Patent Publication Number: US-2023161197-A1

Title: Backlights including patterned reflectors

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application Serial No. 63/016503 filed on Apr. 28, 2020, the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The present disclosure relates generally to backlights for displays. More particularly, it relates to backlights including patterned reflectors and/or a diffusive layer. 
     TECHNICAL BACKGROUND 
     Liquid crystal displays (LCDs) are commonly used in various electronics, such as cell phones, laptops, electronic tablets, televisions, and computer monitors. LCDs are light valve-based displays in which the display panel includes an array of individually addressable light valves. LCDs may include a backlight for producing light that may then be wavelength converted, filtered, and/or polarized to produce an image from the LCD. Backlights may be edge-lit or direct-lit. Edge-lit backlights may include a light emitting diode (LED) array edge-coupled to a light guide plate that emits light from its surface. Direct-lit backlights may include a two-dimensional (2D) array of LEDs directly behind the LCD panel. 
     Direct-lit backlights may have the advantage of improved dynamic contrast as compared to edge-lit backlights. For example, a display with a direct-lit backlight may independently adjust the brightness of each LED to set the dynamic range of the brightness across the image. This is commonly known as local dimming. To achieve desired light uniformity and/or to avoid hot spots in direct-lit backlights, however, a diffuser plate or film may be positioned at a distance from the LEDs, thus making the overall display thickness greater than that of an edge-lit backlight. Lenses positioned over the LEDs have been used to improve the lateral spread of light in direct-lit backlights. The optical distance (OD) between the LEDs and the diffuser plate or film in such configurations (e.g., from at least 10 to typically about 20-30 millimeters), however, still results in an undesirably high overall display thickness and/or these configurations may produce undesirable optical losses as the backlight thickness is decreased. While edge-lit backlights may be thinner, the light from each LED may spread across a large region of the light guide plate such that turning off individual LEDs or groups of LEDs may have only a minimal impact on the dynamic contrast ratio. 
     SUMMARY 
     In some embodiments of the present disclosure, a backlight that includes a plurality of light sources coupled to a substrate, and a patterned diffuser over the plurality of light sources is disclosed. The patterned diffuser including a plurality of patterned reflectors coupled to a patterned diffuser body, where each patterned reflector is aligned with a corresponding light source. The backlight extends along a longitudinal direction, and the substrate has a maximum longitudinal substrate dimension (L Max ,S) and the patterned diffuser body has a maximum longitudinal patterned diffuser body dimension (L Max , PDB ), each of L Max , S  and L Max , PDB , respectively, measured in the longitudinal direction. The backlight has a thermal alignment tolerance in the longitudinal direction at 60° C. is 500 microns or less, where the thermal alignment tolerance at the 60° C. is the absolute value of [the smaller of L Max , S  and L Max , PDB]  x [60° C. - 23.5° C. (room temperature)] x [substrate coefficient of thermal expansion (CTE s ) - light guide plate coefficient of thermal expansion (CTE PDB )]. 
     Some embodiments of the present disclosure relate to a backlight each light source includes a size measured in a plane parallel to the longitudinal direction. Each patterned reflector is aligned with a corresponding light source and includes a thickness profile. The thickness profile includes a substantially flat section and a curved section extending from and surrounding the substantially flat section. The substantially flat section varies in thickness by no more than plus or minus 20 percent of an average thickness of the substantially flat section. The substantially flat section includes a size in a plane parallel to the longitudinal direction equal to or greater than the size of each light source. 
     Yet other embodiments of the present disclosure relate to a backlight where each patterned reflector is aligned with a corresponding light source and includes a first solid section, a plurality of second solid sections surrounding the first solid section, and a plurality of open sections interleaved with the plurality of second solid sections. The first solid section includes a size in a plane parallel to the longitudinal direction to or greater than the size of each light source. 
     Yet other embodiments of the present disclosure relate to a backlight where each patterned reflector is aligned with a corresponding light source and includes a solid first section, a second section surrounding the solid first section, and a plurality of openings extending through the second section. The openings increase in size as a distance from a center of the solid first section increases. The solid first section includes a size in a plane parallel to the longitudinal direction equal to or greater than the size of each light source. 
     The backlights disclosed herein are thin direct-lit backlights with improved light efficiency. The backlights have an improved ability to hide light sources resulting in a thinner backlight. The improved ability to hide the light sources allows for the removal of so-called “hot” spots directly above the light sources of the backlight, thus resulting in a uniform brightness across the display. Furthermore, the construction of the backlights described herein provide for the manufacture of large backlight panels while maintaining these properties across a range of operating temperatures. 
     Additional features and advantages will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments as described herein, including the detailed description which follows, the claims, as well as the appended drawings. 
     It is to be understood that both the foregoing general description and the following detailed description are merely exemplary and are intended to provide an overview or framework to understanding the nature and character of the claims. The accompanying drawings are included to provide a further understanding and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the description explain principles and operation of the various embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A  is top view of a backlight as described herein. 
         FIG.  1 B  is a cross-sectional view of the backlight of  FIG.  1 A  taken along cut line A-A. 
         FIG.  2 A  is cross-sectional view of a backlight as described herein that includes two light source boards and one patterned diffuser. 
         FIG.  2 B  is cross-sectional view of a backlight as described herein that includes one light source board and two patterned diffusers. 
         FIGS.  3 A- 3 C  are various views of an exemplary backlight including patterned reflectors; 
         FIG.  4    is a cross-sectional view of an exemplary liquid crystal display (LCD) including the exemplary backlight of  FIGS.  3 A- 3 C ; 
         FIG.  5    is a cross-sectional view of an exemplary backlight including patterned reflectors; 
         FIG.  6    is a cross-sectional view of an exemplary backlight including patterned reflectors and a diffusive layer; 
         FIG.  7    is a cross-sectional view of another exemplary backlight including patterned reflectors; 
         FIG.  8    is a cross-sectional view of another exemplary backlight including patterned reflectors and a diffusive layer; 
         FIG.  9    is a cross-sectional view of another exemplary backlight including patterned reflectors and a diffusive layer; 
         FIG.  10    is a cross-sectional view of another exemplary backlight including patterned reflectors and a diffusive layer; 
         FIG.  11    is a cross-sectional view of an exemplary backlight including patterned reflectors and an optical component; 
         FIGS.  12 A and  12 B  are various views of another exemplary backlight including patterned reflectors; 
         FIGS.  13 A and  13 B  are various views of another exemplary backlight including patterned reflectors; 
         FIG.  14    is a cross-sectional view of another exemplary backlight including an encapsulation layer; 
         FIG.  15    is a cross-sectional view of another exemplary backlight including an encapsulation layer; 
         FIG.  16    is a cross-sectional view of an exemplary backlight including an encapsulation layer bonded to a first layer of an optical film stack; 
         FIG.  17    is a cross-sectional view of an exemplary backlight including a light guide plate bonded to an encapsulation layer; 
         FIG.  18    is a cross-sectional view of an exemplary backlight including a diffusive layer bonded to an encapsulation layer; 
         FIG.  19    is a cross-sectional view of an exemplary backlight including a diffusive layer bonded to a first layer of an optical film stack; 
         FIG.  20    is a cross-sectional view of an exemplary backlight including a light guide plate bonded to an encapsulation layer and a further encapsulation layer bonded to a first layer of an optical film stack; 
         FIG.  21    is a cross-sectional view of an exemplary backlight including a light guide plate bonded to a first layer of an optical film stack and a further encapsulation layer bonded to an encapsulation layer; and 
         FIG.  22    is a graph of pattern shift versus tile size for three different combinations of patterned diffuser body and substrate. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts. However, this disclosure may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. 
     Ranges can be expressed herein as from “about” one particular value, and/or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. 
     Directional terms as used herein - for example up, down, right, left, front, back, top, bottom, vertical, horizontal - are made only with reference to the figures as drawn and are not intended to imply absolute orientation. 
     Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus, specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components; plain meaning derived from grammatical organization or punctuation, and; the number or type of embodiments described in the specification. 
     As used herein, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having two or more such components, unless the context clearly indicates otherwise. 
     In some embodiments, a backlight  100  having improved light distribution over a large area is provided. As shown in  FIGS.  1 A through  2 B , the backlight  100  includes a plurality of light sources  106  coupled to a substrate  102 , and a patterned diffuser  107  over the plurality of light sources  106 . The patterned diffuser  107  includes a plurality of patterned reflectors  112  coupled to a patterned diffuser body  108 , where each patterned reflector  112  is positioned to align with a corresponding light source  108 . The backlight  100  can have a longitudinal direction (i.e., a direction parallel to the longest in-plane distance from one edge of the backlight  100  to another). For example, cut line A-A in  FIG.  1 A  is taken along a longitudinal direction. 
     As used herein the patterned diffuser body  108  is the body to which the patterned reflectors  112  are coupled that dictates the relative position of the patterned reflectors  112  in the longitudinal (and lateral directions). In particular, thermal expansion or contraction of the patterned diffuser body  108  will change the relative spacing of the patterned reflectors  112 . In some embodiments, the patterned diffuser body  108  can be a light guide plate, a diffuser, or other component meeting the optical and physical properties described herein. In some embodiments, the patterned diffuser plate  108  can comprise or be glass, glass-ceramic, polymer, ceramic, or another material substrate. In some embodiments, the patterned diffuser body  108  is a light guide plate. As used herein, when the term light guide plate  108  is used, it should be understood that another patterned diffuser body  108  could be used in place of the light guide body  108 . 
     In a similar manner, the substrate  102  of the light source board  103  dictates the relative position of the light sources  106  in the longitudinal (and lateral directions). In particular, thermal expansion or contraction of the patterned diffuser body  108  will change the relative spacing of the light sources  106 . 
     As shown in  FIGS.  2 A- 2 B , the substrate  102  and the patterned diffuser body  108  have a maximum longitudinal substrate dimension (L Max ,S) and a maximum longitudinal patterned diffuser body dimension (L Max , PDB ), respectively, in the longitudinal direction. In some embodiments, as shown in  FIG.  2 A , the maximum longitudinal patterned diffuser body dimension (L Max , PDB ) is greater than the maximum longitudinal substrate dimension (L Max , s ). Is other embodiments, as shown in  FIG.  2 B , the maximum longitudinal substrate dimension (L Max ,S) is greater than the maximum longitudinal patterned diffuser body dimension (L Max , PDB ). Alternately, as shown in  FIG.  1 B , the maximum longitudinal substrate dimension (L Max ,S) and the maximum longitudinal patterned diffuser body dimension (L M   3X , PDB ) are the same in some embodiments. 
     As shown in  FIG.  1 B , as the backlight  100  is heated, the substrate  102  and the patterned diffuser body (e.g., light guide plate)  108  will undergo longitudinal expansion  160  and  162 , respectively. The relative differences between the amounts of longitudinal expansion  160 ,  162  can cause the corresponding light source  106  and patterned reflector  112  to fall out of alignment, which will produce defects in the backlight  100 . 
     In some embodiments, the thermal alignment tolerance in the longitudinal direction at a backlight operating temperature is 500 microns or less. As used herein, the thermal alignment tolerance at 60° C. is the absolute value of [the smaller of L Max , S  and L Max , PDB]  x [60 - 23.5° C.] x [substrate coefficient of thermal expansion (CTE s ) — patterned diffuser body coefficient of thermal expansion (CTE PDB )]. In this equation, room temperature is set at 23.5° C. In this way, when the backlight  100  is at 60° C., the maximum shift (misalignment) of an individual patterned reflector  112  relative to a corresponding light source  106  will be less than 500 microns. The thermal alignment tolerance can be calculated using values other than 60° C. Examples include, but are not limited to, 0° C., 80° C., 100° C., and 120° C. 
     A key attribute for alignment between patterned diffuser  107  and the light source board  103  is coefficient of thermal expansion (CTE) of the patterned diffuser body  108  and the substrate  102 , respectively. Although to achieve light uniformity, there are multiple optical films and patterns of patterned reflectors, the CTE of patterned diffuser  107  is dominated by the patterned diffuser body (e.g., light guide plate)  108  since the volume fraction of those optical components are negligible. In the same manner, the substrate  102  for the light source board  103  has a large volume fraction that dominates the alignment capability of the light sources  106 . 
     As described in Table 1, the CTE of some material candidates for the substrate  102  and the patterned diffuser body  108  include Eagle XG Glass (EXG available from Corning), soda-lime glass (SLG), and FR-4 (a polymer-based printed circuit board). Thus, using EXG as the substrate  102  and the patterned diffuser body  108  would result in the lowest pattern shift, which enables larger tiling size of the backlight  100  for a full size of the display (e.g., a large screen television). Since there exists size effect in terms of the pattern shift, there is restriction of the tiling size. Thus, using EXG as both the patterned diffuser body  108  and the substrate  102  can achieve the large tiling size for the backlight  100  with excellent light performance, including many local dimming zones. 
     
       
         
           
               
               
             
               
                 Materials 
                 CTE (ppm/ ◦ C) 
               
             
            
               
                 EXG 
                 3.17 
               
               
                 SLG 
                 9.5 
               
               
                 FR-4 
                 12 ∼ 13 
               
            
           
         
       
     
       FIG.  22    shows a graph of pattern shift (i.e., thermal alignment tolerance) versus tile size with a pattern shift of less than 300 microns at 60° C. As can be seen, the EXG/FR-4 combination allows for a maximum tile size of between 0.5-0.6 meters, the EXG/SLG combination allows for a maximum tile size of approximately 0.8 meters, while the combination of EXG/EXG can be infinite in size theoretically. 
     In some embodiments, the difference between the substrate coefficient of thermal expansion (CTE s ) and the patterned diffuser body coefficient of thermal expansion (CTE PDB )(ΔCTE) is 7.0 or less. In some embodiments, ΔCTL is 6.5 or less, or 6.0 or less, or 5.5 or less, or 5.0 or less, or 4.5 or less, or 4.0 or less, or 3.5 or less, or 3 or less, or 2.5 or less, or 2.0 or less. 
     In some embodiments, the thermal alignment tolerance in the longitudinal direction at the backlight operating temperature is 400 microns or less. In some embodiments, the thermal alignment tolerance in the longitudinal direction at the backlight operating temperature is 300 microns or less, or 250 microns or less, or 200 microns or less, or 150 microns or less, or 100 microns. 
     In some embodiments, at least one of L Max , S  and L Max , PDB  is at least 0.50 meters. In some embodiments, at least one of L Max , S  and L Max , PDB  is at least 0.75 meters, or at least 1.00 meters, or at least 1.25 meters, or at least 1.50 meters, or at least 1.75 meters, or at least 2.00 meters. 
     In some embodiments, the thermal alignment tolerance in the longitudinal direction at the backlight operating temperature is 400 microns or less and at least one of L Max , S  and L Max , PDB  is at least 0.50 meters, or at least 0.75 meters, or at least 1.00 meters, or at least 1.25 meters, or at least 1.50 meters, or at least 1.75 meters, or at least 2.00 meters. 
     In some embodiments, the thermal alignment tolerance in the longitudinal direction at the backlight operating temperature is 300 microns or less and at least one of L Max , S  and L Max , PDB  is at least 0.50 meters, or at least 0.75 meters, or at least 1.00 meters, or at least 1.25 meters, or at least 1.50 meters, or at least 1.75 meters, or at least 2.00 meters. 
     In some embodiments, as shown in  FIG.  2 A , the backlight  100  comprises at least two light source boards  103  in the longitudinal direction. In some embodiments, as shown in  FIG.  2 B , the backlight  100  comprises at least two patterned diffusers  107  in the longitudinal direction. 
     In some embodiments, the backlight  100  is formed from one light source board  103  and one patterned diffuser  107  in the longitudinal direction and L Max , S  = L Max , PDB , and both L Max , S  and L Max , PDB  are greater than 0.50 meters. In some embodiments, the backlight  100  is formed from one light source boards  103  and one patterned diffuser  107  in the longitudinal direction and L Max , S  = L Max , PDB , and both L Max , S  and L Max , PDB  are greater than 0.75 meters, or greater than 1.00 meter, or greater than 1.25 meters, or greater than 1.50 meters, or greater than 1.75 meters, or greater than 2.00 meters. 
     In some embodiments, the substrate  102  and the patterned diffuser body  108  are both formed of a glass (e.g., the same or a different glass). In some embodiments, the substrate  102  and the patterned diffuser body  108  are both formed of a plastic (e.g., the same or a different plastic). In some embodiments, the substrate  102  and the patterned diffuser body  108  are both formed of the same material. 
     In some embodiments, as shown in  FIG.  1 B , the pitch  126  of the light sources  106  can be the same as the pitch  127  of the patterned reflectors  112 . 
     In some embodiments, the backlight  100  includes a first reflective layer  104  on the substrate  102 . 
     In some embodiments, the plurality of patterned reflectors  112  are on a first surface of the patterned diffuser body  108 . In some embodiments, the backlight  100  includes a diffusive layer  130  on a second surface of the patterned diffuser body  108  opposite to the first surface. In some such embodiments, as shown in  FIG.  6   , the first surface faces the substrate. In other such embodiments, as shown in  FIG.  8   , the second surface faces the substrate. 
     In some embodiments, as shown in  FIG.  6   , the backlight  100  includes a first layer  146  of an optical film stack over the light guide plate  108  and the diffusive layer  130  is bonded to the first layer  146  of the optical film stack. 
     In some embodiments, as shown in  FIGS.  17  and  18   , the backlight  100  includes at least one encapsulation layer encapsulating the plurality of light sources. In some embodiments, as shown in  FIGS.  14  and  15   , the backlight  100  includes an encapsulation layer encapsulating the plurality of patterned reflectors. 
     Additional features and details of the configurations of the backlight  100  follow. Referring now to  FIGS.  1 A- 3 C , various views of an exemplary backlight  100  are depicted.  FIG.  3 A  is a cross-sectional view of backlight  100 . Backlight  100  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a light guide plate  108 , and a plurality of patterned reflectors  112 . The plurality of light sources  106  are arranged on substrate  102  and are in electrical communication with the substrate  102 . The reflective layer  104  is on the substrate  102  and surrounds each light source  106 . In certain exemplary embodiments, the substrate  102  may be reflective such that the reflective layer  104  may be excluded. The light guide plate  108  is over the plurality of light sources  106  and optically coupled to each light source  106 . In certain exemplary embodiments, an optical adhesive (not shown) may be used to couple the plurality of light sources  106  to the light guide plate  108 . The optical adhesive (e.g., phenyl silicone) may have a refractive index greater than or equal to a refractive index of the light guide plate  108 . The plurality of patterned reflectors  112  are arranged on the upper surface of the light guide plate  108 . Each patterned reflector  112  is aligned with a corresponding light source  106 . 
     Each patterned reflector  112  includes a thickness profile including a substantially flat section as indicated at  113  and a curved section as indicated at  114  extending from and surrounding the substantially flat section  113 . The substantially flat section  113  may have a rough surface profile. In certain exemplary embodiments, the substantially flat section  113  varies in thickness by no more than plus or minus 20 percent of an average thickness of the substantially flat section. In this embodiment, the average thickness (measured in the direction orthogonal to the light guide plate  108 ) is defined as the maximum thickness (T max ) of the substantially flat section plus the minimum thickness (T min ) of the substantially flat section divided by two (i.e., (T max +T min )/2). For example, for an average thickness of the substantially flat section  113  of about 100 micrometers, the maximum thickness of the substantially flat section would be equal to or less than about 120 micrometers and the minimum thickness of the substantially flat section would be equal to or greater than about 80 micrometers. In other embodiments, the substantially flat section  113  varies in thickness by no more than plus or minus 15 percent of an average thickness of the substantially flat section. For example, for an average thickness of the substantially flat section  113  of about 80 micrometers, the maximum thickness of the substantially flat section would be equal to or less than about 92 micrometers and the minimum thickness of the substantially flat section would be equal to or greater than about 68 micrometers. In yet other embodiments, the substantially flat section  113  varies in thickness by no more than plus or minus 10 percent of an average thickness of the substantially flat section. For for an average thickness of the substantially flat section  113  of about 50 micrometers, the maximum thickness of the substantially flat section would be equal to or less than about 55 micrometers and the minimum thickness of the substantially flat section would be equal to or greater than about 45 micrometers. The curved section  114  may be defined as the absolute ratio of the change in thickness over the change in the distance from the center of the patterned reflector  112 . The slope of the curved section  114  may decrease with the distance from the center of the patterned reflector  112 . In certain exemplary embodiments, the slope is highest near the substantially flat section  113 , rapidly decreases with the distance from the center of the patterned reflector  112 , and then slowly decreases with further distance from the center of the patterned reflector 
     The size L0 (i.e., width or diameter) of each substantially flat section  113  as indicated at  120  (in a plane parallel to the longitudinal direction) may be greater than the size (i.e., width or diameter) of each corresponding light source  106  as indicated at  124  (in a plane parallel to the longitudinal direction). It should be noted that references to parallel to the longitudinal direction also parallel to a surface of the substrate  102 . The size  120  of each substantially flat section  113  may be less than the size  124  of each corresponding light source 106 times a predetermined value. In certain exemplary embodiments, when the size  124  of the each light source  106  is greater than or equal to about 0.5 millimeters, the predetermined value may be about two or about three, such that the size of each substantially flat section  113  is less than three times the size of each light source  106 . When the size  124  of each light source  106  is less than 0.5 millimeters, the predetermined value may be determined by the alignment capability between the light sources  106  and the patterned reflectors  112 , such that the size of each substantially flat section  113  of each of patterned reflector  112  is within a range between about 100 micrometers and about 300 micrometers greater than the size of each light source  106 . Each substantially flat section  113  is large enough such that each patterned reflector  112  can be aligned to the corresponding light source  106  and small enough to achieve suitable luminance uniformity and color uniformity. 
     The size L1 (i.e., width or diameter) of each patterned reflector  112  is indicated at  122  (in a plane parallel to the longitudinal direction) and the pitch P between adjacent light sources  106  is indicated at  126 . While the pitch is illustrated along one direction in  FIG.  3 A , it is noted that the pitch may be different in a direction orthogonal to the direction illustrated. The pitch may, for example, be about 90, 45, 30, 10, 5, 2, 1, or 0.5 millimeters, larger than about 90 millimeters, or smaller than about 0.5 millimeters. In certain exemplary embodiments, the ratio L1/P of the size  122  of each patterned reflector  112  over the pitch  126  is within a range between about 0.45 and 1.0. The ratio may vary with the pitch  126  of the light sources  106  and the distance between the emission surface of each light source and the corresponding patterned reflector  112 . For example, for a pitch  126  equal to about 5 millimeters and a distance between the emission surface of each light source and the corresponding patterned reflector equal to about 0.2 millimeters, the ratio may equal about 0.50, 0.60, 0.70, 0.80, 0.90, or 1.0. 
     Each patterned reflector  112  reflects at least a portion of the light emitted from the corresponding light source  106  into the light guide plate  108 . Each patterned reflector  112  has a specular reflectance and a diffuse reflectance. The specularly reflected light exits from the bottom surface of the light guide plate  108 . While this light travels laterally primarily due to the reflection between the reflective layer  104  and the light guide plate  108 , or due to the reflection between the reflective layer  104  and the quantum dot film, diffuser sheet, or diffuser plate (shown below in  FIG.  4   ), some loss of light may occur due to imperfect reflection from the reflective layer  104 . 
     The diffusively reflected light has an angular distribution between 0° and 90° measured from the normal of the light guide plate  108 . About 50 percent of the diffusively reflected light has an angle exceeding the critical angle (θ TIR ) of the total internal reflection. Thus, this light can travel laterally due to the total internal reflection without any loss, until the light is subsequently extracted out of the light guide plate  108  by patterned reflectors  112 . 
       FIG.  3 B  is a top view of the plurality of light sources  106  and reflective layer  104  on substrate  102 . Light sources  106  are arranged in a 2D array including a plurality of rows and a plurality of columns. While nine light sources  106  are illustrated in  FIG.  3 B  in three rows and three columns, in other embodiments backlight  100  may include any suitable number of light sources  106  arranged in any suitable number of rows and any suitable number of columns. Light sources  106  may also be arranged in other periodic patterns, for example, a hexagonal or triangular lattice, or as quasi-periodic or non-strictly periodic patterns. For example, the spacing between light sources  106  may be smaller at the edges and/or corners of the backlight. 
     Substrate  102  ( FIG.  3 A ) may be a printed circuit board (PCB), a glass or plastic substrate, or another suitable substrate for passing electrical signals to each light source  106  for individually controlling each light source. Substrate  102  may be a rigid substrate or a flexible substrate. For example, substrate  102  may include flat glass or curved glass. The curved glass, for example, may have a radius of curvature less than about 2000 millimeters, such as about 1500, 1000, 500, 200, or 100 millimeters. The reflective layer  104  may include, for metallic foils, such as silver, platinum, gold, copper, and the like; dielectric materials (e.g., polymers such as polytetrafluoroethylene (PTFE)); porous polymer materials, such as polyethylene terephthalate (PET), Poly(methyl methacrylate) (PMMA), polyethylene naphthalate (PEN), polyethersulfone (PES), etc.; multi-layer dielectric interference coatings, or reflective inks, including white inorganic particles such as titania, barium sulfate, etc., or other materials suitable for reflecting light and tuning the color of the reflected and transmitted light, such as colored pigments. 
     Each of the plurality of light sources  106  may, for example, be an LED (e.g., size larger than about 0.5 millimeters), a mini-LED (e.g., size between about 0.1 millimeters and about 0.5 millimeters), a micro-LED (e.g., size smaller than about 0.1 millimeter), an organic LED (OLED), or another suitable light source having a wavelength ranging from about 400 nanometers to about 750 nanometers. In other embodiments, each of the plurality of light sources may have a wavelength shorter than 400 nanometers and/or longer than 750 nanometers. The light from each light source  106  is optically coupled to the light guide plate  108 . As used herein, the term “optically coupled” is intended to denote that a light source is positioned at a surface of the light guide plate  108  and is in an optical communication with the light guide plate  108  directly or through an optically clear adhesive, so as to introduce light into the light guide plate that at least partially propagates due to total internal reflection. The light from each light source  106  is optically coupled to the light guide plate  108  such that a first portion of the light travels laterally in the light guide plate  108  due to the total internal reflection and is extracted out of the light guide plate by the patterned reflectors  112 , and a second portion of the light travels laterally between the reflective layer  104  and the patterned reflectors  112  due to multiple reflections at the reflective surfaces of the reflective layer  104  and the patterned reflectors  112  or between an optical film stack (shown in  FIG.  4   ) and the reflective layer  104 . 
     According to various embodiments, the light guide plate  108  may include any suitable transparent material used for lighting and display applications. As used herein, the term “transparent” is intended to denote that the light guide plate has an optical transmission of greater than about 70 percent over a length of 500 millimeters in the visible region of the spectrum (about 420-750 nanometers). In certain embodiments, an exemplary transparent material may have an optical transmittance of greater than about 50 percent in the ultraviolet (UV) region (about 100-400 nanometers) over a length of 500 millimeters. According to various embodiments, the light guide plate may include an optical transmittance of at least 95 percent over a path length of 50 millimeters for wavelengths ranging from about 450 nanometers to about 650 nanometers. 
     The optical properties of the light guide plate may be affected by the refractive index of the transparent material. According to various embodiments, the light guide plate  108  may have a refractive index ranging from about 1.3 to about 1.8. In other embodiments, the light guide plate  108  may have a relatively low level of light attenuation (e.g., due to absorption and/or scattering). The light attenuation (α) of the light guide plate  108  may, for example, be less than about 5 decibels per meter for wavelengths ranging from about 420-750 nanometers. The light guide plate  108  may include polymeric materials, such as plastics (e.g., polymethyl methacrylate (PMMA), methylmethacrylate styrene (MS), polydimethylsiloxane (PDMS)), polycarbonate (PC), or other similar materials. The light guide plate  108  may also include a glass material, such as aluminosilicate, alkali-aluminosilicate, borosilicate, alkali-borosilicate, aluminoborosilicate, alkali-aluminoborosilicate, soda lime, or other suitable glasses. Nonlimiting examples of commercially available glasses suitable for use as a glass light guide plate  108  include EAGLE XG®, Lotus™, Willow®, Iris™, and Gorilla® glasses from Corning Incorporated. In examples where substrate  102  includes curved glass, light guide plate  108  may also include curved glass to form a curved backlight. 
       FIG.  3 C  is a top view of the plurality of patterned reflectors  112  on the light guide plate  108 . Each patterned reflector  112  may include a substantially flat section  113  and a curved section  114 . In addition, each patterned reflector  112  may include individual dots  115  on the light guide plate  108 . The substantially flat section  113  may be more reflective than the curved section  114 , and the curved section  114  may be more transmissive than the substantially flat section  113 . Each curved section  114  may have properties that change in a continuous and smooth way with distance from the substantially flat section  113 . While in the embodiment illustrated in  FIG.  3 C , each patterned reflector  112  is circular in shape, in other embodiments each patterned reflector  112  may have another suitable shape (e.g., rectangular, hexagonal, etc.). With the patterned reflectors  112  fabricated directly on the upper surface of the light guide plate  108 , the patterned reflectors  112  increase the ability of hiding the light sources  106 . Fabricating patterned reflectors  112  directly on the upper surface of the light guide plate  108  also saves space. 
     In certain exemplary embodiments, each patterned reflector  112  is a diffuse reflector, such that each patterned reflector  112  further enhances the performance of the backlight  100  by scattering some light rays at high enough angles such that they can propagate in the light guide plate  108  by total internal reflection. Such rays will then not experience multiple bounces between the patterned reflectors  112  and the reflective layer  104  or between an optical film stack and the reflective layer  104  and therefore avoid loss of optical power, thereby increasing the backlight efficiency. In certain exemplary embodiments, each patterned reflector  112  is a specular reflector. In other embodiments, some areas of each patterned reflector  112  have a more diffuse character of reflectivity and some areas have a more specular character of reflectivity. 
     Each patterned reflector  112  may be formed, for example, by printing (e.g., inkjet printing, screen printing, microprinting, etc.) a pattern with white ink, black ink, metallic ink, or other suitable ink. Each patterned reflector  112  may also be formed by first depositing a continuous layer of a white or metallic material, for example by physical vapor deposition (PVD) or any number of coating techniques such as for example slot die or spray coating, and then patterning the layer by photolithography or other known methods of area-selective material removal. 
     In certain exemplary embodiments where white light sources  106  are used, the presence of different reflective and absorptive materials in variable density in the patterned reflectors  112  may be beneficial for minimizing the color shift across each of the dimming zones of the backlight. Multiple bounces of light rays between the patterned reflectors and the reflective layer  104  ( FIG.  3 A ) may cause more loss of light in the red part of the spectrum than in the blue, or vice versa. In this case, engineering the reflection to be color neutral, for example by using slightly colored reflective/absorptive materials, or materials with the opposite sign of dispersion (in this case, dispersion means spectral dependence of the reflection and/or absorption) may minimize the color shift. 
       FIG.  4    is a cross-sectional view of an exemplary liquid crystal display (LCD)  140 . LCD  140  includes a backlight  100  including patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . In addition, LCD  140  includes optionally a diffuser plate  146  over backlight  100 , optionally a quantum dot film  148  over the diffuser plate  146 , optionally a prismatic film  150  over the quantum dot film  148 , optionally a reflective polarizer  152  over the prismatic film  150 , and a display panel  154  over the reflective polarizer  152 . 
     To maintain the alignment between the light sources  106  and the patterned reflectors  112  on the light guide plate  108  for the proper functioning of the backlight  100 , it is advantageous if the light guide plate  108  and the substrate  102  are made of the same or similar type of material so that both the patterned reflectors  112  on the light guide plate  108  and the light sources  106  on the substrate  102  are registered well to each other over a large range of operating temperatures. In certain exemplary embodiments, the light guide plate  108  and the substrate  102  are made of the same plastic material. In other embodiments, the light guide plate  108  and the substrate  102  are made of the same type of glass. 
     An alternative solution to keep the light guide plate  108  and light sources  106  on the substrate  102  in alignment is to use a highly flexible substrate. The highly flexible substrate may be made of a polyimide or other high temperature resistant polymer film to allow component soldering. The highly flexible substrate may also be made of materials such as FR4 or fiberglass, but of a significantly lower thickness than usual. In certain exemplary embodiments, an FR4 material of 0.4 millimeters thickness may be used for substrate  102 , which may be sufficiently flexible to absorb the dimensional changes resulting from changing operating temperatures. 
       FIG.  5    is a simplified cross-sectional view of an exemplary backlight  200 . Backlight  200  is similar to backlight  100  previously described and illustrated with reference to  FIGS.  1 A- 3 C  except that in backlight  200 , each patterned reflector  112  faces the corresponding light source  106 . While  FIG.  5    illustrates a single light source  106  and a corresponding single patterned reflector  112  for simplicity, it will be understood that backlight  200  may include any suitable number of light sources  106  and corresponding patterned reflectors  112 . Backlight  200  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . Backlight  200  also includes the first layer  146  of an optical film stack (not shown) over the light guide plate  108 . The first layer  146  of the optical film stack may include a diffuser plate, a quantum dot film, a prismatic film, or another suitable plate or film. In this embodiment, each patterned reflector  112  is on a first surface of the light guide plate  108 , where the first surface of the light guide plate faces the plurality of light sources  106 . 
       FIG.  6    is a simplified cross-sectional view of an exemplary backlight  202 . Backlight  202  is similar to backlight  200  previously described and illustrated with reference to  FIG.  5   . Backlight  202  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . In addition, backlight  202  includes a diffusive layer  130 . Backlight  202  also includes the first layer  146  of an optical film stack (not shown) over the diffusive layer  130 . 
     Diffusive layer  130  is on a second surface of the light guide plate  108  opposite to the first surface of the light guide plate. Diffusive layer  130  faces away from the plurality of light sources  106 . Diffusive layer  130  improves the lateral spreading of the light emitted from the light sources  106 , thereby improving light uniformity. The diffusive layer  130  may have specular and diffuse reflectance and specular and diffuse transmittance. The specular reflectance or transmittance is the percent of reflected or transmitted light along the specular direction with 0 or 8 degrees depending on the measurement setup, while the diffuse reflectance or transmittance is the percent of reflected or transmitted light excluding the specular reflectance or transmittance. The diffusive layer  130  may have a haze and a transmittance. The diffusive layer  130  may have a haze, for example, of about 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, or 99 percent or higher, and a transmittance of about 20, 30, 40, 50, 60, 70, 80, 90, or 95 percent or higher. In certain exemplary embodiments, the diffusive layer  130  has a haze of about 70 percent and a total transmittance of about 90 percent. In other embodiments, the diffusive layer  130  has a haze of about 88 percent and a total transmittance of about 96 percent. Haze is defined as the percent of transmitted light that is scattered so that its direction deviates more than 2.5 degrees from the direction of the incident beam, and transmittance is defined as the percent of transmitted light, per American Society for Testing and Materials (ASTM) D1003 “Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics.” Haze and transmittance can be measured by various haze meters. 
     Diffusive layer  130  diffuses rays from the light source  106 . As a result, the patterned reflector  112  of backlight  202  may be thinner than a patterned reflector of a backlight not including diffusive layer  130  while still effectively hiding the light source  106 . Diffusive layer  130  also diffuses rays that otherwise would undergo total internal reflection. In addition, diffusive layer  130  diffuses any rays that are reflected back by the quantum dot film, diffuser sheet, or diffuser plate  146 . Thus, the diffusive layer  130  increases the light recycling effect caused by the quantum dot film, diffuser sheet, or diffuser plate  146  and any prismatic films (not shown) over the diffuser plate or diffuser sheet, such as one or two brightness enhancement films. 
     In certain exemplary embodiments, diffusive layer  130  includes a uniform or continuous layer of scattering particles. Diffusive layer  130  is considered to include a uniform layer of scattering particles where the distance between neighboring scattering particles is less than one fifth the size of the light source. Regardless of the location of diffusive layer  130  relative to the light source, diffusive layer  130  exhibits a similar diffusive property. The scattering particles may, for example, be within a clear or white ink that includes micro-sized or nano-sized scattering particles, such as alumina particles, TiO 2  particles, PMMA particles, or other suitable particles. The particle size may vary, for example, within a range from about 0.1 micrometers and about 10.0 micrometers. In other embodiments, diffusive layer  130  may include an anti-glare pattern. The anti-glare pattern may be formed of a layer of polymer beads or may be etched. In this embodiment, diffusive layer  130  may have a thickness, for example, of about 1, 3, 7, 14, 21, 28, or 50 micrometers, or another suitable thickness. 
     In certain exemplary embodiments, diffusive layer  130  may include a pattern that may be applied to the light guide plate  108  via screen printing. The diffusive layer  130  may be screen printed on a primer layer (e.g., an adhesive layer) applied to the light guide plate  108 . In other embodiments, diffusive layer  130  may be applied to the light guide plate  108  by laminating the diffusive layer to the light guide plate via an adhesive layer. In yet other embodiments, diffusive layer  130  may be applied to the light guide plate  108  by embossing (e.g., thermal or mechanical embossing) the diffusive layer into the light guide plate, stamping (e.g., roller stamping) the diffusive layer into the light guide plate, or injection molding the diffusive layer. In yet other embodiments, diffusive layer  130  may be applied to the light guide plate  108  by etching (e.g., chemical etching) the light guide plate. In some embodiments, diffusive layer  130  may be applied to the light guide plate  108  with a laser (e.g., laser damaging). 
     In yet other embodiments, diffusive layer  130  may include a plurality of hollow beads. The hollow beads may be plastic hollow beads or glass hollow beads. The hollow beads, for may be glass bubbles available from 3M Company under the trade designations “3M GLASS BUBBLES iM30K”. These glass bubbles have glass compositions including SiO 2  in a range from about 70 to about 80 percent by weight, alkaline earth metal oxide in a range from about 8 to about 15 percent by weight, and alkali metal oxide in a range from about 3 to about 8 percent by weight, and B 2 O 3  in a range from about 2 to about 6 percent by weight, where each percent by weight is based on the total weight of the glass bubbles. In certain exemplary embodiments, the size (i.e., diameter) of the hollow beads may vary, for example, from about 8.6 micrometers to about 23.6 micrometers, with a median size of about 15.3 micrometers. In another embodiment, the size of the hollow beads may vary, for example, from about 30 micrometers to about 115 micrometers, with the median size of about 65 micrometers. In yet other embodiments, diffusive layer  130  may include a plurality of nano-sized color conversion particles such as red and/or green quantum dots. In yet other embodiments, diffusive layer  130  may include a plurality of hollow beads, nano-sized scattering particles, and nano-sized color conversion particles such as red and/or green quantum dots. 
     The hollow beads may first be uniformly mixed with a solvent (e.g., Methyl Ethyl Ketone (MEK)), subsequently mixed with any suitable binder (e.g., Methyl methacrylate and silica), and then fixed by thermal or ultraviolet (UV) curing if necessary to form a paste. The paste may then be deposited onto the surface of the light guide plate  108  through slot coating, screen printing, or any other suitable means to form the diffusive layer  130 . In this embodiment, the diffusive layer  130  may have a thickness, for example, between about 10 micrometers and about 100 micrometers. In another the diffusive layer  130  may have a thickness between about 100 micrometers and about 300 micrometers. Multiple coatings may be used to form a thick diffusive layer if needed. In each example, the haze of the diffusive layer  130  may be more than 99 percent as measured with a haze meter such as BYK-Gardner’s Haze-Gard. Two advantages of using hollow beads within diffusive layer  130  includes 1) reducing the weight of the diffusive layer  130 ; and 2) achieving a desired haze level at a small thickness. 
       FIG.  7    is a simplified cross-sectional view of another exemplary backlight  204 . Backlight  204  is similar to backlight  100  previously described and illustrated with reference to  FIGS.  1 A- 3 C . For backlight  204 , each patterned reflector  112  faces away from the corresponding light source  106 . Backlight  204  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . Backlight  204  also includes the first layer  146  of an optical film stack (not shown) over the light guide plate  108 . Each patterned reflector  112  is on a first surface of the light guide plate  108 , where the first surface of the light guide plate faces away from the plurality of light sources  106 . 
       FIG.  8    is a simplified cross-sectional view of another exemplary backlight  206 . Backlight  206  is similar to backlight  204  previously described and illustrated with reference to  FIG.  7   . Backlight  206  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . In addition, backlight  202  includes a diffusive layer  130 . Backlight  206  also includes the first layer  146  of an optical film stack (not shown) over the plurality of patterned reflectors  112 . 
     Diffusive layer  130  is on a second surface of the light guide plate  108  opposite to the first surface of the light guide plate. In this embodiment, the diffusive layer  130  faces the plurality of light sources  106  and the plurality of patterned reflectors  112  face away from the plurality of light sources  106 . Diffusive layer  130  may include any of the features of diffusive layer  130  previously described with reference to  FIG.  6   . 
       FIG.  9    is a simplified cross-sectional view of another exemplary backlight  208 . Backlight  208  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a first light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . In addition, backlight  208  includes a diffusive layer  130 , a second light guide plate  132 , and an adhesive layer  134 . Diffusive layer  130  is on a first surface of the second light guide plate  132 . A second surface of the second light guide plate  132  opposite to the first surface is coupled to the plurality of patterned reflectors  112  and the first light guide plate  108  via the adhesive layer  134 . In this embodiment, the plurality of patterned reflectors  112  face away from the plurality of light sources  106  and are embedded in the adhesive material  134 . 
     Diffusive layer  130  may include any of the features of diffusive layer  130  previously described with reference to  FIG.  6   . Adhesive layer  134  may include an optically clear adhesive (e.g., phenyl silicone) or another suitable material to bond the second light guide plate  132  to the plurality of patterned reflectors  112  and the first light guide plate  108 . In certain exemplary embodiments, second light guide plate  132  may include any of the features of light guide plate  108  previously described with reference to  FIGS.  1 A- 3 C . Using a separate second light guide plate  132  upon which the diffusive layer  130  is formed, which is then bonded to the first light guide plate  108  enables additional flexibility in fabricating the diffusive layer  130  and the plurality of patterned reflectors  112 . In addition, using a separate second light guide plate  132  enables the separate examination of the diffusive layer  130  on the second light guide plate  132  and the plurality of patterned reflectors  112  on the first light guide plate  108  prior to assembling backlight  208 . 
       FIG.  10    is a simplified cross-sectional view of another exemplary backlight  210 . Backlight  210  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a first light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . In addition, backlight  202  includes a diffusive layer  130 , a second light guide plate  132 , and an adhesive layer  134  as previously described and illustrated with reference to  FIG.  9   . Diffusive layer  130  is on a first surface of the second light guide plate  132 . A second surface of the second light guide plate  132  opposite to the first surface is coupled to the first light guide plate  108  via the adhesive layer  134 . In this embodiment, the plurality of patterned reflectors  112  face the plurality of light sources  106 . In other embodiments, the adhesive layer  134  may be excluded and the first light guide plate  108  may be separated from the second light guide plate  132  by an air gap. 
       FIG.  11    is a simplified cross-sectional view of an exemplary backlight  212 . Backlight  212  is similar to backlight  200  previously described and illustrated with reference to  FIG.  5    except that backlight  212  includes an optical component  136 . Backlight  212  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , a light guide plate  108 , and a plurality of patterned reflectors  112  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . Backlight  212  also includes the first layer  146  of an optical film stack (not shown) over the optical component  136 . Each patterned reflector  112  is on a first surface of the light guide plate  108 , where the first surface of the light guide plate faces the plurality of light sources  106 . 
     The optical component  136  is on a second surface of the light guide plate  108  opposite to the first surface, where the second surface of the light guide plate faces away from the plurality of light sources  106 , such that the optical component  136  faces away from the plurality of light sources  106 . The optical component  136  may include a quantum dot film, a prismatic or lenticular lens, or another suitable optical component. In the example of the prismatic or lenticular lens, the prismatic or lenticular lens may be linear or circular. The prismatic or lenticular lens may include nano-sized and/or micro-sized scattering particles as described above with reference to the diffusive layer  130 . The micro-sized scattering particles can be hollow beads. The prismatic lens may have a rounded or sharp apex angle. In the example of the quantum dot film, by placing the quantum dot film directly on top of the light guide plate  108  the quantum dot film may be better protected from moisture and/or oxygen. The optical component  136  may be embedded in an adhesive material, and optionally be bonded to the adjacent optical component, for example, the first layer  146  of the optical film stack. 
       FIGS.  12 A and  12 B  are various views of another exemplary backlight  214 .  FIG.  12 A  is a simplified cross-sectional view of backlight  214  and  FIG.  12 B  is a bottom view of a patterned reflector  312  on a light guide plate  108 . Backlight  214  is similar to backlight  200  previously described and illustrated with reference to  FIG.  5   , except that in backlight  214  patterned reflectors  312  are used in place of patterned reflectors  112 . Backlight  214  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , and a light guide plate  108  as previously described and illustrated with reference to  FIGS.  3 - 3 C . Backlight  214  also includes the first layer  146  of an optical film stack (not shown) over the light guide plate  108 . 
     Each patterned reflector  312  is on a first surface of the light guide plate  108 , where the first surface of the light guide plate faces the plurality of light sources  106 . In other embodiments, the first surface of the light guide plate  108  may face away from the plurality of light sources  106  such that the patterned reflectors  312  face away from the plurality of light sources  106 . Each patterned reflector  312  includes a first solid section  313 , a plurality of second solid sections  314  surrounding the first solid section  313 , and a plurality of open sections  315  interleaved with the plurality of second solid sections  314 . As illustrated in  FIG.  12 B , each second solid section  314  and each open section  315  may be ring-like, such as circular, elliptical, or another suitable shape. 
     Patterned reflector  312  includes a pattern of reflective material to create a variable diffusive reflector. The reflective material may include, for example, metallic foils, such as silver, platinum, gold, copper, and the like; dielectric materials (e.g., polymers such as PTFE); porous polymer materials, such as PET, PMMA, PEN, PES, etc., multi-layer dielectric interference coatings, or reflective inks, including white inorganic particles such as titania, barium sulfate, etc., or other materials suitable for reflecting light. 
     An area ratio A(r) of each second solid section  314  may equal As(r) / (As(r) + Ao(r)), where r is the distance from the center of the corresponding patterned reflector  312 , As(r) is the area of the corresponding second section  314 , and Ao(r) is the area of the corresponding open section  315 . The area ratio A(r) of each second solid section  314  decreases with the distance r, and a rate of the decrease decreases with the distance r. 
     The size L0 (i.e., width or diameter) of each first solid section  313  as indicated at  320  (in a plane parallel to the longitudinal direction) may be greater than the size (i.e., width or diameter) of each corresponding light source  106  as indicated at  124  (in a plane parallel to the longitudinal direction). The size  320  of each first solid section  313  may be less than the size  124  of each corresponding light source 106 times a predetermined value. In certain exemplary embodiments, when the size  124  of the each light source  106  is greater than or equal to about 0.5 millimeters, the predetermined value may be about two or about three, such that the size of each first solid section  313  is less than three times the size of each light source  106 . When the size  124  of each light source  106  is less than 0.5 millimeters, the predetermined value may be determined by the alignment capability between the light sources  106  and the patterned reflectors  312 , such that the size of each first solid section  313  of each of patterned reflector  312  is within a range between about 100 micrometers and about 300 micrometers greater than the size of each light source  106 . Each first solid section  313  is large enough such that each patterned reflector  312  can be aligned to the corresponding light source  106  and small enough to achieve suitable luminance uniformity and color uniformity. 
     Each patterned reflector  312  may be formed, for by printing (e.g., inkjet printing, screen printing, microprinting, etc.) a pattern with white ink, black ink, metallic ink, or other suitable ink. Each patterned reflector  312  may also be formed by first depositing a continuous layer of a white or metallic material, for example by physical vapor deposition (PVD) or any number of coating techniques such as for example slot die or spray coating, and then patterning the layer by photolithography or other known methods of area-selective material removal. 
       FIGS.  13 A and  13 B  are various views of another exemplary backlight  216 .  FIG.  13 A  is a simplified cross-sectional view of backlight  216  and  FIG.  13 B  is a bottom view of a patterned reflector  412  on a light guide plate  108 . Backlight  216  is similar to backlight  200  previously described and illustrated with reference to  FIG.  5   , except that in backlight  216  patterned reflectors  412  are used in place of patterned reflectors  112 . Backlight  216  may include a substrate  102 , a reflective layer  104 , a plurality of light sources  106 , and a light guide plate  108  as previously described and illustrated with reference to  FIGS.  1 A- 3 C . Backlight  216  also includes the first layer  146  of an optical film stack (not shown) over the light guide plate  108 . 
     Each patterned reflector  412  is on a first surface of the light guide plate  108 , where the first surface of the light guide plate faces the plurality of light sources  106 . In other embodiments, the first surface of the light guide plate  108  may face away from the plurality of light sources  106  such that the patterned reflectors  412  face away from the plurality of light sources  106 . Each patterned reflector  412  includes a first solid section  413 , a second section  414  surrounding the first solid section  413 , and a plurality of openings  415  extending through the second section  414 . As illustrated in  FIG.  13 B , the openings  415  increase in size (i.e., width or diameter) as a distance from the center of the solid first section  413  increases. Each opening  415  may be circular, elliptical, or another suitable shape. In other embodiments, the features of patterned reflectors  312  previously described and illustrated with reference to  FIGS.  12 A and  12 B  may be combined with the features of patterned reflectors  412  to form patterned reflectors including both ring-like openings (e.g.,  315 ) and discrete openings (e.g.,  415 ). 
     The size L0 (i.e., width or diameter) of each first solid section  413  as indicated at  420  (in a plane parallel to the longitudinal direction) may be greater than the size (i.e., width or diameter) of each corresponding light source  106  as indicated at  124  (in a plane parallel to the longitudinal direction). The size  420  of each first solid section  413  may be less than the size  124  of each corresponding light source 106 times a predetermined value. In certain exemplary embodiments, when the size  124  of the each light source  106  is greater than or equal to about 0.5 millimeters, the predetermined value may be about two or about three, such that the size of each first solid section  413  is less than three times the size of each light source  106 . When the size  124  of each light source  106  is less than 0.5 millimeters, the predetermined value may be determined by the alignment capability between the light sources  106  and the patterned reflectors  112 , such as a predetermined value of about 100, 200, or 300 micrometers. Each first solid section  413  is large enough such that each patterned reflector  412  can be aligned to the corresponding light source  106  and small enough to achieve suitable luminance uniformity and color uniformity. 
     Each patterned reflector  412  may be formed, for example, by printing (e.g., inkjet printing, screen printing, microprinting, etc.) a pattern with white ink, black ink, metallic ink, or other suitable ink. Each patterned reflector  412  may also be formed by first depositing a continuous layer of a white or metallic material, for example by physical vapor deposition (PVD) or any number of coating techniques such as for example slot die or spray coating, and then patterning the layer by photolithography or other known methods of area-selective material removal. 
       FIG.  14    is a simplified cross-sectional view of another exemplary backlight  230 . Backlight  230  is similar to backlight  100  previously described and illustrated with reference to  FIGS.  1 A- 3 C , except that backlight  230  include an encapsulation layer  510 . Backlight  230  also includes the first layer  146  of an optical film stack (not shown) over the encapsulation layer  510 . In this embodiment, the encapsulation layer  510  is on the light guide plate  108  and encapsulates each of the plurality of patterned reflectors  112 . In other embodiments, the plurality of patterned reflectors  312  previously described and illustrated with reference to  FIGS.  12 A- 12 B  or the plurality of patterned reflectors  412  previously described and illustrated with reference to  FIGS.  13 A- 13 B  may be used in place of the plurality of patterned reflectors  112 . Encapsulation layer  510  may prevent damage (e.g., scratches) to each patterned reflector  112  due to potential contact with the quantum dot film, diffuser sheet, or diffuser plate  146  during fabrication of the backlight  230 . Encapsulation layer  510  may also improve the adhesion of each patterned reflector  112  to the light guide plate  108 . 
       FIG.  15    is a simplified cross-sectional view of another exemplary backlight  232 . Backlight  232  is similar to backlight  200  previously described and illustrated with reference to  FIG.  5   , except that backlight  232  includes an encapsulation layer  510 . In this embodiment, the encapsulation layer  510  is on the lower surface of the light guide plate  108  and encapsulates each of the plurality of patterned reflectors  112 . In other embodiments, the plurality of patterned reflectors  312  previously described and illustrated with reference to  FIGS.  12 A- 12 B  or the plurality of patterned reflectors  412  previously described and illustrated with reference to  FIGS.  13 A- 13 B  may be used in place of the plurality of patterned reflectors  112 . In this embodiment, encapsulation layer  510  may prevent damage (e.g., scratches) to each patterned reflector  112  due to potential contact with the light sources  106  during fabrication of the backlight  232 . 
     Encapsulation layer  510  may be an optically clear adhesive, a clear resin, a diffusive resin, or another suitable material. Encapsulation layer  510  may be thermally curable, UV curable, or pressure sensitive. While encapsulation layer  510  fully encapsulates each patterned reflector  112  in the embodiment illustrated in  FIGS.  14  and  15   , in other embodiments encapsulation layer  510  may partially encapsulate each patterned reflector  112  such that a portion of each patterned reflector  112  remains exposed. 
       FIG.  16    is a simplified cross-sectional view of an exemplary backlight  234 . Backlight  234  is similar to backlight  230  previously described and illustrated with reference to  FIG.  14   , except that in backlight  234  the encapsulation layer  510  is bonded to the first layer  146  of the optical film stack. The encapsulation layer  510  may be directly bonded to the first layer  146  of the optical film stack or bonded to the first layer  146  of the optical film stack via an adhesive material or another suitable material. By bonding the encapsulation layer  510  to the first layer  146  of the optical film stack, the overall thickness of the backlight  234  may be reduced and/or the mechanical stability of the backlight  234  may be improved. 
       FIG.  17    is a simplified cross-sectional view of an exemplary backlight  236 . Backlight  236  is similar to backlight  230  previously described and illustrated with reference to  FIG.  14   , except that backlight  236  includes an encapsulation layer  500 . The light guide plate  108  may be directly bonded to the encapsulation layer  500  or bonded to the encapsulation layer  500  via an adhesive material or another suitable material. By bonding the light guide plate  108  to the encapsulation layer  500 , the overall thickness of the backlight  236  may be reduced and/or the mechanical stability of the backlight  236  may be improved. 
     As shown in  FIGS.  17 ,  18 ,  20 , and  21   , the encapsulation layer  500  encapsulates each of the plurality of light sources  106 . The encapsulation layer  500  may include a clear resin material, a silicone, or another suitable material. The clear resin material, silicone, or another suitable material should have a transmittance of over about 60 percent and preferably over about 90 percent. The encapsulation layer  500  may include nano-sized or micro-sized scattering particles. 
       FIG.  18    is a simplified cross-sectional view of an exemplary backlight  238 . Backlight  238  is similar to backlight  236  previously described and illustrated with reference to  FIG.  17   , except that backlight  238  includes a diffusive layer  130  as previously described and illustrated with reference to  FIG.  6    bonded between the light guide plate  108  and the encapsulation layer  500 . 
       FIG.  19    is a simplified cross-sectional view of an exemplary backlight  240 . Backlight  240  is similar to backlight  232  previously described and illustrated with reference to  FIG.  15   , except that backlight  240  includes a diffusive layer  130  bonded between the light guide plate  108  and the first layer  146  of the optical film stack. 
       FIG.  20    is a simplified cross-sectional view of an exemplary backlight  242 . Backlight  242  is similar to backlight  236  previously described and illustrated with reference to  FIG.  17   , except that in backlight  242  the encapsulation layer  510  is bonded to the first layer  146  of the optical film stack. By bonding the light guide plate  108  to the encapsulation layer  500  and by bonding the encapsulation layer  510  to the first layer  146  of the optical film stack, the overall thickness of the backlight  242  may be reduced and/or the mechanical stability of the backlight  242  may be improved. 
       FIG.  21    is a simplified cross-sectional view of an exemplary backlight  244 . Backlight  244  is similar to backlight  232  previously described and illustrated with reference to  FIG.  15   , except that backlight  244  includes an encapsulation layer  500 , the light guide plate  108  is bonded to the first layer  146  of the optical film stack, and the encapsulation layer  510  is bonded to the encapsulation layer  500 . By bonding the light guide plate  108  to the first layer  146  of the optical film stack and by bonding the encapsulation layer  510  to the encapsulation layer  500 , the overall thickness of the backlight  244  may be reduced and/or the mechanical stability of the backlight  244  may be improved. Similar to  FIG.  19   , the light guide plate  108  may have a diffusive layer  130  on the upper surface and be bonded to the first layer  146  of the optical film stack through the diffusive layer  130 , while the encapsulation layer  510  is bonded to the encapsulation layer  500 . 
     It will be apparent to those skilled in the art that various modifications and variations can be made to embodiments of the present disclosure without departing from the spirit and scope of the disclosure. Thus, it is intended that the present disclosure cover such modifications and variations provided they come within the scope of the appended claims and their equivalents.