Optical film for reducing sparkle

Abstract

An optical stack includes an optical film including first and second layers. Each of the first and second layers has a structured first major surface and an opposite second major surface. The structured first major surfaces of the first and second layers are disposed on and substantially conform to one another. The structured first major surface of each of the first and second layers include a plurality of irregularly arranged and substantially tightly packed domains. Each of the domains include a plurality of substantially regularly arranged structures. The structures have an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers. The optical film is configured to reduce sparkle of a display system having a pixel spatial frequency by at least 15% without decreasing a modulation transfer function of the display system at the pixel spatial frequency by more than about 45%.

Description

[0001] PA101636W002

[0002] OPTICAL FILM FOR REDUCING SPARKLE

[0003] TECHNICAL FIELD

[0004] The present description generally relates to optical films, and more specifically to optical films for reducing sparkle in displays.

[0005] BACKGROUND

[0006] 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.

[0007] SUMMARY

[0008] The present description 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 tool made using a microparticle self-assembly process, according to some embodiments.

[0009] In some aspects, the present description provides an optical stack including an optical film that includes first and second layers. Each of the first and second layers has a structured first major surface and an opposite second major surface. The structured first major surfaces of the first and second layers are disposed on and can substantially conform to one another, such that for each of the first and second layers: the second major surface is not directly fixedly attached to any other layer or is directly fixedly attached to a room-temperature adhesive layer substantially coextensive with the second major surface; and the structured first major surface includes a plurality of irregularly arranged and substantially tightly packed domains. Each of the domains includes a plurality of substantially regularly arranged structures. The structures have an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, such that for substantially normally incident light in a visible wavelength range, a scattering distribution function of the optical film can be substantially azimuthally symmetric. The optical film is configured to reduce sparkle of a display system having a pixel spatial frequency by at least 15 percent without decreasing a modulation transfer function of the display system at the pixel spatial frequency by more than about 45 percent.

[0010] In some aspects, the present description provides an optical stack including an optical film that includes first and second layers. Each of the first and second layers has a structured first major surface and an opposite second major surface. The structured first major surfaces of the first and second layers are disposed on and can substantially conform to one another, such that the second major surface of the first layer is not directly fixedly attached to any other layer or is directly fixedly attached to a roomtemperature adhesive layer substantially coextensive with the second major surface of the first layer. The second layer can be an adhesive layer. The structured first major surface of each of the first and second layers include a plurality of irregularly arranged and substantially tightly packed domains. Each of the domains include a plurality of substantially regularly arranged structures. The structures can have an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, such that for substantially normally incident light in a visible wavelength range, a scattering distribution function of the optical film is substantially azimuthally symmetric. The optical film is configured to reduce sparkle of a display system having a pixel spatial frequency by at least 15 percent without decreasing a modulation transfer function of the display system at the pixel spatial frequency by more than about 45 percent.

[0011] 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.

[0012] BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 is a schematic cross-sectional view of an optical stack or optical film, according to some embodiments.

[0014] FIGS. 2-3 are schematic cross-sectional view of optical stacks, according to some embodiments.

[0015] FIGS. 4A-4C schematically illustrate a method of making an optical stack, according to some embodiments.

[0016] FIGS. 5-6 are schematic top views of portions of films, according to some embodiments.

[0017] FIG. 7 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.

[0018] FIG. 8 is a schematic geometry for the measurement of scattering profile and a schematic conoscopic plot of a scattering distribution function, according to some embodiments.

[0019] FIG. 9 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.

[0020] FIG. 10 is a schematic plot of a peak intensity versus azimuthal angle at a specific scattering angle, according to some embodiments.

[0021] FIG. 11 is schematic cross-sectional view of a display that includes an optical film, according to some embodiments.

[0022] FIG. 12 is a schematic top view of a display panel having a pixelated display surface, according to some embodiments.

[0023] FIG. 13 is an optical microscope image of a tool for making an optical film, according to some embodiments.

[0024] FIG. 14 is a plot of sparkle of displays including an optical film that includes a first layer disposed on a second layer as a function of the refractive index (RI) of the first layer, according to some embodiments.

[0025] FIG. 15 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 first layer disposed on a second layer as a function of the refractive index (RI) of the first layer, according to some embodiments. FIG. 16 is a box plot of sparkle for various displays, according to some embodiments.

[0026] FIG. 17 is a box plot of DOI for the displays of FIG. 16.

[0027] FIG. 18 is a plot of sparkle decrease versus MTF decrease for the displays of FIGS. 16-17.

[0028] FIG. 19 is a plot of normalized azimuthally averaged intensity distributions of light transmitted by optical films, according to some embodiments.

[0029] DETAILED DESCRIPTION

[0030] 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.

[0031] According to some embodiments of the present description, an optical film (e.g., for sparkle reduction as described elsewhere herein) is provided where the optical film does not include a substrate other than possibly a releasably attached liner. It has been found that such optical films have greater placement flexibility than optical films including a substrate due to optical artifacts undesirably generated by the substrate (e.g., substrate birefringence can increase ambient reflection from organic light emitting diode (OLED) displays when placed between the circular polarizer of the display and the display surface). It has been found, according to some embodiments, that a beaded layer (e.g., a layer formed via self-assembly of beads or particles as described further elsewhere herein) including a suitable type and amount of surfactant or release additive, for example, can be coated onto a traditional film substrate and then backfilled with a resin where the surfactant or release additive allows the backfill layer, and any additional layers added to the backfill layer, to be substantially cleanly removed from the beaded layer. Alternatively, or in addition, according to some embodiments, a release treatment can be applied to the beaded layer prior to backfilling and this can provide a substantially clean release. The resulting exposed structured surface of the backfill layer can be backfilled with a second backfill material to result in an optical film with an embedded interface, no substrate (other than possibly release liners that will subsequently be removed), and no beads. The optical film can provide similar sparkle performance as optical films including the beaded layer by suitable selection of the refractive indices of the backfill layers.

[0032] 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. According to some embodiments of the present description, an optical film is provided that is suitable for reducing sparkle. In some embodiments, self-assembly of particles (e.g., microparticles having an average diameter in a range of about 4 to about 15 micrometers) is utilized in making the optical film. 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 selfassembled particles can be used to make a tool which is used to form the structures (e.g., in a cast and cure process) of the optical film. 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 provide 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 FIG. 4A, which can be adjusted (e.g., increased) by adjusting (e.g., increasing) the particle diameter d and / or the ratio h / d) of the tool, and / or adjusting (e.g., increasing) a difference in refractive index between the resulting fdm structures and a backfdl material over the structures. Suitable optical fdms 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.

[0033] FIG. 1 is a schematic cross-sectional view of an optical stack or optical film 100, according to some embodiments. In some embodiments, the optical film 100 includes first and second layers 110 and 120, where each of the first and second layers 110 and 120 has a structured first major surface (111 and 121, respectively) and an opposite second major surface (112 and 122, respectively). In some embodiments, the structured first major surfaces 111, 121 of the first and second layers 110, 120 are disposed on and substantially conform (e.g., conform, or nominally conform, or conform up to variation small (e.g., less than 10%) compared to a height or diameter of the structures) to one another. In some embodiments, each of the first and second layers 110, 120 is a polymeric layer. A polymeric layer generally has a continuous organic polymer phase and can optionally include additives (e.g., inorganic nanoparticles, ultraviolet absorbers, wavelength-selective dyes or pigments, or any other optional additive known to be useful to include in polymer formulations) dispersed in the continuous polymer phase. The optical stack or film generally extends along x- and y-directions and has a thickness along a z-direction, where the x-, y-, and z-directions are mutually orthogonal.

[0034] FIGS. 2-3 are schematic cross-sectional view of optical stacks 200 and 300, respectively, according to some embodiments. Each of the optical stacks 200 and 300 include optical film 100 disposed between first and second release liners 131 and 132 and include an adhesive layer 141 disposed between the first layer 110 and the first release layer 131. For optical stack 200, the second layer 120 is disposed directly on the second release liner 132 (e.g., the second layer 120 can be an adhesive layer). For optical stack 300, a second adhesive layer 142 is disposed between the second layer 120 and the second release liner 132.

[0035] In some embodiments, for each of the first and second layers 110, 120, the second major surface 112, 122 is not directly fixedly attached to any other layer or is directly fixedly attached to a roomtemperature adhesive layer substantially coextensive with the second major surface. In some embodiments, the second major surface 112 of the first layer 110 is not directly fixedly attached to any other layer or is directly fixedly attached to a room-temperature adhesive layer substantially coextensive with the second major surface of the first layer, and the second layer is an adhesive layer. In some embodiments, the first and second layers 110, 120 comprise respective first and second radiation-cured layers. In some embodiments, the optical stack further includes a first optically clear adhesive layer 141 disposed on the second major surface 112 of first layer 110. The adhesive layer 141 may be fixedly or releasably attached to the second major surface 112. In some embodiments, the second major surface 112 of the first layer 110 is fixedly attached to the first optically clear adhesive layer 141. In some embodiments, the first optically clear adhesive layer 141 is releasably attached to the second major surface 112 of the first layer 110. In some embodiments, the optical stack further includes a second optically clear adhesive layer 142 disposed on the second major surface 122 of the second layer 120. The adhesive layer 142 may be fixedly or releasably attached to the second major surface 122. In some embodiments, the second major surface 122 of the second layer 120 is fixedly attached to the second optically clear adhesive layer 142. In some embodiments, the second optically clear adhesive layer 142 is releasably attached to the second major surface 122 of the second layer 120. In some embodiments, the second layer 120 is an adhesive layer and so the second optically clear adhesive layer 142 can be omitted. In some embodiments, the second layer 120 is an adhesive layer, and the first layer 110 comprises a radiation-cured polymer.

[0036] As used herein, a “room-temperature adhesive” is an adhesive adapted to form a bond to a nonadhesive layer at room temperature (about 23 deg. C). A room -temperature adhesive can be a pressure sensitive adhesive and / or an optically clear adhesive, for example. A light (e.g., ultraviolet light) cured adhesive is a room-temperature adhesive when elevated temperature is not needed for the adhesive to cure and form a bond to an adjacent layer. A hot-melt adhesive that needs an elevated temperature to achieve bonding is not a room-temperature adhesive. A thermoplastic polymer layer bonded to adjacent thermoplastic polymer layers as a result of the layers being coextruded at an elevated temperature is not a room-temperature adhesive. Useful room-temperature adhesives include, for example, optically clear adhesives available from 3M Company (St. Paul, MN) or Norland Products (Jamesburg, NJ). An optically clear adhesive is generally an adhesive with a high visible light transmittance (e.g., greater than 75, 80, 85, or 90 percent) and a low optical haze (e.g., less than 10, 5, 4, 3, or 2 percent).

[0037] In some embodiments, the optical stack further includes a release liner 132. In some embodiments, the second layer 120 is an adhesive layer and the second major surface 122 of the second layer 120 is releasably attached to a release surface of the release liner. In some embodiments, an optically clear adhesive layer 141 is fixedly attached to the second major surface 112 of the first layer 110. In some embodiments, the optical stack further includes first and second release liners 131 and 132, where the optically clear adhesive layer 141 is releasably attached to the first release liner 131, and the second layer 120 (which can be an adhesive layer) is releasably attached to the second release liner 132. In some embodiments, the first and second release liners 131 and 132 have respective higher and lower peel forces Fl and F2 from the optical stack. The peel forces can be measured in a 90-degree peel test, for example. In some embodiments, the first release liner 131 is selected to have a higher peel force than that of the second release liner 132 (Fl > F2 via suitable selection of release coatings utilized) since it is typically desired that the first release liner 131 remain attached while the first layer 110 is removed from a tool used in forming the first layer 110 (see, e.g., FIGS. 4A-4C). The release coatings can comprise silicone, polydimethylsiloxane (PDMS), fluoropolymer, or other known release chemistries. Useful silicone-based and non-silicone-based release liners are available from 3M Company (St. Paul, MN), for example.

[0038] In some embodiments, as described further elsewhere herein, for each of the first and second layers 110 and 120, the structured first major surface 111, 121 (i.e., the structured first major surface of each of the first and second layers) comprises a plurality of irregularly arranged and substantially tightly packed domains, each of the domains comprising a plurality of substantially regularly arranged structures, the structures having an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, such that for substantially normally incident light in a visible wavelength range, a scattering distribution function of the optical film is substantially azimuthally symmetric. In some embodiments, as described further elsewhere herein, the optical film 100 is configured to reduce sparkle of a display system having a pixel spatial frequency by at least 15, 18, 20, 22, 24, 26, 28, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, or 43 percent without decreasing a modulation transfer function (MTF) of the display system at the pixel spatial frequency by more than about 45, 40, 35, 30, 25, 23, 21, 20, 19, 18, or 17 percent.

[0039] FIGS. 4A-4C schematically illustrate a method of making an optical stack, according to some embodiments.

[0040] FIG. 4A is a schematic illustration of a tool 400a (e.g., a fdm tool) including a tool layer 241 disposed on a substrate 230, according to some embodiments. The tool layer 241 has a major structured surface 212 that includes structures 312. FIG. 4B shows an optical stack 400b including a layer 110 formed (e.g., via a cast and cure process, for example) on the structured surface 212 of the tool layer 241. An adhesive layer 141 and liner 131 are added to the layer 110. The tool layer 241 is then removed from the layer 110 and a layer 120 is formed on the resulting structured surface 121 (e.g., via coating and / or backfilling) as schematically illustrated in FIG. 4C for optical stack 400c. A release liner 132 can be added to layer 120 or an adhesive layer (e.g., corresponding to adhesive layer 142 schematically illustrated in FIG. 3) can be added to layer 120 and then the release liner 132 added to the adhesive layer. In some embodiments, the layer 110 has a storage modulus at 20 deg. C of no more than 2500, 2000, 1500, 1000, 900, 800, 700, or 600 MPa. In some such embodiments, or in other embodiments, the storage modulus at 20 deg. C is at least 1, 5, 10, 20, 50, or 100 MPa. In some embodiments, the layer 110 has a storage modulus at 20 deg. C of no more than 2500, 2000, 1500, 1000, 900, 800, 700, or 600 MPa. In some such embodiments, or in other embodiments, the storage modulus at 20 deg. C is at least 1, 5, 10, 20, 50, or 100 MPa.

[0041] The beaded layer 241 can include a suitable type and amount of surfactant or release additive, for example, to allow the beaded layer to be cleanly removed from the backfdl layer. Suitable surfactants or release additives include silicone-based compounds such as silicone polyether acrylate (e.g., available under the trade designation “TEGO Rad 2250” from Evonik Goldschmidt Corp., Hopewell, VA), polydimethylsiloxane (PDMS), or fluoropolymer, for example. The surfactants or release additives can be added at a sufficient amount to produce substantially clean release. The amount may be in a range of about 0.08 to 2 solids weight percent, for example, where the appropriate amount may depend on the type of surfactant of release additive utilized. For example, for silicon-based compounds such as TEGO Rad 2250, 0. 1 to 1, 0.15 to 0.7, or 0.2 to 0.4, weight percent based on total solids weight may be used. In addition to the surfactants or release additives added for release of the backfill from the beaded layer, additional surfactants can be included in the beaded layer for other purposes such as aiding in the backfill wetting out on the beaded layer. Alternatively, or in addition to including surfactants or release additives in the beaded layer, a suitable release treatment can be applied to the beaded layer prior to backfilling, and this can provide a substantially clean release, according to some embodiments. Suitable release treatments include, for example, plasma treatment and / or silicone, polydimethylsiloxane (PDMS), and fluoropolymer coatings. For example, in a plasma treatment process the ratio of hexamethyldisiloxane (HMDSO) to oxygen can change the number methyl groups relative to OH groups at the surface which can change the surface energy.

[0042] The tool 400a include particles 514 dispersed in a binder 140 (e.g., a polymeric binder). A layer 241 including the particles 514 in the binder 140 is disposed on a substrate 230 which can be a polymeric substrate (e.g., polyethylene terephthalate (PET), or an amorphous polyester such as polyethylene terephthalate glycol (PETG), or cyclo olefin polymer (COP), or biaxially oriented polypropylene (BOPP)), for example. The particles 514 have an average diameter d, an average pitch p, and an average spacing g between adjacent particles. The particles 514 define structures 312 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 of the peak-to-valley height over domains 510 (see, e.g., FIG. 5) of the structures. In some embodiments, the binder 140 substantially covers an entire surface of each particle in at least a majority of the particles 514. In other embodiments, the binder 140 may not wet the surface of the particles 514 and may leave a significant portion of the surface (e.g., top surface) of the particles 514 exposed.

[0043] The particles 514 can be coated onto substrate 230 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 514 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.

[0044] 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. 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. 5 which may be about equal to the pitch p in FIG. 4A) of the structures 512. 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 512. 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 512. 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 512. 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 the structured interface of the optical film made from the tool. 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. FIG. 5 is a schematic top view of an illustrative portion of a film 500, according to some embodiments. The film 500 can schematically represent an optical film of the present description or a tool for making an optical film. The film 500 includes a plurality of structures 512 that can form a plurality of substantially coplanar structured domains 510. 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 512 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 film 500. 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.

[0045] In some embodiments, the arrays of adjacent domains have different orientations. The substantially regular array of structures 512 can be characterized as including structures 512 substantially repeating along first and second basis vectors 521 and 522 (which are along differing first and second directions). The basis vectors 521, 522 are not colinear so that the basis vectors can define a two- dimensional array. The basis vectors for different domains 510 can be different. Domains 510a-510d are schematically illustrated in FIG. 5 and the basis vectors 521, 522 are shown for domains 510b and 510d. The basis vector 521 of domain 510b is not parallel to either the basis vector 521 or the basis vector 522 of domain 5 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 521 and 522, where the first and second directions 521 and 522 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 521 and 522 remain substantially constant from domain to domain as the first and second directions 521 and 522 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 film 500. For example, the film 500 can extend primarily along orthogonal width and length directions which define the plane of the film 500.

[0046] The structures and domains of the film 500 schematically illustrated in FIG. 5 can schematically represent structures and domains of the structured first major surface of the first and / or second layer 110, 120 or can schematically represent structures and domains of a tool used to make optical film 100, for example. In some embodiments, a tool for making an optical film includes a plurality of particles 514 that define a substantially regular array of structures 512 which can be used to form a corresponding substantially regular array of structures of the optical film formed from the tool. For example, a film including the plurality of particles 514 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. As described further elsewhere herein, a liner with adhesive can be applied to the cured resin layer and then the tool can be removed leaving the cured resin layer attached to the liner through the adhesive. The resulting structured surface of the cured resin layer can be backfilled and another liner disposed on the backfill layer. This backfill layer can be an adhesive layer, or a separate adhesive layer can be included between the backfill layer and the liner. In this way, a substrateless (no substrate other than liners which can be subsequently removed) optical film can be made in a process that utilizes a single release step (releasing the cast resin from the beaded layer).

[0047] In some embodiments, the particles 514 are disposed substantially in a monolayer of the particles. The particles 514 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 510 in greater than 50, 60, 70, 80, 90, or 95 percent of the domains, the particles 514 in the domain are disposed substantially in a monolayer of the particles. In some embodiments, the particles 514 of the tool used to make the optical film form less than a full monolayer. This may be referred to as a sub-monolayer. In some embodiments, the structures 512 and / or particles 514 define lake regions 516 between structured domains 510 that are free or substantially free of structures 512 and / or particles 514. For example, in some embodiments, the plurality of particles 514 defines lake regions 516 between structured domains 510 where each lake region 516 is free of the particles 514. In some embodiments, the particles 514 include a two-dimensional array of particles 514 and further include additional particles (e.g., particle 518) disposed on the two-dimensional array of particles 514. 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 514 of each domain 510 are arranged to form a regular two-dimensional first array of the particles 514. In some embodiments, for each domain in a sub-plurality (at least two but less than all) of the domains 510 (e.g., domains 510c and 5 lOd), the plurality of particles 514 further include at least one particle 518 disposed on the particles arranged in the regular two-dimensional first array. In some embodiments, for each domain 510, the plurality of particles 514 further includes at least one particle 518 disposed on the particles arranged in the regular two-dimensional first array (e.g., each domain can appear as domain 510c or 5 lOd).

[0048] In some embodiments, including the optical film 100 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) in the tool used to make the optical film 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 the refractive index contrast between the layers on each side of the structured interface in the resulting optical film. Typically, this index contrast is at least about 0.1. FIG. 6 is a schematic top view of an illustrative portion of a film 500, according to some embodiments. The structured domains 510 have orthogonal lateral dimensions dl and d2 and have an average spacing S2 therebetween. The structures of the structured domains 510 are not explicitly shown in the schematic illustration of FIG. 5. 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 512. 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 the majority of the structured domains includes at least about 60%, or at least about 70%, or at least about 80% of the structured domains.

[0049] The structures 512 of the tool or of the resulting optical film have an average largest lateral dimension SI. The average is the unweighted mean of largest lateral dimension (e.g., diameter) of each structure 512. For tools 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. 4A). The plurality of domains 510 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.

[0050] The layer 241 of the tool 400a (see, e.g., FIG. 4A) has a structured first major surface 212 including a plurality of irregularly arranged and substantially tightly packed domains (e.g., 510a-5 lOd), where each of the domains includes a plurality of substantially regularly arranged structures (e.g., structures 512 defined by particles 514). 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. An optical layer made from the tool 400a can have structures corresponding to an inverse of the structures 512 and when the structures of the optical layer are backfilled, the backfill can have structures corresponding to structures 512. The structured surface of the optical layer and / or the backfill (or an interface between the optical layer and backfill) may similarly include a plurality of irregularly arranged and substantially tightly packed domains (e.g., 510a-5 lOd), where each of the domains includes a plurality of substantially regularly arranged structures.

[0051] In some embodiments, the particles 514 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 514 are substantially spherical. The structures 512 (of the tool or the resulting optical film) can have an average in-plane diameter in any of these ranges (e.g., in some embodiments, each of the structures 512 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).

[0052] FIG. 7 is a schematic cross-sectional view of an illustrative optical film 600, 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 X in a wavelength range of I 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 A I 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 e-2times the peak intensity of the beam. For example, the beam waist diameter can be twice the angle “BW / 2” depicted in FIG. 19. 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 film 600 can be any optical film described herein. For example, optical film 600 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.

[0053] A scattering distribution function describes the relative intensity of scattered incident light and is generally a function of a scattering angle 0 and an azimuthal angle <p 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. 8. The azimuthally averaged intensity distribution function can be determined by averaging the scattering distribution function over all azimuthal angles (p. 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.

[0054] FIG. 8 is a schematic geometry for the measurement of scattering profile 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 (p 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 600) 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. 8 can correspond to the negative z-direction in FIG. 7 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. 8. 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.

[0055] FIG. 9 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. 9 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.

[0056] The size of the structures of the optical film can affect the intensity distribution. In some embodiments, an optical film includes a first layer 110 including a structured major surface 111, and / or a second layer 120 including a structured major surface 121, and / or an interface between first and second layers can be structured, where the structured major surface or interface includes a plurality of irregularly arranged and substantially tightly packed domains 510 where each of the domains includes a plurality of substantially regularly arranged structures 512. Each of the structures 512 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.

[0057] In some embodiments, for a substantially normally incident substantially Gaussian light beam 333 having a beam waist diameter BW (see, e.g., FIG. 19) of 0.9 to 1.3 degrees (or in a range described elsewhere herein) and a wavelength of about 532 run (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 a scattering angle of no more than the first scattering angle al (e.g., from the first scattering angle al or from zero degrees) 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 < 15, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2.5, 2.25, or 2. In some embodiments, 12 / 11 > 0.3, 0.35, 0.4, 0.5, 0.6, 0.7, or 0.8. In some embodiments, Ip 1 / Ip2 < 100, 75, 50, 40, 30, 20, 18, 16, 15, 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 scattering bands, and where Ip2 / Ip3 < 8, 7, 6, 5.5, 5, 4.5, 4, 3.5, 3, 2.8, 2.6, 2.5, 2.4, 2.3, 2.2, 2.1, 2, 1.9, 1.8, 1.7. or 1.6, 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.

[0058] In some embodiments, the scattering intensity at a scattering angle of about 20 degrees is less than a scattering intensity at a scattering angle of about 4 degrees or at the scattering angle Va or a2 by at least a factor of about 4, 5, 6, 8, 10, 12, 15, 20, or 25. It has been found, according to some embodiments, that a substantial fall off in scattering 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 4, 5, 6, 8, 10, 12, 15, 20, or 25 between the second scattering angle (or first valley polar angle) Va and a scattering angle of about 20 degrees. In some embodiments, the scattering distribution function of the optical film along the first scattering direction 444 drops by a factor of at least 4, 5, 6, 8, 10, 12, 15, 20, or 25 between the first valley scattering angle Va and a scattering angle of about 20 degrees.

[0059] 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 scattering peak 171 is located at a scattering angle a2 in a range of about 3 degrees to about 8, 7.5, 7, 6.5, 6, 5.5, or 5 degrees. The scattering angle a2 can be at least about 3.25, 3.5, 3.75, or 4 degrees. In some embodiments, for each pair of adjacent scattering angles in the first through fourth scattering angles, the scattering 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 can generally be determined by the size of the particles 514 and the packing density and irregularity of the arrangement of the particles 514 in the tool used to make the structures of the optical film. 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.

[0060] 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.

[0061] 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.

[0062] 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 scattering distribution function of the optical film along at least a first scattering direction (e.g., x-direction or scattering direction 444) in a first plane (e.g., xz-plane or the plane defined by the scattering direction 444 and the z' -direction in FIG. 8) 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 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 al through a3, where the first scattering angle al is less than about 2 degrees from a normal to the optical film. The scattering distribution function can be substantially azimuthally symmetric so that the normalized (divided by first peak Ip 1) scattering distribution function along the first scattering direction can be substantially the same as the normalized azimuthally averaged intensity distribution. The peak and valley intensities of the scattering 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 scattering distribution function along the first scattering direction is such that Ipl / 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 < 8, 7, 6, 5.5, 5, 4.5. 4, 3.5, 3, 2.8, 2.6, 2.5, 2.4, 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 has a valley intensity Ivl, and where Ipl / Ivl < 180, 170, 160, 150, 140, 120, 100, 90, or 85.

[0063] In some embodiments, the domains 510 (see, e.g., FIG. 5) 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.

[0064] 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.

[0065] 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).

[0066] 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 DI 003- 13 test standard, for example.

[0067] FIG. 10 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 <p I to <p2) so that a ratio of a standard deviation o 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.

[0068] In some embodiments, optical characteristics of the structures and media surrounding the structures (e.g., refractive indices of the first and second layers 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.

[0069] FIG. 11 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 second layer 120 of the optical film can face away from the display panel 680 and the first layer 110 can face the display panel 680, or the first layer 110 of the optical film can face away from the display panel 680 and the second layer 120 can face the display panel 680. The pixels can be arranged at pitches Pl and P2 in respective first and second in-plane directions (x- and y-directions). FIG. 12 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 in a range described elsewhere herein) without substantially reducing an effective resolution of the display (e.g., without reducing effective resolution as characterized by MTF and / or DOI by more than about 45% or in a range described elsewhere herein). The optical film typically reduces the sparkle without generating significant rainbow mura.

[0070] In some embodiments, a display 760 includes a pixelated display surface 681 and an optical film 600 disposed thereon. In some embodiments, the display 760 can include a circular polarizer (e.g., one of 631 and 631'). For example, the display can 760 can be an OLED display which includes a circular polarizer to reduce ambient reflection as is conventional for OLED displays. In some embodiments, the display 760 includes a circular polarizer 631, where the optical film 600 is disposed between the circular polarizer 631 and the display surface 681. In some embodiments, the display 760 includes a circular polarizer 631' disposed between the optical film 600 and the display surface 681. In some embodiments, the display 760 includes an anti-glare layer 633 (e.g., anti-glare cover glass), where the optical film 600 is disposed between the anti-glare layer 633 and the display surface 681. The display 760 may further include other elements commonly included in displays.

[0071] 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. 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, 23, 21, 20, 19, 18, or 17 percent. In some such embodiments, or in other embodiments, the optical film reduces sparkle of the display by at least 15, 18, 20, 22, 24, 26, 28, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, or 43 percent. 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.

[0072] EXAMPLES

[0073] All parts, percentages, ratios, etc. in the Examples and the rest of the specification are by weight, unless noted otherwise. Abbreviations include um = micrometer; scfin = standard cubic feet per minute; and ppm = parts per million. Other standard abbreviations may also be used.

[0074] Sparkle and DOI Measurements

[0075] The sparkle performance of optical films was 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 %. Materials Used in the Examples

[0076] Prepatory Examples PE1-PE3

[0077] Particle formulations A, B and C were prepared according to the following table.

[0078] 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.

[0079] An optical microscope image of the monolayer bead coating of Prepatory Example PEI is shown in FIG. 13.

[0080] 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.

[0081] 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 (Y apel 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.

[0082] 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. 14-15, respectively, as a function of the refractive index of the backfill layer. Sparkle and DOI results for Prepatory Examples PEI - PE3 were roughly comparable to those of CE1 but Prepatory Examples PE1-PE3 did not produce the undesired rainbow mura produced by CE1.

[0083] 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. Prepatory Example PEI with a 1.61 index backfill resulted in an Ip 1 / Ip2 of about 5.

[0084] Prepatory Examples PE4-PE8

[0085] Particle formulation D was prepared according to the following table.

[0086] 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.

[0087] Overcoat / Backfill formulation E was prepared according to the following table. Overcoating / backfill formulations were supplied through a hopper, 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 the bead coated film 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.

[0088] 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.

[0089] 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. 16-17, respectively. A corresponding scatter plot of sparkle decrease versus MTF decrease relative to the display without an anti-sparkle film (“No AS”) is shown in FIG. 18.

[0090] 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. 19. 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. The ratio 12 / 11 was determined where II is an integral over scattering angle of the azimuthally averaged intensity distribution from about zero degrees 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.

[0091] Examples 1-8

[0092] Examples 1-8 are prepared by making samples as in Prepatory Examples P1-P8, respectively. Then a liner with an adhesive layer is attached to the resulting backfill layer and then the bead coating is removed from the backfill layer. The Prepatory Examples P1-P8 can be modified by adding a suitable surfactant in the beaded layer to aid in removing the bead coating from the backfill layer as this has been found to allow the bead coating to be cleanly removed as described further elsewhere herein. Alternatively, or in addition, the Prepatory Examples P1-P8 can be modified by release treating the beaded layer prior to backfilling. The resulting exposed structured surface is then backfilled with a second backfill resin (e.g., corresponding to layer 120 schematically illustrated in FIG. 4C). The resulting film has a similar scattering intensity distribution, sparkle reduction, and DOI as the respective Prepatory Examples PE1-PE8 when the second backfill resin has a similar refractive index as the bead coating (e.g., PMMA resin will have a substantially same refractive index as PMMA beads).

[0093] Example 9

[0094] A beaded coating was made by first dispersing acrylic beads (SSX-108) in a mixture of solvent and UV-curable monomer and photoinitiator as indicated in the following table.

[0095] The coating solution was 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 (Viking EO2). The flow rate supplied to the coating head was controlled by setting the gear pump speed. The flow rate was measured by a micromotion mass flow meter. The flow rate was about 5.09 g / min per inch width (2.0 g / min / cm) and the web speed was about 40 ft / min (12.2 m / min). The solution was filtered through a filtration system. A recirculation loop was used to recycle the coating solution to the hopper when not coating. The filtered coating solution was fed to a slot die where it was coated onto a 2 mil (50.8 micrometers) PET substrate that was supported by a back-up roll. The solvent was then removed in a conventional oven with three ten-foot (3.05 m) zones utilizing air foil nozzles under the web for some samples, or 2 fifteen-foot (4.57 m) zones utilizing air foil nozzles under the web for other samples. Typical temperature set points for Zones 1, 2, and 3 when three zones were used were 220, 160, and 140 degrees Fahrenheit (104, 71.1, 60 degrees C), respectively. A final cure step was then used to complete the cure of the coating using an inerted Fusion UV Systems curing system (VPS / I600 Gaithersburg, MD) with an H-bulb against a chilled roll to prevent web distortion. The coated product was then wound onto a core at one pound per lineal inch tension. Substantially monolayer bead coatings with 8um, PMMA diameter beads were made with at or near hemisphere bead exposure based on bead / monomer ratio.

[0096] Bead coatings were then overcoated / backfilled with a second formulation. For die coating, an acrylic resin similar to R1 and having a refractive index of about 1.65 was diluted in solvent and a surfactant BYK 3505 was added to aide in wetting of the bead coating and to aid in release of the bead coating from the resulting cured resin layer. The components of the second formulation are provided in the following table.

[0097] The coating solution was supplied through a hopper to a gear pump (Viking EO2). Flow rate supplied to the coating head was controlled by setting the gear pump speed a and was measured by a micromotion mass flow meter. The solution is filtered through a filtration system). A recirculation loop was used to recycle the coating solution to the hopper when not coating. The filtered coating solution is fed to a slot die where it was coated onto the bead coating on PET. The solvent was then removed in a conventional oven with three ten-foot (3.05 m) zones utilizing air foil nozzles under the web, or 2 fifteen-foot (4.57 m) zones utilizing air foil nozzles under the web. For samples made using three zones, the temperature set points for Zones 1, 2, and 3 were 120, 140, and 160 degrees Fahrenheit (48.9, 60, 71.1 degrees C), respectively. A final cure step was then used to complete the cure of the coating using an inerted Fusion UV Systems curing unit (VPS / I600 Gaithersburg, MD) with an H-bulb against a chilled roll to prevent web distortion. The coated product was then wound onto a core at one pound per lineal inch tension. The pump setting was 4.27 g / min per inch width (1.68 g / min / cm) and the web speed was 20 ft / min (6.1 m / min). On planar film, the pump setting produced a lOum thick coating.

[0098] CEF18 optically clear adhesive was then hand laminated to a section of the cured overcoat and the bead coating was separated from the overcoat. The beaded layer was removed leaving the imprint of the beads in the cured overcoat layer.

[0099] The overcoat can then be backfilled with another resin to provide an optical film as schematically depicted in FIG. 1, for example.

[0100] 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.

[0101] Terms such as “substantially” 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 “substantially” with reference to a property or characteristic 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 and when it would be clear to one of ordinary skill in the art what is meant by an opposite of that property or characteristic, the term “substantially” will be understood to mean that the property or characteristic is exhibited to a greater extent than the opposite of that property or characteristic is exhibited.

[0102] 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.

[0103] 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 stack comprising: an optical film comprising first and second layers, each of the first and second layers having a structured first major surface and an opposite second major surface, the structured first major surfaces of the first and second layers disposed on and substantially conforming to one another, such that for each of the first and second layers: the second major surface is not directly fixedly attached to any other layer or is directly fixedly attached to a room-temperature adhesive layer substantially coextensive with the second major surface; and the structured first major surface comprises a plurality of irregularly arranged and substantially tightly packed domains, each of the domains comprising a plurality of substantially regularly arranged structures, the structures having an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, such that for substantially normally incident light in a visible wavelength range, a scattering distribution function of the optical film is substantially azimuthally symmetric, wherein the optical film is configured to reduce sparkle of a display system having a pixel spatial frequency by at least 15 percent without decreasing a modulation transfer function of the display system at the pixel spatial frequency by more than about 45 percent.

2. The optical stack of claim 1, wherein the first and second layers comprise respective first and second radiation-cured layers.

3. The optical stack of claim 1 further comprising a first optically clear adhesive layer disposed on the second major surface of the first layer.

4. The optical stack of claim 3, wherein the first optically clear adhesive layer is releasably attached to the second major surface of the first layer.

5. The optical stack of claim 1 further comprising a second optically clear adhesive layer disposed on the second major surface of the second layer.

6. The optical stack of claim 5, wherein the second optically clear adhesive layer is releasably attached to the second major surface of the second layer.

7. The optical stack of claim 1, 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 run, an azimuthally averaged intensity distribution of light transmitted by the optical stack as a function ofscatering angle measured from a normal to the optical stack comprises first and second scatering bands having respective first and second scatering peaks and a valley disposed therebetween, the first and second scatering peaks having corresponding first and second peak intensities Ip 1 and Ip2, the valley having a corresponding valley intensity Ivl, the first scatering peak located at a first scatering angle less than about 2 degrees, the valley located at a second scatering angle greater than the first scatering angle and less than about 6 degrees, wherein Ip2 / Ivl < 15.

8. An optical stack comprising: an optical film comprising first and second layers, each of the first and second layers having a structured first major surface and an opposite second major surface, the structured first major surfaces of the first and second layers disposed on and substantially conforming to one another, such that the second major surface of the first layer is not directly fixedly atached to any other layer or is directly fixedly atached to a room-temperature adhesive layer substantially coextensive with the second major surface of the first layer, the second layer being an adhesive layer, the structured first major surface of each of the first and second layers comprising a plurality of irregularly arranged and substantially tightly packed domains, each of the domains comprising a plurality of substantially regularly arranged structures, the structures having an average in-plane diameter in a range from about 4 micrometers to about 15 micrometers, such that for substantially normally incident light in a visible wavelength range, a scatering distribution function of the optical film is substantially azimuthally symmetric, wherein the optical film is configured to reduce sparkle of a display system having a pixel spatial frequency by at least 15 percent without decreasing a modulation transfer function of the display system at the pixel spatial frequency by more than about 45 percent.

9. The optical stack of claim 8, wherein the first layer comprises a radiation-cured polymer.

10. The optical stack of claim 8 further comprising a release liner, the second major surface of the second layer releasably atached to a release surface of the release liner.

11. The optical stack of claim 8 further comprising an optically clear adhesive layer fixedly atached to the second major surface of the first layer.

12. The optical stack of claim 11 further comprising first and second release liners, the optically clear adhesive layer releasably atached to the first release liner, the second layer releasably atached to the second release liner, such that the first and second release liners have respective higher and lower peel forces from the optical stack.

13. The optical stack of claim 8, 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 stack as a function of scattering angle measured from a normal to the optical stack 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 Ip 1 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, wherein Ip2 / Ivl < 15.

14. The optical stack of claim 8, 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 stack as a function of scattering angle measured from a normal to the optical stack 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, the first scattering angle al less than about 2 degrees from the normal to the optical stack, 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.

15. The optical stack of claim 8, 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 stack along at least a first scattering direction in a first plane substantially perpendicular to the optical stack comprises first through third scattering bands having respective first through third scattering peaks having respective first through third peak intensities Ipl, 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 stack, wherein:Ip 1 / Ip2 < 100; andIp2 / Ip3 < 6.

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