Article with anti-glare surface exhibiting low flicker at minimal color noise

Abstract

Disclosed herein are articles having scattering regions configured to provide a relatively low degree of flicker and minimal color noise. The scattering region may be a portion of a surface of the article including a plurality of first regions disposed at a first height and a plurality of second regions disposed at a second height. The scattering region in the Fourier domain is designed and configured such that the article exhibits a radial power spectral density comprising a first range of scattering angles wherein the radial PSD increases as the scattering angle of the light relative to the specular direction increases; a peak angle theta peak, wherein the radial PSD comprises a peak; and a second range of scattering angles, the angle being greater than the [theta] peak, in which the radial PSD decreases rapidly as the scattering angle increases.

Description

Technical Field

[0001] [Cross - Reference to Related Applications]

[0002] This application claims the benefit of priority of U.S. Provisional Application No. 63 / 420,222, filed on October 28, 2022, under 35 U.S.C. § 119, which is incorporated herein by reference in its entirety.

[0003] The present disclosure relates to articles having an antiglare surface that exhibit low flicker with minimal color noise. Background Art

[0004] Displays that cover a display article with a substrate transparent to visible light. Such display articles include smart phones, tablet computers, televisions, computer screens, vehicle interior displays, and the like. Displays are often liquid crystal displays and organic light - emitting diodes, etc. The substrate protects the display, and the transparency of the substrate allows the user of the device to view the display. Glare is a phenomenon associated with a degradation in viewing experienced under bright light sources. Moreover, reflected images not from a bright light source but from the environment can also cause a degradation in the viewing of the display. For example, the visually distinct reflection image of the user himself or the light of the surrounding environment may cause distraction, reduced readability, and visual fatigue.

[0005] There are several techniques for reducing glare, including antireflection coatings and antiglare techniques. Antireflection coatings can reduce glare by directly reducing the total amount of reflection. However, some existing antireflection coatings may not reduce reflection to a sufficient extent across the entire visible spectrum such that the user does not notice such reflections. Antiglare techniques attempt to spread the light reflection over a wide range of angles to reduce the peak intensity of the reflection and make the distracting reflected image less obvious to the user. However, reflections with too large an angle can result in a relatively high haze, thereby reducing the contrast of the displayed image.

[0006] Accordingly, an alternative to existing antiglare and antireflection coating techniques that allows for beneficial control of the angular distribution of scattered light would be beneficial. Summary of the Invention

[0007] Aspects (1) of the present disclosure relate to an article comprising: a substrate comprising: a first major surface; a second major surface opposite 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 substrate, and a plurality of second regions disposed at a second height relative to the imaginary base plane, wherein: the first height is greater than the second height by an etch depth, the etch depth being greater than or equal to 80 nm and less than or equal to 600 nm, the scattering region comprises a radial PSD which comprises: a range of first scattering angles, wherein the radial PSD increases as the scattering angle of light relative to the specular direction increases; a peak angle θ 峰值 , wherein the radial PSD comprises a peak; and a range of second scattering angles, greater than θ 峰值 , wherein at a first scattering angle greater than or equal to 2° and less than or equal to 15° relative to the specular direction, the radial PSD is reduced to 10% of the peak.

[0008] Aspects (2) of the present disclosure relate to an article as described in aspect (1), wherein within the range of second scattering angles, at a second scattering angle greater than the first scattering angle and greater than or equal to 3.5°, and less than or equal to 30° relative to the specular direction, the radial PSD is reduced to 1% of the peak.

[0009] Aspects (3) of the present disclosure relate to an article as described in aspect (2), wherein within the range of first scattering angles, at a scattering angle greater than or equal to 0.05°, the radial PSD is less than 10% of the peak.

[0010] Aspects (4) of the present disclosure relate to an article as described in any one of aspects (2) to (3), wherein: relative to the specular direction, the first scattering angle is greater than or equal to 6° and less than or equal to 13°, and relative to the specular direction, the second scattering angle is greater than or equal to 12.5° and less than or equal to 30.0°.

[0011] Aspects (5) of the present disclosure relate to an article as described in any one of aspects (2) to (3), wherein: relative to the specular direction, the first scattering angle is greater than or equal to 2° and less than or equal to 7°, and relative to the specular direction, the second scattering angle is greater than or equal to 3.5° and less than or equal to 13.5°.

[0012] Aspects (6) of the present disclosure relate to an article as described in aspect (5), wherein within the range of second scattering angles, at a third scattering angle less than or equal to 8° relative to the specular direction, the radial PSD is reduced to a value of 0.1% of the peak.

[0013] Aspects (7) of the present disclosure relate to an article as described in aspect (5), wherein within the range of the second scattering angle, at a third scattering angle less than or equal to 16° relative to the specular direction, the radial PSD is reduced to a value of 0.01% of the peak value.

[0014] Aspects (8) of the present disclosure relate to an article as described in any one of aspects (1) to (7), wherein θ 峰值 is greater than or equal to 0.3 and less than or equal to 0.5°.

[0015] Aspects (9) of the present disclosure relate to an article as described in any one of aspects (1) to (8), wherein: within the scattering region, the first major surface includes a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions, and the plurality of inclined transition surfaces are inclined such that the height of the first major surface decreases as the distance from the boundary of the plurality of first regions increases.

[0016] Aspects (10) of the present disclosure relate to an article as described in aspect (9), wherein at least some of the plurality of inclined transition surfaces extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between certain ones of the plurality of first regions and the plurality of second regions connected by the inclined transition surfaces, and the lateral distance extended by the inclined transition surfaces is measured in a direction parallel to the surface normal of the inclined transition surface and parallel to the imaginary base plane.

[0017] Aspects (11) of the present disclosure relate to an article as described in any one of aspects (1) to (10), wherein the article exhibits: a transmission haze less than or equal to 2.0%, and a sparkle less than or equal to 2.5% when measured at 140 ppi.

[0018] Aspects (12) of the present disclosure relate to an article as described in any one of aspects (1) to (11), wherein the first average modulation transfer function of the article 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, and when viewed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function is at least 0.55.

[0019] Aspects (13) of the present disclosure relate to an article as described in any one of aspects (1) to (12), wherein when viewed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function is at least 0.7.

[0020] Aspect (13) (Note: should be 14) of the present disclosure relates to a product as described in any one of aspects (1) to (13), wherein the second average modulation transfer function of the product 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, and when the product is viewed at a viewing angle of 20° and light with a brightness of 45,000 lux is incident on the first major surface at an incident angle of 45°, the second average modulation transfer function is at least 0.6.

[0021] Aspect (14) (Note: should be 15) of the present disclosure relates to a product as described in aspect (1), wherein: within the scattering zone, the first major surface includes: a plurality of third regions, arranged at a third height relative to the imaginary base plane, a plurality of fourth regions, arranged at a fourth height relative to the imaginary base plane, and the fourth height is different from the first height, the second height and the third height.

[0022] Aspect (15) (Note: should be 16) of the present disclosure relates to a product as described in aspect (15), wherein the product exhibits: a specular reflectance (Rs) less than or equal to 4.0, and an image coupling clarity less than 65%.

[0023] Aspect (17) of the present disclosure relates to an article as described in any of aspects (1) to (16), wherein the substrate is a glass substrate, and wherein the article further includes a display disposed adjacent to the second major surface and configured to emit light through the substrate.

[0024] Aspect (18) of the present disclosure relates to an article, comprising: a substrate comprising: a first major surface; a second major surface opposite 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 substrate, a plurality of second regions disposed at a second height relative to the imaginary base plane, and a plurality of inclined transition surfaces extending between boundaries of the plurality of first regions and the plurality of second regions, wherein: the first height is greater than the second height by an etch depth, the etch depth being greater than or equal to 80 nm and less than or equal to 600 nm, the scattering region comprises a radial PSD having a peak angle (θ 峰值 ) includes a first scattering angle range on one side, where the radial PSD increases with the scattering angle θ relative to the specular reflection. 峰值 increases with the increase of 峰值 ), wherein the radial PSD decreases with increasing scattering angle relative to the specular reflection, and the bidirectional reflectance distribution function ("BRDF") of the article is less than 10° at a scattering angle of 20° relative to the specular direction. -5multiplied by the peak intensity value, and the BRDF is measured with light having a wavelength of 520 nm incident on the first major surface at an incident angle of 20°.

[0025] Aspects (19) of the present disclosure relate to an article as described in aspect (18), wherein at a scattering angle of 30° relative to the specular direction, the BRDF includes an amplitude less than 1.7e -4 sr -1 .

[0026] Aspects (20) of the present disclosure relate to an article as described in any one of aspects (18) to (19), wherein within a range of a second scattering angle, at a first scattering angle greater than or equal to 2° and less than or equal to 15° relative to the specular direction, the radial PSD is reduced to 10% of the peak at θ 峰值 .

[0027] Aspects (21) of the present disclosure relate to an article as described in aspect (20), wherein within a range of a second scattering angle, at a second scattering angle greater than the first scattering angle and greater than or equal to 3.5°, and less than or equal to 30° relative to the specular direction, the radial PSD is reduced to a value of 1% of the peak.

[0028] Aspects (22) of the present disclosure relate to an article as described in aspect (21), wherein within a range of a second scattering angle, at a third scattering angle less than or equal to 8° relative to the specular direction, the radial PSD is reduced to a value of 0.1% of the peak.

[0029] Aspects (23) of the present disclosure relate to an article as described in aspect (22), wherein within a range of a second scattering angle, at a third scattering angle less than or equal to 16° relative to the specular direction, the radial PSD is reduced to a value of 0.01% of the peak.

[0030] Aspects (24) of the present disclosure relate to an article as described in any one of aspects (20) to (23), wherein within a range of a first scattering angle, at a scattering angle greater than or equal to 0.05°, the radial PSD is less than 10% of the peak.

[0031] Aspects (25) of the present disclosure relate to an article as described in any one of aspects (18) to (24), wherein θ 峰值 is greater than or equal to 0.3 and less than or equal to 0.5°.

[0032] Aspects (26) of the present disclosure relate to an article as described in any of aspects (18) to (26), wherein: within the scattering region, the first major surface includes a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions, and the plurality of inclined transition surfaces are inclined such that the height of the first major surface decreases as the distance from the boundary of the plurality of first regions increases.

[0033] Aspects (27) of the present disclosure relate to an article as described in aspect (26), wherein at least some of the plurality of inclined transition surfaces extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between a particular one of the plurality of first regions connected by the inclined transition surface and the plurality of second regions, and the lateral distance extending through the inclined transition surface is measured in a direction parallel to the surface normal of the inclined transition surface and parallel to the imaginary base plane.

[0034] Aspects (28) of the present disclosure relate to an article as described in any of aspects (18) to (27), wherein the article exhibits: a transmission haze less than or equal to 2.0%, and a sparkle less than or equal to 2.5% when measured at 140 ppi.

[0035] Aspects (29) of the present disclosure relate to an article including: a substrate including: a first major surface; a second major surface opposite the first major surface; and a scattering region formed in the first major surface, wherein within the scattering region, the first major surface includes: a plurality of first regions disposed at a first height relative to an imaginary base plane extending through the substrate, a plurality of second regions disposed at a second height relative to the imaginary base plane, and a plurality of inclined transition surfaces extending between the boundaries of the plurality of first regions and the plurality of second regions, wherein: the plurality of inclined transition surfaces are inclined such that the height of the first major surface decreases as the distance from the boundary of the plurality of first regions increases, at least some of the plurality of inclined transition surfaces extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between a particular one of the plurality of first regions connected by the inclined transition surface and the plurality of second regions, wherein the lateral distance extending through the inclined transition surface is measured in a direction parallel to the surface normal of the inclined transition surface and parallel to the imaginary base plane, and the scattering region includes a radial PSD that includes: a range of first scattering angles, wherein the radial PSD increases as the scattering angle of light relative to the specular direction increases; a peak scattering angle θ 峰值 , wherein the radial PSD includes a peak; and a range of second scattering angles greater than θ 峰值 , and at a first scattering angle greater than or equal to 2° and less than or equal to 15° relative to the specular direction, the radial PSD decreases to 10% of the peak.

[0036] Aspects (30) of the present disclosure relate to an article as described in aspect (29), wherein within the range of the first scattering angle, at a scattering angle greater than or equal to 0.05°, the radial PSD is less than 10% of the peak.

[0037] Aspects (31) of the present disclosure relate to an article as described in any one of aspects (29) to (30), wherein θ 峰值 is greater than or equal to 0.3 and less than or equal to 0.5°.

[0038] Aspects (32) of the present disclosure relate to an article as described in any one of aspects (29) to (31), wherein: relative to the specular direction, the first scattering angle is greater than or equal to 6° and less than or equal to 13°, and within the range of the second scattering angle, at a second scattering angle greater than or equal to 12.5° and less than or equal to 30.0° relative to the specular direction, the radial PSD is reduced to 1% of the peak.

[0039] Aspects (33) of the present disclosure relate to an article as described in any one of aspects (29) to (31), wherein: relative to the specular direction, the first scattering angle is greater than or equal to 2° and less than or equal to 7°, and within the range of the second scattering angle, at a second scattering angle greater than or equal to 3.5° and less than or equal to 13.5° relative to the specular direction, the radial PSD is reduced to 1% of the peak.

[0040] Aspects (34) of the present disclosure relate to an article as described in aspect (33), wherein within the range of the second scattering angle, at a third scattering angle less than or equal to 8° relative to the specular direction, the radial PSD is reduced to a value of 0.1% of the peak.

[0041] Aspects (35) of the present disclosure relate to an article as described in aspect (34), wherein within the range of the second scattering angle, at a third scattering angle less than or equal to 16° relative to the specular direction, the radial PSD is reduced to a value of 0.01% of the peak.

[0042] Aspects (36) of the present disclosure relate to an article as described in any one of aspects (29) to (35), wherein the article exhibits: a transmission haze less than or equal to 2.0%, and a flutter less than or equal to 2.5% when measured at 140 ppi.

[0043] Aspect (37) of the present disclosure relates to an article as described in any one of aspects (29) to (36), wherein the first average modulation transfer function of the article 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, and when the article is viewed at a viewing angle of 0° and light with a brightness of 45,000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function is at least 0.07, and the second average modulation transfer function of the article 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, and when the article is viewed at a viewing angle of 20° and light with a brightness of 45,000 lux is incident on the first major surface at an incident angle of 45°, the second average modulation transfer function is at least 0.6.

[0044] Aspect (38) of the present disclosure relates to a product as described in aspect (29), wherein: within the scattering zone, the first major surface includes: a plurality of third regions, arranged at a third height relative to an imaginary base plane, a plurality of fourth regions, arranged at a fourth height relative to the imaginary base plane, and the fourth height is different from the first height, the second height and the third height.

[0045] Aspect (39) of the present disclosure relates to the article of aspect (38), wherein the article exhibits: a specular reflectance (Rs) less than or equal to 4.0, and an image coupling clarity less than 65%.

[0046] It should be understood that the embodiments presented in both the above general description and the following embodiments are exemplary only and are intended to provide an overview or framework for understanding the nature and characteristics of the claims. This specification includes drawings to provide further understanding, and is incorporated into and constitutes a part of this specification. The drawings illustrate one or more embodiments (groups) and, together with the description, are used to explain the principles and operations of the various embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings, which are incorporated in and form a part of the specification, illustrate several aspects of the present invention and, together with the description, explain the principles of the present invention. In the drawings:

[0048] Figure 1 Depicting a stereoscopic view of a display article according to one or more embodiments of the present disclosure;

[0049] Figure 2 schematically depicts one or more embodiments according to the present disclosure, Figure 1 A portion of a scattering area of ​​a display article;

[0050] Figure 3A Schematically depict, in accordance with one or more embodiments of the present disclosure, Figure 2 the height profile view of the scattering region depicted in;

[0051] Figure 3B Schematically depict Figure 2 a cross-sectional view of the transition surface between two regions at different heights of the scattering region, in accordance with one or more embodiments of the present disclosure as shown;

[0052] Figure 4 A plot of the multiple target radial power spectral densities of the scattering region, in accordance with one or more embodiments of the present disclosure;

[0053] Figure 5 A flowchart of a method for formulating a phase map of the scattering region based on the target radial power spectral density ("PSD") of the scattering region, in accordance with one or more embodiments of the present disclosure;

[0054] Figure 6A A plot of the modeled glossiness and haze performance of exemplary articles as a function of the α parameter of the target radial PSD used to form those samples, in accordance with one or more embodiments of the present disclosure;

[0055] Figure 6B Depict, in accordance with one or more embodiments of the present disclosure, the simulated color appearance of the reflected light from the samples represented in, for various degrees of detector saturation and for α values in the range from 0.1 to 1.0 Figure 6A ;

[0056] Figure 6C Depict, in accordance with one or more embodiments of the present disclosure, the simulated color appearance of the reflected light from the samples represented in, for various degrees of detector saturation and for α values in the range from 1.0 to 10.0 Figure 6A ;

[0057] Figure 6D A plot of the target radial PSD before and after modification by phase thresholding to provide a binary phase mask, in accordance with one or more embodiments of the present disclosure;

[0058] Figure 6E Depict, in accordance with one or more embodiments of the present disclosure, a block of the phase map after phase thresholding;

[0059] Figure 6FFor one or more embodiments in accordance with the present disclosure, plots of the radial PSD that, both before and after modification, achieve a 50% local fill fraction for each phase after phase thresholding;

[0060] Figure 7 For one or more embodiments in accordance with the present disclosure, a flowchart of a method of fabricating an article having a scattering region by performing one or more etching steps on a surface of the article;

[0061] Figure 8 Schematically depicts, for one or more embodiments in accordance with the present disclosure, an apparatus for measuring the washout performance of an article;

[0062] Figure 9 Schematically depicts, for one or more embodiments in accordance with the present disclosure, an interior of a vehicle including a display and an ambient light source that emits light incident on and scattered from the display;

[0063] Figures 10A to 10F For one or more embodiments in accordance with the present disclosure, when illuminated under conditions by the apparatus depicted in Figure 8 Images of a plurality of patterns emitted by a sample having an existing anti-glare surface finish;

[0064] Figures 11 to 12 For one or more embodiments in accordance with the present disclosure, a plot of a modulation transfer function measurement from the image shown in Figures 10A to 10F ;

[0065] Figures 13A to 13D For one or more embodiments in accordance with the present disclosure, when illuminated under conditions by the apparatus depicted in Figure 8 Images of a plurality of patterns emitted by a sample having a scattering region formed by the target radial PSD described herein;

[0066] Figure 14 For one or more embodiments in accordance with the present disclosure, for a first set of exemplars fabricated by the method depicted in Figure 5 and Figure 7 A plot of specular reflectance (Rs) measurement values as a function of scintillation measurement values;

[0067] Figure 15A Schematically depicts, for one or more embodiments in accordance with the present disclosure, a portion of a modeled surface having a first region disposed at a first height, a second region disposed at a second height, and a transition surface extending between the first and second regions;

[0068] Figure 15B Depicting, throughFigure 15A The depicted line 1504, according to one or more embodiments of the present disclosure Figure 15A Cross-sectional view of the modeled surface depicted in;

[0069] Figure 15C Depicting, according to one or more embodiments of the present disclosure, along Figure 15A Drawing of the surface height measurement of line 1504 of the transition surface spanning the modeled surface depicted in;

[0070] Figure 15D Depicting, according to one or more embodiments of the present disclosure Figure 14 Drawing of the modeled specular reflection reduction spectrum of the modeled surface depicted in A;

[0071] Figure 16A Schematically depicting, according to one or more embodiments of the present disclosure, a portion of the modeled surface as Figure 15A A modified version of the modeled surface depicted in, which includes feature rounding such that the ramp of the modified surface transitions more gradually between the first region and the transition surface;

[0072] Figure 16B Depicting, according to one or more embodiments of the present disclosure Figure 16A The depicted modeled surface passing through Figure 16A Cross-sectional view of the depicted line 1504;

[0073] Figure 16C Depicting, according to one or more embodiments of the present disclosure, along Figure 16A Drawing of the surface height measurement of line 1504 of the transition surface spanning the modeled surface depicted in;

[0074] Figure 16D Depicting Figure 16A Drawing of the modeled specular reflection reduction spectrum of the modeled surface according to one or more embodiments of the present disclosure depicted in;

[0075] Figure 17 Drawing of the modeled radial PSD of multiple modeled surfaces with different degrees of feature rounding according to one or more embodiments of the present disclosure;

[0076] Figure 18A And 18B Depicting, according to one or more embodiments of the present disclosure, by Figure 5 And Figure 7 Images of the plan view and three-dimensional view of the first article without feature rounding produced by the method depicted in;

[0077] Figure 18C and 18D Describe one or more embodiments according to the present disclosure, by Figure 5 and Figure 7 An image of a plan view and a stereoscopic view of a second product having a rounded feature produced by the method described in;

[0078] Figure 18E According to one or more embodiments of the present disclosure, Figures 18A to 18D a plot of radial PSD measured from the surfaces of the first article and the second article depicted in ; and

[0079] Figure 19 A plot of bidirectional reflectance distribution functions measured from multiple samples both containing and excluding rounded features according to one or more embodiments of the present disclosure, and obtained by Figure 5 and Figure 7 The method depicted in utilises different target radial PSD production methods. DETAILED DESCRIPTION

[0080] Referring generally to the accompanying drawings, described herein are articles including surfaces having scattering regions designed to provide an advantageous combination of anti-glare ("AG") performance attributes. The scattering regions are designed in the spatial frequency domain based on a target radial power spectral density ("PSD") for the article, and the target radial PSD is converted into a phase distribution (or "phase map") for forming a plurality of surface features in the scattering regions. The surface features may include surface regions disposed at different heights relative to an imaginary base plane extending through the article and transition surfaces extending between such regions. The surface features are constructed such that the scattering regions exhibit a radial PSD that includes a range of first scattering angles, wherein the radial PSD increases with increasing scattering angle relative to specular reflection; a peak scattering angle θ 峰值 , wherein the radial PSD includes a peak; and a second scattering angle range, wherein the radial PSD decreases as the scattering angle relative to the specular reflection increases. The method of forming multiple surface features described herein helps the radial PSD decrease rapidly as the scattering angle increases within the second scattering angle range, such that within the second scattering angle range, at a first scattering angle less than or equal to 15° relative to the specular reflection, the PSD decreases to 10% of the peak value, and at a second scattering angle less than or equal to 30° relative to the specular reflection, the PSD decreases to 1% of the peak value. Such a rapid decrease within the second scattering angle range helps the articles described herein exhibit a favorable combination of AG performance attributes for various applications while introducing minimal observable color noise.

[0081] In order to achieve the radial PSD described herein that decreases rapidly within the range of the second scattering angle, the boundaries of the surface zones disposed at different heights may be rounded so that the transition of the slope of the first major surface (e.g., between a zone disposed at one of the heights and the transition surface) is smoother than a surface having features that are not rounded by the methods described herein. As a result, within the scattering region, adjacent regions of the first major surface disposed at different heights relative to the imaginary base plane may be separated by a lateral distance, measured in a direction parallel to the surface normal of the transition surface and parallel to the imaginary base plane of the transition surface, that is greater than or equal to 1.0 μm (e.g., greater than or equal to 1.0 μm and less than or equal to 10 μm, greater than or equal to 1.0 μm and less than or equal to 9.0 μm, or equal to 1.0 μm and less than or equal to 8.0 μm, greater than or equal to 1.0 μm and less than or equal to 7.0 μm, greater than or equal to 1.0 μm and less than or equal to 6.0 μm, greater than or equal to 1.0 μm and less than or equal to 5.0 μm, greater than or equal to 2.0 μm and less than or equal to 5.0 μm). Such a gradual surface height transition may be achieved by controlling the surface energy between the resist and the article during the etching process that forms the scattering region described herein. The lack of definition in surface height transitions reduces radial PSD at high scattering angles and helps achieve favorable color rendering and transmission haze performance.

[0082] A situation where the articles described herein may be particularly useful is in the context of vehicle interior displays. The vehicle interior may include one or more displays (e.g., a center instrument display, a dashboard display, a pillar display, a seat back display, and others). Such displays may be fixedly oriented relative to the driver. The vehicle is subject to ambient light conditions when in operation, which may result in relatively severe glare. For example, sunlight may enter the vehicle interior through the side windows or windshield and reflect or scatter from the display, resulting in bright glare, thereby distracting the driver and reducing the performance of the display due to color rendering. The articles described herein may reduce such color rendering due to the rapid decay of the radial PSD achieved within the range of the second scattering angles in commonly encountered ambient light conditions. Such favorable color rendering performance may be achieved while also providing favorable flicker and transmission haze performance.

[0083] As used herein, the term "radial PSD", when used to describe the surface of a particular article, refers to a profile calculated from a surface height profile measured from the surface. Specifically, a 1x1 mm surface height profile is used to measure the surface area using white light interferometry. The surface height profile data array is input into the Gwyddion data analysis program to calculate the radial power spectral density. The term "radial PSD" is intended to be distinguished from the term "target radial PSD". The target radial PSD is not calculated from the measured surface height profile, but is calculated mathematically from the far-field scattering pattern of the surface that meets the requirements.

[0084] As used herein, "specular reflectance (Rs)" or "Rs" is defined as the peak intensity of light reflected from the first surface of a substrate within a cone angle of + / - 0.1°. The specular reflectance can be measured using a Rhopoint IQ meter, which reports the Rs value in gloss units.

[0085] The characteristics of the articles described herein may be in terms of image clarity values. "Clarity of the reflected image", "clarity of the image", "DOI", or similar terms are defined by Method A of ASTM procedure D5767 (ASTM 5767), entitled "Standard Test Methods for Instrumental Measurements of Distinctness-of-Image Gloss of Coating Surfaces." According to Method A of ASTM 5767, the glass reflectance coefficient is measured on at least one rough surface of a glass article at the specular viewing angle and at angles slightly off the specular viewing angle (0.2° to 0.4° away from the specular). Such measurements can be made using a goniophotometer (Rhopoint IQ (goniophotometer) 20° / 60° / 85°, Rhopoint Instruments), which has been calibrated according to the certified black glass standards specified in ASTM procedures D523 and D5767.

[0086] The term "haze" or "transmittance haze" as used herein refers to the percentage of transmitted light scattered outside a cone of approximately + / - 2.5° according to ASTM D1003, entitled "Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics", the content of which is incorporated herein by reference in its entirety. It should be noted that although the title of ASTM D1003 refers to plastics, the standard has also been applied to substrates including glass materials. For optically smooth surfaces, the transmittance haze is typically close to zero.

[0087] As used herein, the terms "sparkle", "sparkle contrast", "display sparkle", "pixel power deviation", "PPD", or similar terms refer to the visual phenomenon that occurs when a textured transparent surface is combined with a pixelated display. Generally, the quantification of sparkle involves imaging a lit or simulated display with a textured surface in the field of view. The sparkle calculation for region P is equal to σ(P) / μ(P), where σ(P) is the standard deviation of the integrated intensity distribution of each display pixel contained within region P divided by the average intensity μ(P). The following guidance is followed: (1) J. Gollier et al., "Apparatus and method for determining sparkle", US9411180B2, United States Patent and Trademark Office, July 20, 2016; (2) A. Stillwell et al., "Perception of Sparkle in Anti-Glare Display Screens", JSID22(2), 129-136 (2014); (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); those skilled in the art can construct an imaging system to quantify sparkle. Alternatively, a commercially available system (e.g., SMS-1000, Display Messtechnik & Systeme GmbH & Co. KG, Germany) can also be used. Unless otherwise described, the following procedure is used to measure sparkle using a 140PPI display. A 140PPI display with only the green sub-pixels lit (e.g., Z50, Lenovo Group Limited, Hong Kong, China) (R = 0, B = 0, G = 255) is imaged at full display brightness using a f = 50mm lens / machine vision camera combination (e.g., C2205031: 2.8 50mm Φ30.5, Tamron, Japan) and Stingray F-125B, Allied Vision Technologies GmbH, Germany). The lens is set to aperture = 5.6, depth of field = 0.3, working distance = approximately 290mm; 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. The camera settings have gain and gamma correction turned off.Periodic intensity variations, e.g., for a display, and aperiodic intensity variations, e.g., removal of defective pixels during an analysis period prior to calculating a flicker metric.

[0088] The anti-glare and anti-reflection properties can be measured with nothing coupled to the surface (described herein as "uncoupled") or with a black absorber coupled to the back surface of the glass (described herein as "coupled").

[0089] Now refer to Figure 1 , which depicts an article 10 according to an exemplary embodiment. The article 10 includes 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 coupled to the substrate 12 and a display 16 within the housing 14. In such embodiments, the substrate 12 at least partially covers the display 16 such that light emitted by the display 16 can be transmitted through the substrate 12.

[0090] Depending on the implementation, the substrate 12 can be various types of materials. For example, in an embodiment such as Figure 1 depicted, the substrate 12 is a glass or glass-ceramic substrate. Various properties and examples of such glass or glass-ceramic substrates are described in more detail herein. In an embodiment, the substrate 12 can be made of a material other than glass such as paper, plastic, or other suitable polymeric materials. In an embodiment, the substrate 12 can include a combination of glass and polymeric materials. In an example, the scattering regions 20 described herein are formed in a polymeric material layer formed on a glass substrate. In an embodiment, the substrate 12 is transparent, or light normally incident on the substrate 12 in the wavelength range of 400 nm to 700 nm exhibits an average transmittance 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 an embodiment, the substrate 12 is opaque or exhibits an average transmittance of less than or equal to 30% in the wavelength range of 400 nm to 700 nm for light normally incident on the substrate. In an embodiment, the substrate 12 is colored to exhibit a colored appearance under ambient lighting (e.g., from sunlight).

[0091] 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 partially defined by the first major surface 18 (e.g., representing the 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 generally planar in shape such that the first major surface 18 and the second major surface 19 are generally flat (except for the plurality of surface features formed in the first major surface 18 as described herein). Embodiments in which the substrate 12 includes a curved shape (e.g., by suitable thermoforming and cold forming techniques) are also contemplated and within the scope of the present disclosure. In such embodiments, the reference herein to a "surface normal" (depicted as surface normal 33 in Figure 1 refers to the local surface normal at the point where light from the external environment 24 is incident on the first major surface 18. In the depicted embodiment, the first major surface 18 generally faces the external environment 24 surrounding the article 10 and is remote from the display 16. In an embodiment, the display 16 emits visible light that transmits through the thickness 21 of the substrate 12, exits the first major surface 18, and enters the external environment 24.

[0092] As Figure 1 depicted, the light energy from the external environment 24 represented by the input light ray 22 is incident on the first major surface 18 at an incident angle θ i (representing the zenith angle at which the input light ray 22 extends relative to the surface normal 33 of the first major surface 18, and the surface normal 33 is depicted as the z-direction in Figure 1 ). The input light ray 22 can represent light from several different sources outside the article 10. For example, the input light ray 22 can represent sunlight 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 input light ray 22 along the scattering direction represented by the scattered light ray 25. The light is scattered in a particular direction, and the scattering amplitude depends on the incident angle θ i relative to the surface normal 33 and the scattering angle θ s . As shown, the scattered light ray 25 is scattered in the scattering direction that, when projected into the plane of the first major surface 18 extending perpendicular to the surface normal 33, extends at an azimuth angle Φ relative to a first direction ( Figure 1 depicted as the x-direction in

[0093] ). As described herein, the scattering region 20 is designed based on a target radial PSD. The target radial PSD is azimuthally averaged with respect to the azimuth angle Φ such that the PSD is statistically isotropic with respect to the azimuth angle. Regardless of the azimuth angle Φ, the target radial PSD varies with the zenith angle θ according to the same functional relationship.s and varies. This target radial PSD beneficially minimizes the effect of the rotational orientation of the article 10 in the external environment 24 on the AG performance.

[0094] Figure 2 Schematically depicts an exemplary embodiment in accordance with the present disclosure, Figure 1 a plan view of region II of the scattering region 20 of the depicted article 10. As shown, the scattering region 20 includes a plurality of surface features 26. As described herein, the plurality of surface features 26 are designed based on a target radial PSD in the Fourier domain. In the depicted example, the plurality of surface features 26 includes a plurality of first regions 28 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 regions of the first major surface 18 that are generally disposed at different heights. In an embodiment, the plurality of first regions 28 and the plurality of second regions 30 may be characterized as flat, meaning that within each region, the surface height of the first major surface 18 does not vary substantially. For example, in an embodiment, within a particular one of the plurality of first regions 28 or within one of the plurality of second regions 30, the surface height variation (or roughness) in terms of root mean square (RMS) variation may be less than 50 nm (or less than 20 nm RMS, or less than 10 nm RMS). For example, in such embodiments, each of the plurality of first regions 28 and the plurality of second regions 30 is characterized by a surface height variation of 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.

[0095] In an embodiment, at least some of the plurality of first regions 28 and the plurality of second regions 30 may not be planar in shape, but include circular surfaces that extend at non-constant heights. In such embodiments, the plurality of first regions 28 and the plurality of second regions 30 may approximate flat surfaces and average heights. For example, each of the plurality of first regions 28 may be considered a region of the first major surface 18 disposed at a first average height, and each of the plurality of second regions 30 may be considered a region of the first major surface 18 disposed at a second average height, where the first average height and the second average height differ by at least 100 nm.

[0096] The plurality of surface features 26 generally vary in size and peripheral shape and include lengthwise axes that extend in a plurality of different directions in a plane parallel to the imaginary base plane 35 (see Figure 3A ). However, the randomness of the structure of the plurality of surface features 26 differs from that of certain existing AG surfaces (e.g., produced by sandblasting) in that the arrangement of the plurality of surface features 26 is reproducible (within manufacturing tolerances) by the method described herein.

[0097] Reference Figures 2 to 3A , in the depicted example, a plurality of first regions 28 are disposed at a first height h relative to an imaginary base plane 35 extending through the substrate 12 1 and a plurality of second regions 30 are disposed at a second height h relative to the imaginary base plane 35 2 . In the depicted example, the plurality of surface features 26 are regions of constant height of the first major surface 18 (it should be understood that the actual structure of the plurality of surface features 26 may include surface height deviations associated with the roughness of the first major surface 18, and due to the effects of processes such as the etching processes described herein for forming the plurality of surface features 26, the surface features 26 may also not accurately extend in the x - y plane). The plurality of surface features 26 may also include closed microstructures (where the boundaries associated with a particular surface feature are closed contours). Additionally, certain regions of the plurality of first regions 28 completely surround some regions of the plurality of second regions 30, and vice versa.

[0098] As Figure 3A illustrated, the plurality of first regions 28 and the plurality of second regions 28 are separated from each other by a transition surface 40 of the first major surface. The transition surface 40 represents a section of the first major surface 18 where the degree of height variation of the first major surface 18 is greater than the degree of variation within the plurality of first regions 28 and the plurality of second regions 30. The average slope of the first major surface 18 within the transition surface 40 may be greater than the average slope within the plurality of first regions 28 and the plurality of second regions 30. In an embodiment, the transition surface 40 includes a region of the first major surface 18 where the surface height changes by greater than or equal to 50 nm per 1 μm of linear distance (e.g., greater than or equal to 100 nm per 1 μm, greater than or equal to 200 nm per 1 μm, greater than or equal to 300 nm per 1 μm, greater than or equal to 400 nm per 1 μm, greater than or equal to 500 nm per 1 μm, greater than or equal to 500 nm per 1 μm of linear distance), which is measured in a direction perpendicular to the direction in which the transition surface 40 extends, where the linear distance is measured in a plane parallel to the imaginary base plane 35.

[0099] Referring Figure 3B , in an embodiment, each transition surface 40 includes a first edge 42 disposed adjacent to one of the plurality of first regions 28 and a second edge 44 disposed adjacent to one of the plurality of second regions 30. The first edge 42 may represent the outer boundary of one of the plurality of first regions 28, and the second edge 44 may represent the outer boundary of an adjacent one of the plurality of second regions 30. As Figure 3B illustrated, the transition surface 40 may include a width w. The width w is measured as the distance between the first edge 42 and the second edge 44 in a plane parallel to the imaginary base plane 35( Figures 1 to 2The lateral distance is also measured in a direction parallel to the projection of the surface normal 46 of the transition surface 40 into the xy plane. In an embodiment, the width w is greater than or equal to 1.0 μm and less than or equal to 10.0 μm (e.g., greater than or equal to 1.0 μm and less than or equal to 9.0 μm, greater than or equal to 1.0 μm and less than or equal to 8.0 μm, greater than or equal to 1.0 μm and less than or equal to 7.0 μm, greater than or equal to 1.0 μm and less than or equal to 6.0 μm, greater than or equal to 1.5 μm and less than or equal to 6.0 μm, greater than or equal to 2.0 and less than or equal to 6.0 μm). Widths within such a range indicate that the transition of the slope of the first major surface 18 lacks sharpness. Instead of relatively sharp corners at the first edge 42 and the second edge 44, the first major surface 18 gradually transitions between slopes (e.g., as in a rounded corner). As described in greater detail herein, such rounded features help reduce high spatial frequency content in the radial PSD of the scatter region 20, thereby providing favorable color rendering performance. Unless otherwise specified, the width w is the maximum measurement of lateral distance on a particular transition surface.

[0100] The width w may be measured using a variety of different techniques. For example, the width w may be physically measured by generating a line profile of the first major surface 18. The line profile may be generated by measuring the surface height of the first major surface 18 by white light interferometry. The line profile may also be obtained by cutting a cross section of the substrate 12 in a direction extending perpendicular to the transition surface 40 and obtaining an image of the cross section (e.g., using a scanning electron microscope using an atomic force microscope). At the point where the width w is measured (in a direction extending parallel to the projection of the surface normal 46 onto the xy plane, the surface normal being located at the first edge 42), the image is sampled in a direction extending perpendicular to the transition surface 40. The width w at a particular point on the transition surface 40 is calculated to be set at heights that differ from each other by h. 1 With h 2 The minimum lateral distance between points within 10% of the difference between 1 With h 2 The difference between represents the etch depth used to produce the article 10). The specific modality used to image the first major surface 18 when measuring the width w may vary depending on the size of the width w. When the width is less than 2.0 μm, an atomic force microscope may be used to image the first major surface 18. When the width w is greater than or equal to 2.0 μm, a line profile may be extracted from white light interferometer data collected with a lateral resolution of less than 0.2 nm. The resulting width w may be measured as being set at heights of h 1 With h 2 The minimum lateral distance between points within 10% of the difference between them.

[0101] Referring again to Figure 3A , the physical structure of the plurality of surface features 26 can be determined using scattered Fourier analysis. As Figure 3A illustrated, the input radiation from the external environment 24 can be approximated as a uniform plane wave and expressed as

[0102]

[0103] where I o represents the uniform intensity of the input radiation, and k xo and k yo represent the wave vector components associated with the wavelength and the incident angle of the input radiation on the first major surface 18 (e.g., the incident angle can be decomposed into components in the x-z and y-z planes, as Figure 1 depicted). In such a case, the scalar near field of the output radiation (after interaction with the first major surface 18) can be approximated as

[0104] u bear (x, y) = ρ u 0 (x, y).e iφ(x，y) (2)

[0105] where ρ is the Fresnel coefficient of the interface, and is the local phase accumulated over the double path of the distance through to the first major surface 18, and H(x, y) represents the pattern formed by the plurality of surface features 26. In this example, the input radiation is approximated as having a uniform intensity distribution, and the interface between the substrate 12 and the external environment 24 is approximated as applying only a spatially varying phase, such that the output radiation in the near field also has a uniform intensity distribution.

[0106] In the example depicted in FIG. 3, the far-field scattering pattern associated with the output radiation can be represented in spatial frequency (k) space and is related to the near field u near (x, y) calculated by Fourier transform using Equation 3 and is expressed as

[0107]

[0108] where k x and k y represent the scattering vector components (k x = |k|*cos(Φ), k y = |k|*sin(Φ)), where k is expressed as

[0109]

[0110] Φ is the azimuth angle depicted in FIG. 3, and λ is the wavelength of the scattered radiation. As used herein, the "PSD" of the scattering region 20 is expressed as

[0111]

[0112] where A is the area of the scattering region 20. As used herein, the term "target radial PSD" refers to Equation 5 when averaged over the entire range of the azimuth angle Φ. The target radial PSD is expressed as the azimuth-averaged PSD (using the following equation <PSD)Φ):

[0113]

[0114] Thus, the target radial PSD depends only on the magnitude of the spatial frequency and the wavelength of the scattered radiation. Unless otherwise stated, the radial PSD is expressed assuming a wavelength of 550 nm. The term "target radial PSD" refers to the result calculated according to Equation 6. The plots of both the target radial PSD and the radial PSD described herein can be functions of the scattering angle (θ s ), or the spatial frequency k. It should be understood that assuming a wavelength of 550 nm, Equation 4 can be used to convert these values.

[0115] In an embodiment, the plurality of surface features 26 are constructed such that H(x, y) approximately matches the target radial PSD when input into Equation 6. A family of examples of the target radial PSD that can be used to design the scattering region 20 is expressed as

[0116]

[0117] In a second range of the scattering angle 404 (refer to Figure 4 ), where α is the exponential decay parameter, k 最大 is the spatial frequency associated with a non-zero scattering angle θ 最大 at which the target radial PSD is equal to 0, and k 峰值 is the spatial frequency most associated with the peak angle θ 峰值 at which the target radial PSD has a peak. Assuming a wavelength of 550 nm, different values of the parameters α, θ 最大 , and θ 峰值 can be used to generate target radial PSDs that provide different performance attributes.

[0118] Figure 4 A plot depicting multiple target radial PSDs generated using multiple different values of α, where θ 最大 = 12.0°, and θ 峰值= 0.3. The target radial PSD includes a range 402 of a first scattering angle, where the target radial PSD increases approximately linearly in proportion to the scattering angle. The range of the first scattering angle 402 extends up to a peak angle θ 峰值 , where the target radial PSD has a peak. The target radial PSD also includes a range 404 of a second scattering angle at scattering angles greater than θ 峰值 , where the target radial PSD decreases at a rate determined by α according to Equation 6. The radial PSD with a low α value (less than 1) is generally larger at higher spatial frequencies (or scattering angles) than the radial PSD with a higher α value (greater than 1). As a result, a lower α value generally provides better scintillation performance than the radial PSD with a higher α value. However, a lower α value generally results in more pronounced color noise, where visible color separation can be introduced into the light by scattering. Selecting an appropriate target radial PSD for a given application represents a trade-off of various performance attributes, as described in more detail herein.

[0119] Once the appropriate target radial PSD is specified, the target radial PSD can be used to determine the phase distribution of the first major surface 18 using the method described herein Figure 5 Flowchart of an exemplary method 500 depicting a pattern of a plurality of surface features 26 that determine a scattering region 20. Reference will be made Figures 1 to 4 to the various components depicted to assist in the description of method 500. Method 500 can be used to form any number of anti-glare surfaces, and the depicted scattering region 20 can be formed by alternative methods.

[0120] At block 502, a target radial PSD for the scattering region 20 is selected. The target radial PSD can be formulated by selecting the values of the parameters α, θ 最大 , and θ 峰值 based on the performance attributes that meet the requirements of a particular application. For example, assuming an etch depth of 140 nm, Figure 6A depicts a plot modeling the transmission haze and scintillation performance of a fabricated article having the Figure 4 depicted radial PSD. As shown, generally, as the α value increases, the expected scintillation increases while the expected transmission haze decreases. Applications requiring a relatively low degree of haze thus require an alpha value greater than 1, and it is understood that such a high alpha value generally results in a scintillation greater than 1.0%. Another consideration in parameter selection is color noise performance. Figure 6B and 6C depict the qualitative simulated color appearance of reflected light with various detector saturation levels. Figure 6B and 6B The x and y axes in the various plots in are decomposed into θ x and θ yScattering angle of the component (see Figure 1 ). Figure 6B Depicts the simulated color appearance for α values ranging from 0.1 to 1, Figure 6C and depicts the simulated color appearance for α values ranging from 1.0 to 10.0. As shown, surfaces with lower α values exhibit distinct color boundaries, and as the α value increases, the color boundaries become less distinct. For α values greater than 4, the appearance does not change significantly. Thus, for applications where the reflected color appearance of article 10 is an important consideration, an α value of 4 or 5 can provide a favorable balance of color noise or scintillation performance (scintillation shown is less than or equal to 1.5% or less than or equal to 1.4%).

[0121] Parameter θ 最大 generally determines the magnitude of the target radial PSD at relatively large scattering angles. As will be described herein with reference to examples, when compared to a target radial PSD with a low θ 最大 value (less than 10), a target radial PSD with a high θ 最大 value (greater than 10) can be associated with excellent scintillation performance at the expense of poor color rendering performance. If excellent color rendering performance is desired (e.g., color rendering metric greater than or equal to 0.6, 0.65, 0.7, or even 0.75 under any of the lighting conditions described herein), then a θ 最大 value between 2 and 5 can be selected, and if a reduction in specular reflectivity is the main concern, then a θ 最大 value greater than 20 can be selected. It has been found that a θ 峰值 less than 1° (e.g., greater than or equal to 0.2° and less than or equal to 0.8°, greater than or equal to 0.3° and less than or equal to 0.5°) can provide favorable haze performance without significantly affecting other performance attributes.

[0122] Referring again to Figure 5, after formulating the target radial PSD, at block 504, a phase map of the scattering region 20 is generated based on the target radial PSD. In an implementation, an inverse Fourier transform of the target radial PSD can be used to generate the phase map. Such an approach typically results in a non-binary complex-valued phase map (and thus is inconsistent with the surface having a plurality of first regions 28 and a plurality of second regions 30 depicted in FIG. 3). The problem with non-binary phases is that certain existing fabrication processes, such as the etching methods described herein, cannot produce such structures. Accordingly, at block 506, a threshold is applied to the phase map such that discrete regions ("pixels") of the phase map form a discrete distribution of phases. The imaginary terms of the generated phases can be discarded, and the threshold can be applied to the real values such that pixels having an average value below the threshold are assigned a first phase (e.g., π / 2), and pixels having an average value above the threshold are assigned a second phase (e.g., -π / 2). In an implementation, the threshold is selected such that an equal number of pixels are calculated to have the first phase and the second phase (e.g., each phase occupies 50% of the surface area of the scattering region). The pixel size can be selected based on the estimated minimum feature size achievable by the etching process described herein. In an implementation, the pixel size is greater than or equal to 200 nm (e.g., greater than or equal to 300 nm, greater than or equal to 400 nm, greater than or equal to 500 nm, greater than or equal to 600 nm, greater than or equal to 700 nm, greater than or equal to 800 nm, greater than or equal to 900 nm, greater than or equal to 1000 nm).

[0123] The problem created by such thresholding to create a discrete distribution of phases compatible with the etching process is that the threshold operation alters the spatial frequency content of the radial PSD. Figure 6D A plot depicting the target radial PSD 620 before thresholding and the second radial PSD 621 calculated from the phase distribution after thresholding. As shown, the second radial PSD 621 contains a first elevated section 622 and a second elevated section 624, where the second radial PSD 621 is higher than the target radial PSD 620. The ability to correct the second elevated section 624 is limited by the stepped shape of the feature. However, a high-pass filtering operation can be used to correct the first elevated section 622.

[0124] It is believed that the first elevated section 622 can be corrected at least in part by ensuring that sub-regions of the phase map have a phase fill portion consistent with the phase fill portion associated with the entire scattering region 20. Accordingly, referring again to Figure 5, at boxes 508 and 510, in the sub-regions of the phase diagram that are pointed out and then modified, each phase does not occupy the desired filled portion. So that, in each pointed-out sub-region, each phase occupies the desired filled portion. For illustration, in the case of an example where the scattering region 20 includes two phases and each phase has a 50% filled portion, the phase diagram can be corrected by ensuring that the sub-regions also have a 50% filled portion for each phase. This local 50% filled portion of each phase in each sub-region can be achieved by flipping the phase of specific pixels (e.g., from the first phase to the second phase or vice versa) in order to reduce the sequence in that sub-region. The basis for such an operation can be understood based on the Hadamard transform, which employs an orthogonal expansion of orthogonal Walsh functions. The Hadamard transform of vector v is the expansion using Walsh functions (W(N,p) n ):

[0125]

[0126] For a given N, the Walsh functions are sorted by the number of times the function value changes from +1 to -1. When plotted over the range of values from 0 to 2 N the Walsh function with value p = 2 m (where m is greater than 0) will alternate with half-cycles of 2 |N-m| and thus "sequence" as 2 |N-m| . The Walsh function where p = 1 is constant and has only a zero-frequency component. The Walsh functions are orthogonal in the frequency domain. This means that the Walsh functions with p = 2 m , m > 0 do not have a zero-frequency component. Indeed, it can be shown that for each Walsh function with p = 2 m , m > 0, it does not have any frequency content less than 2 m-1 . That is, the subset of Walsh functions with p = 2 m and m > 0 has an increasing lower frequency limit. In view of this, it can be concluded that a Hadamard transform image that does not contain frequencies below 2 m-1 also does not contain the sequence 1, 2, 4, 8,... 2 m Walsh functions. That is, for a given image, the absence of any subset of W(N,2 m ) Walsh functions in the Hadamard transform of the image is a necessary but not sufficient condition for the absence of low-frequency components. This serves as the theoretical basis for the pixel phase flipping operation described herein.

[0127] In view of the foregoing, the applicant believes that the first elevated section 622 can be at least partially corrected by flipping pixels to achieve a 50% local fill fraction in various sub-regions of the pixel map, in order to reduce the order of the phase map. This can be done by an algorithm that scans a pixel map generated by random phase generation and thresholding with a predetermined block size (e.g., a predetermined array containing x × y pixels). The block size can start from an initial position on the phase map (e.g., such that the corners of the block are aligned with the corners of the phase map), analyze the pixels contained in the block to determine the fill fraction of each block, and compare the local fill fraction of the block with the value (i.e., 50%) of the entire scattering region 20. If the local fill fraction matches the fill fraction associated with the entire scattering region 20, the algorithm can analyze a new block (e.g., by moving the analyzed block one pixel in the Figure 2 x or y direction depicted in

[0128] ). If the local fill fraction does not match the fill fraction associated with the entire scattering region 20, the algorithm identifies a pixel sub-array within the block that is inconsistent with the desired fill fraction of the block and flips the phase values of one or more pixels within at least one sub-array such that the block has the desired fill fraction. If doing so would tend to reduce the local order within the block, only the pixels within a given sub-array are flipped. Figure 6E depicts an example that creates a frame 630 of a phase map generated by iterative phase retrieval and thresholding. The frame 630 includes an 8x8 pixel array 632. The size of the frame 630 is selected based on the Hadamard transform analysis described above. As discussed above, the Walsh function W(N,2 m ) is constant over adjacent blocks of length 2 N-m (in one dimension). In view of this, if the local fill fraction of each frame of this length is 50%, the image cannot contain the Walsh function W(N,2 m ) or any lower-order Walsh function (i.e., any Walsh function W(N,1) to W(N,2 m-1 ). In other words, achieving a 50% local fill fraction at a particular ratio means that the changes in the pattern must have a period smaller than that ratio. If the frame size is relatively small, the phase map varies with a smaller period (having a larger high-frequency content) and tends to scatter more light at higher scattering angles. If the frame size is very large, it has been found that this condition does not significantly reduce the radial PSD at low scattering angles. In an embodiment, the frame size is approximately 60 μm x 60 μm (e.g., from 25 μm x 25 μm to 125 μm x 125 μm). It has been found that this size is small enough to reduce the low-frequency content in the radial PSD without significantly changing θ 最大 .

[0129] In block 630, pixels 632a assigned a first phase value are represented as "+", while pixels 632b assigned a second phase value are represented as "-". Analysis of the phase values in block 630 shows that the block has two more pixels 632b than pixels 632a. Accordingly, to achieve a 50% fill portion for block 630 to meet the requirement, one of the pixels 632b needs to be converted to a pixel 632a. The pixel 632b selected for conversion is chosen to avoid increasing the high-frequency content of the phase map. For illustration, the first subarray 634 of block 630 includes four of the pixels 632b having the second phase value, and the second subarray 636 includes three of the pixels 632a having the first phase value and one of the pixels 632b. Converting one of the pixels 632b in the first subarray 634 will tend to increase the high-frequency content of the phase map because this will reduce the area where the phase map is at a constant value. Converting the pixel 632b in the second subarray 636 to one of the pixels 632a will tend to reduce the high-frequency content of the phase map by increasing the area where the phase map is at a constant value. Accordingly, in an embodiment, this algorithm can convert the phase value of a pixel by identifying a 2x2 subarray ([ Figure 6A depicted in the example) that contains only a single pixel having the phase to be converted (the second phase value in the example) to ensure a 50% fill portion block and convert the phase value associated with that single pixel.

[0130] Figure 6F Plots depicting the unmodified radial PSD 638 after thresholding and the modified radial PSD 640 after thresholding. The depicted PSDs are generated based on Equation 7, where α = 4, θ 峰值 = 0.3°, and θ 最大 = 12°. To generate the unmodified radial PSD 638, a phase map is generated and thresholded to achieve a binary phase map with a 50% phase fill portion. To generate the modified radial PSD 640, the phase map used to generate the unmodified radial PSD 638 is modified to achieve a local 50% on a 96 μm × 96 μm block (representing 8x8 pixels) according to the method described herein. As shown, at low scattering angles, particularly for scattering angles less than 0.1°, the modified radial PSD 640 is less than the unmodified radial PSD 638. For example, as shown, the modified radial PSD 640 is 10% of the peak at θ 峰值 at a scattering angle greater than 0.05° (about 0.07°), where the unmodified radial PSD 638 is 10% of the peak at a scattering angle less than 0.05°. The modified radial PSD 640 is approximately 2% of the peak at specular reflection, while the unmodified radial PSD 638 has a minimum of approximately 6.5% of the peak at specular reflection. Additionally, the modification of the phase mask does not appear to substantially change θ峰值 The radial PSD at the scattering angles above. Such results demonstrate the efficacy of the phase masking modification method described herein and also demonstrate that such modification can result in a reduction in small-angle scattering.

[0131] Figure 7 A flowchart depicting an exemplary method 700 of fabricating an article 10 according to an exemplary embodiment of the present disclosure. Reference will be made to Figures 1 to 6F The various components and processes depicted therein assist in describing method 700. The method for forming article 10 is not particularly limited and any suitable method may be used. At block 702, a pattern of a plurality of surface features 26 is determined. In an embodiment, the pattern is determined by performing method 500 described herein with reference to Figure 5 by selecting a target radial PSD, generating a phase map based on the target radial PSD, thresholding the generated phase map, and modifying the phase map to provide a locally filled portion of the phase in a sub-region of the phase map.

[0132] At block 704, a resist is deposited 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 an embodiment, various nanoimprint or photolithography techniques may be used to deposit and pattern the resist layer. In such embodiments, the minimum feature size (e.g., minimum linear dimension) associated with the plurality of surface features 26 may be set to at least 400 nm (e.g., greater than or equal to 500 nm, greater than or equal to 600 nm, greater than or equal to 700 nm, greater than or equal to 800 nm, greater than or equal to 900 nm, greater than or equal to 1.0 μm, greater than or equal to 1.5 μm, greater than or equal to 2.0 μm, greater than or equal to 2.5 μm, greater than or equal to 5.0 μm) to facilitate the use of existing resist application and patterning techniques. In an embodiment, for example, thermoplastic nanoimprint lithography may be used to form the resist, and the resist may be formed of a thermoplastic polymer that is spin-coated onto the substrate 12 and then imprinted with a mold to form a first pattern that at least partially corresponds to the pattern of the plurality of surface features 26 on the first major surface 18. The resist may then be thermally cured to form an etch mask. Other methods of forming the resist (e.g., gravure offset printing, other printing techniques) have also been contemplated and are within the scope of the present disclosure.

[0133] Lithographic techniques (e.g., nanoimprint lithography, optical lithography) can also be used, and a resist can be deposited onto the first major surface 18 by a suitable application method (e.g., spin coating). In such embodiments, a mask including a first pattern that at least partially corresponds to the pattern defined for the plurality of surface features 26 is aligned with the first major surface 18, and the resist can be exposed to radiation from a suitable light source (e.g., UV radiation) to cause the resist to cure and form an etch mask. The resist can then be developed such that portions of the first major surface 18 are left exposed through the cured resist. Any suitable lithographic technique can be used to pattern the resist.

[0134] At block 706, during deposition of the resist onto the first major surface 18, controlling the adhesion force between the resist and the first major surface 18 helps with the rounding feature during etching. Such adhesion force can control undercut in the etching process, which can change the shape of the edges of the plurality of surface features 26. Specifically, such adhesion force control can increase the width w of the transition surface 40 described herein with reference to Figure 3B to more than 1.0 μm to help reduce the radial PSD at relatively high scattering angles above θ 峰值 . In an embodiment, before applying the resist, an adhesion promoter (e.g., hexamethyldisilazane (HDMS) or N,N-dimethyl-N-(3-(trimethoxysilyl)propyl)octadecane-1-ammonium chloride (YSAM C18)) is applied to the first major surface 18. Controlling the chemistry of the adhesion promoter (in terms of the hydrophobic group) can provide a certain degree of control over undercut during etching and the rounding feature. Alternatively or additionally, the amount of the adhesion promoter applied on the surface also affects the amount of the adhesion force. The adhesion promoter can also be removed from the first major surface 18 before applying the resist to modify the adhesion force of the resist. The applicant has found that any process that modifies the surface chemistry and water contact angle of the first major surface 18 can modify the adhesion force with the resist and thus affect the amount of the rounding feature. Any suitable technique can be used to reduce the adhesion force between the resist and the first major surface 18 to achieve the rounding feature. In an embodiment, before depositing the resist, any adhesion promoter described in U.S. Patent No. 9,884,782, filed on April 1, 2015, which is incorporated herein by reference in its entirety, can be applied to the glass such that after applying the adhesion promoter, the substrate 12 exhibits a water contact angle greater than or equal to 40° and less than or equal to 70° (e.g., greater than or equal to 45° and less than or equal to 60°, greater than or equal to 48° and less than or equal to 52°). It has been found that such a water contact angle is associated with a suitable amount of the rounding feature.

[0135] At block 708, the exposed regions of the first major surface 18 (through the cured and patterned resist) are exposed to a suitable etchant for a suitable etch period determined based on the target etch depth. Each region of the first major surface 18 exposed through the patterned resist formed at block 504 can be in direct contact with the etchant, which can degrade the substrate 12 and remove material therefrom to form regions on the first major surface 18 that are set at a reduced height relative to the imaginary base plane 35 compared to the regions of the first major surface 18 covered by the patterned resist. In an embodiment, the etchant contacting the first major surface 18 is HF / HNO 3 etchant. In an embodiment, the etchant consists of hydrofluoric acid (HF, 49 w / w%) and nitric acid (HNO 3 , 69 w / w%) in combination with 0.1 - 5 v / v% HF and 0.1 - 5 v / v% HNO 3 . A typical concentration for achieving the etch depths discussed herein is 0.1 v / v% HF / 1 v / v% HNO 3 to 0.5 v / v% HF / 1 v / v% HNO 3 solution. In an embodiment, the etching can be performed using a dip or spray etching process, with a temperature range from room temperature to about 45°C.

[0136] Block 710 is a decision block where it is determined whether the scatter region 20 is to combine more than two heights. Referring Figure 3A to, in an embodiment, the plurality of surface features 26 can include a plurality of third regions 32 disposed at a third height h 3 relative to the imaginary base plane 35 and a plurality of fourth regions 34 disposed at a fourth height h 4 relative to the imaginary base plane 35. The third height h 3 can be the same as the fourth height h 4 or the difference therebetween can be a second etch depth, which can be the same as or different from the etch depth differentiating h 1 and h 2 . Combining the plurality of third regions 32 and the plurality of fourth regions 34 can provide specific performance improvements relative to a single etch design, such as improved specular reflectance reduction and reduced DOI. The presence of multiple layers enables interference measurement suppression of specular reflection over a wide optical wavelength range. The performance attributes of the multi-layer design will be described in more detail herein with reference to examples.

[0137] If multiple layers are desired, method 700 can return to block 702 again to determine the pattern for additional etching steps. In an embodiment, the same target radial PSD used in the first etching step can be used to generate the pattern for the second etching. However, when the resist is disposed on the first major surface 18, the substrate 12 can be rotated by a certain angle (e.g., 90°, 180°, or any other angle) so that the pattern is applied to the first major surface 18 in a different orientation in the second etching as compared to the first etching. In an embodiment, a different target radial PSD than that used in the first etching can be used to generate the pattern for the second etching.

[0138] Substrate properties

[0139] Various properties of the substrate 12 will now be described in accordance with embodiments of the present disclosure.

[0140] In an embodiment, the substrate 12 is a glass substrate or a glass-ceramic substrate. In an embodiment, 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 components, such as alumina, calcium oxide, sodium oxide, boron oxide, etc. In some practices, the bulk composition of the substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, and phosphosilicate glass. In other practices, the bulk composition of the substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, phosphosilicate glass, soda-lime glass, alkali metal aluminosilicate glass, and alkali metal aluminoborosilicate glass. In a further practice, the substrate 12 is a glass-based substrate, including, but not limited to, a glass-ceramic material comprising about 90 wt% or more of a glass component and a ceramic component. In other practices of the article 10, the substrate 12 can be a polymer material having durability and mechanical properties suitable for the development and maintenance of the scattering region 20.

[0141] In an embodiment, the substrate 12 has a bulk composition including an alkali metal aluminosilicate glass that includes alumina, at least one alkali metal, and in some embodiments, greater than 50 mol% SiO 2 , in other embodiments, at least 58 mol% SiO 2 , and in other embodiments, at least 60 mol% SiO 2 , where the ratio (Al 2 O 3 (mol%) + B 2 O 3 (mol%)) / Σ alkali metal modifiers (mol%) > 1, where the modifier is an alkali metal oxide. In a particular embodiment, the glass comprises, consists essentially of, or consists of: about 58 mol% to about 72 mol% of SiO2 ; about 9 mol% to about 17 mol% of Al 2 O 3 ; about 2 mol% to about 12 mol% of B 2 O 3 ; about 8 mol% to about 16 mol% of Na 2 O; 0 mol% to about 4 mol% of K 2 O, wherein the ratio (Al 2 O 3 (mol%) + B 2 O 3 (mol%)) / Σ alkali metal modifiers (mol%) > 1, wherein the modifier is an alkali metal oxide.

[0142] In an embodiment, the substrate 12 has a body composition comprising an alkali metal aluminosilicate glass that comprises, consists essentially of, or consists of: about 61 mol% to about 75 mol% of SiO 2 ; about 7 mol% to about 15 mol% of Al 2 O 3 ; 0 mol% to about 12 mol% of B 2 O 3 ; about 9 mol% to about 21 mol% of Na 2 O; 0 mol% to about 4 mol% of K 2 O; 0 mol% to about 7 mol% of MgO; and 0 mol% to about 3 mol% of CaO.

[0143] In an embodiment, the substrate 12 has a body composition comprising an alkali metal aluminosilicate glass that comprises, consists essentially of, or consists of: about 60 mol% to about 70 mol% of SiO 2 ; about 6 mol% to about 14 mol% of Al 2 O 3 ; 0 mol% to about 15 mol% of B 2 O 3 ; 0 mol% to about 15 mol% of Li 2 O; 0 mol% to about 20 mol% of Na 2 O; 0 mol% to about 10 mol% K 2 O; 0 mol% to about 8 mol% of MgO; 0 mol% to about 10 mol% of CaO; 0 mol% to about 5 mol% of ZrO 2 ; 0 mol% to about 1 mol% of SnO 2 ; 0 mol% to about 1 mol% of CeO 2 ; less than about 50 ppm of As2 O 3 ; Sb below about 50 ppm 2 O 3 ; wherein 12 mol% ≤ Li 2 O + Na 2 O + K 2 O ≤ 20 mol% and 0 mol% ≤ MgO + Ca ≤ 10 mol%.

[0144] In an embodiment, the substrate 12 has a body composition including an alkali metal aluminosilicate glass, the glass comprising, consisting essentially of, or consisting of: about 64 mol% to about 68 mol% of SiO 2 ; about 12 mol% to about 16 mol% of Na 2 O; about 8 mol% to about 12 mol% of Al 2 O 3 ; 0 mol% to about 3 mol% of B 2 O 3 ; about 2 mol% to about 5 mol% of K 2 O; about 4 mol% to about 6 mol% of MgO; and 0 mol% to about 5 mol% of CaO, wherein: 66 mol% ≤ SiO 2 + B 2 O 3 + CaO ≤ 69 mol%; Na 2 O + K 2 O + B 2 O 3 + MgO + CaO + SrO > 10 mol%; 5 mol% ≤ MgO + CaO + SrO ≤ 8 mol%; (Na 2 O + B 2 O 3 )—Al 2 O 3 ≤ 2 mol%; 2 mol% ≤ Na 2 O—Al 2 O 3 ≤ 6 mol%; and 4 mol% ≤ (Na 2 O + K 2 O)—Al 2 O 3 ≤ 10 mol%.

[0145] In an embodiment, the substrate 12 has a body composition that includes SiO 2 , Al 2 O 3 , P 2 O 5 , and at least one alkali metal oxide (R 2O), where 0.75 > [(P 2 O 5 (mol%) + R 2 O(mol%)) / M 2 O 3 (mol%)] ≤ 1.2, where M 2 O 3 ═ Al 2 O 3 + B 2 O 3 . In an embodiment, [(P 2 O 5 (mol%) + R 2 O(mol%)) / M 2 O 3 (mol%)] = 1 and, in an embodiment, the glass does not contain B 2 O 3 and M 2 O 3 ═ Al 2 O 3 . In an embodiment, substrate 12 includes: about 40 to about 70 mol% of SiO 2 ; 0 to about 28 mol% of B 2 O 3 ; about 0 to about 28 mol% of Al 2 O 3 ; about 1 to about 14 mol% of P 2 O 5 ; and about 12 to about 16 mol% of R 2 O. In some embodiments, the glass substrate includes: about 40 to about 64 mol% of SiO 2 ; 0 to about 8 mol% of B 2 O 3 ; about 16 to about 28 mol% of Al 2 O 3 ; about 2 to about 12 mol% of P 2 O 5 ; and about 12 to about 16 mol% of R 2 O. Substrate 12 may further include at least one alkaline earth metal oxide such as, but not limited to, MgO or CaO.

[0146] In some embodiments, substrate 12 has a bulk composition that is substantially lithium-free; that is, the glass includes less than 1 mol% of Li 2 O, and in other embodiments, less than 0.1 mol% of Li 2 O, and in other embodiments, contains 0.01 mol% of Li 2O, and in still other embodiments, contains 0 mol% of Li 2 O. In some embodiments, these glasses do not contain at least one of arsenic, antimony, and barium; that is, the glass comprises less than 1 mol%, and in other embodiments, less than 0.1 mol%, and in still other embodiments, 0 mol% of As 2 O 3 、Sb 2 O 3 、and / or BaO.

[0147] In an embodiment, the substrate 12 has a body composition comprising, consisting essentially of, or consisting of a glass composition, such as Eagle Glass, Glass, Glass 2, Glass 3, Glass4, or Glass 5.

[0148] In an embodiment, the substrate 12 has an ion-exchangeable glass composition that is strengthened by chemical or thermal means known in the art. In an embodiment, the substrate 12 is chemically strengthened by ion exchange. In this process, metal ions at or near the first major surface 18 of the substrate 12 are exchanged for larger metal ions having the same valence as the metal ions in the glass substrate. The exchange is typically carried out by contacting the substrate 12 with an ion-exchange medium, such as, by way of example, a molten salt bath containing larger metal ions. The metal ions are typically monovalent metal ions, such as, by way of example, alkali metal ions. In a non-limiting example, chemical strengthening of a substrate 12 containing sodium ions by ion exchange is achieved by immersing the substrate 12 in an ion-exchange bath comprising a molten potassium salt, such as potassium nitrate (KNO 3 ) or the like. In a particular embodiment, the ions in the surface layer of the substrate 12 adjacent to 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, the monovalent cations in the surface layer of the substrate 12 can be replaced by monovalent cations other than alkali metal cations, such as Ag + or the like.

[0149] In such embodiments, replacing smaller metal ions with larger metal ions in an ion-exchange process creates a zone of compressive stress in substrate 12 that extends from the first major surface 18 to a depth (referred to as the "layer depth") under compressive stress. This compressive stress in substrate 12 is balanced by a tensile stress (also referred to as "central tension") within substrate 12. In some embodiments, the first major surface 18 of substrate 12 described herein has a compressive stress of at least 350 MPa when strengthened by ion exchange, and the zone under compressive stress extends to a depth of at least 15 μm, i.e., the depth of the layer enters thickness 21 below the first major surface 18.

[0150] The ion-exchange process is typically carried out by immersing substrate 12 in a molten salt bath containing larger ions to be exchanged for smaller ions in the glass. Those skilled in the art will appreciate that the parameters of the ion-exchange process, including, but not limited to, bath composition and temperature, immersion time, number of immersions of the glass in the salt bath (or baths (etc.)), use of multiple salt baths, additional steps such as annealing, washing, and the like are typically determined by the composition of the glass and the desired layer depth and compressive stress of the glass resulting from the strengthening operation. By way of example, ion exchange of an alkali metal glass can be achieved by immersion in a molten bath containing at least one salt containing a larger alkali metal ion such as, but not limited to, nitrates, sulfates, and chlorides. The temperature of the molten salt bath is typically in the range of about 380 °C to as high as about 450 °C, and the immersion time ranges from as high as about 15 minutes to about 16 hours. However, different temperatures and immersion times than those described above can also be used. When used with substrate 12 having an alkali metal aluminosilicate glass composition, such ion-exchange treatment results in a depth (layer depth) of the compressive stress zone ranging from about 10 μm to at least 50 μm, where the compressive stress ranges from about 200 MPa to as high as about 800 MPa, and the central tension is less than about 100 MPa.

[0151] Since the etching process that can be used to create the scattering zone 20 in substrate 12 can remove alkali metal ions that would otherwise be replaced by larger alkali metal ions during the ion-exchange process, the compressive stress zone in the article 10 is preferentially developed after the formation and development of the scattering zone 20.

[0152] Example

[0153] The embodiments of the present disclosure can be further understood in view of the following examples.

[0154] The first set of examples consists of the performance of methods 500 and 700 described herein with reference to Figure 5 and Figure 7 Specifically, the target radial PSD is using α values of 4 and 5, and θ of 0.3 and 0.5峰值 and θ of 4, 8, 12, 16, and 32 最大 were developed. These examples were formed in a 0.7 mm thick Corning glass thick piece. Method 500 was performed on each example to determine the pattern for resist deposition (using a 50% fill portion for each height). The samples were etched through the resist to various etch depths following Method 700 (the etch depth was measured using a 2D tactile profilometer and subsequently verified using white light interferometry on a 1x1 mm area). The target radial PSD and etch depth are summarized in Table 1 below (the examples marked with "*" include the rounding features performed by block 706 in Method 700). The DOI values were reported in gloss units according to ASTM E430.

[0155] Table 1

[0156]

[0157] As illustrated in Table 1, multiple performance attributes of the samples were measured, including transmission haze, scintillation (PPD), image coupling clarity, specular reflectance (Rs), and color rendering metric in two different configurations. The color rendering metric relates to how the scattering region 20 affects the display black level contrast in the presence of an external light source. Higher color rendering metric values are associated with excellent performance. Samples with circular features exhibited a higher color rendering metric performance greater than or equal to 0.68 (and in some cases greater than or equal to 0.70, greater than or equal to 0.75, or even greater than or equal to 0.80). More details regarding the measurement and calculation of the color rendering metric are provided in more detail herein. Various ranges of the performance attributes achieved by a subset of the first set of examples are provided in Table 2 below.

[0158] Table 2

[0159]

[0160] As illustrated in Table 2, samples generated using a target radial PSD with a relatively low θ 最大 value (e.g., θ 最大 = 4°) tend to exhibit excellent transmission haze performance (in some cases, providing a transmission haze value less than or equal to 3.0%, less than or equal to 2.75%, less than or equal to 2.5%, less than or equal to 2.0%, less than or equal to 1.75%, less than or equal to 1.50%, less than or equal to 1.25%, less than or equal to 1.0%, or even less than or equal to 0.75%). However, using a relatively high θ 最大 value (e.g., θ 最大Samples generated with a target radial PSD of = 32° tend to exhibit excellent specularity performance (in some cases less than or equal to 1.0%, less than or equal to 0.9%, less than or equal to 0.8%, less than or equal to 0.7%, less than or equal to 0.6%, or even less than or equal to 0.55%). The last row in Table 2 contains some samples with a rounding feature, which generally results in better color rendering and haze performance compared to samples without rounding but formed using the same target radial PSD.

[0161] The "color rendering" metric included in Tables 1 and 2 is defined to quantify the impact of glare events (e.g., exposure to sunlight) on the contrast and resolution of a combined display. Such a metric is useful for examining the performance of cover materials for applications that may be exposed to external light sources (e.g., automotive interior displays, outdoor displays). To quantify "color rendering", the modulation transfer function (MTF) of the anti-glare surface is measured under various lighting conditions, and the average MTF over multiple spatial frequencies is used to evaluate the impact of the lighting conditions on the display performance. The MTF at a specific spatial frequency f is expressed as

[0162]

[0163] where

[0164]

[0165] and I(f) 最大 and I(f) 最小 are the maximum and minimum intensities of the input or output modulated image at spatial frequency f. In this expression, MF in represents the MF value associated with the input pattern transmitted through the sample cover material. MF outThe value represents the MTF value when the covering material is disposed on an input pattern (e.g., from a display) and under the lighting conditions being tested. A higher MTF value generally means that the lighting conditions have a smaller impact on the display performance (and thus the performance of the scattering region of the covering material is better). In an embodiment, for a given lighting condition, an MTF value greater than or equal to 0.60 (e.g., greater than or equal to 0.65, greater than or equal to 0.70, greater than or equal to 0.75, greater than or equal to 0.76, greater than or equal to 0.77, greater than or equal to 0.78, greater than or equal to 0.79, greater than or equal to 0.80, greater than or equal to 0.81, greater than or equal to 0.82, greater than or equal to 0.83, greater than or equal to 0.84, greater than or equal to 0.85, greater than or equal to 0.86, greater than or equal to 0.87, greater than or equal to 0.88, greater than or equal to 0.89, greater than or equal to 0.90, greater than or equal to 0.91, greater than or equal to 0.92, greater than or equal to 0.93, greater than or equal to 0.94, and greater than or equal to 0.95) is preferred, indicating a minimum degradation of the display performance caused by exposure to external light.

[0166] Figure 8 Schematically depicts a device 800 for measuring the color rendering effect. As shown, a sample 802 (e.g., corresponding to the substrate 12 described herein) is placed on a display 804. The sample 802 is positioned such that the scattering region faces outward (not towards the display 804). As illustrated in block 805, which depicts a front view of the sample 802 and the display 804, the display 804 generates a plurality of target patterns 806, where the intensity of the light emitted by the display 804 varies with a specific spatial frequency f i varies. A plurality of first light sources 808 are distributed around the sample 802. The plurality of first light sources 808 (e.g., indoor lights) are configured to emit relatively low-intensity light to simulate the sample 802 encountering normal ambient conditions (e.g., indoor light). As reported herein, the plurality of first light sources 808 are configured to emit white light having 130 lux and a color temperature of 2100k. A projection light source 810 is configured to emit a relatively high-intensity light source to simulate sunlight illumination. The projection light source 810 is positioned such that the light emitted therefrom is incident on the sample at an incident angle θ i is incident on the sample. In an embodiment, the projection light source 810 is movable or otherwise adjustable to change the incident angle θ i . In an embodiment, the projection light source 810 emits light over an emission region such that the light emitted by the projection light source 810 is incident on the sample 802 at a range of incident angles θ i is incident on the sample 802.

[0167] The camera 812 is positioned to receive the light scattered from the sample 802. The camera is positioned such that the light scattered from the sample 802 will be at a viewing angle θv (or the range of the viewing angle) enters the camera 812. In an embodiment, the camera 812 is movable or otherwise adjustable to change the viewing angle θ v . The computing system 814 receives the images generated by the camera 812 and analyzes the images to calculate the MTF values of each of the plurality of target patterns 806 emitted by the display 804. For each target pattern 806, the computing system 814 can use equations 9 and 10 to calculate the MTF values and generate an output that measures the dependence of the MTF values on spatial frequency. The plurality of first light sources 808 and the projection light source 810 allow the MTF values to be measured under a plurality of different illumination conditions to determine the efficacy of the pattern on the sample 802 in reducing color bleeding. When only the first light source 808 emits light, the "in-room light color bleeding" effect can be measured. When both the first light source 808 and the projection light source 810 emit light, the "sunlight color bleeding" effect can be measured.

[0168] Such color bleeding measurements are particularly useful for evaluating the performance of the overlay material of an automotive interior display. Figure 9An interior of a vehicle 1000 is shown that includes three different vehicle interior systems 100, 200, 300 according to exemplary embodiments. The vehicle interior system 1000 includes a central control panel base 110, the surface 120 of which includes a display 130. The vehicle interior system 200 includes an instrument panel base 210 having a surface 220 that includes a display 230. The instrument panel base 210 generally includes an instrument panel 215, and the instrument panel 215 may also include a display 216. The vehicle interior system 300 includes an instrument panel steering wheel axle distance 310 having a surface 320 and a display 330. In one or more embodiments, the vehicle interior system may include a base that is an armrest, a pillar, a seatback, a floor, a headrest, a door panel, or any part of the vehicle interior that includes a surface. In an embodiment, the displays 130, 230, 330 are flat and include cover glass having a flat main surface. In an embodiment, one or more of the displays 130, 230, 330 are curved, and the curved display may include curved cover glass that may be thermoformed or cold formed to have such a curvature. For example, such embodiments may incorporate an opaque layer formed of a photocurable ink as described herein and disposed on a cold formed glass substrate. Such cold forming may involve any of the techniques described in U.S. Early Publication No. 2019 / 0329531A1, titled "Laminating thin strengthened glass to curved molded plastic surface for decorative and display cover application," U.S. Early Publication No. 2019 / 0315648A1, titled "Cold-formed glass article and assembly process thereof," U.S. Early Publication No. 2019 / 0012033A1, titled "Vehicle interior systems having a curved cover glass and a display or touch panel and methods for forming the same," and U.S. Patent Application No. 17 / 214,124, titled "Curved glass constructions and methods for forming same," the entire contents of which are incorporated herein by reference in their entirety.

[0169] The various components of the vehicle interior 1000 may be illuminated by various light sources. As Figure 9As depicted, for example, a first ambient light source 900 may emit light that is transmitted through a first side window of the vehicle and incident on the display 216 at an incident angle θ i1 The display 216 may be oriented such that the light scattered at a specific scattering angle θ v1 will enter the driver's field of view and distract the driver. A second ambient light source 902 may emit light that is transmitted through a second side window of the vehicle and incident on the display 130 at an incident angle θ i2 The display 130 may be oriented such that the light scattered at a specific scattering angle θ v2 will enter the driver's field of view and distract the driver. The first ambient light source 900 and the second ambient light source 902 may represent sunlight at various time points. Indeed, the ISO 15002 / SA 1757 standard specifies a first condition where 45 kLux of light (direct sunlight) is incident on the display 216 at an angle of 20° and scattered to the driver at a scattering angle of 0° (i.e., where θ i1 = 20°) and θ v1 = 0°, associated with the "color wash" 1 metric in this document), and a second condition where 45 kLux of light (direct sunlight) is incident on the display 130 at an angle of 45° and scattered to the driver at a scattering angle of 20° (i.e., where θ i2 = 45° and θ v2 = 20°, associated with the "color wash" 2 metric in this document). Figure 8 The depicted apparatus 800 enables testing of the color wash of this condition by varying the orientation of the sample 802 and adjusting the projection light source 810.

[0170] Using Figure 8 the apparatus 800 depicted in, the two conditions of ISO 15002 / SA 1757 described herein are used to test samples constructed according to the methods described herein. Using 4 is used as the display 804. Using a Pixelink 3.1MP PL - B776 as the camera 812. The projection light source 810 (manufactured by Mightex Systems, model LCS - 6500 - 65 - 22) uses a collimated LED light source (emitting 45000 lux of white light). Multiple projection light sources are used and positioned to emit light incident on the sample 802 at incident angles of 20° and 45°. The sample 802 and the camera 812 are also mounted on a rotating stage such that the viewing angle θ v and the incident angle θ i are adjustable for the two conditions. Laboratory light is used as the first light source 808 and is measured to have a brightness of 132 lux.

[0171] In the first set of measurements, sample 802 had a standard AG surface treatment (by sandblasting the first major surface 18, referred to herein as "Counterexample 1"). The results are as Figures 10A to 10F depicted. Figures 10A to 10C Depicts the imaging pattern under the first condition described herein (i.e., where θ i1 = 20° and θ v1 = 0°). Figure 10A Depicts image 1002, where the display 804 is not covered by the sample 802 in a dark room. Figure 10B Depicts image 1004, where the display 804 is covered by the sample 802 when only the first light source 808 emits light (laboratory lights on). Figure 10C Depicts image 1006, where the display 804 is covered by the sample 802 and both the first light source 808 and the projection light source 810 emit light. Figures 10D to 10F Depicts the imaging pattern under the second condition described herein (i.e., where θ i2 = 45° and θ v2 = 20°). Figure 10D Depicts image 1008, where the display 804 is not covered by the sample 802 in a dark room. Figure 10E Depicts image 1010, where the display 804 is covered by the sample 802 when only the first light source 808 emits light (laboratory lights on). Figure 10F Depicts image 1012, where the display 804 is covered by the sample 802 and both the first light source 808 and the projection light source 810 emit light.

[0172] Figure 11 and Figure 12 are plots 1102 and 1104 of the MTF values obtained from the images depicted from Figure 9 A to Figure 9 F. Figure 11 Contains a first series 1106 representing the various MTF values obtained from the image 1004 depicted in Figure 10B (for the case of the first condition where only the first light source 808 is on). Figure 11 Also contains a second series 1108 representing the various MTF values obtained from the image 1006 depicted from Figure 10C (for the case of the first condition where both the first light source 808 and the projection light source 810 are activated). Figure 12 Contains a first series 1110 representing the various MTF values obtained from the image 1010 depicted in Figure 10E (for the case of the second condition where only the first light source 808 is on). Figure 12 Also contains a representation from Figure 10FA second series 1112 of various MTF values obtained for the depicted image 1012 (for the case of a second condition where both the first light source 808 and the projection light source 810 are activated). These experimental results indicate that: (1) the device can solve for the very small attenuation caused by indoor light conditions, indicating a very high sensitivity of the measuring device; (2) the sample 802 only causes degradation of the image contrast, but does not affect the resolution of the display; (3) this setting can distinguish the effects of different group actions on the performance of the display; (4) the device can characterize the "color rendering effect" at different angles.

[0173] To quantitatively evaluate the effect of the sample 802, the MTF values at the spatial frequencies associated with the points 1114, 1116, 1118, 1120, and 1120 in the first series 1106 are averaged (the MTF values at a spatial frequency of 1.67 cycles / mm, for each of the series 1106, 1108, 1110, and 1112, are on average 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm. The "color rendering" metric described herein is the average of the MTF values at these spatial frequencies for each condition.

[0174] For samples having a scattering region designed based on the target radial PSD according to Equation 7 (Examples 22 and 5), measurement sets similar to those described herein are performed. Specifically, another set of tests is performed using two different samples: the first (Example 22) is constructed based on the target radial PSD, where α = 4, θ Figures 10A to 12 = 0.3°, and θ 峰值 = 0.3°, and the second (Example 5, see Table 1) is constructed based on the target radial PSD, where α = 4, θ 最大 = 0.5°, θ 峰值 = 0.5°, and θ 最大 = 4°. The etch depth for these examples is 150 nm. The rounding feature of the second sample is performed through the performance of block 706 of the depicted method 700. Each sample is tested under the test conditions discussed above (where θ Figure 7 = 20° and θ i1 = 0°; and where θ v1 = 45° and θ i2 = 45° and θ v2 = 20°). Figure 13A An image 1300 is depicted where the projection light source 810 illuminates the first sample under a first condition. Figure 13B An image 1302 is depicted where the projection light source 810 illuminates the first sample under a second condition. Figure 13C An image 1304 is depicted where the projection light source 810 illuminates the second sample under a first condition. Figure 13DDepict Image 1306, where the projection light source 810 irradiates the second sample under the second condition. Conventional AG counterexamples (such as Figures 10A to 12 depicted) and the results of the first and second samples are summarized in Table 3 below.

[0175] Table 3

[0176]

[0177] As shown in Table 3, although Example 22 (without the rounding feature) provides the best results in terms of reduced specular reflectance (where the coupled specular reflectance (Rs) value is less than 9) and coupled DOI (where the coupled DOI is less than 55%). Example 5 provides very excellent rendering performance, where the rendering metric under the first condition is greater than or equal to 0.80 and the rendering metric under the second condition is greater than 0.70. Compared with Counterexample 1, such rendering performance is achieved while still providing improved haze, coupled DOI, and specular reflection performance. These examples demonstrate the ability of the articles described herein to achieve a unique combination of performance attributes: transmission haze less than 2.0% (or even less than 1.5% or less than 1.25%), coupled Rs less than 15, flutter (as measured at 140 ppi) less than 2.5%, the rendering metric under the first condition greater than or equal to 0.7, and the rendering metric under the second condition greater than 0.55. Articles formed by the methods with the rounding feature described herein are particularly well-suited for automotive applications because such a combination of performance attributes represents consistent display performance under a variety of ambient lighting conditions.

[0178] Figure 14 Depict Plot 1400 as a plot of the flutter and specular reflectance (Rs) measurements for the first set of examples (including the samples provided in Table 1 and others). The Rs and flutter results are plotted against each other to form Plot 1400. For each subset of examples formed using a target radial PSD with the same θ 最大 value (but with varying α values), the results are fitted to different curves. Curve 1402 fits the results formed using a target radial PSD with θ 最大 = 32°. Curve 1404 fits the results formed using a target radial PSD with θ 最大 = 16°. Curve 1406 fits the results formed using a target radial PSD with θ 最大 = 12°. Curve 1408 fits the results formed using a target radial PSD with θ 最大 = 8°. Curve 1410 fits the results formed using a target radial PSD with θ 最大 = 4° and θ 峰值 = 0.5°. Curve 1412 fits the results formed using a target radial PSD with θ最大 = 4° and θ 峰值 = 0.3° for the target radial PSD. As shown, the example formed using a target radial PSD with θ 最大 = 32° provides the most favorable combination of results in terms of scintillation and Rs, where multiple samples provide a scintillation of less than 1% and an Rs of less than 10.

[0179] It should be noted that in Plot 1400, each of the curves 1402, 1404, 1406, 1408, 1410, and 1412 suggests a similar minimum Rs value for each subset of the examples, which ranges from approximately 5 to approximately 9. Each example in the first set of examples represented in Plot 1400 is formed as a binary surface (such that the first major surface 18 within the scattering region 20 includes a plurality of first regions 28 and a plurality of second regions 30, where the plurality of first regions 38 fills approximately 50% of the surface area within the scattering region 20, and the plurality of second regions 30 fills the other 50%). Without wishing to be bound by theory, it is believed that in the case of an incident plane wave (as depicted in FIG. 3), the specular reflection from the binary image (associated with the height profile H(x, y) within the scattering region 20) depends only on the filled portion of the binary image and not on the image itself. In view of this, it is not surprising that each of the curves 1402, 1404, 1406, 1408, 1410, and 1412 shows a similar lower limit of Rs. The variation in the measured Rs values can be explained by the variation in the light source used to measure the specular reflectance from a uniform plane wave.

[0180] Although the above-described examples referred to Figure 14 are binary surfaces having an approximately 50% filled portion associated with each surface height, it is believed that the filled portion can be varied and still provide acceptable specular reflectance results. When using a binary surface, it is believed that the surface area portion assumed by each height can be greater than or equal to 40% and less than or equal to 60% (e.g., greater than or equal to 42.5% and less than or equal to 57.5%, greater than or equal to 45% and less than or equal to 55%, greater than or equal to 47.5% and less than or equal to 52.5%), while still providing an acceptable reduction in specular reflectance (compared to the untextured version, the substrate 12 without the scattering region). For illustration, referring to Figure 2 , one of the plurality of first regions 28 and the plurality of second regions 30 can have a combined surface area that constitutes more than 50% of the total surface of the scattering region 20 (e.g., greater than 50% and less than or equal to 60%), while the other of the plurality of first regions 28 and the plurality of second regions 30 can have a combined surface area that constitutes less than 50% of the total surface area of the scattering region 20 (e.g., less than 50% and greater than or equal to 40%), while still providing acceptable specular reflection performance.

[0181] Additional modeling is performed to examine the impact of the rounding feature on the optical performance. Figure 15A Depicts a portion of the modeled surface 1500. The surface is generated using the target radial PSD, where θ 最大 = 4°, θ 峰值 = 0.5°, α = 4. As Figure 15A illustrated, the surface 1500 includes a first zone 28 set at a first height and a second zone 30 set at a second height, where the first height and the second height differ by approximately 130 nm. The transition surface 1506 is the case where the surface 1500 transitions between the first height and the second zone. In this example, it is assumed that within the transition surface 1506, the surface 1500 extends perpendicular to the direction in which the surface extends in the first zone 28 and the second zone 30. Figure 15B Depicts a cross-sectional view of the surface 1500 through the Figure 15A depicted line 1504. As illustrated, the line 1504 extends parallel to the surface normal of the transition surface 1506. The transition surface 1506 is depicted as having an undefined slope. Figure 15C Depicts a plot 1504 showing the occurrence of surface height measurements across the surface 1500. As illustrated, a first set of height occurrences 1510 at the second height accounts for 50% of the measured height occurrences, and a second set of height occurrences 1512 at the first height accounts for the other 50% of the measured height occurrences. This indicates that no height is measured between the first height and the second height, which is consistent with the undefined slope of the transition surface 1506. Figure 15D Depicts a plot 1514 showing the estimated specular reflectance reduction as a function of wavelength. As illustrated, the minimum specular reflectance for this design occurs at approximately 525 nm.

[0182] To estimate the impact of the rounding feature, the surface 1500 is modified such that the slope transitions from the first zone 28 and the second zone 30 to the transition surface 1506. Specifically, the corners 1518 and 1520 (refer to Figure 15B ) are rounded by applying a Gaussian blur filter (the imgaussfilt image filter in Matlab TM ) to define the amount of the rounding feature. Figure 16B Depicts a portion of the modified surface 1600. Due to the rounding feature, the modified surface 1600 includes a transition surface 1602 between zone 28 and zone 30, and zone 28 and zone 30 have a finite slope (in this example, the slope causes the transition surface 1602 to extend in a plane at an angle of 3° relative to the first zone 28). Figure 16B Depicts a cross-sectional view of the modified surface 1600 through the Figure 16A depicted line 1504. As illustrated, at the corners 1605 and 1607, the slope of the modified surface 1600 is steeper than in Figure 15BAt the corners 1518 and 1520 depicted, the transition is more gradual than between the values at regions 28 and 30 and the values within the transition surface 1602. That is, in the modified surface 1600, the ramp has a smoother transition than in the surface 1500. Figure 16C A plot 1604 depicting the occurrence of surface height measurements across the modified surface 1600. As shown, a first set of height occurrences 1606 at a second height account for approximately 30% of the measured height occurrences, and a second set of height occurrences 1608 at a first height account for approximately 30% of the measured height occurrences. This indicates that approximately 40% of the height occurrences are at heights other than the first and second heights, which is consistent with the limiting ramp of the transition surface 1602. In this case, the lateral distance between the first region 28 and the second region 30 (along line 1504, referring to Figure 16A ) is approximately 2.3 μm (corresponding to the width w depicted in Figure 3B ). Additionally, the ramp of the probability count curve is 170% / μm. Figure 16D A plot 1610 of curves 1612 and 1614 that model the specular reflectance of the modified surface 1600. Curve 1612 represents the modeled specular reflectance when the modified surface 1600 has the same etch depth as the example depicted in Figure 15B , and curve 1614 represents the modeled specular reflectance when the etch depth of the modified surface 1600 is increased by 15% such that the minimum reaches approximately 525 nm. As shown, the smoother transition associated with the modified surface 1600 is not expected to reduce the minimum specular reflectance, but rather shift the wavelength at which the specular reflectance is lowest. It is believed that this wavelength shift can be compensated for by adjusting the etch depth.

[0183] Figure 17 A plot 1700 depicting the modeled radial PSD of four surfaces if the degree of rounding features varies. As shown, the value d in the legend represents the lateral distance between the edges of the first region 28 and the second region 30 (measured in a direction perpendicular to the corresponding transition surface) (corresponding to the width w depicted in Figure 3B ). As shown, for examples with larger values of d, the radial PSD decreases. Samples with a larger amount of rounding features (such that the ramp of the first major surface 18 transitions from a minimum to a maximum over a larger lateral distance) are predicted to have a lower PSD at relatively large scattering angles greater than or equal to 7°. It is believed that these lower PSDs of samples with a larger number of rounding features provide superior rendering performance to non-rounded samples by providing a lower scattering amplitude at high scattering angles.

[0184] The radial PSD was measured from two different samples to confirm the modeled results relative to Figures 16A to 17 described. Samples were generated using a target radial PSD, where θ 最大= 4, α = 4, and θ 峰值 = 0.5. Figure 18A and Figure 18B are images (adhesion between the resist and the substrate not controlled) respectively showing a plan view and a three-dimensional view of a surface 1800 formed without a rounding feature. The images are generated from white light interferometer measurements of the surface 1800. As shown, the surface 1800 includes a first region 28 disposed at a first height, a second region 30 disposed at a second height, and a transition surface 1802 extending between the first region 28 and the second region 30. Figure 18C and 18D are images (adhesion between the resist and the substrate controlled) respectively showing a plan view and a three-dimensional view of a surface 1804 formed with a rounding feature. The images are generated from white light interferometer measurements of the surface 1802. As shown, the surface 1800 includes a first region 28 disposed at a first height, a second region 30 disposed at a second height, and a transition surface 1806 extending between the first region 28 and the second region 30. Due to the rounding feature, the transition surface 1806 has a smaller slope than the transition surface 1802 shown in Figures 18A to 18B . The width w (refer to Figure 3B ) of the measured height of the surface 1804 transitioning from the first height to the second height is between 2.0 μm and 10.0 μm.

[0185] Figure 18E are plots 1808 of the radial PSDs 1810 and 1812 measured respectively from the surfaces 1800 and 1804 depicted in Figures 18A to 18D . The radial PSDs 1810 and 1812 are plotted based on the white light interferometry data depicted in Figures 18A to 18D in Gwyddion. The radial PSDs 1810 and 1812 are generated from white light interferometry data (with a lateral resolution of approximately 360 nm) from a 1x1 mm area of each surface. The radial PSDs 1810 and 1812 are generated from the complete 1x1 mm area, but the images in Figures 18A to 18D represent sub-sections of the imaging area. It has been found that the specific 1x1 mm area used does not affect the resulting radial PSD. As shown, at scattering angles greater than 5°, the radial PSD 1810 associated with the surface 1800 is significantly higher than the radial PSD 1812 associated with the surface 1804. Indeed, the radial PSD 1812 drops to 0.1% of its peak at scattering angles less than or equal to 8° relative to the specular direction. The radial PSD 1812 drops to 0.01% of its peak at a third scattering angle less than or equal to 16° relative to the specular direction. In contrast, the radial PSD 1810 is greater than 10 of its peak at a scattering angle of 10° -3times. The so - low measured radial PSD provided by the rounding feature demonstrates the achieved efficacy of the rounding feature by the method described herein.

[0186] Bidirectional reflectance distribution function (BRDF) measurements were performed on five different samples fabricated according to the method described herein. The first sample does not have a rounding feature and is formed based on a target radial PSD, where θ 最大 = 4°, α = 4, and θ 峰值 = 0.3°. The second sample does not have a rounding feature and is formed based on a target radial PSD, where θ 最大 = 4°, α = 4, and θ 峰值 = 0.5°. The third sample has a rounding feature and is formed based on a target radial PSD, where θ 最大 = 8°, α = 5, and θ 峰值 = 0.3°. The fourth sample has a rounding feature and is formed based on a target radial PSD, where θ 最大 = 8°, α = 5, and θ 峰值 = 0.3°. The fifth sample does not have a rounding feature and is formed based on a target radial PSD, where θ 最大 = 8°, α = 4, and θ 峰值 = 0.3°. The measurements were performed in reflection mode using the REFLET 180S system of Synopsys, Inc. Figure 19 Plot 1900 depicting the results measured at a wavelength of 520 nm and an incident angle of 20°. As shown, the samples with the rounding feature exhibit lower scattering intensities relative to specular reflection at scattering angles greater than 20°. When normalized with respect to the specular reflection peak, the efficacy of the rounding feature in reducing the scattering amplitude at relatively high scattering angles is even more pronounced. At a scattering angle of 20° with respect to specular reflection, the third and fourth samples (samples with the rounding feature) exhibit a scattering intensity less than 10 -6 times (the value exhibited by sample 4 is less than 10 -7 multiplied by the intensity at the specular reflection peak). Conversely, the samples without the rounding feature all exhibit a BRDF amplitude at a 20° scattering angle greater than 10 -5 times their specular peak. In terms of the actual (non - normalized) BRDF amplitude, the samples with the rounding feature each exhibit a BRDF amplitude less than 1.7e -4 sr -1 at a 30° scattering angle, or less than 1.5e -4 sr -1 at a 40° scattering angle. This relatively low BRDF amplitude achieved by the samples with the rounding feature at high scattering angles demonstrates that such samples have excellent rendering performance.

[0187] An additional set of samples was fabricated using multiple etches. Table 4 below provides the parameters associated with each step, including the target radial PSD for each etch and etch depth, and the results of the optical property measurements.

[0188] Table 4

[0189]

[0190] Additional measurements were made on samples with multiple etch steps, and the set of performance attributes expected to be achieved through various etch sequences are summarized in Table 5 below.

[0191] Table 5

[0192]

[0193] As shown by the comparison between Tables 1 and 2 and Tables 4 and 5, samples fabricated using multiple etch steps tend to have increased scintillation and haze relative to samples fabricated using a single etch step. However, in multiple etch designs, specular reflection and coupled image clarity can be significantly reduced. The presence of multiple layers enables interferometric suppression of specular reflection over a wider optical bandwidth. As illustrated in Table 4, Rs values obtained through multiple etch designs are typically less than 4.0, and in some cases less than 3.0 and even less than 2.0. In contrast, Rs values for single etch designs are much higher. The coupled clarity of image values achieved through multiple etch designs is typically less than 65%, and in some cases less than 55%, and in one example even less than 30%. Generally, the design used will be specified by the performance attribute requirements of a particular application. In the case of applications requiring low haze, scintillation, and excellent color rendering performance (such as in automotive interior displays), a single etch design may be required, while applications requiring excellent specular reflectance reduction and / or DOI may be suitable for multiple etch designs.

[0194] Unless expressly stated otherwise, no method set forth herein is to be construed as requiring that its steps be performed in a particular order. Accordingly, where method claims do not actually recite an order to be followed by their steps, or where such steps are not specifically limited to a particular order in the claims or specification, no particular order is to be inferred. Further, as used herein, "a" is intended to include one or more than one component or element and is not to be construed as meaning only one.

[0195] 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 those skilled in the art can conceive of modifications, combinations, sub-combinations, and variations of the disclosed embodiments that incorporate the spirit and substance of the embodiments, the embodiments should be construed to include all such modifications and their equivalents within the scope of the appended claims.

Claims

1. A product, wherein the product include: A substrate, comprising: a first major surface; a second major surface, the second major surface being opposite to 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 substrate, and a plurality of second regions, the second regions being disposed at a second height relative to the imaginary base plane, wherein: The first height is greater than the second height by an etching depth, the etching depth being greater than or equal to 80 nm and less than or equal to 600 nm, The scattering region includes a radial PSD, and the radial PSD includes: a first range of scattering angles, wherein the radial PSD increases with increasing scattering angle of the light relative to the specular direction, Peak angle θ 峰值 , wherein the radial PSD includes a peak, and The range of the second scattering angle is greater than θ 峰值 , where at the first scattering angle that is greater than or equal to 2° and less than or equal to 15° relative to the mirror surface direction, the radial PSD is reduced to 10% of the peak value.

2. The article of claim 1, wherein within the second scattering angle range, at a second scattering angle greater than the first scattering angle and greater than or equal to 3.5° and less than or equal to 30° relative to the specular direction, the radial PSD decreases to 1% of the peak value.

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

4. The product according to any one of claims 2 to 3, in: Relative to the mirror direction, the first scattering angle is greater than or equal to 6° and less than or equal to 13°, and Relative to the mirror direction, the second scattering angle is greater than or equal to 12.5° and less than or equal to 30.0°.

5. The product according to any one of claims 2 to 3, in: Relative to the mirror direction, the first scattering angle is greater than or equal to 2° and less than or equal to 7°, and Relative to the mirror direction, the second scattering angle is greater than or equal to 3.5° and less than or equal to 13.5°.

6. The article of claim 5, wherein within the second scattering angle range, at a third scattering angle less than or equal to 8° relative to the specular direction, the radial PSD decreases to a value of 0.1% of the peak value.

7. The article of claim 5, wherein within the second scattering angle range, at a third scattering angle less than or equal to 16° relative to the specular direction, the radial PSD decreases to a value of 0.01% of the peak value.

8. The article according to any one of claims 1 to 7, wherein said θ 峰值 is greater than or equal to 0.3 and less than or equal to 0.5°.

9. The article according to any one of claims 1 to 8, in: Within the scattering region, the first major surface includes a plurality of inclined transition surfaces extending between boundaries of the plurality of first regions and the plurality of second regions, and The plurality of inclined transition surfaces are inclined such that a height of the first major surface decreases with increasing distance from a boundary of the plurality of first regions.

10. The article according to claim 9, wherein at least some of the plurality of inclined transition surfaces extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between certain ones of the plurality of first regions and the plurality of second regions connected by the inclined transition surface, wherein the lateral distance extended by the inclined transition surface is measured in a direction parallel to the surface normal of the inclined transition surface and parallel to the imaginary base plane.

11. The article according to any one of claims 1 to 10, wherein the article exhibits: a transmission haze of less than or equal to 2.0%, and a sparkle of less than or equal to 2.5% when measured at 140 ppi.

12. The article according to any one of claims 1 to 11, wherein the first average modulation transfer function of the article 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, and when viewing the article at a 0° viewing angle and light with a luminance of 45000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function is at least 0.

55.

13. The article according to any one of claims 1 to 12, wherein when viewing the article at the 0° viewing angle and light with a luminance of 45000 lux is incident on the first major surface at the 20° incident angle, the first average modulation transfer function is at least 0.

7.

14. The article according to any one of claims 1 - 13, wherein the second average modulation transfer function of the article 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, and when viewing the article at a 20° viewing angle and light with a luminance of 45000 lux is incident on the first major surface at an incident angle of 45°, the second average modulation transfer function is at least 0.

6.

15. The article according to claim 1, wherein: within the scattering region, the first major surface comprises: a plurality of third regions disposed at a third height relative to the imaginary base plane, and a plurality of fourth regions disposed at a fourth height relative to the imaginary base plane, and the fourth height is different from the first height, the second height, and the third height.

16. The article according to claim 15, wherein the article exhibits: a specular reflectance (Rs) of less than or equal to 4.0, and an image coupling clarity of less than 65%.

17. The article according to any one of claims 1 to 16, wherein the substrate is a glass substrate, and the article further comprises a display disposed adjacent to the second major surface and configured to emit light through the substrate.

18. An article, the article comprising: a first major surface; a second major surface opposite 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 substrate, and a plurality of second regions, the second regions being disposed at a second height relative to the imaginary base plane, wherein: The first height is greater than the second height by an etching depth, the etching depth being greater than or equal to 80 nm and less than or equal to 600 nm, The scattering region includes a radial PSD that includes a range of a first scattering angle on one side of a peak angle (θ 峰值 ), where the radial PSD increases as the scattering angle increases, and a second scattering angle range on a second side of θ 峰值 where the radial PSD decreases as the scattering angle increases, The bidirectional reflectance distribution function ("BRDF") of the article is less than 10 -5 times the peak intensity value at a scattering angle of 20° relative to the specular surface, and The BRDF is measured from light having a wavelength of 520 nm incident on the first major surface at an incident angle of 20°.

19. The article according to claim 18, wherein at a scattering angle of 30° relative to the mirror surface, the BRDF includes an amplitude of less than 1.7e -4 sr -1 .

20. The article according to any one of claims 18 to 19, wherein within the range of the second scattering angle, at a first scattering angle greater than or equal to 2° and less than or equal to 15° with respect to the specular direction, the radial PSD is reduced to 10% of the peak at θ 峰值 at the peak.

21. The article of claim 20, wherein within the second scattering angle range, at a second scattering angle greater than the first scattering angle and greater than or equal to 3.5° and less than or equal to 30° relative to the specular direction, the radial PSD decreases to a value of 1% of the peak value.

22. The article of claim 21, wherein within the second scattering angle range, at a third scattering angle less than or equal to 8° relative to the specular direction, the radial PSD decreases to a value of 0.1% of the peak value.

23. The article of claim 22, wherein within the second scattering angle range, at a third scattering angle less than or equal to 16° relative to the specular direction, the radial PSD decreases to a value of 0.01% of the peak value.

24. The article of any one of claims 20 to 23, wherein within the first range of scattering angles, at scattering angles greater than or equal to 0.05°, the radial PSD is less than 10% of the peak value.

25. The article according to any one of claims 18 to 24, wherein θ 峰值 is greater than or equal to 0.3 and less than or equal to 0.5°.

26. The article according to any one of claims 18 to 25, in: Within the scattering region, the first major surface includes a plurality of inclined transition surfaces extending between boundaries of the plurality of first regions and the plurality of second regions, and The plurality of inclined transition surfaces are inclined such that a height of the first major surface decreases with increasing distance from a boundary of the plurality of first regions.

27. An article as described in claim 26, wherein at least some of the plurality of inclined transition surfaces extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between one of the plurality of first zones connected by the inclined transition surfaces and the plurality of second zones, wherein the lateral distance extending through the inclined transition surface is measured in a direction parallel to the surface normal of the inclined transition surface and parallel to the imaginary base plane.

28. The article of any one of claims 18 to 27, wherein the article exhibits: Transmission haze, less than or equal to 2.0%, and Flicker is less than or equal to 2.5% when measured at 140ppi.

29. A product, the product include: A substrate, comprising: a first major surface; a second major surface, the second major surface being opposite to 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 substrate, a plurality of second regions, the second regions being disposed at a second height relative to the imaginary base plane, and a plurality of inclined transition surfaces extending between boundaries of the plurality of first regions and the plurality of second regions, wherein: The plurality of inclined transition surfaces are inclined such that the height of the first main surface decreases with increasing distance from the boundaries of the plurality of first regions, at least some of the plurality of inclined transition surfaces extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between some of the plurality of first regions and the plurality of second regions connected by the inclined transition surfaces, wherein the lateral distance extending through the inclined transition surfaces is measured in a direction parallel to a surface normal of the inclined transition surfaces and parallel to the imaginary base plane, and The scattering region includes a radial PSD, and the radial PSD includes: a first range of scattering angles, wherein the radial PSD increases with increasing scattering angle of the light relative to the specular direction, Peak scattering angle θ 峰值 , wherein the radial PSD includes a peak, and The range of the second scattering angle is greater than θ 峰值 , where at the first scattering angle that is greater than or equal to 2° and less than or equal to 15° relative to the mirror surface direction, the radial PSD is reduced to 10% of the peak value.

30. The article of claim 29, wherein within the first range of scattering angles, at scattering angles greater than or equal to 0.05°, the radial PSD is less than 10% of the peak value.

31. The article according to any one of claims 29 to 30, wherein θ 峰值 is greater than or equal to 0.3 and less than or equal to 0.5°.

32. The article according to any one of claims 29 to 31, in: Relative to the mirror direction, the first scattering angle is greater than or equal to 6° and less than or equal to 13°, and Within the second scattering angle range, at the second scattering angle greater than or equal to 12.5° and less than or equal to 30.0° relative to the specular direction, the radial PSD decreases to 1% of the peak value.

33. The article according to any one of claims 29 to 31, in: Relative to the mirror direction, the first scattering angle is greater than or equal to 2° and less than or equal to 7°, and Within the second scattering angle range, at the second scattering angle greater than or equal to 3.5° and less than or equal to 13.5° relative to the specular direction, the radial PSD decreases to 1% of the peak value.

34. The article of claim 33, wherein within the second scattering angle range, at a third scattering angle less than or equal to 8° relative to the specular direction, the radial PSD decreases to a value of 0.1% of the peak value.

35. The article of claim 34, wherein within the second scattering angle range, at a third scattering angle less than or equal to 16° relative to the specular direction, the radial PSD decreases to a value of 0.01% of the peak value.

36. The article of any one of claims 29 to 35, wherein the article exhibits: Transmission haze, less than or equal to 2.0%, and Flicker is less than or equal to 2.5% when measured at 140ppi.

37. The article according to any one of claims 29 to 36, wherein: the first average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, and viewing the article at a 0° viewing angle and with light having a luminance of 45000 lux incident on the first major surface at an incident angle of 20°, the first average modulation transfer function is at least 0.07, and the second average modulation transfer function of the article, averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm, and viewing the article at a 20° viewing angle and with light having a luminance of 45000 lux incident on the first major surface at an incident angle of 45°, the second average modulation transfer function is at least 0.

6.

38. The article according to claim 29, wherein: within the scattering region, the first major surface includes: a plurality of third regions disposed at a third height relative to the imaginary base plane, and a plurality of fourth regions disposed at a fourth height relative to the imaginary base plane, and the fourth height is different from the first height, the second height, and the third height.

39. The article according to claim 38, wherein the article exhibits: a specular reflectance (Rs) less than or equal to 4.0, and an image coupling clarity of less than 65%.

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