EP4634708A1 - Articles with scattering regions to preferentially scatter light in one or more directions - Google Patents

Abstract

Described herein are articles with scattering regions comprising a plurality of microstructures that are elongated in a first direction so as to preferentially scatter light in one or more directions. Each of the plurality of microstructures comprises a feature size measured in a second direction that is perpendicular to the first direction. The feature size varies as function of position within the microstructure to achieve favorable transmission haze performance while also suppressing scattering of light at relatively high scattering angles relative to specular to improve display washout from external light sources. A two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scattering directions that are parallel with the first direction.

Description

ARTICLES WITH SCATTERING REGIONS TO PREFERENTIALLY SCATTER LIGHT IN ONE OR MORE DIRECTIONS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application Serial No. 63/432575 filed on December 14, 2022, the content of which is relied upon and incorporated herein by reference in its entirety.

FIELD

[0002] The disclosure relates articles comprising surfaces with scattering regions configured to preferentially scatter light incident thereon in one or more directions.

BACKGROUND

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

[0004] Several techniques exist to reduce glare, including anti-reflective coatings and antiglare technologies. An anti -reflection coating can reduce glare by directly reducing the total amount of reflection. However, certain existing anti-reflection coatings may fail to diminish reflections to a great enough extent throughout the visible spectrum to render such reflections unnoticed by users. Anti-glare technologies attempt to spread reflection of light to a large range of angles to reduce the peak intensity of the reflection and render distracting reflected images less distinct to the user. However, reflection at angles that are too large can result in relatively high haze that can reduce the contrast of the displayed images. [0005] Accordingly, an alternative to existing anti-glare and anti-reflective coating technologies that allows favorable control of the angular distribution of scattered light would be beneficial.

SUMMARY

[0006] An aspect (1) of the present disclosure pertains to an article comprising a first major surface; a second major surface opposing the first major surface; and a scattering region formed in the first major surface, wherein: within the scattering region, the first major surface comprises a plurality of microstructures that are elongated in a first direction, each of the plurality of microstructures comprises a feature size measured in a second direction that is perpendicular to the first direction, the feature size varies as function of position within the microstructure, and a two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scattering directions that are parallel with the first direction.

[0007] An aspect (2) of the present disclosure pertains to an article according to the aspect (1), wherein the two-dimensional power spectral density, is symmetric about at least two distinct axes of symmetry, wherein the two-dimensional power spectral density comprises n-fold rotational about a spectral direction, where n is a finite integer.

[0008] An aspect (3) of the present disclosure pertains to an article according to any of the aspects (l)-(2), wherein each of the plurality of microstructures comprises an average feature size that is greater than or equal to 1.0 pm and less than or equal to 35 pm.

[0009] An aspect (4) of the present disclosure pertains to an article according to any of the aspects (l)-(3), wherein the average feature size is less than or equal to 20 pm.

[0010] An aspect (5) of the present disclosure pertains to an article according to any of the aspects (l)-(4), wherein boundaries of the plurality of microstructures do not extend in straight lines.

[0011] An aspect (6) of the present disclosure pertains to an article according to any of the aspects (l)-(5), wherein a boundary of at least one of the plurality of microstructures forms a closed contour.

[0012] An aspect (7) of the present disclosure pertains to an article according to any of the aspects (l)-(6), wherein: the plurality of microstructures comprises a plurality of first regions of the first major surface that are disposed at a first height relative to an imaginary base plane extending through the article and a plurality of second regions disposed at a second height relative to the imaginary base plane, and each of the plurality of first regions is adjacent to at least one of the plurality of second regions.

[0013] An aspect (8) of the present disclosure pertains to an article according to any of the aspects (l)-(7), wherein the first height differs from the second height by an etch depth that is greater than or equal to 100 nm and less than or equal to 250 nm.

[0014] An aspect (9) of the present disclosure pertains to an article according to any of the aspects ( l)-(8), wherein: at least one of the plurality of first regions is completely surrounded by one of the plurality of second regions, and at least one of the plurality of second regions is completely surrounded by one of the plurality of first regions.

[0015] An aspect (10) of the present disclosure pertains to an article according to any of the aspects ( l)-(9), wherein the scattering region comprises a plurality of second microstructures that are elongated in a third direction that is different from the first direction.

[0016] An aspect (11) of the present disclosure pertains to an article according to any of the aspects (l)-(9), wherein the plurality of microstructures are arranged so as to preferentially scatter the light along a second direction that is perpendicular to the first direction.

[0017] An aspect (12) of the present disclosure pertains to an article according to any of the aspects (l)-(l 1), wherein the two-dimensional power spectral density comprises a suppressed region extending along an axis that intersects a specular direction.

[0018] An aspect (13) of the present disclosure pertains to an article according to any of the aspects (1)-(12), wherein the at least one peak region comprises an outer boundary that is associated with a scattering direction extending at an angle of no more than 10° from the specular direction.

[0019] An aspect (14) of the present disclosure pertains to an article according to any of the aspects ( l)-( 13), wherein, when the light is incident on the first major surface in a plane of incidence that is parallel to the first direction, a magnitude of a bidirectional reflectance distribution function (“BRDF”) of the article is less than 10'⁵ times a peak magnitude of the BRDF at scattering angles greater than 20° from specular.

[0020] An aspect (15) of the present disclosure pertains to an article according to any of the aspects ( l)-( 14), wherein a magnitude of the BRDF is less than 10'⁶ times the peak magnitude at scattering angles greater than 30° from specular.

[0021] An aspect (16) of the present disclosure pertains to an article according to any of the aspects ( l)-( 15), wherein the article exhibits a transmission haze that is less than or equal to 5% and a sparkle that is less than or equal to 3% when measured at 140 ppi. [0022] An aspect (17) of the present disclosure pertains to an article according to any of the aspects ( l)-( 16), wherein the article exhibits an average coupled specular reflectance that is less than or equal to 30% for light from 400 nm to 700 nm that is normally incident on the first major surface.

[0023] An aspect (18) of the present disclosure pertains to an article according to any of the aspects ( l)-( 17), wherein the article exhibits an average transmittance that is greater than or equal to 90% for light from 400 nm to 700 nm that is normally incident on the first major surface.

[0024] An aspect (19) of the present disclosure pertains to an article according to any of the aspects ( l)-( 18), wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 0° viewing angle diminishes by less than 30% as a result of light having an illuminance of 45000 lux being incident on the first major surface at an angle of incidence of 20°.

[0025] An aspect (20) of the present disclosure pertains to an article according to any of the aspects ( l)-( 19), wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed ata 20° viewing angle diminishes by less than 35% as a result of light having an illuminance of 45000 lux being incident on the first major surface at an angle of incidence of 45°.

[0026] An aspect (21) of the present disclosure pertains to an article comprising: a glass-based substrate comprising: a first major surface; a second major surface opposing the first major surface; and a scattering region formed in the first major surface, wherein, within the scattering region, the first major surface comprises: a plurality of first regions disposed at a first height relative to an imaginary base plane extending through the glass-based substrate, and a plurality of second regions disposed at a second height relative to the imaginary base plane, wherein: the plurality of first regions and the plurality of second regions are elongated in a first direction, the plurality of first regions and the plurality of second regions comprise an average feature size in a second direction extending perpendicular to the first direction, the average feature size is greater than or equal to 1.0 pm and less than or equal to 35 pm, the first height differs from the second height by an etch depth that is greater than or equal to 100 nm and less than or equal to 250 nm, and a two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scattering directions that are parallel with the first direction.

[0027] An aspect (22) of the present disclosure pertains to an article according to the aspect (21), wherein: each one of the plurality of first regions is disposed directly adjacent to at least one of the plurality of second regions, the average feature size is less than or equal to 20 pm, boundaries of the plurality of first regions and the plurality of second regions do not extend in straight lines, and a boundary at least one of the plurality of first regions forms a closed contour. [0028] An aspect (23) of the present disclosure pertains to an article according to any of the aspects (21 )-(22), wherein: at least one of the plurality of first regions is completely surrounded by one of the plurality of second regions, and at least one of the plurality of second regions is completely surrounded by one of the plurality of first regions.

[0029] An aspect (24) of the present disclosure pertains to an article according to any of the aspects (21)-(23), wherein the two-dimensional power spectral density comprises a suppressed region extending along an axis that intersects a specular direction.

[0030] An aspect (25) of the present disclosure pertains to an article according to any of the aspects (21)-(24), wherein the at least one peak region comprises an outer boundary that is associated with a scattering direction extending at an angle of no more than 10° from the specular direction.

[0031] An aspect (26) of the present disclosure pertains to an article according to any of the aspects (21)-(25), wherein, when the light is incident on the first major surface in a plane of incidence that is parallel to the first direction, a magnitude of a bidirectional reflectance distribution function (“BRDF”) of the article is less than 10'⁵ times a peak magnitude of the BRDF at scattering angles greater than 20° from specular.

[0032] An aspect (27) of the present disclosure pertains to an article according to any of the aspects (21)-(26), wherein a magnitude of the BRDF is less than 10'⁶ times the peak magnitude at scattering angles greater than 30° from specular.

[0033] An aspect (28) of the present disclosure pertains to an article according to any of the aspects (21)-(27), wherein the article exhibits a transmission haze that is less than or equal to 10% and a sparkle that is less than or equal to 4% when measured at 140 ppi.

[0034] An aspect (29) of the present disclosure pertains to an article according to any of the aspects (21)-(28), wherein the article exhibits an average coupled specular reflectance that is less than or equal to 30% for light from 400 nm to 700 nm that is normally incident on the first major surface. [0035] An aspect (30) of the present disclosure pertains to an article according to any of the aspects (21)-(29), wherein the article exhibits an average transmittance that is greater than or equal to 90% for light from 400 nm to 700 nm that is normally incident on the first major surface.

[0036] An aspect (31) of the present disclosure pertains to an article according to any of the aspects (21)-(30), wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 0° viewing angle diminishes by less than 30% as a result of light having a luminance of 45000 lux being incident on the first major surface at an angle of incidence of 20°.

[0037] An aspect (32) of the present disclosure pertains to an article according to any of the aspects (21)-(31), wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 20° viewing angle diminishes by less than 35% as a result of light having a luminance of 45000 lux being incident on the first major surface at an angle of incidence of 45°.

[0038] An aspect (33) of the present disclosure pertains to an article comprising a first major surface; a second major surface opposing the first major surface; and a scattering region formed in the first major surface, wherein: within the scattering region, the first major surface comprises a plurality of microstructures that are elongated in a first direction, each of the plurality of microstructures comprises a feature size measured in a second direction that is perpendicular to the first direction, and boundaries of the plurality of first regions and the plurality of second regions do not extend in straight lines, a boundary at least one of the plurality of first regions forms a closed contour, a two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scattering directions that are parallel with the first direction, and the two- dimensional power spectral density, is symmetric about at least two distinct axes of symmetry, wherein the angular power spectral density comprises n-fold rotational symmetry around a surface normal of the first major surface, where n is a finite integer.

[0039] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understanding the nature and character of the claims. The accompanying drawings are comprised to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the description serve to explain principles and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings incorporated in and forming a part of the specification illustrate several aspects of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings:

[0041] FIG. 1 depicts a perspective view of a display article, according to one or more embodiments of the present disclosure;

[0042] FIG. 2 schematically depicts a portion of a scattering region of the display article of FIG. 1, according to one or more embodiments of the present disclosure;

[0043] FIG. 3 schematically depicts a height profile of the scattering region depicted in FIG. 2, according to one or more embodiments of the present disclosure;

[0044] FIG. 4A graphically depicts a target power spectral density (“PSD”) of a scattering region for light that is normally incident on the scattering region in an angular coordinate space using a first set of parameters, according to one or more embodiments of the present disclosure; [0045] FIG. 4B graphically depicts a target PSD of a scattering region for light that is normally incident on the scattering region in the angular coordinate space using a second set of parameters selected to alter the shapes of peak scattering regions relative to the first set of parameters used to generate the target PSD depicted in FIG. 4A, according to one or more embodiments of the present disclosure;

[0046] FIG. 4C graphically depicts a target PSD of a scattering region for light that is normally incident on the scattering region in the angular coordinate space using a third set of parameters selected to alter the shapes of peak scattering regions relative to the first set of parameters used to generate the target PSD depicted in FIG. 4A, according to one or more embodiments of the present disclosure;

[0047] FIG. 4D graphically depicts a target PSD of a scattering region for light that is normally incident on the scattering region in the angular coordinate space using a fourth set of parameters selected to increase a width a suppressed region relative to the third set of parameters used to generate the target PSD depicted in FIG. 4C, according to one or more embodiments of the present disclosure; [0048] FIG. 4E graphically depicts a target PSD of a scattering region for light that is normally incident on the scattering region in the angular coordinate space using a fifth set of parameters, according to one or more embodiments of the present disclosure;

[0049] FIG. 4F graphically depicts a target PSD of a scattering region for light that is normally incident on the scattering region in the angular coordinate space using a sixth set of parameters selected to decrease the size of an area with a peak scattering amplitude relative to the fifth set of parameters used generate the target PSD depicted in FIG. 4E, according to one or more embodiments of the present disclosure;

[0050] FIG. 5 is a flow diagram of a method of forming a plurality of microstructures in a surface of an article, according to one or more embodiments of the present disclosure;

[0051] FIG. 6 is an image of a scattering region formed in an article in accordance with a first set of examples of the present disclosure;

[0052] FIG. 7 schematically depicts an apparatus for measuring washout caused by light being incident on a display article, according to one or more embodiments of the present disclosure; [0053] FIG. 8 schematically depicts a vehicle interior system comprising displays having light from ambient light sources incident on cover articles of the displays, according to one or more embodiments of the present disclosure;

[0054] FIGS. 9A-9F are images of test patterns transmitted through a counter example article with an anti-glare surface treatment when the article are subjected to various external lighting conditions, according to one or more embodiments of the present disclosure;

[0055] FIG. 10 is a graph showing modulation transfer function magnitude as a function of spatial frequency for the counter example glass article when subjected to a first lighting condition, according to one or more embodiments of the present disclosure;

[0056] FIG. 11 is a graph showing modulation transfer function magnitude as a function of spatial frequency for the counter example glass article when subjected to a second lighting condition, according to one or more embodiments of the present disclosure;

[0057] FIG. 12 is a plot of a bidirectional reflectance distribution function for an example article when light is incident on a scattering region thereof at an angle of incidence of 50°, according to one or more embodiments of the present disclosure; and

[0058] FIG. 13 schematically depicts an article including multiple regions with microstructures being elongated in different directions, according to one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0059] Referring generally to the figures, described herein are articles comprising a surface with a scattering region that is designed to preferentially scatter light in one or more directions. In the scattering region, the surface comprises a plurality of microstructures that are elongated so as to preferentially scatter light in particular directions. The microstructures can be a variety of different structures (e.g., protrusions and cavities in the first major surface, regions of different surface height, regions where the surface height of the surface is changing as a function of position on the surface). The directions in which the scattering regions preferentially scatter light can be determined by orientation of the article in the environment in which the article is disposed. As a result, the scattering regions described herein allow for strategic placement and orientation within the environment to direct scattered light away from areas where glare may be most detrimental for a given application.

[0060] In an aspect, the plurality of microstructures of the scattering regions described herein are designed in the Fourier domain based a target power spectral density (“PSD”) that is azimuthally anisotropic. The target PSD is selected to have desired characteristics for a particular application. For example, in a display cover application, the microstructures can be arranged and specifically constructed to reduce specular reflectance (e.g., such that the glass article exhibits a specular reflectance less than 30%), while maintaining low haze (e.g., less than 10% in transmission) and sparkle (e.g., less than 4%) over a wavelength range of interest (e.g., the visible spectrum). In other examples (e.g., when the substrate is opaque or colored), the scattering region can be used for decorative applications such that the article possesses a visual appearance that varies depending on a viewing angle when illuminated by a light source (ambient light or other light source). The articles described herein are useful in a variety contexts.

[0061] A context where the scattering regions described herein may be particularly useful is in the context of automotive interior displays. Automotive interiors may include one or more displays (e.g., center counsel displays, dashboard displays, pillar displays, seatback displays, and others). Such displays may be fixed in orientation relative to the driver. When in operation, vehicles are subject to ambient light conditions that can cause relatively severe glare. For example, sunlight can enter the vehicle interior through a side window or windshield and reflect or scatter off of the displays, causing bright glare that can distract the driver. The preferential scattering provided by the scattering regions described herein can be constructed to direct commonly encountered glare sources in vehicles away from the driver. The PSD exhibited by the first major surface can include peak regions and suppressed regions. The plurality of microstructures may be designed based on the location of the display relative to likely positions of occupants’ eyes to prevent scattering of ambient (or other) light from distracting the occupants. The drivers’ eyes, for example, may be positioned in the suppressed regions such that light entering the vehicle interior from a side window is preferentially scattered to areas outside of the drivers’ field of vision, thereby reducing glare likely to distract the driver.

[0062] The microstructures in the scattering region may also be designed to provide such glare reduction while largely avoiding detrimental effects on display performance. In embodiments, for example, the plurality of microstructures may include a plurality of first regions of the surface disposed at a first height relative to an imaginary base plane extending through the substrate and a plurality of second regions of the surface disposed at a second height relative to the imaginary base plane. The first and second regions can be elongated in a first direction and arranged such that a height of the surface varies substantially periodically as a function of distance in a second direction. The microstructures can comprise an average feature size Sr in the second direction. Sr can be selected based on performance objectives (e.g., peak scattering directions, specular reflectance reduction, haze). For example, relatively low Sr values (e.g., less than 10 pm) are generally associated lower sparkle, but may result in higher transmission haze than relatively high Sr values (e.g., greater than 20 pm). In embodiments, for example, the feature size may be less than 20 pm to provide a favorable combination of transmission haze and sparkle performance. Performance objectives for a particular application may be used to determine a particular design of the plurality of microstructures. The scattering regions described herein provide flexibility to achieve various performance objectives.

[0063] As used herein, the term “two-dimensional power spectral density” or “ 2D PSD,” when used in describing a surface of a particular article, refers to a profile calculated from a surface height profile that is measured from the surface Particularly, the surface height profile of a 1x1 mm area of the surface is measured using white light interferometry. The surface heights are measured with a lateral resolution of about 360 nm. The surface height profile data array is input to a suitable data analysis program (e.g., Gwyddion) to compute the two-dimensional power spectral density. The term “2D PSD” is to be differentiated from the term “target radial PSD.” The target radial PSD is not calculated from a measured surface height profile of a surface, but is instead calculated mathematically as an ideal radial PSD for a particular design. Unless otherwise specified, 2D PSDs are reported at a wavelength of 550 nm. [0064] As used herein, the term “specular reflectance (Rs)” or “Rs” is defined as the peak intensity of reflected light from a first surface of a substrate within a cone of angles of +/- 0.1°. Specular reflectance may be measured using a Rhopoint IQ meter, which reports an Rs value in Gloss Units (“GU”) normalized to a reference highly polished black glass with a refractive index of 1.567 for the Sodium D line.

[0065] Articles described herein may be characterized by uncoupled distinctness-of-image value. “Distinctness-of-reflected image,” “distinctness-of-image,” “DOI” or like term is defined by method A of ASTM procedure E430 (ASTM E430), entitled “Standard Test Methods of Gloss of High-Gloss Surfaces by Abridged Goniophotometry.” Such measurements can be made using a goniophotometer (Rhopoint IQ (Goniophotometer) 20°/60°/85°, Rhopoint Instruments).

[0066] As used, herein, the term “haze” or “transmission haze” refers to the percentage of transmitted light scattered outside an angular cone of about ±2.5° in accordance with ASTM DI 003, 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 DI 003 refers to plastics, the standard has been applied to substrates comprising a glass material as well. For an optically smooth surface, transmission haze is generally close to zero.

[0067] As used herein, the terms “sparkle,” “sparkle contrast,” “display sparkle,” “pixel power deviation,” “PPD”, or like terms refers to the visual phenomenon that occurs when a textured transparent surface is combined with a pixelated display. Generally speaking, quantitation of sparkle involves imaging a lit display or simulated display with the textured surface in the field of view. The calculation of sparkle for an area P is equal to o(P)/p(P), where o(P) is the standard deviation of the distribution of integrated intensity for each display pixel contained within area P divided by the mean intensity p(P). Following the guidance in: (1) J. Gollier, et al., “Apparatus and method for determining sparkle,” US9411180B2, United States Patent and Trademark Office, 20 July 2016; (2) A. Stillwell, et al., “Perception of Sparkle in Anti-Glare Display Screens,” JSID 22(2), 129-136 (2014); and (3) C. Cecala, et al., “Fourier Optics Modeling of Display Sparkle from Anti-Glare Cover Glass: Comparison to Experimental Data”, Optical Society of America Imaging and Applied Optics Congress, JW5B.8 (2020); one skilled in the art can build an imaging system to quantify sparkle. Alternatively, a commercially available system (e.g. the SMS-1000, Display Messtechnik & Systeme GmbH & Co. KG, Germany) can also be used. Unless described otherwise, sparkle is measured with a 140 PPI display using the following procedure. A 140 PPI display (e.g. Z50, Lenovo Group Limited, Hong Kong) with only the green subpixels lit (R = 0, B = 0, G = 255), at full display brightness is imaged using a f = 50 mm lens/machine vision camera combination (e.g. C220503 1:2.8 50 mm 030.5, Tamron, Japan) and Stingray F-125 B, Allied Vision Technologies GmbH, Germany). The lens settings are aperture = 5.6, depth of field = 0.3, working distance = about 290 mm; with these settings, the ratio of display pixels to camera pixels is approximately 1 to 9. The field of view for analysis contains approximately 7500 display pixels. Camera settings have the gain and gamma correction turned off. Periodic intensity variations from, e.g. the display, and non-periodic intensity variations, e.g. dead pixels, are removed during analysis prior to the calculation of sparkle.

[0068] ‘ ‘Gloss,” “gloss level,” or like terms refer to, for example, surface luster, brightness, or shine, and more particularly to the measurement of specular reflectance calibrated to a standard (such as, for example, a certified black glass standard) in accordance with ASTM procedure D523, the contents of which are incorporated herein by reference in their entirety. Common gloss measurements are typically performed at incident light angles of 20°, 60°, and 85°, with the most commonly used gloss measurement being performed at 60°. Unless otherwise noted, the amount of gloss is reported under ASTM D523. Unless otherwise noted results are provided in gloss units (“GUs") over a 100-2000 scale for 20° measurements and a 100-1000 scale for 60° measurements.

[0069] Anti -glare performance can be measured with the nothing coupled to the surface (herein described as “uncoupled”) or a black absorber (index-matched to the glass sample) coupled to a rear surface of the glass (herein described as “coupled”).

[0070] Referring now to FIG. 1, an article 10 is depicted, according to an example embodiment. The article 10 comprises a substrate 12. In the depicted embodiment, the article 10 is a display article (e.g., a display cover article) and further includes a housing 14 to which the substrate 12 is coupled and a display 16 within the housing 14. In such embodiments, the substrate 12 at least partially covers the display 16 such that light that the display 16 emits can transmit through the substrate 12.

[0071] The substrate 12 may be a variety of materials depending on the implementation. For example, in embodiments, such as in the embodiment depicted in FIG. 1, the substrate 12 is a glass or glass-ceramic substrate. Various properties and examples for such glass or glassceramic substrates are described in greater detail herein. In embodiments, the substrate 12 may be constructed of a material other than glass such as paper, plastic or other suitable polymeric material, or the combination of two or more than two materials of glass, plastic, paper, and other polymeric suitable material. In embodiments, the substrate 12 is transparent, or exhibits an average transmittance for light normally incident on the substrate 12 that is in a wavelength range of 400 nm to 700 nm of greater than or equal to 70% (e.g., greater than or equal to 80%, greater than or equal to 85%, greater than or equal to 90%, greater than or equal to 92%, greater than or equal to 92.5%, greater than or equal to 93%). In embodiments, the substrate 12 is opaque or exhibits an average transmittance for light normally incident on the substrate that is in a wavelength range of 400 nm to 700 nm that is less than or equal to 30%. In embodiments, the substrate 12 is tinted to exhibit a colored appearance under ambient illumination (e.g., from sunlight).

[0072] The substrate 12 includes a first major surface 18, a second major surface 19, a scattering region 20 defined on the first major surface 18, and a thickness 21 that the first major surface 18 bounds in part (e.g., representing a minimum distance between the first major surface 18 and the second major surface 19 at a particular point on the first major surface 18). In the depicted embodiment, the substrate 12 is substantially planar in shape such that the first major surface 18 and the second major surface 19 are generally flat (with the exception of plurality of microstructures formed in the first major surface 18, as described herein). Embodiments where the substrate 12 comprises a curved shape (e.g., via suitable hot-forming and cold-forming techniques) are also contemplated and within the scope of the present disclosure. In such embodiments, the “surface normal 33” referenced herein are to a local surface normal at a point where light from an external environment 24 is incident on the first major surface 18. In the depicted embodiment, the first major surface 18 generally faces toward the external environment 24 surrounding the article 10 and away from the display 16. In embodiments, the display 16 emits visible light that transmits through the thickness 21 of the substrate 12, out the first major surface 18, and into the external environment 24.

[0073] In embodiments, the substrate 12 can be constructed of multiple materials. For example in embodiments, the substrate 12 comprises a glass layer and a second layer of a suitable material (e.g., a suitable polymeric material). The second layer may form the first major surface 18 of the article 10. The scattering region 20 described herein may be formed in the second layer. Such an approach may facilitate flexibility of approaches that can be used to construct the scattering region 20 described herein.

[0074] As described herein, the scattering region 20 is structured to preferentially scatter light originating from the external environment 24 in one or more preferred directions. In embodiments, the scattering region 20 is structured to preferentially scatter light originating from the external environment 24 along a peak scattering axis 50. As used herein, the term “peak scattering axis” is used to denote an axis along which a PSD associated with a scattering region has a local maximum in amplitude. The peak scattering axis 50 depicted in FIG. 1 is for light incident on a particular location (represented by the box 27) of the first major surface 18. The peak scattering axis 50 may vary (in terms of orientation) depending on a location where light impinges on the first major surface 18. In embodiments, the scattering region 20 is constructed such that light is preferentially scattered in the same set of directions irrespective of location of incidence on the first major surface 18 (i.e., each peak scattering axis may extend parallel to the depicted peak scattering axis 50). In embodiments, the scattering region 20 is constructed such that light is preferentially scattered in different directions, depending on location of incidence on the first major surface 18. While examples are described herein where the scattering region 20 is configured to preferentially scatter light along a peak scattering axis 50 at a particular location on the first major surface 18, embodiments are contemplated where the scattering region 20 is configured to preferentially scatter light along multiple peak scattering axes at a single location of incidence are also contemplated.

[0075] As depicted in FIG. 1, light from the external environment 24, represented by incoming light ray 22, may be incident on the first major surface 18 at an angle of incidence 0i (representing a zenith angle that the incoming light ray 22 extends relative to the surface normal 33 of the first major surface 18, depicted as the z-direction in FIG. 1). The incoming light ray 22 may represent light from a number of difference sources from outside of the article 10. For example, the incoming light ray 22 may represent sunlight that is incident on the first major surface 18 or light from another external light source (e.g., light reflected or scattered from an external object, light generated by another source). The scattering region 20 scatters the light represented by the incoming light ray 22 in a scattering direction, represented by the scattered light ray 25. The scattered light ray 25 has an amplitude depending on the angle of incidence 0i and a scattering angle 0_S relative to the surface normal 33. As shown, the scattered light ray 25 is scattered in a scattering direction that, when projected into a plane of the first major surface 18 extending perpendicular to the surface normal 33, extends at an azimuthal angle <I> relative to a first direction (the x-direction depicted in FIG. 1).

[0076] As described herein, the scattering region 20 is constructed such that the amplitude of the scattered light ray 25 is maximum when propagating along a peak scattering axis (extending parallel to the peak scattering axis 50 in some embodiments). In the depicted example, the peak scatering axis extends along the second direction, such that the scattered light ray 25 possesses a relatively high amplitude when <b is equal to 90°. Light scatering in directions off of the peak scatering axis may have relatively low scatering amplitudes. The peak scatering axis may at least partially be determined by the orientation of the substrate 12 in the external environment 24. Altering the orientation of the substrate 12 therefore determines the alignment of the peak scatering axis and beneficially provides flexibility for determining regions in the external environment 24 through which scatered light will propagate and will not propagate. [0077] As described herein, the scatering region 20 is designed based on a target far field scatering direction represented by a target PSD. The PSD determines scatering amplitudes as a function of the azimuthal angle <I> and the scatering angle 0_S. An angular coordinate space can be defined with values of 0_X and 0y, where 0x = <5 and 0_y = 9O°-0_X. In the angular coordinate space, the PSD defines ranges of 0_X and 0y values that result in relatively low and relatively high scatering amplitudes. The structure of the scatering region 20 is determined based on the target PSD via the methods described herein. As will be further described herein, the target PSD, comprises a peak region that is disposed entirely on one side of the 0_y = O axis of the angular coordinate space. In embodiments, in the angular coordinate space, the target PSD is selected to be symmetric about at least two distinct axes of symmetry. In embodiments, the target PSD is selected to comprise at least two peak regions of relatively high scatering amplitude that are symmetrically disposed on either side of a first axis of symmetry and a suppressed region that comprises a boundary that is symmetric about the first axis of symmetry. Each of the peak regions and the suppressed regions may also have peripheral shapes that are symmetrical about both the first axis of symmetry and a second axis of symmetry extending in a different direction than the first axis of symmetry.

[0078] The scatering regions described herein may exhibit a 2D PSD that is expressed in a coordinate system with coordinates (k_x, k_y), where k_x and k_y are directional components of a spatial frequency k associated with scattered light (based on the azimuthal angle <!>). The spatial frequency k for scatered light may vary depending on the angle of incidence 0i and wavelength X of the scatered light based on the following relation p k = (sin 0₍ — sin 0_S) (A) where p is an integer. Using the relation A, one can also solve for the scatering angle 0_S for a particular spatial frequency k.

[0079] FIG. 2 schematically depicts a plan view of the region II of the scatering region 20 of the article 10 depicted in FIG. 1, according to an example embodiment of the present disclosure. As shown, the scattering region 20 comprises a plurality of microstructures 26 that are elongated in the first direction (the x-direction in the depicted example) such that the scattering region 20 preferentially scatters light in the second direction (the y-direction in the depicted example). As used herein, the term “elongated” refers to a direction along which a maximum length line segment extends through a single microstructure without impinging the boundary of that microstructure. In the example depicted in FIG. 2, the plurality of microstructures 26 are elongated in the first direction because, as depicted, a line segment extending in that direction can extend through an entirety of the depicted portions of the plurality of microstructures 26 without impinging on the boundaries thereof, while line segments extending in any other direction would impinge on the boundaries of a single one of the plurality of microstructures 26.

[0080] It should be understood that FIG. 2 represents a simplified version of the scattering region 20 for the purposes of discussion. The plurality of microstructures 26 may have a form other than depicted in FIG. 2. With reference to FIGS. 2-3, in the depicted example, the plurality of microstructures 26 comprise a plurality of first regions 28 of the first major surface 18 and a plurality of second regions 30 of the first major surface 18. The plurality of first regions 28 and the plurality of second regions 30 are generally disposed at different heights. In embodiments, the plurality of first regions 28 and the plurality of second regions 30 can be characterized as being planar in the sense that, within each of the regions, the surface height of the first major surface 18 does not substantially vary. For example, in embodiments, within a particular one of the plurality of first regions 28 or one of the plurality of second regions 30, the surface height variation (or roughness) may be less than 50 nm, in terms of root-meansquare (RMS) variation (or less than 20 nm RMS, or less than 10 nm RMS). For example, in these embodiments, each of the plurality of first regions 28 and the plurality of second regions 30 can be characterized by a surface height variation from 0. 1 nm RMS to 50 nm RMS, from 0. 1 nm RMS to 20 nm RMS, from 0. 1 nm RMS to 10 nm RMS, or from 0.1 nm RMS to 1 nm RMS.

[0081] In the example depicted in FIGS 2-3, the plurality of first regions 28 and the plurality of second regions 30 are planar. The plurality of first regions 28 are disposed at a first height hi relative to an imaginary base plane 35 extending through the substrate 12 and the plurality of second regions 30 are disposed at a second height h2 relative to the imaginary base plane 35. In the depicted example, the plurality of microstructures 26 are regions of constant height of the first major surface 18 (with the understanding that the actual structure of the plurality of microstructures 26 may include surface height deviations associated with the roughness of the first major surface 18 and may also not exactly extend in the x-y plane due to effects of the process of forming the plurality of microstructures 26, such as the etching process described herein). While the plurality of first regions 28 and the plurality of second regions 30 are depicted to have boundaries extending in the first direction along entireties thereof in FIG. 2, such a structure is a simplification. Actual boundaries of the plurality of microstructures 26 include portions that do not extend in the first direction and generally do not have linear shapes, but rather change in direction depending on location on the first major surface 18. The boundaries of the plurality of microstructures 26 have non-linear shapes.

[0082] The plurality of microstructures 26 may also include closed microstructures (where a boundary associated with a particular microstructure is a closed contour). As depicted in FIG. 2, for example, the plurality of first regions 28 includes a closed first region 28a that is completely surrounded by one of the plurality of second regions 30 and the plurality of second regions 30 includes a closed second region 30a that is completely surrounded by one of the plurality of first regions 28.

[0083] The non-uniform directions in which the plurality of microstructures 26 extend, in combination with the closed micro structures, are representative of ways in which the scattering region 20 differs in structure from a typical diffraction grating. Certain existing reflective diffraction gratings may include a surface with height that periodically varies in height relative to an imaginary base-plane, with regions of the same height extending parallel to one another and to adjacent regions of different heights. Such diffraction grating structures result in scattering pattern that is highly dependent on the wavelength of light (with the peak scattering angle being determined with the grating equation). The scattering region 20, by having a structure where the microstructures have boundaries extending in variable directions and having close boundaries, provides scattering patterns that are less wavelength dependent than those associated with diffraction gratings, resulting in less angular separation of different wavelengths of light.

[0084] In embodiments, the plurality of microstructures 26 comprise an average feature size Sr. The actual feature size of each of the plurality of microstructures 26 may vary along the first direction (the x-direction). The average feature size Sr represents an average width of the plurality of microstructures 26 in the second direction (with the average width being calculated as an average of the average widths of each of the plurality of microstructures 26). The average widths of each of the plurality of microstructures 26 may be tightly distributed about the average of the average widths of all of the plurality of microstructures 26 (such that none of the plurality of microstructures 26 comprises an average width that deviates from the average of the average widths by more than 30% of the average). The height of the first major surface 18 relative to the imaginary base plane 35 varies substantially periodically in the second direction within the scattering region 20. In embodiments, the average feature size Sr represents an approximate half period with which the surface height of the first major surface 18 varies in the second direction within the scattering region 20. As described herein, the average feature size Sr may be used to determine a scattering distribution for the light, with the size of peak regions in the PSD being inversely proportional to the average feature size Sr (smaller average feature sizes are associated with larger peak regions). In embodiments, the average feature size Sris greater than or equal to 1.0 pm and less than or equal to 100 pm (e.g., greater than or equal to greater than or equal to 2.0 pm and less than or equal to 100 pm, greater than or equal to 3.0 pm and less than or equal to 100 pm, greater than or equal to 4.0 pm and less than or equal to 100 pm, greater than or equal to 5.0 pm and less than or equal to 100 pm, greater than or equal to 5.0 pm and less than or equal to 75 pm, greater than or equal to 5.0 pm and less than or equal to 50 pm, greater than or equal to 6.0 pm and less than or equal to 45 pm, greater than or equal to 6.0 pm, and less than or equal to 40 pm, greater than or equal to 6.0 pm and less than or equal to 35 pm, greater than or equal to 7 pm and less than or equal to 32 pm, greater than or equal to 5 pm and less than or equal to 20 pm).

[0085] The physical structure of the plurality of microstructures 26 may be determined using scalar diffraction theory and a suitable optimization algorithm, as described herein. As shown in FIG. 3, incoming radiation from the external environment 24 may be approximated as uniform planewave approximated as where I_o represents a uniform intensity of incoming radiation and k_xo and k_yo represent wave vectors associated with the wavelength of the radiation and the angle of incidence on the first major surface 18 (e.g., the angle of incidence may be broken up into components in x-z and y- z planes depicted in FIG. 1). In such a case, the scalar near field for the outgoing radiation (after interaction with the first major surface 18) can be approximated as

27 where p is the Fresnel coefficient of the interface, and (x, y) = — A. 2H(x, y) is the local phase accumulated through the double passage of the distance to the first major surface 18, H(x, y), with H(x,y) representing the pattern formed by the plurality of microstructures 26. In this example, incoming radiation is approximated as having a uniform intensity distribution and the interface between the substrate 12 and the external environment 24 is approximated as only applying a spatially varying phase such that the outgoing radiation in the near field also has a uniform intensity distribution.

[0086] In this example depicted in FIG. 3, the far field scattering pattern associated with the outgoing radiation may be represented in the reciprocal k space and is related to the near field computed using Equation 3 through a Fourier transform and expressed as

In embodiments, the plurality of microstructures 26 are structured so that H(x,y), when input into Equation 3, substantially matches a target far field distribution. As described herein, the target far field distribution is selected to selectively scatter light along one or more peak scattering axes. The structure and arrangement of the plurality of microstructures 26 may be determined using a process of starting from a target PSD and using the target PSD to find phase information associated with the target far-field scattering pattern using a suitable algorithm (e.g., using a suitable phase retrieval algorithm, such as the Gerchberg-Saxton algorithm). The phase information may then be converted to the H(x,y) value contained in Equation 3 for determining the structure of the surface.

[0087] An initial step in determining the structure of the plurality of microstructures 26 is formulating a target PSD in the angular coordinate space described herein. In examples, an azimuthally uniform function may be utilized as a starting point in formulating a target PSD. The azimuthally uniform function may then by modified to reduce scattering amplitudes in desired regions of the angular coordinate space. An example azimuthally uniform function may any of the by the Laguerre-Gaussian (“LG”) modes, expressed as where I is an azimuthal index, k_max is a wavenumber associated with a maximum scattering intensity (associated with 0_O), and ci is a normalization factor. The LG modes beneficially provide an (/ - 1^th) order zero at wavenumbers equal to 0 (representing specular reflection), with greater I values being associated with a flatter distribution of scattering amplitudes around specular reflectance. The LG modes also beneficially decay exponentially at large wavenumbers (associated with large angles of scattering). [0088] A modified LG mode expression was selected as an example target PSD in the angular coordinate space described herein. In this example, it was assumed that Oi = 0°, and the modified LG mode expression is defined as where, as described herein m, 0_O, A0_X, and A0_y are parameters that can be input and used to determine optical performance attributes tailored to a particular application. In Equation 5, the term m operates in a manner similar to the azimuthal index I in the previously-described LG modes, determining the order of the zero when 0 = 0 (and therefore 0y=O) and the flatness of the distribution. A comparison between Equations 4 and 5 reveals that this example target PSD differs from an LG mode in two major respects. First, the term outside of the exponential is only a function of the second angle 0_y. As a result, when Oy is equal to zero (representing a circumstance when the scattered light ray 25 is in the x-z plane depicted in FIG. 1), there is a no scattering amplitude (because Equation 5 is zero). Light is thus preferentially scattered along the second direction (when 0_y does not equal zero) as a result of this modification. Secondly, the term in the exponential is modified by the parameters A0_X, A0y, and 0_O. These parameters permit the target PSD to be modified to determine the size and location of peak and suppressed regions of the target PSD, with the peak regions representing regions of relatively high scattering amplitude and the suppressed regions of the target PSD having relatively low or zero scattering amplitudes. The operation of the parameters A0_X, A0_y, and 0_O will now be described in view of several examples. While Equation 5 was used to compute the surfaces in the examples described herein, it should be noted that various target PSDs are contemplated and within the scope of the present disclosure.

[0089] FIGS. 4A, 4B, 4C, 4D, and 4F depict graphical representations of target PSDs 400, 410, 420, 430, 440, and 450, respectively. Each of the target PSDs 400, 410, 420, 430, 440, and 450 contains a different combination of the parameters m, A0_x, AOy, and 0_o to demonstrate how adjusting the value of a particular parameter effects a far field scattering pattern. Each of the target PSDs 400, 410, 420, 430, 440, and 450 depicted in FIGS. 4A-4F is for light that is normally incident on the first major surface 18 (see FIG. 1) and graphically depicted in the angular coordinate space described herein (the x-axis of each plot represents values for 0_x and the y-axis of each plot represents values for 0_y, with the origin of each plot representing specular reflection. As shown in FIG. 4A, the target PSD 400 comprises a first peak region 402 and a second peak region 404 of relatively high scattering amplitudes (the plots depict PSD amplitudes in units having an arbitrary scale). The first and second peak regions 402 and 404 are symmetrically disposed on different sides of a first axis of symmetry 406 (the first and second peak regions 402 and 404 are entirely disposed on either side of the first axis of symmetry 406, which corresponds to scattering directions where 0_y = 0). Additionally, each of the first and second peak regions 402 and 404 individually comprises a shape that is symmetric about a second axis of symmetry 408 extending perpendicular to the first axis of symmetry 406. In the depicted example, the first and second axes of symmetry 406 and 408 coincide with the 0_X axis and the 0_y axis. Embodiments where the first and second axes of symmetry 406 and 408 are removed from the 0_X axis and the 0y axis are also contemplated and within the scope of the present disclosure (e.g., Equation 5 may be modified to provide a target PSD having any suitable shape in the angular coordinate space).

[0090] Referring still to FIG. 4A, the target PSD 400 also comprises a suppressed region 409 of relatively low scattering amplitude that extends between the first and second peak regions 402 and 404 and also surrounds the first and second peak regions 402 and 404. The suppressed region 409 extends along the first axis of symmetry 406 (such that the first axis of symmetry 406 extends through the suppressed region 409). The suppressed region 409 comprises a shape that is symmetric about the first and second axes of symmetry 406 and 408. As such, the target PSD 400 is symmetrical about both the first axis of symmetry 406 and the second axis of symmetry 408. As determined by the factor outside of the exponential in Equation 5, the suppressed region 409 extends along the first axis of symmetry 406. To generate the target PSD 400, the following parameter values were used: m = 1, A0_X = 2, A0_y = 4, and 0_O = 0. As shown, such a parameter set results in the suppressed region 409 being relatively narrow between the first and second peak regions 402 and 404. As shown, the target PSD 400 has a minimum amplitude over a range of values for 0_y that is from about -0.25° to 0.25°. As a result of the A0y parameter being larger than the A0_X parameter, the first and second peak regions 402 and 404 are elongated in the direction of the first axis of symmetry 406 (corresponding to the x-direction). When A0y does not equal A0_x. scattering orders may comprise elliptical gaussian beam that are elongated in a particular direction depending on the values of A0_y and A0_X. In the target PSD, the first peak region 402 has an outer boundary 403. A point on the outer boundary 403 that is disposed furthest from the origin in the angular coordinate space is located a maximum angular distance 407 from the origin. In the example shown the maximum angular distance 407 is less than or equal to 10° (e.g., less than or equal to 9°, less than or equal to 8°, less than or equal to 7°, less than or equal to 6°, less than or equal to 5°). As a result, regions outside of the maximum angular distance 407 are located in the suppressed region 409, indicating that the target PSD 550 beneficially confines scattering light to relatively low scattering angles, thereby providing favorable haze performance.

[0091] The target PSDs 410, 420, 430, 440, and 450 depicted in FIGS. 4B-4F will now be described in comparison with the target PSD 400 and one another. To provide the target PSD 410 depicted in FIG. 4B, , the following parameter values were used: m = 1, AOx = 4, A0_y = 2, and 0_O = 0. That is, the A0_y and A0_X values are reversed relative to those associated with the target PSD 400. As shown, such a parameter change results in the first and second peak regions 402 and 404 being elongated along the 0_y axis rather than the 0_X axis as in FIG. 4A. To provide the target PSD 420 depicted in FIG. 4C, the following parameter values were used: m = 1, A0x = 4, A0_y = 3, and 0_O = 0. As shown, such a parameter change results in the first and second peak regions 402 and 404 being less compressed along the 0_X axis than the target PSD 410 depicted in FIG. 4B and, as a result, the peak scattering amplitudes in each of the first and second peak regions 402 and 404 is lower. To provide the target PSD 430 depicted in FIG. 4D, the following parameter values were used: m = 3, A0_X = 4, A0y = 3, and 0_O = 0. As shown, in comparison with the target PSD 420 depicted in FIG. 4C, increasing the parameter m from 1 to 3 substantially increases the width of the suppressed region 409 between the first and second peak regions 402 and 404. In the target PSD 430, the suppressed region 409 has a minimum amplitude over a range of values for 0_y that is from about -4° to 4°. By tweaking m, the width of the suppressed region 409 can be changed, which also increases the peak scattering angles relative to specular.

[0092] To provide the target PSD 440 depicted in FIG. 4E, m = 1, A0x = 4, A0_y = 4, and 0_O = 2. To provide the target PSD 450 depicted in FIG. 4F, m = 1, A0_X = 4, A0_y = 4, and 0_O = 4. As is revealed by a comparison between the target PSD 440 and the target PSD 450, increasing the 0_O parameter effectively increases the radius of the LG mode being modified (with the suppressed region 409 being wider, covering a greater range of 0_y, in the target PSD 450). More pronounced effects (wider suppressed regions covering 4° on either side of the 0_y = 0 axis) can be achieved by using high 0_O values (greater than or equal to 4) in combination with high values for A0_X and A0y (greater than or equal to 4). In the target PSD 440, the first peak region 402 comprises a central region 452 where the target PSD 440 as a highest relative amplitude. In the target PSD 450, the first peak region 402 comprises a central region 454 where the target PSD 440 as a highest relative amplitude. The central region 452 is generally larger in the angular coordinate space than the central region 454. The central region 452 covers about 2° angular ranges in both the 0_X and 0y directions, whereas the central region 454 covers about 0.5° angular ranges in both the 0_X and 0_y directions. As a result, the target PSD will generally have a flatter distribution around peak amplitudes when smaller 0_O values are selected, with everything else being held constant. These examples demonstrate that the angular distribution of scattered light may be engineered using the target PSD formulated in Equation 5.

[0093] Once determined, the target PSD selected represents an intensity distribution of the far- field scattering pattern. The intensity distribution is input into a suitable algorithm to determine a phase distribution (p(x, y) = — A. 2W(x, y) in Equations 2-3 to provide the desired far-field scattering pattern. As described herein, the H(x, y) term represents the height of the first major surface 18 relative to the imaginary base plane 35 within the scattering region 20. Suitable algorithms that may be used include iterative phase retrieval algorithms, such as the Gerchberg- Saxton algorithm. The Gerchberg-Saxton algorithm may find a source phase distribution (associated with the first major surface 18 within the scattering section 20) by successively applying inverse Fourier and Fourier transforms to source and target amplitude distributions and updating the phase term until the source phase distribution generates the target PSD within a predetermined error criterion. The output of such an iterative phase retrieval algorithm can then be used to calculate a height pattern for the first major surface 18 in the scattering region 20.

[0094] In embodiments, as described herein with respect to FIGS. 2-3, the scattering region 20 comprises a plurality of regions of the first major surface 18, where each of the plurality of regions is disposed at a height relative to the imaginary base plane 35. The heights at which the plurality of regions are disposed relative to the imaginary base plane 35 may form a discrete distribution of heights (represented by the heights hi and I12 depicted in FIG. 3). To formulate such a distribution of heights, discretization may be applied during iterations of the phase retrieval algorithm. Any error resulting from the discretization can be included in the optimization in the following iterations, and thus can be mitigated. In embodiments, target phase values (p are converted to modified phase values <p' during each iteration using the following equation

< >' = Arg[Re[e¹^] + i w Imfe¹^]], (6) where w is a weighting parameter between [l, oo) . Effectively, the imaginary part of the phasor e is increased in order to align it more and more to the imaginary axis, until only phase values of either + - or — - are output by the algorithm. In embodiments, the weighting parameter w is gradually changed from 1 to ~5 over the total number of iterations. Once the binary phase pattern is determined, an etch height is added. In embodiments, the desired etch height is calculated by balancing desired optical performance attributes such as sparkle, haze, and specular reflectance. . In embodiments, the iterative phase retrieval results in each phase having a 50% fill fraction of the scattering region 200 when random phases are distributed uniformly around a circle. Phase fill fractions other than 50% can also be achieved by uniformly distributing random phases along an ellipse in the complex plane. The eccentricity of the ellipse can be used to adjust the fill fraction.

[0095] Referring again to FIGS. 1-3, the plurality of microstructures 26 in the first major surface 18 may be formed using any suitable technique. FIG. 5 depicts a flow diagram of an example method 500 of fabricating the article 10, according to an example embodiment of the present disclosure. Reference to various components depicted in FIGS. 1-3 will be made to aid in describing the method 500. It should be understood that the particular method used to form scattering region 20 is not particularly limiting and that any suitable method may be used. [0096] At block 502, the pattern for the plurality of microstructures 26 is determined by formulating a target PSD. In embodiments, for example, the target PSD is formulated by selecting a set of parameters (m, 0_O, A0x, A0y) for Equation 5 based on a particular application for the article 10. For example, in certain applications, it may be desirable to distributed scattered light in directions having a relatively large angular offset (e.g., greater than or equal to 4.0°) from specular reflection. Such values may utilize m values that are greater than or equal to 2. As discussed herein, the 0_O parameter determines a radial width of the far field scattering pattern where relatively high scattering amplitudes are observed. If it is desired to confine scattered light having high amplitudes to a relatively narrow angular range, relatively large 0_O (e.g., 3, 4, 5, 6) values may be selected. The parameters A0_X and A0_y may be used to determine the shape of scattered beams (e.g., whether the scattered light is elongated in any particular direction). The set of parameters (m, 0_O, A0_X, A0y) may also be selected such that suppressed regions of the target PSD (such as the suppressed region 409 described relative to FIGS. 4A-4F) coincide with a desired location in the environment of the article 10 (e.g., such that light incident on the article 10 is not scattered into eyes of an observer). Once the target PSD is formulated, a suitable phase retrieval algorithm may be used to determine the pattern for the plurality of microstructures 26.

[0097] At block 504, a resist is disposed on the first major surface 18 and patterned. The nature of the deposition and patterning of the resist may vary depending on the fabrication technique used. In embodiments, various nanoimprint or photolithographic techniques may be used to deposit and pattern the resist layer. In such embodiments, a minimum feature size (e.g., minimum linear dimension) associated with the plurality of microstructures 26 may be set to at least 1 pm (e.g., greater than or equal to 1.5 pm, greater than or equal to 2.0 pm, greater than or equal to 2.5 pm, greater than or equal to 5.0 pm) to facilitate use of existing resist application and patterning techniques. In embodiments, for example, the resist may be formed using thermoplastic nanoimprint lithography, and the resist may be formed of a thermoplastic polymer that is spin-coated onto the substrate 12 and subsequently imprinted via a mold to form a first pattern that at least partially corresponds to the pattern for the plurality of microstructures 26 on the first major surface 18. The resist may be subsequently thermally cured to form an etching mask. Other methods of forming the resist (e.g., Gravure offset printing, other printing techniques) are also contemplated and within the scope of the present disclosure.

[0098] Photolithography (e.g., photo imprint nanolithography, optical photolithography) techniques may also be used, and the resist may be deposited onto the first major surface 18 via a suitable application method (e.g., spin coating). In such embodiments, a mask comprising a first pattern at least partially corresponding to the pattern determined for the plurality of microstructures 26 is aligned with the first major surface 18, and the resist may be exposed to radiation from a suitable light source (e.g., UV radiation) to cause the resist to cure and form an etching mask. The resist may subsequently be developed such that portions of the first major surface 18 are left exposed through the cured resist. Any suitable photolithographic technique may be used to pattern the resist.

[0099] At block 506, exposed areas of the first major surface 18 (through the cured and patterned resist) are exposed to a suitable etchant for a suitable etchant period determined based on a target etch depth. Each area of the first major surface 18 that is exposed through the patterned resist formed in the block 504 may directly contact the etchant, which may degrade the substrate 12 and remove material therefrom to form regions on the first major surface 18 that are disposed at a diminished height relative to the imaginary base plane 35 as compared to areas of the first major surface 18 that are covered by the patterned resist. In embodiments, the etchant that contacts the first major surface 18 is an HF/HNO3 etchant. In embodiments, the etchant consists of hydrofluoric acid (HF, 49 w/w%) and nitric acid (HNO3, 69 w/w%) combinations with 0.1-5 v/v% HF and 0.1-5 v/v% HNO3. Typical concentrations used to achieve the etching depths discussed herein are 0. 1 v/v% HF/1 v/v% HNO3 to 0.5 v/v% HF/1 v/v% HNO3 solutions. In embodiments, the etching can be carried out using a dip or spray etching process from room temperature to about 45° C. In embodiments, the blocks 504 and 506 may be repeated to form more complex microstructures (e.g., a second resist may be disposed on the first major surface 18 after removal of the first resist to facilitate forming microstructures disposed at more than two heights relative to the imaginary base plane 35).

Substrate Properties

[00100] Various properties of the substrate 12 will now be described, according to embodiments of the present disclosure.

[00101] In embodiments, the substrate 12 is a glass substrate or a glass-ceramic substrate. 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 aluminoboro silicate glass. In further implementations, the substrate 12 is a glass-based substrate, including, but not limited to, glass-ceramic materials that comprise a glass component at about 90% or greater by weight and a ceramic component. In other implementations of the article 10, the substrate 12 can be a polymer material, with durability and mechanical properties suitable for the development and retention of the scattering region 20.

[00102] 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 % SiCh, in other embodiments, at least 58 mol % SiCh, and in still other embodiments, at least 60 mol % SiCh, wherein the ratio (AI2O3 (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 % SiCh; about 9 mol %to about 17 mol % AI2O3; 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 (AI2O3 (mol%) + B2O3 (mol%)) / alkali metal modifiers (mol%) > 1, where the modifiers are alkali metal oxides.

[00103] 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 % SiCh; about 7 mol % to about 15 mol % AI2O3; 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.

[00104] 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 % SiCh; about 6 mol % to about 14 mol % AI2O3; 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 %.

[00105] 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 % SiCh; about 12 mol % to about 16 mol % Na2O; about 8 mol % to about 12 mol % AI2O3; 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 %; Na₂0+K₂0+B₂03+Mg0+Ca0+Sr0>10 mol %; 5 mol %^MgO+CaO+SrO^8 mol %; (Na2O+B2O3) — AhO3=2 mol %; 2 mol %=Na2O — AhO3=6 mol %; and 4 mol %^(Na2O+K2O) — AhO3=10 mol %.

[00106] In embodiments, the substrate 12 has a bulk composition that comprises SiO2, AI2O3, P2O5, and at least one alkali metal oxide (R2O), wherein 0.75>[(P2Os (mol %)+R2O (mol %))/M2O3 (mol %) |= l .2. where M2O3=AhO3 +B2O3. In embodiments,

[(P2Os (mol %)+R₂O (mol %))/M2O3 (mol %)]=1 and, in embodiments, the glass does not include B2C>3 and M2O3=AhO3. The substrate 12 comprises, in embodiments: about 40 to about 70 mol % SiCh; 0 to about 28 mol % B2O3; about 0 to about 28 mol % AI2O3; 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 % SiCh; 0 to about 8 mol % B2O3; about 16 to about 28 mol % AI2O3; 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.

[00107] 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, Sb20s, and/or BaO.

[00108] In embodiments, the substrate 12 has a bulk composition that comprises, consists essentially of or consists of a glass composition, such as Coming® Eagle XG® glass, Coming® Gorilla® glass, Coming® Gorilla® Glass 2, Coming® Gorilla® Glass 3, Coming® Gorilla® Glass 4, or Coming® Gorilla® Glass 5.

[00109] 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 first major surface 18 of the substrate 12 are exchanged for larger metal ions having the same valence as the metal ions in the glass substrate. 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 ion. 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 first major 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.

[00110] 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 first major 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 first major surface 18 ofthe 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 pm below the first major surface 18 into the thickness 21.

[00111] 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 10 pm up to at least 50 pm, with a compressive stress ranging from about 200 MPa up to about 800 MPa, and a central tension of less than about 100 MPa.

[00112] As the etching processes that can be employed to create the scattering 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 article 10 after the formation and development of the scattering region 20.

Examples

[00113] Embodiments of the present disclosure may be further understood in view of the following examples.

[00114] A first set of examples was constructed using Equation 5 with the parameters m = 2, 0o = 1, A0_X = 0.5 and A0y = 0.5 as the target PSD. In this first set of examples, the 0_O value was varied from 0.5 to 1.0 to 2.0. For each of the target PSDs, an iterative phase retrieval algorithm was used to determine surface height distributions for the glass. Resists were formed on the first major surface 18 using photolithography and the glass was etched to a depth of around 150 nm in the pattern determined using the target PSD.

[00115] FIG. 6 depicts one of the samples after etching. As shown, the article 600 comprises a first major surface 601 with a plurality of first regions 602 and a plurality of second regions 604. The plurality of second regions 604 were exposed to a chemical etchant such that, after the etching, the plurality of second regions 604 were disposed at a different height relative to an imaginary base plane extending through the article 600 than the plurality of first regions 602, which were covered during the etching by the patterned resist. As shown, the plurality of first regions 602 and the plurality of second regions 604 were elongated in a first direction (the x-direction depicted in FIG. 6) so as to preferentially scatter light in a second direction (the y- direction depicted in FIG. 6). Each of the plurality of microstructures comprises a feature size 610 when measured along a line 608 extending in the second direction. The average feature size 610 varies as a function of position in the first direction. In this example, the regions had an average feature size 610 of 15.5 pm. As shown, one of the plurality of first regions 602a is completely surrounded by one of the plurality of second regions 604 and one of the plurality of second regions 604a is completely surrounded by one of the plurality of first regions 602.

[00116] It was found that, depending on the desired values for the parameter 0_O, the width of the microstructures in the preferential scattering direction varies, as shown in the Table 1 below.

Table 1

As shown, the average feature size 610 in the direction perpendicular to the lengthwise direction of the plurality of microstructures 26 scales in inverse proportion to the values for the parameter 0_O. Once a pattern associated with a first set of the parameters m, 0_O, A0_X, and A0y is generated, one can scale that pattern linearly to alter the width of the peak regions associated with the far field scattering pattern.

[00117] A plurality of etched samples according to the first set of examples were prepared and measured for various properties. Samples having scales of 4096 pm and 8192 pm (per the Table 1) were formed using multiple etch times. Etch depths for these samples were measured using both stylus and interferometric techniques. The etch depth and fdl fraction measurements are provided in the Table 2 below.

Table 2

[00118] As shown in the Table 2, for each of the samples, the etch depth for the lower of the plurality of regions ranged from 118.7 nm to 208.4 nm when measured using a stylus and from 110 nm to 215 nm when measured optically. In embodiments, the particular etch depth may be selected depending on the wavelength range of operation. For example, if it is desired to suppress specular reflectance of light in the wavelength range of 400 nm to 700 nm, the etch depth may be selected to be approximately X_c/4, where A is the central wavelength of the range (550 nm in these examples). The samples in the Table 2 exhibited etch depths ranging from approximately A/4 to X_c/2.

[00119] In the last column of the Table 2, the fdl fractions associated with each of the heights was measured. This pattern was designed to have 50% fdl fraction for each of the two heights relative to the imaginary base plane. [00120] Optical attributes of each of the samples represented in the Table 2 were measured. The attributes were measured with the samples in two different orientations. For the first set of measurements, the microstructures (the plurality of first regions 602 and the plurality of second regions 604) were aligned in the x-direction (labelled “H” in the Table 3). For the second set of measurements, the microstructures were rotated by 90° to extend in the y- direction (labelled “V” in the Table 3). Sparkle, distinctness of image (“DOI”), gloss, specular reflectance, and reflection haze were measured for each of the samples in each orientation (in both an uncoupled and coupled state). The results are provided below in the Table 3. All values are percentages unless indicated otherwise. Measurements were output directly from a Rhopoint IQ goniophotometer.

Table 3

Table 3 (Cont.) [00121] As shown, the samples with the longer scale patterns (with 8192 pts in the pattern scaling to 8192 pm, Examples 1-5 and 11-12) exhibited higher overall sparkle (PPD) (greater than 4%), higher coupled DOI (greater than 60%,) higher gloss, and higher coupled specular reflectance (Rs greater than 20) than the samples with the shorter scale patterns (with 8192 pts in the pattern scaling to 4096 pm). The 8192 pm patterns exhibited lower transmission haze of less than 2%. The 4096 pm design exhibited lower sparkle of less than or equal to 2.2% (on both 220 PPI and 140 PPI displays), lower coupled DOI of less than 50%, lower specular reflectance of less than 15%. Based on these results, the 4096 pm designs (with the lower average feature size of 15.5 pm) appeared to be more advantaged for display cover applications, given the lower specular reflectance and sparkle.

[00122] In order to further characterize the performance of the samples described in the Tables 2 and 3 above, additional metrics were formulated. For example, a “washout metric” was formulated to quantify the effects of glare events (e .g ., exposure to sunlight) on the contrast and resolution of an incorporating display. Such a metric is useful to examine cover material performance for applications likely to be exposed to light from external light sources (e.g., automotive interior displays, outdoor displays). To quantify “washout,” a modulation transfer function (MTF) of an anti -glare surface is measured under various illumination conditions, and the average value of the MTF over a number of spatial frequencies is used to evaluate the effect of illumination conditions on display performance. The MTF at a particular spatial frequency f may be expressed as where and I(f)max and I(f)_min are the maximum and minimum intensities of an input or an output modulation image at the spatial frequency f. In this expression, MFm represents the MF value associated with an input pattern being emitted through a sample cover material. The MF_0Ut value represents the MF value when the cover material is disposed over the input pattern (e.g., from a display) and under the illumination condition being tested. Higher MTF values generally mean that the illumination condition has less of an effect on display performance (and therefore better performance of the scattering region of the cover material). In embodiments, MTF values of greater than or equal to 0.65 (e.g., greater than or equal to 0.70, greater than or equal to 0.71, greater than or equal to 0.72, greater than or equal to 0.73, greater than or equal to 0.74, greater than or equal to 0.75, greater than or equal to 0.76, greater than or equal to 0.77, greater than or equal to 0.78, greater than or equal to 0.79, greater than or equal to 0.80, greater than or equal to 0.81, greater than or equal to 0.82, greater than or equal to 0.83, greater than or equal to 0.84, greater than or equal to 0.85, greater than or equal to 0.86, greater than or equal to 0.87, greater than or equal to 0.88, greater than or equal to 0.89, and greater than or equal to 0.90) are preferred for a given illumination condition, indicating minimal degradation of display performance caused by exposure to the external light.

[00123] FIG. 7 schematically depicts an apparatus 700 for measuring the washout effect. As shown, a sample 702 (e.g., corresponding to the substrate 12 described herein) is placed over a display 704. The sample 702 is positioned so that the scattering region faces outward (not towards the display 704). As shown in the box 705 (which depicts a front view of the sample 702 and the display 704), the display 704 generates a plurality of target patterns 706 where the intensity of light emitted by the display 704 varies with a particular spatial frequency fi. A plurality of first light sources 708 are distributed around the sample 702. The plurality of first light sources 708 are configured to emit a relatively low intensity light (such as, white light with 1301ux, color temperature 2100k) to simulate the sample 702 encountering normal ambient conditions (e.g., room light). A projection light source 710 is configured to emit a relatively high intensity light source to simulate sunlight illumination. The projection light source 710 is positioned such that light emitted thereby is incident on the sample with an angle of incidence 0i. In embodiments, the projection light source 710 is movable or otherwise adjustable so as to change the angle of incidence 0i. In embodiments, the projection light source 710 emits light over an emission area, such that light emitted by the projection light source 710 is incident on the sample 702 at a range of angles of incidence 0i.

[00124] A camera 712 is positioned to receive light scattered from the sample 702. The camera is positioned such that light scattered from the sample 702 will enter the camera 712 at a viewing angle 0v (or range of viewing angles). In embodiments, the display is rotatable to change the viewing angle 0_V. A computing system 714 receives an image generated by the camera 712 and analyzes the image to compute a plurality of MTF values for each of the plurality of target patterns 706 emitted by the display 704. For each of the target patterns 706, the computing system 714 may calculate an MTF value using Equations 6 and 7 and generate an output that measures the dependency of the MTF value on spatial frequency. The plurality of first light sources 708 and the projection light source 710 allow the MTF values to be measured under a plurality of different lighting conditions to determine the efficacy of the patern on the sample 702 in reducing washout. When just the first light sources 708 are emiting light, a “room light washout” effect can be measured. When both the first light sources 708 and the projection light source 710 are emiting light, a “sunlight washout” effect can be measured.

[00125] Such washout measurements may be particularly useful in evaluating the performance of cover materials for automotive interior displays. FIG. 8 shows a vehicle interior 1000 that includes three different vehicle interior systems 100, 200, 300, according to an exemplary embodiment. Vehicle interior system 100 includes a center console base 110 with a surface 120 including a display 130. Vehicle interior system 200 includes a dashboard base 210 with a surface 220 including a display 230. The dashboard base 210 typically includes an instrument panel 215 which may also include display 216. Vehicle interior system 300 includes a dashboard steering wheelbase 310 with a surface 320 and a display 330. In one or more embodiments, the vehicle interior system may include a base that is an arm rest, a pillar, a seat back, a floorboard, a headrest, a door panel, or any portion of the interior of a vehicle that includes a surface. In embodiments, the displays 130, 230, 330 are flat and comprise cover glass with planar major surfaces. In embodiments, one or more of the displays 130, 230, 330 are curved, and the curved display may include curved cover glass that may be hot-formed or cold-formed to possess such curvature. For example, such embodiments may incorporate opaque layers formed of the photocurable inks described herein disposed on cold-formed glass substrates. Such cold-forming may involve any of the techniques described in U.S. Pre-Grant Publication No. 2019/0329531 Al, entitled “Laminating thin strengthened glass to curved molded plastic surface for decorative and display cover application,” U.S. Pre-Grant Publication No. 2019/0315648 Al, entitled “Cold-formed glass article and assembly process thereof,” U.S. Pre-Grant Publication No. 2019/0012033 Al, entitled “Vehicle interior systems having a curved cover glass and a display or touch panel and methods for forming the same,” and U.S. Patent Application No. 17/214,124, entitled “Curved glass constructions and methods for forming same,” which are hereby incorporated by reference in their entireties.

[00126] Various components of the vehicle interior 1000 may be subjected to illumination from various light sources. As depicted in FIG. 8, for example, a first ambient light source 800 may emit light that is transmited through a first side window of the vehicle and incident on the display 216 with at an angle of incidence On. The display 216 may be oriented such that light scatered at a particular scatering angle 0_vi will enter the driver’s field of vision and distract the driver. A second ambient light source 802 may emit that is transmited through a second side window of the vehicle and incident on the display 130 with at an angle of incidence 0i2. The display 130 may be oriented such that light scattered at a particular scattering angle 0v2 will enter the driver’s field of vision and distract the driver. The first and second ambient light sources 800 and 802 may represent sunlight at various points in time. Indeed, ISO 15002/SA 1757 standards specify a first condition where 45k lux light (direct sunlight) is incident on the display 216 at an angle of 20° and scatters into the driver at a scattering angle of 0° (i.e., where Oil = 20° and Ovi = 0°) and a second condition where 45k lux light (direct sunlight) is incident on the display 130 at an angle of 45° and scatters into the driver at a scattering angle of 20° (i.e., where 0i2 = 45° and 0v2 = 20°). The apparatus 700 depicted in FIG. 7 enables such conditions to be tested for washout by varying the orientation of the sample 702 and adjusting the projection light source 710.

[00127] Using the apparatus 700 depicted in FIG. 7, the two conditions of ISO 15002/SA 1757 described herein were used to test a sample constructed in accordance with the methods described herein. An Apple® mini-iPad® 4 was used as the display 704. A Pixelink 3. 1 MP PL-B776 was used as the camera 712. A collimated LED white light source (made by Mightex Systems, model of LCS-6500-65-22) was used at the projection light source 710. The emitting of the LED light source was set at a level which produces an illumination of 45000 lux at the sample surface. The projection light source was positioned so as to emit light incident on the sample 702 at angles of incidence of 20° and 45°. The sample 702 was also mounted on a rotation stage so as to render the viewing angle 0v and angle of incidence 0i adjustable for the two conditions. Lab room light was used as the first light sources 708 and was measured to have an illuminance of 132 lux on at the sample surface.

[00128] In a first set of measurements, the sample 702 had a standard AG surface treatment (by sandblasting the first major surface 18). The results are depicted in FIGS. 9A-9F. FIGS. 9A-9C depict the imaged patterns under the first condition described herein (i.e., where 0ii = 20° and 0_vi = 0°). FIG. 9 A depicts an image 900 where the display 704 was uncovered by the sample 702 in a dark room. FIG. 9B depicts an image 902 where the display 704 was covered by the sample 702 when only the first light sources 708 were emitting light (lab lights were turned on). FIG. 9C depicts an image 904 where the display 704 was covered by the sample 702 and both the first light sources 708 and the projection light source 710 were emitting light. FIGS. 9E-9F depict the imaged patterns under the second condition described herein (i.e., where 0ii = 45° and 0_vi = 20°). FIG. 9C depicts an image 900 where the display 704 was uncovered by the sample 702 in a dark room. FIG. 9E depicts an image 902 where the display 704 was covered by the sample 702 when only the first light sources 708 were emitting light (lab lights were turned on). FIG. 9F depicts an image 904 where the display 704 was covered by the sample 702 and both the first light sources 708 and the projection light source 710 were emitting light.

[00129] FIGS. 10 and 11 are plots 1002 and 1004 of the MTF values obtained from the images depicted in FIGS. 9A-9F. FIG. 10 includes a first series 1004 representing various MTF values obtained from the image 902 depicted in FIG. 9B (for the first condition where only the first light sources 708 were on). FIG. 10 also includes a second series 1006 representing various MTF values obtained from the image 904 depicted in FIG. 9C (for the first condition where both the first light sources 708 and the projection light source 710 were activated). FIG. 11 includes a first series 1102 representing various MTF values obtained from the image 908 depicted in FIG. 9E (for the second condition where only the first light sources 708 were on). FIG. 11 also includes a second series 1104 representing various MTF values obtained from the image 910 depicted in FIG. 9F (for the second condition where both the first light sources 708 and the projection light source 710 were activated). These experimental results indicate that: ( 1 )the very small degradation caused by the room light condition can be resolved by this setup, indicating the sensitivity of the measurement setup is high; (2) the sample 702 only produced the degradation of image contrast, but doesn’t affect the resolution of the display; (3) the setup can distinguish the impacts of different group effects on display performance; and (4) the setup can characterize “washout effect” at different angles.

[00130] To quantitatively evaluate the impact of the sample 702, the MTF values at the spatial frequencies associated with the points 1008, 1010, 1012, 1014, and 1016 in the first series 1004 were averaged (MTF values at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm were averaged for each of the series 1004, 1006, 1102, and 1104). The “washout metric” described herein was an average of the MTF values over these spatial frequencies for each condition.

[00131] A similar set of measurements as those described herein with respect to FIGS. 9A- 11 were taken on a sample 702 having a scattering region designed to provide a PSD in accordance with Equation 5 described herein. Particularly, another set of tests was conducted using a sample 702 constructed according to the Example 3 in Table 2. The measurements were conducted with the sample 702 placed in two different orientations: a first where the plurality of microstructures 26 (see FIG. 2) were oriented with their lengthwise direction parallel to the light from the proj ection light source 710 (see FIG. 7) (termed “H” or “horizontal” in the Table 3 above and its accompanying description); and a second where the plurality of microstructures 26 were oriented with their lengthwise direction perpendicular to the light form the projection light source (termed “V” or “vertical” in the Table 3 above and its accompanying description). Put another way, in the first orientation, the light from the projection light source 710 was incident on the first major surface 18 in the x-z plane depicted in FIG. 1, and, in the second orientation, the light from the proj ection light source 710 was incident on the first maj or surface 18 in the y-z plane depicted in FIG. 1. Each of the conditions discussed above were tested (where On = 20° and 0_vi = 0°; and where 0i2 = 45° and 0_V2 = 20°) with the sample 702 in each orientation. The results for both the conventional AG Counter Example (depicted in FIGS. 9A-11) and Example 3 are summarized in the Table 4 below.

Table 4

[00132] As shown in the Table 4, when the plurality of microstructures 26 were oriented parallel to the incident plane of the light from the projection light source 710, the sample 702 constructed according to Example 3 herein performed much better from a washout perspective than the Counter Example with a conventional AG surface. In the first condition (where 0n = 20° and 0_vi = 0°), the washout metric (the average of the MTF value according to Equations 6 and 7) for Example 3 was 0.84, which was much higher than the 0.66 value obtained with the Counter Example. When the plurality of microstructures 26 were oriented perpendicular to the incident plane of the light from the projection light source 710, the washout metric was much lower, indicating that the projection light source 710 more significantly impacted display performance. These results demonstrate how the orientation of the article can significantly affect washout performance.

[00133] BRDFs with light from the projection light source 710 (laser source) at an angle of incidence 0i of 50° were also taken for the Counter Example and a sample 702 conducted in accordance with Example 1 described in the Table 2 herein. Measurements were taken in reflection mode using the REFLET 180S system from Synopsys, Inc. Example 1 was measured in both orientations (with the microstructures parallel to the incident plane of the light from the proj ection light source 710 and perpendicular to the light from the proj ection light source 710). The results are depicted in FIG. 12. As shown, Example 1 oriented with the microstructures parallel to the incidence plane of the light from the projection light source 710 resulted in a BRDF that quickly reduced in magnitude from the maximum at specular reflectance . As shown, for Example 1 in the parallel orientation, a magnitude of the BRDF is less than 10'⁵ times a peak magnitude of the BRDF at scattering angles greater than 20° from specular. For Example 1 in the parallel orientation, magnitude of the BRDF is less than 10'⁶ times the peak magnitude at scattering angles greater than 30° from specular. As a result, in a scattering angle range of 10° to 20°, Example 1 in the parallel orientation had the lowest amplitude. In the scattering angle range of 10° to 20°, however, the Counter Example had a lower scattering amplitude than Example 1 oriented in the perpendicular orientation. These results demonstrate that washout luminance caused by scattering light on the first major surface 18 can be managed by controlling the angular orientation of the article 10 depending on the expected plane of incidence. For applications such as the automotive interior application, these results indicate that the scattering regions described herein can effectively reduce scattering at large angles as compared to certain existing AG surface treatments, thereby reduce washout luminance and beneficially prevent glare from detrimentally affecting display performance to a significant extent.

[00134] While the preceding examples described herein include scattering regions where the microstructures have lengthwise directions that extend parallel to one another, it should be appreciated that articles comprising a plurality of sets of microstructures having lengthwise directions extending in different directions are also contemplated and within the scope of the present disclosure. For example, FIG. 13 depicts an article 1300 including a plurality of vertical microstructure regions 1302 where the plurality of microstructures comprising lengthwise directions extending along a first axis and a plurality of horizontal microstructure regions 1304 wherein the plurality of microstructures comprise lengthwise directions extending along a second axis extending in a different direction than the first axis. In the depicted example, the first axis is perpendicular to the second axis. Embodiments are envisioned that include regions having microstructures extending in any number of different directions. The microstructures in adjacent regions may not extend perpendicular to one another, but any suitable direction. Any arrangement of regions is contemplated and within the scope of the present disclosure. The microstructures may also spatially vary in other aspects (e.g., average dimension in the direction perpendicular to the lengthwise direction, etch depth) to provide a BRDF that varies depending on location of incidence on the surface.

[00135] Embodiments are also envisioned where the microstructures described herein can be combined with other types of anti-glare surfaces. In embodiments, for example, a substrate may include a first region that is covered with a plurality of microstructures similar to those described with respect to the Examples herein, and a second region that is covered with a conventional isotropic anti-glare surface treatment (e.g., sandblasting). In an example, the second region may extend around the periphery of the substrate while the first region may cover a central portion of the substrate. Such an example may be useful in camera lenses, as the first region may lower transmission haze through the camera lens, while providing isotropic scattering around the border.

[00136] Certain examples described herein included a binary surface, where the microstructures are plateaus of the substrate surface disposed at a discrete distribution of heights relative to an imaginary base plane. Alternative embodiments are envisioned where, rather than plateaus, each of the microstructures are constructed as blazed grating segments. For example, each “period” of surface height variation in the direction perpendicular to the lengthwise direction of the microstructures may include a segment of the major surface of the substrate where the height of the major surface relative to the imaginary base plane varies as a function of position in the direction perpendicular to the lengthwise direction. To illustrate with an example, referring to FIG. 2, adjacent ones of the plurality of first regions 28 and the plurality of second regions 30 may be combined into a combined region where the height of the first major surface 18 (see FIG. 1) relative to the imaginary base plane 35 (see FIG. 3) varies as a function of distance in the y-direction from the boundary of the combined region (e.g., the height of the first major surface 18 may linearly increase or decrease as one travels along the y-direction depicted in FIG. 2). Such a blazed structure only scatters light to one side of the surface normal of the article in reflection and may facilitate greater control over scattered light. It is envisioned that UV imprinting may be utilized in constructing such blazed patterns. [00137] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not actually recite an order to be followed by its steps or it is not otherwise specifically stated in the claims or descriptions that the steps are to be limited to a specific order, it is in no way intended that any particular order be inferred. In addition, as used herein, “a” is intended to comprise one or more than one component or element, and is not intended to be construed as meaning only one.

[00138] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit or scope of the disclosed embodiments. Since modifications, combinations, sub-combinations and variations of the disclosed embodiments incorporating the spirit and substance of the embodiments may occur to persons skilled in the art, the disclosed embodiments should be construed to comprise everything within the scope of the appended claims and their equivalents.

Claims

What is claimed is:

1. An article comprising: a first major surface; a second major surface opposing the first major surface; and a scattering region formed in the first major surface, wherein: within the scattering region, the first major surface comprises a plurality of microstructures that are elongated in a first direction, each of the plurality of microstructures comprises a feature size measured in a second direction that is perpendicular to the first direction, the feature size varies as function of position within the microstructure, and a two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scattering directions that are parallel with the first direction.

2. The article according to claim 1, wherein the two-dimensional power spectral density, is symmetric about at least two distinct axes of symmetry, wherein the two-dimensional power spectral density comprises n-fold rotational about a spectral direction, where n is a finite integer.

3. The article according to any one of claims 1-2, wherein each of the plurality of microstructures comprises an average feature size that is greater than or equal to 1.0 pm and less than or equal to 35 pm.

4. The article according to claim 3, wherein the average feature size is less than or equal to 20 pm.

5. The article according to any of claims 1-4, wherein boundaries of the plurality of microstructures do not extend in straight lines.

6. The article according to any of claims 1-5, wherein a boundary of at least one of the plurality of microstructures forms a closed contour.

7. The article according to any of claims 1-6, wherein: the plurality of microstructures comprises a plurality of first regions of the first major surface that are disposed at a first height relative to an imaginary base plane extending through the article and a plurality of second regions disposed at a second height relative to the imaginary base plane, and each of the plurality of first regions is adjacent to at least one of the plurality of second regions.

8. The article according to claim 7, wherein the first height differs from the second height by an etch depth that is greater than or equal to 100 nm and less than or equal to 250 nm.

9. The article according to claim 7, wherein: at least one of the plurality of first regions is completely surrounded by one of the plurality of second regions, and at least one of the plurality of second regions is completely surrounded by one of the plurality of first regions.

10. The article according to any one of claims 1-9, wherein the scattering region comprises a plurality of second microstructures that are elongated in a third direction that is different from the first direction.

11. The article according to any one of claims 1-9, wherein the plurality of microstructures are arranged so as to preferentially scatter the light along a second direction that is perpendicular to the first direction.

12. The article according to any one of claims 11, wherein the two-dimensional power spectral density comprises a suppressed region extending along an axis that intersects a specular direction.

13. The article according to any one of claims 11-12, wherein the at least one peak region comprises an outer boundary that is associated with a scattering direction extending at an angle of no more than 10° from the specular direction.

14. The article according to claim 13, wherein, when the light is incident on the first major surface in a plane of incidence that is parallel to the first direction, a magnitude of a bidirectional reflectance distribution function (“BRDF”) of the article is less than 10'⁵ times a peak magnitude of the BRDF at scattering angles greater than 20° from specular.

15. The article according to claim 14, wherein a magnitude of the BRDF is less than 10'⁶ times the peak magnitude at scattering angles greater than 30° from specular.

16. The article according to any one of claims 1-15, wherein the article exhibits a transmission haze that is less than or equal to 5% and a sparkle that is less than or equal to 3% when measured at 140 ppi.

17. The article according to claim 16, wherein the article exhibits an average coupled specular reflectance that is less than or equal to 30% for light from 400 nm to 700 nm that is normally incident on the first major surface.

18. The article according to any one of claims 16-17, wherein the article exhibits an average transmittance that is greater than or equal to 90% for light from 400 nm to 700 nm that is normally incident on the first major surface.

19. The article according to any one of claims 1-18, wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 0° viewing angle diminishes by less than 30% as a result of light having an illuminance of 45000 lux being incident on the first major surface at an angle of incidence of 20°.

20. The article according to any one of claims 1-19, wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 20° viewing angle diminishes by less than 35% as a result of light having an illuminance of 45000 lux being incident on the first major surface at an angle of incidence of 45°.

21. An article comprising: a glass-based substrate comprising: a first major surface; a second major surface opposing the first major surface; and a scatering region formed in the first major surface, wherein, within the scatering region, the first major surface comprises: a plurality of first regions disposed at a first height relative to an imaginary base plane extending through the glass-based substrate, and a plurality of second regions disposed at a second height relative to the imaginary base plane, wherein: the plurality of first regions and the plurality of second regions are elongated in a first direction, the plurality of first regions and the plurality of second regions comprise an average feature size in a second direction extending perpendicular to the first direction, the average feature size is greater than or equal to 1.0 pm and less than or equal to 35 pm, the first height differs from the second height by an etch depth that is greater than or equal to 100 nm and less than or equal to 250 nm, and a two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scatering directions that are parallel with the first direction.

22. The article according to claim 21, wherein: each one of the plurality of first regions is disposed directly adjacent to at least one of the plurality of second regions, the average feature size is less than or equal to 20 pm, boundaries of the plurality of first regions and the plurality of second regions do not extend in straight lines, and a boundary at least one of the plurality of first regions forms a closed contour.

23. The article according to any of one of claims 21-22, wherein: at least one of the plurality of first regions is completely surrounded by one of the plurality of second regions, and at least one of the plurality of second regions is completely surrounded by one of the plurality of first regions.

24. The article according to any one of claims 21-23, wherein the two-dimensional power spectral density comprises a suppressed region extending along an axis that intersects a specular direction.

25. The article according to any one of claims 21-23, wherein the at least one peak region comprises an outer boundary that is associated with a scattering direction extending at an angle of no more than 10° from the specular direction.

26. The article according to any one of claims 21-25, wherein, when the light is incident on the first major surface in a plane of incidence that is parallel to the first direction, a magnitude of a bidirectional reflectance distribution function (“BRDF”) of the article is less than 10'⁵ times a peak magnitude of the BRDF at scattering angles greater than 20° from specular.

27. The article according to claim 26, wherein a magnitude of the BRDF is less than 10'⁶ times the peak magnitude at scattering angles greater than 30° from specular.

28. The article according to any one of claims 21-27, wherein the article exhibits a transmission haze that is less than or equal to 10% and a sparkle that is less than or equal to 4% when measured at 140 ppi.

29. The article according to any one of claims 21-28, wherein the article exhibits an average coupled specular reflectance that is less than or equal to 30% for light from 400 nm to 700 nm that is normally incident on the first major surface.

30. The article according to any one of claims 21 -29, wherein the article exhibits an average transmittance that is greater than or equal to 90% for light from 400 nm to 700 nm that is normally incident on the first major surface.

31. The article according to any one of claims 21-30, wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 0° viewing angle diminishes by less than 30% as a result of light having a luminance of 45000 lux being incident on the first major surface at an angle of incidence of 20°.

32. The article according to any one of claims 21-31, wherein an average modulation transfer function of the article that is averaged at spatial frequencies of 1.67 cycles/mm, 4.11 cycles/mm, 7.33 cycles/mm, 10.38 cycles/mm, and 13.08 cycles/mm when the article is viewed at a 20° viewing angle diminishes by less than 35% as a result of light having a luminance of 45000 lux being incident on the first major surface at an angle of incidence of 45°.

33. An article comprising: a first major surface; a second major surface opposing the first major surface; and a scattering region formed in the first major surface, wherein: within the scattering region, the first major surface comprises a plurality of microstructures that are elongated in a first direction, each of the plurality of microstructures comprises a feature size measured in a second direction that is perpendicular to the first direction, and boundaries of the plurality of first regions and the plurality of second regions do not extend in straight lines, a boundary at least one of the plurality of first regions forms a closed contour, a two-dimensional power spectral density of the first major surface comprises a peak region that is entirely disposed on one side of an axis associated with scattering directions that are parallel with the first direction, and the two-dimensional power spectral density, is symmetric about at least two distinct axes of symmetry, wherein the angular power spectral density comprises n-fold rotational symmetry around a surface normal of the first major surface, where n is a finite integer.