equal to 65° (prior to deposition of a risk or other masking material) should provide sufficient adhesion.

[0134] After the resist is paterned, exposed areas of the first major surface 18 (through the cured and paterned resist and / or stop layer) are exposed to a suitable etchant for a suitable etching period determined based on a target etch depth in the primary etching step. In some aspects, the etchant comprises hydrofluoric acid (HF), Buffered Oxide Etch solutions (BOE), a metal hydroxide, or any combination thereof. In some aspects, the metal hydroxide in an alkali metal hydroxide, an alkaline earth metal hydroxide, or any combination thereof. Alkali metal hydroxides include lithium hydroxide, sodium hydroxide, potassium, hydroxide, rubidium hydroxide, cesium hydroxide, or any combination thereof. Alkaline earth metal hydroxides include magnesium hydroxide, calcium hydroxide, strontium hydroxide, barium hydroxide, or any combination thereof. Buffered Oxide Etch solutions comprise varying volume ratios of 40% NH4F to 49%HF in water, such that volume ratios vary from 20: 1 (least HF) to 1 : 1 (most HF), so as to maintain the pH of the etching solution throughout the etching process due to buffering in the solution. Irrespective of the particular etchant used, the etching period may be determined based on a desired depth of the pinhole features. In aspects, a desired depth of the pinhole features may be at least 1 pm. It has been found to be preferrable that the primary etching step results in pinhole features having a depth that is greater than the lateral size of the features. For example, in aspects the depth may be 1 pm, 1.1 pm, 1.2 pm, 1.3 pm,1.4 pm, 1.5 pm, 1.6 pm, 1.7 pm, 1.8 pm, 1.9 pm, 2.0 pm, 2.5 pm, 3.0 pm, 3.5 pm, 4.0 pm,4.5 pm, 5.0 pm, 6.0 pm, 7,0 pm 8.0 pm, or any depth between such values, or within any range bounded by any two of such values. The structure of individual pinhole features will be described in greater detail with respect to FIG. 6.

[0135] In the primary etching step, each area of the first major surface 18 that is exposed through the paterned resist may directly contact the etchant, which may degrade the substrate 12 and remove material therefrom. In aspects, the etchant that contacts the first major surface 18 is an HF / HNO3 etchant. In aspects, the etchant consists of hydrofluoric acid (HF, 49 w / w%) and nitric acid (HNO3, 69 w / w%) combinations with 0.1-10 v / v% HF and 0.1-10 v / v% HNO3. Typical concentrations used to achieve the etching depths discussed herein are 1.0 v / v% HF / 0. 1 v / v% HNO3 to 5 v / v%HF / 0.5 v / v% HNO3 solutions. In aspects, the etching can be carried out using a dip or spray etching process from room temperature to about 45 °C.Atorney Docket No.: SP24-234

[0136] Referring still to FIG. 4, after the primary etching step is complete, a secondary etching step is performed at block 406 by applying a secondary etchant to the textured region 20 to round out the pinhole features and form the plurality of surface features 26. In the secondary etching step, an entirety of the textured region 20 can come into direct contact with the secondary etchant after removal of the masks used in the primary etching step (i.e., the stop layer and resist layer can be removed prior to initiation of the secondary etching step). It has been found that such a secondary etching step rounds out the features formed in the primary etching step. The secondary etching step can be done using any suitable etching process, such as a dip process or a spray process. For example, in a dip process, the article can be dipped into a secondary etching solution comprising a concentration ratio of HF and HC1 from 0.5M HF / 0.5M HC1 to 3M HF / 3M HC1, such that an etching rate of the article is greater than 0.1 pm / min or greater than 0.5 pm / min. In such aspects, the article can be exposed to the secondary etching solution for a time period of at least 10 minutes. For example, the second etching step could be greater than or equal to 10 minutes to and less than or equal to 60 minutes, greater than or equal to 10 minutes and less than or equal to 40 minutes, or greater than or equal to 10 minutes and less than or equal to 30 minutes.

[0137] In aspects, the secondary etching step can be performed so as to remove at least 5 pm of the material of the substrate 12 from the first major surface 18 within the textured region 20. The amount of material removed from the first major surface 18 can be determined by comparing the maximum thickness of the substrate 12 before and after the secondary etching step. In aspects, the secondary etching step can be performed to remove 5 pm, 10 pm, 15, pm 20 pm, 25 pm, 30 pm, 35 mm, 40 pm, 45 pm, 50 pm, 60 pm, 70 pm, 80 pm, 90 pm, 100 pm, or any amount of material between such values, or any amount with any range bounded by two of such values from the first major surface 18. As described in greater detail herein, a higher amount of material removal may result in greater amounts of feature rounding, which can reduce the aaveand amax exhibited by the textured region 20. Aspects made using a secondary etching step with at least 40 pm of material removal may exhibit lower aave and amaxvalues than aspects made using a secondary etching step with less than or equal to 25 pm of material removal, holding other factors (e.g., patern of pinhole features, primary etching step) constant. The effects of the secondary etching step on the surface angle distribution exhibited by the textured region 20 are described in greater detail with respect to FIGS. 7A and 7B. The amount of material removal in the secondary etching step needed for an article to exhibit a relatively low haze (less than or equal to 30%) may be roughly proportional to the spacing of the surface features. For articles formed using the patern depicted in FIG. 5A for the plurality of pinholeAtorney Docket No.: SP24-234 features, smaller minimum separation distances (e.g., less than or equal to 15 pm) may be associated with less material removal in the secondary etching step to exhibit a haze of less than 30%, as compared with larger minimum separation distances of 20 pm or more.

[0138] Conditions for conducting the primary and etching steps, depending on the etchants used, will now be described in greater detail.

[0139] In aspects, at least one of the primary etching step and secondary etching step comprises any suitable composition conditions when employing HF. For example, in some aspects, at least one of the primary etching step and the secondary etching step employs a composition comprising HF in an amount (wt.%) of at least: 0.1, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 8, 10, 12, 14, 16, 18, or 20, based on total weight of the composition; alternatively, or additionally, at least one of the primary etching step and the secondary etching step employs a composition comprising HF in an amount (wt.%) of 20, 18, 16, 14, 12, 10, 8, 6, 5, 4.5, 4, 3.5, 3, 2.5, 2, 1.5, 1, 0.5, or 0.1 or less, based on total weight of the composition. In some aspects, the primary etching step employs a concentration of HF that is lower than in the secondary etching step. In some aspects, the primary etching step comprises HF in an amount of 0.1-20 wt.%, or 0.5-2 wt.%, or any other amount disclosed herein, and the secondary etching step comprises HF in an amount of 1-20 wt.%, or 8-12 wt.%, or any other amount disclosed herein.

[0140] In some aspects, at least one of the primary etching step and the secondary etching step comprises any suitable temperature conditions when employing HF. For example, in some aspects, when employing HF, at least one of the primary etching step and the secondary etching step is conducted at a temperature (°C) of at least: 15, 20, RT, 25, 30, 35, 40, 45, 50, 55, or 60; alternatively, or additionally, when employing HF at least one of the primary etching step and the secondary etching step is conducted at a temperature of 60, 55, 50, 45, 40, 35, 30, 25, RT, 20, or 15 or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, when employing HF at least one of the primary etching step and the secondary etching step is conducted at a temperature (°C) of 15- 60, 30-50, 30-45, 30-40, 30-35, 35-60, 35-55, 35-50, 35-45, 35-40, 40-60, 40-55, 40-50, 40-45, or 45-60. As used herein, “RT” means room temperature and generally refers to the ambient temperature of the environment (e.g., the room or facility) in which the removal step is taking place. Generally, RT is about 15-25 °C, such as about 18 °C, about 20 °C, about 22 °C, about 18-22 °C, about 18-20 °C, or about 20-22 °C, depending on the room or facility. In some aspects, the primary etching step using HF is conducted at a temperature of RT to 50 °C, 20- 35 °C, or any other temperature disclosed herein, and the secondary etching step is conducted at a temperature of RT to 50 °C, or 25-40 °C, or any other amount disclosed herein.Atorney Docket No.: SP24-234

[0141] In some aspects, at least one of the primary etching step and the secondary etching step comprises any suitable time conditions when employing HF. For example, in some aspects, when employing HF, at least one of the primary etching step and the secondary etching step is conducted for a time period (min) of at least: 1, 5, 10, 20, 40, 60, 80, 100, or 120; alternatively, or additionally, when employing HF at least one of the primary etching step and the secondary etching step is conducted for a time period (min) of 120, 100, 80, 60, 40, 20, 10, 5, or 1 or less. In some aspects, the primary etching step employing HF is conducted for a time period of 1- 60 min, or 5-40 min, or any other time period disclosed herein, and the secondary etching step employing HF is conducted for a time period of 1-120 min, or 40-80 min, or any other time period disclosed herein.

[0142] In aspects, at least one of the primary etching step and the second etching step comprise any suitable composition conditions when employing a metal hydroxide. Such etching steps may utilize an etching solution not including HF. For example, in some aspects, at least one of the primary etching step and the secondary etching step employs a composition comprising a metal hydroxide (e.g., NaOH and / or KOH) in an amount (wt.%) of at least: 1, 2, 5, 10, 20, 30, 40, 50, 60, or 70, based on total weight of the composition; alternatively, or additionally, at least one of the primary etching step and the secondary etching step employs a composition comprising a metal hydroxide (e.g., NaOH and / or KOH) in an amount (wt.%) of 70, 60, 50, 40, 30, 20, 10, 5, 2, or 1 or less, based on total weight of the composition. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. For example, in some aspects, the amount (wt.%) of metal hydroxide (e.g., NaOH and / or KOH), based on total weight of the composition, can be 1-70, 1-60, 1-50, 1-40, 1-30, 1-20, 1-10, 1-50, 1-2, 2-70, 2-60, 2-50, 2-40, 2-30, 2-20, 2-10, 2-5, 5-70, 5-60, 5-50, 5-40, 5-30, 5-20, 5-10, 10- 70, 10-60, 10-50, 10-40, 10-30, 10-20, 20-70, 20-60, 20-50, 20-40, 20-30, 30-70, 30-60, 30-50, 30-40, 40-70, 40-60, 40-50, 50-70, 50-60, or 60-70. Each of the foregoing amounts can be used herein to refer to a single metal hydroxide, or to the total amount of metal hydroxide. In some aspects, the primary etching step employs a concentration of metal hydroxide that is lower than in the secondary etching step. In some aspects, the primary etching step comprises metal hydroxide in an amount of 1-50 wt.%, or 2-10 wt.%, or any other amount disclosed herein, and the secondary etching step comprises metal hydroxide in an amount of 10-70 wt.%, or 20-50 wt.%, or any other amount disclosed herein.

[0143] In some aspects, at least one of the primary etching step and the secondary etching step comprises any suitable temperature conditions when employing metal hydroxide (e.g., NaOH and / or KOH. For example, in some aspects, when employing metal hydroxide, at leastAtorney Docket No.: SP24-234 one of the primary etching step and the secondary etching step is conducted at a temperature (°C) of at least: RT, 20, 30, 40, 50, 70, 90, 110, 130, 150, or 165; alternatively, or additionally, when employing metal hydroxide at least one of the primary etching step and the secondary etching step is conducted at a temperature of 165, 150, 130, 110, 90, 70, 50, 40, 30, 20, or RT or less. For clarity, any two of the foregoing open-ended ranges can be combined to form a closed range. In some aspects, the primary etching step using metal hydroxide is conducted at a temperature of RT to 150 °C, 50-130 °C, or any other temperature disclosed herein, and the secondary etching step is conducted at a temperature of 70-165 °C, or 90-150 °C, or any other amount disclosed herein.

[0144] In some aspects, at least one of the primary etching step and the secondary etching step comprises any suitable time conditions when employing metal hydroxide (NaOH and / or KOH). For example, in some aspects, when employing metal hydroxide, at least one of the primary etching step and the secondary etching step is conducted for a time period (min) of at least: 1, 5, 10, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, or 240; alternatively, or additionally, when employing metal hydroxide at least one of the primary etching step and the secondary etching step is conducted for a time period (min) of 240, 220, 200, 180, 160, 140, 120, 100, 80, 60, 40, 20, 10, 5, or 1 or less. In some aspects, the primary etching step employing metal hydroxide is conducted for a time period of 1-120 min, or 40-140 min, or any other time period disclosed herein, and the secondary etching step employing metal hydroxide is conducted for a time period of 10-240 min, or 100-180 min, or any other time period disclosed herein.

[0145] FIG. 6 schematically depicts changes to the first major surface 18 that can result from the secondary etching step described herein. The top portion of FIG. 6 depicts a top surface of the substrate 12 after the primary etching step and removal of the resist layer and stop layer (if included). As shown, the substrate 12 comprises a first pinhole feature 600 and a second pinhole feature 602. The first and second pinhole features 600 and 602 may represent neighboring pinhole features in the patern determined during block 402 of the method 400. The first and second pinhole features 600 and 602 are depicted to each include a width W, a depth D, and a pitch P. The width W and the pitch P are determined by the openings in the resist layer and stop layer based on the patern for the pinhole features. The width W is a maximum lateral dimension of each feature in a direction parallel the x-y plane. The width W may be determined based on the size of the openings in the resist layer and stop layer (when included) based on the patern of pinhole features. As described herein, W is generally less than 8 pm, preferably less than 2 pm, and more preferably less than 1 pm.Atorney Docket No.: SP24-234

[0146] The pitch P is a lateral distance between geometric centers of first and second pinhole features 602 and 604 in a direction parallel the X-Y plane, and may be greater than the minimum center-to-center separation distance used to generate the patern for the pinhole features. The pitch P may vary depending on the referenced features that are adjacent to one another (i.e., the pitch P depend on the particular pair of pinhole features being measured). In aspects, the pitch P (pm) can be 5-50, 5-45, 5-40, 5-35, 5-30, 5-25, 5-20, 5-15, 5-10, 10-50, 10-45, 10-40, 10-35, 10-30, 10-25, 10-20, 10-15, 15-50, 15-45, 15-40, 15-35, 15-30, 15-25, 15- 20, 20-50, 20-45, 20-40, 20-35, 20-30, 20-25, 25-50, 25-45, 25-40, 25-35, 25-30, 30-50, 30-45, 30-40, 30-35, 35-50, 35-45, 35-40, 40-50, 40-45, or 45-50, depending on the adjacent features at which the pitch P is measured. The pitch P may also have an average value Pave in any of the preceding ranges.

[0147] The depth D of the pinhole features is determined by the etchant used in the primary etching step and the length of time of the primary etching step. It has been found that surface angle distributions exhibiting peaks at peak angles greater than 2° can be generated if the depth D is greater than or equal to 1.0 pm, and preferably greater than 1.5 pm and less than or equal to 10 pm. In aspects, it is preferable that D > W such that an aspect ratio A (DAV) of each pinhole feature formed in the primary etching step is greater than 1.0 and less than or equal to 5.0. In aspects, A of the pinhole features can be from 1.1 - 5.0, 1. 1-4.5, 1. 1-4.0, 1. 1-3.5, 1.1- 3.0, 1. 1-2.5, 1.1-2.0, or 1.0-2.5. It has been found that, due to mask adhesion and anisotropic etching, the pinhole features tend to exhibit a trapezoidal cross-sectional shape, where the feature gets narrower with increasing vertical distance from the top surface of the substrate 12. As a result the pinhole features have a botom width wb that is less than the width W.

[0148] As shown in the top portion of FIG. 6, the surface of the substrate 12 in which the first and second pinhole features 600 and 602 are formed is above the x-y plane of defining the first major surface 18 of the resultant article 10. After formation of the pinhole features, an entirety of the surface is etched in the secondary etching step. The secondary etching step is modelled to remove a series of spherical portions of the material of the substrate 12 at each point of contact between the substrate 12 and the secondary etchant used in the secondary etching step. In aspects, the secondary etching step is conducted until the botoms of at least two pinhole features merge so that the botoms of the pinhole features define a majority of the first major surface 18 of the article 10. The dashed circles 604a and 604b represent spheres of material removal during the secondary etching step originating from the botom comers of the first pinhole feature 600. The dashed circles 606a and 606b represent spheres of material removal during the secondary etching step originating from the botom comers of the secondAtorney Docket No.: SP24-234 pinhole feature 602. As shown, the spheres of material removal comprise a radius R, with R being proportional to the time period of the secondary etching step (R may increase approximately linearly with time in the secondary etching step).

[0149] It has been found that, to maximize the amax value exhibited by the region of the first major surface 18 of the article 10 formed from the first and second pinhole features 602 and 604, it is preferred if the secondary etching step be performed such that the circles 604a and 606a centered at the botom comers that are closer to one another just merge. That is, the secondary etching step should be performed so that D, R, and P satisfy the following relation:2D = 2R = P-D (1)For any two pinhole features satisfying the above relation, the amax value would be estimated to be approximately 90°. As shown in the botom portion of FIG. 6, a secondary etching step of such a length results in a lowering of the surface of the substrate 12 by about R, so that the first major surface 18 is formed to have a first surface feature 608 and a second surface feature 610, with each ofthe secondary surface features exhibiting an amax value of approximately 90°. If the secondary etching step continues beyond when the contours defining the first and second pinhole features 600 and 602 initially touch, the transition between the features will become further rounded and the steepest portions of the features will be removed. This will lower the Umax exhibited by the resultant features. This phenomenon is represented by the dashed line 612.

[0150] As shown in the botom portion of FIG. 6, the first surface feature 608 may have a first central portion 614 and the second surface feature 610 may have a second central portion 616. It has been found that the first and second central portions 614 and 616 may be planar if the pinhole features are too wide, especially if the secondary etching step is conducted just long enough for the features to coalesce. Such planar areas may lead to the textured region 20 exhibiting a relatively low aaVe value, which may tend to lead to a higher specular reflectance. Accordingly, for applications where it is desired to minimize specular reflectance, it is preferred to limit W of the pinhole features to less than or equal to 1.5 pm or, more preferably, to less than or equal to 1.0 pm (e.g., such that W is from 0.5 pm to 1.0 pm).

[0151] As described herein, the spacing between adjacent pinhole features is generally not constant to avoid color artifacts. As such, while a secondary etch step may cause some pairs of feature to exhibit the profile depicted in the botom portion of FIG. 6 in a certain direction, other pairs of pinhole features may not merge at all or may merge to a greater extent, causing reduced amax values for such features, and the textured region 20. Accordingly, in aspects, the patern for the plurality of pinhole features determined at block 402 of the method 400Atorney Docket No.: SP24-234 described herein may be designed so that the pitch P is consistent over the entire geometric area of the patern. For example, the plurality of pinhole features may exhibit an average pitch Pave and the patern for the plurality of pinhole features may exhibit a maximum pitch Pmax (a maximum center-to-center distance between two adjacent features) and a minimum pitch Pmin (a minimum center-to-center distance between two adjacent features), such that Pmax are both within 25% of Pave (i.e., (Pave - Pmin) < 0.25*Pave and (Pmax “ Pave) < 0.25*Pave). Such pitch consistency will tend to result in the surface features having higher amax values and tend to raise the ciave values exhibited by the textured region 20 by reducing planar regions. Consistent spacing of the pinhole features will also result in sharper peaks in the surface angle distribution exhibited by the textured region 20 at peak angles above 2°, as described herein.

[0152] FIGS. 7A and 7B demonstrate the effect of the length of the secondary etch step on the surface profde and surface angle distribution exhibited by the textured region 20. FIG. 7A includes a modelled surface height profile 700 and surface angle distribution 702 for a first example article and FIG. 7B includes a modelled surface height profile 704 and surface angle distribution 706 for a second example article. The example articles represented in FIGS. 7A and 7B are both based on the same patern of pinhole features. The patern is the patern described above with respect to FIG. 5A (circular pinhole features), with a minimum center- to-center separation distance 506 of 10 pm. FIG. 7A represents the article after a secondary etching step was conducted to remove 20 pm of material from the surface of the substrate 12 (i.e., so that R = 20 pm in FIG. 6). FIG. 7B represents the article after a secondary etching step was conducted to remove 50 pm of material from the surface of the substrate 12 (i.e., so that R = 50 pm in FIG. 6). As shown, the surface height profile 700 of the first examples includes regions 703 of substantially constant height at 20 pm below the starting point of the secondary etching step. The regions 703 may be plateaus that are planar in shape. The second example lacks such planar regions at 50 pm beneath the starting point of the secondary etching step, indicating that all of the pinhole features coalesced to a certain extent from the longer secondary etch.

[0153] This greater degree of coalescing caused by the longer secondary etching step results in a different surface angle distribution exhibited by each modelled example. As shown in FIG. 7A, the surface angle distribution 702 of the first example has a peak 705 at approximately 14.9°. As shown in FIG. 7B, the surface angle distribution 704 has a peak 707 at approximately 5.8°. The surface angle distribution 706 has a steeper drop off at angles higher than the peak 707 than the surface angle distribution 702. The longer secondary etching step dramaticallyAtorney Docket No.: SP24-234 reduces the aaveand maximum amax exhibited by the second example as compared to the first example. The first example will tend to exhibit a higher degree of diffractive scatering than the second example, leading to the first example exhibiting lower specular reflectance, but worse washout than the second example. This demonstrates how the secondary etching step can be used to control the surface angle distribution and surface shape (e.g., presence of planar portions) on the first major surface 18.

[0154] Referring now to FIG. 8, determining the WI value exhibited by an article will now be described in greater detail. The WI has been formulated to quantify the effects of glare events (e.g., exposure to sunlight) on the contrast and resolution of an incorporating display. Such a metric is useful to examine cover material performance for applications likely to be exposed to light from external light sources (e.g., automotive interior displays, outdoor displays). To quantify “washout,” a modulation transfer function (MTF) of an anti-glare surface is measured under various illumination conditions, and the average value of the MTF over a number of spatial frequencies is used to evaluate the effect of illumination conditions on display performance. The MTF at a particular spatial frequency f may be expressed aswhereand I(f)max and I(f)min are the maximum and minimum intensities of an input or an output modulation image at the spatial frequency f. In this expression, MFin represents the MF value associated with an input patern being emited through a sample cover material (without ambient light in a dark room). The MF0Ut value represents the MF value when the cover material is disposed over the input patern (e.g., from a display) and under the illumination condition being tested. Higher MTF values generally mean that the illumination condition has less of an effect on display performance (and therefore beter performance of the textured region of the cover material). In aspects, MTF values of greater than or equal to 0.60 (e.g., greater than or equal to 0.65, greater than or equal to 0.70, greater than or equal to 0.75 greater than or equal to 0.76, greater than or equal to 0.77, greater than or equal to 0.78, greater than or equal to 0.79, greater than or equal to 0.80, greater than or equal to 0.81, greater than or equal to 0.82, greater than or equal to 0.83, greater than or equal to 0.84, greater than or equal to 0.85, greater than or equal to 0.86, greater than or equal to 0.87, greater than or equal to 0.88, greater than or equal to 0.89, greater than or equal to 0.90, greaterthan or equal to 0.91, greaterthan or equal to 0.92, greater than or equal to 0.93, greater than or equal to 0.94, and greater than or equal toAtorney Docket No.: SP24-234 0.95) are preferred for a given illumination condition, indicating minimal degradation of display performance caused by exposure to the external light.

[0155] The WI value described herein may be computed using the following expression:That is, the WI value is 1 - an average value of the MTF value computed at paterns with five different spatial frequencies. Unless otherwise noted herein, the WI is computed by averaging the MTF value at paterns with spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm. Lower WI values are associated with superior washout performance (in that ambient light will tend to degrade display images less for cover materials exhibiting lower WI values).

[0156] FIG. 8 schematically depicts an apparatus 800 for measuring the washout effect. As shown, a sample 802 (e.g., corresponding to the substrate 12 described herein) is placed over a display 804. The sample 802 is positioned so that the textured region faces outward (not towards the display 804). As shown in the box 805 (which depicts a front view of the sample 802 and the display 804), the display 804 generates a plurality of target paterns 806 where the intensity of light emited by the display 804 varies with a particular spatial frequency fi. A plurality of first light sources 808 are distributed around the sample 802. The plurality of first light sources 808 (e.g., room lights) are configured to emit a relatively low intensity light to simulate the sample 802 encountering normal ambient conditions (e.g., room light). As reported herein, the plurality of first light sources 808 were configured to emit white light with 130 lux and a color temperature of 2100k) . A projection light source 810 is configured to emit a relatively high intensity light source to simulate sunlight illumination. The projection light source 810 is positioned such that light emited thereby is incident on the sample with an average angle of incidence 6i. In aspects, the projection light source 810 is movable or otherwise adjustable so as to change the angle of incidence 6i. In aspects, the projection light source 810 emits light over an emission area, such that light emited by the projection light source 810 is incident on the sample 802 at a range of angles of incidence 6i.

[0157] A camera 812 is positioned to receive light scatered from the sample 802. The camera is positioned such that light scattered from the sample 802 will enter the camera 812 at a viewing angle 6V(or range of viewing angles). In aspects, the camera 812 is movable or otherwise adjustable to change the viewing angle 6V. A computing system 814 receives an image generated by the camera 812 and analyzes the image to compute a plurality of MTF values for each of the plurality of target paterns 806 emited by the display 804. For each ofAtorney Docket No.: SP24-234 the target paterns 806, the computing system 814 may calculate an MTF value using Equations 2-3 and generate an output that measures the dependency of the MTF value on spatial frequency. The plurality of first light sources 808 and the projection light source 810 allow the MTF values to be measured under a plurality of different lighting conditions to determine the efficacy of the patern on the sample 802 in reducing washout. When just the first light sources 808 are emiting light, a “room light washout” effect can be measured . When both the first light sources 808 and the projection light source 810 are emiting light, a “sunlight washout” effect can be measured.

[0158] Such washout measurements may be particularly useful in evaluating the performance of cover materials for automotive interior displays. FIG. 9 shows a vehicle interior 1000 that includes three different vehicle interior systems 100, 200, 300, according to an exemplary embodiment. Vehicle interior 1000 includes a center console base 110 with a surface 120 including a display 130. Vehicle interior system 200 includes a dashboard base 210 with a surface 220 including a display 230. The dashboard base 210 typically includes an instrument panel 215 which may also include display 216. Vehicle interior system 300 includes a dashboard steering wheelbase 310 with a surface 320 and a display 330. In one or more aspects, the vehicle interior system may include a base that is an arm rest, a pillar, a seat back, a floorboard, a headrest, a door panel, or any portion of the interior of a vehicle that includes a surface. In aspects, the displays 130, 230, 330 are flat and comprise cover glass with planar major surfaces. In aspects, one or more of the displays 130, 230, 330 are curved, and the curved display may include curved cover glass that may be hot-formed or cold-formed to possess such curvature. Such cold-forming may involve any of the techniques described in U.S. Pre-Grant Publication No. 2019 / 0329531 Al, entitled “Laminating thin strengthened glass to curved molded plastic surface for decorative and display cover application,” U.S. Pre-Grant Publication No. 2019 / 0315648 Al, entitled “Cold-formed glass article and assembly process thereof,” U.S. Pre-Grant Publication No. 2019 / 0012033 Al, entitled “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 / 214,124, entitled “Curved glass constructions and methods for forming same,” which are hereby incorporated by reference in their entireties.

[0159] Various components of the vehicle interior 1000 may be subjected to illumination from various light sources. As depicted in FIG. 9, for example, a first ambient light source 900 may emit light that is transmited through a first side window of the vehicle and incident on the display 216 with at an angle of incidence On. The display 216 may be oriented such that light scatered at a particular scatering angle 6viwill enter the driver’s field of vision and distractAtorney Docket No.: SP24-234 the driver. A second ambient light source 902 may emit that is transmited through a second side window of the vehicle and incident on the display 130 with at an angle of incidence 0i2. The display 130 may be oriented such that light scatered at a particular scatering angle 0V2 will enter the driver’s field of vision and distract the driver. The first and second ambient light sources 900 and 902 may represent sunlight at various points in time. Indeed, the ISO 15002 / SA 1757 standards specify a first condition where 45k lux light (direct sunlight) is incident on the display 216 at an angle of 20° and scaters into the driver at a scattering angle of 0° (i.e., where On = 20° and 0vi= 0°, associated with the “washouti” metric herein) and a second condition where 45k lux light (direct sunlight) is incident on the display 130 at an angle of 45° and scaters into the driver at a scatering angle of 20° (i.e., where 0i2 = 45° and 0V2 = 20°, associated with the “washout2” metric herein). The apparatus 800 depicted in FIG. 8 enables such conditions to be tested for washout by varying the orientation of the sample 802 and adjusting the projection light source 810. Unless otherwise noted herein, WI values are providing in accordance with the conditions for the wahouti metric.

[0160] For the Examples described herein the configuration associated with the washouti was used to measure WI. 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 collimated LED light source (emiting 45000 lux white light) was used at the projection light source 810 (made by Mightex Systems, model of LCS-6500-65-22). A projection light source was used and positioned so as to emit light incident on the sample 802 at angles of incidence of 20°. The sample 802 and camera 812 were also mounted on a rotation stage so as to render the viewing angle 0Vand angle of incidence 0i adjustable for the two conditions. Lab room light was used as the first light sources 808 and was measured to have a luminance of 132 lux.

[0161] Referring now to FIG. 10, measurement of an RIVF exhibited by an article will now be described in greater detail. FIG. 10 schematically depicts an apparatus 1001 for measuring RIVF. As shown, a sample 1002 (e.g., corresponding to the article 10 described herein) is placed over a display 1004. The sample 1002 is positioned so that the textured region faces outward (not towards the display 1004). An illumination light source 1006 emits light towards an image patern 1008 (a square wave patern printed on a suitable substrate) with a luminance of 1000 lux and color temperature 5000k. Light from the illumination light source 1006 is directed by the image patern 1008 towards the sample 1002. The distance of the image patern center to the display center is 500mm. The textured region of the sample 1002 then directs the light towards a camera 1010 to generate the RIVF of the sample 1002. The distance of the camera lens to the center of the display is 400mm.Atomey Docket No.: SP24-234

[0162] The image patern 1008 is a square wave. The image generated by the camera 1010 can be computed having as a Fourier series, expressed aswith 2L being the period, A being the amplitude of the DC component, and 2B being the modulation depth. A and B are variables that change based on the sample 1002 being measured. Unless otherwise noted herein, RIVF is measured with an image patern 1008 having L = 13 mm (so that the square wave exhibits a period of 26 mm). Because the visibility of an image is relative to both image contrast and sharpness, the modulation depth of the reflected image bars is used to reflect the role of image contrast, and the amplitude profde of FFT components of the reflected image bars to evaluate the role of image sharpness. To minimize the impact of measurement conditions on measurement results and to eliminate the dependence of the RIVF on target patern, the modulation and sharpness transfer factors are used to quantitatively evaluate the degradations of contrast and sharpness due to an AG or AR surface, respectively.

[0163] The modulation depth (2B) can be computed aswhere, Imax and Imin are the maximum and minimum intensity of the intensity modulation of a square-wave image. The contrast degradation can then be computed by a modulation transfer factor (MTFr) which is defined aswhere, MD0Ut is the MD of the target patern reflected by the sample 1002, and MDinis the MD of the target patern reflected by an optical smooth surface (a substrate of the same material as the article 10, but without a textured region, such as an as-formed glass substrate from a fusion-draw process without surface treatments when the article is formed from a glass substrate a glass substrate). MTFris in the range of 0~l.

[0164] The sharpness degradation of reflected target image due to the textured region can be described by sharpness transfer factor (STFr) which is defined aswhere, SF0Ut is the sharpness factor (SF) of the target patern reflected by the sample 1002, SFm is the SF of the target patern reflected by an optical smooth surface. STFr is in the range of 0~l. The S Fin is calculated by summing the amplitudes of high odd order components (>3) of the input patern which is the target patern 1008 reflected by an optical smooth surface (a substrate of the same material as the article 10, but without a textured region, such as an as-Atorney Docket No.: SP24-234 formed glass substrate from a fusion-draw process without surface treatments when the article is formed from a glass substrate). The SF0Ut is calculated by summing the amplitudes of high odd order components (>3) of the output patern which is the image patern 1008 reflected by a sample under test.

[0165] The RIVF can then be computed by combining MTFrand STFrin the following expression:RIVF = c(MTFr)a+ (1 - c STFr(9) where c, a and are the weight factors which are determined by the contributions of image contrast and sharpness to the reflected image visibility, respectively. Factor c is in the range of 0 to 1. The factors c, a and Paxc calibrated by human perception study results. RIVF is in the range of 0~ 1 , the larger the RIVF, the more visible a reflected image is . Based on the perception studies it has been determined that the factors of c, a and fi can be chosen to be 0.33, 0.355, and 0.381, respectively. As may be appreciated, different aspects may exhibit similar RIVF values while one embodiment may exhibit a sharper reflected image with a lower modulation depth and another embodiment may exhibit a modulated image with a high modulation depth and a lower sharpness.Examples

[0166] Aspects of the present disclosure may further understood in view of the following examples.

[0167] Examples 1-7

[0168] Examples 1-7 each include textured regions formed using the method described herein. The textured regions were formed in substrates formed of Gorilla Glass® manufactured by Coming Incorporated (the composition of the substrate used for Examples 1-4 was different than that used for Examples 5-7). The Examples were formed using the method 400 described herein, using the patern depicted in FIG. 5 A for the pinhole features. The paterns utilized 2 pm pinhole feature size having a fill fraction of 0.5%. The etching steps varied in accordance with the Table A below.Table AAttorney Docket No.: SP24-234

[0169] Examples 1-4 were constructed using a minimum center-to-center separation distance of 20 pm. Surface height profiles and associated histograms for 200 pm by 200 pm portions ofthe textured regions for Examples 1, 2, 3, and 4 are shown in FIGS. 11A, 1 IB, 11C, and 1 ID, respectively. Surface angle distributions calculated from the surface height profiles for Examples 1-4 are shown in FIGS. 14A, 14B, 14C, and 14D. Examples 5-6 were constructed using a minimum center-to-center separation distance of 15 pm. Surface height profiles and associated histograms for -200 pm by -200 pm portions of the textured regions for Examples 5 and 6 are shown in FIGS. 12A-12B, respectively. Surface angle distributions calculated from the surface eight profiles from Examples 5-6 are shown in FIGS. 15A-15B. Example 7 was constructed using a minimum center-to-center separation distance of 10 pm. A surface height profile and associated histogram for a -200 pm by -200 pm portion of the textured region for Examples 7 is shown in FIG. 13. A surface angle distribution for the Example 7 calculated from the surface height profile is shown in FIG. 16. The surface angle distributions were calculated from a 1 mm by 1 mm area of the surfaces including the area used to generate the surface height profiles. Smaller areas of the surface height profiles are shown to render it easier to see the features.

[0170] As is revealed in FIGS. 11A-13, each of Examples 1-7 can be characterized in that the surface height histogram exhibits a relatively broad peak containing the median height. The peaks are broad in that they decrease to 50% of peak values at surface heights that are at least 0.3 pm from the height at which the peak values are exhibited on at least one side of the peak.Atorney Docket No.: SP24-234 Such broad peaks are indicative a high degree of feature rounding. As is revealed in FIGS 14A-17, each of Examples 1-7 can also be characterized in that the surface angle distribution exhibits a peak at a peak angle that is greater than 2° . Moreover, the peaks are relatively narrow in that only a single histogram bin (associated with a 1° range in the depicted examples) is at the peak value. The peaks can be further characterized in having relatively narrow widths, in that they each decrease 90% of the peak value at an angle that is no more than 1.8° from the peak angle on at least one side of the peak.

[0171] Examples 1-7 were measured for a variety of optical properties and surface angle distribution properties. Optical properties were measured with a Bruker Contour GT-X surface profder. . . . Surface measurement (e.g., Sq, Sdq, Rsm) values were calculated over a 1 mm by 1 mm field of view collected with a 50x objective and 0.55x zoom lens. Surface angle distributions and associated characteristics were calculated from the surface height profile measured with the interferometer. The results are listed in Table 1.Table 1Attorney Docket No.: SP24-234

[0172] Example 1 is considered an outlier because the surface height histogram contains a relatively large peak outside of the broad peak containing the median height. Examples 2-7 each exhibit Sq values in the range of 0.2 pm to 0.4 pm, Sdq values in the range of 0.05 pm to 0.2 pm, Wave values in a range from 3.5 ° to 11°, and maximum amax values in a range from 5.5° to 20°). The Rsm value exhibited by a particular example is -proportional to the minimum center-to-center separation distance used to determine the pattern of pinhole features. Regarding optical performance, all of Examples 2-7 each exhibit a PPDuo that is less than or equal to 2.5% (in a range from 1.7% to 2.5%) a coupled specular reflectance that is less than 2 GU (in a range from 0.4 GU to 1.75 GU), and a transmission haze that is greater than or equal to 7.5% (in a range from 7.8% to 55%). Indeed, Examples 2-7 exhibit a wide range of coupled DOI and transmittance haze values. Examples 3, 5, and 7 each exhibit relatively low DOI values (less than 40%, even less than 10%) and haze values that are greater than 10%. Examples 2 and 6 exhibit high haze (greater than 10%) and DOI (greater than 70%). Certain ones of the examples exhibits relatively low WI (less than 0.6) and RIVF (less than 0.5) values. It is believed that the low washout and haze values are attributable to the relatively low aaVe value exhibited by that surface.

[0173] Examples 8-20

[0174] Examples 8-20 each include textured regions formed using the method described herein. The textured regions were formed in substrates formed of Gorilla Glass® manufactured by Coming Incorporated. The Examples were formed using the method 400 described herein, using the pattern depicted in FIG. 5A for the pinhole features. The patterns utilized a varying feature size with a 20 pm minimum center-to-center separation distance. Examples 8-20 utilized the same pattern for pinhole features other than the pinhole feature size. The etching steps for each of Examples 8-20 was varied in accordance with the conditions described in the Table B below.Table BAttorney Docket No.: SP24-234

[0175] Surface angle distributions for a 1 mm x 1 mm area for Examples 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 are shown in FIGS. 17A, 17B, 17C, 17D, 17E, 17F, 17G, 17H, 171, 17J, 17K, 17L and 17M, respectively. The surface angle distributions were calculated from surface height profded measured with a Bruker Contour GT-X interferometer with a 5 Ox objective and 0.55x zoom lens over a 1 mm by 1 mm field of view. As shown, each of the surface angle distributions exhibits a peak at a peak angle greater than 2°. The peaks can be further characterized in having relatively narrow widths, in that they each decrease 90% of the peak value at an angle that is no more than 1.5° from the peak angle on at least one side of the peak.

[0176] The surface angle distributions of other comparative surfaces were also measured. FIGS. 19A and 19B depict surface angle distributions measured for Comparative Examples 1 and 2. Comparative examples 1 and 2 were formed having a two-height surface distributions, using the method described in International Patent Application No. PCT / US2023 / 035747, entitled “ARTICLES WITH ANTI-GLARE SURFACES EXHIBITING LOW SPARKLE WITH MINIMAL COLOR ARTIFACTS,” filed on October 24, 2023, hereby incorporated by reference in its entirety (described herein as a “binary surface”). Surface angle distributions for Comparative Examples 1-2 are shown in FIGS. 19A and 19B. Comparative Examples 3 and 4 were formed having two-height surface distributions, but with feature rounding using the methods described in U.S. Provisional Patent Application No. 63 / 542,398, entitled “ARTICLES WITH ANTI-GLARE SURFACES WITH SLOPED TRANSITION SURFACES AND ASSOCIATED METHODS,” filed on October 4, 2023, and hereby incorporated by reference in its entirety (described herein as “rounded binary surfaces”). Surface angle distributions for Comparative Examples 3-4 are shown in FIGS. 19C and 19D.Atorney Docket No.: SP24-234 Comparative Examples 5-6 were formed using a sandblast-and-etch process. Surface angle distributions for Comparative Examples 3-4 are shown in FIGS. 19E and 19F.

[0177] As shown, Examples 8-20 differ from Comparative Examples 1-4 in that the surface angle distributions of Comparative Examples 1-4 do not exhibit a peak at a peak angle greater than or equal to 2°. Examples 9-21 differ from Comparative Examples 5-6 in that Comparative Examples 5-6 exhibit much broader peaks that do not drop off as fast as those of Examples 9- 21. Indeed, as shown in FIGS. 19E-19F, the surface angles associated with Comparative Examples 5-6 do not decline to less than 90% of their peak values until angles that differ from the peak angle by more than 2° are reached. Such broad peaks are associated with the random feature shapes generated in sandblasting and etching that are less controlled than the processes described herein.

[0178] Each of Examples 8-20 and Comparative Examples 1-6 were also measured for various optical performance and surface angle distribution characteristics. Surface measurements (e.g., Sq, Sdq, Rsm) values were taken with a Bruker Contour GT-X interferometer with a 50x objective and 0.55x zoom lens over a 1 mm by 1 mm field of view. Surface angle distributions and associated characteristics were calculated from the surface height profile measured with the interferometer. Optical performance measurements without units are in gloss units. Surface angle distributions measurements are in degrees. Surface height profile measurements (e.g., Rsm, Sq) are provided in pm. The results are provided in Tables 2-3 below.Table 2Attorney Docket No.: SP24-234Table 3

[0179] As shown, in terms of surface height profile, there are several differences between Examples 8-20 and Comparative Examples 1-6. Examples 8-20 have Rsm values lying withinAtorney Docket No.: SP24-234 a range of 27 pm to 32 pm, whereas comparative examples 1-6 have Rsm values of less than 0.05 pm. Such a difference is indicative of the feature spacing to provide the surface angle distributions described herein. Moreover, it can be seen that Examples 8-20 have Sq values that are at least 0.1 pm, whereas each of Comparative Examples 1-4 have Sq values that are less than 0.1 pm. This is indicative of the relatively deep surface features formed via the methods described herein. Examples 8-20 also tend to have relatively low Sdq values (from 0.01 to 0.1) as compared to Examples 1-7 (at least those of Examples 1-7 not having WI and RIVF values less than 0.6).

[0180] In terms optical performance, Examples 8-20 performed beter from a sparkle perspective than Comparative Examples 5-6. Each of examples 8-20 exhibited a PPDuo value of less than 3% (in a range from 1.46% to 2.9%), while Comparative Examples 5-6 each exhibited PPD o values of greater than 4.5%. Certain ones of Examples 8-20 (e.g., Examples 9 and 11-21) exhibited a relatively high coupled DOI of greater than 70%, while Comparative Examples 5-6 were relatively low DOI (less than 40%). However, Examples 9 and 11-21 each exhibited a relatively low haze of less than 10%, whereas Comparative Examples 5-6 each exhibited a haze of greater than 20%.

[0181] It has been further demonstrated that the Examples herein demonstrate superior performance in terms of a combination of WI, RIVF and PPD as compared to existing articles. RIVF, WI, and sparkle were measured for various examples formed from the same process described herein with respect to Examples 8-20, as well as comparative examples with a binary surface structure and sandblasted surfaces. FIG. 20 is a plot of WI as a function of RIVF value for the samples measured. The size of the circle of each ploted point indicates the PPDuo value. The circle 2000 indicates a PPDuo value of 2%. Circles that are larger than the circle 2000 have a higher PPD, 40 value. As shown, on the Examples according to the present disclosure exhibit a WI and RIVF that are each less than 0.5. The Examples exhibit such combinations of RIVF and WI values while also exhibiting PPD140 values that are less than 3%.

[0182] Bidirectional Scatering Distribution Function (BSDF) measurements were taken for the Examples represented in FIG. 20. Measurements were taken in reflection mode using the REFLET 1802S system from Synopsys, Inc. The measurement wavelength range (i.e., spectral range of light source of scatered light) was from 400 nm to 1700 nm with light at an incident angle of 20°. The BSDF intensity is measured at 20° by averaging the reflection scatering measured at 0 deg (+ / - 5°) - to compute a BSDF200value. This value was ploted as function of the WI value described herein. As shown, each of the Examples exhibiting a WI value ofAtorney Docket No.: SP24-234 less than 0.5 also exhibited a BSDF200of less than 0.02. This demonstrates a correlation between the BSDF200value and the WI value for the Examples described herein.

[0183] As is demonstrated from Examples 1-20 herein, a wide variety of combinations of optical performance atributes can be achieved via the articles fabricated via the methods described herein. Each of Examples 1-20 exhibited a PPDuo value of less than 3%. As is revealed by Examples 1-7, 8, and 10, when the textured region 20 is formed so as to exhibit a surface angle distribution with an average surface angle that is greater than or equal to 3'° and a Sq value that is greater than or equal to 0.2, the textured region 20, may exhibit a coupled specular reflectance that is less than or equal to 2 GU. Such examples exhibiting a low specular reflectance exhibited amaxvalues that are greater than or equal to 7°. Some of such Examples (Examples 2, 3, 4, 8, and 10) further exhibited WI values of less than 0.6 and RIVF values of less than 0.5 when, for these Examples, the Sq value was maintained to less than or equal to 0.3. Moreover, such examples exhibiting a particularly low coupled specular reflectance can exhibit a large range of haze and DOI values. Examples, 2, 3, 6, 8, and 10 each exhibited a transmission haze greater than or equal to 10% and less than or equal to 30%. Examples 3, 8, and 10 further exhibited a coupled DOI that is less than or equal to 40%.

[0184] As is revealed by Examples 3, 4, and 8-20, when the textured region is formed so as to exhibit a Sdq value that is greater than or equal to 0.01 and less than or equal to 0.15, the textured region may exhibit WI and RIVF values that are both less than 0.5. Such examples may exhibit a aavevalue that is greater than or equal to 1.5° and less than or equal to 6.5° so as to exhibit RIVF and WI values that are both less than 0.48. Some of such Examples (Examples 4, 9, 11, 12, 13, 14, 15, 17, 18, 19, and 20) further exhibited such performance while also exhibiting a relatively low transmission haze that is greater than or equal to 1% and less than or equal to 10% by exhibiting relatively low aaveor amaxvalues.* * *

[0185] Embodiments of the present disclosure may be further understood in view of the following information.

[0186] Certain ones of the Examples described herein can be characterized by the percentage of the surface area in the textured region 20 that is associated with a surface angle a that is less than 0.5°. It has been observed that there is a strong correlation between specular reflectance and RIVF performance and a limited percentage of the surface area of the textured region 20 being associated with a surface angle a less than 0.5°. As used herein, the term “flat area” is used to represent the surface area percentage of the textured region 20 having a surface angle a of less than 0.5°. In particular, articles exhibiting a flat area that is less than 3% have beenAtorney Docket No.: SP24-234 found to exhibit a favorable combination of specular reflectance and RIVF performance. As shown in Table 1, examples 2-7 each exhibit a flat area of less than 3%. As described herein, each of Examples 2-7 exhibit a coupled specular reflectance of less than 2 GU. As shown in Table 2, each of Examples 8 and 10 also exhibit a flat area of less than 3% and coupled specular reflectance of less than 2. Moreover, it was found that, for the examples using the pinhole paterns to form the Examples 1-20, that only those examples exhibiting a flat area of less than 3% exhibited a RIVF of less than 0.25. As such, examples exhibiting a flat area of less than 3% were found to be capable of exhibiting a coupled specular reflectance of less than 2 GU and a RIVF of less than 0.25.

[0187] As shown in Table 3, the flat area is markedly different for the Comparative Examples 1-4 than the Examples 1-20. Indeed, Comparative Examples 1-4 each have a flat area of more than 65%. These results are indicative of the reduced degree of feature rounding produced by the approaches for forming the textured regions in those counter examples. As shown, each of Counter Examples 1-4 exhibited a coupled specular reflectance of above 8 GU .

[0188] The textured region 20 can be further characterized by a set of Q-fold ordering parameters. These Q-fold ordering parameters vary in value depending on the particular location at which they are measured in the textured region 20. Particularly, the Q-fold ordering parameter is calculated by determining geometric centers of each one of the plurality of surface features 26. The geometric center of a particular one of the plurality of surface features 26 is a pair of coordinates in the X-Y plane centered within the external boundary of the particular one of the plurality of surface features 26. The Q-fold ordering parameter can also be calculated based on the patern for the plurality of pinhole features used to fabricate the particular textured region 20 being analyzed (the center of a pinhole feature should correspond to a center of a surface feature). The Q-fold ordering parameter at a particular point in the textured region 20 can be calculated by varying the value Q, with Q being an integer of at least 2, and determining the number of nearest neighbors used to determine the value of the parameter at the particular point. To calculate the Q-fold ordering parameter, at each point in the textured region 20, the Q nearest neighbors are identified and lines are drawn that connect the analyzed point to the geometric centers of the nearest surface features. Angles between each of these lines and an arbitrary reference line (e.g., in the Y-direction) are then calculated. These angles are then input into the following equationAtorney Docket No.: SP24-234 where H is the Q-fold ordering parameter, Q is the ordering parameter determining the number of nearest neighbors used in the calculation, and ak are the angles that the lines connecting the analyzed point to the geometric centers of the nearest neighbors make with the arbitrary reference line. In aspects, the value H can be computed at each geometric center of each one of the plurality of surface features 26 (excluding those truncated at the edge of the textured region 20, if any truncated features are present) to generate a series of H values that are placed in a histogram. The histogram quantifies a degree of randomness in the arrangement of the plurality of surface features 26. H values range between 0 and 1, with 1 indicating the highest degree of ordering.

[0189] A number of Q-fold ordering parameter histograms were generated from samples fabricated via the methods described herein. Histograms for 2-fold, 3-fold, 4-fold, 5-fold, and 6-fold ordering parameters were generated. A first sample (“LIO”) characterized in this manner was formed with a pinhole feature design comparable to Example 7 (with a minimum center-to-center separation distance of 10 pm). A second sample (“LI 5”) characterized in this manner was consistent with Example 6 herein. A third sample (“L20”) characterized in this manner was consistent with Example 3 herein. Finally, a comparative example formed an existing nanotexturing process was also characterized. The results are shown in FIGS. 21A- 21E. Each of LIO, 15, and L20 were formed using the same patern of pinhole features (but with different feature sizes and / or spacing), the results labelled “design” are calculated from the patern of pinhole features (e.g., prior to secondary etching) rather than a formed textured region. One thing to note about the results is that none of the histograms of 2-fold, 3-fold, 4- fold, 5 -fold, and 6-fold ordering parameter histograms for the samples fabricated in accordance with the present disclosure exhibits a distinct peak at ordering parameter values above 0.7. This is indicative of the lack of ordering the features described herein.

[0190] FIG. 21 A plots the results for the 2-fold ordering parameter. As shown, the samples fabricated in accordance with the methods described herein each exhibit a peak in the 2-fold ordering parameter histogram at a value less than 0.5, while the counter example exhibits a peak near unity, indicating that the counter example exhibits a relatively high degree of 2-fold ordering. FIG. 2 IB plots the results for the 3-fold ordering parameter. As shown, the samples fabricated according to the present disclosure exhibit histograms having a sharper peak at a value of about 0.3 than do the comparative example, which exhibits a greater proportion of the surface having ordering above the peak than do the samples fabricated in accordance with the present disclosure. The peaks associated with the design herein are sharp in that the ordering parameter drops to less than 50% of the value at the peak at ordering parameters within 0.05Atorney Docket No.: SP24-234 of the value at which the peak is exhibited. FIG. 21C plots the results for the 4-fold ordering parameter. As shown, the samples fabricated according to the present disclosure exhibit histograms with a sharp peak at a value of about 0.25, while the comparative example does not exhibit a distinctive peak between 0.2 and 0.4. FIG. 2 ID plots the results for the 5-fold ordering parameter. As shown, the samples fabricated according to the present disclosure exhibit histograms that are asymmetrically shaped about the value 0.5, with the 5-fold ordering parameters having a value between 0.5 and 0.8 constituting a greater percentage of the textured region (i.e., have a higher average number of counts) than 5-fold ordering parameters between 0.2 and 0.5, whereas the counter example has a histogram with the opposite asymmetry. FIG. 2 IE plots the results for the 6-fold ordering parameter. As shown, the counter example histogram exhibits a higher degree of asymmetry about the 6-fold ordering parameter value of 0.5. Put differently, the counter example exhibits a peak at a 6-fold ordering parameter value of about 0.3, such that a majority of the surface is associated with a 6-fold ordering parameter of less than 0.4. The samples fabricated in accordance with the present disclosure, in contrast, do not exhibit such a peak below 0.4, such that a majority of those surfaces is associated with a 6-fold ordering parameter above 0.4.

[0191] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not actually recite an order to be followed by its steps or it is not otherwise specifically stated in the claims or descriptions that the steps are to be limited to a specific order, it is in no way intended that any particular order be inferred. In addition, as used herein, “a” is intended to comprise one or more than one component or element and is not intended to be construed as meaning only one.

[0192] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit or scope of the disclosed aspects. Since modifications, combinations, sub-combinations and variations of the disclosed aspects incorporating the spirit and substance of the aspects may occur to persons skilled in the art, the disclosed aspects should be construed to comprise everything within the scope of the appended claims and their equivalents.

Claims

Attorney Docket No.: SP24-234ClaimsWhat is claimed is:

1. An article comprising: a substrate comprising: a first major surface; and a second major surface opposing the first major surface, a textured region formed in the first major surface, wherein, within the textured region, the first major surface comprises a plurality of surface features that are depressions in the first major surface where a height of the first major surface decreases with lateral distance from local peaks in the first major surface, wherein: the textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, the surface angle distribution decreases to 90% of the peak at an angle within 1.8° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 pm, and the textured region exhibits a Rsm value that is greater than or equal to 5 pm and less than or equal to 100 pm.

2. The article of claim 1, wherein the surface angle distribution exhibits an average surface angle that is greater than or equal to 1.5°.

3. The article of any of claims 1-2, wherein the surface angle distribution exhibits a maximum surface angle that is greater than or equal to 5°.

4. The article of any of claims 1-3, wherein the textured surface region exhibits a PPDuo that is less than or equal to 3.0%.

5. The article of any of claims 1-4, wherein the textured surface region exhibits a coupled specular reflectance that is less than or equal to 6 GU.Atorney Docket No.: SP24-2346. The article of any of claims 1-5, wherein the textured surface region exhibits corrected color shifts AC„. and ACV t. that are each respectively within a range of 0.0 to 0.5.

7. The article of any of claims 1-6, wherein the plurality of surface features each comprise contours of constant surface height that exhibit at least one of a circular shape, a square shape, a polygon shape, a hexagonal shape, and an elliptical shape, in a plan view of the first major surface.

8. The article of claim 7, wherein all of the plurality of surface features comprise contours having a circular shape.

9. The article of claim 7, wherein different ones of the plurality of surface features comprise contours exhibiting different shapes.

10. The article of claim 9, wherein a first portion of the plurality of surface features comprise contours exhibiting a circular shape and a second portion of the plurality of surface features comprise contours exhibiting an elliptical shape.

11. The article of any of claims 1-10, wherein geometric centers of the plurality of surface features exhibit a random distribution throughout the textured region.

12. The article of any of claims 1-11, wherein the textured region is devoid of planar portions at a constant surface height.

13. The article of any of claims 1-11, wherein the textured region comprises planar portions separating at least some of the plurality of surface features.

14. The article of claim 13, wherein the planar portions make up less than 10% of a surface area of the textured region.

15. The article of any of claims 1-14, wherein: the surface angle distribution exhibits an average surface angle that is greater than or equal to 3°,Attorney Docket No.: SP24-234 the textured region exhibits a Sq value that is greater than or equal to 0.2, and the textured region exhibits a coupled specular reflectance that is less than or equal to 2 GU.

16. The article of claim 15, wherein a washout index calculated via a first average modulation transfer function of the textured region that is 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 less than 0.6 when the article is viewed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an angle of incidence of 20°.

17. The article of claim 16, wherein the textured region exhibits a reflected image visibility factor that is less than or equal to 0.5, the reflected image visibility factors being computed asRIVF = 0.33 * (MTFr)0 355+ (1 - 0.33) ST Fr)0381where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image pattern is directed towards the textured region, the square wave image pattern having a period of 26 mm.

18. The article of claim 15, wherein the textured region exhibits a transmission haze that is greater than or equal to 7.5% and less than or equal to 55%.

19. The article of claim 18, wherein: the transmission haze is greater than or equal to 10% and less than or equal to 30%, the textured region exhibits a coupled DOI that is less than or equal to 40%.

20. The article of any of claims 15-19, wherein the surface angle distribution exhibits a maximum surface angle that is greater than or equal to 7.0°.

21. The article of any of claims 1-14, wherein: the surface angle distribution decreases to 90% of the peak at an angle within 1.5° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sdq value that is greater than or equal to 0.01 and less than or equal to 0.15, a washout index calculated via a first average modulation transfer function of the textured region that is averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33Atorney Docket No.: SP24-234 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is less than 0.5 when the article is viewed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an angle of incidence of 20°, and the textured region exhibits a reflected image visibility factor that is less than or equal to 0.5, the reflected image visibility factor being computed asRIVF = 0.33 * (MTFr)0 355+ (1 - 0.33) ST Fr)0381where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image patern is directed towards the textured region, the square wave image patern having a period of 26 mm.

22. The article of claim 21, wherein the surface angle distribution exhibits an average surface angle that is greater than or equal to 1.5° and less than or equal to 5°.

23. The article of any of claims 21-22, wherein the textured region exhibits a transmission haze that is greater than or equal to 1% and less than or equal to 10%.

24. The article of any of claims 1-23, wherein less than 3% of the textured region exhibits a surface angle that is less than 0.5°.

25. The article according to any of claims 1-24, wherein the textured region exhibits histograms of 2-fold, 3 -fold, 4-fold, 5 -fold, and 6-fold ordering parameters, wherein none of the histograms of 2-fold, 3 -fold, 4-fold, 5 -fold, and 6-fold ordering parameters exhibits a distinct peak at an ordering parameter value above 0.7.

26. The article of any of claims 1-25, wherein at least one of: the textured region exhibits a histogram of 2-fold ordering parameters exhibiting a peak at a value of less than 0.5, the textured region exhibits a histogram of 3 -fold ordering parameters exhibiting a ordering peak at a 3-fold ordering peak value between 0.2 and 0.4, wherein the histogram drops to less than 50% of the ordering peak at values within 0.05 of the 3-fold ordering peak value, the textured region exhibits a histogram of 4-fold ordering parameters exhibiting a ordering peak at a 4-fold ordering peak value between 0.2 and 0.4,Atorney Docket No.: SP24-234 the textured region exhibits a histogram of 5 -fold ordering parameters exhibiting a higher average over a first range of 5-fold ordering parameters from 0.5 to 0.8 than a second range of 5-fold ordering parameters from 0.2 to 0.5, and the textured region exhibits a histogram of 6-fold ordering parameters indicating that a majority of the textured region exhibits a 6-fold ordering parameter above 0.4.

27. A method of forming a textured region on a first major surface of a substrate for an article, the method comprising: determining a patern for a plurality of pinhole features, wherein the plurality of pinhole features in the patern exhibit a maximum feature size that is less than 2 pm and a pinhole feature fill fraction that is less than or equal to 5% of a surface area of the textured region, disposing one or more etching masks on the first major surface that allow etching only on select regions of the first major surface for forming the plurality of pinhole features, performing a primary etching step using one or more etchants to form the plurality of pinhole features in the first major surfaces based on the patern, wherein the plurality of pinhole features have a depth D of at least 1 pm following the primary etching step; and performing a secondary etching step by applying a secondary etchant to an entirety of the textured region to form a plurality of surface features in the textured region, wherein, after the secondary etching step: the textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, the surface angle distribution decreases to 90% of the peak at an angle within 1.8° of the peak angle on at least one side of the peak angle, the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 pm, and the textured region exhibits a Rsm value that is greater than or equal to 5 pm and less than or equal to 100 pm.

28. The method of claim 27, wherein the secondary etching step is performed so as to remove at least 5 pm of the material substrate from the first major surface within the textured region.

29. The method of any of claims 27-28, wherein the maximum feature size is in a range from 0.5 pm to 1.5 pm.Attorney Docket No.: SP24-23430. The method of any of claims 27-29, wherein determining the pattern comprises calculating positions of geometric centers of the plurality of pinhole features using a spacing distribution algorithm to randomly distribute the plurality of pinhole features throughout the textured region.

31. The method of any of claims 27-30, wherein, in the pattern, each of the plurality of pinhole features comprise the same peripheral shape and size.

32. The method of any of claims 27-31, wherein, in the pattern, the plurality of pinhole features differ from one another in at least one of size and peripheral shape.

33. The method of any of claims 27-32, wherein at least one of the primary etching step and secondary etching step employs an etching solution comprising HF.

34. The method of any of claims 27-33, wherein at least one of the primary etching step and secondary etching step employs a metal hydroxide and not HF.

35. The method of any of claims 27-34, wherein: in the pattern, the plurality of pinhole features exhibit a pitch P that is a lateral distance between geometric centers of adjacent ones of the plurality of pinhole features, and an average value of the pitch is greater than or equal to 5 pm and less than or equal to 50 pm.

36. The method of claim 35, wherein: the secondary etch step is performed so that a removal depth R of material is removed from the first major surface, for at least some of the plurality of features, 2*R is within 10% of the quantity (P - D).

37. An article comprising: a substrate comprising: a first major surface; and a second major surface opposing the first major surface,Atorney Docket No.: SP24-234 a textured region formed in the first major surface, wherein, within the textured region, the first major surface comprises a plurality of surface features that are depressions in the first major surface where a height of the first major surface decreases with lateral distance from local peaks in the first major surface, wherein: the textured region exhibits a Sq value that is greater than or equal to 0. 1 pm and less than or equal to 0.6 pm, and the textured region exhibits a Rsm value that is greater than or equal to 5 pm and less than or equal to 100 pm, less than 3% of the textured region exhibits a surface angle that is less than 0.5°, the textured region exhibits a reflected image visibility factor that is less than or equal to 0.25, the reflected image visibility factors being computed asRIVF = 0.33 * (MTFr)0 355+ (1 - 0.33) ST Fr)0381where MTFrand STFrare respectively the modulation transfer factor and the sharpness transfer factor associated with the textured region when a square wave image patern is directed towards the textured region, the square wave image patern having a period of 26 mm, and the textured region exhibits a coupled specular reflectance that is less than or equal to 2 GU.

38. The article of claim 37, wherein the textured region exhibits a surface angle distribution comprising a peak at a peak angle greater than 2°, wherein the surface angle distribution decreases to 90% of the peak at an angle within 1.8° of the peak angle on at least one side of the peak angle.

39. The article according to any of claims 37-38, wherein the textured region exhibits histograms of 2-fold, 3 -fold, 4-fold, 5 -fold, and 6-fold ordering parameters, wherein none of the histograms of 2-fold, 3 -fold, 4-fold, 5 -fold, and 6-fold ordering parameters exhibits a distinct peak at an ordering parameter value above 0.7.Attorney Docket No.: SP24-23440. The article of any of claims 37-39, wherein at least one of: the textured region exhibits a histogram of 2-fold ordering parameters exhibiting a peak at a value of less than 0.5, the textured region exhibits a histogram of 3 -fold ordering parameters exhibiting a ordering peak at a 3-fold ordering peak value between 0.2 and 0.4, wherein the histogram drops to less than 50% of the ordering peak at values within 0.05 of the 3-fold ordering peak value, the textured region exhibits a histogram of 4-fold ordering parameters exhibiting a ordering peak at a 4-fold ordering peak value between 0.2 and 0.4, the textured region exhibits a histogram of 5 -fold ordering parameters exhibiting a higher average over a first range of 5-fold ordering parameters from 0.5 to 0.8 than a second range of 5-fold ordering parameters from 0.2 to 0.5, and the textured region exhibits a histogram of 6-fold ordering parameters indicating that a majority of the textured region exhibits a 6-fold ordering parameter above 0.4.

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