Optical Film

Abstract

The optical film includes multiple polymer layers. A plot of the average layer thickness versus layer number of the polymer layers includes a knee-knee region separating a left region including at least N1 sequentially arranged polymer layers with lower layer numbers from a middle region including at least N2 sequentially arranged polymer layers with higher layer numbers. N1 is greater than about 50, and N2 is greater than about 10. A linear fit to the at least N1 sequentially arranged polymer layers in the left region has a positive linear slope greater than about 0.04 nm per layer number, and a linear fit to the at least N2 sequentially arranged polymer layers in the middle region has a negative linear slope greater than about 0.05 nm per layer number.

Description

[Background technology]

[0001] Optical films, such as reflective polarizer films and mirror films, can include alternating polymer layers. Summary of the Invention

[0002] The present disclosure generally relates to optical films. The optical films can include multiple polymer layers. The optical films can be, for example, reflective polarizers or optical mirrors.

[0003] In some embodiments of the present disclosure, an optical film is provided that includes a plurality of polymer layers arranged along at least a portion of the thickness of the optical film and numbered sequentially from 1 to N, where N is an integer greater than about 100. The plurality of polymer layers includes a polymer end layer at each end thereof. A plot of average layer thickness versus layer number of the plurality of polymer layers includes a first bend region that separates a left region including at least N1 sequentially arranged polymer layers having lower layer numbers from a middle region including at least N2 sequentially arranged polymer layers having higher layer numbers, where N1 is an integer greater than about 50 and N2 is an integer greater than about 10, and the polymer layers have a linear fit to the at least N1 sequentially arranged polymer layers in the left region that has a positive linear slope greater than about 0.04 nm per layer number with an r-squared value greater than about 0.8, and a linear fit to the at least N2 sequentially arranged polymer layers in the middle region that has a negative linear slope greater than about 0.05 nm per layer number with an r-squared value greater than about 0.8.

[0004] In some aspects of the present disclosure, an optical film is provided that includes a plurality of polymer layers each having a polymer end layer at each of its ends. The polymer end layers and each layer therebetween can have an average thickness of less than about 300 nm. A plot of the average layer thickness versus the layer number of the plurality of polymer layers includes a left region that includes at least N4 sequentially arranged polymer layers, where N4 is an integer greater than about 5; a first intermediate region that includes at least N1 sequentially arranged polymer layers, where N1 is an integer greater than about 50; a second intermediate region that includes at least N2 sequentially arranged polymer layers, where N2 is an integer greater than about 10; and a right region that includes at least N3 sequentially arranged polymer layers, where N3 is an integer greater than about 3. A linear fit to at least N4 sequentially arranged polymer layers in the left region has an r-squared value greater than about 0.8 and a negative linear gradient with a magnitude greater than about 0.04 nm per layer number. A linear fit to at least N1 sequentially arranged polymer layers in the first intermediate 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 at least N2 sequentially arranged polymer layers in the second intermediate region has an r-squared value greater than about 0.8 and a negative linear gradient with a magnitude greater than about 0.05 nm per layer number. A linear fit to at least N3 sequentially arranged polymer layers in the right region has an r-squared value greater than about 0.6 and a positive linear gradient with a magnitude greater than about 1.2 nm per layer number.

[0005] In some aspects of the present disclosure, an optical film is provided that includes a plurality of polymer layers arranged along at least a portion of the thickness of the optical film and sequentially numbered from 1 to N. N is an integer greater than about 100. The plurality of polymer layers includes a polymer end layer at each of its ends. The polymer end layers and each layer therebetween can have an average thickness of less than about 300 nm. The mth layer in the plurality of polymer layers has an average thickness tm, where m < N, and the average thickness of each polymer layer in the plurality of polymer layers having a layer number n such that m ≤ n ≤ N is

Number

[0006] In some embodiments of the present disclosure, an optical film is provided that includes a plurality of polymer layers arranged along at least a portion of the thickness of the optical film and numbered sequentially from 1 to P, where P is an integer greater than about 100. The plurality of polymer layers includes a polymer end layer at each end thereof. The polymer end layer and each layer therebetween may have an average thickness of less than about 300 nm. A plot of the average layer thickness versus layer number of the plurality of polymer layers includes a first bend region that separates a left region including at least P1 sequentially arranged polymer layers having lower layer numbers from a right region including at least P2 sequentially arranged polymer layers having higher layer numbers, where P1 is an integer greater than about 50 and P2 is an integer greater than about 10, and the polymer layers have a negative linear slope of greater than about 0.1 nm per layer number with an r-squared value greater than about 0.8. For substantially normally incident light having a first polarization state, the optical transmittance of the optical film versus wavelength includes the band edges between about 850 nm and about 950 nm, at least over the wavelength range in which the optical transmittance increases from about 10% to about 70%, and a best linear fit to the band edges correlating the optical transmittance to wavelength has an r-squared value greater than about 0.8 and a slope greater than about 3% / nm.

[0007] In some embodiments of the present disclosure, an optical film is provided that includes a plurality of polymer layers arranged along at least a portion of the thickness of the optical film and numbered sequentially from 1 to N, where N is an integer greater than about 200. The plurality of polymer layers includes a polymer end layer at each end thereof. The polymer end layers and each layer therebetween may have an average thickness of less than about 300 nm. A plot of average layer thickness versus layer number for the plurality of polymer layers includes a knee region separating 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, where Q1 is an integer greater than about 100 and Q2 is an integer greater than about 10, and the polymer layers are such that a linear fit to the at least Q1 sequentially arranged polymer layers in the left region has a positive linear slope of greater than about 0.04 nm per layer number with an r-squared value of greater than about 0.8, and a linear fit to the at least Q2 sequentially arranged polymer layers in the right region has a sufficient magnitude to include a band edge of the optical transmittance of the optical film versus wavelength from about 800 nm to about 1100 nm for substantially normally incident light having a first polarization state. A best linear fit to the band edge correlating optical transmittance to wavelength over at least a wavelength range in which optical transmittance increases from about 10% to about 80% may have a slope of greater than about 3% / nm.

[0008] In some embodiments of the present disclosure, an optical film is provided that includes a plurality of polymer layers arranged along at least a portion of the thickness of the optical film and numbered sequentially from 1 to N, where N is an integer greater than about 200. The plurality of polymer layers includes a polymer end layer at each end thereof. The polymer end layers and each layer therebetween may have an average thickness of less than about 300 nm. A plot of average layer thickness versus layer number of the plurality of polymer layers includes a knee region that separates a left region including at least 100 sequentially arranged polymer layers with lower layer numbers from a right region including at least 10 sequentially arranged polymer layers with higher layer numbers, and a third order polynomial fit to at least 15 sequentially arranged polymer layers including the knee region has a positive third order coefficient and a negative second order coefficient with an r-squared value greater than about 0.8.

[0009] In some embodiments of the present description, an optical film is provided that includes a plurality of polymer layers numbered sequentially from 1 to N, where N is an integer greater than about 100. Each of the polymer layers may have an average thickness of less than about 300 nm. A plot of the average layer thickness versus layer number of the plurality of polymer layers includes a knee region that includes the thickest polymer layer in the plurality of polymer layers, and for substantially perpendicular incident light and a first wavelength range ranging from about 400 nm to about 800 nm and a second wavelength range ranging from about 950 nm to about 1300 nm, the plurality of polymer layers reflects more than about 80% of the incident light having a first polarization state in the first wavelength range, transmits more than about 40% of the incident light having a second polarization state orthogonal to the first polarization state in the first wavelength range, and transmits more than about 60% of the incident light in the second wavelength range for each of the first and second polarization states, and for the first polarization state, the optical transmission of the optical film versus wavelength includes a band edge of about 800 nm to about 1100 nm. A best linear fit to the bandedge correlating optical transmittance to wavelength may have a slope of greater than about 3% / nm over at least the wavelength range in which optical transmittance increases from about 10% to about 70%. For substantially normal incidence light and a third wavelength range extending from a smaller wavelength L1 to a larger wavelength L2, the optical transmittance has an average value greater than about 75%, with 30 nm≦L2-L1≦50 nm, where L1 is greater than and within about 20 nm of the wavelength corresponding to about 50% optical transmittance at the bandedge.

[0010] These and other aspects will become apparent from the following detailed description, but in no way should this brief summary be construed as limiting the claimed subject matter. [Brief description of the drawings]

[0011] [Figure 1] 1 is a schematic cross-sectional view of an exemplary optical film. [Diagram 2] 1 is a schematic cross-sectional view of an exemplary optical film. [Diagram 3]1 is an exemplary plot of average layer thickness versus layer number for multiple polymer layers, the plot having a knee region separating a middle region from a right region. [Figure 4] A portion of the plot in FIG. [Diagram 5] A portion of the plot in FIG. [Figure 6] A portion of the plot in FIG. [Figure 7] A portion of the plot in FIG. [Figure 8] 1 is an exemplary plot of average layer thickness versus layer number for multiple polymer layers, the plot having a knee region separating the left region from the right region. [Figure 9] A portion of the plot in FIG. 8 is shown. [Figure 10] A portion of the plot in FIG. 8 is shown. [Figure 11] 1 is an exemplary plot of average layer thickness versus layer number for multiple polymer layers according to some embodiments. [Figure 12] A portion of the plot in FIG. 11 is shown. [Figure 13] A portion of the plot in FIG. 11 is shown. [Figure 14] A portion of the plot in FIG. 11 is shown. [Figure 15] 1 is a schematic exemplary plot of average layer thickness versus layer number for some of a plurality of polymer layers. [Figure 16] 1 is an exemplary plot of light transmission through an optical film versus wavelength. [Figure 17] 17 is a portion of the plot in FIG. 16. [Figure 18] 1 is a plot of light transmission of an optical film versus wavelength according to some embodiments. [Figure 19] 19 is a portion of the plot in FIG. 18. [Figure 20] 19 is a portion of the plot in FIG. 18. [Figure 21] 19 is a portion of the plot in FIG. 18. [Figure 22] 1 is a schematic plot of light transmission as a function of wavelength for an exemplary reflective polarizer. [Figure 23] 1 is a plot of average layer thickness versus layer number for various exemplary optical films. [Figure 24] 13A-13C are block state transmission spectra for substantially normal incidence of various reflective polarizers. [Diagram 25] 13A-13C are block state transmission spectra for substantially normal incidence of various reflective polarizers. [Figure 26] 13A-13C are block state transmission spectra for substantially normal incidence of various reflective polarizers. [Figure 27] 1 is a plot of average layer thickness versus layer number for two reflective polarizers. [Figure 28] 28 shows the block state transmission spectrum for substantially normally incident light of the reflective polarizer of FIG. 27. [Figure 29] FIG. 1 is a schematic cross-sectional view of a display system. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] In the following description, reference is made to the accompanying drawings which form a part hereof, and in which various embodiments are shown by way of illustration. The drawings are not necessarily to scale. It is to be understood that other embodiments are contemplated and may be made without departing from the scope or spirit of the specification. Accordingly, the following detailed description is not to be taken in a limiting sense.

[0013] In some embodiments, the optical film has a layer thickness profile selected to provide a desired transition between, for example, the reflection band and the pass band. The layer thickness profile described herein can, in some embodiments, result in an optical film having a higher transmittance at near infrared wavelengths close to and above the band edge wavelength, and / or a higher reflectance at near infrared wavelengths close to and below the band edge wavelength, compared to other optical films. According to some embodiments, the optical film may be used in liquid crystal displays (LCDs) and may be advantageously used, for example, when it is desired to reflect visible light for a range of angles of incidence (which may be achieved by having a reflection band for normally incident light that extends into the near infrared, with the reflection band shifting with increasing angles of incidence), and when it is desired to transmit infrared light from an infrared light source used, for example, for fingerprint detection.

[0014] 1-2 show schematic cross-sectional views of optical films 100 and 100' according to some embodiments. The optical films 100, 100' include multiple polymer layers 10, 11 arranged along at least a portion of the thickness (along the z direction, with reference to an illustrated xyz coordinate system) of the optical film. Each polymer layer 10, 11 has an average thickness t that can be less than about 300 nm.

[0015] The number of polymer layers 10, 11 in the optical film 100 or 100' can be substantially greater than that shown diagrammatically in Figures 1-2. For example, the multiple polymer layers 10, 11 can include a total of 50-800 layers. In some embodiments, the multiple polymer layers 10, 11 include more than about 100 layers or more than about 200 layers.

[0016] The optical films 100, 100' include outermost layers 146 and 147 having thicknesses ta and tb, respectively. Each thickness 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 thickness of the outermost layers 146 and 147 can affect the transmission spectrum of the optical film due to light reflected from the surfaces of the layers 146 and 147, which can undergo optical interference with light reflected from other layers. In the case of the optical film 100', the plurality of polymer layers 10, 11 includes a first and a second plurality of polymer layers, the first (141) and the second (142) of polymer layers, which are separated from each other along the thickness of the optical film by at least one intermediate layer 143a, 143b, each intermediate layer 143a, 143b having an average thickness tc of more than about 500 nm, or more than about 1 micrometer, or more than about 2 micrometers, or more than about 3 micrometers, or more 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 a packet 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. The protective boundary layers can be formed in the same process as layers 11, 12, but a skin layer may be added downstream after the layers are compressed to enter the film die.

[0017] The multiple polymer layers 10, 11 may include alternating first and second polymer layers 10 and 11, which may be referred to as interference layers. An interference layer may be described as reflecting and transmitting light primarily through optical interference, if the reflectance and transmittance of the interference layer can be reasonably described by, or can be reasonably accurately modeled as a result of, optical interference. As is known in the art, multilayer optical films including alternating polymer layers can be used to obtain desired reflection and transmission bands by appropriately selecting layer thicknesses. Multilayer optical films and methods for making multilayer optical films are described, for example, in U.S. Pat. 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 with sharp band edges are known in the art and are described, for example, in US Pat. No. 6,967,778 (Wheatley et al.).

[0018] As further described elsewhere herein, the transmission and reflectance of the optical film 100, 100' may be specified for substantially normal incidence (e.g., within 30 degrees, or within 20 degrees, or within 10 degrees of normal incidence) light 50 and / or for light 170 having an incidence angle θ (incidence angle direction that is normal to the optical film), and may be specified for first and / or second polarization states (e.g., first and second polarization states 171 and 172). In the illustrated embodiment, the electric field is polarized along the y-axis in the first polarization state 171 and polarized in the xy-plane in the second polarization state 172. In some embodiments, the optical film 100, 100' is a reflective polarizer. The pass (respectively, block) polarization state of the reflective polarizer may be a p-polarization state (p-polarized) or an s-polarization state (s-polarized), with the projection of the electric field into the plane of the reflective polarizer (the xy-plane) being parallel to the pass (respectively, block) axis of the reflective polarizer. In some embodiments, the first polarization state 171 is the block state of the reflective polarizer, and the second polarization state 172 is the pass state of the reflective polarizer, regardless of the plane of incidence. A portion of the incident light 50, 170 (e.g., light 270) is typically reflected, and a portion (e.g., light 370) is typically transmitted. In some embodiments, for the second polarization state 172 (and / or the pass polarization state) and the first wavelength range, the reflective polarizer has a greater average light transmission for light incident at a smaller angle of incidence (e.g., light 50) and a lesser average light transmission for light incident at a larger angle of incidence (e.g., light 170). Such a reflective polarizer may be referred to as a collimating reflective polarizer when the reflective polarizer is included in a recycling backlight, because a portion of the light in the pass polarization state incident at an oblique angle is reflected by the reflective polarizer, then recycled, and finally transmitted when it enters the reflective polarizer at a smaller angle of incidence. Collimating reflective polarizers are known in the art and are described, for example, in US Pat. Nos. 9,441,809 (Nevitt et al.) and 9,551,818 (Weber et al.).In other embodiments, optical films 100, 100' are mirror films that are substantially reflective (e.g., an average reflectance of at least about 60%, or at least about 70%, or at least about 80%) of substantially normally incident light 50 at least in the visible wavelength range (e.g., 400 nm to 700 nm) for each of the first and second polarization states 171 and 172.

[0019] In some embodiments, optical film 100 or 100' is an infrared-transmissive optical film, such as an infrared-transmissive reflective polarizer or an infrared-transmissive optical mirror. For example, the reflective polarizer or optical mirror may transmit about 60% (or more than about 70%, or more than about 75%, or more than about 80%) of substantially normally incident light 50 in the 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] FIG. 3 is a plot 20 of average layer thickness versus layer number for multiple polymer layers 10, 11, according to some embodiments. The thickness profile may be for multiple polymer layers 10, 11, or a packet of film (e.g., 141 or 142) across an entire film. The average layer thickness is the layer thickness averaged over the area of ​​the layer (e.g., unweighted average). FIGS. 4-7 show a portion of the plot of FIG. 3. The layer thickness profile may be selected through suitable feedblock design and processing. For example, axial rod heater power levels in a multi-layer feedblock as described in U.S. Pat. No. 6,783,349 (Neavin et al.) may be used to control the layer thickness profile.

[0021] The average layer thickness may be measured using an atomic force microscope (AFM). To reduce errors in the measurement, the average thickness of the layers may be determined as a running average. The layers may be numbered from the thinnest layer to the thickest layer, and the running average may be an average over 20 layers, including 10 layers with lower layer numbers, the particular layer, and 9 layers with higher layer numbers. Fewer layers are used in the running average near the end of the profile because fewer layers are available before or after the particular layer. For example, for a film or packet with 325 layers, the average thickness of layer 1 is the average thickness of layers 1-10, the average thickness of layer 2 is the average thickness of layers 1-11, the average thickness of layer 101 is the average thickness of layers 91-110, the average thickness of layer 325 is the average thickness of layers 315-325, and the average thickness of layer 324 is the average thickness of layers 314-325.

[0022] In some embodiments, the optical film 100, 100' includes a plurality of polymer layers 10, 11 arranged along at least a portion of the thickness (z-direction) of the optical film and numbered sequentially from 1 to N, where N is an integer greater than about 100. The plurality of polymer layers 10, 11 includes a polymer end layer 22, 23 or 22, 223 at each end thereof. In some embodiments, the polymer end layers 22, 23 and each layer 10, 11 therebetween have an average thickness of less than about 300 nm (see, e.g., FIG. 1). The optical film may optionally include at least one layer 143a, 143b (see, e.g., FIG. 2) between the polymer end layers 22, 23 having an average thickness tc greater than about 500 nanometers or in any of the thickness ranges described elsewhere herein. Any such thickness layer that may be included in the optical film may be considered a separate layer not included in the plurality of polymer layers 10, 11 and may be omitted in the sequential numbering from 1 to N. The numbering from 1 to N may refer to alternating layers within a single packet. For example, the layers numbered sequentially from 1 to N may be layers of the first plurality of polymer layers 141 starting with end layer 223 and ending with end layer 22, or starting with end layer 22 and ending with end layer 223. In some embodiments, the polymer end layers 22, 223 and each layer 10, 11 therebetween have an average thickness of less than about 300 nm.

[0023] In some embodiments, a plot 20 of average layer thickness t versus layer number for the multiple polymer layers 10, 11 includes a first bend region 30 separating a left region 31 including at least N1 sequentially ordered polymer layers having lower layer numbers from a middle region 32 including at least N2 sequentially ordered polymer layers having higher layer numbers, where a linear fit 41 (see, e.g., FIG. 4) to the at least N1 sequentially ordered polymer layers in the left region has a positive linear slope 42 greater than about 0.04 nm per layer number with an r-squared value 43 greater than about 0.8, and a linear fit 44 (see, e.g., FIG. 5) to the at least N2 sequentially ordered polymer layers in the middle region 32 has a negative linear slope 45 greater than about 0.05 nm per layer number with an r-squared value 46 greater than about 0.8, where N1 is an integer greater than about 50 (e.g., at least 47, or at least 49, or at least 50, or at least 51). In some embodiments, N1 is greater than about 100, or greater than about 150, or greater than about 180. N2 is an integer greater than about 10. In some embodiments, N2 is greater than about 15 or greater than about 20.

[0024] In some embodiments, the polymer layers have a higher layer number than the polymer layers in the middle region, and the optical film 100, 100' further comprises a second bend region 33 separating the middle region 32 from the right region 34 and comprising at least N3 sequentially ordered polymer layers, and a linear fit 47 (see, e.g., FIG. 6) to the at least N3 sequentially ordered polymer layers in the right region has a positive linear slope 48 with a magnitude greater than about 1.2 nm per layer number, with an r-squared value 49 greater than about 0.6. N3 is an integer greater than about 3 (e.g., at least 3). In some embodiments, N3 is at least about 3, 4, 5, or 6.

[0025] In some embodiments, optical film 100, 100' includes multiple polymer layers 10, 11 that include a polymer end layer at each end thereof (e.g., layers 22, 23 of optical film 100, or layers 22, 223 of optical film 100'). The polymer end layers and each layer therebetween may have an average thickness of less than about 300 nm. A plot 20 of average layer thickness t versus layer number for the plurality of polymer layers includes a left region 36 including at least N4 sequentially ordered polymer layers; a first intermediate region 31 including at least N1 sequentially ordered polymer layers; a second intermediate region 32 including at least N2 sequentially ordered polymer layers; and a right region 34 including at least N3 sequentially ordered polymer layers, wherein a linear fit 70 (see, e.g., FIG. 7 ) to the at least N4 sequentially ordered polymer layers in the left region has an r-squared value 72 greater than about 0.8 and a negative linear slope 71 of greater than about 0.04 nm per layer number, and the at least N1 sequentially ordered polymer layers in the first intermediate region 31 are A linear fit 41 (see, e.g., FIG. 4) to the ordered polymer layers has a positive linear slope 42 greater than about 0.04 nm per layer number with an r-squared value 43 greater than about 0.8, a linear fit 44 (see, e.g., FIG. 5) to the at least N2 ordered sequential polymer layers in the second middle region 32 has a negative linear slope 45 greater than about 0.05 nm per layer number with an r-squared value 46 greater than about 0.8, and a linear fit 47 (see, e.g., FIG. 6) to the at least N3 ordered sequential polymer layers in the right region 34 has a positive linear slope 48 greater than about 1.2 nm per layer number with an r-squared value 49 greater than about 0.6. In some embodiments, N1 is an integer greater than about 50, N2 is an integer greater than about 10, N3 is an integer greater than about 3, and N4 is an integer greater than about 5 (e.g., at least 5). N1, N2, and N3 can be any of the ranges described elsewhere herein. In some embodiments, N4 is at least 5, or at least 6, or at least 7. Note that the same region can be referred to as a first region or a second region, or a middle region or a left or right region, for example, depending on other factors or regions considered.

[0026] In some embodiments, the positive linear slope 42 of the linear fit 41 has a magnitude greater than about 0.05 nm per layer number, or greater than about 0.06 nm per layer number, or greater than about 0.07 nm per layer number. In some such embodiments, or in other embodiments, the r-squared value 43 of the linear fit 41 is 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.

[0027] In some embodiments, the negative linear slope 45 of the linear fit 44 has a magnitude greater than about 0.06 nm per layer number, or greater than about 0.07 nm per layer number, or greater than about 0.08 nm per layer number. In some such embodiments, or in other embodiments, the r-squared value 46 of the linear fit 44 is 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.

[0028] In some embodiments, the positive linear slope 48 of the linear fit 47 has a magnitude greater than about 1.4 nm per layer number, or greater than about 1.5 nm per layer number, or greater than about 1.6 nm per layer number. In some such embodiments, or in other embodiments, the r-squared value 49 of the linear fit 47 is greater than about 0.6, or greater than about 0.7, or greater than about 0.8, or greater than about 0.85.

[0029] In some embodiments, the negative linear slope 71 for the linear fit 70 has a magnitude of greater than about 0.1 nm per layer number, or greater than about 0.5 nm per layer number, or greater than about 0.8 nm per layer number, or greater than about 1 nm per layer number, or greater than about 1.2 nm per layer number, or greater than about 1.4 nm per layer number. In some such embodiments, or in other embodiments, the r-squared value of the linear fit 70 is 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.

[0030] In some embodiments, a first bend region 35 separates the left region 36 from the first intermediate region 31, and the polymer layer in the first intermediate region 31 has a higher layer number than the polymer layer in the left region 36. In some such embodiments, or in other embodiments, a second bend region 30 separates the first intermediate region 31 from the second intermediate region 32, and the polymer layer in the second intermediate region 32 has a higher layer number than the polymer layer in the first intermediate region 31. In some such embodiments, or in other embodiments, a third bend region 33 separates the second intermediate region 32 from the right region 34, and the polymer layer in the right region 34 has a higher layer number than the polymer layer in the second intermediate region 32.

[0031] Figure 8 is a plot 86 of average layer thickness versus layer number for multiple polymer layers 10, 11, according to some embodiments. The thickness profile can be for multiple polymer layers 10, 11 across an entire film, or for a packet of film (e.g., 141 or 142). Figures 9-10 show a portion of the plot of Figure 8.

[0032] In some embodiments, optical film 100, 100' includes a plurality of polymer layers 10, 11 arranged along at least a portion of the thickness (z-direction) of the optical film and numbered sequentially from 1 to P (e.g., corresponding to sequentially numbered layers 1 to N as described elsewhere). P can be, for example, an integer greater than about 100. The plurality of polymer layers 10, 11 includes a polymer end layer at each end thereof (e.g., layers 22, 23 of optical film 100, or layers 22, 223 of optical film 100'). The polymer end layers and each layer therebetween can have an average thickness of less than about 300 nm. A plot 86 of average layer thickness t versus layer number for the multiple polymer layers 10, 11 includes a first bend region 80 separating a left region 81 including at least P1 sequentially arranged polymer layers having lower layer numbers from a right region 82 including at least P2 sequentially arranged polymer layers having higher layer numbers, where a linear fit 83 (see, e.g., FIG. 10 ) to the at least P2 sequentially arranged polymer layers in the right region 82 has a negative linear slope 84 of magnitude greater than about 0.1 nm per layer number with an r-squared value 85 greater than about 0.8. In some embodiments, P1 is an integer greater than about 50 and P2 is an integer greater than about 10. In some embodiments, P1 is at least 50, or at least 100, or at least 150, or at least 200. In some such embodiments, or in other embodiments, P2 is at least 10, or at least 15, or at least 18.

[0033] In some embodiments, a linear fit 87 (see, e.g., FIG. 9 ) to at least P1 sequentially arranged polymer layers in the left region 81 has a positive linear slope 88 with an r-squared value 89 greater than about 0.8 and a magnitude ranging from about 0.01 nm per layer number to about 0.25 nm per layer number. In some embodiments, the linear fit 87 has a positive linear slope 88 ranging from about 0.02 nm per layer number, or about 0.03 nm per layer number, or about 0.04 nm per layer number to about 0.2 nm per layer number, or 0.15 nm per layer number. In some such embodiments, or in other embodiments, the linear fit 87 has an r-squared value 89 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.

[0034] In some embodiments, the negative linear slope 84 of the linear fit 83 has a magnitude greater than about 0.15 nm per layer number, or greater than about 0.2 nm per layer number, or greater than about 0.22 nm per layer number. In some such embodiments, or in other embodiments, the r-squared value 85 of the linear fit 83 is 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.

[0035] In some embodiments, optical film 100, 100' includes a plurality of polymer layers 10, 11 arranged along at least a portion of the thickness of the optical film and numbered sequentially from 1 to N, where N is an integer greater than about 100 or greater than about 200. The plurality of polymer layers includes a polymer end layer at each end (e.g., layers 22, 23 in optical film 100 or layers 22, 223 in optical film 100'), and the polymer end layers and each layer therebetween have an average thickness of less than about 300 nm. The optical film can have, for example, layer thickness profiles shown in Figures 11-14.

[0036] Figure 11 is a plot 110 of average layer thickness versus layer number for multiple polymer layers 10, 11, according to some embodiments. The thickness profile can be for multiple polymer layers 10, 11 across an entire film, or for a packet of film (e.g., 141 or 142). Figures 12-14 show portions of the plot of Figure 11.

[0037] In some embodiments, a plot 110 of average layer thickness t versus layer number for the multiple polymer layers 11, 12 includes a bend region 111 separating a left region 112 including at least Q1 sequentially ordered polymer layers having lower layer numbers from a right region 113 including at least Q2 sequentially ordered polymer layers having higher layer numbers, where the polymer layers are such that a linear fit 114 (see, e.g., FIG. 12 ) to the at least Q1 sequentially ordered polymer layers in the left region 112 has an r-squared value 116 greater than about 0.8 and a positive linear slope 115 of greater than about 0.04 nm per layer number, and a linear fit 115 to the at least Q2 sequentially ordered polymer layers in the right region 113 has an r-squared value 116 greater than about 0.8 and a positive linear slope 115 of greater than about 0.04 nm per layer number. The fit 117 (see, e.g., FIG. 13) has a negative linear slope 118 of sufficient magnitude such that the optical film's optical transmittance 130 (see, e.g., FIG. 18) versus wavelength for substantially normally incident light 50 having a first polarization state includes a band edge 131 between about 800 nm and about 1100 nm, at least over the wavelength range in which the optical transmittance at the band edge increases from about 10% to at least about 80%, and the best linear fit 132 (see, e.g., FIG. 19) correlating the optical transmittance to wavelength to the band edge 131 has a slope 133 of greater than about 3% / nm, or a slope of greater than about 4% / nm, or any of the ranges described elsewhere herein for band edge slopes. In some embodiments, the best linear fit 132 has an r-squared value 138 of 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, 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.

[0038] In some embodiments, the linear fit 117 to the at least Q2 sequentially arranged polymer layers in the right region 113 has a negative linear slope 118 with an r-squared value 119 greater than about 0.8 and a magnitude greater than about 0.1 nm per layer number. In some embodiments, the negative linear slope 118 of the linear fit 117 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 in other embodiments, the r-squared value 119 of the linear fit 117 is greater than about 0.8, or greater than about 0.85, or greater than about 0.9.

[0039] In some embodiments, the positive linear slope 115 of the linear fit 114 has a magnitude greater than about 0.05 nm per layer number, or greater than about 0.06 nm per layer number, or greater than about 0.07 nm per layer number. In some such embodiments, or in other embodiments, the r-squared value 116 of the linear fit 114 is greater than about 0.8, or greater than about 0.85, or greater than about 0.9, or greater than about 0.95.

[0040] In some embodiments, a plot 110 of average layer thickness t versus layer number for a plurality of polymer layers includes a knee region 111 that separates a left region 112 including at least 100 sequentially ordered polymer layers having lower layer numbers from a right region 113 including at least 10 sequentially ordered polymer layers having higher layer numbers, where a third order polynomial fit 120 (see, e.g., FIG. 14 ) to at least 15 sequentially ordered polymer layers including the knee region 111 has a positive third order coefficient 121 and a negative second order coefficient 122 with an r-squared value 123 greater than about 0.8. In some embodiments, the r-squared value 123 is greater than about 0.85, or greater than about 0.9. In some embodiments, the left region 112 includes at least 150 or at least 180 sequentially ordered polymer layers. In some embodiments, the right region 113 includes at least 12 or at least 14 sequentially ordered polymer layers.

[0041] In some embodiments, the optical films 100, 100' include a plurality of polymer layers 10, 11 sequentially numbered from 1 to N, where N is an integer greater than about 100 or at least 150, and each of the polymer layers 10, 11 has an average thickness of less than about 300 nm. The optical films 100, 100' may 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 110 of the average layer thickness t versus the layer number of the plurality of polymer layers 10, 11 includes a bent region 111 that includes the thickest polymer layer 124 within the plurality of polymer layers 10, 11 such that the optical films 100, 100', or the plurality of polymer layers 10, 11 have the reflectivity and transmittance characteristics described elsewhere herein.

[0042] In some embodiments, the layer thickness profile of region 32, 82, or 113 decreases by increasing the layer number, as described by an exponential function further described elsewhere herein.

[0043] FIG. 15 is a schematic plot of the average layer thickness 321 versus the layer number for the m-th layer 328 to the N-th layer 329, according to some embodiments. In some embodiments, the m-th layer 328 within the plurality of polymer layers 10, 11 has an average thickness tm, where m < N, and the average thickness of each polymer layer within the plurality of polymer layers 10, 11 having layer numbers n, where m ≦ n ≦ N, is

Equation

Number

Number

[0044] FIG. 16 is a plot of the optical transmission 60 of the optical film 100, 100' versus wavelength, according to some embodiments. FIG. 17 is a portion of the plot of FIG. 16 near the band edge 61. The optical transmission 60 can be for substantially normally incident light 50 having a first polarization state 171. In some embodiments, the optical film is a reflective polarizer that substantially transmits light having a second polarization state 172 that is orthogonal to the first polarization state 171. In other embodiments, the optical film is a mirror film that has an optical transmission similar to the optical transmission 60 of substantially normally incident light 50 having the second polarization state 171. The layer thickness profile of FIG. 3 of packets reflecting longer wavelengths in an optical film that includes packets reflecting shorter wavelengths can produce an optical transmission 60. The layer thickness profile of FIG. 8 can produce a similar optical transmission. In some embodiments, the optical film 100, 100', or multiple polymer layers 10, 11, are substantially non-absorbing, such that the optical reflectance R of the optical film is substantially equal to 100% minus the optical transmittance of the optical film.

[0045] In some embodiments, for substantially normal incident light 50 and a first wavelength range W1 ranging from about 400 nm to about 800 nm and a second wavelength range W2 ranging from about 950 nm to about 1300 nm, the plurality of polymer layers 10, 11 or optical film 100, 100' reflects more than about 80% of the incident light having a first polarization state 171 in the first wavelength range W1, transmits more than about 40% of the incident light having a second polarization state 172 in the first wavelength range W1 that is orthogonal to the first polarization state 171, and in some embodiments transmits more than about 60% of the incident light in the second wavelength range W2 for each of the first and second polarization states 171 and 172. In some embodiments, the plurality of polymer layers 10, 11 or optical film 100, 100' transmits more than about 50% of the incident light having the second polarization state 172 in the first wavelength range W1. In some embodiments, the polymer layers 10, 11 or optical film 100, 100' transmit more than about 70%, or more than about 80%, of the incident light in the second wavelength range W2 for each of the first and second polarization states 171 and 172. In some embodiments, for substantially perpendicular incident light 50, the optical film 100, 100' or polymer layers 10, 11 reflect more than about 80% of the incident light 50 in the first wavelength range W1 for the first polarization state 171 and the orthogonal second polarization state 172. In some such embodiments, or in other embodiments, the polymer layers 10, 11 or optical film 100, 100' transmit more than about 60%, or more than 70%, or more than about 80% of the incident light in the second wavelength range W2 for each of the first and second polarization states 171 and 172.

[0046] In some embodiments, for substantially normally incident light 50 having a first polarization state 171, the optical transmission 60 of the optical film versus wavelength includes a band edge 61 between about 850 nm and about 950 nm, and over at least a wavelength range W3 in which the optical transmission increases from about 10% to at least about 70% (e.g., from about 10% to about 70%, or from about 10% to about 80%, or from about 10% to at least about 80%), a best linear fit 62 (see, e.g., FIG. 17 ) to the band edges correlating the optical transmission to wavelength has a slope 63 greater than about 3% / nm. In some embodiments, the slope 63 is 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, the best linear fit 62 has an r-squared value 64 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.

[0047] FIG. 18 is a plot of the optical transmission 130 of the optical film 100, 100' versus wavelength. FIGS. 19-21 are a portion of the plot of FIG. 18. The optical transmission 130 can be for substantially normally incident light 50 having a first polarization state 171. In some embodiments, the optical film is a reflective polarizer that substantially transmits light having a second polarization state 172 that is orthogonal to the first polarization state 171. In other embodiments, the optical film is a mirror film that has an optical transmission similar to the optical transmission 130 for substantially normally incident light 50 having the second polarization state 171. The layer thickness profile of FIG. 11 for packets reflecting longer wavelengths in an optical film that includes packets reflecting shorter wavelengths can produce the optical transmission 130.

[0048] In some embodiments, the multiple polymer layers 10, 11 or optical film 100, 100' reflects more than about 80% of incident light 50 having a first polarization state 171 in a first wavelength range W1, transmits more than about 40% or more than about 50% of incident light having a second polarization state 172 orthogonal to the first polarization state in the first wavelength range W1, and transmits more than about 60% of incident light in a second wavelength range W2 for each of the first and second polarization states 171 and 172, and the optical film's light transmission 130 versus wavelength for the first polarization state 171 includes a band edge 131 between about 800 nm and about 1100 nm. In some embodiments, the band edge 131 is between about 850 nm and about 950 nm. In some embodiments, the best linear fit 132 to the band edge 131 correlating optical transmittance to wavelength (see, e.g., FIG. 19 ) over at least the wavelength range where optical transmittance at the band edge increases from about 10% to at least about 70% has a slope 133 of greater than about 3% / nm, or is either in the range described elsewhere for the band edge slope (e.g., a slope of greater than about 4% / nm).

[0049] In some embodiments, the wavelength range W5 (see, e.g., FIG. 19 ) from a first wavelength λa where the best linear fit 132 is 20% to a second wavelength λb where the best linear fit 132 is 80% is less than about 30 nm wide, or less than about 20 nm wide, or less than about 15 nm wide. In some embodiments, the wavelength range from the smallest wavelength greater than about 600 nm where the transmittance is at least about 20% to the smallest wavelength greater than about 600 nm where the transmittance is at least about 80% is less than about 30 nm wide, or less than about 20 nm wide, or less than about 15 nm wide.

[0050] In some embodiments, a quadratic polynomial fit 134 (see, e.g., FIG. 20) to the optical transmission 130 over a wavelength range at least 200 nm wide between the band edge and about 2000 nm or about 1600 nm or about 1300 nm has an r-squared value 139 greater than about 0.6 and a minimum optical transmission Tmin 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 139 is greater than about 0.7 or greater than about 0.75. In some embodiments, the quadratic polynomial fit 134 has a positive quadratic coefficient 181 and a negative linear coefficient 182. In some embodiments, the quadratic polynomial fit 134 has a minimum optical transmission Tmin less than about 75%. In some embodiments, the minimum optical transmission Tmin is greater than about 60% or greater than about 65%.

[0051] In some embodiments, for substantially normal incidence light and a third wavelength range W4 spanning a smaller wavelength L1 to a larger wavelength L2 (see, e.g., FIG. 21), the optical transmittance 130 has an average value of greater than about 75%, or greater than about 80%, or greater than about 85%, and 30 nm≦L2-L1≦50 nm, where L1 is greater than and within about 20 nm of a wavelength 135 corresponding to about 50% optical transmittance at the band edge. 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 135.

[0052] FIG. 22 is a schematic plot of optical transmission as a function of wavelength of a reflective polarizer for light having a pass polarization state (e.g., second polarization state 172) according to some embodiments. The pass polarization state can be a p-polarization state (p-pol) or an s-polarization state (s-pol) with the projection of the electric field onto the plane of the reflective polarizer being parallel to the pass axis (e.g., x-axis) of the reflective polarizer. Optical transmission 433 for substantially vertically incident light 50 and optical transmission 435 for light 170 at an incidence angle θ are shown. Average transmissions Tp0 and Tpθ over a wavelength range from λ1 to λ2 are shown. λ1 can be about 400 nm and λ2 can be, for example, about 600 nm, about 700 nm, or about 800 nm. The wavelength range from λ1 to λ2 can correspond to a first wavelength range W1. In some embodiments, λ3 can be about 950 nm and λ4 can be, for example, about 2000 nm, or about 1600 nm, or about 1100 nm, or about 1300 nm, or about 1200 nm. The wavelength range from λ3 to λ4 can correspond, for example, to the second wavelength range W2. In some embodiments, the transmittance increases sharply for wavelengths greater than λ2, resulting in a greater transmittance in the second wavelength range W2 than in the first wavelength range W1. In some embodiments, for the second polarization state and the first wavelength range W1, the reflective polarizer has an average light transmittance Tp0 of greater than about 40%, or greater than about 45%, or greater than about 50%, or greater than about 55%, or greater than about 60%. In some embodiments, for the second polarization state 172 and the first wavelength range W1, the reflective polarizer has a greater average light transmission (e.g., Tp0) for light incident at a smaller angle of incidence (e.g., from zero degrees to about 20 degrees, or about zero degrees) and a smaller average light transmission (e.g., Tpθ) for light incident at a larger angle of incidence (e.g., from about 30 degrees to about 50 degrees, or about 45 degrees). In some embodiments, the second polarization state 172 is a p-polarization state, and the larger angle of incidence is less than about 50 degrees. In some embodiments, for light in the pass polarization state for each of p-polarization and s-polarization, the reflective polarizer has a greater average light transmission (e.g., Tp0) for light incident at a smaller angle of incidence and a smaller average light transmission (e.g., Tpθ) for light incident at a larger angle of incidence.In some embodiments, for the second (pass) polarization state at any plane of incidence, the reflective polarizer has a greater average light transmission (e.g., Tp0) for substantially normally incident light and a lesser average light transmission (e.g., Tpθ) for light incident at an angle of incidence of about 45 degrees. In some embodiments, the difference between the greater and lesser average light transmission (e.g., Tpθ-Tp0) is at least about 10%, or at least about 20%, or at least about 30%.

[0053] The linear fit described herein can be a linear least squares fit as known in the art. The polynomial fit can be a least squares fit as well. Such a fit minimizes the residual sum of squares, where the residual is the difference between the data and the fitted curve (linear or polynomial). The least squares analysis can determine the r-square value, which is sometimes called the coefficient of determination.

[0054] In some embodiments, the optical film includes an optically diffusing layer arranged on the multiple polymer layers 11, 12. The optically diffusing layer can be arranged on one of the outermost layers 146 or 147, for example. The optically diffusing layer can be any suitable optically diffusing layer. Suitable optically diffusing layers include those described in U.S. Provisional Patent Application No. 63 / 021751, filed May 8, 2020, entitled "OPTICAL FILMS AND STACKS INCLUDING OPTICALLY DIFFUSIVE LAYER," the contents of which are incorporated herein by reference to the extent that they do not conflict with the statements herein. Other suitable optically diffusing layers include those described in U.S. Provisional Patent Application No. 62 / 704399, filed May 8, 2020, entitled "OPTICAL CONSTRUCTION AND DISPLAY SYSTEM INCLUDING SAME," the contents of which are incorporated herein by reference to the extent that they do not conflict with the statements herein.

[0055] In some embodiments, the optical film includes an optical layer disposed on a plurality of polymer layers 11, 12, with a structured major surface facing outwardly of the polymer layers 11, 12. The optical layer can be disposed, for example, on one of the outermost layers 146 or 147, or one of the outermost layers 146 or 147 can be an optical layer. The structured surface can reduce friction with and / or wet-out by adjacent layers or films. For example, the optical layer can include an array of discrete, spaced apart optical bumps, as described in U.S. Provisional Patent Application No. 63 / 021773, filed May 8, 2020, and entitled "OPTICAL FILM WITH DISCONTINUOUS COATING," the contents of which are incorporated herein by reference to the extent not inconsistent with the statements herein. As another example, the optical layer can include a plurality of spaced apart elongated structures extending along the same first direction as described in U.S. Provisional Patent Application No. 63 / 021,756, filed May 8, 2020, and entitled “OPTICALLY DIFFUSIVE FILM WITH ELONGATED STRUCTURES,” the contents of which are incorporated by reference herein to the extent not inconsistent herewith.

[0056] In some embodiments, each of the outermost layers of the optical film includes particles partially protruding from the outermost layer to form outwardly facing major surfaces of the plurality of polymer layers, as described in U.S. Provisional Patent Application No. 63 / 021765, filed May 8, 2020, and entitled "REFLECTIVE POLARIZER WITH IMPROVED OPTICAL CHARACTERISTICS," the contents of which are incorporated by reference herein to the extent not inconsistent with the description herein.

[0057] 29 is a schematic cross-sectional view of a display system 1000 for sensing a finger 161 of a user 1160 applied to the display system 1000. The display system 1000 comprises a display panel 770 configured to generate an image 271 for viewing by a user 160; a light guide 90 for providing illumination 188 to the display panel 770; an optical film 400; a sensor 125 for sensing a finger 161 of a user 160 disposed near the light guide 90 opposite the optical film 400; an optical film 500 disposed between the light guide 90 and the sensor 125; and an infrared source 220 configured to emit infrared light 221 toward the finger 161 of the user 160, where the sensor 125 is configured to receive at least a portion 222 of the infrared light 221 reflected by the finger 161. In some embodiments, the infrared light source 220 is disposed under a cover glass of the display system 1000. In some embodiments, the infrared light source 220 is disposed below the optical film 500 (e.g., the infrared light source 220 can be arranged such that the optical film 500 is between the light guide 90 and the infrared light source 220). The display system 1000 can optionally include an optical diffuser arranged between the optical film 400 and the light guide 90. The optical film 400 and / or the optical film 500 can be any of the optical films described herein. In some embodiments, a display system 1000 for sensing a finger 161 of a user 160 applied to the display system 1000 is provided. The display system 1000 includes a display panel 770 configured to generate an image 271 for display by the user 160, a sensor 125 for sensing the finger 161 of the user 160, and an optical film described herein (e.g., the optical film 400 and / or the optical film 500) arranged between the display panel 770 and the sensor 125. In some embodiments, the display system 1000 includes a first optical film (e.g., optical film 400) and a second optical film (e.g., optical film 500) described herein arranged between the display panel 770 and the sensor 125.

[0058] In some embodiments, the optical film 400 includes a plurality of polymer layers 460 (individual layers are not shown in the schematic diagram of FIG. 29), which may correspond to the plurality of polymer layers 11, 12 shown in FIG. 1 or FIG. 2, for example. In some embodiments, the optical film 400 includes an optically diffusing layer 410 arranged on the plurality of polymer layers 460. In some embodiments, the optical film 400 includes an optical layer 470 disposed on the plurality of polymer layers 460 and having a structured major surface 471 facing away from the plurality of polymer layers 460. In some embodiments, the optical film 400 is an infrared-transmitting reflective polarizer. In some embodiments, the reflective polarizer is a collimating reflective polarizer. Such a polarizer can provide a collimating effect by reflecting light with a larger angle of incidence toward the optical film 500, which may be a mirror film including an optically diffusing layer so that the light circulates. Liquid crystal displays (LCDs) often include brightness enhancing prism films (typically crossed prism films) to increase the on-axis brightness of the display. In some cases, such films may be omitted when a collimating reflective polarizer is included. In some embodiments of the display system 1000, there is no brightness enhancing prism film disposed between the display panel 770 and the optical film 500.

[0059] In some embodiments, optical film 500 includes multiple polymer layers 560 (individual layers not shown in the schematic diagram of FIG. 29), which may correspond to, for example, multiple polymer layers 11, 12 shown in FIG. 1 or 2. In some embodiments, optical film 500 includes an optical diffusing layer 510 disposed on multiple polymer layers 560. In some embodiments, optical film 400 is an infrared transmissive optical mirror.

[0060] Related display systems are described in U.S. Provisional Patent Application No. 63 / 021760, filed May 8, 2020, entitled "DISPLAY SYSTEM WITH FINGER SENSING," and U.S. Provisional Patent Application No. 63 / 021739, filed May 8, 2020, the contents of which are incorporated by reference herein to the extent not inconsistent herewith, and in U.S. Provisional Patent Application No. 63 / 021739, filed May 8, 2020, the contents of which are incorporated by reference herein to the extent not inconsistent herewith, and the U.S. Provisional Patent Application No. 63 / 021739, filed May 8, 2020, the contents of which are incorporated by reference herein to the extent not inconsistent herewith. EXAMPLES

[0061] [Table 1]

[0062] A numerical modeling study was completed using three different layer thickness profiles consisting of 650 microlayers sandwiched between two thicker skin layers. The 650 microlayers were alternating between a birefringent high index optical layer (HIO) and an isotropic low index optical layer (LIO). The refractive indices used in this model at 633 nm are shown in the table below. These indices were estimated from a multilayer optical reflective polarizer. The film was produced via a multilayer coextrusion process using PEN as the HIO material and a polymer blend of 15.0 weight percent PETG, 40.8 weight percent PCTG, 17.0 weight percent PC1804, and 27.2 weight percent PC2405 as the LIO material. The film was then continuously stretched in a standard tenter with a 6:1 stretch ratio in the transverse direction and restrained (no orientation or relaxation) in the machine direction. The oven temperature used for orientation was 270 degrees Fahrenheit. The exponents were estimated by using the numerical model that gave the best fit between the measured spectrum and the calculated spectrum of the 650 microlayer film. Layer thicknesses were measured using an atomic force microscope (Dimension ICON from Bruker Instruments, Billerica, MA).

[0063] [Table 2]

[0064] The thickness profiles of the three model layers are shown in FIG. 23 and are defined as follows: Layer profile 1: Proposed layer profile designed to provide reflectivity from about 400 nanometers to about 930 nanometers for the block polarization state. Bed profile 2: Compared to bed profile 1, exponential relationship

number

[0065] To simulate the optical performance of these layer profiles with these materials, a numerical optical model was used to calculate the resulting transmission spectra of these reflective polarizers in the blocked state. Calculations were performed for each layer profile. Each skin layer consisted of LIO material and had thicknesses of 1.5, 2.5, and 5.0 micrometers. The table below defines the parameters of reflective polarizers 1-9 and shows the calculated average transmission in 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 where the transmission reaches 20% relative to the wavelength where 80% is finally achieved.

[0066] [Table 3]

[0067] The reflective polarizers with "down" apodization are exemplary reflective polarizers (Reflective Polarizers 3, 6, and 9), while those with "standard" and "up" apodization are comparative reflective polarizers.

[0068] The resulting block state transmission spectra are shown in Figure 24 for 1.5 micrometer thick skin layers (reflective polarizers 1, 2, and 3), Figure 25 for 2.5 micrometer thick skin layers (reflective polarizers 4, 5, and 6), and Figure 26 for 5.0 micrometer thick skin layers (reflective polarizers 7, 8, and 9).

[0069] Figures 27 and 28 show experimental layer thickness profiles and transmission spectra of reflective polarizers 10 and 11, respectively, showing the relationship between layer thickness profiles and transmission spectrum shape. The materials, layer configurations, and process conditions used to make these films are 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 feedblock described in U.S. Patent No. 6,783,349 (Neavin et al.). The skin layers were 1.5 micrometers thick for reflective polarizers 10 and 11. Figure 27 shows the measured layer thickness profiles of the last 325 layers delivered by the feedblock system for the two reflective polarizer films. Figure 28 shows the resulting block state transmission spectra of reflective polarizers 10 and 11. Reflective polarizer 11 had fewer layers with a high positive slope compared to reflective polarizer 10. Reflective polarizer 11 exhibited higher transmittance than reflective polarizer 10 for the wavelength range adjacent to the right band edge (910-950 nm).

[0070] The mirror film can be fabricated with a layer thickness profile similar to reflective polarizers 1 through 11. The mirror film is expected to have a transmission spectrum for each of the two orthogonal polarization states similar to the transmission spectrum of the corresponding reflective polarizer for the block polarization state.

[0071] Terms such as "about" will be understood by those of skill in the art in the context in which they are used and described herein. If the use of "about" as applied to quantities describing feature sizes, quantities, and physical properties is not clear to those of skill in the art in the context in which it is used and described herein, "about" will be understood to mean within 10 percent of a particular value. A quantity given as about a particular value may be exactly that particular value. For example, if it is not clear to those of skill in the art in the context in which it is used and described herein, an amount having a value of about 1 means that the amount has a value between 0.9 and 1.1, and the value may be 1.

[0072] All references, patents, or patent applications referenced above are hereby incorporated by reference in their entirety. In the event of any inconsistency or contradiction between any portion of the incorporated reference and this application, the information in the foregoing description shall take precedence.

[0073] Descriptions of elements in a figure should be understood to apply equally to corresponding elements in other figures unless otherwise indicated. Although specific embodiments have been illustrated and described herein, those skilled in the art will appreciate that the specific embodiments illustrated and described may be replaced by various alternative and / or equivalent embodiments without departing from the scope of the present disclosure. The present application is intended to cover any adaptations, or variations, or combinations of the specific embodiments discussed herein. Accordingly, the present disclosure is intended to be limited only by the claims and the equivalents thereof. In the following, exemplary embodiments are presented. [Item 1] 1. An optical film comprising a plurality of polymer layers disposed along at least a portion of a thickness of the optical film, the plurality of polymer layers being numbered sequentially from 1 to N, where N is an integer greater than about 100, the plurality of polymer layers including polymer end layers at both ends thereof, a plot of average layer thickness versus layer number of the plurality of polymer layers including a first knee region separating a left region including at least N1 sequentially ordered polymer layers having lower layer numbers from a middle region including at least N2 sequentially ordered polymer layers having higher layer numbers, where N1 is an integer greater than about 50 and N2 is an integer greater than about 10, the polymer layers having a linear fit to the at least N1 sequentially ordered polymer layers in the left region having a positive linear slope greater than about 0.04 nm per layer number with an r-squared value greater than about 0.8 and a linear fit to the at least N2 sequentially ordered polymer layers in the middle region having a negative linear slope greater than about 0.05 nm per layer number with an r-squared value greater than about 0.8. [Item 2] For substantially normal incident light and a first wavelength range ranging from about 400 nm to about 800 nm and a second wavelength range ranging from about 950 nm to about 1300 nm, the plurality of polymer layers reflecting greater than about 80% of the incident light having a first polarization state in the first wavelength range; transmits greater than about 40% of the incident light having a second polarization state in the first wavelength range, the second polarization state being orthogonal to the first polarization state; transmits greater than about 60% of the incident light in the second wavelength range for each of the first and second polarization states. Item 2. The optical film according to item 1. [Item 3] 3. The optical film of claim 2, wherein for the second polarization state and the first wavelength range, the optical film has a greater average light transmittance for light incident at a smaller angle of incidence and a lesser average light transmittance for light incident at a larger angle of incidence. [Item 4] 4. The optical film of any one of items 1 to 3, wherein the optical transmittance of the optical film versus wavelength for substantially normally incident light having a first polarization state includes the band edges between about 850 nm and about 950 nm, and a best linear fit to the band edges correlating the optical transmittance to wavelength has a slope of greater than about 3% / nm, at least over the wavelength range in which the optical transmittance increases from about 10% to about 70%. [Item 5] 5. The optical film of any one of items 1 to 4, wherein the polymer layers have a higher layer number than the polymer layers in the middle region, and further comprises a second bend region separating the middle region from a right region comprising at least N3 sequentially arranged polymer layers, N3 being an integer greater than 3, and wherein a linear fit to the at least N3 sequentially arranged polymer layers in the right region has a positive linear slope with an r-squared value greater than about 0.6 and a magnitude greater than about 1.2 nm per layer number. [Item 6] 6. The optical film of any one of items 1 to 5, wherein the polymer end layers and each layer therebetween have an average thickness of less than about 300 nm. [Item 7] 6. The optical film of any one of the preceding claims, wherein at least one layer between the polymer end layers has an average thickness greater than about 500 nm. [Item 8] 1. An optical film comprising a plurality of polymer layers including a polymer end layer at each end thereof, the polymer end layers and each layer therebetween having an average thickness of less than 300 nm; A plot of average layer thickness versus layer number of the plurality of polymer layers is provided, a left region comprising at least N4 sequentially arranged polymer layers, where N4 is an integer greater than about 5; a first intermediate region comprising at least N1 sequentially arranged polymer layers, N1 being an integer greater than about 50; a second intermediate region comprising at least N2 sequentially arranged polymer layers, where N2 is an integer greater than about 10; a right region comprising at least N3 sequentially arranged polymer layers, where N3 is an integer greater than about 3; Including, The linear fit to the at least N4 successively arranged polymer layers in the left region has an r-squared value greater than about 0.8 and a negative linear gradient with a magnitude greater than about 0.04 nm per layer number. The linear fit to the at least N1 successively arranged polymer layers in the first intermediate 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 N2 successively arranged polymer layers in the second intermediate region has an r-squared value greater than about 0.8 and a negative linear gradient with a magnitude greater than about 0.05 nm per layer number. The linear fit to the at least N3 successively arranged polymer layers in the right region has an r-squared value greater than about 0.6 and a positive linear gradient with a magnitude greater than about 1.2 nm per layer number. Optical film. [Item 9] The first bending region separates the left region from the first intermediate region, where the polymer layers in the first intermediate region have a higher layer number than the polymer layers in the left region. The second bending region separates the first intermediate region from the second intermediate region, where the polymer layers in the second intermediate region have a higher layer number than the polymer layers in the first intermediate region. The third bending region separates the second intermediate region from the right region, where the polymer layers in the right region have a higher layer number than the polymer layers in the second intermediate region. The optical film according to item 8. [Item 10] An optical film, including a plurality of polymer layers arranged sequentially from 1 to N along at least a part of the thickness of the optical film, where N is an integer greater than about 100. The plurality of polymer layers include polymer end layers at both ends. The polymer end layers and each layer therebetween have an average thickness of less than about 300 nm. The m-th layer in the plurality of polymer layers has an average thickness tm, where m < N. The average thickness of each polymer layer in the plurality of polymer layers having a layer number n with m ≤ n ≤ N is

number

Claims

1. an optical film comprising a plurality of polymer layers disposed along at least a portion of a thickness of the optical film, the plurality of polymer layers being numbered sequentially from 1 to N, N being an integer greater than 100, the plurality of polymer layers including polymer end layers at both ends thereof, a plot of average layer thickness versus layer number of the plurality of polymer layers comprising a first knee region separating a left region including at least N1 sequentially ordered polymer layers having lower layer numbers from a middle region including at least N2 sequentially ordered polymer layers having higher layer numbers, N1 being an integer greater than 50 and N2 being an integer greater than 10, the polymer layers wherein a linear fit to the at least N1 sequentially ordered polymer layers in the left region has a positive linear slope greater than 0.04 nm in magnitude per layer number with an r-squared value greater than 0.8 and a linear fit to the at least N2 sequentially ordered polymer layers in the middle region has a negative linear slope greater than 0.05 nm in magnitude per layer number with an r-squared value greater than 0.8, both r-squared values ​​being determined by least squares analysis; the optical film further comprises a second bend region separating the intermediate region from a right region comprising at least N3 sequentially ordered polymer layers, the polymer layers having a higher layer number than the polymer layers in the intermediate region, N3 being an integer greater than 3, and a linear fit to the at least N3 sequentially ordered polymer layers in the right region having a positive linear slope. Optical film.

2. For substantially normally incident light and a first wavelength range extending from 400 nm to 800 nm and a second wavelength range extending from 950 nm to 1300 nm, the plurality of polymer layers reflecting greater than 80% of the incident light having a first polarization state in the first wavelength range; transmits more than 40% of the incident light having a second polarization state in the first wavelength range, the second polarization state being orthogonal to the first polarization state; transmits greater than 60% of the incident light in the second wavelength range for each of the first and second polarization states. The optical film according to claim 1 .

3. 3. The optical film of claim 2, wherein for the second polarization state and the first wavelength range, the optical film has a greater average light transmittance for light incident at a smaller angle of incidence and a lesser average light transmittance for light incident at a larger angle of incidence.

4. 2. The optical film of claim 1, wherein the optical transmittance of the optical film versus wavelength for substantially normally incident light having a first polarization state includes the band edges between 850 nm and 950 nm, and a best linear fit to the band edges correlating the optical transmittance to wavelength has a slope of greater than 3% / nm over at least the wavelength range in which the optical transmittance increases from 10% to 70%.

5. 2. The optical film of claim 1, wherein a positive linear slope of a linear fit to the at least N3 sequentially arranged polymer layers in the right region has a magnitude greater than 1.2 nm per layer number, and a linear fit to the at least N3 sequentially arranged polymer layers in the right region has an r-squared value greater than 0.

6.

6. The optical film of any one of claims 1 to 5, wherein the polymer end layers and each layer therebetween have an average thickness of less than 300 nm.

7. The optical film of any one of claims 1 to 5, wherein at least one layer between the polymer end layers has an average thickness greater than 500 nm.

8. 1. An optical film comprising a plurality of polymer layers including a polymer end layer at each end thereof, the polymer end layers and each layer therebetween having an average thickness of less than 300 nm; A plot of average layer thickness versus layer number of the plurality of polymer layers is provided, a left region comprising at least N4 sequentially arranged polymer layers, N4 being an integer greater than 5; a first intermediate region comprising at least N1 sequentially arranged polymer layers, N1 being an integer greater than 50; a second intermediate region comprising at least N2 sequentially arranged polymer layers, where N2 is an integer greater than 10; a right region comprising at least N3 sequentially arranged polymer layers, N3 being an integer greater than 3; Including, a linear fit to the at least N4 sequentially ordered polymer layers in the left region has a negative linear slope greater than 0.04 nm per layer number with an r-squared value greater than 0.8; a linear fit to the at least N1 sequentially ordered polymer layers in the first intermediate region has a positive linear slope greater than 0.04 nm per layer number with an r-squared value greater than 0.8; a linear fit to the at least N2 sequentially ordered polymer layers in the second intermediate region has a negative linear slope greater than 0.05 nm per layer number with an r-squared value greater than 0.8; and a linear fit to the at least N3 sequentially ordered polymer layers in the right region has a positive linear slope greater than 1.2 nm per layer number with an r-squared value greater than 0.6, all r-squared values ​​determined by least squares analysis. Optical film.

9. a first bend region separates the left region from the first middle region, wherein the polymer layer in the first middle region has a higher layer number than the polymer layer in the left region; a second bend region separates the first intermediate region from the second intermediate region, wherein the polymer layer in the second intermediate region has a higher layer number than the polymer layer in the first intermediate region; a third bend region separates the second middle region from the right region, wherein the polymer layer in the right region has a higher layer number than the polymer layer in the second middle region; The optical film according to claim 8 .

10. 1. An optical film comprising a plurality of polymer layers disposed along at least a portion of a thickness of the optical film, the plurality of polymer layers being numbered sequentially from 1 to N, where N is an integer greater than 100, the plurality of polymer layers including polymer end layers at both ends thereof, the polymer end layers and each layer therebetween having an average thickness of less than 300 nm, an mth layer in the plurality of polymer layers having an average thickness tm, where m<N, and the average thickness of each polymer layer in the plurality of polymer layers having layer number n, where m≦n≦N, is [0010] [In the formula, A is a real number, 0.01tm≦A≦0.25tm, and d is an integer, 0.005N≦d≦0.1N] The optical film according to claim 1, wherein the optical density is within 10% of the above.

11. 1. An optical film comprising a plurality of polymer layers disposed along at least a portion of a thickness of the optical film, the plurality of polymer layers being numbered sequentially from 1 to P, where P is an integer greater than 100, the plurality of polymer layers including polymer end layers at both ends thereof, the polymer end layers and each layer therebetween having an average thickness of less than 300 nm; a plot of average layer thickness versus layer number of the plurality of polymer layers includes a first knee region separating a left region including at least P1 sequentially ordered polymer layers having lower layer numbers from a right region including at least P2 sequentially ordered polymer layers having higher layer numbers, P1 being an integer greater than 50 and P2 being an integer greater than 10, the polymer layers being such that a linear fit to the at least P2 sequentially ordered polymer layers in the right region has a negative linear slope of magnitude greater than 0.1 nm per layer number with an r-squared value greater than 0.8; the optical transmittance of the optical film versus wavelength for substantially normally incident light having a first polarization state includes a band edge from 850 nm to 950 nm, at least over a wavelength range in which the optical transmittance increases from 10% to 70%, and a best linear fit to the band edges correlating the optical transmittance to wavelength has an r-squared value greater than 0.8 and a slope greater than 3% / nm; All r-squared values ​​are determined by least squares analysis. Optical film.

12. 1. An optical film comprising a plurality of polymer layers disposed along at least a portion of a thickness of the optical film, the plurality of polymer layers being numbered sequentially from 1 to N, N being an integer greater than 200, the plurality of polymer layers including polymer end layers at both ends thereof, the polymer end layers and each layer therebetween having an average thickness of less than 300 nm, a plot of average layer thickness versus layer number of the plurality of polymer layers including a knee region separating 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 being an integer greater than 100 and Q2 being an integer greater than 10, the polymer layers including at least Q1 sequentially arranged polymer layers in the left region including at least Q2 sequentially arranged polymer layers having higher layer numbers, an optical film in which a linear fit to the sequentially arranged polymer layers has a positive linear slope of greater than 0.04 nm per layer number with an r-squared value greater than 0.8, the r-squared value being determined by least squares analysis; the polymer layers having a linear fit to at least Q2 sequentially arranged polymer layers in the right region, for substantially normally incident light having a first polarization state, a negative linear slope of sufficient magnitude that the optical transmittance of the optical film versus wavelength includes a band edge from 800 nm to 1100 nm, where the best linear fit to the band edge correlating the optical transmittance to wavelength has a slope of greater than 3% / nm, at least over the wavelength range where the optical transmittance at the band edge increases from 10% to at least 80%.

13. 1. An optical film comprising a plurality of polymer layers numbered sequentially from 1 to N, disposed along at least a portion of a thickness of the optical film, N being an integer greater than 200, the plurality of polymer layers comprising polymer end layers at both ends, the polymer end layers and each layer therebetween having an average thickness less than 300 nm, a plot of average layer thickness versus layer number of the plurality of polymer layers comprising a knee region separating a left region comprising at least 100 sequentially ordered polymer layers having lower layer numbers from a right region comprising at least 10 sequentially ordered polymer layers having higher layer numbers, a third order polynomial fit to at least 15 sequentially ordered polymer layers comprising the knee region has a positive third order coefficient and a negative second order coefficient with an r-squared value greater than 0.8, the r-squared value being determined by least squares analysis.

14. 1. An optical film comprising a plurality of polymer layers numbered sequentially from 1 to N, N being an integer greater than 100, each of said polymer layers having an average layer thickness less than 300 nm, a plot of average layer thickness versus layer number of said plurality of polymer layers including a knee region including a thickest polymer layer in said plurality of polymer layers, for substantially normally incident light and a first wavelength range spanning 400 nm to 800 nm and a second wavelength range spanning 950 nm to 1300 nm, said plurality of polymer layers having reflecting greater than 80% of the incident light having a first polarization state in the first wavelength range; transmit greater than 40% of the incident light having a second polarization state in the first wavelength range, the second polarization state being orthogonal to the first polarization state; transmit greater than 60% of the incident light in the second wavelength range for each of the first and second polarization states; For a first polarization state, the optical transmittance of the optical film versus wavelength includes a band edge from 800 nm to 1100 nm, where a best linear fit to the band edge correlating the optical transmittance to the wavelength has a slope greater than 3% / nm over at least a wavelength range where the optical transmittance increases from 10% to at least 70% at the band edge, where the optical transmittance has an average value greater than 75% for substantially normally incident light and a third wavelength range extending from a smaller wavelength L1 to a larger wavelength L2, and where 30 nm≦L2-L1≦50 nm, L1 being greater than and within 20 nm of the wavelength corresponding to 50% optical transmittance at the band edge. Optical film.

15. 15. The optical film of claim 14, wherein the plurality of polymer layers comprises first and second plurality of polymer layers, the first and second plurality of polymer layers separated from one another along a thickness of the optical film by at least one intermediate layer, each intermediate layer having an average thickness greater than 500 nm.

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