Optical film for reducing sparkle and display including same

Abstract

An optical film includes a major surface including a plurality of irregularly arranged domains. For a substantially normally incident light beam, an intensity distribution of light transmitted by the optical film as a function of scattering angle measured from a normal to the optical film includes first and second scattering peaks and a valley disposed therebetween. The first scattering peak is located at a first scattering angle less than about 2 degrees and the valley is located at a second scattering angle greater than the first scattering angle and less than about 6 degrees. An integral over scattering angle of the intensity distribution from the first scattering angle to the second scattering angle is I1. An integral over scattering angle of the intensity distribution from the second scattering angle to a third scattering angle in a range of about 10 to 12 degrees is I2. I2 / I1 ≥ 0.4.

Description

[0001] OPTICAL FILM FOR REDUCING SPARKLE AND DISPLAY INCLUDING SAME

[0002] Background

[0003] Sparkle in a display is an undesired optical effect that may be described as a grainy pattern that appears to flicker with small changes in position of a viewer relative to the display.

[0004] Summary

[0005] The present disclosure generally relates to optical films and to displays that include an optical film for reducing sparkle. The optical film can include a plurality of structures forming a plurality of domains. The structures may be formed using a microparticle self-assembly process, according to some embodiments.

[0006] In some aspects, the present description provides an optical film including a first optical layer including a structured first major surface including a plurality of irregularly arranged and substantially tightly packed domains. Each of the domains includes a plurality of substantially regularly arranged structures. Each of the structures can have an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers. For a substantially normally incident substantially Gaussian light beam having a beam waist diameter of 0.9 to 1.3 degrees and a wavelength of about 532 nm, an azimuthally averaged intensity distribution of light transmitted through the optical film as a function of scattering angle measured from a normal to the optical film includes first and second scattering bands having respective first and second scattering peaks and a valley disposed therebetween. The first and second scattering peaks have corresponding first and second peak intensities Ipl and Ip2 and the valley has a corresponding valley intensity Ivl. The first scattering peak is located at a first scattering angle less than about 2 degrees and the valley is located at a second scattering angle greater than the first scattering angle and less than about 6 degrees. An integral over scattering angle of the azimuthally averaged intensity distribution from the first scattering angle to the second scattering angle is II. An integral over scattering angle of the azimuthally averaged intensity distribution from the second scattering angle to a third scattering angle in a range of about 10 to 12 degrees is 12. Ip2 / Ivl < 10 and 12 / 11 > 0.4.

[0007] In some aspects, the present description provides an optical film including a first optical layer including a structured first major surface including a plurality of irregularly arranged and substantially tightly packed domains. Each of the domains includes a plurality of substantially regularly arranged structures. Each of the structures can have an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers. For a substantially normally incident substantially Gaussian light beam having a beam waist diameter of 0.9 to 1.3 degrees and a wavelength of about 532 nm, an azimuthally averaged intensity distribution of light transmitted by the optical film as a function of scattering angle measured from a normal to the optical film includes first through fourth scattering bands having respective first through fourth scattering peaks having respective peak intensities Ipl, Ip2, Ip3, and Ip4 located at increasing respective first through fourth scattering angles al, a2, a3, and a4. The first scattering angle al is less than about 2 degrees from a normal to the optical film. Each of (a3-a2) / (a2-al) and (a4-a3) / (a2-al) is in a range of about 0.7 to about 1.1. A valley between the first and second peaks is located at a first valley scattering angle greater than the first scattering angle and less than about 6 degrees. An integral over scattering angle of the azimuthally averaged intensity distribution from the first scattering angle to the first valley scattering angle is II. An integral over scattering angle of the azimuthally averaged intensity distribution from the first valley scattering angle to a scattering angle in a range of about 10 to 12 degrees is 12. 12 / 11 > 0.4.

[0008] In some aspects, the present description provides an optical film including a first optical layer including a structured first major surface including a plurality of irregularly arranged and substantially tightly packed domains. Each of the domains includes a plurality of substantially regularly arranged structures. Each of the structures can have an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers. For a substantially normally incident substantially Gaussian light beam having a beam waist diameter of about 0.9 to 1.3 degrees and a wavelength of about 532 nm, a scattering distribution function of the optical film along at least a first scattering direction in a first plane substantially perpendicular to the optical film includes first through third scattering bands having respective first through third scattering peaks having respective first through third peak intensities Ip 1, Ip2, and Ip3 located at increasing respective first through third scattering angles. The first scattering angle can be less than about 2 degrees from a normal to the optical film. Ip 1 / Ip2 < 100 and Ip2 / Ip3 < 2.3.

[0009] These and other aspects will be apparent from the following detailed description. In no event, however, should this brief summary be construed to limit the claimable subject matter.

[0010] Brief Description of the Drawings

[0011] FIGS. 1-2 are schematic top views of portions of optical films, according to some embodiments.

[0012] FIGS. 3A-3D are schematic cross-sectional views of portions of optical films, according to some embodiments.

[0013] FIG. 4 is a schematic cross-sectional view of a portion of an optical film including layers of particles, according to some embodiments.

[0014] FIGS. 5A-5C are schematic cross-sectional views of portions of optical films including a layer disposed on a structured surface, according to some embodiments.

[0015] FIG. 6 is a schematic cross-sectional view of an optical film, light substantially normally incident on the film, and light transmitted by the optical film, according to some embodiments.

[0016] FIG. 7 is a schematic geometry for the measurement of scattering profile and a schematic conoscopic plot of a scattering distribution function, according to some embodiments.

[0017] FIG. 8 is a schematic plot representing an azimuthally averaged intensity distribution as a function of scattering angle or a scattering distribution function as a function of scattering angle, according to some embodiments. FIG. 9 is a schematic plot of a peak intensity versus azimuthal angle at a specific scattering angle, according to some embodiments.

[0018] FIG. 10 is schematic cross-sectional view of a display that includes an optical film, according to some embodiments.

[0019] FIG. 11 is a schematic top view of a display panel having a pixelated display surface, according to some embodiments.

[0020] FIG. 12 is an optical microscope image of an exemplary optical film.

[0021] FIG. 13 is a plot of sparkle of displays including an optical film that includes a second optical layer (backfill) disposed on a first optical layer as a function of the refractive index (RI) of the second optical layer, according to some embodiments.

[0022] FIG. 14 is a plot of a distinctiveness of image (DOI), which is related to modulation transfer function (MTF), for displays including an optical film that includes a second optical layer (backfill) disposed on a first optical layer as a function of the refractive index (RI) of the second optical layer, according to some embodiments.

[0023] FIG. 15 is a box plot of sparkle for various displays, according to some embodiments.

[0024] FIG. 16 is a box plot of DOI for the displays of FIG. 15.

[0025] FIG. 17 is a plot of normalized azimuthally averaged intensity distributions of light transmitted by optical films, according to some embodiments.

[0026] Detailed Description

[0027] In the following description, reference is made to the accompanying drawings that form a part hereof and in which various embodiments are shown by way of illustration. The drawings are not necessarily to scale. It is to be understood that other embodiments are contemplated and may be made without departing from the scope or spirit of the present description. The following detailed description, therefore, is not to be taken in a limiting sense.

[0028] Sparkle in a display is an undesired optical effect that may be described as a grainy pattern that appears to flicker with small changes in position of a viewer relative to the display. Sparkle can be caused by light from pixels in the display interacting with non-uniformity on a surface of a display above the pixels, leading to non-uniform optical paths. Light from a pixel may appear to move around or flicker as the viewer moves due to the interaction of the pixel light with the surface non-uniformity. Sparkle is described in U.S. Pat. No. 10,353,214 (Sitter et al.), for example.

[0029] According to some embodiments of the present description, an optical film is provided that is suitable for reducing sparkle. In some embodiments, the optical film is made from the self-assembly of particles (e.g., microparticles having an average diameter in a range of about 4 to about 15 micrometers). Self-assembly of the particles can result in a plurality of substantially coplanar structured domains where each structured domain includes a substantially regular array of structures. The structures can be formed by the particles, or the self-assembled particles can be used to make a tool which is used to form the structures (e.g., in a cast and cure process). It has been found that such structured domains can result in desired scattering properties of the optical film, according to some embodiments, which may be characterized by peaks and valleys in a scattering distribution function of the optical film. In some embodiments, the optical film is incorporated into a display in order to reduce sparkle of the display. Related optical films have been used for color correction in organic light emitted diode displays as described in Int. Pat. Appl. Pub. No. WO 2021 / 240268 (Menke et al.), for example. However, optical films useful for color correction generally provides scattering in desired ranges of scattering angles that is too weak for sparkle reduction (e.g., too weak for relatively small scattering angles such as from about 1.5 to 6 degrees) or results in substantially reduced effective resolution (e.g., as quantified by modulation transfer function (MTF) or distinctness of image (DOI) as described further elsewhere herein) when positioned in a display at an appropriate location for sparkle reduction. The reduction in effective resolution may result from the scattering intensity dropping too slowly between a relatively small scattering angle (e.g., about 4 degrees) and a relatively large scattering angle (e.g., about 20 degrees). It has been found, according to some embodiments, that the scattering strength at desired scattering angles can be adjusted to suitable levels for sparkle reduction by adjusting (e.g., increasing) a peak to valley height (e.g., the height h in FIGS. 3A-3C, which can be adjusted (e.g., increased) by adjusting (e.g., increasing) the particle diameter d and / or the ratio h / d) of the structures, and / or adjusting (e g., increasing) a difference in refractive index between the structures and a backfill material over the structures. The layer including the structures (e.g., formed from particles) may be referred to as a first optical layer and the layer of backfill material may be referred to as a second optical layer. Suitable optical films for sparkle reduction may be characterized, according to some embodiments, by one or more of: a ratio of integrals over scattering angle ranges described further elsewhere herein of an intensity distribution transmitted by the optical film; and / or a slow fall off in successive peak intensities of the first few peaks of a scattering distribution function of the optical film and / or a substantial fall off in the scattering distribution function between about 4 degrees and about 20 degrees, for example. The optical film, according to some embodiments, can reduce sparkle of the display without substantially reducing an effective resolution of the display and without generating significant rainbow mura. In comparison, conventional optical films that include a periodic diffraction grating for reducing sparkle typically also produce significant undesired rainbow mura. Such diffractive films are also often sensitive to moire while optical films according to some embodiments of the present description do not exhibit moire

[0030] FIG. 1 is a schematic top view of an illustrative portion of an optical film 100, according to some embodiments. The optical film 100 includes a plurality of structures 112 that can form a plurality of substantially coplanar structured domains 110. Substantially coplanar domains can be coplanar or approximately coplanar but with some minor variation about, or displacements from, a plane such as those that would be expected from ordinary manufacturing variations, for example. Each structured domain includes a substantially regular array of structures 112 arranged along orthogonal first and second directions (e.g., x- and y-directions). The first and second directions are typically in-plane directions orthogonal to a thickness direction (e.g., z-direction) of the optical film 100. A substantially regular array or substantially regular arrangement can be a regular array or arrangement or an array or arrangement that is approximately regular but with some minor displacements of structures from nominal positions such as those that would be expected from ordinary manufacturing variations, for example. Similarly, a substantially periodic arrangement can be a periodic arrangement or an arrangement that is approximately periodic but with some minor displacements of structures from nominal positions such as those that would be expected from ordinary manufacturing variations, for example.

[0031] In some embodiments, the arrays of adjacent domains have different orientations. The substantially regular array of structures 112 can be characterized as including structures 112 substantially repeating along first and second basis vectors 121 and 122 (which are along differing first and second directions). The basis vectors 121, 122 are not colinear so that the basis vectors can define a two- dimensional array. The basis vectors for different domains 110 can be different. Domains 110a-l lOd are schematically illustrated in FIG. 1 and the basis vectors 121, 122 are shown for domains 110b and 1 lOd. The basis vector 121 of domain 110b is not parallel to either the basis vector 121 or the basis vector 122 of domain 1 lOd. In some embodiments, for each domain, the plurality of substantially regularly arranged structures are substantially periodically arranged along each of different (not parallel) in-plane first and second directions 121 and 122, where the first and second directions 121 and 122 change irregularly from domain to domain. In some embodiments, for each domain, the in-plane first and second directions define an angle in a range of about 30 to 90 degrees therebetween. In some embodiments, the angle between the first and second directions 121 and 122 remain substantially constant from domain to domain as the first and second directions 121 and 122 change irregularly from domain to domain. For example, the angle for each of the domains can be about equal to a same angle which may be about 60 degrees, for example. Inplane directions refer to directions in the plane (xy-plane) of the first optical layer or the optical film 100. For example, the optical film 100 can extend primarily along orthogonal width and length directions which define the plane of the optical film 100.

[0032] In some embodiments, the optical film includes a plurality of particles 114 that define the substantially regular array of structures 112. In other embodiments, a layer including a plurality of particles arranged in domains that include substantially regular arrays of the particles is used as a tool to form structures on a substrate. For example, the layer including the plurality of particles can be used at a tool in a cast and cure process where a curable (e g., ultraviolet (UV) curable) resin is cast against the structured surface of the tool and cured. In some cases, the layer including the plurality of particles is used as a first tool to make a second tool in a cast and cure process, and then the second tool is used to make an optical film in a cast and cure process, for example.

[0033] In some embodiments, the particles 114 are disposed substantially in a monolayer of the particles. The particles 114 can be considered substantially in a monolayer even when a small number of the particles are missing from a full monolayer or a small number of the particles are stacked on other particles. In some embodiments, for each domain 110 in greater than 50, 60, 70, 80, 90, or 95 percent of the domains, the particles 114 in the domain are disposed substantially in a monolayer of the particles.

[0034] In some embodiments, the particles 114 form less than a full monolayer. This may be referred to as a sub-monolayer. In some embodiments, the structures 112 and / or particles 114 define lake regions 116 between structured domains 110 that are free or substantially free of structures 112 and / or particles 114. For example, in some embodiments, the plurality of particles 114 defines lake regions 116 between structured domains 110 where each lake region 116 is free of the particles 114. In some embodiments, the particles 114 include a two-dimensional array of particles 114 and further include additional particles disposed on the two-dimensional array of particles 114. For example, a particle 118 disposed on two- dimensional array of particles 114 in domain 110c in the embodiment schematically illustrated in FIG. 1. A layer of particles including particles in addition to particles of a full monolayer may be referred to as a supra-monolayer. In some embodiments, the particles 114 of each domain 110 are arranged to form a regular two-dimensional first array of the particles 114. In some embodiments, for each domain in a subplurality (at least two but less than all) of the domains 110 (e.g., domains 110c and 1 lOd), the plurality of particles 114 further include at least one particle 118 disposed on the particles arranged in the regular two-dimensional first array. In some embodiments, for each domain 110, the plurality of particles 114 further includes at least one particle 118 disposed on the particles arranged in the regular two- dimensional first array (e.g., each domain can appear as domain 110c or 1 lOd, or each domain can appear as in FIG. 4). In some embodiments, for at least one of the domains (e.g., for each domain in a subplurality of the domains 110), the plurality of particles 114 further includes particles arranged in a regular two-dimensional second array disposed on the first array (see, e.g., FIG. 4).

[0035] In some embodiments, including the optical film in a display reduces the sparkle of the display but may also reduce the modulation transfer function (MTF) of the display. The preferred particle concentration (e g., from sub-monolayer to supra-monolayer) can depend on a desired balance between maximizing the reduction in sparkle and minimizing the reduction in MTF. The preferred particle concentration may also depend on whether or not a backfill layer (e.g., layer 150 depicted in FIGS. 5A- 5C) is included and on the refractive index of the backfill layer. Typically, particles substantially disposed in a monolayer is preferred with a backfill layer included that provides an index contrast between the backfill layer and the particles of at least about 0. 1.

[0036] The structures 112 have an average largest lateral dimension SI. The average is the unweighted mean of largest lateral dimension (e.g, diameter) of each structure 112. In embodiments where the structures are defined by particles, the largest lateral dimension of the structure may be approximately equal to the diameter of the particle or to an average pitch of the particles in a domain. The average diameter of the particle may be denoted by d (see, e.g., FIG. 3 A). The plurality of domains 110 have an average spacing S2 therebetween. In some embodiments, S2 / S1 > 0.5. In some embodiments, S2 / S1 is at least about 0.6, 0.7, 0.8, 0.9 or 1. In some embodiments, S2 / S1 is no more than about 4, 3, 2, 1.5, or 1.2. FIG. 2 is a schematic top view of an illustrative portion of optical film 100 according to some embodiments. The structured domains 110 have orthogonal lateral dimensions dl and d2 and have an average spacing S2 therebetween. The structures of the structured domains 110 are not explicitly shown in the schematic illustration of FIG. 2. In some embodiments, each structured domain in at least a majority of the structured domains has orthogonal first and second lateral dimensions dl and d2 where at least one of dl and d2 is greater than about 4, or greater than about 5, or greater than about 6 times an average largest lateral dimension SI of the structures 112. In some embodiments, each structured domain in at least a majority of the structured domains has orthogonal first and second lateral dimensions dl and d2 where each of dl and d2 is greater than about 4, or greater than about 5, or greater than about 6 times an average largest lateral dimension S 1 of the structures. In some embodiments, the at least a majority of the structured domains includes at least about 60%, or at least about 70%, or at least about 80% of the structured domains.

[0037] FIGS. 3A-3D are schematic cross-sectional views of illustrative portions (e.g., each portion corresponding to a structured domain or a portion of a structured domain) of optical films 200a to 200d, respectively. The optical films 200a to 200d may correspond to optical film 100, for example. In the illustrated embodiments, the optical films 200a-200d include particles 114 dispersed in a binder 140 (e.g., a polymeric binder). A first optical layer 141, which may alternatively, or in addition, be referred to as a structured layer, including the particles 114 in the binder 140 is disposed on a substrate 130. Substrate 130 can be a polymeric substrate (e.g., polyethylene terephthalate (PET) or cyclo olefin polymer (COP)), for example. In some embodiments, the substrate 130 is non-birefringent (e.g., having a birefringence of less than about 0.05 and / or a retardance for substantially normally incident light of less than about 10 nm for at least one wavelength in a range of about 400 nm to about 700 nm). In some embodiments, the optical film is substantially non-birefringent (e g., a retardance for substantially normally incident light of less than about 10 nm for at least one wavelength in a range of about 400 nm to about 700 nm). In some embodiments, the first optical layer 141 is disposed on a substrate 130, where the substrate 130 has a birefringence of less than about 0.05, 0.04, 0.03, 0.02, or 0.01 for at least one wavelength in a range of about 400 nm to about 700 nm. First optical layer 141 can alternatively be formed from a tool including particles in a binder as described further elsewhere herein. The particles 114 have an average diameter d, an average pitch p, and an average spacing g between adjacent particles. The particles 114 define structures 112 in a structured major surface 212 having have an average peak-to-valley height h. Here, the valley can be defined as the lowest point between three adjacent particles when the particles are arranged in an approximately triangular lattice, for example. The average peak-to-valley height h should be understood to be the mean over the domains 110 of the peak-to-valley height. In some embodiments, the binder 140 coats the top surface of the particles to athickness e. In some embodiments, the binder does not coat the top surface of the particles so the thickness e can be zero. The quantities d, p, g, and e are schematically shown as approximately equal in the different embodiments of FIGS. 3A-3D, but it will be understood that these quantities can depend on material and processing parameters. The first optical layer 141 has a structured first major surface 212 including a plurality of irregularly arranged and substantially tightly packed domains (e.g., 110a- 1 lOd), where each of the domains includes a plurality of substantially regularly arranged structures (e.g., structures 112 defined by particles 114). The domains can be described as substantially tightly packed when adjacent domains are spaced apart by gaps (e.g., defining the average spacing S2) substantially smaller (e.g., by at least a factor of 2, 3, 5, 10, or 20) than an average largest lateral dimension of the adjacent domains.

[0038] The particles 114 can be coated onto substrate 130 in a mixture including monomers and solvent. The solvent can be evaporated and the monomers cured to form the binder 140. As the solvent is removed, the particles 114 can self-assemble into ordered domains. The self-assembly may be driven by capillary action. Useful methods for processing particles, monomers and solvent are described in U.S. Pat. Appl. Pub. No. 2015 / 0011668 (Kolb, et al.), for example.

[0039] The average peak-to-valley height h can be controlled by selecting the ratio (e.g., by volume or by weight) of monomer to particles. This ratio is generally decreasing from FIG. 3A to FIG. 3D. When a low ratio of monomer to particles is utilized, voids 142 may be formed near the substrate 130 between adjacent particles 114 as schematically illustrated in FIG. 3D. In some embodiments, a ratio of particles to binder by weight is in a range of about 0.3 to about 3, or about 0.4 to about 2.8, or about 0.5 to about 2.5, for example. In some embodiments, the average peak-to-valley height h is no more than about half the average largest lateral dimension (e.g., SI illustrated in FIG. 1 which may be about equal to the pitch p in FIGS. 3A-3D) of the structures 112. In some embodiments, the average peak-to-valley height h is no more than about 0.4 times the average largest lateral dimension of the structures 112. In some embodiments, the average peak-to-valley height h is in a range of about 0.2 to about 0.4 times the average largest lateral dimension of the structures 112. In some embodiments, the average peak-to-valley height h is at least about half the average largest lateral dimension. In some embodiments, the average peak-to- valley height h is in a range of about 0.4 to about 0.6, or about 0.5 to about 0.6 times the average largest lateral dimension of the structures 112. In some embodiments, the average peak-to-valley height h is about half the average largest lateral dimension. The desired average peak-to-valley height h can depend on the refractive index contrast across structured major surface 212. A higher refractive index contrast can be used with a lower height h or a lower refractive index contrast can be used with a higher height h, for example.

[0040] In some embodiments, the binder substantially covers an entire surface of each particle in at least a majority of the particles 114. In other embodiments, the binder 140 may not wet the surface of the particles 114 and may leave a significant portion of the surface of the particles 114 exposed.

[0041] In some embodiments, the particles 114 have an average diameter d in a range of about 2 micrometers to about 15 micrometers, or about 3 micrometers to about 15 micrometers, or about 4 micrometers to about 15 micrometers, or about 5 to about 15 micrometers, or about 4 micrometers to about 12 micrometers, or about 5 micrometers to about 12 micrometers, or about 5 micrometers to about 11 micrometers, or about 6 micrometers to about 10 micrometers, or about 7 micrometers to about 9 micrometers. In some embodiments, the particles 114 are substantially spherical. The structures 112 can have an average in-plane diameter in any of these ranges (e.g., in some embodiments, each of the structures 112 has an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, or from about 5 micrometers to about 12 micrometers). The average in-plane diameter is the mean of the diameter (largest dimension) over directions in the plane (xy-plane) of the optical film. A particle can be considered substantially spherical if its outline fits within the intervening space between two, concentric, truly spherical outlines differing in diameter from one another by up to about 30% of the diameter of the larger of these outlines. In some embodiments, each particle in at least a majority of the particles fits within the intervening space between two, concentric, truly spherical outlines differing in diameter from one another by up to about 20% or 10% of the diameter of the larger of these outlines. In the case of a non-spherical particle, the diameter of the particle can be understood to be the diameter of a sphere having the same volume as the particle. The average diameter d can be the mean or median particle diameter. For example, the average diameter can be the Dv50 size (median size in a volume distribution or, equivalently, particle size where 50 percent of the total volume of the particles is provided by particles having a size no more than the Dv50 size). In some embodiments, the plurality of particles has a substantially monodispersed particle size distribution (e.g., in some embodiments, at least 80% of the particles can have a diameter within 20% of the average diameter or at least 90% of the particles can have a diameter within 10% of the average diameter).

[0042] FIG. 4 is a schematic cross-sectional view of an illustrative portion (e.g., a portion corresponding to a structured domain or a portion of a structured domain) of an optical film 300. The optical film 300 can correspond to optical film 100, for example, except that the plurality of particles 114 includes particles 117, which can be disposed in a regular two-dimensional first array 111, and includes particles 118 disposed on the particles 117 where the particles 118 can be arranged in a regular two-dimensional second array 113. In some embodiments, the optical film includes a plurality of particles 114 defining the plurality of structures 112. In some embodiments, for each domain 110, the plurality of particles 114 includes particles 117 arranged to form a regular two-dimensional first array 111 of the particles. In some embodiments, for at least one of the domains, the plurality of particles 114 further includes particles 118 arranged in a regular two-dimensional second array 113 disposed on the first array 111. In some embodiments, the plurality of particles 114 is disposed substantially in a monolayer of the particles. In some embodiments, the plurality of particles 114 defines lake regions between adjacent domains, where each lake region 116 is free of the particles. In some embodiments, each structured domain in at least a majority of the structured domains has orthogonal first and second lateral dimensions each greater than about 4, 5 or 6 times an average largest lateral dimension of the structures. The first and second lateral dimensions can be up to about 500, 400, 300, 200, 100, 75, or 50 times the average largest lateral dimension of the structures, for examples.

[0043] In any of the optical films described herein, a layer (e.g., a planarizing backfill layer) may be disposed over the structures 112. FIGS. 5A-5C are schematic cross-sectional views of illustrative portions (e.g., each portion corresponding to a structured domain or a portion of a structured domain) of optical films 400a to 400c, respectively. The optical films 400a-400c include a plurality of structures 112 defining a structured major surface 212 and includes a layer (second optical layer) 150 disposed on the structured major surface 212. The layer 150 may be a polymeric layer and may be described as a backfill layer. In some embodiments, the layer 150 has a first major surface 151 facing and substantially conforming (e.g., nominally conforming or conforming up to variations small compared to the particle diameter or structure size) to the structured major surface 212 and has an opposite second major surface 152. The second major surface 152 may be substantially planar and / or unstructured as schematically illustrated in FIG. 5A, or may be structured as schematically illustrated in FIG. 5C, or may be substantially planar with some minor surface structure as schematically illustrated in FIG. 5B. In some embodiments, the layer 150 substantially planarizes the structured major surface 212 by providing a substantially planar surface 152 (e.g., nominally planar or planar up to variations small compared to the particle diameter or structure size). In some embodiments, the particles 114 form the structures 112. In other embodiments, self-assembled particles are used to make a tool which is used to make a structured layer (directly or after making an intermediate tool from the tool including the particles) and the particles 114 are omitted from any of the optical films 400a to 400c. In some embodiments, the optical film 400a-400c includes a first optical layer 141 including a plurality of structures 112 forming a plurality of substantially coplanar structured domains defining a structured major surface 212 of the first optical layer 141. In some embodiments, the optical film 400a-400c includes a second optical layer 150 disposed on the structured major surface 212. In some embodiments, the optical film 400a, 400b includes a polymeric layer 150 disposed on and substantially planarizing the structured major surface 212.

[0044] In some embodiments, an average thickness tb (see, e.g., FIG. 5A) of the second optical layer 150 be sufficiently large that the second major surface 152 is substantially planar. In some embodiments, the average thickness tb is at least 0.005, 0.01, 0.02, 0.04, 0.08, 0.1, 0.2, 0.3, or 0.4 times the average diameter d. The average thickness of the second optical layer 150 can be up to 10, 5, 4, 3, or 2 times the average diameter d, for example. Typically, when the average thickness tb of second optical layer 150 is sufficiently large compared to the average diameter d (see, e.g., FIG. 5 A), the sparkle reduction does not vary substantially with varying tb. However, for thinner second optical layers 150 (see, e.g., FIGS. 5B- 5C), the average thickness tb can be adjusted to adjust optical performance of the optical film since the resulting surface structure of second major surface 152 can affect the optical performance.

[0045] In some embodiments, the binder 140 is substantially index matched to the particles 114, whether or not the layer 150 is present. In some embodiments, the binder 140 has a refractive index nl, and the particles 114 have a refractive index np, where |np-nl| < 0.02. In some embodiments, |np-nl| is less than about 0.015, or less than about 0.01. In other embodiments, |np-nl| > 0.02, 0.025, 0.03, 0.035, or 0.04. |np-nl| can be up to about 0.07, 0.06, 0.055, 0.05, 0.045, or 0.04, for example. In some embodiments, the layer 150 has a refractive index n2, where |n2-np| > 0.08. In some embodiments, |n2-np| is greater than about 0.08, or greater than about 0.1, or greater than about 0.12, or greater than about 0.13, or greater than about 0.14, or greater than about 0.15. |n2-np| can be up to about 0.3, 0.27, 0.25, 0 23, 0.22, 0.21, or 0.2, for example. Refractive indices may be specified for at least one wavelength (e.g., 500 nm, 532 nm, 550 nm, or 633 nm) in a range of about 400 nm to about 700 nm. If no wavelength is otherwise indicated, refractive indices can be understood to be determined at 532 nm. In some embodiments, the (e.g., polymeric) layer 150 includes inorganic nanoparticles (e.g., zirconia nanoparticles) to increase the refractive index of the layer. A polymeric layer generally has a continuous organic polymer phase and can optionally include additives such as inorganic nanoparticles dispersed in the continuous polymer phase.

[0046] In some embodiments, the optical film 400a-400c further includes a second optical layer 150 having opposing first and second major surfaces 151 and 152, where the first major surface 151 of the second optical layer 150 is disposed on, and substantially conforms to, the structured first major surface 212 of the first optical layer 141. In some embodiments, the second optical layer 150 includes one or more of a polymer and an inorganic material. The second optical layer 150 can be a polymeric layer (i.e., a layer having a continuous phase of organic polymer), for example. The second optical layer 150 can have an index of refraction substantially different (e.g., different by at least about 0.03 or 0.05 for at least one visible wavelength) from an index of refraction of the first optical layer 141. In some embodiments, for at least one wavelength in a range of about 400 nm to about 700 nm, the index of refraction of the second optical layer 150 is greater than the index of refraction of the first optical layer 141 by at least about 0.03, 0.05, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, or 0.15. The difference can be up to about 0.3, 0.25, 0.22, 0.21, or 0.2, for example. In some embodiments, the first optical layer 141 includes beads 114 disposed in a binder 140, where the beads 114 defines the substantially regularly arranged structures 112 and comprises the index of refraction of the first optical layer 141 (i.e., the beads can have the index of refraction of the first optical layer that is substantially different from that of the second optical layer). In some embodiments, for at least one wavelength in a range of about 400 nm to about 700 nm, an absolute value of a difference between the index of refraction of the second optical layer 150 and an index of refraction of the beads is at least about 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, or 0.15, and, in some embodiments, an absolute value of a difference between an index of refraction of the binder and the index of refraction of the beads is in a range of about 0.02, 0.025, 0.03, 0.035, or 0.04 to about 0.07, 0.06, 0.05, 0.045, or 0.04. For example, in some embodiments, for at least one wavelength in a range of about 400 nm to about 700 nm, an absolute value of a difference between the index of refraction of the second optical layer 150 and an index of refraction of the beads is at least about 0.1, and an absolute value of a difference between an index of refraction of the binder and the index of refraction of the beads is in a range of about 0.025 to about 0.06. In some embodiments, an absolute value of a difference between the indices of refraction of the first and second optical layers 141 and 150 times an average height h of the structures is in a range of about 0.2, 0.3, 0.4, 0.5, or 0.6 micrometers to about 1.2 micrometers. The absolute value of the difference between the indices of refraction of the first and second optical layers 141 and 150 times the average height h can be up to about 1.1, 1, 0.9, 0.8, 0.7, or 0.6 micrometers, for example. The difference between the indices of refraction of the first and second optical layers 141 and 150 can be the difference between the index of refraction of the particles 114 and the index of refraction of the backfill material of the second optical layer 150. In some embodiments, the second optical layer 150 substantially planarizes the structured first major surface 212. It has been found, according to some embodiments, that a small non-zero difference (e.g., between 0.02 and 0.07) in refractive index between the particles and binder can result in improved sparkle reduction performance of the optical film.

[0047] FIG. 6 is a schematic cross-sectional view of an illustrative optical film 500, substantially normally incident (e.g., nominally normally incident or within 20 degrees, or 15 degrees, or 10 degrees, or 5 degrees to a normal to a major surface of the film or to the x-y plane when the film extends generally along orthogonal x- and y-directions) light 333 which can have a wavelength , in a wavelength range of XI to X2, and transmitted light 334, according to some embodiments. The light 333 can be in a visible wavelength range (i.e., the wavelength(s) of the light 333 can be in a visible wavelength range). Visible wavelength ranges can be understood to be any range between about 380 nm and about 720 nm. For example, the wavelength range of XI to X2 can be a visible wavelength range from about 380 nm to about 720 nm, or from about 400 nm to about 700 nm, or can be a narrower range (e.g., having a width of less than about 40 nm or less than about 20 nm) about a specified wavelength (e.g., 532 nm). In some embodiments, the visible wavelength range is a green wavelength range (e.g., about 500 nm to about 580 nm or about 520 nm to about 560 nm). For example, XI can be about 500 nm and X2 can be about 560 nm. In some embodiments, the substantially normally incident light 333 has a wavelength X of about 532 nm. For example, the light 333 can be substantially monochromatic (e.g., having an intensity versus wavelength having a peak intensity at a peak wavelength and a FWHM of less than 2% of the peak wavelength) light having a wavelength (e.g., the peak wavelength) of about 532 nm. In some embodiments, light 333 is a substantially Gaussian light beam. A substantially Gaussian light beam is a light beam having an intensity distribution (e.g., intensity versus position or angle) that can reasonably accurately be described as having a Gaussian shape. For example, laser light beams are often substantially Gaussian light beams. The light beam can have a beam waist diameter which is conventionally defined as diameter where the beam intensity is e"2(about 0.135) times a peak intensity of the beam. The beam waist diameter can be expressed as twice a beam waist radius which can be expressed as an angle measured from an axis of the beam where the beam intensity is c2times the peak intensity of the beam. For example, the beam waist diameter can be twice the angle BW / 2 depicted in FIG. 17. The beam waist diameter can be determined using the same test instrument (e.g., imaging sphere) used to determine the scattering distribution function by removing the optical film from the test instrument. In some embodiments, light 333 is a substantially normally incident substantially Gaussian light beam having a beam waist diameter of 0.9 to 1.3 degrees, or 0.95 to 1.2 degrees, or 0.98 to 1.15 degrees, or 1 to 1. 12 degrees, or about 1.06 degrees, and a wavelength of about 532 nm. For example, light 333 can be from a 532 nm laser. Optical fdm 500 can be any optical film described herein. For example, optical film 500 can include self-assembled particles forming a structured surface or can include a structured surface formed from a tool made using self-assembled particles. At least a portion of the incident light 333 is transmitted as a transmitted light 334.

[0048] A scattering distribution function describes the relative intensity of scattered incident light and is generally a function of a scattering angle 9 and an azimuthal angle cp defining the direction of the scattered light. Scattering angles should be understood to be non-negative unless indicated differently. The scattering distribution function can be defined as the bidirectional scattering distribution function (BSDF) for substantially normally incident light 333 and for transmitted light 334 (also referred to as the bidirectional transmittance distribution function or BTDF). An example of measuring the scattering distribution function is schematically depicted in FIG. 7. The azimuthally averaged intensity distribution function can be determined by averaging the scattering distribution function over all azimuthal angles ip. The substantially normally incident light 333 can be a substantially Gaussian light beam having a beam waist diameter in a range described elsewhere herein. It is typically desired to specify a range of the beam waist diameter since the scattering distribution function generally depends on this diameter.

[0049] FIG. 7 is a schematic geometry for the measurement of scattering profde and a schematic conoscopic plot of an illustrative scattering distribution function 450, according to some embodiments. The scattering distribution function along a scattering direction defined by azimuthal angle cp is the scattering distribution function along a radial direction (a direction of changing 0 for fixed <p) in a conoscopic plot. A scattering direction 444 is schematically illustrated. The conoscopic plot is shown in a detector plane 452 (x'y’-plane referring to the illustrated x'y’z’ coordinate system). The scattering angle 0 may be referred to as a polar angle (angle between the direction of scattered light 334 and z’ direction which can be a direction normal to the optical film) and the azimuthal angle ip is an angle between the direction 444 (direction defined by projection of the direction of scattered light 334 onto the detector plane 452) and the x' direction. The z' direction in FIG.7 can correspond to the negative z-direction in FIG. 6 and other figures. In some embodiments, the scattering distribution function is substantially azimuthally symmetric (substantially independent of the azimuthal angle <p) . For example, the scattering distribution function 450 is substantially azimuthally symmetric in the embodiment schematically illustrated in FIG. 7. The degree of azimuthal non-uniformity can be characterized by the azimuthal nonuniformity parameter ANU defined by taking the standard deviation divided by the mean of the scattering distribution function over the full range of azimuthal angles for a given scattering angle and then averaging this quantity over scattering angles in a range of 10 to 70 degrees and multiplying by 100. A scattering distribution function having an ANU less than about 20 can be considered substantially azimuthally symmetric. In some embodiments, the ANU is less than about 15, or less than about 10, or less than about 8. In comparison, the ANU for an optical film having a single crystalline ordered domain is about 225.

[0050] FIG. 8 is a schematic plot representing an azimuthally averaged intensity distribution as a function of scattering angle or a scattering distribution function as a function of scattering angle which can be for a given azimuthal angle or can be an average over azimuthal angles or can be integrated over azimuthal angles, according to some embodiments. The distribution 550 schematically illustrated in FIG. 8 may correspond to the scattering distribution function 450 along the scattering direction 444, for example. The scattering distribution function can be substantially azimuthally symmetric so that the normalized (divided by first peak Ip 1) scattering distribution function for a given azimuthal angle can be substantially the same as the normalized azimuthally averaged intensity distribution.

[0051] In some embodiments, an optical film includes a first optical layer 141 including a structured first major surface 212 including a plurality of irregularly arranged and substantially tightly packed domains 110 where each of the domains includes a plurality of substantially regularly arranged structures 112. Each of the structures 112 can have an average in-plane diameter in a range from about 2 micrometers to about 15 micrometers, or about 3 micrometers to about 15 micrometers, or about 4 micrometers to about 15 micrometers, or about 5 micrometers to about 15 micrometers, or about 5 micrometers to about 12 micrometers, or about 5 micrometers to about 11 micrometers, or about 6 micrometers to about 10 micrometers, or about 7 micrometers to about 9 micrometers. In some embodiments, for a substantially normally incident substantially Gaussian light beam 333 having a beam waist diameter BW (see, e.g., FIG. 17) of 0.9 to 1.3 degrees (or in a range described elsewhere herein) and a wavelength of about 532 nm (or in a range described elsewhere herein), an azimuthally averaged intensity distribution of light transmitted by the optical film as a function of scattering angle measured from a normal to the optical film comprises first and second scattering bands (e.g., bands with scattering angles in the schematically illustrated local full-width at half maxima) having respective first 170 and second 171 scattering peaks 170 and 171 (peaks should be understood to be local maxima) and a valley 181 (valleys should be understood to be local minima) disposed therebetween, where the first and second scattering peaks 170 and 171 have corresponding first and second peak intensities Ipl and Ip2 and the valley 181 has a corresponding valley intensity Ivl. The first scattering peak 170 can be located at a first scattering angle al less than about 2 degrees, the valley can be located at a second scattering angle Va greater than the first scattering angle and less than about 6, 5.5, 5, 4.5, 4, or 3.5 degrees. The azimuthally averaged intensity distribution can further include at least third through fifth scattering peaks 172, 173 and 174 at corresponding scattering angles a3, a4 and a5 with corresponding peak intensities Ip3, Ip4 and Ip5. The first through fifth peaks 170-174 can alternate with first through fourth valleys 181, 182, 183 and 184 at respective first through fourth valley scattering angles Va, Vb, Vc, and Vd. In some embodiments, the azimuthally averaged intensity distribution transmitted by the optical film as a function of scattering angle measured from a normal to the optical film comprises first through fourth scattering bands having respective first through fourth scattering peaks having respective peak intensities Ipl, Ip2, Ip3, and Ip4 located at increasing respective first through fourth scattering angles al, a2, a3, and a4, where the first scattering angle al less than about 2 degrees from a normal to the optical film, and where each of (a3- a2) / (a2-al) and (a4-a3) / (a2-al) is in a range of about 0.7 to about 1.1, or about 0.8 to about 1.05, or about 0.85 to about 1. Scattering angles should be understood to be polar angles unless indicated differently. In some embodiments, an integral over scattering angle of the azimuthally averaged intensity distribution from the first scattering angle al (or first scattering angle al) to the second scattering angle Va (or first valley scattering angle Va) is II, and an integral over scattering angle of the azimuthally averaged intensity distribution from the second scattering angle Va (or first valley scattering angle Va) to a (e.g., third) scattering angle in a range of about 10 to 12 degrees (e g., 9.5, 10, 11, 12 or 12.5 degrees) is 12. The third scattering angle can correspond to Vc, for example. In some embodiments, Ip2 / Ivl < 10, 9, 8, 7, 6, 5, 4, 3, 2.5, 2.25, or 2. In some embodiments, 12 / 11 > 0.4, 0.5, 0.6, 0.7, or 0.8. In some embodiments, Ipl / Ip2 < 100, 75, 50, 40, 30, 20, 18, 16, 14, 12, 10, 9, 8.5, 8, or 7.5. In some embodiments, Ip 1 / Ip2 > 0.5, 0.7, 0.9, 1, 1.2, 1.5, 1.75, or 2. In some embodiments, Ipl / Ivl < 150, 140, 120, 100, 90, or 85, for example. In some embodiments, Ipl / Ivl > 5, 7, 10, 15, 20, 40, 50, 60, or 70. In some embodiments, the azimuthally averaged intensity distribution further comprises a third scattering band having a third scattering peak 172 having a third peak intensity Ip3, where the second scattering band is disposed between the first and third scatering bands, and where Ip2 / Ip3 < 2.3, 2.2, 2.1, 2, 1.9, 1.8, 1.7. or l .6, for example. In some embodiments, Ip2 / Ip3 > 0.5, 0.7, 0.9, 1, 1.1, or 1.2, for example. In some embodiments, 1 < Ip3 / Ip4 < 10, 8, 6, 5, 4, or 3.5.

[0052] In some embodiments, the scatering intensity at a scatering angle of about 20 degrees is less than a scatering intensity at a scattering angle of about 4 degrees or at the scatering angle Va or a2 by at least a factor of about 6, 8, 10, 12, 15, 20, or 25. It has been found, according to some embodiments, that a substantial fall off in scatering intensity between about 4 degrees, Va or a2 and about 20 degrees can result in only a modest reduction in effective resolution or DOI, for example. In some embodiments, the azimuthally averaged intensity distribution drops by a factor of at least 5, 6, 8, 10, 12, 15, 20, or 25 between the second scatering angle (or first valley polar angle) Va and a scatering angle of about 20 degrees. In some embodiments, the scatering distribution function of the optical film along the first scatering direction 444 drops by a factor of at least 5, 6, 8, 10, 12, 15, 20, or 25 between the first valley scatering angle Va and a scatering angle of about 20 degrees.

[0053] Typically, al < Va < a2 < Vb < a3. In some embodiments, additional peaks and valleys are present such that a3 < Vc < a4 and, in some embodiments, a4 < Vd < a5. In some embodiments, al is less than about 2, 1.5, 1, or 0.5 degrees. In some embodiments, al is substantially 0 degrees (e.g., less than about 1, 0.5, or 0.25 degrees). In some embodiments, the second scatering peak 171 is located at a scatering angle a2 in a range of about 3 degrees to about 8, 7.5, 7, 6.5, 6, 5.5, or 5 degrees. The scatering angle a2 can be at least about 3.25, 3.5, 3.75, or 4 degrees. In some embodiments, for each pair of adjacent scatering angles in the first through fourth scatering angles, the scatering angles in the pair are separated by at least about 1 degree and no more than about 8, 7, 6, or 5 degrees. The scattering angles of each pair can be separated by at least about 2, 2.5, 3, or 3.5 degrees, for example The various scattering angles are generally determined by the size of the particles 114 and the packing density and irregularity of the arrangement of the particles 114. In some embodiments, al is substantially 0 degrees, and ai for i=2 through 4 is Thetal times i-1 where Thetal is in a range of about 3.5 degrees to about 5 degrees, or about 3.8 degrees to about 4.8 degrees, or about 4 degrees to about 4.6 degrees.

[0054] In some embodiments, the scattering peaks extend from a baseline curve 190 of the azimuthally averaged intensity distribution that smoothly connects valleys of the azimuthally averaged intensity distribution. In some embodiments, an integral over the baseline curve from the first scattering angle al to a scattering angle of about 60 degrees is lb, an integral over the azimuthally averaged intensity distribution from the first scattering angle al to the scattering angle of about 60 degrees is Is, and Ib / Is > 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, and 0.37. Ib / Is can be up to about 1, 0.8, 0.6, or 0.5, for example.

[0055] In some embodiments, the first scattering band has a full width at half maximum FWHM1. Half of the FWHM1 of the first scattering band is shown in FIG. 8, for example, since the distribution can be substantially symmetrically extended to negative scattering angles (corresponding to a positive scattering angle and an azimuthal angle changed by 180 degrees). In some embodiments, the second through fourth scattering bands have respective second through fourth local full width at half maxima FWHM2 through FWHM4, where each of the FWHM2 through FWHM4 is in a range of about 1 to 4 degrees, or about 1.5 to 3 degrees. In some embodiments, 1 degree < FWHM2 < 3 degrees and FWHM3 > 1.1 x FWHM2. In some embodiments, FWHM2 < FWHM3 < FWHM4.

[0056] In some embodiments, for a substantially normally incident substantially Gaussian light beam 333 having a beam waist diameter of about 0.9 to 1.3 degrees (or in a range described elsewhere herein) and a wavelength of about 532 nm (or in a range described elsewhere herein), a scatering distribution function of the optical film along at least a first scatering direction (e g., x-direction or scatering direction 444) in a first plane (e.g., xz-plane or the plane defined by the scatering direction 444 and the z' -direction in FIG. 7) substantially perpendicular (e g., within 20, 15, 10, or 5 degrees of perpendicular to the plane of the optical film) to the optical film comprises first through third scatering bands having respective first through third scatering peaks having respective first through third peak intensities Ip 1, Ip2, and Ip3 located at increasing respective first through third scatering angles al through a3, where the first scatering angle al is less than about 2 degrees from a normal to the optical film. The scatering distribution function can be substantially azimuthally symmetric so that the normalized (divided by first peak Ip 1) scatering distribution function along the first scatering direction can be substantially the same as the normalized azimuthally averaged intensity distribution. The peak and valley intensities of the scatering distribution function along the first scattering direction can have ratios in any of the respective ranges described for the azimuthally averaged intensity distribution of the optical film. For example, in some embodiments, the scatering distribution function along the first scatering direction is such that Ip 1 / Ip2 < 100, 75, 50, 40, 30, 20, 18, 16, 14, 12, 10, 9, 8.5, 8, or 7.5. In some such embodiments, or in other embodiments, the scattering distribution function along the first scattering direction is such that Ip2 / Ip3 < 2.3, 2.2, 2.1, 2, 1.9, 1.8, 1.7, or 1.6. In some such embodiments, or in other embodiments, the scattering distribution function of the optical film along at least the first scattering direction in the first plane comprises a valley disposed between the first and second scattering peaks, where the valley having a valley intensity Ivl, and where Ipl / Ivl < 150, 140, 120, 100, 90, or 85.

[0057] In some embodiments, the domains 110 (see, e.g., FIG. 1) are arranged sufficiently irregularly so that Ipl / Ivl < 150 (or in a range described elsewhere herein) and / or so that Ip2 / Ivl < 10 (or in a range described elsewhere herein) and / or so that the scattering distribution function of the optical film is substantially azimuthally symmetric, for example. For regularly arranged domains the scattering distribution function can be azimuthally asymmetric and / or Ivl can be small so that Ipl / Ivl is much larger than 150 and / or Ip2 / Ivl is much larger than 10.

[0058] The peaks and valleys of the scattering distribution function along the first scattering direction can be at scattering angles in any of the ranges described for the azimuthally averaged intensity distribution of light transmitted by the optical film. For example, the second scattering angle a2 of the scattering distribution function can be located at a scattering angle in a range of about 3 degrees to about 8 degrees or in another range described elsewhere herein.

[0059] In some embodiments, the scattering peaks extend from a baseline curve 190 of the scattering distribution function that smoothly connects valleys of the scattering distribution function in the first plane, where an integral over the baseline curve from the first scattering angle al to a scattering angle of about 60 degrees is lb, and an integral over the scattering distribution function in the first plane from the first scattering angle al to the scattering angle of about 60 degrees is Is. In some embodiments, Ib / Is > 0.3 (or Ib / Is can be in a range described elsewhere herein).

[0060] In some embodiments, the relatively strong scattering (e.g., compared to color correcting optically diffusive films) needed for the optical film to substantially reduce sparkle results in the optical film having a relatively high optical haze. In some embodiments, the optical film has an optical haze of greater than about 80, 81, 82, 83, or 84 percent. The optical haze can be up to about 95 or 90 percent, for example. The optical haze can be determined according to the ASTM D 1003- 13 test standard, for example.

[0061] FIG. 9 is a schematic plot of the first peak intensity Ip2 versus azimuthal angle, according to some embodiments. In some embodiments, the first peak intensity Ip2 is substantially constant over an azimuthal range of at least 180 degrees (e.g., from <pl to q>2) so that a ratio of a standard deviation G to an average Ip2avgof the first peak intensity over the azimuthal range is less than about 0.5, 0.4, 0.3, 0.2, 0.15, 0.1, or 0.08. The azimuthal range can be 360 degrees or can be less than 360 degrees. In some embodiments, the azimuthal range is at least 250 degrees. In some embodiments, optical characteristics of the structures and media surrounding the structures (e.g., refractive indices and geometric properties of the structures which affect the properties) are chosen so that the scattering distribution function has the properties (e.g., ratio of peak intensity to valley intensity, FWHM, etc.) described elsewhere herein.

[0062] FIG. 10 is a schematic cross-sectional view of an illustrative display 760 that includes an optical film 600, which can be any of the optical films described herein, disposed on a display panel 680, which can be a liquid crystal display panel (LCD) or an organic light emitting diode (OLED) panel, for example. The first optical layer 141 of the optical film can face away from the display panel 680 and the second optical layer 150 can face the display panel 680. The pixels are arranged at a pitch Pl, P2 in the first and second in-plane directions. FIG. 11 is a schematic top view of the display panel 680, according to some embodiments. In some embodiments, the optical film reduces sparkle of the display 760 (e g., by at least 15% or 20%) without substantially reducing an effective resolution of the display (e.g., without reducing effective resolution as characterized by DOI by more than 40% or 35%) and without generating significant rainbow mura.

[0063] In some embodiments, the display 760 includes a display panel 680 having a pixelated display surface 681 having a pixel spatial frequency (e g., 1 / P1 or 1 / P2; if Pl and P2 are different, the pixel spatial frequency can be taken to be the smallest spatial frequency defined by Pl and P2); and any of the optical films of the present description disposed adjacent to, and spaced apart from, the pixelated display surface 681. The display 760 may further include an antiglare cover glass 633 with the optical film 600 disposed between the antiglare cover glass 633 and the display panel 680. In some embodiments, the optical film reduces sparkle of the display by at least 15% without decreasing a modulation transfer function (MTF) at the pixel spatial frequency by more than about 45, 40, 35, 30, or 25 percent. In some such embodiments, or in other embodiments, the optical film reduces sparkle of the display by at least 18, 20, 22, 24, 26, 28, 30, 32, 34, or 35%. For example, the sparkle of the display can be reduced from about 7% without the optical film to about 4.5% when the optical film is included (a reduction of about 35.7%). The sparkle can be determined as a ratio of standard deviation to a mean of an intensity distribution of a light output 761 of the display panel low pass filtered to remove display pixel modulation from the intensity distribution. The sparkle can be expressed as a percent by multiplying the ratio by 100%. The MTF may be decreased by the optical film by at least 5%, for example. The sparkle can be determined according to IEC 62977-3-9 (2023). Annex B2 of that test standard describes suitable low pass filtering to remove the display pixel modulation from the intensity distribution. A suitable instrument for measuring sparkle is the SMS-1000 Sparkle Measurement System available from Display-Messtechnik & Systeme, Rottenburg am Neckar, Germany. The SMS-1000 can also determine a distinctiveness of image (DOI) which is defined as a modulation transfer factor (MTF) for a spatial frequency of the pixel pattern of the display as a percent of a reference MTF at the same spatial frequency determined from the display without the sparkle reduction optical film and without the antiglare cover glass of the display. The percentage reduction in MTF at the pixel spatial frequency can be determined as the percentage reduction in DOI determined by the SMS- 1000.

[0064] Examples

[0065] All parts, percentages, ratios, etc. in the Examples and the rest of the specification are by weight, unless noted otherwise. Abbreviations include um = micrometer; scfm = standard cubic feet per minute; and ppm = parts per million. Other standard abbreviations may also be used.

[0066] Sparkle and DOI Measurements

[0067] The sparkle performance of the optical films were evaluated using a custom built test system. The optical film under test was placed in between a photolithographically patterned chromium mask (with 75.6 um x 23.5 um pixels that are separated by 72.5 um in one direction and 20.2 um in orthogonal direction mimicking a typical LCD pixel layout) and -1100 um thick matte cover glass (EAGLEETCH XS AG 70 Gloss glass, available from Europtec). The whole stack was then illuminated by a Lambertian white light source (Part # 83873 Metaphase Technologies, Bristol, PA). For sparkle measurements, the pixels on the mask were then imaged using a complementary metal oxide semiconductor (CMOS) camera (Blackfly, Teledyne FLIR LLC, Wilsonville, OR) equipped with a 50mm lens with f / 8 aperture (C203218, Tamron Co. Ltd. Japan). The sparkle values were then calculated as the variance of local intensity after removing the low frequency modulations from the pixels. Detail description of calculations of sparkle is described in U.S. Pat. No. 10,353,214 (Sitter et al.), or in the product literature of a sparkle measurement system SMS-1000 (Display-Messtechnik & Systeme, Rottenburg am Neckar, Germany), for example. The same images captured by the camera were used to calculate the Distinctness of Image (DOI) by measuring the intensity modulation (peak-to-valley amplitude) with the mask only and then with the test film and cover glass on top of the mask. DOI is calculated as: DOI = (Modulation with test film and cover glass / modulation with mask only) * 100 %.

[0068] Materials Used in the Examples

[0069] Examples 1-3

[0070] Particle formulations A, B and C were prepared according to the following table. Solutions were supplied through a hopper, which had a pneumatic mixer with the blade near the hopper outlet, constantly running to prevent bead settling, to a gear pump. The solution was filtered through a filtration system A recirculation loop was used to recycle the coating solution when not coating. The filtered coating solution was fed to a slot die where it was coated onto a 2mil (50 um) PET substrate. The solvent was then removed in a conventional flotation oven with three ten-foot (3m) zones. Typical temperature set points for Zones 1, 2, and 3 were 220 (104.4), 140 (60), 160 (71.1) degrees Fahrenheit (Celsius), respectively A final cure step was then used to complete the cure of the coating using an inerted UV curing unit with an H-bulb. The coated product was then wound onto a core at one pound per lineal inch (175. 1 Newtons per lineal meter) tension. Substantially monolayer bead coatings with 8um (SSX-108) and 5um (MX-500) diameter beads were made with at or near hemisphere bead exposure based on bead / monomer ratio. Process conditions are provided in the following table.

[0071] An optical microscope image of the monolayer bead coating of Example 1 is shown in FIG. 12. Bead coatings were then overcoated / backfill coated with an optically clear high refractive index formulation High index formulations with indices ranging from 1.68 to 1.53 were made by addition of varying amounts SR399LV monomer (refractive index of 1.527) to a base UV curable high index 1.6815 formulation. The formulation of the base UV curable high index 1.6815 formulation is provided the table below. Formulations having refractive indices of 1.64, 1.61, 1.59 and 1.57 included 10, 20, 30 and 40 wt.% of SR399LV with the remainder of the formulation being the base UV curable high index 1.6815 formulation.

[0072] Overcoating / backfill formulations were coated with a #12 Mayer rod. The coatings then travelled a 10 ft (3 m) span in the room environment, and passed through two 5 ft (1.5 m) long zones of small gap drying with plate temperatures set at 190 °F (88 °C). Related gap drying is described in U.S. Pat. Nos. 5,581,905 (Huelsman et al.); 5,694,701 (Huelsman et al.); and 6,134,808 (Yapel et al ), for example. The substrate was moving at a speed of 305 (cm / min). Finally, the dried coating entered a UV chamber equipped with a Fusion System Model I300P where an H-bulb was used. The UV chamber was purged by nitrogen at a flow rate of 11 scfin (310 liters / min) which resulted in an oxygen concentration of approximately 50 ppm.

[0073] Sparkle measurements of high index overcoated beaded coatings were made versus blank (no anti-sparkle solution) and a comparative anti-sparkle film (Comparative Example CE1) made as described in U.S. Pat. No. 10,353,214 (Sitter et al.) with a 2-dimensonal sinusoidal structured interface (see, e g., FIGS. 6A-6B of that reference) with an 8 um pitch for comparison. Sparkle and DOI measurements were made as described under “Sparkle and DOI Measurements” where the backfilled optical film was disposed between the antiglare cover glass and the chromium with the backfill layer facing the chromium mask. Sparkle and DOI results are shown in FIGS. 13-14, respectively, as a function of the refractive index of the backfill layer. Sparkle and DOI results for Examples 1-3 were roughly comparable to those of CE1 but Examples 1-3 did not produce the undesired rainbow mura produced by CE1. The transmission scattering distribution function for various samples were determined using an imaging sphere (Radiant Vision Systems IS-SA) modified to accept a substantially normally incident light having a wavelength of 532 nm (Thorlabs CPS532). Transmission versus scattering angle was tabulated by taking an azimuthal average over a uniform section of the output conoscopic image. The substantially normally incident light was a substantially monochromatic substantially Gaussian light beam having a beam waist diameter of about 1.06 degrees as determined using the imaging sphere. Example 1 with a 1.61 index backfill resulted in an Ip 1 / Ip2 of about 5.

[0074] Examples 4-8

[0075] Particle formulation D was prepared according to the following table.

[0076] Solutions were supplied through a hopper, which had a pneumatic mixer with the blade near the hopper outlet, constantly running to prevent bead settling, to a gear pump. The solution was filtered through a filtration system. A recirculation loop was used to recycle the coating solution when not coating. The filtered coating solution was fed to a slot die where it is coated onto a 15um COP substrate with a 2mil (50um) carrier PET film. The solvent was then removed in a gap dryer with four, five-foot (1.5 m) zones set to 130 (54.4), 160 (71.1), 175 (79.4), and 175 (79.4) degrees Fahrenheit (Celsius), respectively, followed by a conventional flotation oven with two fifteen-foot (4.6 m) zones. The gap dryer was similar to those described in U.S. Pat. Nos. 5,581,905 (Huelsman et al ); 5,694,701 (Huelsman et al.); and 6,134,808 (Y apel et al.), for example. Temperature set points for Zones 1 and 2 were 220 (104.4) and 160 (71.1) degrees Fahrenheit (Celsius), respectively. A final cure step was then used to complete the cure of the coating using an inerted UV curing unit with H-bulbs. The coated product was then wound onto a core at one pound per lineal inch (175.1 Newtons per lineal meter) tension. Substantially monolayer bead coatings with 8um (SSX-108) diameter beads were made with at or near hemisphere bead exposure based on bead / monomer ratio. The coating line speed was 60 ft / min (1828.8 cm / min). The pump rates that were used are given in the following table.

[0077] Overcoat / Backfill formulation E was prepared according to the following table.

[0078] Overcoating / backfdl formulations were supplied through a hopper, to a gear pump. The solution was fdtered through a fdtration system. A recirculation loop was used to recycle the coating solution when not coating. The fdtered coating solution was fed to a slot die where it is coated onto the bead coated fdm on COP, as outlined above. The solvent was then removed in a gap dryer with four, five-foot zones set to 80 (26.7), 80 (26.7), 100 (37.8), and 100 (37.8) degrees Fahrenheit (Celsius), respectively, followed by a conventional oven with two fifteen-foot (4.6 meters) zones. The gap dryer was similar to those described in U.S. Pat. Nos. 5,581,905 (Huelsman et al.); 5,694,701 (Huelsman et al.); and 6,134,808 (Yapel et al.), for example. Temperature set points for Zones 1 and 2 were 120 (48.9) and 140 (60) degrees Fahrenheit (Celsius), respectively. A final cure step was then used to complete the cure of the coating using an inerted UV curing unit with H-bulbs. The coated product was then wound onto a core at one pound per lineal inch tension. The coating line speed was 30 ft / min (914.4 cm / min) and the pump rate was 4.4 g / min per inch width (1.72 g / min per cm width) for each of these Examples.

[0079] Comparative Example CE2 was made as described for Example 13 of Int. Pat. Appl. Pub. No. WO 2021 / 240268 (Menke et al.). For comparison, a sample with no anti-sparkle film (“No AS”) but with a PET spacer layer of about the same thickness as the optical film examples was also tested.

[0080] Sparkle and DOI measurements were made as described under “Sparkle and DOI Measurements” where the backfilled optical film was disposed between the antiglare cover glass and the chromium mask with the backfill facing the chromium mask. Results for sparkle and DOI are shown in FIGS. 15-16, respectively.

[0081] The scattering intensity distribution was determined using the imaging sphere as described elsewhere in the Examples. The intensity distribution was azimuthally averaged and normalized (so that Ipl = 1). The resulting normalized scattering distributions are shown in FIG. 17. Results are provided in the following table which includes results for the light source without an optical film. The first scattering angle al was about 0 degrees.

[0082] The ratio 12 / 11 was determined where II is an integral over scattering angle of the azimuthally averaged intensity distribution from the first scattering angle al to the first valley scattering angle Va, and an 12 is integral over scattering angle of the azimuthally averaged intensity distribution from the first valley scattering angle Va to a scattering angle of 11 degrees. Results are provided in the following table.

[0083] Terms such as “about” will be understood in the context in which they are used and described in the present description by one of ordinary skill in the art. If the use of “about” as applied to quantities expressing feature sizes, amounts, and physical properties is not otherwise clear to one of ordinary skill in the art in the context in which it is used and described in the present description, “about” will be understood to mean within 10 percent of the specified value. A quantity given as about a specified value can be precisely the specified value. For example, if it is not otherwise clear to one of ordinary skill in the art in the context in which it is used and described in the present description, a quantity having a value of about 1, means that the quantity has a value between 0.9 and 1.1, and that the value could be 1. All references, patents, and patent applications referenced in the foregoing are hereby incorporated herein by reference in their entirety in a consistent manner. In the event of inconsistencies or contradictions between portions of the incorporated references and this application, the information in the preceding description shall control. Descriptions for elements in figures should be understood to apply equally to corresponding elements in other figures, unless indicated otherwise. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and / or equivalent implementations can be substituted for the specific embodiments shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations, or variations, or combinations of the specific embodiments discussed herein. Therefore, it is intended that this disclosure be limited only by the claims and the equivalents thereof.

Claims

What is claimed is:

1. An optical film comprising: a first optical layer comprising a structured first major surface comprising a plurality of irregularly arranged and substantially tightly packed domains, each of the domains comprising a plurality of substantially regularly arranged structures, each of the structures having an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, wherein for a substantially normally incident substantially Gaussian light beam having a beam waist diameter of 0.9 to 1.3 degrees and a wavelength of about 532 nm, an azimuthally averaged intensity distribution of light transmitted by the optical film as a function of scattering angle measured from a normal to the optical film comprises first and second scattering bands having respective first and second scattering peaks and a valley disposed therebetween, the first and second scattering peaks having corresponding first and second peak intensities Ipl and Ip2, the valley having a corresponding valley intensity Ivl, the first scattering peak located at a first scattering angle less than about 2 degrees, the valley located at a second scattering angle greater than the first scattering angle and less than about 6 degrees, an integral over scattering angle of the azimuthally averaged intensity distribution from the first scattering angle to the second scattering angle being II, an integral over scattering angle of the azimuthally averaged intensity distnbution from the second scattering angle to a third scattering angle in a range of about 10 to 12 degrees being 12, wherein:Ip2 / Ivl < 10; and12 / 11 > 0.4.

2. The optical film of claim 1, wherein Ip 1 / Tp2 < 100.

3. The optical film of claim 1, wherein the azimuthally averaged intensity distribution further comprises a third scattering band having a third scattering peak having a third peak intensity Ip3, the second scattering band disposed between the first and third scattering bands, Ip2 / Ip3 < 2.3.

4. The optical film of claim 1, wherein the second scattering peak is located at a scattering angle in a range of about 3 degrees to about 8 degrees5. The optical film of claim 1, wherein for each domain, the plurality of substantially regularly arranged structures are substantially periodically arranged along each of different in-plane first and second directions, wherein the first and second directions change irregularly from domain to domain.

6. The optical film of any one of claims 1 to 5 further comprising a second optical layer having opposing first and second major surfaces, the first major surface of the second optical layer disposed on, and substantially conforming to, the stmctured first major surface of the first optical layer, the second optical layer having an index of refraction substantially different from an index of refraction of the first optical layer.

7. The optical film of claim 6, wherein the first optical layer comprises beads disposed in a binder, wherein for at least one wavelength in a range of about 400 nm to about 700 nm, an absolute value of a difference between the index of refraction of the second optical layer and an index of refraction of the beads is at least about 0.1, and an absolute value of a difference between an index of refraction of the binder and the index of refraction of the beads is in a range of about 0.025 to about 0.06.

8. The optical film of claim 6, wherein an absolute value of a difference between the indices of refraction of the first and second optical layers times an average height of the structures is in a range of about 0.2 micrometers to about 1.2 micrometers.

9. The optical film of claim 1, wherein the azimuthally averaged intensity distribution drops by a factor of at least 5 between the second scattering angle and a scattering angle of about 20 degrees.

10. An optical film comprising: a first optical layer comprising a structured first major surface comprising a plurality of irregularly arranged and substantially tightly packed domains, each of the domains comprising a plurality of substantially regularly arranged structures, each of the structures having an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, wherein for a substantially normally incident substantially Gaussian light beam having a beam waist diameter of 0.9 to 1.3 degrees and a wavelength of about 532 nm, an azimuthally averaged intensity distribution of light transmitted by the optical film as a function of scattering angle measured from a normal to the optical film comprises first through fourth scattering bands having respective first through fourth scattering peaks having respective peak intensities Ip 1 , Ip2, Ip3, and Ip4 located at increasing respective first through fourth scattering angles al, a2, a3, and a4, the first scattering angle al less than about 2 degrees from a normal to the optical film, each of (a3-a2) / (a2-al) and (a4-a3) / (a2-al) being in a range of about 0.7 to about 1.1, a valley between the first and second peaks located at a first valley scattering angle greater than the first scattering angle and less than about 6 degrees, an integral over scattering angle of the azimuthally averaged intensity distribution from the first scattering angle to the first valley scattering angle being II, an integral over scattering angle of the azimuthally averaged intensity distribution from the first valley scattering angle to a scattering angle in a range of about 10 to 12 degrees being 12,wherein 12 / 11 > 0.4.

11. The optical film of claim 10, wherein Ip2 / Ip3 < 2.3.

12. The optical film of claim 10, wherein 1 < Ip3 / Ip4 < 10.

13. The optical film of any one of claims 10 to 12, wherein the valley has a valley intensity Ivl, Ipl / Ivl < 150.

14. An optical film comprising: a first optical layer comprising a structured first major surface comprising a plurality of irregularly arranged and substantially tightly packed domains, each of the domains comprising a plurality of substantially regularly arranged structures, each of the structures having an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, wherein for a substantially normally incident substantially Gaussian light beam having a beam waist diameter of about 0.9 to 1.3 degrees and a wavelength of about 532 nm, a scattering distribution function of the optical film along at least a first scattering direction in a first plane substantially perpendicular to the optical film comprises first through third scattering bands having respective first through third scattering peaks having respective first through third peak intensities Ip 1, Ip2, and Ip3 located at increasing respective first through third scattering angles, the first scattering angle less than about 2 degrees from a normal to the optical film, wherein:Ipl / Ip2 < 100; andIp2 / Ip3 < 2.3.

15. The optical film of claim 14, wherein for each domain, the plurality of substantially regularly arranged structures are substantially periodically arranged along each of different in-plane first and second directions, wherein the first and second directions changes irregularly from domain to domain.

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