WO2022011073A1

WO2022011073A1 - Anti-glare substrate for a display article including a textured region with primary surface features and secondary surface features imparting a surface roughness that increases surface scattering

Info

Publication number: WO2022011073A1
Application number: PCT/US2021/040775
Authority: WO
Inventors: Jiangwei Feng; Corinne Elizabeth ISAAC; Shenping Li; Wageesha Senaratne; William Allen Wood
Original assignee: Corning Inc
Current assignee: Corning Inc
Priority date: 2020-07-09
Filing date: 2021-07-08
Publication date: 2022-01-13
Anticipated expiration: 2023-01-09
Also published as: TW202217364A; US12352924B2; WO2022011072A1; TWI885182B; WO2022011073A9; US20220011467A1; US20220009824A1; JP2023534198A; KR102816633B1; EP4178924B1; EP4178925A1; WO2022011070A1; CN116113610B; EP4375255A2; CN115843290A; TW202217422A; CN116113610A; US20250035820A1; US20220011466A1; CN120928487A

Abstract

A substrate for a display article is described herein that includes (a) a primary surface; and (b) a textured region on at least a portion of the primary surface; the textured region comprising: (i) primary surface features, each comprising a perimeter parallel to a base-plane extending through the substrate disposed below the textured region, wherein the perimeter of each of the primary surface features comprises a longest dimension of at least 5 µm; and (ii) one or more sections each comprising secondary surface features having a surface roughness (Ra) within a range of 5 nm to 100 nm. In some instances, an arrangement of the surface features reflect a random distribution. A method of forming the same is disclosed.

Description

ANTI‐GLARE SUBSTRATE FOR A DISPLAY ARTICLE INCLUDING A TEXTURED REGION WITH PRIMARY SURFACE FEATURES AND SECONDARY SURFACE FEATURES IMPARTING A SURFACE ROUGHNESS THAT INCREASES SURFACE SCATTERING CLAIM OF PRIORITY [0001] This Application claims the benefit of priority to U.S. Provisional Application No. 63/049,843, filed 09 July 2021, the content of which is incorporated herein by reference in its entirety. CROSS‐REFERENCE TO RELATED APPLICATIONS [0002] The present application relates to, but does not claim priority to, commonly owned and assigned U.S. Patent Application Serial No. __________ (D31977), entitled “TEXTURED REGION TO REDUCE SPECULAR REFLECTANCE INCLUDING A LOW REFRACTIVE INDEX SUBSTRATE WITH HIGHER ELEVATED SURFACES AND LOWER ELEVATED SURFACES AND A HIGH REFRACTIVE INDEX MATERIAL DISPOSED ON THE LOWER ELEVATED SURFACES” and filed on ______________; U.S. Patent Application Serial No. __________ (D32630/32632), 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” and filed on __________; U.S. Patent Application Serial No. __________ (D32647), entitled “DISPLAY ARTICLES WITH DIFFRACTIVE, ANTIGLARE SURFACES AND THIN, DURABLE ANTIREFLECTION COATINGS” and filed on __________; and U.S. Patent Application Serial No. __________ (D32623), entitled “DISPLAY ARTICLES WITH DIFFRACTIVE, ANTIGLARE SURFACES AND THIN, DURABLE ANTIREFLECTION COATINGS” and filed on __________. The entire disclosures of each of the foregoing U.S. patent applications, publications and patent documents are incorporated herein by reference. FIELD OF INVENTION [0003] The disclosure relates to an anti‐glare substrate for display articles where the anti‐glare substrate includes a textured region with primary surface features and secondary surface features imparting a surface roughness that increases surface scattering. BACKGROUND [0004] Substrates transparent to visible light are utilized to cover displays of display articles. Such display articles include smart phones, tablets, televisions, computer monitors, and the like. The displays are often liquid crystal displays, 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. [0005] The substrate reflecting ambient light, especially specular reflection, reduces the ability of the user to view the display through the substrate. Specular reflection in this context is the mirror‐like reflection of ambient light off the substrate. For example, the substrate may reflect visible light reflecting off or emitted by an object in the environment around the device. The visible light reflecting off the substrate reduces the contrast of the light from the display transmitting to the eyes of the user through the substrate. At some viewing angles, instead of seeing the visible light that the display emits, the user sees a specularly reflected image. Thus, attempts have been made to reduce specular reflection of visible ambient light off of the substrate. [0006] Attempts have been made to reduce specular reflection off of the substrate by texturing the reflecting surface of the substrate. The resulting surface is sometimes referred to as an "antiglare surface." For examples, sandblasting and liquid etching the surface of the substrate can texture the surface, which generally causes the surface to reflect ambient light diffusely rather than specularly. Diffuse reflection generally means that the surface still reflects the same ambient light but the texture of the reflecting surface scatters the light upon reflection. The more diffuse reflection interferes less with the ability of the user to see the visible light that the display emits. [0007] Such methods of texturing (i.e., sandblasting and liquid etching) generate features on the surface with imprecise and unrepeatable geometry (the features provide the texture). The geometry of the textured surface of one substrate formed via sandblasting or liquid etching can never be the same as the geometry of the textured surface of another substrate formed via sandblasting or liquid etching. Commonly, only a statistical quantification of the surface roughness (i.e., R_a) of the textured surface of the substrate is a repeatable target of the texturing. [0008] There are a variety of metrics by which the quality of the "antiglare" surface is judged. Those metrics include (1) the distinctness‐of‐image, (2) pixel power deviation, (3) apparent Moiré interference fringes, (4) transmission haze, (5) specular reflection, and (6) reflection color artifacts. Distinctness‐of‐image, which more aptly might be referred to as distinctness‐of‐ reflected‐image, is a measure of how distinct an image reflecting off the surface appears. The lower the distinctness‐of‐image, the more the textured surface is diffusely reflecting rather than specularly reflecting. Surface features can magnify various pixels of the display, which distorts the image that the user views. Pixel power deviation, also referred to as "sparkle," is a quantification of such an effect. The lower the pixel power deviation the better. Moiré interference fringes are large scale interference patterns, which, if visible, distort the image that the user sees. Preferably, the textured surface produces no apparent Moiré interference fringes. Transmission haze is a measure of how much the textured surface is diffusing the visible light that the display emitted upon transmitting through the substrate. The greater the transmission haze, the less sharp the display appears (i.e., lowered apparent resolution). Specular reflection reduction is again a measure of how much of the reflected ambient light off the textured surface is specular. The lower the better. Reflection color artifacts are a sort of chromatic aberration where the textured surface diffracts light upon reflection as a function of wavelength ‐ meaning that the reflected light, although relatively diffuse, appears segmented by color. The less reflected color artifacts that the textured surface produces the better. Some of these attributes are discussed in greater detail below. [0009] Targeting a specific surface roughness alone cannot optimize all of those metrics simultaneously. A relatively high surface roughness that sandblasting or liquid etching produces might adequately transform specular reflection into diffuse reflection. However, the high surface roughness can additionally generate high transmission haze and pixel power deviation. A relatively low surface roughness, while decreasing transmission haze, might fail to sufficiently transform specular reflection into diffuse reflection ‐ defeating the "antiglare" purpose of the texturing. [0010] Accordingly, a new approach to providing a textured region of the substrate is needed ‐ one that is reproducible from substrate‐to‐substrate and one that causes the textured surface to reflect ambient light sufficiently diffusely rather than specularly so as to be "antiglare" (e.g., a low distinctness‐of‐image, low specular reflection) but simultaneously also delivers low pixel power deviation, low transmission haze, and low reflection color artifacts. SUMMARY [0011] The present disclosure provides a new approach that specifically places primary surface features having a specific geometry throughout a textured region according to a predetermined placement. The primary surface features cause the substrate to reflect rather diffusely and are reproducible from substrate‐to‐substrate because the placement of each primary surface feature is by design. In addition, secondary surface features are incorporated into the textured region to increase the surface roughness to within a certain range. The increased surface roughness imparts surface scattering to the textured region, which generally lowers pixel power deviation and specular reflection, and sometimes distinctness of image too. [0012] According to a first aspect of the present disclosure, a substrate for a display article, the substrate comprising: (a) a primary surface; and (b) a textured region on at least a portion of the primary surface; the textured region comprising: (i) primary surface features, each comprising a perimeter parallel to a base‐plane extending through the substrate disposed below the textured region, wherein the perimeter of each of the primary surface features comprises a longest dimension of at least 5 µm; and (ii) one or more sections each comprising secondary surface features having a surface roughness (R_a) within a range of 5 nm to 100 nm. [0013] According to a second aspect of the present disclosure, the substrate of the first aspect, wherein the primary surface features form a pattern. [0014] According to a third aspect of the present disclosure, the substrate of any one of the first through second aspects, the longest dimension of each of the primary surface features is about the same. [0015] According to a fourth aspect of the present disclosure, the substrate of any one of the first through third aspects, wherein an arrangement of the surface features reflect a random distribution. [0016] According to a fifth aspect of the present disclosure, the substrate of any one of the first through fourth aspects, wherein the perimeter of each primary surface features is elliptical. [0017] According to a sixth aspect of the present disclosure, the substrate of any one of the first through fourth aspects, wherein the perimeter of each primary surface features is circular. [0018] According to a seventh aspect of the present disclosure, the substrate of any one of the first through fourth aspects, wherein each primary surface feature provides a surface, and the surface is either concave or convex. [0019] According to an eighth aspect of the present disclosure, the substrate of any one of the first through seventh aspects, wherein the textured region further comprises: a surrounding portion into which the primary surface features are set or out of which the primary surface features project. [0020] According to a ninth aspect of the present disclosure, the substrate of any one of the first through eighth aspects, wherein (i) the primary surface features that are adjacent to one another have perimeters that are separated by a distance within a range of 1 µm to 100 µm; and (ii) the primary surface features that are adjacent to one another are separated by a center‐to‐center distance within a range of 5 µm to 150 µm. [0021] According to a tenth aspect of the present disclosure, the substrate of any one of the first through ninth aspects, wherein each of the primary surface features comprises a change in elevation perpendicular to the base‐plane that is within a range of 0.05 µm to 0.50 µm. [0022] According to an eleventh aspect of the present disclosure, the substrate of any one of the first through sixth and eighth through tenth aspects, wherein (i) each primary surface features provides a surface, and (ii) the secondary surface features are disposed on the surfaces of the primary surface features. [0023] According to a twelfth aspect of the present disclosure, the substrate of any one of the first through sixth, ninth, and tenth aspects, wherein the textured region further comprises: a surrounding portion into which the primary surface features are set into or out of which the primary surface features project; wherein, each primary surface feature provides a surface, wherein, the secondary surface features are disposed on both the surrounding portion and on the surfaces of the primary surface features, and wherein, the surface roughness at the surfaces of the primary surface features is less than the surface roughness at the surrounding portion. [0024] According to a thirteenth aspect of the present disclosure, the substrate of any one of the first through sixth, ninth, and tenth aspects further comprises: a surrounding portion into which the primary surface features are set into or out of which the primary surface features project; wherein, the secondary surface features are disposed on the surfaces of the primary surface features but not on the surrounding portion. [0025] According to a fourteenth aspect of the present disclosure, the substrate of any one of the first through thirteenth aspects, wherein the substrate comprises a glass or glass‐ceramic. [0026] According to a fifteenth aspect of the present disclosure, the substrate of any one of the first through fourteenth aspects, wherein (i) the textured region exhibits a transmission haze within a range of 1.5% to 3.5%; (ii) the textured region exhibits a pixel power deviation within a range of 1.5% to 3.5%; (iii) the textured region exhibits a distinctness‐of‐image within a range of 2.% to 5.0%; and (iv) the textured region exhibits a specular reflectance within a range of 5 GU to 20 GU. [0027] According to a sixteenth aspect of the present disclosure, a method of forming a textured region of a substrate, the method comprising: (i) forming primary surface features into a primary surface of a substrate according to a predetermined positioning of each primary surface feature thus forming a textured region, each primary surface feature comprising a largest dimension parallel to a base‐plane through the substrate disposed below the primary surface of at least 5 µm; and (ii) forming secondary surface features into one or more sections of the textured region, thereby increasing the surface roughness (R_a) of the one or more sections to within a range of 5 nm to 100 nm. [0028] According to a seventeenth aspect of the present disclosure, the method of the sixteenth aspect further comprises: determining the positioning of each primary surface feature utilizing a spacing distribution algorithm. [0029] According to an eighteenth aspect of the present disclosure, the method of any one of the sixteenth through seventeenth aspects, wherein forming the primary surface features into the primary surface comprises contacting the primary surface with an etchant while an etching mask is disposed on the primary surface to permit only selective etching of the substrate to form the primary surface features. [0030] According to a nineteenth aspect of the present disclosure, the method of the eighteenth aspect, wherein (i) the etchant comprises hydrofluoric acid and nitric acid; and (ii) the etchant contacts the substrate for a time period within a range of 10 seconds to 60 seconds. [0031] According to a twentieth aspect of the present disclosure, the method of any one of the sixteenth through nineteenth aspects further comprising: forming the etching mask by exposing a photorsesist material disposed on the primary surface of the substrate to a curing agent while a lithography mask is disposed on the photoresist material, the lithography mask comprising material and voids through the material to selectively expose portions of the photoresist material to the curing agent, wherein the voids of the lithography mask are positioned according to the predetermined positioning of the primary surface features. [0032] According to a twenty‐first aspect of the present disclosure, the method of any one of the sixteenth through twentieth aspects, wherein forming the secondary surface features into one or more sections of the textured region comprises contacting the textured region of the substrate with a second etchant, different than the etchant used to form the primary surface features. [0033] According to a twenty‐second aspect of the present disclosure, the method of any one of the sixteenth through twenty‐first aspects, wherein the second etchant comprises acetic acid and ammonium fluoride. [0034] According to a twenty‐third aspect of the present disclosure, the method of any one of the sixteenth through twenty‐second aspects, wherein (i) forming the primary surface features into the primary surface comprises contacting the primary surface with an etchant while an etching mask is disposed on the primary surface to permit only selective etching of the substrate to form the primary surface features, and (ii) forming the secondary surface features into one or more sections of the textured region comprises contacting the one or more sections of the textured region of the substrate with a second etchant, different than the etchant used to form the primary surface features, while the etching mask used to form the primary surface features remains on the substrate. BRIEF DESCRIPTION OF THE DRAWINGS [0035] In the figures: [0036] FIG. 1 is perspective view of a display article, illustrating a substrate with a textured region disposed over a display; [0037] FIG. 2 is closer‐up perspective view of area II of FIG. 1, illustrating the textured region of the substrate of FIG. 1 including primary surface features that are arranged in a hexagonal pattern; [0038] FIG. 3 is an elevation view of a cross‐section of the substrate of FIG. 1 taken through line III‐III of FIG. 2, illustrating the textured region further including secondary surface features, smaller than the primary surface features, disposed on the textured region including the primary surface features; [0039] FIG. 4 is an overhead view of embodiments of a textured region, illustrating the primary surface features having an elliptical perimeter and projecting from a surrounding portion; [0040] FIG. 5 is another overhead view of embodiments of a textured region, illustrating the primary surface features having a hexagonal perimeter that are arranged hexagonally but separated by a distance (wall‐to‐wall) and a center‐to‐center distance; [0041] FIG. 6 is a schematic flow chart of a method of forming the textured region of FIG. 1, illustrating steps such as determining the positioning of each primary surface feature using a spacing distribution algorithm; [0042] FIG. 7A, pertaining to a modeled Example 1, is a graph that illustrates distinctness‐of‐ image generally decreasing as a function of (i) increasing change of elevation (height) of the primary surface features and (ii) increasing sigma value assigned for the secondary surface features, which is a measure of the surface scattering that the secondary surface features impart to the textured region; [0043] FIG. 7B, pertaining to Example 1, is a graph that illustrates the change in distinctness‐of‐ image that the presence of the secondary surface features impart compared to if there were no secondary surface features, as a function of the assigned sigma value and height of the primary surface features; [0044] FIG. 7C, pertaining to Example 1, is a graph that illustrates the sigma value that imparts the textured region with the minimum distinctness‐of‐image value generally decreases as a function of decreasing height of the primary surface features; [0045] FIG. 7D, pertaining to Example 1, is a graph that illustrates that pixel power deviation generally increases as a function of height of the primary surface features and decreases as a function of increasing sigma value assigned to the secondary surface features; [0046] FIG. 7E, pertaining to Example 1, is a graph that illustrates pixel power deviation generally decreases as a function of increasing sigma value and decreases as a function of decreasing height of the primary surface features; [0047] FIG. 7F, pertaining to Example 1, is a graph that illustrates transmission haze generally increases as a function of increasing sigma values assigned for the secondary surface features; [0048] FIG. 7G, pertaining to Example 1, is a graph that illustrates transmission haze generally increasing as a function of increasing sigma value assigned for the secondary surface features, but only after a threshold minimum sigma value; [0049] FIG. 8A, pertaining to Examples 2A‐2D, reproduce atomic force microscopy images of secondary surface features with various topographies, a result of varying a composition of an etchant utilized to form the secondary surface features; [0050] FIG. 8B, pertaining to Examples 2A‐2D, is a graph that illustrates transmission haze generally increasing as a function of increasing sigma (surface scattering) value, which were variable as a function of etchant composition; [0051] FIG. 9A, pertaining to Examples 3A‐3B, is a graph that illustrates pixel power deviation varying as a function of orientation angle of the textured region (because of the hexagonal perimeter) of the primary surface features, and the presence of the secondary surface features lowering pixel power deviation compared to when no such secondary surface features were present; [0052] FIG. 9B, pertaining to Examples 3A‐3B, is a schematic diagram illustrating that orientation angle concerns the angle that an edge of the substrate forms with the display beneath the substrate; [0053] FIG. 10A, pertaining to Examples 4A‐4H, is a graph that illustrates that the inclusion of the secondary surface features resulted in a lower pixel power deviation and, further, that the resulting pixel power deviation can vary depending on the surface roughness (R_a) that the secondary surface features impart, and thus the composition of the etchant used to form the secondary surface features; [0054] FIG. 10B, pertaining to Examples 4A‐4H, is a graph that illustrates that the presence of the secondary surface features did not change measured specular reflectance compared to substrates that did not have the secondary surface features; [0055] FIG. 10C, pertaining to Examples 4A‐4H, is a graph that illustrates that the presence of the secondary surface features produced a lower distinctness‐of‐image compared to substrates that did not have the secondary surface features; [0056] FIG. 10D, pertaining to Examples 4A‐4H, is a graph that illustrates that the presence of the secondary surface features produces greater transmission haze compared to substrates that did not have the secondary surface features, and increasingly so as the surface roughness (R_a) that the secondary surface features imparts increases; [0057] FIG. 11A, pertaining to Examples 5A‐5O, is a graph that illustrates that the presence of secondary surface features resulted in a lower pixel power deviation compared to substrates that did not have the secondary surface features; [0058] FIG. 11B, pertaining to Examples 5A‐5O, is a graph that illustrates that the presence of secondary surface features resulted in a lower specular reflectance compared to substrates that did not have the secondary surface features; [0059] FIG. 11C, pertaining to Examples 5A‐5O, is a graph that illustrates that the presence of secondary surface features resulted in a higher distinctness‐of‐image compared to substrates that did not have the secondary surface features; [0060] FIG. 11D, pertaining to Examples 5A‐5O, is a graph that illustrates that the presence of secondary surface features resulted in a higher transmission haze compared to substrates that did not have the secondary surface features; [0061] FIG. 12A, pertaining to Examples 6A‐6B, are atomic force microscopy images of the primary surface features and the surrounding portion (left) and the secondary surface features (middle and right), for both when the secondary surface features were disposed only on the primary surface features (top) and when the secondary surface features were disposed over both the primary surface features and the surrounding portion (bottom); [0062] FIG. 12B, pertaining to Examples 6A‐6B, is a graph illustrating that incorporating the secondary surface features over the entire textured region resulted in a lowed pixel power deviation compared to substrates where the secondary surface features were incorporated only on the primary surface features; [0063] FIG. 12C, pertaining to Examples 6A‐6B, is a graph illustrating that incorporating the secondary surface features over the entire textured region resulted in a higher transmission haze compared to substrates that incorporated the secondary surface features only on the primary surface features; [0064] FIG. 12D, pertaining to Examples 6A‐6B, is a graph illustrating that incorporating the secondary surface features over the entire textured region did not substantially affect specular reflectance compared to substrates that incorporated the secondary surface features only on the primary surface features; [0065] FIG. 12E, pertaining to Examples 6A‐6B, is a graph illustrating that incorporating the secondary surface features over the entire textured region slightly affected specular reflectance compared to substrates that incorporated the secondary surface features only on the primary surface features, and increasingly so as wavelength deviated from about 455 nm; [0066] FIG. 13A, pertaining to Example 7, are white light interferometer graphs illustrating the topography of the primary surface features and the surrounding portion (top) and the secondary surface features (bottom) disposed at the primary surface features (left) and the surrounding portion (right); and [0067] FIG. 13B, pertaining to Example 7, are atomic force microscopy images of the secondary surface features disposed at a primary surface feature (left) and the surrounding portion (right), illustrating that the secondary surface features at the surrounding portion imparted a higher surface roughness (R_a) than the at the primary surface features (because the surrounding portion was not previously etched and thus more sensitive to the etching that imparted the secondary surface features). DETAILED DESCRIPTION [0001] Referring now to FIG. 1, a display article 10 includes a substrate 12. In embodiments, the display article 10 further includes a housing 14 to which the substrate 12 is coupled and a display 16 within the housing 14. In such embodiments, the substrate 12 at least partially covers the display 16 such that light that the display 16 emits transmits through the substrate 12. [0002] The substrate 12 includes a primary surface 18, a textured region 20 defined on the primary surface 18, and a thickness 22 that the primary surface 18 bounds in part. The primary surface 18 generally faces toward an external environment 24 surrounding the display article 10 and away from the display 16. The display 16 emits visible light that transmits through the thickness 22 of the substrate 12, out the primary surface 18, and into the external environment 24. [0068] Referring now to FIGS. 2‐5, in embodiments, the textured region 20 includes primary surface features 26. A base‐plane 28 extends through the substrate 12 below the textured region 20. The base‐plane 28 provides a conceptual reference point and is not a structural feature. Each primary surface feature 26 includes a perimeter 30. The perimeter 30 is parallel to the base‐ plane 28. The perimeter 30 has a longest dimension 32. For example, in the embodiments illustrated at FIG. 2, the perimeter 30 is hexagonal and thus the longest dimension 32 of the perimeter 30 is the long diagonal of the hexagonal perimeter 30. The longest dimension 32 is parallel to the base‐plane 28 as well. The longest dimension 32 of each primary surface feature 26 is at least 5 µm. The perimeter 30 can be shaped other than hexagonal. In embodiments, the perimeter 30 of each of the primary surface features 26 is polygonal. In embodiments, the perimeter 30 of each of the primary surface features 26 is elliptical (see, e.g., FIG. 4). In other embodiments, the perimeter 30 of each of the primary surface features 26 is circular. [0069] In addition, the textured region 20 further includes one or more sections 34 that have secondary surface features 36. The secondary surface features 36 are smaller than the primary surface features 26. The secondary surface features 36 impart a surface roughness to the one or more sections 34 of the textured region 20. The surface roughness imparted is 5 nm, 10 nm, 15 nm, 20 nm, 25 nm, 30 nm, 35 nm, 40 nm, 45 nm, 50 nm, 55 nm, 60 nm, 65 nm, 70 nm, 75 nm, 80 nm, 85 nm, 90 nm, 95 nm, or 100 nm, or within any range bounded by any two of those values (e.g., 5 nm to 100 nm, and so on). As used herein, surface roughness (R_a) is measured with an atomic force microscope, such as an atomic force microscope controlled by a NanoNavi control station distributed by Seiko Instruments Inc. (Chiba, Japan), with a scan size of 5 µm by 5 µm. Surface roughness (R_a), as opposed to other types of surface roughness values such as R_q, is the arithmetical mean of the absolute values of the deviations from a mean line of the measured roughness profile. [0070] The positioning, perimeter 30, and longest dimension 32 of each of the primary surface features 26 is by design, as opposed to the purely uncontrolled and coincidental placement of surface features via sandblasting or open etching (i.e., etching without a mask that would define the placement of each surface feature). In embodiments, such as those embodiments illustrated at FIG. 2, the primary surface features 26 form a pattern. In other words, the positioning of a grouping of the primary surface features 26 repeats at the textured region 20. The embodiments illustrated at FIG. 2 are a hexagonal pattern. In embodiments, the longest dimension 32 of each of the primary surface features 26 is about the same or the same within manufacturing tolerances. [0071] In other embodiments, such as those illustrated at FIG. 4, the primary surface features 26 do not form a pattern – that is, the arrangement of the surface features reflect a random distribution. To not form a pattern, the primary surface features 26 can be randomly distributed within certain constraints, such as a center‐to‐center distance 38 that varies but is greater than a minimum value. In addition, to not form a pattern, the longest dimension 32 of each primary surface feature 26 can be aligned not parallel to each other. A reason to avoid arranging the primary surface features 26 not in a pattern is to avoid the textured region 20 reflecting ambient light with Moiré fringe interference patterns. When the primary surface features 26 form a pattern, a possible consequence is the generation of Moiré fringe interference patterns upon reflection of ambient light. [0072] Each of the primary surface features 26 includes a surface 40 facing the external environment 24. The primary surface 18 of the substrate 12 at the textured region 20 includes all of surfaces 40 that the primary surface features 26 provide. In embodiments, such as those illustrated at FIGS. 3 and 4, the surface 40 of each primary surface feature 26 is concave. In other embodiments, the surface 40 of each primary surface feature 26 is convex. In embodiment, the surfaces 40 of some primary surface features 26 of the textured region 20 are concave, while the surfaces 40 of other primary surface features 26 of the textured region 20 are convex. In embodiments, the surface 40 of each primary surface feature 26 of the textured region 20 is planar and parallel to the base‐plane 28. [0073] In embodiments, the textured region 20 further includes a surrounding portion 42 (see, e.g., FIGS. 4 and 5). In embodiments, the primary surface features 26 project out from the surrounding portion 42 away from the base‐plane 28 and toward the external environment 24. In embodiments, the primary surface features 26 are set into the surrounding portion 42 toward the base‐plane 28 and away from the external environment 24. The elevation 44 (see FIG. 13A) of the surrounding portion 42 from the base‐plane 28 may be relatively constant within manufacturing capabilities. The elevation 46 (see FIG. 13A) of the surfaces 40 of the primary surface feature 26 may all be approximately the same, within manufacturing capabilities. The textured region 20 may thus have a bi‐modal surface structure – with one or more surfaces (e.g., the surfaces 40 of the primary surface features 26) having one mean elevation (e.g., elevation 46), and one or more surfaces (e.g., the surface provided by the surrounding portion 42) having a second mean elevation (e.g., elevation 44). [0074] In embodiments, the perimeters 30 of primary surface features 26 that are adjacent are separated by a distance 48 (e.g., wall‐to‐wall distance). In embodiments, the distance 48 is 1 µm, 2 µm, 3 µm, 4 µm, 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, 10 µm, 15 µm, 20 µm, 25 µm, 30 µm, 35 µm, 40 µm, 45 µm, 50 µm, 55 µm, 60 µm, 65 µm, 70 µm, 75 µm, 80 µm, 85 µm, 90 µm, 95 µm, or 100 µm, or within any range bounded by any two of those values (e.g., 25 µm to 75 µm, 50 µm to 60 µm, 1 µm to 100 µm, and so on). In embodiments, primary surface features 26 that are adjacent are separated by a center‐to‐center distance 38 of 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, 10 µm, 15 µm, 20 µm, 25 µm, 30 µm, 35 µm, 40 µm, 45 µm, 50 µm, 55 µm, 60 µm, 65 µm, 70 µm, 75 µm, 80 µm, 85 µm, 90 µm, 95 µm, 100 µm, 110 µm, 120 µm, 130 µm, 140 µm, or 150 µm, or within any range bounded by any two of those values (e.g., 100 µm to 150 µm, 5 µm to 150 µm and so on). [0075] Each primary surface feature 26 has a change in elevation 50 perpendicular to the base‐ plane 28. For a primary surface feature 26 that is convex or projects from the surrounding portion 42, the change in elevation 50 is the height of the primary surface feature 26. For a primary surface feature 26 that is concave or set into the surrounding portion 42, the change in elevation 50 is the depth of the primary surface feature 26. In embodiments, the change in elevation 50 of each primary surface feature 26 is the same or about the same (varies by 25% or less). In embodiments, the change in elevation 50 of each primary surface feature 26 is 0.05 µm, 0.10 µm, 0.15 µm, 0.20 µm, 0.25 µm, 0.30 µm, 0.35 µm, 0.40 µm, 0.45 µm, or 0.50 µm, or within any range bounded by any two of those values (e.g., 0.05 µm to 0.50 µm, and so on). When the textured region 20 provides surfaces structured in a bi‐modal distribution of elevations, the change in elevation 50 is the distance between the two elevations. [0076] In embodiments, the one or more sections 34 that include the secondary surface features 36 include the surfaces 40 of the primary surface features 26. In other words, in those embodiments, the secondary surface features 36 are disposed on the surface 40 of the primary surface features 26. In embodiments, the secondary surface features 36 are disposed on the surface 40 of the primary surface features 26 but not the surrounding portion 42. [0077] In embodiments, the one or more sections 34 that include the secondary surface features 36 include the surrounding portion 42 and the surfaces 40 of the primary surface features 26. In other words, in those embodiments, the secondary surface features 36 are disposed on both the surrounding portion 42 and on the surfaces 40 of the primary surface features 26. In embodiments, the section 34 that includes the secondary surface features 36 is coextensive with the textured region 20 meaning that the secondary surface features 36 are disposed throughout the entirety of the textured region 20. In embodiments, the surface roughness (R_a) at the surfaces 40 of the primary surface features 26 is less than the surface roughness at the surrounding portion 42. [0078] Through adjustment of the parameters of the primary surface features 26, such as the change in elevation 50, longest dimension 32, shape of the perimeter 30, and center‐to‐center distance 38, and the addition of the secondary surface features 36, the distinctness‐of‐image, pixel power deviation, and transmission haze that the textured region 20 generates can be optimized. In general, incorporation of the primary surface features 26 alone would cause the textured region 20 to reflect ambient light with a lower distinctness‐of‐image but transmit light from the display 16 with a higher pixel power deviation and higher transmission haze. The larger the change in elevation 50 of the primary surface features 26, the larger these effects on distinctness of image, pixel power deviation, and transmission haze. The incorporation of the secondary surface features 36 mitigates the negative effect that the primary surface features 26 might have on pixel power deviation. The surface roughness that the secondary surface features 36 impart increases the scattering of the textured region 20. This increased scattering increases the amount of diffuse reflection that the textured region 20 generates upon reflecting ambient light thus further lowering specular reflection and rehabilitating (lowering) the pixel power deviation simultaneously, and distinctness‐of‐image in some instances. Thus, the textured region 20 can simultaneously generate low values for all of the specular reflection, distinctness‐of‐ image, pixel power deviation, and transmission haze – something that previous methods of created the textured region 20 could not achieve. In addition, the designer of the textured region 20 has many more variables with which the designer can work to optimize the textured region 20 for any given application than with previous methods such as sandblasting or open etching. [0079] In embodiments, the substrate 12 includes a glass or glass‐ceramic. In embodiments, 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 aluminoborosilicate 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 display 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. [0080] In embodiments, the substrate 12 has a bulk composition that comprises an alkali aluminosilicate glass that comprises alumina, at least one alkali metal and, in some embodiments, greater than 50 mol % SiO₂, in other embodiments, at least 58 mol % SiO₂, and in still other embodiments, at least 60 mol % SiO₂, wherein the ratio (Al₂O₃ (mol%) + B₂O₃ (mol%)) / ∑ alkali metal modifiers (mol%) > 1, where the modifiers are alkali metal oxides. This glass, in particular embodiments, comprises, consists essentially of, or consists of: about 58 mol % to about 72 mol % SiO₂; about 9 mol % to about 17 mol % Al₂O₃; about 2 mol % to about 12 mol % B₂O₃; about 8 mol % to about 16 mol % Na₂O; and 0 mol % to about 4 mol % K₂O, wherein the ratio (Al₂O₃ (mol%) + B₂O₃ (mol%)) / ∑ alkali metal modifiers (mol%) > 1, where the modifiers are alkali metal oxides. [0081] In embodiments, the substrate 12 has a bulk composition that comprises an alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 61 mol % to about 75 mol % SiO₂; about 7 mol % to about 15 mol % Al₂O₃; 0 mol % to about 12 mol % B₂O₃; about 9 mol % to about 21 mol % Na₂O; 0 mol % to about 4 mol % K₂O; 0 mol % to about 7 mol % MgO; and 0 mol % to about 3 mol % CaO. [0082] In embodiments, the substrate 12 has a bulk composition that comprises an alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 60 mol % to about 70 mol % SiO₂; about 6 mol % to about 14 mol % Al₂O₃; 0 mol % to about 15 mol % B₂O₃; 0 mol % to about 15 mol % Li₂O; 0 mol % to about 20 mol % Na₂O; 0 mol % to about 10 mol % K₂O; 0 mol % to about 8 mol % MgO; 0 mol % to about 10 mol % CaO; 0 mol % to about 5 mol % ZrO₂; 0 mol % to about 1 mol % SnO₂; 0 mol % to about 1 mol % CeO₂; less than about 50 ppm As₂O₃; and less than about 50 ppm Sb₂O₃; wherein 12 mol %≦Li₂O+Na₂O+K₂O≦20 mol % and 0 mol %≦MgO+Ca≦10 mol %. [0083] In embodiments, the substrate 12 has a bulk composition that comprises an alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 64 mol % to about 68 mol % SiO₂; about 12 mol % to about 16 mol % Na₂O; about 8 mol % to about 12 mol % Al₂O₃; 0 mol % to about 3 mol % B₂O₃; about 2 mol % to about 5 mol % K₂O; about 4 mol % to about 6 mol % MgO; and 0 mol % to about 5 mol % CaO, wherein: 66 mol %≦SiO₂+B₂O₃+CaO≦69 mol %; Na₂O+K₂O+B₂O₃+MgO+CaO+SrO>10 mol %; 5 mol %≦MgO+CaO+SrO≦8 mol %; (Na₂O+B₂O₃)—Al₂O₃≦2 mol %; 2 mol %≦Na₂O—Al₂O₃≦6 mol %; and 4 mol %≦(Na₂O+K₂O)— Al₂O₃≦10 mol %. [0084] In embodiments, the substrate 12 has a bulk composition that comprises SiO₂, Al₂O₃, P₂O₅, and at least one alkali metal oxide (R₂O), wherein 0.75>[(P₂O₅(mol %)+R₂O (mol %))/M₂O₃(mol %)]≦1.2, where M₂O₃═Al₂O₃+B₂O₃. In embodiments, [(P₂O₅(mol %)+R₂O (mol %))/M₂O₃(mol %)]=1 and, in embodiments, the glass does not include B₂O₃and M₂O₃═Al₂O₃. The substrate 12 comprises, in embodiments: about 40 to about 70 mol % SiO₂; 0 to about 28 mol % B₂O₃; about 0 to about 28 mol % Al₂O₃; about 1 to about 14 mol % P₂O₅; and about 12 to about 16 mol % R₂O. In some embodiments, the glass substrate comprises: about 40 to about 64 mol % SiO₂; 0 to about 8 mol % B₂O₃; about 16 to about 28 mol % Al₂O₃; about 2 to about 12 mol % P₂O₅; and about 12 to about 16 mol % R₂O. The substrate 12 may further comprise at least one alkaline earth metal oxide such as, but not limited to, MgO or CaO. [0085] In some embodiments, the substrate 12 has a bulk composition that is substantially free of lithium; i.e., the glass comprises less than 1 mol % Li₂O and, in other embodiments, less than 0.1 mol % Li₂O and, in other embodiments, 0.01 mol % Li₂O, and in still other embodiments, 0 mol % Li₂O. In some embodiments, such glasses are free of at least one of arsenic, antimony, and barium; i.e., the glass comprises less than 1 mol % and, in other embodiments, less than 0.1 mol %, and in still other embodiments, 0 mol % of As₂O₃, Sb₂O₃, and/or BaO. [0086] In embodiments, the substrate 12 has a bulk composition that comprises, consists essentially of or consists of a glass composition, such as Corning^® Eagle XG^® glass, Corning^® Gorilla^® glass, Corning^® Gorilla^® Glass 2, Corning^® Gorilla^® Glass 3, Corning^® Gorilla^® Glass 4, or Corning^® Gorilla^® Glass 5. [0087] In embodiments, 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 embodiments, the substrate 12 is chemically strengthened by ion exchange. In that process, metal ions at or near the primary surface 18 of the substrate 12 are exchanged for larger metal ions having the same valence as the metal ions in the substrate 12. The exchange is generally carried out by contacting the substrate 12 with an ion exchange medium, such as, for example, a molten salt bath that contains the larger metal ions. The metal ions are typically monovalent metal ions, such as, for example, alkali metal ions. In one non‐limiting example, chemical strengthening of a substrate 12 that contains sodium ions by ion exchange is accomplished by immersing the substrate 12 in an ion exchange bath comprising a molten potassium salt, such as potassium nitrate (KNO₃) or the like. In one particular embodiment, the ions in the surface layer of the substrate 12 contiguous with the primary surface 18 and the larger ions are monovalent alkali metal cations, such as Li⁺ (when present in the glass), Na⁺, K⁺, Rb⁺, and Cs⁺. Alternatively, monovalent cations in the surface layer of the substrate 12 may be replaced with monovalent cations other than alkali metal cations, such as Ag⁺ or the like. [0088] In such embodiments, the replacement of small metal ions by larger metal ions in the ion exchange process creates a compressive stress region in the substrate 12 that extends from the primary surface 18 to a depth (referred to as the “depth of layer”) that is under compressive stress. This compressive stress of the substrate 12 is balanced by a tensile stress (also referred to as “central tension”) within the interior of the substrate 12. In some embodiments, the primary surface 18 of the substrate 12 described herein, when strengthened by ion exchange, has a compressive stress of at least 350 MPa, and the region under compressive stress extends to a depth, i.e., depth of layer, of at least 15 μm below the primary surface 18 into the thickness 22. [0089] Ion exchange processes are typically carried out by immersing the substrate 12 in a molten salt bath containing the larger ions to be exchanged with the smaller ions in the glass. It will be appreciated by those skilled in the art that parameters for the ion exchange process, including, but not limited to, bath composition and temperature, immersion time, the number of immersions of the glass in a salt bath (or baths), use of multiple salt baths, additional steps such as annealing, washing, and the like, are generally determined by the composition of the glass and the desired depth of layer and compressive stress of the glass as a result of the strengthening operation. By way of example, ion exchange of alkali metal‐containing glasses may be achieved by immersion in at least one molten bath containing a salt, such as, but not limited to, nitrates, sulfates, and chlorides, of the larger alkali metal ion. The temperature of the molten salt bath typically is in a range from about 380°C up to about 450°C, while immersion times range from about 15 minutes up to about 16 hours. However, temperatures and immersion times different from those described above may also be used. Such ion exchange treatments, when employed with a substrate 12 having an alkali aluminosilicate glass composition, result in a compressive stress region having a depth (depth of layer) ranging from about 5 μm up to at least 50 μm, with a compressive stress ranging from about 200 MPa up to about 800 MPa, and a central tension of less than about 100 MPa. [0090] As the etching processes that can be employed to create the textured region 20 of the substrate 12 can remove alkali metal ions from the substrate 12 that would otherwise be replaced by a larger alkali metal ion during an ion exchange process, a preference exists for developing the compressive stress region in the display article 10 after the formation and development of the textured region 20. [0091] In embodiments, the display article 10 exhibits a pixel power deviation (“PPD”). The details of a measurement system and image processing calculation used to obtain PPD values described in U.S. Patent No. 9,411,180 entitled “Apparatus and Method for Determining Sparkle,” and the salient portions of which are related to PPD measurements are incorporated by reference herein in their entirety. Further, unless otherwise noted, the SMS‐1000 system (Display‐Messtechnik & Systeme GmbH & Co. KG) is employed to generate and evaluate the PPD measurements of this disclosure. The PPD measurement system includes: a pixelated source comprising a plurality of pixels (e.g., a Lenovo Z50 140 ppi laptop), wherein each of the plurality of pixels has referenced indices i and j; and an imaging system optically disposed along an optical path originating from the pixelated source. The imaging system comprises: an imaging device disposed along the optical path and having a pixelated sensitive area comprising a second plurality of pixels, wherein each of the second plurality of pixels is referenced with indices m and n; and a diaphragm disposed on the optical path between the pixelated source and the imaging device, wherein the diaphragm has an adjustable collection angle for an image originating in the pixelated source. The image processing calculation includes: acquiring a pixelated image of the transparent sample, the pixelated image comprising a plurality of pixels; determining boundaries between adjacent pixels in the pixelated image; integrating within the boundaries to obtain an integrated energy for each source pixel in the pixelated image; and calculating a standard deviation of the integrated energy for each source pixel, wherein the standard deviation is the power per pixel dispersion. As used herein, all PPD values, attributes and limits are calculated and evaluated with a test set‐up employing a display device having a pixel density of 140 pixels per inch (PPI). In embodiments, the display article 10 exhibits a PPD of 1.0%, 1.1%, 1.2%, 1.3%, 1.4%, 1.5%, 1.6%, 1.7%, 1.8%, 1.9%, 2.0%, 2.25%, 2.5%, 2.75%, 3.0%, 3.25%, 3.5%, 3.75%, 4.0%, 4.25%, 4.5%, 4.75%, 5.0%, 5.5%, 6.0%, 6.5%, or within any range bounded by any two of those values (e.g., 0.8% to 2.0%, 0.9% to 2.25%, 2.0% to 5.0%, 4.0% to 6.0%, and so on). In embodiments, the display article 10 exhibits a PPD of less than 4.0%, less than 4.0%¸ less than 3.0%¸ or less than 2.0%. [0092] In embodiments, the substrate 12 exhibits a distinctness‐of‐image (“DOI”). As used herein, “DOI” is equal to 100*(R_S‐ R_0.3˚)/R_S, where R_S is the specular reflectance flux measured from incident light (at 20˚ from normal) directed onto the textured region 20, and R_0.3 is the reflectance flux measured from the same incident light at 0.3˚ from the specular reflectance flux, R_S. Unless otherwise noted, the DOI values and measurements reported in this disclosure are obtained according to the ASTM D5767‐18, entitled “Standard Test Method for Instrumental Measurement of Distinctness‐of‐Image (DOI) Gloss of Coated Surfaces using a Rhopoint IQ Gloss Haze & DOI Meter” (Rhopoint Instruments Ltd.). The values are reported here as “coupled” meaning that the sample is coupled with index matching fluid to the back‐side surface of the substrate during the measurement to reduce backside reflections. In embodiments, the substrate 12 exhibits a distinctness‐of‐image (“DOI”) of 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95%, 96%, 96%, 97%, 98%, 99%, or 99.9%, or within any range bounded by any two of those values (e.g., 20% to 40%, 10% to 96%, 35% to 60%, and so on). [0093] In embodiments, the substrate 12 exhibits a transmission haze. As used herein, the term “transmission haze” refers to the percentage of transmitted light scattered outside an angular cone of about ±2.5° in accordance with ASTM D1003, entitled “Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics,” the contents of which are incorporated by reference herein in their entirety. Note that although the title of ASTM D1003 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. In embodiments, the substrate 12 exhibits a transmission haze of 0.7%, 0.8%, 0.9%. 1.0%, 1.5%, 2%, 3%, 4%, or 5%, or within any range bounded by any two of those values (e.g., 0.7% to 3%, 2% to 4%, and so on). [0094] In embodiments, the substrate 12 exhibits a specular reflectance of 1 GU, 2 GU, 3 GU, 4 GU, 5 GU, 10 GU, 15 GU, 20 GU, 25 GU, 30 GU, 40 GU, 50 GU, 60 GU, 70 GU, 80 GU, or within any range bounded by any two of those values (e.g., 1 GU to 3 GU, 5 GU to 30 GU, 50 GU to 80 GU, and so on). In embodiments, the substrate 12 exhibits a specular reflectance that is less than less than 25 GU less than 20 GU, less than 15 GU, less than 10 GU, less than 5 GU, or less than 2 GU. Specular reflectance here, noted as “c‐Rspec” “or “coupled Rspec” in the Examples that follow, refers to the value obtained in gloss units (GU) using a Rhopoint IQ goniophotometer. The values are indicative of how much specular reflection is measured when the sample is optically coupled to a perfect absorber. A value of 100 GU means 4.91% specular reflection from a polished flat black glass surface of refractive index 1.567 at 20 degrees angle of incidence. [0095] Referring now to FIGS. 6‐10, a method 100 of forming the textured region 20 is herein disclosed. At a step 102, the method 100 includes forming the primary surface features 26 into the primary surface 18 of the substrate 12 according to a predetermined positioning of each primary surface feature 26. The step 102, at least for the moment, forms the textured region 20. [0096] In embodiments, at a step 104, the method 100 further includes determining the positioning of each primary surface feature 26 utilizing a spacing distribution algorithm. Example spacing distribution algorithms include Poisson disk sampling, maxi‐min spacing, and hard‐sphere distribution. For example, Poisson disk sampling inserts a first object (e.g., a point or a circle with a diameter) into an area of a plane. Then the algorithm inserts a second object within the area, placing the center at a random point within the area. If the placement of the second object satisfies the minimum center‐to‐center distance from the first object, then the second object stays in the area. The algorithm then repeats this process until no more such objects can be placed within the area that satisfies the minimum center‐to‐center distance. The result is a random distribution, but specific placement, of the objects. From the random distribution but specific placement of the objects, the positioning of the primary surface features 26 are determined. For example, if the objects positioned via the spacing distribution algorithm are points, then the points can be the center of circles with a certain diameter, or the center of hexagons with certain geometry. In other embodiments, the points are triangulated, inellipses formed in the triangles, and then the triangulations and points are removed leaving ellipses, which can be shape of the primary surface features 26. [0097] In embodiments, the step of 102 forming the primary surface features 26 into the primary surface 18 includes contacting the primary surface 18 with an etchant while an etching mask is disposed on the primary surface 18 to permit only selective etching of the substrate 12 to form the primary surface features 26. The etching mask includes voids that allow the etchant to remove material from the primary surface 18 of the substrate 12 and, outside of the voids, the etching mask prevents the etchant from contacting the primary surface 18 of the substrate 12. In embodiments, the voids allow the etchant to remove material and thereby to create the primary surface features 26 set into the surrounding portion 42, which the etching mask protects from the etchant. In embodiments, the voids allow the etchant to remove material of the substrate 12 where the surrounding portion 42 is to be but not where the primary surface features 26 are to be, resulting in the primary surface features 26 projecting from the surrounding portion 42. In short, the etching mask incorporates the predetermined positioning of each primary surface feature 26 as either a positive or negative. [0098] In embodiments, the etchant includes one or more of hydrofluoric acid and nitric acid. In embodiments, the etchant includes both hydrofluoric acid and nitric acid. The etchant can be sprayed onto the substrate 12 while the etching mask is on the substrate 12. The substrate 12 with the etching mask can be dipped into a vessel containing the etchant. In embodiments, the etchant contacts the substrate 12 for a time period of 10 seconds, 20 seconds, 30 seconds, 40 seconds, 50 seconds, or 60 seconds, or within any range bounded by any two of those values (e.g., 10 seconds to 60 seconds, and so on). After the period of time has concluded, the substrate 12 is rinsed in deionized water and dried. The longer the period of time that the etchant contacts the substrate 12, the deeper the etchant etches into the substrate 12 and thus the greater the change in elevation 50 of the primary surface features 26. [0099] In embodiments, at a step 106, the method 100 further includes forming the etching mask by exposing a photoresist material disposed on the primary surface 18 of the substrate 12 to a curing agent while a lithography mask is disposed on the photoresist material. The thickness of the photoresist material can vary from about 3 µm to about 20 µm depending on how the photoresist material is added to the primary surface 18 of the substrate 12. The photoresist material can be added via spin coating (< 3 µm thickness), screen coating (< 15 µm thickness), or as a dry film (< 20 µm thickness). [0100] The lithography mask includes material and voids through the material to selectively expose portions of the photoresist material to the curing agent. The voids of the lithography mask are positioned according to the predetermined positioning of the primary surface features 26, either as a positive or negative. The placement of each of the primary surface features 26 is determined, such as with the spacing distribution algorithm and the lithography mask incorporates that determined placement. The lithography mask then allows selective curing of the etching mask, which then incorporates that predetermined placement of the primary surface features 26. Then finally the etching mask allows for selective etching of the substrate 12, which translates the determined placement of the primary surface features 26 onto the primary surface 18 of the substrate 12 as the textured region 20. The substrate 12 with the etching mask can be baked before the etching mask contacts the etchant in order to ensure adhesion to the substrate 12. [0101] At a step 108, which occurs after the step 102, the method 100 further includes forming the secondary surface features 36 into the one or more sections 34 of the textured region 20. This step 108 increases the surface roughness (R_a) at the one or more sections 34 to within the range of 5 nm to 100 nm. In embodiments, the step 108 of forming the secondary surface features 36 into one or more sections 34 of the textured region 20 comprises contacting the one or more sections 34 of the textured region 20 of the substrate 12 with a second etchant. The second etchant is different than the etchant that was utilized to etch the primary surface features 26 into the primary surface 18 of the substrate 12. In embodiments, the second etchant includes acetic acid and ammonium fluoride. In embodiments, the second etchant includes (in wt%): 85 to 98 acetic acid, 0.5 to 7.5 ammonium fluoride, and 0 to 11 water. The water can be deionized water. In embodiments, the second etchant contacts the one or more sections 34 for a time period within a range of 15 seconds to 5 minutes. In embodiments, the second etchant contacts the one or more sections 34 while the etching mask used to form the primary surface features 26 remains on the substrate 12. This would result in the increase of the surface roughness (R_a) of only the primary surface features 26 and not the surrounding portion 42, or only the surrounding portion 42 and not the primary surface features 26. After the period of time has concluded the substrate 12 is rinsed with deionized water and dried. Both etching steps 102, 108 can be conducted at room temperature. [0102] The method 100 is scalable and low‐cost. In addition, the method 100 is repeatable and is able to reproduce the textured region 20 with the essentially the same geometry from substrate 12 to substrate 12. That is different than the previous methods, such as sand‐blasting or open etching, where the geometry of the textured region 20 varied from one substrate 12 to the next. [0103] EXAMPLES [0104] Example 1 – Example 1 is computer modeling that explores the impact of the second surface features. Example 1 assumes that the textured region is as illustrated in FIGS. 2 and 3, with primary surface features arranged in a hexagonal pattern. Each primary surface feature has a hexagonal perimeter and an aspheric surface facing the external environment. Each aspheric surface is governed by the equation: ^

where z(r) is the sag – the z‐component of the displacement of the surface from the vertex, at the distance from z axis. The z‐axis is perpendicular to the base‐plane. The a₀, a₄, a₆ are all coefficients that describe the deviation of the surface from the axially symmetric quadric surface specified by R and κ. If the coefficients are all zero, which they are assumed to be here, then R is the radius of curvature and κ is the conic constant, as measured at the vertex. When the change in elevation of the surface along the z‐axis is a negative value, then the surface of the primary surface features are concave. In contrast, when the change in elevation of surface of the primary surface features along the z‐axis is positive, then the surface of the primary surface features is convex. [0105] Example 1 further assumes that the secondary surface features generate a light scattering distribution that can be described by the Gaussian scattering function: ଶ ^_^

where, θ is the angle (degree) from the specular direction, I(θ) is radiance in the θ direction, I₀ is radiance in the specular direction, and σ (sigma) is the standard deviation (or scattering factor) of the Gaussian distribution, in degree. As σ increases, the scattering angle increases. [0106] Zemax ray tracing software (Zemax, LLC of Kirkland, Washington, USA) was utilized to model distinctness‐of‐image, pixel power deviation, and transmission haze as a function of change of elevation (height) of the primary surface features and the σ provided by the secondary surface features. The modeling assumed that the substrate had a thickness of 0.3 mm, that the refractive index of the substrate was 1.49, and the substrate had no light absorption. [0107] FIG. 7A reproduces a graph of the calculations of the model pertaining to distinctness‐of‐ image. As the graph reveals, increasing change in elevation (i.e., height or depth) of the primary surface features decreases distinctness‐of‐image. When no secondary surface features are present (sigma = 0) on the primary surface features, then the primary surface features do not begin to decrease distinctness‐of‐image until the change in elevation (height or depth) is greater than 0.08 µm. However, when secondary surface features are present on the primary surface features, increasing height of the primary surface features instantly causes a decrease in distinctness‐of‐image. [0108] FIG. 7B reproduces a graph illustrating the difference the presence of secondary surface features on the primary surface features makes for decreasing distinctness‐of‐image compared to if the secondary surface features were absent. When sigma=0.20 degree, the presence of the secondary surface features further decreases the distinctness‐of‐image, compared to if no secondary surface features were present, for all heights of the primary surface features from ‐ 0.24 µm to + 0.24 µm. The presence of the secondary surfaces features (providing σ = 0.20 degrees) decreases the distinctness‐of‐image by a maximum of ~29% when the height of the primary surface features is ~ 0.10 µm, compared to if no secondary surface features were present. When σ = 0.41 degree, the presence of the secondary surface features further decreases the distinctness‐of‐image, compared to if no secondary surface features were present, for all heights of the primary surface features from ‐0.27 µm to + 0.27. The presence of the secondary surfaces features (providing σ = 0.41 degrees) decreases the distinctness‐of‐image by a maximum of ~25% when the height of the primary surface features is ~ 0.18 µm, compared to if no secondary surface features were present. [0109] In short, for any given height/depth of the primary surface features, there is an optimal σ value to be incorporated as the secondary surface features in order to maximize the contribution that the secondary surface features has on decreasing the distinctness‐of‐image. The graph reproduced at FIG. 7C reveals the optimum value for σ , to minimize distinctness‐of‐image, as a function of change in elevation (height) of the primary surface features. The smallest distinctness‐of‐image values of 92%, 66%, 49% respectively for primary surface feature heights of 0.00 (flat), ‐0.10 µm, and ‐0.14 µm are achieved with σ being 0.14, 0.20, and 0.28 degree, respectively. [0110] Next, the modeling software calculated pixel power deviation as a function of the height of the primary surface features and σ value. FIGS. 7D and 7E each reproduce a graph of the calculations. The graphs reveals that, as the height of the primary surface features increases, the pixel power deviation increases. However, as the value for σ provided by the secondary surface features increases, for any given height of the primary surface features, the pixel power deviation decreases. The secondary surface features cause scattering that evens the angular and spatial distributions of the light transmitting through the primary surface features and thus reduces the pixel power deviation. The effect that the secondary surface features have on reducing pixel power deviation becomes greater as the height of the primary surface features increases. In short, the presence of the secondary surface features on the primary surface features introduces surface scattering that can reduce distinctness‐of‐image (for a given range of heights of the primary surface features) and generally reduces pixel power deviation. [0111] Finally, the modeling software calculated transmission haze as a function of the height of the primary surface features and σ value. FIGS. 7F and 7G each reproduce a graph of the calculations. The graph of FIG. 7F reveals that increasing σ value increases generally increases pixel power deviation, and increasing the height of the primary surface features magnifies the affect that increasing σ value on increasing pixel power deviation (but only slightly). The graph of FIG. 7G reveals however that σ has to be above a certain value before σ causes an increase in pixel power deviation. In the instance of FIG. 7G, where the primary surface features were assumed to have a height of ‐0.1 µm and a width of 100 µm, the σ only begins to increase pixel power deviation when the value for σ is about 0.35 or higher. The value for σ can be greater than 0.35, in order to further reduce pixel power deviation and distinctness‐of‐image, if those benefits outweigh the increase in transmission haze. For example, even at a σ value of 0.7 degree, which maximizes the reduction in pixel power deviation and distinctness‐of‐image, the transmission haze is only 20%, which may be acceptable for a given application. [0112] Thus, as long as the σ value is configured to be right below 0.35, the affect that the secondary features have on decreasing distinctness‐of‐image and pixel power deviation does not simultaneously cause an increase in transmission haze. For example, when the height of the primary surface features are ‐0.1 µm and the σ value is 0.41 degree, the calculated distinctness‐ of‐image is ~74%, the pixel power deviation is ~2.5%, and the transmission haze is ~1%. When the height of the primary surface features are ‐0.1 µm and the σ value is 0.2 degree, the calculated distinctness‐of‐image is ~64%, the pixel power deviation is ~3.5%, and the transmission haze is ~0%. When the height of the primary surface features are ‐0.08 µm and the σ value is 0.41 degree, the calculated distinctness‐of‐image is ~85%, the pixel power deviation is ~2%, and the transmission haze is ~0%. When the height of the primary surface features are ‐ 0.08 µm and the σ value is 0.20 degree, the calculated distinctness‐of‐image is ~73%, the pixel power deviation is ~2.5%, and the transmission haze is ~0%. [0113] In sum, the modeling demonstrates that the incorporation of the secondary surface features on the primary surface features to impart the surface roughness that causes a certain scattering level can result in a low distinctness‐of‐image, low pixel power deviation, and low transmission haze all simultaneously – something not achievable with previous methods of forming the textured region. [0114] Examples 2A‐2D – For Examples 2A‐2D, four (4) samples of glass were prepared. Each sample was etched with an etchant of differing compositions to model the effect that the etchant would have on the generation of secondary surface features to impart a surface roughness within a range of 5 nm to 100 nm. All compositions of the etchant included acetic acid and ammonium fluoride (NH₄F) in varying weight percentages. Table 1, immediately, below summarizes the compositions of the four etchants tested.

Each etchant composition contacted the primary surface of the glass substrate for a time period of 2 minutes. [0115] After the etchant for each example etched the glass sample for the 2‐minute period of time, the surface roughness was determined utilizing an atomic force microscope with a 5 µm by 5 µm scan size. Images that the atomic force microscope captured for each example are reproduced at FIG. 8. The images show the secondary surface features that impart the desired surface roughness. Table 2 immediate below reports the measured surface roughness for each sample. In addition, the σ value, the surface scattering factor, was measured for each sample. Here, the measurement method of the surface scattering factor is as follows. First, the transmission haze of a sample is measured. Then, a raytracing model with Gaussian scattering function for describing surface scattering is used to find proper surface scattering factor which results the same transmission haze as the measured one. Those values too are reported in Table 2 below.

[0116] In general, the higher the weight percentage of water, the higher the surface roughness that was generated during the same two minute period of time. In turn, the higher the surface roughness, the higher the surface scattering σ value. Thus, the surface roughness can be controlled via manipulating the water content of the composition of the etchant, and thus the acetic acid and ammonium fluoride content of the composition of the etchant. [0117] In addition, the transmission haze, coupled distinctness‐of‐image, and pixel power deviation was measured for each sample. Table 3, immediately below, reproduces the results.

Analysis of the results reveal that the higher the surface roughness, the greater the transmission haze. [0118] A graph reproduced at FIG. 8B reproduces the results. In addition, a reproduced at FIG. 8D sets forth measured transmission haze as a function of measured surface scattering σ (sigma) value for each sample, and then a line is modeled to fit the data. The modeled line fitting measured data agrees with the ray scattering model of Example 1 that indicated that the surface scattering σ value had to reach a certain value before it began to impart increased transmission haze. [0119] Examples 3A and 3B – Examples 3A and 3B demonstrate the effect that the secondary surface features (imparting the surface roughness) has on pixel power deviation for samples were primary surface features are also present. For the samples of both Example 3A and 3B, primary surface features were etched into a glass substrate. The composition of the etchant included 1 wt% hydrofluoric acid (HF) and 2 wt% nitric acid (HNO₃). The etchant contacted the primary surface of the glass substrate for 25 seconds, resulting the primary surface features having a depth of 150 nm from a surrounding portion. A dry film resist etching mask was utilized to position the primary surface features in a hexagonal pattern set into the surrounding portion (see FIG. 5). The perimeter of each primary surface feature was hexagonal as well. Each primary surface feature was separated by a center‐to‐center distance of 120 µm. Adjacent primary surface features were separated, perimeter to perimeter, by a distance of 55 µm. One of the samples was retained as Example 3A and no secondary surface features were subsequently added to the sample of Example 3A [0120] For Example 3B, the sample was subjected to a second etching step to impart secondary surface features. The second etching step used an etchant with a composition of 92 wt% acetic acid, 2 wt% ammonium fluoride, and 6 wt% water (deionized). The etchant contacted the primary surface with the primary surface features for a period of time of 2 minutes. The etchant formed the secondary surface features within the textured region, which imparted a surface roughness (R_a) of ~28 nm. [0121] The pixel power deviation that the samples of both Example 3A and Example 3B generated were measured. The measured pixel power deviation was sensitive to the orientation of the sample to the display pixel array, because the primary surface features had a hexagonal perimeter. A graph reproduced at FIG. 9A reproduces the measured pixel power deviation for both Examples 3A and 3B as a function of the orientation angle 52 of the sample. The schematic illustration at FIG. 9B shows what orientation angle means. In short, the substrate is over the display, with the textured region at the primary surface facing away from the display. The display has pixels 54. The substrate forms the orientation angle relative to the display. As the substrate is rotated relative to the display about an axis extending through the substrate orthogonal to the primary surface, the orientation angle changes. [0122] Analysis of the graph of FIG. 9A reveals that the Example 3B, with the added secondary surface features over the primary surface features to impart surface roughness, lowered the pixel power deviation compared to Example 3A, which included only the primary surface features. The secondary surface features lowered the pixel power deviation by ~0.2% to 2.5% (in absolute terms), depending on orientation angle of the substrate relative to the display. For example, at the orientation angle of 85%, the pixel power deviation of Example 3A was 6.5%, while the pixel power deviation of Example 3B was 4.0%, for a reduction (in absolute terms) of 2.5%, (or a 41.7% relative reduction in pixel power display, where 6.5%‐4.0%=2.5% and 2.5%/6.5%*100% is 41.7%). The results suggest that the effect that the secondary surface features has on the pixel power deviation of the sample is a function of the geometry of the primary surface features. [0123] Examples 4A‐4H – For each of Examples 4A‐4H, a glass substrate was obtained having dimensions of 4 mm by 4 mm by 0.7 mm. The glass substrate was then subjected to a first etching step to etch primary surface features set into a surrounding portion. Each primary surface feature had a perimeter that was circular. The diameter of the perimeter was 40 µm. An etching mask was utilized to place each of the primary surface features. The placement of each of the primary surface features was generated using a spacing distribution algorithm. The spacing distribution algorithm required a minimum center‐to‐center distance between circles of 50 µm. The placement of the primary surface features pursuant to the spacing distribution algorithm was thus randomized and did not form a pattern. The placement of the primary surface features made pursuant to the spacing distribution algorithm was transferred to a lithograph mask, which was then used to cure AZ 4210 lithography ink disposed on the primary surface of the substrate. The uncured portions of the lithograph ink was removed and the cured portion remained as the etching mask. The primary surface features occupied about 50% of the area of the textured region, and the depth of the primary surface features was 0.18 µm. The etchant of the first etching step comprised 1 wt% hydrofluoric acid (HF) and 2 wt% nitric acid (HNO₃). The etchant contacted the substrate for a period of time to achieve the target 150nm depth based on etch rate. For of the samples were then set aside as Example 4A‐4D and not subjected to a second etching step to impart secondary surface features. [0124] The remaining four samples were assigned to be Examples 4E‐4H and each subjected to a second etching step using an etchant including acetic acid, ammonium fluoride, and water (deionized). The etchant for Examples 4E and 4F had a composition of 92 wt% acetic acid, 2 wt% ammonium fluoride, and 6 wt% water (deionized). The second etching step for Examples 4E and 4F formed secondary surface features that imparted a surface roughness (Ra) of ~28nm. The etchant for Examples 4G and 4H had a composition of 90 wt% acetic acid, 1 wt% ammonium fluoride, and 9 wt% water (deionized). In each of Examples 4E‐4H, the etchant contacted the sample of a time period of 2 minutes. The second etching step for Examples 4G and 4H formed secondary surface features that imparted a surface roughness (Ra) of ~54nm. [0125] Referring now to FIGS. 10A‐10D, the pixel power deviation (FIG. 10A), the specular reflectance (FIG. 10B), the distinctness‐of‐image (FIG. 10C), and the transmission haze (FIG. 10D) were measured for each example. The measurements are set forth in the aforementioned graphs at FIGS. 10A‐10D. Analysis of the graphs reveal that the second etching step that formed the secondary surface features that added surface roughness to the textured region resulted in a lowering of pixel power deviation and distinctness‐of‐image but resulted in increasing the transmission haze. The higher surface roughness of that the secondary surface features imparted to Examples 4G and 4H did not result in a different scale of lowering of distinctness‐of‐image compared to Examples 4E and 4F. However, the higher surface roughness of that the secondary surface features imparted to Examples 4G and 4H did result in a larger decrease in pixel power deviation compared to Examples 4E and 4F but with a larger increase in transmission haze. The addition of the secondary surface features did not appear to affect measured specular reflectance. [0126] Examples 5A‐5O – For Examples 5A‐5O, a spacing distribution algorithm was utilized to randomly but specifically place points within an area. Each of the points were to be separated by a minimum distance of 105 µm. The points were then triangulated, an inellipse drawn in each triangle, and then the points and triangles were removed. The longest dimension of the ellipses now remaining in the area were scaled down so that the ellipses occupied 50 percent of the area. The placement of the ellipses was then transferred to a lithography mask. The lithography mask was used to form an etching mask on the primary surface of a glass substrate. Each substrate was then etched with the etching mask on the substrate. The etchant utilized had a composition of 0.15wt% hydrofluoric acid and 1wt% nitric acid. The etchant contacted the primary surface with the etching mask for a period of time set forth in Table 4 immediately below that varied among the samples. The etchant formed primary surface features having an elliptical perimeter set into a surrounding portion. The depth of the primary surface features varied, and the depth for each sample is set forth below.

[0127] After removal of the etching mask, the samples of 5M‐5O were then subjected to a second etching step to form secondary surface features at the primary surface. The second etching step used an etchant with a composition of 92 wt% acetic acid, 2 wt% ammonium fluoride, and 6 wt% water (deionized). The etchant contacted the substrate for a time period of 120 seconds. The secondary surface features so formed imparted a surface roughness (Ra) of ~ 28nm to the textured region at the primary surface. [0128] The pixel power deviation, distinctness‐of‐image, specular reflection, and transmission haze were measured for the sample of each of Examples 5A‐5O. The measured results are set forth in the graphs of FIGS. 11A‐11D, which plot the measured value as a function of the depth of the primary surface features with the elliptical perimeter. Analysis of the graphs reveal that the secondary surface features to impart surface roughness of Examples 5M‐5O resulted in a lower pixel power deviation and specular reflectance compared to when no such secondary surface features were included in Examples 5A‐5L. However, the secondary surface features to impart surface roughness of Examples 5M‐5O resulted in a higher distinctness‐of‐image and transmission haze compared to when no such secondary surface features were included in Examples 5A‐5L. In general, the introducing of the secondary surface features to the primary surface features can be either increase or decrease the distinctness‐of‐image, which depends on the design of the primary surface features. Unlike the model of Example 1, the design of the primary surface features of this experimental sample resulted in the increasing of the distinctness‐of‐image. [0129] Example 6A‐6C –Examples 6A and 6B are two different sets of samples, each with primary surface features having an elliptical perimeter, just as in Examples 5A‐5O. The difference was that for the samples of Example 6A, the etching mask used while forming the primary surface features was kept on the substrate while the second etching step was performed to generate the secondary surface features. For the samples of Example 6B, the etching mask was removed before the second etching step was performed to generate the secondary surface features. Thus, in the samples of Example 6A, the secondary surface features and the added surface roughness were formed only on surfaces provided by the primary surface features and not the surrounding portion. In contrast, with the samples of Example 6B, the secondary surface features and the added surface roughness were formed on the entire textured region including both the surrounding portion and the surfaces provided by the primary surface features. [0130] A scanning electron microscope captured images of a sample from both Example 6A and Example 6B. The images are reproduced at FIG. 12A. The images on the left show the primary surface features with the elliptical perimeters set into the surrounding portion. The images in the middle show the secondary surface features. The images on the right show the etching depth of the secondary surface features. [0131] The pixel power deviation, transparency haze, and specular reflectance of samples from both Examples 6A and 6B were measured. A Rhopoint instrument was utilized to determine specular reflectance. The graphs reproduced at FIGS. 12B‐12D set forth the measured data. Analysis of the graphs reveal that the samples of Example 6B, where the etching mask was removed before the second etching step to impart second surface features throughout the entire textured region, resulted in a lower pixel power deviation but higher transmission haze compared to the samples of Example 6A, where the etching mask was maintained during the second etching step and thus the second surface features were imparted only to the surfaces provided by the primary surface features. [0132] The Rhopoint instrument utilized to measure specular reflectance did not measure a difference between the samples of Examples 6A and 6B. However, the device could measure differences in specular reflectance when a 6 degree angle of incidence for the light to be reflected and a 2 degree aperture to measure the specular reflectance. The graph reproduced at FIG. 12E shows the measured data for samples of Examples 6A and 6B, as well as for a sample (Example 6C) where only the primary surface features were present and did not include the secondary surface features to impart surface roughness. Analysis of the graph of FIG. 12E reveals that the presence of the secondary surface features in Examples 6A and 6B reduced specular reflectance compared to when the secondary surface features were absent in Example 6C. The difference in specular reflectance between Examples 6A and 6B is wavelength dependent. [0133] Example 7 – For Example 7, a sample was prepared similar to the samples Examples 5M‐ 5O, where primary surface features with an elliptical perimeter are set into a surrounding portion in a first etching step forming textured region, and then secondary surface features are etched throughout the entire textured region to increase surface roughness. The sample so prepared was then analyzed with a white light interferometer to measure the three dimensional profile of the textured region. FIG. 13A illustrates the three dimensional profile that was measured. The top half illustrates relative elevation differences between primary surface features and the surrounding portion. The bottom half illustrates the topography of the secondary surface features, with the topography of the secondary surface features added to the surfaces that the primary surface features are provided illustrated at the left, and the topography of the secondary surface features added to the surrounding portion illustrated at the right. The three dimensional profile of the secondary features within the primary surface features is measurably different than the three dimensional profile of the secondary features at the surrounding portion – with the surrounding portion showing deeper secondary features. [0134] An atomic force microscope was utilized to image and determine the surface roughness (Ra) imparted by the secondary surface features at both (i) a surface provided by a primary surface feature and (ii) at the surrounding portion. The images are reproduced at FIG. 13B. The image on the left is of the secondary surface features at the surface provided by the primary surface feature, and shows a surface roughness (R_a) of 15.3 nm. The image on the right is of the secondary surface features at the surrounding portion, and shows a surface roughness (R_a) of 33.5 nm. The image on the right and the higher surface roughness (R_a) value at the surrounding portion matches the topography date illustrated at FIG. 13A. The surrounding portion was covered by the etching mask during the formation of the primary surface features and thus had not been contacted with an etchant, unlike the primary surface features which were created by the first etching step. Thus, it is believed that the surrounding portion, previously untouched by an etchant, was more sensitive to the second etching step to impart the secondary surface features.

Claims

CLAIM(S) What is claimed is: 1. A substrate for a display article, the substrate comprising: a primary surface; and a textured region on at least a portion of the primary surface; the textured region comprising: primary surface features, each comprising a perimeter parallel to a base‐plane extending through the substrate disposed below the textured region, wherein the perimeter of each of the primary surface features comprises a longest dimension of at least 5 µm; and one or more sections each comprising secondary surface features having a surface roughness (R_a) within a range of 5 nm to 100 nm.

2. The substrate of claim 1, wherein the primary surface features form a pattern.

3. The substrate of any one of claims 1‐2, wherein the longest dimension of each of the primary surface features is about the same.

4. The substrate of any one of claims 1‐3, wherein an arrangement of the surface features reflect a random distribution.

5. The substrate of any one of claims 1‐4, wherein the perimeter of each primary surface features is elliptical.

6. The substrate of any one of claims 1‐4, wherein the perimeter of each primary surface features is circular.

7. The substrate of any one of claims 1‐4, wherein each primary surface feature provides a surface, and the surface is either concave or convex.

8. The substrate of any one of claims 1‐7, wherein the textured region further comprises: a surrounding portion into which the primary surface features are set or out of which the primary surface features project.

9. The substrate of any one of claims 1‐8, wherein the primary surface features that are adjacent to one another have perimeters that are separated by a distance within a range of 1 µm to 100 µm; and the primary surface features that are adjacent to one another are separated by a center‐ to‐center distance within a range of 5 µm to 150 µm.

10. The substrate of any one of claims 1‐9, wherein each of the primary surface features comprises a change in elevation perpendicular to the base‐plane that is within a range of 0.05 µm to 0.50 µm.

11. The substrate of any one of claims 1‐6 and 8‐10, wherein each primary surface features provides a surface, and the secondary surface features are disposed on the surfaces of the primary surface features.

12. The substrate of any one of claims 1‐6, 9, and 10, wherein the textured region further comprises: a surrounding portion into which the primary surface features are set into or out of which the primary surface features project; wherein, each primary surface feature provides a surface, wherein, the secondary surface features are disposed on both the surrounding portion and on the surfaces of the primary surface features, and wherein, the surface roughness at the surfaces of the primary surface features is less than the surface roughness at the surrounding portion.

13. The substrate of any one of claims 1‐6, 9, and 10 further comprising: a surrounding portion into which the primary surface features are set into or out of which the primary surface features project; wherein, the secondary surface features are disposed on the surfaces of the primary surface features but not on the surrounding portion.

14. The substrate of any one of claims 1‐13, wherein the substrate comprises a glass or glass‐ceramic.

15. The substrate of any one of claims 1‐14, wherein the textured region exhibits a transmission haze within a range of 1.5% to 3.5%; the textured region exhibits a pixel power deviation within a range of 1.5% to 3.5%; the textured region exhibits a distinctness‐of‐image within a range of 2.% to 5.0%; and the textured region exhibits a specular reflectance within a range of 5 GU to 20 GU.

16. A method of forming a textured region of a substrate, the method comprising: forming primary surface features into a primary surface of a substrate according to a predetermined positioning of each primary surface feature thus forming a textured region, each primary surface feature comprising a largest dimension parallel to a base‐plane through the substrate disposed below the primary surface of at least 5 µm; and forming secondary surface features into one or more sections of the textured region, thereby increasing the surface roughness (R_a) of the one or more sections to within a range of 5 nm to 100 nm.

17. The method of claim 16 further comprising: determining the positioning of each primary surface feature utilizing a spacing distribution algorithm.

18. The method of any one of claims 16‐17, wherein forming the primary surface features into the primary surface comprises contacting the primary surface with an etchant while an etching mask is disposed on the primary surface to permit only selective etching of the substrate to form the primary surface features.

19. The method of claim 18, wherein the etchant comprises hydrofluoric acid and nitric acid; and the etchant contacts the substrate for a time period within a range of 10 seconds to 60 seconds.

20. The method of any one of claims 16‐19 further comprising: forming the etching mask by exposing a photorsesist material disposed on the primary surface of the substrate to a curing agent while a lithography mask is disposed on the photoresist material, the lithography mask comprising material and voids through the material to selectively expose portions of the photoresist material to the curing agent, wherein the voids of the lithography mask are positioned according to the predetermined positioning of the primary surface features.

21. The method of any one of claims 16‐20, wherein forming the secondary surface features into one or more sections of the textured region comprises contacting the textured region of the substrate with a second etchant, different than the etchant used to form the primary surface features.

22. The method of any one of claims 16‐21, wherein the second etchant comprises acetic acid and ammonium fluoride.

23. The method of any one of claims 16‐22, wherein forming the primary surface features into the primary surface comprises contacting the primary surface with an etchant while an etching mask is disposed on the primary surface to permit only selective etching of the substrate to form the primary surface features, and forming the secondary surface features into one or more sections of the textured region comprises contacting the one or more sections of the textured region of the substrate with a second etchant, different than the etchant used to form the primary surface features, while the etching mask used to form the primary surface features remains on the substrate.