Display system having finger sensing

Abstract

A display system for detecting a user's finger applied to a display panel includes a sensor for detecting the finger, a sensing light source configured to emit first light having a first wavelength W1, and a reflective polarizer disposed between the display panel and the sensor. For substantially normally incident light, the optical transmittance versus wavelength of the reflective polarizer in a first polarization state has a band edge, and in a first wavelength range (30 nm≦L2−L1≦50 nm) that spans from a short wavelength L1 to a long wavelength L2 and includes W1, the optical transmittance averages greater than about 75% when L1 is greater than and within about 20 nm of a wavelength L3 that corresponds to about 50% optical transmittance at the band edge.

Description

Background Art

[0001] A liquid crystal display (LCD) can include a reflective polarizer between the LCD panel and the optical waveguide.

Summary of the Invention

[0002] The present disclosure generally relates to a display system configured to sense a user's finger applied to the display system.

[0003] In some aspects of the present specification, a display system for sensing a user's finger applied to the display system is provided. The display system includes a display panel configured to generate an image for a user to view, a sensor for sensing a user's finger disposed in proximity to the display panel, a sensing light source configured to emit first light having a first wavelength W1 toward the user's finger, and a reflective polarizer disposed between the display panel and the sensor. The sensor is configured to receive and detect at least a portion of the first light reflected by the finger. The reflective polarizer includes a plurality of polymer layers that total at least 50, and for substantially normal incident light, the light transmittance of the reflective polarizer in the first polarization state versus wavelength includes a band edge, and the best linear fit to the band edge correlating the light transmittance to wavelength over a wavelength range where the light transmittance increases from about 10% to at least about 70% at the band edge has a slope greater than about 2.5% / nm, extends from a short wavelength L1 to a long wavelength L2, and for a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) including W1, L1 is greater than a wavelength L3 corresponding to a light transmittance of about 50% at the band edge and within about 20 nm from L3, and has an average light transmittance of greater than about 75%.

[0004] In some aspects of the present specification, a display system for sensing a user's finger applied to the display system is provided. The display system includes a display panel configured to generate an image for a user to view, a sensor for sensing a user's finger disposed proximate to the display panel, a sensing light source, a reflective polarizer disposed between the display panel and the sensor, and a light guide disposed between the reflective polarizer and the sensor, and an optical mirror disposed between the light guide and the sensor, and an array of individual spaced-apart optical ridges formed on the optical mirror, and a structured mirror facing the light guide. The reflective polarizer includes a plurality of polymer layers and may further include a first outer layer coextruded with the plurality of polymer layers. The reflective polarizer has an average particle size of about 7 to about 9 micrometers and includes a plurality of first particles partially protruding from a first major surface of the first outer layer to form a first structured major surface, and a first light diffusing layer disposed to conform to the first structured major surface. Opposing first and second major surfaces of the first light diffusing layer substantially conform to the first structured major surface. The first optical diffusing layer includes a plurality of nanoparticles dispersed therein, and the nanoparticles may define a plurality of voids therebetween. The reflective polarizer may further include a second outer layer on the opposite side of the first outer layer, and the second outer layer is coextruded with the plurality of polymer layers and the first outer layer. The reflective polarizer may include a plurality of second particles partially protruding from a second major surface of the second outer layer to form a second structured major surface.

[0005] In some aspects of the present specification, a display system for sensing a user's finger applied to the display system is provided. The display system includes a display panel configured to generate an image for a user to view, a sensor for sensing a user's finger disposed proximate to the display panel, a sensing light source, a reflective polarizer disposed between the display panel and the sensor, a light guide that provides illumination to the display panel and is disposed between the reflective polarizer and the sensor, and an optical mirror disposed between the light guide and the sensor, and an array of individual spaced-apart optical ridges formed on the optical mirror, and a structured mirror facing the light guide.

[0006] These and other aspects will become apparent from the following detailed description. However, in no event should this brief summary be construed as limiting the subject matter of the claims.

Brief Description of the Drawings

[0007]

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Mode for Carrying Out the Invention

[0008] In the following description, reference is made to the accompanying drawings which form a part of this specification and in which various embodiments are shown by way of example. The drawings are not necessarily to scale. It should be understood that other embodiments may be contemplated and may be practiced without departing from the scope or spirit of this specification. Accordingly, the following mode for carrying out the invention is not to be construed in a limiting sense.

[0009] According to some embodiments, a display system for sensing a user's finger applied to the display system includes a reflective polarizer and a sensing light source configured to emit a first light having a first wavelength W1 toward the user's finger (e.g., an infrared light source used for finger sensing). The reflective polarizer can be configured such that for substantially normal incident light, the first wavelength exceeds but is close to the band-edge wavelength (e.g., within about 70 nm, or within about 50 nm, or within about 40 nm). In some embodiments, the light transmittance of the reflective polarizer versus wavelength in the first polarization state includes the band-edge, extends from a short wavelength L1 to a long wavelength L2, and for a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) including W1, when L1 is longer than a wavelength L3 corresponding to a light transmittance of about 50% at the band-edge and within about 20 nm from L3, has an average light transmittance greater than about 75%. In some embodiments, the light transmittance has a maximum value within about 60 nm of the wavelength L2, and the first wavelength W1 is within about 30 nm or within about 20 nm of the local maximum. In some embodiments, the reflective polarizer includes a packet of polymer layers including a first portion having a layer thickness profile that generally increases with a first gradient, and a second portion adjacent to the first portion and having a layer thickness profile that generally decreases with a second gradient having a magnitude substantially larger than the first gradient.

[0010] According to some embodiments, the display system includes at least one optical diffusion layer. For example, the reflective polarizer can have a structured outer surface and includes a first optical diffusion layer disposed on and conforming to the structured outer surface. The display system can optionally further include an optical diffusion film including a second optical diffusion layer. The optical diffusion layer (e.g., at least one of the first and second optical diffusion layers) can include particles dispersed to form aggregates of particles having voids (gaps) therebetween. In some embodiments, the optical diffusion layer provides a substantially high degree of normal transmittance in the infrared range rather than in the visible range. Alternatively or additionally, according to some embodiments, the optical diffusion layer can provide a substantially higher degree of diffusive transmittance in the visible range rather than in the infrared range. In some embodiments, the particles are nanoparticles and the aggregates have an average particle size of less than about 1 micron. In other embodiments, the aggregates can be larger (e.g., up to about 10 microns, or from about 1 micron to about 10 microns, or from about 5 microns to about 10 microns).

[0011] According to an embodiment, a plurality of spaced-apart elongated structures are disposed on the optical layer (e.g., on the side of the optical diffusion film opposite the reflective polarizer), can impart a surface roughness that reduces the coefficient of friction and eliminates or reduces damage to adjacent films, and can prevent optical defects (e.g., wet-out, moiré patterns, Newton's rings, and similar effects) between adjacent films. In some cases, these elongated structures may be printed on the optical film or may be fabricated and disposed by another process (e.g., microreplication).

[0012] In some embodiments, the display system further includes a structured mirror that includes a discontinuous coating on the surface of the optical mirror. The discontinuous coating can impart a surface roughness that reduces the coefficient of friction and eliminates or reduces damage to adjacent films. In some embodiments, the discontinuous coating may be substantially transmissive to near-infrared wavelengths, enabling an infrared sensor function behind the LCD panel. In some embodiments, the discontinuous coating may include individual raised features such as rounded ridges. In some embodiments, the individual features may be added to the optical mirror using techniques such as flexographic printing (or similar printing processes). In some embodiments, other techniques or processes may be used to add the individual features to the optical mirror.

[0013] Figures 1 and 2 are schematic cross-sectional views of reflective polarizers 100 and 100', respectively, according to some embodiments. Reflective polarizers 100, 100' include a plurality of polymer layers 10, 11 disposed along at least a portion of the thickness of the reflective polarizer (along the z direction with reference to the illustrated x-y-z coordinate system). Each of the polymer layers 10, 11 has an average thickness t that can be less than about 350 nm or less than about 300 nm.

[0014] The number of polymer layers 10, 11 within reflective polarizer 100 or 100' can be substantially greater than that schematically shown in Figures 1 and 2. For example, the plurality of polymer layers 10, 11 can include a total of 50 to 1000 layers or 100 to 800 layers. In some embodiments, the plurality of polymer layers 10, 11 includes more than about 100 layers, or more than about 150 layers, or more than about 200 layers.

[0015] The reflective polarizers 100, 100' each include outermost layers 146 and 147 having thicknesses ta and tb, respectively. Each of the thicknesses ta, tb can be, for example, greater than about 500 nm, or greater than about 1 micrometer, or greater than about 2 micrometers, or greater than about 3 micrometers, or greater than about 5 micrometers. The thicknesses of the outer layers 146 and 147 can affect the transmission spectrum of the reflective polarizer due to the light reflected from the surfaces of the layers 146 and 147 that can undergo optical interference with the light reflected from other layers. In the case of the reflective polarizer 100', the plurality of polymer layers 10, 11 include a first plurality of polymer layers (141) and a second plurality of polymer layers (142), and the first and second pluralities of polymer layers are separated from each other along the thickness of the reflective polarizer by at least one intermediate layer 143a, 143b, and each of the intermediate layers 143a, 143b has an average thickness tc that is, for example, greater than about 500 nm, or greater than about 1 micrometer, or greater than about 2 micrometers, or greater than about 3 micrometers, or greater than about 5 micrometers. The at least one intermediate layer 143a, 143b can be, for example, two protective boundary layers, or a single layer formed from two protective boundary layers. As is known in the art, protective boundary layers are often included adjacent to packets of alternating interference layers to protect the interference layers from damage during processing. The outermost layer 146 and / or 147 can be, for example, a protective boundary layer or a combination of a protective boundary layer and an additional outer skin layer.

[0016] In some embodiments, the plurality of polymer layers 10, 11 are disposed along at least a portion of the thickness of the reflective polarizers 100, 100' and include a plurality of first polymer layers sequentially numbered from 1 to N (e.g., each of the layers 10, 11 of the first plurality of layers 141 of the reflective polarizer 100' or the layers 10, 11 of the reflective polarizer 100), where N is an integer greater than about 150. The plurality of first polymer layers include polymer end layers 665, 667 at both ends thereof. Each of the polymer end layers and the layers therebetween can have an average thickness of less than about 350 nm or less than about 300 nm. In some embodiments, the plurality of polymer layers 10, 11 further include a plurality of second polymer layers (e.g., the layers 10, 11 of the second plurality of layers 142 of the reflective polarizer 100') spaced apart from the plurality of first polymer layers along the thickness direction of the reflective polarizer 100' by one or more intermediate layers 143a, 143b, each of the plurality of first and second polymer layers has an average thickness of less than about 350 nm or less than about 300 nm, and each of the one or more intermediate layers has an average thickness of greater than about 500 nm. In some embodiments, the total layer numbers of each of the plurality of first and second polymer layers are at least 150 in total, or at least 200 in total.

[0017] The plurality of polymer layers 10, 11 can include alternating first and second polymer layers 10 and 11 that can be referred to as an interference layer. The interference layer may be described as mainly reflecting and transmitting light by optical interference if the reflectance and transmittance of the interference layer can be reasonably explained by optical interference or can be reasonably and accurately modeled as a result of optical interference. As is known in the art, by using a multilayer optical film (e.g., a reflective polarizer film) including alternately arranged polymer layers and suitably selecting the layer thickness, desired reflectance and transmittance in a desired wavelength range can be achieved. Multilayer optical films and methods of making multilayer optical films are described, for example, in U.S. Patent Nos. 5,882,774 (Jonza et al.), 6,179,948 (Merrill et al.), 6,783,349 (Neavin et al.), 6,967,778 (Wheatley et al.), and 9,162,406 (Neavin et al.). In some embodiments, the optical filter has sharp band edges. Optical films having sharp band edges are known in the art and are described, for example, in U.S. Patent No. 6,967,778 (Wheatley et al.).

[0018] As further described elsewhere in this specification, the transmittance and reflectivity of the reflective polarizers 100, 100' can be specified for light 40 that is incident substantially perpendicularly (e.g., nominally perpendicularly, or incident within 30 degrees, or within 20 degrees, or within 10 degrees) and / or for light 170 having an incident angle θ, and can also be specified for the first and / or second polarization states (e.g., the first and second polarization states 171 and 172). The electric field is polarized along the y-axis in the first polarization state 171 and along the x-axis in the second polarization state 172 in the illustrated embodiment. The passing (respectively blocking) polarization state of the reflective polarizer can be a p-polarization state (p-pol) or an s-polarization state (s-pol) involving the projection of the electric field onto the plane of the reflective polarizer (x-y plane) that is parallel to the passing (respectively blocking) axis of the reflective polarizer. In some embodiments, regardless of the plane of incidence, the first polarization state 171 is the blocking state of the reflective polarizer and the second polarization state 172 is the passing state of the reflective polarizer. A portion of the incident light 40, 170 (e.g., light 270) is typically reflected and a portion (e.g., light 470) is typically transmitted. In some embodiments, for the second polarization state 172 (and / or the passing polarization state) and the first wavelength range, the reflective polarizer has a greater average light transmittance for light incident at a smaller incident angle (e.g., light 40) and a smaller average light transmittance for light incident at a larger incident angle (e.g., light 170). Such a reflective polarizer can be referred to as a collimating reflective polarizer because when the reflective polarizer is included in a recycling backlight, a portion of the light in the passing polarization state incident at an oblique angle is reflected by the reflective polarizer and then recycled and ultimately transmitted when it is incident on the reflective polarizer at a smaller incident angle. Collimating reflective polarizers are known in the art and are described, for example, in U.S. Patent Nos. 9,441,809 (Nevitt et al.) and 9,551,818 (Weber et al.).

[0019] In some embodiments, the reflective polarizer 100 or 100' is an infrared-transmissive reflective polarizer. For example, the reflective polarizer can transmit more than about 60% (or more than about 70%, or more than about 75%, or more than about 80%) of the substantially vertically incident light 40 within a wavelength range of about 950 nm to about 1200 nm or about 950 nm to about 1300 nm for each of the orthogonal first and second polarization states 171 and 172.

[0020] The light 40 (or 170) can be incident on either side of the reflective polarizers 100, 100' (e.g., along the -z direction as schematically shown in FIG. 1 or along the +z direction as schematically shown in FIG. 3A). Similarly, the incident light shown in other figures can also be incident from either side of the illustrated optical elements.

[0021] Figure 3A is a schematic cross-sectional view of a reflective polarizer 200 according to some embodiments. The reflective polarizer includes a plurality of layers 14 (the individual layers are not shown in the schematic view of Figure 3A. See, for example, Figures 1-2). The reflective polarizer 200 generally corresponds to the reflective polarizer 100 or 100' except that the reflective polarizer 200 includes first and second outer layers 20 and 50 each containing particles 23 and 53, respectively, and otherwise may correspond to layers 146 and 147. In some embodiments, the reflective polarizer 200 includes a plurality of first particles 23 that partially protrude from the first major surface 21' of the first outer layer 20 to form a first structured major surface 21. The plurality of polymer layers 14 can be co-extruded with the first outer layer 20. In some embodiments, the second outer layer 50 is co-extruded with the plurality of polymer layers 14 and the first outer layer 20. In some embodiments, the reflective polarizer 200 includes a plurality of second particles 53 that partially protrude from the second major surface 51' of the second outer layer 50 to form a second structured major surface 51. In some embodiments, the first particles 23 have an average particle size of about 7 to about 9 microns. It has been found that undesirable optical effects can occur when a reflective or partially reflective film (e.g., another reflective polarizer) is placed on a reflective polarizer having a structured surface. It has been found that selecting the average particle size of the first particles in the range of about 7 to about 9 microns substantially reduces or eliminates these undesirable optical effects. In some embodiments, the second particles may also have an average particle size of about 7 to 9 microns. In other embodiments, the second structured surface 51 is typically arranged to face a diffuser rather than, for example, a film with a higher reflectivity (see, for example, Figures 21-23), so the average particle sizes of the second particles 53 and the first particles 23 are in different ranges. In some embodiments, the second particles 53 have an average particle size smaller than the average particle size of the first particles 23. In some embodiments, the second particles 53 have an average particle size of less than about 6 microns, or the average particle size can be, for example, in the range of about 1 micron or about 2 microns to about 6 microns. In some embodiments, the second particles 53 have an average particle size approximately the same as (e.g., within 10% or within 5%) the average particle size of the first particles 23.In some embodiments, the second particles 53 have an average particle size larger than the average particle size of the first particles 23. In some embodiments, the second particles 53 have an average particle size greater than about 3 microns, or greater than about 5 microns, or greater than about 10 microns, or greater than about 15 microns. In some embodiments, the second particles have an average particle size, for example, in the range of about 3 microns to about 20 microns.

[0022] In some embodiments, the second outer layer 50 includes a plurality of particles 53 that are partially recessed therein to form the second structured major surface 51. In some embodiments, the first outer layer 20 includes a plurality of particles 23 that are partially recessed therein to form the first structured major surface 21. Related reflective polarizers having a structured outer major surface are described in U.S. Provisional Application No. 63 / 021765, entitled "REFLECTIVE POLARIZER WITH IMPROVED OPTICAL CHARACTERISTICS," filed on May 8, 2020, and are incorporated herein by reference in a manner not inconsistent with the present specification.

[0023] Particles can be applied by coating onto the outermost major surface of a cast web, the coating dried, and the cast web stretched (e.g., by uniaxially or biaxially stretching the film) to form an optical film. As a result, the particles partially sink into the outer layer of the film, such that the particles are fixed on the surface and can protrude partially from the major surface of the outer layer. The coating can optionally be applied during sequential stretching in a sequential stretching process to vary the elastic modulus / thickness of the outermost layer, which can affect the particles that partially sink into the outermost layer. FIG. 3B is a scanning electron microscope (SEM) image of a cross-section of a portion of a multilayer optical film reflective polarizer showing particles 53 that protrude partially from the major surface of the outer layer 50 of the reflective polarizer to form a structured major surface. FIG. 3C is an SEM image of a cross-section of a portion of a multilayer optical film reflective polarizer showing particles 23 that protrude partially from the major surface of the outer layer 20 of the reflective polarizer to form a structured major surface. The reflective polarizer includes an optical diffusive layer 30 that substantially conforms to the structured major surface. Even when a continuous portion of the outer layer (e.g., a continuous polymer phase) is coextruded with a plurality of polymer layers and particles or other components (e.g., polymers from a particle coating) are added to the outer layer thereafter (after coextrusion), the layer exhibits the characteristics of the coextruded layer (e.g., binds to adjacent layers without an adhesive), and thus the outer layer of the film can be described as being coextruded with the plurality of polymer layers of the film. For example, the outer layer coextruded with polymer layers 11, 12 may be described as containing particles that have partially sunk into the outer layer, and may be described as being coextruded with polymer layers 11, 12 even if the particles partially sank into the layer after the outer layer was first formed by coextrusion with polymer layers 11, 12. The particles can be surface-coated particles where the surface coating on the particles is formed from a polymer from the mixture used to coat the particles onto the outer layer. In some embodiments, the mixture containing the particles includes a polyester (e.g., the mixture can be an aqueous mixture containing a water-soluble polyester), and in some embodiments, the coextruded outer layer includes a polyester.In some such embodiments, this provides a close refractive index match between the coating polyester and the coextruded skin layer, and the coated polyester can be stretched under conditions similar to those of the coextruded web. Also, the coated polyester can be compatible with the coated optical diffusing layer.

[0024] Alternatively, instead of describing the coextruded skin layer as including particles added after coextrusion, the reflective polarizer can be described as including particles that partially protrude from the major surface of the coextruded layer.

[0025] In other embodiments, the particles are included in one of the first and second skin layers but not the other, forming the respective major surfaces. For example, the structured surface can be formed by embossing, casting and curing, or other techniques that do not utilize particles for the structure.

[0026] The first structured major surface 21 faces away from the plurality of polymer layers 14. The optical diffuser layer 30 is disposed to conform to the first structured major surface 21 of the outer layer 20, such that the opposing first and second major surfaces 31 and 32 of the optical diffuser layer 30 substantially conform to the first structured major surface 21. For example, the first and second major surfaces 31 and 32 can conform to the first structured major surface 21, or can nominally conform to the first structured major surface 21, or can conform to the first structured major surface 21 within a slight variation (e.g., less than about 30%, or less than about 20%, or less than about 10% of the height of the structure or the average particle size of the particles 23) of the height of the structure of the structured major surface 21. In some embodiments, the first and second major surfaces 31 and 32 define an average spacing S of from about 200 to about 5000 nm therebetween. In some embodiments, the average spacing S is from about 200 nm to about 2000 nm, or from about 200 nm to about 1500 nm, or from about 300 nm to about 1200 nm. The reflection and transmission characteristics of the reflective polarizer 100 can be described for substantially normal incident light 40 (e.g., nominally normal, or light incident within 30 degrees, or within 20 degrees, or within 10 degrees of the normal (z-direction) to the x-y plane when the optical structure extends in the x-y plane and has a thickness in the z-direction), as further described elsewhere.

[0027] FIG. 4A is a schematic cross-sectional view of an optical diffusion layer 30 according to some embodiments. The optical diffusion layer 30 schematically shown in FIG. 4A can be, for example, a part of the optical diffusion layer 30 schematically shown in FIG. 3A. FIG. 4B is a scanning electron microscope (SEM) image of an exemplary optical diffusion layer 30. The optical diffusion layer 30 includes a plurality of nanoparticles 33 dispersed between a first major surface 31 and a second major surface 32 of the optical diffusion layer 30. The nanoparticles can have an average particle size of about 10 nm to about 150 nm or about 20 nm to about 150 nm, and define a plurality of voids 34 therebetween. In some embodiments, the nanoparticles 33 in the optical diffusion layer 30 aggregate to form a plurality of nanoparticle aggregates 35 having an average particle size of about 100 nm to about 10 microns or about 100 nm to about 1000 nm. In other embodiments, the aggregates may be larger (e.g., up to about 10 microns, or about 1 micron to about 10 microns, or about 5 microns to about 10 microns). In some embodiments, the polymer material 36 can bind the nanoparticles 33 to each other to form a plurality of nanoparticle aggregates 35 that define voids 34 therebetween. In some embodiments, in a plane (e.g., the x-z plane) of a cross-section of the optical diffusion layer 30 in the thickness direction (e.g., the z direction) of the optical diffusion layer 30, the voids 34 occupy about 5% to about 50% of the area of the plane of the cross-section. In some embodiments, the voids 34 occupy about 5% to about 45% or about 40% of the area of the plane of the cross-section. In some embodiments, the voids 34 occupy about 10% or about 15% to about 50%, or about 45%, or about 40% of the area of the plane of the cross-section.

[0028] In some embodiments, the optical diffusion layer 30 is formed by coating a mixture of particles, monomers, and a solvent, and then curing and drying the mixture. The monomers cure to form a polymer binder (polymer material 36), binding the aggregates of particles together, and the solvent evaporates to form voids between the aggregates. The solvent can evaporate at least partially during curing and / or the subsequent drying process can be used to complete the evaporation of the solvent. In some embodiments, curing and drying include a pre-curing process, then a drying process, and then a post-curing process. In some embodiments, the monomers are ultraviolet (UV) curable and a photoinitiator is included in the mixture. The size of the aggregates can be adjusted by varying the UV output used to cure the monomers, and generally, the higher the output, the smaller the aggregate size. It has been found that a relatively small amount of photoinitiator with a relatively high UV output results in a small aggregate size and a non-fragile layer, while a relatively large amount of photoinitiator can result in a fragile layer. The void fraction can be adjusted by varying the amount of solvent used in the mixture, and generally, the higher the solvent loading, the higher the void fraction. In some embodiments, the mixture contains about 20 to about 60 wt% solids.

[0029] In some embodiments, the polymer material 36 is or includes a radiation-curable (e.g., UV-curable) polymer. In some embodiments, the polymer material 36 is or includes an acrylate. In some embodiments, the polymer material 36 is or includes pentaerythritol triacrylate.

[0030] The average particle size of the nanoparticles 33 or other particles described herein can be the average or median size. For example, the average particle size can be the Dv50 size (the median size in the volume distribution, or equivalently, the particle size provided by particles having a size such that 50 percent of the total volume of the particles is below the Dv50 size). In some embodiments, the nanoparticles 33 have an average particle size in the range of from about 20 nm to about 150 nm, or from about 30 nm to about 120 nm, or from about 30 nm to about 100 nm, or from about 50 nm to about 90 nm, or from about 60 nm to about 90 nm. In some embodiments, the nanoparticles 33 are silica or contain silica.

[0031] The percentage of the cross-sectional area occupied by the voids 34 can be determined using image analysis techniques. For example, the optical diffusion layer can be cut by a microtome, then a scanning electron microscope (SEM) image of the cross-section can be taken, and then the image can be analyzed using image analysis software to determine the percentage of the area occupied by the voids. The average particle size of the aggregates can also be determined from the analysis of the image. The particle size of the aggregates in the cross-section can be the equivalent circular diameter of the aggregates (i.e., the diameter of a circle having the same area as the aggregates in the cross-section).

[0032] The particles 23 can have an average particle size (e.g., diameter) that is at least about 2, 3, 5, 10, 20, or 50 times the average particle size of the particle aggregates 35.

[0033] The related optical diffusive layer is described in U.S. Provisional Application No. 63 / 021751, entitled "OPTICAL FILMS AND STACKS INCLUDING OPTICALLY DIFFUSIVE LAYER", filed on May 8, 2020, and is incorporated herein by reference to the extent not inconsistent with the present specification. The reflective polarizer including the related optical diffusive layer is described in U.S. Provisional Application No. 62 / 704399, entitled "OPTICAL CONSTRUCTION AND DISPLAY SYSTEM INCLUDING SAME", filed on May 8, 2020, and is incorporated herein by reference to the extent not inconsistent with the present specification.

[0034] In some embodiments, the display system includes a reflective polarizer and a sensor for sensing a user's finger disposed proximate to the display panel, and optionally may further include an optical diffusive film disposed between the reflective polarizer and the sensor.

[0035] FIG. 5A is a schematic cross-sectional view of an optical diffusive film 300 according to some embodiments. FIG. 5B is a schematic plan view of a major surface 131 of the optical diffusive film 300 according to some embodiments. The optical diffusive film 300 includes an optical substrate layer 110 having a first major surface 111 and a second major surface 112, and an optical layer 130 disposed on the second major surface 112 of the optical substrate layer 110. In some embodiments, an adhesive layer 133 may be disposed between the optical layer 130 and the optical substrate layer 110. Alternatively, the optical layer 130 may be formed directly on the optical substrate layer 110, and the adhesive layer 133 may be omitted. In some embodiments, the optical layer 130 includes a structured major surface 131 and an unstructured major surface 132. In some embodiments, the structured major surface 131 faces away from the optical substrate layer 110 and includes a plurality of spaced-apart elongated structures 140.

[0036] In some embodiments, the elongated structure 140 may extend along the same first direction (e.g., the x direction as shown in FIG. 5A) and be arranged with a substantially uniform density across the structured main surface 131 (e.g., as shown in FIG. 5B). In some embodiments, the optical diffusion film 300 further includes an optical diffusion layer 120 disposed on the first main surface 111 of the optical substrate layer 110. In some embodiments, an adhesive layer 133' is disposed between the optical diffusion layer 120 and the optical substrate layer 110. Alternatively, the optical diffusion layer 120 may be formed directly on the optical substrate layer 110, and the adhesive layer 133' may be omitted.

[0037] In some embodiments, the optical diffusion layer 120 includes a plurality of nanoparticles 121 dispersed therein. In some embodiments, the nanoparticles 121 have an average particle size of about 10 nm to about 300 nm. In some embodiments, the nanoparticles 121 include silica (e.g., the nanoparticles 121 can be silica nanoparticles) and can provide diffusion (scattering effect) for at least some wavelengths of light. The optical diffusion layer 120 may be the same as that described for the optical diffusion layer 30. For example, in some embodiments, the optical diffusion layer 120 includes a polymer material (e.g., corresponding to the polymer material 36) that binds the nanoparticles of the optical diffusion layer 120 to each other to form a plurality of nanoparticle aggregates (e.g., corresponding to the aggregates 35) that define a plurality of voids (e.g., corresponding to the voids 34) therebetween. In some embodiments, in the plane of the cross-section of the optical diffusion layer 120 in the thickness direction of the optical diffusion layer 120, the nanoparticles 121 of the optical diffusion layer 120 have an average particle size of about 20 nm to about 150 nm, the average particle size of the nanoparticle aggregates is in the range of about 100 nm to about 10 microns, and the voids occupy about 5% to about 50% or about 15% to about 45% of the area of the plane of the cross-section, or any range described elsewhere.

[0038] The elongated structures 140 may be arranged in an irregular random pattern or, optionally, in a regular array or pattern. In some embodiments, the elongated structures 140 extend (i.e., have a longest dimension) along a first direction such as the x-axis shown in FIGS. 5A-5B and are arranged along a second, orthogonal direction such as the y-axis shown in FIGS. 5A-5B. The assignment of the coordinate / reference system shown in FIGS. 5A-5B (i.e., the x-direction, y-direction, and z-direction) is for illustrative purposes only, and other reference systems and configurations may be used while remaining consistent with the present disclosure. In some embodiments, the elongated structures 140 have an average length (e.g., La) along the first direction and an average width (e.g., Lb) along a second, orthogonal direction (e.g., the y-direction), and the average length is at least about 2 times or at least about 2.5 times the average width. The second is orthogonal to the first direction and orthogonal to the thickness direction (z-direction). In some embodiments, the elongated structures 140 have an average peak height H of from about 2 microns to about 7 microns or from about 3 microns to about 6.5 microns. The elongated structures 140 can be formed, for example, using a high-definition process (a process used to generate microstructures such as casting and curing processes known in the art).

[0039] In some embodiments, the optical structure includes a reflective polarizer 100, 100', or 200 disposed on the optical diffuser film 300. The optical structure can be used in a display system, as further described elsewhere.

[0040] Figures 6A - 6B are schematic cross - sectional views of layer or film 150 and layer or film 150', respectively, with light 40a and 40b incident substantially perpendicularly to the layer or film. Layer or film 150 may correspond to, for example, any of the optical diffusion layers or optical diffusion films or reflective polarizers or optical structures described herein. Layer or film 150' can correspond to, for example, any of the substrate layers or optical layers described herein. Light 40a has a wavelength in the range of λ1 - λ2, and light 40b has a wavelength in the range of λ3 - λ4. In some embodiments, the range of λ1 - λ2 is the visible range, and the range of λ3 - λ4 is the infrared range. For example, in some embodiments, λ1 is about 450 nm, λ2 is about 650 nm, λ3 is about 930 nm, and λ4 is about 970 nm. For light 40a with a wavelength range of λ1 - λ2, layer or film 150 has an average direct transmittance Vs, an average diffuse transmittance Vd, and an average total transmittance Vt (Vt = Vs+Vd). For light 40b with a wavelength range of λ3 - λ4, layer or film 150 has an average direct transmittance Is, an average diffuse transmittance Id, and an average total transmittance It (It = Is+Id). A high diffuse transmittance (e.g., high Vd) corresponds to a high optical haze.

[0041] In some embodiments, for substantially perpendicular incident light (40, 40a, 40b), and for a visible wavelength range of about 450 nm to about 650 nm and an infrared wavelength range of about 930 nm to about 970 nm, the optical diffusion layer (e.g., 30 or 120 or 150) has an average direct transmittance Vs in the visible wavelength range and an average direct transmittance Is in the infrared wavelength range, and Is / Vs ≧ 2.5. In some embodiments, Is / Vs ≧ 3. In some embodiments, the optical diffusion layer has an average total transmittance It in the infrared wavelength range, and Is / It ≧ 0.6 or Is / It ≧ 0.7. In some embodiments, the optical diffusion layer has an average total transmittance Vt in the visible wavelength range, and It / Vt > 1, or It / Vt > 2, or It / Vt > 3.

[0042] In some embodiments, for substantially normal incident light (40, 40a, 40b), in each of the first and second polarization states (171, 172) that are orthogonal to each other, the optical substrate layer (e.g., 110 or 150') has an average positive transmittance (Vs, Is) of greater than about 70% in each of the visible and infrared wavelength ranges. In some embodiments, the optical substrate layer (e.g., 110 or 150') is or includes a polyester film (e.g., a polyethylene terephthalate [PET] film).

[0043] In some embodiments, the display system includes a reflective polarizer and further includes a structured mirror. The structured mirror can include optical ridges on an optical mirror. The optical ridges can be formed, for example, by printing or high-precision processing (e.g., casting and curing).

[0044] Figures 7A and 7B provide alternative embodiments of a structured mirror 700 having spaced-apart optical ridges according to this description. Figure 7A shows a structured mirror 700 including an optical mirror 710 and a discontinuous layer 721 including an array of individual spaced-apart optical ridges 720. In the embodiment of Figure 7A, the optical ridges 720 are spaced in an arrangement that may be regular (e.g., rectangular, square, or hexagonal) or irregular (e.g., random or pseudo-random) and are disposed directly on the surface of the optical mirror 710. In some embodiments, the optical ridges 720 cover a certain percentage of the surface area of the optical mirror 710 and are rounded ridges that can contribute to wet-out resistance performance (and reduction of other undesirable optical effects such as Newton's rings) while maintaining substantially transmissive to at least some wavelengths of near-infrared light. In some embodiments, the area coverage rate of the surface of the optical mirror 710 may be from about 10% to about 40%.

[0045] FIG. 7B shows an alternative embodiment of the structured mirror 700’, which includes an optical mirror 710 and a continuous layer 721’ featuring optical ridges 720’ separated by substantially planar lands 722. The embodiment of FIG. 7B differs from the embodiment of FIG. 7A mainly in that, rather than having the optical ridges 720 disposed directly on the optical mirror 710 (as in FIG. 7A), the continuous layer 721’ and the optical ridges 720’ are formed as a single component disposed on the optical mirror 710. Similar to the embodiment of FIG. 7A, in some embodiments, the area coverage ratio of the optical ridges 720’ on the optical mirror 710 (including the lands 722 of the continuous layer 721’) may be from about 10% to about 40%.

[0046] Suitable materials for the optical ridges 720, 720’ include, for example, OP1028 Premium Gloss HS Overprint Varnish, OP2018 Imprintable Matte UV Varnish, and 9308 UV Flexo Ink (all manufactured by Nazdar Ink Technologies (Shawnee, KS)).

[0047] In some embodiments, for substantially normal incident light, the optical mirror 710 has an average light reflectance of greater than about 30% (or within the ranges described elsewhere in this specification) within the visible wavelength range for at least a first polarization state, and a positive transmittance of greater than about 20% (or within the ranges described elsewhere in this specification) at at least one wavelength within the infrared wavelength range for each of the first polarization state and an orthogonal second polarization state. In some embodiments, the optical ridges 720, 720’ have an average light transmittance of greater than about 50%, or greater than about 60%, or greater than about 70% for each of the visible and infrared wavelength ranges in each of the first and second polarization states.

[0048] The related optical ridge is described in U.S. Provisional Patent Application No. 63 / 021773, entitled "OPTICAL FILM WITH DISCONTINUOUS COATING," filed on May 8, 2020, and is incorporated herein by reference to the extent not inconsistent with the present specification.

[0049] The optical mirror 710 can include a plurality of alternating first and second polymer layers 11 and 12 (see, e.g., FIGS. 1-2 where 100, 100' alternately include the optical mirror), and each of the first and second polymer layers has a thickness of less than about 500 nm, or less than about 350 nm, or less than about 300 nm. The optical mirror can include a single packet or multiple packets separated by a thicker intermediate layer, as further described elsewhere in this specification. In some embodiments, the optical mirror 710 includes alternating first and second dielectric layers, and at least one of the first and second layers is an inorganic layer. For example, the optical mirror 710 can be a dielectric reflector. In some embodiments, the optical mirror 710 is a metal layer or includes a metal layer.

[0050] Figures 8-9 are schematic plots of transmittance versus wavelength for a reflective polarizer, or an optical structure including a reflective polarizer, or another optical element, for substantially normal incident light 40 in a first polarization state (transmittance 136 in FIG. 8) and a second orthogonal polarization state (transmittance 134 in FIG. 9), respectively, according to some embodiments. In some embodiments, for substantially normal incident light 40 and a predetermined wavelength range (e.g., a range extending from λ1 to λ2 and / or at least from 450 nm to 650 nm), the reflective polarizer 100, 100, or 200 has an average light transmittance Tp of at least about 40% in a first polarization state 171 and an average light reflectance R of at least about 70% in a second orthogonal polarization state 172. In some embodiments, the average light transmittance Tp is at least about 50%, or at least about 55%, or at least about 60%. In some embodiments, the average light reflectance R is at least about 80%, or at least about 85%, or at least about 90%. The transmittance 135 versus wavelength for light 170 incident at a certain angle of incidence θ is also schematically shown in FIG. 8. In some embodiments, in a first polarization state (transmission) and a predetermined wavelength range (e.g., the visible range from about 450 nm to about 650 nm, the infrared range from about 930 nm to about 970 nm, or the range from about 400 nm to about 800 nm), the reflective polarizer or the optical structure has a large average light transmittance (e.g., transmittance 136) for light incident at a small angle of incidence and a small average light transmittance (e.g., transmittance 135) for light incident at a large angle of incidence. The small angle of incidence can be in the range from 0 degrees to about 20 degrees, or can be, for example, about 0 degrees. The large angle of incidence can be in the range from about 30 degrees to about 50 degrees, or can be, for example, about 45 degrees. In some embodiments, for a predetermined wavelength range, the reflective polarizer or the optical structure has a large average light transmittance for substantially normal incident light in a first (transmission) polarization state with respect to any incident plane and a small average light transmittance for light incident at an angle of incidence of about 45 degrees. In some embodiments, the difference between the large average light transmittance and the small average light transmittance is at least 10%, or at least 20%, or at least 30%.

[0051] In some embodiments, the transmittance of substantially perpendicularly incident light in the second polarization state is high for short wavelengths within a predetermined wavelength range and low for longer second wavelengths within the predetermined wavelength range. Such an inclined cut-off state transmittance can, for example, reduce color shift associated with the viewing angle.

[0052] The average transmittance (each reflectance) is the average of the transmittance (each reflectance) over a predetermined wavelength range. In the case of a reflective polarizer or an optical structure where absorption is negligibly small, the reflectance R is approximately 100% minus the transmittance. The transmittance 136 is the passing state transmittance of the reflective polarizer or the optical structure, and the transmittance 134 is the cut-off state transmittance of the reflective polarizer or the optical structure. Alternatively, the transmittance 134 can represent, for example, the total transmittance or the normal transmittance of an optical mirror for any polarization state or non-polarization. It can be understood that the transmittance and the reflectance are the total transmittance and the total reflectance, respectively, unless otherwise indicated. The average transmittance Tp in the first (passing) polarization state and the average transmittance Tbl in the second (cut-off) polarization state (or any polarization state of the optical mirror) for substantially perpendicularly incident light 40 in the wavelength range λ1 to λ2 are shown in FIGS. 8 to 9. The indicated values of R are approximately the average light reflectance for substantially perpendicularly incident light 40 within the wavelength range of λ1 to λ2.

[0053] In some embodiments, for example, λ1 may be about 400 nm or about 450 nm, and λ2 may be about 650 nm, about 700 nm, or about 800 nm. In some embodiments, for example, λ3 may be about 930 nm or about 950 nm, and λ4 may be about 1100 nm or about 970 nm.

[0054] In some embodiments, the transmittance 134 represents the transmittance of an optical mirror (e.g., optical mirror 710). In some embodiments, for substantially normal incident light 40, the optical mirror has an average light reflectivity R of greater than about 30% in the visible wavelength range of about 450 nm to about 650 nm in at least a first polarization state (e.g., one or both of polarization states 171, 172). In some embodiments, the average light reflectivity R is greater than about 50%, or greater than about 60%, or greater than about 70%, or greater than about 80% in the visible wavelength range in each of the first and second polarization states. In some embodiments, the transmittance 134 represents the direct transmittance of the optical mirror. In some embodiments, for substantially normal incident light 40, the optical mirror has a direct transmittance of greater than about 20% for at least one wavelength (e.g., λ3 or λ4 or a wavelength therebetween) within the infrared wavelength range of about 930 nm to about 970 nm in each of the first polarization state and the orthogonal second polarization state. In some embodiments, the direct transmittance is greater than about 40%, or greater than about 50%, or greater than about 60%, or greater than about 70%, or greater than about 80% for at least one wavelength within the infrared wavelength range in each of the first and second polarization states.

[0055] FIG. 10 is a schematic plot of the light transmittance 630 of a reflective polarizer (e.g., reflective polarizers 100, 100', or 200) in a first (blocking) polarization state with respect to substantially vertically incident light 40 versus wavelength. The light transmittance 630 has a band edge 631. In some embodiments, the best linear fit to the band edge 631, which correlates the light transmittance to wavelength over at least a wavelength range in which the light transmittance increases from about 10% to at least about 70% (e.g., from about 10% to about 70%, or from about 10% to about 80%) at the band edge, has a gradient greater than about 2.5% / nm, greater than about 3% / nm, or greater than about 3.5% / nm, or greater than about 4% / nm, or greater than about 4.5% / nm, or greater than about 5% / nm. In some embodiments, for a first wavelength range R1 extending from a short wavelength L1 to a long wavelength L2, where 30 nm ≦ L2 - L1 ≦ 50 nm and L1 is greater than the wavelength L3 corresponding to a light transmittance of about 50% at the band edge 631 and within about 20 nm from L3, the light transmittance 630 has an average T1 greater than about 75%, or greater than about 80%, or greater than about 85%. In some embodiments, the reflective polarizer is used in a display system having a sensing light source (e.g., an infrared light source used for finger sensing) configured to emit light having a first wavelength W1 for fingerprint detection. In some embodiments, the first wavelength W1 is within the first wavelength range R1. W1 can be, for example, about 850 nm or about 940 nm. In some embodiments, the wavelength L3 is in the range of about 800 nm to about 1100 nm, or about 810 nm to about 840 nm, or about 900 nm to about 930 nm. For example, in some embodiments, the wavelength L3 is in the range of about 810 nm to about 840 nm and the wavelength W1 is about 850 nm, or the wavelength L3 is in the range of about 900 nm to about 930 nm and the wavelength W1 is about 940 nm.

[0056] In some embodiments, the high transmittance in the first wavelength range R1 is achieved, at least in part, due to a sharp band edge. For example, the band edge 631 can have a gradient within the range described elsewhere. Optical films with sharp band edges are known in the art and are described, for example, in U.S. Patent No. 6,967,778 (Wheatley et al.). In some embodiments, the high transmittance in the first wavelength range R1 is achieved, at least in part, due to the layer thickness profile near the sides of the reflective polarizer that includes thicker alternating polymer layers. In some embodiments, the reflective polarizer includes a first portion having a layer thickness profile that generally increases with a first gradient, and a second portion adjacent to the first portion and having a layer thickness profile that generally decreases with a second gradient having a magnitude substantially larger than the first gradient. The reflective polarizer includes a packet of polymer layers. The thicknesses of the outer layers 20 and 50 can also affect the transmission spectrum of the reflective polarizer in the first wavelength range R1 due to the light reflected from the surfaces of the outer layers that can undergo optical interference with the light reflected from the other layers. In some embodiments, each of the outer layers 20 and 50 has an average thickness in the range of, for example, about 1 micron to about 5 microns.

[0057] FIG. 11 is a plot 210 of the average layer thickness versus the layer numbers of the plurality of polymer layers 10, 11 according to some embodiments. The thickness profile can be for the entire reflective polarizer or for a plurality of polymer layers 10, 11 within a packet (e.g., 141 or 142) of the reflective polarizer. FIGS. 12 - 14 are a portion of the plot of FIG. 11.

[0058] The layer thickness profile can be selected through appropriate feed block design and processing. For example, the layer thickness profile can be controlled using the axial rod heater power levels within a multilayer feed block as described in U.S. Patent No. 6,783,349 (Neavin et al.).

[0059] The average layer thickness profile can be measured using an atomic force microscope (AFM). To reduce measurement error, the average thickness of the layer can be determined as a moving average. The layers can be numbered from the thinnest layer to the thickest layer, and the moving average can be averaged over 20 layers including 10 layers with lower layer numbers, a specific layer, and 9 layers with higher numbers. Near the ends of the profile, fewer layers are available before or after the specific layer, so fewer layers are used for the moving average. For example, in the case of a film or packet having 325 layers, the average thickness of layer 1 is the average thickness of layers 1 to 10, the average thickness of layer 2 is the average thickness of layers 1 to 11, the average thickness of layer 101 is the average thickness of layers 91 to 110, the average thickness of layer 325 is the average thickness of layers 315 to 325, and the average thickness of layer 324 is the average thickness of layers 314 to 325.

[0060] In some embodiments, a plot 210 of the average layer thickness t against the layer numbers of the plurality of polymer layers 11, 12 includes a sharp bend region 211 that separates a left region 212 including at least Q1 sequentially arranged polymer layers having lower layer numbers from a right region 213 including at least Q2 sequentially arranged polymer layers having higher layer numbers. A linear fit 214 (see, e.g., FIG. 12) to at least Q1 sequentially arranged polymer layers in the left region 212 has an r-squared value 216 greater than about 0.8 and a positive linear gradient 215 with a magnitude greater than about 0.04 nm per layer number. A linear fit 217 (see, e.g., FIG. 13) to at least Q2 sequentially arranged polymer layers in the right region 213 has a negative linear gradient 218 of a sufficiently large magnitude. Thus, for substantially vertically incident light 40 in a first polarization state, the light transmittance 230 (see FIG. 15) of the reflective polarizer versus wavelength has a band edge 231 between about 800 nm and about 1100 nm, and the best linear fit 232 (see, e.g., FIG. 16) to the band edge 231 that correlates the light transmittance to wavelength over a wavelength range where the light transmittance increases from about 10% to at least about 80% at least at the band edge has a gradient 233 greater than about 3% / nm, or greater than about 4% / nm, or within any range of the ranges described herein for the band edge gradient. In some embodiments, the best linear fit 232 has an r-squared value 238 greater than about 0.8, or greater than about 0.85, or greater than about 0.9, or greater than about 0.93, or greater than about 0.95. Q1 is an integer greater than about 100. In some embodiments, Q1 is at least 100, or at least 150, or at least 180. Q2 is an integer greater than about 10. In some embodiments, Q2 is at least 10, or at least 12, or at least 14.

[0061] In some embodiments, the linear fit 217 to at least Q2 sequentially arranged polymer layers in the right region 213 has an r-squared value 219 greater than about 0.8 and a negative linear gradient 218 with a magnitude greater than about 0.1 nm per layer number. In some embodiments, the negative linear gradient 218 of the linear fit 217 has a magnitude greater than about 0.12 nm per layer number, or greater than about 0.14 nm per layer number, or greater than about 0.16 nm per layer number. In some such embodiments or other embodiments, the r-squared value 119 of the linear fit 217 is greater than about 0.8, or greater than about 0.85, or greater than about 0.9.

[0062] In some embodiments, the positive linear gradient 215 of the linear fit 214 has a magnitude greater than about 0.05 nm per layer number, or greater than 0.06 per layer number, or greater than about 0.07 nm per layer number. In some such embodiments or other embodiments, the r-squared value 216 of the linear fit 214 is greater than about 0.8, or greater than about 0.85, or greater than about 0.9, or greater than about 0.95.

[0063] In some embodiments, a plot 210 of the average layer thickness t versus the layer number of a plurality of polymer layers includes a sharp bend region 211 that separates a left region 212 including at least 100 sequentially arranged polymer layers having lower layer numbers from a right region 213 including at least 10 sequentially arranged polymer layers having higher layer numbers. A cubic polynomial fit 320 (see, e.g., FIG. 14) to at least 15 sequentially arranged polymer layers including the sharp bend region 211 has an r-squared value 323 greater than about 0.8 and has a positive cubic coefficient 321 and a negative quadratic coefficient 322. In some embodiments, the r-squared value 323 is greater than about 0.85, or greater than about 0.9. In some embodiments, the left region 212 includes at least 150 or at least 180 sequentially arranged polymer layers. In some embodiments, the right region 213 includes at least 12 or at least 14 sequentially arranged polymer layers.

[0064] In some embodiments, the reflective polarizers 100, 100', or 200 include a plurality of polymer layers 10, 11 sequentially numbered from 1 to N, where N is an integer greater than about 150, and each of the polymer layers 10, 11 has an average thickness of less than about 350 nm or less than about 300 nm. The reflective polarizers 100, 100' can include other layers (e.g., 146, 147, 143a, 143b) in addition to the polymer layers 10, 11 that are, for example, thicker than about 500 nm. In some embodiments, a plot 210 of the average layer thickness t versus the layer number of the plurality of polymer layers 10, 11 includes a sharp bend region 211 that includes the thickest polymer layer 224 within the plurality of polymer layers 10, 11 such that the reflective polarizers 100, 100', 200, or the plurality of polymer layers 10, 11 have the reflectivity and transmittance characteristics described elsewhere herein.

[0065] FIG. 15 is a plot of the light transmittance 230 of the reflective polarizers 100, 100' versus wavelength. FIGS. 16-18 are portions of the plot of FIG. 15. The light transmittance 230 can be for substantially normal incident light 40 having a first polarization state 171. In some embodiments, the reflective polarizer substantially transmits light having a second polarization state 172 that is orthogonal to the first polarization state 171. The layer thickness profile of FIG. 11 for the packets that reflect the long wavelengths in the reflective polarizer, including packets that reflect the short wavelengths, can generate the light transmittance 230. Suitable materials for the alternating polymer layers include, for example, polyethylene naphthalate (PEN) as the high refractive index material and a polymer blend of various copolyesters and polycarbonates as the low refractive index material.

[0066] In some embodiments, the plurality of polymer layers 10, 11, or reflective polarizers 100, 100' reflect more than about 80% of the incident light 40 having a first polarization state 171 in a first wavelength range extending from about 400 nm to about 800 nm, transmit more than about 40%, or more than about 50% of the incident light having a second polarization state 172 orthogonal to the first polarization state 171 in the first wavelength range, transmit more than about 60% of the incident light within a second wavelength range extending from about 950 nm to about 1300 nm in each of the first and second polarization states 171 and 172, and the light transmittance 230 of the optical film versus wavelength in the first polarization state 171 includes a band edge 231 from about 800 nm to about 1100 nm. In some embodiments, the band edge 231 is from about 850 nm to about 950 nm. In some embodiments, the best linear fit 232 (see, e.g., FIG. 16) correlating the light transmittance to wavelength over at least a wavelength range where the light transmittance increases from about 10% to at least about 70% at the band edge has a gradient 233 greater than about 3% / nm, or within any of the ranges described elsewhere for the band edge gradient (e.g., greater than about 4% / nm).

[0067] In some embodiments, the wavelength range R2 (see, e.g., FIG. 16) from a first wavelength λa where the best linear fit 232 is 20% to a second wavelength λb where the best linear fit 232 is 80% is less than about 30 nm in width, or less than about 20 nm in width, or less than about 15 nm in width. In some embodiments, the wavelength range from the minimum wavelength greater than about 600 nm where the transmittance is at least about 20% to the minimum wavelength greater than about 600 nm where the transmittance is at least about 80% is less than about 30 nm in width, or less than about 20 nm in width, or less than about 15 nm in width.

[0068] In some embodiments, the quadratic polynomial fit 234 (see, e.g., FIG. 17) to the light transmittance 230 over a wavelength range of at least 200 nm width between the band edge and about 2000 nm or about 1600 nm or about 1300 nm has an r-squared value 239 greater than about 0.6 and a minimum light transmittance Tmin of less than about 80%. The wavelength range between the band edge and about 2000 nm or about 1600 nm or about 1300 nm can be, for example, in the range of about 950 nm to about 1200 nm. In some embodiments, the r-squared value 239 is greater than about 0.7, or greater than about 0.75. In some embodiments, the quadratic polynomial fit 234 has a positive quadratic coefficient 281 and a negative linear coefficient 282. In some embodiments, the quadratic polynomial fit 234 has a minimum light transmittance Tmin of less than about 75%. In some embodiments, the minimum light transmittance Tmin is greater than about 60%, or greater than about 65%.

[0069] As is known in the art, the linear fits described herein can be linear least-squares fits. Polynomial fits can likewise be least-squares fits. Such fits minimize the sum of the squares of the residuals, where the residuals are the differences between the data and the fit curve (line or polynomial). The least-squares analysis can be used to determine an r-squared value, sometimes called the coefficient of determination.

[0070] In some embodiments, for substantially normal incident light and in a first wavelength range R2 extending from a short wavelength L1 to a long wavelength L2 (see, e.g., FIG. 18) (where 30 nm ≤ L2 - L1 ≤ 50 nm and L1 is greater than the wavelength L3 corresponding to about 50% light transmittance at the band edge and within about 20 nm from L3), the light transmittance 230 has an average greater than about 75%, or greater than about 80%, or greater than about 85%. In some embodiments, 35 nm ≤ L2 - L1 ≤ 45 nm. In some embodiments, L1 is within about 18 nm or within about 16 nm of the wavelength L3.

[0071] The related reflective polarizer is described in U.S. Provisional Patent Application No. 63 / 021743, entitled "OPTICAL FILM", filed on May 8, 2020, and is incorporated herein by reference to the extent not inconsistent with the present specification.

[0072] Figures 19-20 are plots of the transmittance versus wavelength of substantially vertically incident unpolarized light 40 of an optical element including an optical diffusion layer. Figure 19 shows the total transmittance, diffuse transmittance, and direct transmittance of a reflective polarizer (e.g., corresponding to reflective polarizer 200), and Figure 20 shows the total transmittance, diffuse transmittance, and direct transmittance of an optical diffusion film (e.g., corresponding to optical diffusion film 300).

[0073] FIG. 19 is a plot of the transmittance versus wavelength of substantially vertically incident light 40 for an exemplary reflective polarizer in which the incident light 40 is unpolarized and the reflective polarizer includes an optical diffusion layer (e.g., corresponding to the optical diffusion layer 30). In some embodiments, for substantially vertically incident light 40, the reflective polarizer has average diffused light transmittances Tb, Tg, and Tr in respective wavelength ranges of about 450 to about 485 nm (wavelength range 180), about 500 to about 565 nm (wavelength range 181), and about 625 to about 680 nm (wavelength range 182), where Tb > Tg > Tr. In some embodiments, Tb, Tg, and Tr are less than about 30%, or less than about 25%, or less than about 20%. In some embodiments, Tb - Tg and Tg - Tr are each greater than about 1%, or greater than about 2%. In some embodiments, Tr - Tg is greater than about 3%, or greater than about 5%. In some embodiments, for substantially vertically incident light 40, the total transmittance of the reflective polarizer has first and second plateau regions 183 and 184 spaced between about 800 and 1100 nm, and each plateau region is at least 20 nm wide. The first and second plateau regions 183 and 184 have average total transmittances P1 and P2, respectively. In some embodiments, P2 is greater than P1 by more than about 20%, or more than 25%, or more than 30%, or more than 35%. In some embodiments, the first plateau region 183 is disposed between 800 nm and the second plateau region 184. In some embodiments, the first plateau region 183 includes 860 nm and the second plateau region 184 includes 950 nm.

[0074] For the reflective polarizer of FIG. 19, substantially vertically incident unpolarized light 40a, and the visible wavelength range of about 450 nm to about 650 nm, the reflective polarizer has an average total transmittance Vt of about 25.27%, an average diffused transmittance Vd of about 10.75%, and an average direct transmittance Vs of about 14.52%. For the reflective polarizer of FIG. 19, substantially vertically incident unpolarized light 40b, and the infrared wavelength range of about 930 nm to about 970 nm, the reflective polarizer has an average total transmittance It of about 86.66%, an average diffused transmittance Id of about 13.89%, and an average direct transmittance Is of about 75.77%.

[0075] FIG. 20 is a plot of transmittance vs. wavelength of exemplary diffusive optical film (e.g., corresponding to diffusive optical film 300) for substantially normal incident light 40 according to some embodiments. In some embodiments, for substantially normal incident light 40 which may be unpolarized, the diffusive optical film has average diffusive light transmittances Tb, Tg, and Tr in respective wavelength ranges of from about 450 to about 485 nm (wavelength range 180), from about 500 to about 565 nm (wavelength range 181), and from about 625 to about 680 nm (wavelength range 182), where Tb>Tg>Tr. In some embodiments, Tb is less than about 80%, or less than about 70%. In some embodiments, Tb is greater than about 40%, or greater than about 50%. In some embodiments, Tr is greater than about 35%, or greater than about 40%. In some embodiments, Tr is less than about 65%, or less than about 60%. In some embodiments, each of Tb - Tg and Tg - Tr is greater than about 1%, or greater than about 2%. In some embodiments, Tb - Tr is greater than about 5%, or greater than about 10%. In some embodiments, the diffusive optical film has a diffusive light transmittance that generally decreases (e.g., decreases monotonically or does not increase) over a wavelength range of from about 450 nm to about 970 nm, and a direct light transmittance that generally increases (e.g., increases monotonically or does not decrease) over a wavelength range of from about 450 nm to about 970 nm. In some such embodiments, the total light transmittance generally increases over a wavelength range of from about 450 nm to about 970 nm.

[0076] For the diffusive optical film of FIG. 20, for substantially normal incident unpolarized light 70a and in the visible wavelength range of from about 450 nm to about 650 nm, the diffusive optical film has an average total transmittance Vt of about 76.06%, an average diffusive transmittance Vd of about 57.43%, and an average direct transmittance Vs of about 18.63%. For the diffusive optical film of FIG. 20, for substantially normal incident unpolarized light 40b and in the infrared wavelength range of from about 930 nm to about 970 nm, the diffusive optical film has an average total transmittance It of about 86.94%, an average diffusive transmittance Id of about 25.69%, and an average direct transmittance Is of about 61.25%.

[0077] FIG. 21 is a schematic exploded cross-sectional view of a display system 1000 for sensing a finger 261 of a user 260 applied to the display system 1000 according to some embodiments. The display system 1000 includes a display panel 370 configured to generate an image 371 for the user 260 to view, an optical waveguide 190 for providing illumination 188 to the display panel 370, a reflective polarizer 201 disposed between the display panel 370 and the optical waveguide 190, a sensor 125 for sensing a finger 261 of the user 260 disposed adjacent to the optical waveguide 190 on the opposite side of the reflective polarizer 201, and a sensing light source 220 configured to emit infrared light 221 (directly or indirectly) toward the finger 261 of the user 260. In the illustrated embodiment, an optical diffusion film or layer 301 is disposed between the reflective polarizer 201 and the optical waveguide 190. The reflective polarizer 201 can correspond to, for example, the reflective polarizers 100, 100', or 200. The optical diffusion film or layer 301 can correspond to, for example, the optical diffusion film 300 or the optical diffusion layer 120. In some embodiments, the reflective polarizer 201 includes a first optical diffusion layer disposed to conform to the structured major surface of the reflective polarizer 201, and the optical diffusion film or layer 301 is or includes a second optical diffusion layer. The sensor 125 is configured to receive at least a portion of the infrared light 222 reflected by the finger 261. In the illustrated embodiment, the display system 1000 further includes a mirror 701 disposed between the optical waveguide 190 and the sensor 125. The mirror 701 can correspond to, for example, the structured mirrors 700 or 700' described elsewhere.

[0078] In some embodiments, the optical waveguide 190 includes a light guide plate 191 and at least one light source 192 configured to emit light 193 into the light guide plate 191. In some embodiments, the light guide plate 191 extends in two orthogonal directions defining a plane (e.g., the x-y plane) of the light guide plate 191, and the light (e.g., illumination 188) exiting the light guide plate 191 generally propagates in a direction forming an angle in the range of about 70 degrees or about 80 degrees to about 89 degrees with respect to the plane of the light guide plate 191. The angle can be, for example, about 85 degrees.

[0079] The sensing light source 220 can be, for example, an infrared light source having a peak emission wavelength of about 850 nm or about 940 nm. The optical components (e.g., the reflective polarizer 201, the optical diffusion film or layer 301, the light guide plate 191, and the mirror 701) disposed between the finger 261 and the sensor 125 are preferably at least partially transmissive to the peak emission wavelength.

[0080] The sensing light source 220 can be disposed at any suitable position within the display system. For example, the sensing light source 220 can be disposed adjacent to any of the various layers of the display system. FIGS. 22-23 schematically show other possible positions of the sensing light source. The positions of the sensing light source shown in FIGS. 21-23 are merely exemplary and are not limiting in any sense.

[0081] FIG. 22 is a schematic exploded cross-sectional view of a display system 1000' for sensing a finger 261 of a user 260 applied to the display system 1000' according to some embodiments. The display system 1000 includes a display panel 370 configured to generate an image 371 for a user 260 to view, an optical waveguide 190 for providing illumination 188 to the display panel 370, and an optical structure 400 disposed between the display panel 370 and the optical waveguide 190, the optical structure 400 including a reflective polarizer 200 disposed on an optical diffusion film 300, and a sensor 125 for sensing a finger 261 of the user 260 disposed adjacent to the optical waveguide 190 on the opposite side of the reflective polarizer 200, and a sensing light source 220' configured to emit infrared light 221 toward the finger 261 of the user 260. A first structured main surface 21 of the reflective polarizer 200 is disposed between the display panel 370 and a plurality of polymer layers 14. In an exemplary embodiment, the display system 1000' includes a cover glass 372 disposed above the display panel 370 and configured to transmit the image 371 for the user 260 to view. The sensing light source 220' is disposed below the cover glass 372. In the illustrated embodiment, the display system 1000 further includes a structured mirror 700'' disposed between the optical waveguide 190 and the sensor 125. The structured mirror 700'' includes an optical mirror 710'' and an array of individual spaced optical ridges 720'' formed on the optical mirror 710'' and facing the optical waveguide 190. The structured mirror 700'' can correspond to the structured mirror 700 or 700' described elsewhere.

[0082] FIG. 23 is a schematic exploded cross-sectional view of a display system 1000'' for sensing a finger 261 of a user 260 applied to the display system 1000'' according to some embodiments. The display system 1000' generally corresponds to the display system 1000' except for the arrangement of the sensing light source 220'. The sensing light source 220'' is disposed such that the structured mirror 700'' comes between the sensing light source 220'' and the optical waveguide 190.

[0083] As further described elsewhere in this specification, in some embodiments, the reflective polarizer 200 is a collimating reflective polarizer that has a large average light transmittance for visible light passing through states (e.g., p-polarized light passing through states) incident at a small incident angle and a small average light transmittance for light incident at a large incident angle. Such a polarizer can provide a collimating effect by reflecting and returning light having a large incident angle back toward the mirror 700'' so as to reuse the light. Liquid crystal displays (LCDs) often include a brightness enhancement prism film (typically a crossed prism film) to improve the on-axis brightness of the display. In some cases, such a film can be omitted when a collimating reflective polarizer is included. In some embodiments of the display systems 1000, 1000', 1000'', no brightness enhancement prism film is disposed between the display panel 370 and the mirror 701 or 700''.

[0084] The related display system is described in U.S. Provisional Patent Application No. 63 / 021739, entitled "DISPLAY CONSTRUCTION AND DISPLAY SYSTEM," filed on May 8, 2020, and is incorporated herein by reference in its entirety to the extent not inconsistent with the present specification.

[0085] Exemplary Reflective Polarizer [Table 1]

[0086] Numerical modeling studies were completed using three different layer thickness profiles consisting of 650 micron layers sandwiched between two thick skin layers. The 650 micron layers were placed alternately between a birefringent high refractive index optical layer (HIO) and an isotropic low refractive index optical layer (LIO). The refractive indices used in this model at 633 nm are shown in the following table. These refractive indices were inferred from a multilayer reflective polarizer film. The film was fabricated by a multilayer coextrusion process using PEN as the HIO material and a polymer blend of 15.0 wt% PETG, 40.8 wt% PCTG, 17.0 wt% PC1804, and 27.2 wt% PC2405 as the LIO material. The film was then continuously stretched in a standard tenter at a draw ratio of 6:1 in the transverse direction and constrained in the longitudinal direction (no stretching or relaxation). The oven temperature used for stretching was 270°F. The refractive indices were inferred by using a numerical model that finds which index provided the best fit between the measured spectrum and the calculated spectrum of the 650 micron layer film. The layer thickness was measured using an atomic force microscope (Dimension ICON manufactured by Bruker Instruments (Billerica, MA)).

Table 2

[0087] Three model layer thickness profiles are shown in Figure 24 and are defined as follows.

[0088] Layer Profile 1: A proposed layer profile designed to provide reflectance from approximately 400 nanometers to approximately 930 nanometers for the blocked polarization state

[0089] Layer Profile 2: Has an "up" configuration apodized using the exponential relationship t = tm - Ae^-(N - n) / d compared to Layer Profile 1, where A is the amplitude coefficient, d is the number of layers into which the apodization feature penetrates, tm is the layer thickness at the start of the apodization feature, N is the total number of layers, and n is the layer number. For Layer Profile 2, A = -20 nm and d = 5.

[0090] Layer profile 3: Utilizes the same functional form as layer profile 2 and has an apodized "down" configuration compared to layer profile 1. For layer profile 3, A = 20 nm and d = 5.

[0091] To simulate the optical performance of these layer profiles using these materials, a numerical optical model was adopted to calculate the transmittance spectra obtained for these reflective polarizers in the blocked state. Calculations were performed for each layer profile, and each skin layer was assumed to consist of LIO material with thicknesses of 1.5, 2.5, and 5.0 micrometers. The following table defines the parameters for reflective polarizers 1 - 9, shows the calculated average transmittance over the 930 - 980 nanometer band for each layer profile, and the average bandwidth (average of all skin thicknesses) for each layer profile. The bandwidth was calculated from the first wavelength at which the transmittance reaches 20% to the wavelength at which the transmittance finally reaches 80%.

Table 3

[0092] The obtained blocked - state transmittance spectra are shown in Figure 25 for skin layers with a thickness of 1.5 micrometers (reflective polarizers 1, 2, and 3), in Figure 26 for skin layers with a thickness of 2.5 micrometers (reflective polarizers 4, 5, and 6), and in Figure 27 for skin layers with a thickness of 5.0 micrometers (reflective polarizers 7, 8, and 9).

[0093] Figures 28 and 29 show the experimental layer thickness profiles and transmission spectra of reflective polarizers 10 and 11, respectively, showing the relationship between the layer thickness profile and the transmission spectrum shape. The materials, layer configurations, and process conditions used to fabricate these films were described above, and the layer thickness profiles were measured with the same atomic force microscope system. The process parameters used to select these layer thickness profiles were the axial rod heater power levels in the multilayer feed block, as described in U.S. Patent No. 6,783,349 (Neavin et al.). The skin layer was 1.5 micrometers thick for reflective polarizers 10 and 11. Figure 28 shows the measured layer thickness profiles of the last 325 layers delivered by the feed block system for two reflective polarizer films. Figure 29 shows the blocking state transmission spectra obtained for reflective polarizers 10 and 11. Reflective polarizer 11 had fewer numbers with a high positive gradient compared to reflective polarizer 10. Reflective polarizer 11 showed a higher transmittance in the wavelength range (910 - 950 nm) adjacent to the right band edge compared to reflective polarizer 10.

[0094] Preparation of bead coating solution: First, the precursor solution WB50 was prepared as follows. 111.9 g (5.5 mol%) of 5-sodium sulfoisophthalic acid, 592.1 g (47.0 mol%) of terephthalic acid, 598.4 g (47.5 mol%) of isophthalic acid, 705.8 g of ethylene glycol, 599 g of neopentyl glycol, 0.7 g of antimony oxide, and 2.5 g of sodium acetate were placed in 1 gallon of polyester ketone. The mixture was heated to 230 °C for 2 hours at 345 kPa (50 psi) under nitrogen while stirring, during which water evolution was observed. The temperature was raised to 250 °C, then the pressure was decreased and a vacuum was applied (0.2 torr), and the temperature was raised to 270 °C. The viscosity of the material increased over 45 minutes, after which a high molecular weight transparent viscous sulfopolyester was discharged. This sulfopolyester was found to have a Tg of 70.3 °C by DSC. The theoretical sulfonate equivalent was 3847 g of polymer per mole of sulfonate. 500 g of the polymer was dissolved in a mixture of 2000 g of water and 450 g of isopropanol at 80 °C. Then the temperature was raised to 95 °C to remove the isopropanol (and part of the water). The final dispersion consisted of an aqueous dispersion with 20 wt% solids.

[0095] The coating solution was prepared by mixing the inputs detailed in the following table and stirring until homogeneous.

Table 4

[0096] Reflection polarizer 12 A multilayer optical (MOF) film was manufactured using two consecutive (laminated) packets of micro-layers, with 325 individual micro-layers in each packet surrounded by a packet bonding layer. The micro-layers within each packet were arranged as alternating layers of Material A and Material B. Material A was birefringent polyester PEN, and Material B was a blend of PC:PCTG and PETG in a ratio of 85:15. The micro-layer packets were designed to have a reflection band over the visible and near-IR wavelength regions. The film was then continuously stretched in a standard tenter at a lateral draw ratio of 6:1 and constrained in the longitudinal direction (no stretching or relaxation). The oven temperature used for stretching was 270°F. The process conditions for the manufacture of this film were selected such that the measured spectrum, as shown in the following table, matched the spectrum calculated using wavelength-dependent refractive index values. Material n x , n y , and n z 's respective refractive indices are along the x-direction (lateral), y-direction (longitudinal), and z-direction (thickness direction). n iso is the isotropic refractive index of the PC:PCTG, PETG blend.

Table 5

[0097] For the incident plane making angles φ of 90 degrees, 0 degrees (normal incidence), and 60 degrees of the angle of incidence θ with respect to the lateral direction in the s-polarized state and p-polarized state, the representative spectra of the reflective polarizer 12 were measured and shown in Fig. 30A. The layer thickness was measured using an atomic force microscope (Dimension ICON manufactured by Bruker Instruments (Billerica, MA)) and shown in Fig. 30B.

[0098] Reflective polarizer 13 Solution A was continuously coated onto the surface of Packet 1 of the unstretched cast web using a gravure roll in a reverse kiss configuration. The coated web was then passed through a coating oven maintained at a temperature above 65 °C for at least 5 seconds. Beads were observed under a microscope on the unstretched cast web that was not grouped together, and the beads appeared to be delivered to the surface of the web at the same concentration as in the coating solution. This bead-coated cast film was stretched and extended to obtain a bead-coated MOF as described for Reflective Polarizer 12.

[0099] The number of beads per unit area was counted using a Keyence microscope, and it was found to be ~ about 175 beads / mm 2 . The representative spectrum of Reflective Polarizer 13 was measured and is shown in Figure 31.

[0100] Reflective Polarizer 14 Solution A was continuously coated onto the surface of Packet 1 of the unstretched cast web using a gravure roll in a reverse kiss configuration. The coated web was then passed through a coating oven maintained at a temperature above 65 °C for at least 5 seconds. Then, the other side (the surface of Packet 2) of the cast web coated with Solution A was continuously coated with Solution B and dried in the same manner as Solution A. Beads were observed under a microscope on the unstretched cast web that was not grouped together, and the beads appeared to be delivered to the surface of the web at the same concentration as in the coating solution. This bead-coated cast film was stretched and extended as described for Reflective Polarizer 12 to obtain a MOF with bead coatings on both sides. The number of beads per unit area was counted using a Keyence microscope, and it was found to be ~ about 175 beads / mm 2 .

[0101] Reflective Polarizer 15 A reflective polarizer 15 very similar to the reflective polarizer 14 was prepared, except that the coating solution B was replaced with the coating solution C. The number of beads per unit area was counted using a Keyence microscope and found to be ~ about 182 beads / mm2. The cross-section of the reflective polarizer 15 was similar to the cross-section schematically shown in Fig. 3A, but the optical diffusion layer 30 was absent. A representative spectrum of the reflective polarizer 15 was measured and is shown in Fig. 32.

[0102] Reflective polarizer 16 The surface of a thick packet of the MOF film as described for the reflective polarizer 15 was coated with a conformal diffuser using a slurry of silica nanoparticles in an acrylic monomer dissolved in its solvent as described below.

[0103] First, 5.95 g of A-174 and 0.5 g of 4-hydroxy-2,2,6,6-tetramethylpiperidine 1-oxyl (5 wt%; 4H-2,2,6,6-TMP1-0) were added to a mixture of 400 g of NALCO 2329 and 450 g of 1-methoxy-2-propanol in a glass jar with stirring at room temperature for 10 minutes to prepare a coating precursor solution. The jar was sealed and placed in an oven at 80 °C for 16 hours. Next, water was removed from the resulting solution using a rotary evaporator at 60 °C until the solid content of the solution was close to 45 wt%. 200 g of 1-methoxy-2-propanol was added to the resulting solution, and then the remaining water was removed using a rotary evaporator at 60 °C. This latter step was repeated twice to further remove water from the solution. Finally, by adding 1-methoxy-2-propanol, the concentration of all silica nanoparticles was adjusted to 42.5 wt% to yield a silica solution containing surface-modified silica nanoparticles with an average particle size of 75 nm.

[0104] Next, a coating solution was prepared. The coating solution was composed of 20.96 wt% of the above-mentioned transparent precursor solution, 5.94 wt% of SR444, 71.55 wt% of isopropyl alcohol, 1.48 wt% of IRGACURE184, and 0.07 wt% of IRGACURE819. The coating solution was pumped into a slot die coater (using a pressure pot) at a rate that produced a wet layer thickness of 7 microns on the reflective polarizer 15.

[0105] Next, the coated substrate was passed through a UV-LED curing chamber containing a quartz window that allowed the passage of UV radiation to polymerize the coating. The UV-LED curing chamber included a rectangular array of 160 UV-LEDs and four downwebs by 40 crosswebs (covering an area of approximately 42.5 cm × 4.5 cm). The LEDs (available from Nichia Inc. (Tokyo, Japan)) operated at a nominal wavelength of 385 nm and provided a UV-A dose of 0.035 joules / square cm when operated at 10 amperes. The UV-LEDs were operated at 3 amperes to produce the film described in this example. The water-cooled UV-LED array was powered by a Lambda power supply (available from TDK-Lambda (Neptune, NJ)). The UV-LEDs were placed above the quartz window of the curing chamber at a distance of approximately 2.5 cm from the substrate. A nitrogen flow was supplied to the UV-LED curing chamber at a flow rate of 141.6 liters / mm. Air was introduced into the nitrogen supply to control the total oxygen level within the UV-LED chamber. The oxygen concentration within the UV-LED curing chamber was monitored using a Series 3000 oxygen meter (available from Alpha Omega Instruments (Cumberland, RI)).

[0106] After polymerization by UV-LED, the solvent in the cured coating was removed and dried at 66 °C for 30 seconds. Next, the dried coating was post-cured using a Fusion System Model 1600 configured with a D valve (available from Fusion UV Systems (Gaithersburg, MD)). A nitrogen flow was supplied to the UV Fusion chamber, resulting in an oxygen concentration in the chamber of approximately 50 ppm. Thereby, a diffuser coating film having a conformal coating of beads was obtained.

[0107] A schematic of the cross-section of the reflective polarizer 16 is shown in FIG. 3A. A representative spectrum of the reflective polarizer 16 was measured and is shown in FIG. 33.

[0108] Exemplary optical diffusion film [Table 6]

[0109] A coating precursor solution was prepared. 5.95 grams of 3-methacryloxypropyl-trimethoxysilane (A-174, Momentive (Waterford, NY)) and 0.5 grams of 4-hydroxy-2,2,6,6-tetramethylpiperidine 1-oxyl (5 wt%; 4H-2,2,6,6-TMP1-0, Sigma Aldrich (Milwaukee, WI)) were added to 400 grams of SiO with a diameter of 75 nm in a glass jar. 2A mixture of sol (NALCO2329, Nalco Company (Naperville, IL)) and 450 grams of 1-methoxy-2-propanol (Sigma Aldrich (Milwaukee, WI)) was added while stirring at room temperature for 10 minutes. The jar was sealed and placed in an oven at 80 °C for 16 hours. Next, water was removed from the resulting solution using a rotary evaporator at 60 °C until the solid content of the solution was close to 45 wt%. 200 grams of 1-methoxy-2-propanol was added to the resulting solution, and then the remaining water was removed using a rotary evaporator at 60 °C. This latter step was repeated twice to further remove water from the solution. Finally, by adding 1-methoxy-2-propanol, the total SiO 2 nanoparticle concentration was adjusted to 42.5 wt%, and surface-modified SiO with an average particle size of 75 nm 2 nanoparticles-containing SiO 2 sol was obtained.

[0110] Coating solution "A" was prepared. Coating solution "A" consisted of 27.98 wt% of the above transparent precursor solution, 7.9 wt% of pentaerythritol triacrylate monomer (SR444, Sartomer), 63.3 wt% of isopropyl alcohol, 0.8 wt% of IRGACURE 184 (BASF, Vandalia, IL), and 0.02 wt% of IRGACURE 819 (BASF, Vandalia, IL). Coating solution "A" was pumped using a Viking CMD (Viking Pump, (Cedar Falls, IA)) pump through a slot die coater onto a primed polyester substrate at a rate to produce a wet layer thickness of 15 microns.

[0111] Next, the coated substrate was passed through a UV-LED curing chamber containing a quartz window that allowed the passage of UV radiation to polymerize the coating. The UV-LED curing chamber contained a rectangular array of UV-LEDs. The LEDs (available from Nichia Inc. (Tokyo, Japan)) operated at a nominal wavelength of 385 nm and provided a UV-A dose of 0.035 joules / square cm when operating at 10 amperes. The UV-LEDs were operated at 8 amperes. The water-cooled UV-LED array was powered by a Genesys 150-22 power supply (available from TDK-Lambda (Neptune, N.J.)). The UV-LEDs were placed approximately 2.5 cm above the quartz window of the curing chamber and 2.5 cm from the substrate. To maintain the oxygen level below 50 ppm, a nitrogen flow was supplied to the UV-LED curing chamber at a flow rate of 22 cubic feet per minute. The oxygen level inside the UV-LED curing chamber was monitored using a Series 3000 oxygen meter (available from Alpha Omega Instruments (Cumberland, RI)).

[0112] After polymerization by the UV-LED, the solvent in the cured coating was removed by transporting the coated substrate to a drying oven at 150°F (66°C) for 30 minutes. Next, the dried coating was post-cured using a Fusion System Model 1600P configured with an H valve (available from Fusion UV Systems (Gaithersburg, MD)). A nitrogen flow was supplied to the UV Fusion chamber, resulting in an oxygen concentration in the chamber of approximately 50 ppm. Thereby, a porous coated polyester film was obtained.

[0113] Test Methods and Results Using a spectrometer (ULTRASCAN PRO, Hunterlab (Reston, VA)), the total near-infrared transmittance and diffuse near-infrared transmittance were measured for each diffuser. The near-infrared scattering ratio was calculated from these measurements by dividing the diffuse near-infrared transmittance by the total near-infrared transmittance. The total transmittance at 940 nm was 90.82%, the diffuse transmittance was 35.2%, and the near-infrared scattering ratio was 39%.

[0114] For each diffuser, the visible transmittance (%T), haze (%H), and clarity (%C) were measured using a haze meter (Haze-gard Plus, BYK-Gardner (Columbia, MD)). The results are provided in the following table. The visible transmittance was 87.5%, the haze was 80.4%, and the clarity was 97.8%.

[0115] The optical diffusion film was fabricated by forming a structured optical layer on the substrate of the diffuser on the opposite side of the optical diffusion layer. The structured optical layer generally appeared as the structured optical layer 130 schematically shown in FIGS. 5A - 5B.

[0116] The geometric shape of the structured surface was characterized by the following parameters. 1. X1: The tip radius of the feature of the structured surface (e.g., corresponding to the elongated structure 140) 2. X2: The feature density (number of features per square mm) 3. The height of the feature was 5 microns.

[0117] Rolls for high-definition structures described by the parameters in the following table were fabricated.

Table 7

[0118] For each roll, the structured optical layer was formed on the substrate of the diffuser on the opposite side of the optical diffusion layer by high-definition refinement from the roll in a continuous process using a 100% solid UV curable resin having a cured refractive index of about 1.5067 and formulated as shown in the following table.

Table 8

[0119] Terms such as "about" will be understood by those skilled in the art in the context in which they are used and described in this specification. Where the use of "about" applied to the size, amount, and quantities representing physical characteristics of a feature portion is not clear to those skilled in the art in the context in which it is used and described in this specification, "about" will be understood to mean within 10 percent of a particular value. An amount given as about a particular value may be exactly the particular value. For example, where it is not clear to those skilled in the art in the context in which it is used and described in this specification, an amount having a value of about 1 means that the amount has a value between 0.9 and 1.1 and that the value may be 1.

[0120] All of the reference documents, patents, or patent applications referred to above are hereby incorporated by reference in their entirety and consistently into this specification. If there is a discrepancy or conflict between the incorporated portion of the reference document and this application, the information in the foregoing description shall prevail.

[0121] It should be understood that the descriptions of the elements in the figures apply equally to the corresponding elements in other figures unless otherwise indicated. Although specific embodiments have been illustrated and described in this specification, it will be understood by those skilled in the art that the specific embodiments illustrated and described may be replaced by various alternative embodiments and / or equivalent embodiments without departing from the scope of the present disclosure. This application is intended to cover any adaptations, variations, or combinations of any of the specific embodiments discussed herein. Accordingly, it is intended that the present disclosure be limited only by the claims and their equivalents. The following shows exemplary embodiments. [Item 1] A display system for sensing a user's finger applied to a display system, a display panel configured to generate an image for the user to view, a sensor for sensing the finger of the user disposed in proximity to the display panel, a sensing light source configured to emit first light having a first wavelength W1 toward the finger of the user, wherein the sensor is configured to receive and detect at least a portion of the first light reflected by the finger, the sensing light source, a reflective polarizer disposed between the display panel and the sensor, including a plurality of polymer layers that total at least 50, and having a light transmittance vs. wavelength for the reflective polarizer in a first polarization state that includes a band edge for substantially normal incident light, the reflective polarizer, the best linear fit to the band edge that correlates the light transmittance to the wavelength has a slope greater than about 2.5% / nm over at least a wavelength range in which the light transmittance increases from about 10% to about 70% at the band edge, ranging from a short wavelength L1 to a long wavelength L2 and in a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) including W1, L1 is greater than a wavelength L3 corresponding to a light transmittance of about 50% along the band edge and within about 20 nm from L3, and the light transmittance has an average greater than about 75%, a display system. [Item 2] The display system according to Item 1, wherein the first wavelength W1 is about 850 nm or about 940 nm. [Item 3] The display system according to Item 1 or 2, wherein the wavelength L3 is from about 800 nm to about 1100 nm. [Item 4] For substantially normal incident light and a predetermined wavelength range, the reflective polarizer has an average light transmittance of at least 40% in a first polarization state and an average light reflectance of at least 70% in a second orthogonal polarization state, according to any one of items 1 to 3 of the display system. [Item 5] In the first polarization state and the predetermined wavelength range, the reflective polarizer has a greater average light transmittance for light incident at a smaller incident angle and a smaller average light transmittance for light incident at a larger incident angle, according to the display system of item 4. [Item 6] The predetermined wavelength range spans at least about 450 nm to about 650 nm, according to the display system of item 4 or 5. [Item 7] The plurality of polymer layers are arranged along at least a part of the thickness (z-axis) of the reflective polarizer and include a plurality of first polymer layers sequentially numbered from 1 to N, where N is an integer greater than about 150. The plurality of first polymer layers include polymer end layers at both ends thereof. The polymer end layers and each layer therebetween have an average thickness of less than about 350 nm. The plot of the average layer thickness against the layer numbers of the plurality of first polymer layers includes a sharp bend region that separates a left region including at least Q1 sequentially arranged first polymer layers having lower layer numbers from a right region including at least Q2 sequentially arranged first polymer layers having higher layer numbers. Q1 is an integer greater than about 100, Q2 is an integer of at least 10. The linear fit to the at least Q1 sequentially arranged first polymer layers in the left region has an r-squared value greater than about 0.8 and a positive linear gradient with a magnitude greater than about 0.04 nm per layer number. The linear fit to the at least Q2 sequentially arranged first polymer layers in the right region has an r-squared value greater than about 0.8 and a negative linear gradient with a magnitude greater than about 0.1 nm per layer number, according to the display system of any one of items 1 to 6. [Item 8] The plurality of polymer layers further includes a plurality of second polymer layers separated from the plurality of first polymer layers along the thickness direction of the reflective polarizer by one or more intermediate layers, each of the plurality of first and second polymer layers has a sum of at least 200, each of the plurality of first and second polymer layers has an average thickness of less than about 300 nm, and each of the one or more intermediate layers has an average thickness of greater than about 500 nm. The display system according to item 6. [Item 9] The quadratic polynomial fit to the light transmittance over a wavelength range of at least 200 nm width between the band edge and about 1300 nm has an r-squared value greater than about 0.6 and a minimum light transmittance of less than about 80%. The display system according to any one of items 1 to 8. [Item 10] The display system according to item 9, wherein the quadratic polynomial fit has a positive quadratic coefficient and a negative linear coefficient. [Item 11] The reflective polarizer is a first outer layer coextruded with the plurality of polymer layers, a plurality of first particles having an average particle diameter of about 7 to about 9 microns and partially protruding from a first main surface of the first outer layer to form a first structured main surface, a first optical diffusion layer disposed to conform to the first structured main surface, wherein opposite first and second main surfaces of the first optical diffusion layer substantially conform to the first structured main surface, and the first optical diffusion layer includes a plurality of nanoparticles dispersed therein, and the nanoparticles define a plurality of voids therebetween. The display system according to any one of items 1 to 10. [Item 12] The reflective polarizer is a second outer layer on the opposite side of the first outer layer, the second outer layer coextruded with the plurality of polymer layers and the first outer layer, a plurality of second particles partially protruding from a second main surface of the second outer layer to form a second structured main surface. The display system according to item 11. [Item 13] The display system further includes an optical diffusion film disposed between the reflective polarizer and the sensor, and the optical diffusion film includes an optical substrate layer, an optical substrate layer, an optical substrate layer, A second optical diffusion layer disposed on the optical substrate layer, facing the reflective polarizer, and including a plurality of nanoparticles dispersed therein, wherein for substantially normal incident light, and for a visible wavelength range of about 450 nm to about 650 nm and an infrared wavelength range of about 930 nm to about 970 nm, the second optical diffusion layer has an average normal transmittance Vs in the visible wavelength range and an average normal transmittance Is in the infrared wavelength range, and Is / Vs ≧ 2.5, the second optical diffusion layer; A structured optical layer disposed on the optical substrate layer, facing away from the reflective polarizer, and including a structured main surface facing away from the optical substrate layer, the structured optical layer extending along the same first direction and including a plurality of spaced-apart elongated structures arranged with a substantially uniform density across the structured main surface of the structured optical layer; The display system according to any one of items 1 to 12, comprising. [Item 14] The display system according to item 13, further comprising an optical waveguide for providing illumination to the display panel, the optical waveguide being disposed between the reflective polarizer and the sensor. [Item 15] The display system according to item 14, further comprising a structured mirror disposed between the optical waveguide and the sensor, the structured mirror comprising an optical mirror and an array of individual spaced-apart optical ridges formed on the optical mirror and facing the optical waveguide, wherein for substantially normal incident light, the optical mirror has an average light reflectance of more than about 30% within the visible wavelength range at least in a first polarization state, and a positive transmittance of more than about 20% for at least one wavelength within the infrared wavelength range in each of the first polarization state and an orthogonal second polarization state.

Claims

1. A display system for sensing a user's finger applied to a display system, a display panel configured to generate an image for the user to view, a sensor for sensing the finger of the user disposed adjacent to the display panel, a sensing light source configured to emit first light having a first wavelength W1 toward the finger of the user, wherein the sensor is configured to receive and detect at least a part of the first light reflected by the finger, the sensing light source, a reflective polarizer disposed between the display panel and the sensor, including a plurality of polymer layers that total at least 50, and for substantially perpendicular incident light, the light transmittance of the reflective polarizer in the blocked polarization state versus wavelength includes a band edge, the reflective polarizer, and at least over a wavelength range where the light transmittance increases from about 10% to about 70% at the band edge, the best linear fit of the light transmittance to the wavelength has a slope greater than about 2.5% / nm, ranging from a short wavelength L1 to a long wavelength L2 and in a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) including W1, L1 is greater than a wavelength L3 corresponding to about 50% light transmittance along the band edge and within about 20 nm from L3, and the light transmittance has an average greater than about 75%, for substantially perpendicular incident light and a predetermined wavelength range, the reflective polarizer has an average light transmittance of at least 40% in a first polarization state and an average light reflectance of at least 70% in a second orthogonal polarization state, a display system.

2. In the first polarization state and the predetermined wavelength range, the reflective polarizer has a greater average light transmittance for light incident at a smaller incident angle and a smaller average light transmittance for light incident at a larger incident angle. The display system according to claim 1.

3. The display system according to claim 1, wherein the predetermined wavelength range spans at least about 450 nm to about 650 nm.

4. A display system for sensing a user's finger applied to a display system, a display panel configured to generate an image for the user to view, A sensor for sensing the finger of the user disposed close to the display panel; A sensing light source configured to emit first light having a first wavelength W1 toward the finger of the user, wherein the sensor is configured to receive and detect at least a part of the first light reflected by the finger; A reflective polarizer disposed between the display panel and the sensor, including a plurality of polymer layers, the total number of which is at least 50, and having a light transmittance vs. wavelength of the reflective polarizer in a blocked polarization state for substantially perpendicular incident light including a band edge; The best linear fit to the band edge correlating the light transmittance to the wavelength over at least a wavelength range in which the light transmittance increases from about 10% to about 70% at the band edge and has a gradient greater than about 2.5% / nm; From a short wavelength L1 to a long wavelength L2, in a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) including W1, L1 is greater than a wavelength L3 corresponding to a light transmittance of about 50% along the band edge and within about 20 nm from L3, and the light transmittance has an average of greater than about 75%; The plurality of polymer layers are arranged along at least a part of the thickness of the reflective polarizer, and include a plurality of first polymer layers sequentially numbered from 1 to N, where N is an integer greater than about 150. The plurality of first polymer layers include polymer end layers at both ends thereof. The polymer end layers and each layer therebetween have an average thickness of less than about 350 nm. A plot of the average layer thickness against the layer numbers of the plurality of first polymer layers includes a sharp bend region that separates a left region including at least Q1 sequentially arranged polymer layers having lower layer numbers from a right region including at least Q2 sequentially arranged polymer layers having higher layer numbers. Q1 is an integer greater than about 100, and Q2 is an integer of at least 10. A linear fit to the at least Q1 sequentially arranged first polymer layers in the left region has an r-squared value greater than about 0.8 and a positive linear gradient with a magnitude greater than about 0.04 nm per layer number. A linear fit to the at least Q2 sequentially arranged first polymer layers in the right region has an r-squared value greater than about 0.8 and a negative linear gradient with a magnitude greater than about 0.1 nm per layer number. A display system.

5. The plurality of polymer layers further include a plurality of second polymer layers separated from the plurality of first polymer layers along the thickness direction of the reflective polarizer by one or more intermediate layers. Each of the plurality of first and second polymer layers has a total of at least 200. Each of the plurality of first and second polymer layers has an average thickness of less than about 300 nm. Each of the one or more intermediate layers has an average thickness of greater than about 500 nm. The display system according to claim 4.

6. A display system for sensing a user's finger applied to the display system, A display panel configured to generate an image for the user to view, A sensor for sensing the finger of the user disposed close to the display panel, A sensing light source configured to emit first light having a first wavelength W1 towards the finger of the user, wherein the sensor is configured to receive and detect at least a part of the first light reflected by the finger. A sensing light source. A reflective polarizer disposed between the display panel and the sensor, comprising a plurality of polymer layers totaling at least 50, and for substantially vertically incident light, the light transmittance of the reflective polarizer in the blocking polarization state versus wavelength includes a band edge, a reflective polarizer, and is provided with Over at least a wavelength range in which the light transmittance increases from about 10% to about 70% at the band edge, the best linear fit to the band edge correlating the light transmittance to the wavelength has a gradient greater than about 2.5% / nm. Ranging from a short wavelength L1 to a long wavelength L2 and in a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) including W1, L1 is greater than a wavelength L3 corresponding to a light transmittance of about 50% along the band edge and within about 20 nm from L3, and the light transmittance has an average of greater than about 75%. A display system in which a quadratic polynomial fit to the light transmittance over a wavelength range of at least 200 nm wide between the band edge and about 1300 nm has an r-squared value greater than about 0.6 and a minimum light transmittance of less than about 80%.

7. The display system according to claim 6, wherein the quadratic polynomial fit has a positive quadratic coefficient and a negative linear coefficient.

8. A display system for sensing a user's finger applied to the display system, A display panel configured to generate an image for the user to view, A sensor for sensing the finger of the user disposed in proximity to the display panel, A sensing light source configured to emit first light having a first wavelength W1 towards the finger of the user, wherein the sensor is configured to receive and detect at least a portion of the first light reflected by the finger, a sensing light source, A reflective polarizer disposed between the display panel and the sensor, comprising a plurality of polymer layers totaling at least 50, and for substantially vertically incident light, the light transmittance of the reflective polarizer in the blocking polarization state versus wavelength includes a band edge, a reflective polarizer, and is provided with Over at least a wavelength range in which the light transmittance increases from about 10% to about 70% at the band edge, the best linear fit to the band edge correlating the light transmittance to the wavelength has a gradient greater than about 2.5% / nm. In a first wavelength range (30 nm ≦ L2 - L1 ≦ 50 nm) extending from a short wavelength L1 to a long wavelength L2 and including W1, L1 is greater than a wavelength L3 corresponding to an optical transmittance of about 50% along the band edge and within about 20 nm from L3, and the optical transmittance has an average of more than about 75%, wherein the reflective polarizer is a first outer layer coextruded with the plurality of polymer layers, a plurality of first particles having an average particle diameter of about 7 to about 9 microns and partially protruding from a first major surface of the first outer layer to form a first structured major surface, a first optical diffusion layer disposed to conform to the first structured major surface, wherein opposite first and second major surfaces of the first optical diffusion layer substantially conform to the first structured major surface, and the first optical diffusion layer includes a plurality of nanoparticles dispersed therein, and the nanoparticles define a plurality of voids therebetween, a display system further comprising

9. wherein the reflective polarizer is a second outer layer on the opposite side of the first outer layer, the second outer layer coextruded with the plurality of polymer layers and the first outer layer, a plurality of second particles partially protruding from a second major surface of the second outer layer to form a second structured major surface, The display system according to claim 8, further comprising

10. further comprising an optical diffusion film disposed between the reflective polarizer and the sensor, the optical diffusion film an optical substrate layer, a second optical diffusion layer disposed on the optical substrate layer, facing the reflective polarizer, and including a plurality of nanoparticles dispersed therein, wherein for substantially normal incident light, and in a visible wavelength range of about 450 nm to about 650 nm and an infrared wavelength range of about 930 nm to about 970 nm, the second optical diffusion layer has an average positive transmittance Vs in the visible wavelength range and an average positive transmittance Is in the infrared wavelength range, and Is / Vs ≧ 2.5, a structured optical layer disposed on the optical substrate layer, facing the opposite side of the reflective polarizer, and including a structured major surface facing the opposite side of the optical substrate layer, the structured optical layer extending along the same first direction and including a plurality of spaced elongated structures disposed at a substantially uniform density across the structured major surface of the structured optical layer, The display system according to any one of claims 1 to 9, comprising

11. The display system according to claim 10, further comprising an optical waveguide for providing illumination to the display panel, wherein the optical waveguide is disposed between the reflective polarizer and the sensor.

12. The display system according to claim 11, further comprising a structured mirror disposed between the optical waveguide and the sensor, the structured mirror comprising an optical mirror and an array of individual spaced optical ridges formed on the optical mirror and facing the optical waveguide, wherein for substantially normal incident light, the optical mirror has an average light reflectivity of more than about 30% within the visible wavelength range in at least a first polarization state and a positive transmittance of more than about 20% for at least one wavelength within the infrared wavelength range in each of the first polarization state and an orthogonal second polarization state.

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