Patent Publication Number: US-2021165137-A1

Title: Multi-faceted diffuser providing specific light distributions from a light source

Description:
REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 16/894,489 filed Jun. 5, 2020, that claims priority to U.S. Provisional Patent Applicant No. 62/880,776, filed on Jul. 31, 2019, which is incorporated herein in its entirety by reference. 
    
    
     BACKGROUND 
     1. Field of the Description 
     The present description relates, in general, to, light transmission, projection, and use in illuminating displays and to related devices or products. More particularly, the present description relates to an optical diffuser designed to produce a specific or predefined light distribution in space through the use of numerous facets (or microstructures or lenses) aiming light in desired directions. The description also relates to the design and production method used to create the new optical diffusers as well as to apparatus (products or devices) that include or make use of the optical diffusers such as microdisplays (such as light emitting diode (LED) screens), lighting devices of many types (e.g., lights used in the automobile industry, indoor and outdoor lighting application, and the like), projection screens, and so on. 
     2. Relevant Background 
     There continues to be a large demand for optical diffusers (or light diffusers or, more simply, “diffusers”) to diffuse or scatter light to transmit light in a desired manner such as to soften light or to spread light out so it does not appear to come from a point source. The demand for diffuse light or soft light will likely grow in the coming years due to the greater reliance on sources such as LEDs, lasers, and the like as light sources and due to the need for diffuse light in more and more devices that include microdisplays. 
     Diffuse light used in microdisplays, such as those in smartphones, compact computing and gaming devices, and the like, is often provided by compact optical systems with a diffuser formed of a translucent material such as ground glass, polyester films, polycarbonate substrates, opal glass, grayed glass, and the like. Conventional diffusers are made using light-scattering materials that produce a distribution of light in all directions and angles. These types of diffusers include those formed of opal or milk glasses and may also include diffusers formed of ground glass and sand blasting glass to create random surfaces to scatter transmitted light passing through the diffuser. While being useful for softening coherent or noncoherent light from a light source, these diffusers provide no control over angular light distribution or transmission, and the efficiencies of light transmission tend to be relatively low as these diffusers often produce total internal reflection (TIR). 
     Other types of diffusers have, as a result, been created to try to address the problems of hot spots and uneven light distribution associated with filament, arc, LED, fiberoptic, laser light sources, and other light sources. These alternative design diffusers have been relatively successful in smoothing and homogenizing sources while also providing uniform light in other applications such as for liquid crystal display (LCD) backlights, LED displays, machine vision, automotive lighting, viewing screens, and the like. Such diffusers may be made by rulings of cross-sectional shapes in a transparent material to distribute light mainly in a given XZ or YZ plane, but, in other cases, simple lenticular designs are used in the diffusers. Other more sophisticated diffusers, which may be called light-shaping diffusers, may use diffractive optical elements (DOEs) and may be used with a laser light source. These diffusers often use phase differences generated in a substrate to diffract light rays into certain directions with the DOEs, and the DOEs may be holographically recorded, randomized surface structures that can increase light transmission efficiency (e.g., to 80 percent or more), provide beam shaping, and homogenize output light. 
     While solving some issues with conventional diffusers, there are still a number of issues with use of even these more sophisticated optical diffusers. For example, one problem associated with highly-engineered holographic diffusers is that they are expensive and cumbersome to record. Another problem is that their structures (or DOEs) are so fine that they cannot be extruded, which is the preferred low-cost method of manufacture, as the material tends to “relax” in extrusion embossing due to the small size of the structures. Therefore, holographic diffusers are generally made in a ultraviolet (UV) cast and cure environment or process that is more expensive than extrusion. Another problem with holographic diffusers is that since the structures are so small (e.g., less than 5 microns) they are especially sensitive to dust, oils from user&#39;s hands, and so on that can render them useless or at least less efficient and less effective in desired scattering. 
     There remains a need for new light or optical diffusers that address these and other problems with existing diffusers. For the most part, diffusers are not engineered well and operate in a rather crude and inefficient manner by wasting light (e.g., low light transmission efficiencies) and not diffusing the light properly, which can leave hot spots. This is particularly true with LED diffusers and LED lighting. Since LEDs tend to provide very bright “spots” or points of light, they are difficult to diffuse and can create very hot areas or spots on the diffuser surface. In other cases, though, the diffusing provided by the LED diffuser is so “heavy” that it blocks most or a great deal of the light, and such low light transmission efficiency is undesirable in many applications such as for use in a display backlight. LED lighting is expected by many to nearly take over the lighting market due to energy efficiencies and general production costs associated with LED light sources, and it highly desirable to solve the problems associated with diffusing LED lighting in the very near future. 
     SUMMARY 
     Briefly, diffusers are described herein for use in providing a user-selected light distribution in space from a wide variety of light sources including LED light sources and coherent light sources without hotspots. The diffusers are designed using a new design method that is effective in processing a user&#39;s input or desired light distribution (such as a Gaussian or non-Gaussian distribution or engineered shapes such as a product logo, an image, letters, or the like) and defining facets or microstructures for a front or light transmission surface of the diffuser. These facets are randomly distributed across this front surface in sets or cells associated with various regions (or brightness levels) within the predefined light distribution, and the assignment process is performed to set the number of facets in each set to achieve the brightness level of that set or cell (e.g., cells with higher brightness levels are assigned a proportionally higher number of facets than ones with lower brightness levels). Further, the facets assigned to each region (e.g., an angular range of the distribution) are randomly directed to direct light within the region and not only at the center of such a region to avoid hotspots. 
     More particularly, an apparatus is provided for producing a predefined light distribution in space. The apparatus includes a light source operable to output light. The apparatus also includes a diffuser with a substrate having a back surface receiving the light output from the light source and a front surface, opposite the back surface, redirecting and transmitting the light received on the back surface to output diffuse light with the predefined light distribution from the diffuser. The substrate is formed of a light-transmissive material (such as a “clear” polycarbonate, PET, glass, ceramic, or the like). The front surface is formed so as to include a plurality of facets that scatter or redirect that light during its transmission through the front surface, thereby diffusing the source-provided light. Each of the plurality of facets is randomly assigned to one of a plurality of sets, and each of the plurality of sets is associated with a region of the predefined light distribution. 
     In some embodiments, each of the facets in each of the plurality of sets has a planar face oriented to redirect the light received on the back surface in a direction within the region of the predefined light distribution associated the one of the plurality of sets to which they are assigned. Further, each of the regions of the predefined light distribution is associated with an angular range and the direction within the region is randomly assigned to each of the facets (e.g., each facet of a set does not direct its light in exactly the same direction while still contributing to the brightness of that particular region or area of the light distribution shape). In some case, each of the facets is defined by a coordinates of the planar face on the front surface of the diffuser and by a normal vector direction to the planar face. 
     In the same or other embodiments, each of the sets of the facets is associated with a brightness cell defining the predefined light distribution. The number of the facets (or portion of available facets) assigned to each of the sets of the facets is selected based on a brightness value assigned to each of the brightness cells. In some cases, the predefined light distribution is a Gaussian distribution, while, in other cases, the predefined light distribution is a line focus, is an engineered shape, includes one or more letters, or includes one or more images. The light source may be a light emitting diode (LED) source, a coherent light source, a filament light source, a fluorescent light source, or a halogen light source. 
     In some preferred implementations, the apparatus further includes at least one additional optical element positioned to receive the output diffuse light, and the apparatus is adapted to function as a display, a projection screen, theater or film production lighting, automobile lighting, indoor or outdoor lighting, or a light curing unit. The diffuser for the apparatus may be formed via extrusion processes or cast and cure using ultraviolet (UV) or E beam curing of the facets. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic or functional block diagram of an apparatus, such as a microdisplay, a lighting device, or the like, with a “facet” or multi-faceted diffuser of the present description; 
         FIG. 2  is a cross-sectional view of an exemplary diffuser of the present description such as may be used in the apparatus of  FIG. 1 ; 
         FIG. 3  is a functional block diagram of a system for designing and producing optical diffusers of the present description such as those presented with reference to  FIGS. 1 and 2 ; 
         FIG. 4  illustrates a screenshot of a user input page or GUI provided to a user of the system of  FIG. 3  by the diffuser design module showing a number of rays in each brightness cell; 
         FIGS. 5A and 5B  illustrate a screenshot of contents of a header file showing data used and/or created by operations of a facet generation algorithm of the present description; 
         FIG. 6  illustrates a graph or plot plotting out relative brightness versus deflection angle for a designed diffuser such as the one of  FIGS. 4-5B   
         FIG. 7  illustrates a graph or plot showing direction of rays transmitted from a diffuser designed according to the present description such as diffuser of  FIG. 4-5B ; 
         FIG. 8  illustrates an exemplary brightness geometry that may be generated by software described herein and includes an orthographic side view of a brightness curve and an isometric view of the curve with value levels shown with gray values; 
         FIG. 9  is a graph showing results of a raytracing for the brightness curves of  FIG. 8 ; 
         FIG. 10  is a screenshot of a GUI provided by the software described herein displaying brightness cells with values associated with a Gaussian-type distribution of light by a designed diffuser; 
         FIG. 11  illustrates a screenshot of a GUI provided by the design module of the present description displaying for a particular brightness distribution of a diffuser a total number of facets associated with or assigned to each brightness cell or set; 
         FIG. 12  illustrates a second exemplary brightness geometry that may be generated by software described herein and includes an orthographic side view of a brightness curve and an isometric view of the curve with value levels shown with gray values; and 
         FIG. 13  is a graph showing results of a raytracing for the brightness curves of  FIG. 12 . 
     
    
    
     DETAILED DESCRIPTION 
     Briefly, embodiments described herein are directed toward optical or light diffusers (or, simply, “diffusers”) that are designed and manufactured to include numerous facets arranged in cells or sets in which the planar faces or outward-facing surfaces have matching orientations and transmission angles (as may be defined by direction cosines of normal to the plane containing each facet surface). The present description is also directed to the method of designing or defining the facets of the diffuser, to methods of manufacturing the diffusers, and to apparatus or products that include or make use of the new diffusers (such as microdisplays, lighting components, and so on). The multi-faceted diffusers or facet diffusers described herein are optically designed to produce a user-specified distribution of light in a single direction or in multiple directions. The diffusers can be engineered through the configuration of the facets on its front or outer surface (light transmission surface) to produce nearly any type of light distribution or shape, and the diffuser design facilitates their manufacture using extrusion processes as well as other fabrication techniques such as cast and cure approaches (e.g., UV or E-beam techniques). 
       FIG. 1  illustrates an apparatus  100  making use of a multi-faceted diffuser design of the present description. The apparatus  100  includes a light source  110  that is operable to produce a light stream  115 , which may be of nearly any wavelength and may be coherent when the light source  110  is a laser-based light source or non-coherent when the light source  110  is a filament source, an LED, an arc source, a fiberoptic source, or the like. Many implementations of the light source  110  provide a point or spot stream  115  such that diffusion is desirable to provide an output light  140  in the apparatus  100  that is distributed in space for a desired use such as for backlighting a display screen  150  when the apparatus  100  is a display device. 
     To this end, the apparatus  100  includes an optical or light diffuser (or “facet” diffuser)  120  that is disposed between the light source  110  and an output of the apparatus  100  (such as between the source  110  and an optional additional optical component  150 ). The diffuser  120  is formed of a substrate or body (e.g., a film or sheet) of a translucent-to-transparent material (e.g., 50 to 90 percent or more light transmissive material) such as a clear polycarbonate, PET, or the like. The diffuser  120  (or its body/substrate) has a back surface  122 , which may be planar, facing the light source  110  for receiving the light stream  115  from the light source  110 , and the surface  122  may be arranged to be orthogonal or at another orientation to the directional or travel axis of the stream  115 . 
     Further, and significantly, the diffuser  120  (or its body/substrate) includes a front surface  124  opposite (and typically parallel to) the back surface  122  that is used to scatter and redirect light  115  passing through the diffuser  120  to produce the diffuse output light  140 . The front surface  124  is formed so as to include a plurality of sets/cells  126 ,  127  each with a plurality of facets. This can be seen with exemplary first set or cell of facets  126  each with a planar face/surface  128  at a defined location (e.g., an X-Y coordinate  129  of a center of the face/surface  128 ) on the front surface  124 . Each facet of the set/cell  126  is configured to have a particular orientation and transmission angle  130 , which may be defined by the direction cosines of normal to the plane including the face/surface  128 . Each set/cell  126  may be adapted or configured to scatter or direct the light transmitted from the front surface  124  in a different manner to provide the diffuse output light  140  such that light  140  has a user-specifiable distribution of light  140  in a single direction or multiple directions. 
     The apparatus  100  may further include optional additional optical components  150  to allow the apparatus  100  to fulfill different purposes. For example, the optical component  150  may be a LCD or other display screen such that the combination of light source  110  and diffuser  120  act as a backlight for the screen/component  150  with diffuse output light  140 . In other cases, the optical component  150  includes a lens and/or optical cover when the apparatus  100  takes the form of a lighting device (e.g., an automobile headlight, taillight, or the like). In other cases, the apparatus  100  may take the form of LED lighting, an LCD/LED display, a projection system, a sign/display, a front projection screen, a mobile phone/smartphone, a barcode scanner, an inspection system, outdoor or indoor lighting, medical instrumentation, fiber optic illumination device, or the like. 
       FIG. 2  illustrates a cross-sectional and greatly enlarged view of an optical diffuser  200  of the present description such as may be used as the diffuser  120  of the apparatus  100  of  FIG. 1 . As shown, the diffuser  200  has a body or substrate  204  with a back or first side  202 , which may be planar as shown. The back side  202  is exposed to an output of a light source (not shown in  FIG. 2  but understood from the light source  110  of  FIG. 1 ) such that it receives incoming light  220  that is illustrated as being composed of numerous parallel rays (or as being non-diffuse light). The body/substrate  204  is formed of material that is highly transmissive of light such as a clear polycarbonate, PET, or other plastic, a glass, a ceramic, or the like that may be 70 to 90 percent transmissive or more (and may be labeled herein as “clear” even though not wholly efficient at transmitting light  220 ). 
     The incoming light  220  is received through the back surface  202  and travels basically unimpeded until it reaches the front or second surface  206  of the diffuser  200 . The front or second surface  206  is opposite to the back or first surface  202 , and it is uniquely formed so as to have numerous facets  210  each with a uniquely oriented and angled (at a transmission angle) to scatter the light  230  that is transmitted from the front surface  206  to provide diffuse light  230 . One ray is shown for each facet  210  for ease of illustration, but, in practice, each will receive and scatter numerous rays of the incoming light  220 . As can be seen from the simplified version of a diffuser  200 , the facets have different orientations and transmission angles, which may be defined by their direction cosines of normal to the plane containing the face/exterior surface of each facet  210  so as to provide a desired distribution of incoming light  220  in the diffuse exiting light  230  in a single direction or multiple directions and with desired light shaping. 
     The diffuser  200  achieves the transmission of diffuse light  230  through the inclusion of the small facets  210 , which may be rectangular (e.g., square) in shape and substantially planar on their faces/exterior surfaces, with dimensions (e.g., sides) in the range of 6 to 350 microns. A more preferred size for the facets  210  may be 12 to 100 microns (as measured along a side), but some embodiments may use larger or smaller facets. All the facets  210  of a diffuser  200  may have matching sizes and shapes in some embodiments (e.g., all facets  210  may be square in shape with equal side lengths chosen from range of 12 to 30 microns (or another useful range)) while other embodiments may use differently sized facets  210  (within a set or cell or among different sets/cells). 
     Each facet  210  is defined, as explained below in more detail, during the design and manufacture process by calculating its direction cosines of normal and arranging them at locations about the front surface  206  to produce refraction of parallel incoming light  220  into a desired direction(s). Many such facets  210  would be designed or calculated such as hundreds of thousands to several million depending on the size of the facets  210  and the size of the diffuser  200 , and each facet orientation and transmission angle (or direction cosines of normal) is selected to direct light  230  to user-specified areas in space. This selectable distribution of diffuse light  230  allows the user to project images or messages in the space or area illuminated by the diffuse light  230 . 
     The general impact of the new design of the diffuser  200  is quite large and disruptive as it allows one to manufacture highly engineered and refined diffusers at a cost equal to or less than traditional diffusers. Further, the diffuser  200  has shown in simulations to have much higher light transmission efficiencies than conventional diffusers such as 90 percent or greater when compared with less than 50 percent for some conventional diffusers. 
       FIG. 3  is a functional block diagram of a system  300  for designing and producing optical diffusers of the present description, such as those presented with reference to  FIGS. 1 and 2 . As shown, the system  300  includes a workstation or computing system  310  that may be used by an operator or designer to design a diffuser to provide a user-specified light distribution. The workstation  310  may be nearly any computing system useful for performing the functions described herein such as a desktop, a laptop, a notebook, a pad, a smartphone, or the like. The workstation  310  includes a processor(s)  312  that processes or executes code, instructions, and/or software to perform or provide the functions described herein of a diffuser design module  320 . Particularly, the design module  320  uses a facet defining algorithm  322  to generate definitions of facets for a diffuser to achieve a user-selectable light distribution. 
     The processor  312  also manages operations of input and output (I/O) devices  314  of the system  310  such as a monitor or display, a keyboard, a mouse, a touchscreen or pad, and so on that allow an operator or designer using the system  310  to input data and to view information presented by the module  320 . To this end, the module  320  may be configured to generate a graphical user interface (GUI)  316  that may be displayed on a monitor of the system  310  provided in the I/O devices  314 , and an operator may interact with the GUI  316  to provide a set of user input  342  that is stored in memory/data storage  350  of the system  310  by processor  312 . 
     The user input  342  along with other information such as size and shape of a front side or surface of a diffuser, transmissivity of the material used to form the diffuser, and the like is used as input by the facet defining algorithm  322  to generate for diffuser a design file  350  that can be stored in memory  340  by the processor  312 . This file  350  is then passed as output as shown with dashed arrow  360  (e.g., by wired or wireless communications) to a diffuser fabrication system  370  such as an extrusion system, a cast and cure system, or the like. The system  370  uses this input file to fabricate diffusers with a front or exterior surface with facets meeting the requirements of the design file  350  for that type of diffuser. 
     Particularly, each design file  350  may include information including facet shape  354  (such as rectangular, square, or the like), facet size  352  (e.g., 12 microns by 12 microns for a square-shaped facet surface/face), and facet number  356 , which may be provided in user input  342  or, more often, is calculated by the module  320  based on the facet size  352  and the size and shape of the diffuser&#39;s front or exterior surface so as to substantially cover this surface with facets. Further, each diffuser&#39;s design file  350  includes facet definitions  358  generated by the facet design algorithm  322 , and these may include a location for each facet (e.g., X-Y coordinates of a center point of the planar face/surface) and its direction of cosines to normal (or orientation and transmission angle of the face/planar surface of the facet). 
     The inventors created a computer program, to implement the diffuser design module  320  with its facet defining algorithm  322 , and this program is adapted to take a designer&#39;s (or customer&#39;s) design for a diffuser as input. Further, the program allows the designer to program and/or modify their design and to execute them to generate a design file (e.g., file  350  in  FIG. 3 ) that can be used to fabricate diffusers according to the program-generated design (e.g., with definitions of each facet on the front or exterior surface of the diffuser). 
     At this point in the description, it may be useful to walk through what input (e.g., user input  342  in  FIG. 3 ) the program requests or uses to create a diffuser design and how the designer/user may enter this in some exemplary but not limiting implementations. In one example, the user, when using the program on their computing device, enters data that represents angle locations for each of two angles. The first angle is along the X-axis and the other is along the Y-axis. The user is presented (in a GUI or the like on their monitor or display device) with brightness cells, and the user can enter desired brightness values for each cell (such as in fractions of one or percentages). The program may have some default or hard-coded values for a few diffusers that have been previously designed, and these can be used by the program to automatically fill the brightness cells with these values, which the designer/user may then modify (or accept). 
     Each cell represents a compound angle at which rays of light will be aimed by the facets of the diffuser being designed. The user input entries can be in fractions of a center cell or the number of rays for the desired direction. The program can automatically calculate the number of rays of input light from the source to go to each cell based on the cell sizes and the overall size of the diffraction substrate (and its exterior or front surface containing the facets). For example, the facets may be sized (by default settings or user input) to have 12-micron square faces/surfaces while the diffuser is defined (again by default or user input) to have a 40,000-micron square area on its front or exterior/transmission surface, and the program would determine that 11,111,111 total facets can be provided on this surface and need to be defined. The program automatically fills the cells in proportion to the user input and total number of facets available.  FIG. 4  illustrates a screen shot  400  of the user input page or GUI displayed to the user by the program that shows the number of rays placed in each cell by the program for use in distributing received light from a source from the diffuser&#39;s multi-faceted front surface in a user-specified manner. 
     The computer program is configured to take the user design information and generate each facet normal that will refract rays along the desired paths (associated with the cells to which they are assigned by the program). Significantly, the program is further configured such that the facets are generated in a random location on the front or exterior surface of the diffuser under design. This allows edges of replicated diffusing substrates according to the design to be joined together to form a larger diffuser (e.g.,  1  to N diffusers formed according to a diffuser design can be assembled in an abutting manner to form a single diffuser with a light distribution defined by the configuration of each sub-diffuser or substrate). This can be extremely important and unique to this description as the tooling costs of a small facet array (one for a front surface of a small-surface area diffusing substrate or diffuser) can be quite expensive. The random nature of the facet locations allows the smaller diffusers/substrates to be stepped or recombined without creating a “jump” or seam in a fabricated diffuser that would be noticeable in the output diffuse light or output light distribution. 
     The following is a segment of code that may be used to implement the facet generation subroutine of the computer program (e.g., facet defining algorithm  322  of  FIG. 3 ) along with narrative description of the functionality and output for portions of the code: 
     
       
         
           
               
             
               
                   
               
             
            
               
                 maxzdc = Cos(MaximumSpecifiedTiltRad) 
               
               
                 ‘set up the unavailable array 
               
               
                 For j = −NBCY To NBCY 
               
            
           
           
               
               
            
               
                   
                 For i = −NBCX To NBCX 
               
            
           
           
               
               
            
               
                   
                 nraysneeded(i, j) = BC(i, j) 
               
            
           
           
               
               
            
               
                   
                 Next i 
               
            
           
           
               
            
               
                 Next j 
               
               
                 nrays = 0 
               
               
                 nraysold = 0 
               
               
                 getout = False 
               
               
                 While getout = False 
               
               
                 ‘ assume that the center of the center cell is at polar angles 0,0 or x=y−0 
               
            
           
           
               
               
            
               
                   
                 For j = −NBCY To NBCY ‘ the cell numbers (locations to be calculated in the following 
               
            
           
           
               
            
               
                 sub ) 
               
            
           
           
               
               
            
               
                   
                 For i = −NBCX To NBCX 
               
            
           
           
               
               
            
               
                   
                 icount = icount + 1 
               
               
                   
                 If icount &gt; 10000 Then ‘check how many rays are available 
               
            
           
           
               
               
            
               
                   
                 If nraysold = ns Then 
               
            
           
           
               
               
            
               
                   
                 getout = True 
               
               
                   
                 Else 
               
               
                   
                 getout = False 
               
            
           
           
               
               
            
               
                   
                 End If 
               
               
                   
                 icount = 0# 
               
               
                   
                 nrays = 0# 
               
               
                   
                 For jj = −NBCY To NBCY 
               
            
           
           
               
               
            
               
                   
                 For ii = −NBCX To NBCX 
               
            
           
           
               
               
            
               
                   
                 nrays = nrays + nraysneeded(ii, jj) 
               
            
           
           
               
               
            
               
                   
                 Next ii 
               
            
           
           
               
               
            
               
                   
                 Next jj 
               
               
                   
                 If getout = False Then 
               
            
           
           
               
               
            
               
                   
                 If nrays &gt; 0 Then 
               
            
           
           
               
               
            
               
                   
                 getout = False 
               
            
           
           
               
               
            
               
                   
                 Else 
               
            
           
           
               
               
            
               
                   
                 getout = True 
               
            
           
           
               
               
            
               
                   
                 End If 
               
            
           
           
               
               
            
               
                   
                 End If 
               
               
                   
                 nraysold = ns 
               
               
                   
                 Form1.Label(0).Caption = “Generating Facet Normals Working on Facet Number 
               
            
           
           
               
            
               
                 ” + Str(ns) + “ rays available ” + Str(nrays) 
               
            
           
           
               
               
            
               
                   
                 DoEvents 
               
            
           
           
               
               
            
               
                   
                 End If 
               
               
                   
                 thetaleftrad = CDbl(i) * BCThetaRadX 
               
               
                   
                 thetabottomrad = CDbl(j) * BCThetaRadY 
               
               
                   
                 If nraysneeded(i, j) &gt; 0# Then 
               
            
           
           
               
               
            
               
                   
                 ‘randomly choose a ray location within the degree band 
               
               
                   
                 ‘xstarting point on sphere 
               
               
                   
                 xstart = r * Sin(thetaleftrad − BCThetaRadX / 2#) 
               
               
                   
                 ystart = r * Sin(thetabottomrad − BCThetaRadY / 2#) 
               
               
                   
                 xstop = r * Sin(thetaleftrad + BCThetaRadX / 2#) 
               
               
                   
                 ystop = r * Sin(thetabottomrad + BCThetaRadY / 2#) 
               
               
                   
                 xdiff = Abs(xstop − xstart) 
               
               
                   
                 ydiff = Abs(ystop − ystart) 
               
               
                   
                 ‘use random number generator to pick an x and y in the spherical ( cell )--- 
               
               
                   
                 xrandom = xdiff * Rnd( ) 
               
               
                   
                 yrandom = ydiff * Rnd( ) 
               
               
                   
                 xi = xstart + xrandom 
               
               
                   
                 yi = ystart + yrandom 
               
               
                   
                 s2 = xi {circumflex over ( )} 2 + yi {circumflex over ( )} 2 
               
               
                   
                 If s2 &lt; r Then ‘ 
               
            
           
           
               
               
            
               
                   
                 zi = Sqr(r {circumflex over ( )} 2 − xi {circumflex over ( )} 2 − yi {circumflex over ( )} 2) 
               
               
                   
                 s1 = Sqr(xi {circumflex over ( )} 2 + yi {circumflex over ( )} 2 + zi {circumflex over ( )} 2) 
               
               
                   
                 ‘cal DC values ( assume that all rays start at 0,0 ) 
               
               
                   
                 e1x = 0# 
               
               
                   
                 e1y = 0# 
               
               
                   
                 e1z = 1# 
               
               
                   
                 e2x = xi / s1 
               
               
                   
                 e2y = yi / s1 
               
               
                   
                 e2z = zi / s1 
               
               
                   
                 s1 = s1 
               
               
                   
                 ‘use these values to calculate normals of facets 
               
               
                   
                 Call facet_normal_finder_and_check(an1, an2, e1x, e1y, e1z, e2x, e2y, e2z, nx, 
               
            
           
           
               
            
               
                 ny, nz, frsn_true) 
               
            
           
           
               
               
            
               
                   
                 If frsn_true = True Then 
               
            
           
           
               
               
            
               
                   
                 If nz &gt; maxzdc Then 
               
            
           
           
               
               
            
               
                   
                 max_angle = True 
               
            
           
           
               
               
            
               
                   
                 Else 
               
            
           
           
               
               
            
               
                   
                 max_angle = False 
               
            
           
           
               
               
            
               
                   
                 End If ‘max angle 
               
               
                   
                 If max_angle = True Then 
               
            
           
           
               
               
            
               
                   
                 ns = ns + 1 
               
               
                   
                 FacetDCX(ns) = nx ‘direction cosines of facet 
               
               
                   
                 FacetDCY(ns) = ny 
               
               
                   
                 FacetDCZ(ns) = nz 
               
               
                   
                 nraysneeded(i, j) = nraysneeded(i, j) − 1 
               
            
           
           
               
               
            
               
                   
                 End If ‘max_angle=t 
               
            
           
           
               
               
            
               
                   
                 End If ‘frsn_true=t 
               
            
           
           
               
               
            
               
                   
                 End If ‘s2&lt;1 
               
            
           
           
               
               
            
               
                   
                 End If ‘nraysneeded&gt;0# 
               
            
           
           
               
               
            
               
                   
                 Next i 
               
            
           
           
               
               
            
               
                   
                 Next j 
               
            
           
           
               
            
               
                 Wend 
               
               
                 Form l.Label(0).Visible = False 
               
               
                 Call Calculate_Maximum_Tilt_Angle 
               
               
                   
               
            
           
         
       
     
     The details of the numbers and data used in these calculations can be output to a header file, which may include data as shown in the screen shot  500  of  FIGS. 5A and 5B  as may be viewed by a diffuser designer on their workstation. This header is also put on top of the vendor file to keep track of the calculation details. The final output file is a very long file containing the direction cosine of each of the 11,111,111 facets in this example. The file is too long to be practical to attach this description. However,  FIG. 6  illustrates a graph or plot  600  plotting out relative brightness versus deflection angle for a designed diffuser such as the one of  FIGS. 4-5B , and  FIG. 7  illustrates a graph or plot  700  showing direction of rays transmitted from a diffuser designed according to the present description such as diffuser of  FIGS. 4-5B . In  FIG. 7 , it can be seen that the total X-directional spread is 60 degrees while total Y-directional spread is 16 degrees. 
     As will be appreciated from the above discussion of the diffuser design module and its associated algorithms, the inventors&#39; ideas can be implemented using software (and/or firmware) that generates data files. The data files are used by a diffuser designer to create refractive elements or facets on a diffuser surface that send rays of incoming light from a light source(s) in desired directions and at desired intensities, with both being user selectable via user input to the software. The software is configured so that various inputs may be used by the user to define the final output (e.g., a diffuser design file with defined facets), and these may include: (a) facet size; (b) array size (e.g., total final output canvas that may be associated with a diffuser&#39;s front/transmission surface); (c) index of refraction for both facet and film on which facet exists (or an indication of which transmissive material is used along with film thickness); (d) angle of light diffusion desired (typically give in degrees); and (e) final product facing direction (facing toward/away from light source). 
     After these general parameters have been defined (through input or values stored and/or accessed by the program), the program provides a user interface to allow the user to use a “cell”-based system or approach to defining how the brightness of the source light is distributed through the defined angular distribution of light diffusion. In some cases, manually inputting brightness values can be tedious for the user of the program. To address this potential issue, the inventors have added a function to the program that allows the input of data files which contain brightness information for each cell (e.g., a starting or default brightness that can be accepted or modified by the user). 
     In one particular prototype implementation, the data files used to prefill the cells were generated in 3D software (e.g., AutoDesk® Maya®).  FIG. 8  illustrates an exemplary brightness geometry that may be generated by the 3D software, and the brightness may be designated visually by vertex height and gray value. In  FIG. 8 , representation  810  is an orthographic side view of a brightness curve while representation  820  is an isometric view of the curve with value levels shown with gray values. In summary, a 3D “brightness” curve is generated by the 3D software with points along the curve then being converted to a format that can be read in by the software and used as appropriate brightness values. The inventors further employed a software routine to perform raytracing of designed diffusers, with  FIG. 9  showing a graph  900  providing results of a raytracing for the brightness curves  810 ,  820  of  FIG. 8 . As can be seen from the graph  900 , the ray count softly drops to zero as the angle of light diffusion increases toward user-specified settings. 
     Once the brightness value file (user input) has been generated and input into the software/design module, the brightness cells are normalized by the software such as to feature a maximum brightness of one. Such a brightness distribution can be seen in the screenshot of the user interface GUI  1000  shown in  FIG. 10 , which includes a cell chart displaying the brightness values of each cell based on the “Gaussian” curve as seen in  FIG. 8 . Each cell represents a certain degree range that is based on the final desired distribution angle. Numbers within each cell represent brightness values for that particular degree range. For example, if the diffuser is being designed to have a 30 degree by 30 degree distribution and there are 15 cells, each cell represents a 2 degree by 2 degree region of the final output of diffuse light. Note, in  FIG. 10 , that the corner cells contain zero facets and, therefore, zero brightness as the intended distribution in this example is ellipsoidal in shape. 
     If the user/designer finds these brightness values satisfactory, they can instruct the algorithm to continue with adjusting the calculate brightness values to reflect the total number of available facets on the diffuser being designed. The final calculation process converts decimal numbers into whole integers (as it is not likely practical to fabricate fractional facets). The total number of facets is determined by facet size (which may be a default value or be selected from predefined ranges by the user/designer via their user input) and by the overall canvas size (or size of the diffuser front/transmission surface being designed). 
       FIG. 11  illustrates a screenshot  1100  of a GUI providing brightness distribution of a diffuser under design showing a total number of facets associated with each brightness cell or set (e.g., number of facets assigned to distributing light in the direction and/or location associated with the brightness cell). The numbers contained in each cell reflects the total number of facets that will be assigned to that cell&#39;s designated degree range and will be tilted (or oriented) upon manufacture to refract incoming light somewhere within that degree range (with the face/surface of each facet in a cell/set having a like direction cosines of normal). 
     If these values are deemed satisfactory by the user/designer, the software then proceeds with the algorithm by assigning facets to cells. Each facet assigned to a cell has its tilt angle randomized while still falling within a range acceptable for the cell so as to allow for a smooth distribution of light. However, some embodiments may have all facets for a single cell pointing at the direct middle angular value for the cell, but, in some cases, this may result in hot spots for each cell degree range (which may not be suited for many light distribution applications). Further, the algorithm is configured such that the assignment of facets across the face/surface of the diffuser is random and is not determined by facet location or cell angle. This random distribution of the facets to the cells/sets combined with the microscopic facet size has been proven by the inventors to produce diffusers that refract light being transmitted through the diffuser in an appropriate manner to achieve a particular distribution regardless of where the incoming light from the light source contacts the back surface of the diffuser and, thus, the facet array on the front or transmission surface of the diffuser. 
     Once the software has assigned all facets that are available to a cell/set, the software outputs a text file (diffuser design file) containing X-Y coordinate data as well as dX/dY/dZ tilt (or orientation) data for each facet. This text file can then be used to manufacture a diffuser with a surface having such cells or sets of facets that can be provided in an optical apparatus to provide user-defined distribution of light from a light source. For example, the text file may be used to create planar array precision tooling into a master (which may be a glass master or the like), and this master may be used to grow or form shims (e.g., nickel shims or the like). The shims may then be used to make transparent castings such as through the use of UV curable fluid, and the quality of the final castings (e.g., the diffusers) match the initial tooling exactly or at least with very high precision. Hence, shining a light through these transparent or semi-transparent castings results in the initial brightness distributions input to the software by the user/designer (such as via the cell GUI shown above). 
     As will be appreciated, the above techniques can be used to generate light distributions with a diffuser to suit nearly any user&#39;s needs and is not limited to the geometry shown in  FIGS. 8 and 9 . As one example,  FIG. 12  illustrates an exemplary brightness geometry that may be generated by the 3D software, and the brightness may be designated visually by vertex height and gray value. In  FIG. 12 , representation  1210  is an orthographic side view of a brightness curve while representation  1220  is an isometric view of the curve with value levels shown with gray values. The input curves are useful for generating a light distribution with a “ring” brightness falloff.  FIG. 13  shows a graph  1300  providing results of a raytracing for the brightness curves  1210 ,  1220  of  FIG. 12 . 
     At this point in the description, it may be useful to provide additional details on the algorithm(s) carried out by the software/computer program used to design diffusers along with some of the mathematical challenges addressed and overcome by the inventors. First, the inventors understood that most present-day diffusers are holographic or utilize lens structures. In the present case, the goal was to be able to create Gaussian and non-Gaussian diffusers that were generated (defined) in software and that could be tooled quickly and effectively. It was also a goal that these types of diffusers would be designed and fabricated such that they would work (e.g., properly diffuse light per a designer&#39;s input) regardless of the area the incoming light from a light source (e.g., an LED, a laser-based light source, and so on) moves through the diffuser in a transmission mode (as well as reflected when desired) such that a light source does not have to be accurately aligned with a center of the diffuser or be stationary behind the diffuser. As will be appreciated by those in the optics and light transmission arts, the transmission mode for the new diffusers proved to be extremely challenging. 
     In order to create the new front/transmission surface of the diffusers with such goals in mind, it was determined by the inventors that the structures or facets should be randomized in their location on the front/transmission surface. Randomized location of sets or cells of facets directing light in certain directions (e.g., degree ranges as discussed above) is useful so that regardless of whether one is using a laser or an LED light the same shape of the light would occur (or distribution) (e.g., a particular input stream is not required for the new diffuser design). This also requires random structures within a subset of structures (e.g., within each brightness cell or set of facets assigned to provide a particular redirection of incoming light). Because of this, smaller tooling could be made (or fabricated diffusers with such smaller tooling) and then put together in a step-and-repeat environment even by overlapping structures without having resulting visible jumps in the light as the light source moves across the structures. The advantage of facet-based structures that can be programmed at any angle in just moments was dramatic and unexpected. For example, programming and tooling for a diffuser design according to this description is relatively fast. Further, the new diffuser design allows replacement of prior holographic-type diffusers, and holographic masters, which can be expensive and difficult create, do not have to be shot or used. 
     The challenge and one unique aspect of the invention is that the mathematics to solve this problem were found to be unusual and unconventional. The following discussion describes some of the contributions provided by the inventors (or accomplishments) as well as the base logic behind the algorithm carried out by the software/computer program described herein. Normally Snell&#39;s law can be used when the normal vector to a surface is known. In this case, the normal vector to a facet&#39;s planar surface/face is not known to find the refraction of the ray to a desired location. In other words, Snell&#39;s law had to be re-written by the inventors mathematically to give the starting ray a refractive surface to find the surface normal that will refract the ray to a desired location. 
     In order to do this, the inventors rewrote or modified Snell&#39;s law in a vector formulation. This rewrite required that the cross product of two vectors form a third vector to hit the desired location of the ray. In the mathematics of the rewrite, the sine of the angle between the two vectors is proportional to the cross product. During initial efforts by the inventors, it appeared there might not be a solution to create an equation (or several equations) that could be solved as part of the software (or its algorithm). In this case, it was surmised that the software could be configured to calculate an optimized solution without a firm solution, and, it should be understood that the present description encompasses software that uses such an optimized solution to finding and defining the normal vectors to each facet. 
     However, it was discovered, in time and through significant efforts by the inventors, that the equation(s) could be solved, and a more preferred embodiment to the algorithm carried out by the software (or diffuser design module/program) involves creating a cross product in a normalized format in which the sine of the angle between the two vectors is proportionate. By solving the equation(s), the diffuser can be designed to contain a very large number (hundreds of thousands to millions) of carefully oriented facets to bend/direct light into any shape or light distribution desired (even letters or symbols) with high efficiency. Importantly, incoming light need not be collimated, it can be input as any incoming vector (or even average of the incoming light vector) and still be refracted/redirected to the desired location by the facets on the front/transmission surface of the diffuser. In the past, this had proven to be extremely difficult if not impossible for most diffusion systems. 
     As noted above, the facets defined for a diffuser may vary in shape (e.g., round, square, rectangular, hexagonal, or the like) and size, with common dimensions (such as sides of a rectangular (and square in some embodiments)) being in the range of about 6 to 8μ to 350μ or more in some cases. With a size, shape, and number (based on size and shape of facets and of front/transmission surface of diffuser) of facets defined, the facet defining algorithm uses random selection of the facets for assignment to a brightness beam/set (which may be associated with a particular range of distribution angles of the overall defined light distribution), and the algorithm further uses random assignment of transmission angles within this cell and its distribution angle range (or within a predetermined region) to avoid hotspots (e.g., not every or even any of the facets will be targeted at center of predetermined region). 
     The light distribution can be defined by user input to achieve nearly any desired light distribution such as for creating a line focus or an engineered diffusion to eliminate hot spots (such as may happen when using LED lights as light sources without use of the present invention). Further, the light distribution may be defined as engineered shapes such as letters or images, and the facets are defined to provide light distributions to present these shapes in space a distance away from the front/transmission surface of the diffuser. Further, the user input may define a direction and/or location of an incoming light stream from a light source, and the algorithm (or diffuser design module) may be configured to manipulate or respond to the direction of the incoming light for a solution to the diffuser needs as part of defining the facets for desired light distribution. The program further can be configured to provide the ability to manipulate the facets by changing (via user input or the like) the refractive index of the materials in the program (e.g., one parameter set by the user input may be a diffuser material and/or a refractive index for the substrate/film to be used in forming the diffuser). 
     The new diffusers may be used with a wide variety of light sources such as LED, fluorescent, laser and halogen lighting or light sources. In one particular implementation, the apparatus with a light diffuser described herein is implemented with an LED light source and is configured for use as or in LED lighting curing units for proper light distribution of curing energy cured inks and coatings for the printing and converting industry. The apparatus in other implementations are used in or to provide projection screens. In other cases, the apparatus includes the new diffusers to provide theater lighting or lighting for film production. In still other examples of useful apparatus with the new diffusers, the apparatus taught herein may take the form of a microdisplay or screen (e.g., an LED screen) of all types (e.g., displays or screens for a PDA, a TV, a smartphone or cellphone, computing devices such as pads, tablets, and the like, or other electronic device with a display or screen). In still other use cases, the new apparatus uses the diffusers for light diffusion in automobile headlights, taillights, and interiors. Other apparatus may include and use the new diffusers for indoor and outdoor lighting applications. 
     The file defining the diffuser&#39;s facets can be used (e.g., to create tooling) for a variety of manufacturing processes. For example, the design file output by the software described herein can be used in a method of manufacture of the diffusers in extrusion processes as well as in a method of manufacture in cast and cure (UV or E Beam) curing of the facets. Further, the design file may be used as input for a method to create larger tooling and seamless tooling due to the use of the random selection processed taught herein. 
     Although the invention has been described and illustrated with a certain degree of particularity, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the combination and arrangement of parts can be resorted to by those skilled in the art without departing from the spirit and scope of the invention, as hereinafter claimed. 
     For example, the light receiving surface of the diffuser (e.g., a back surface which faces the light source) may be configured to include the facets while the front surface may be planar. This reverse orientation compared to that described above is not shown in the figures, but it will be readily understood by those skilled in the arts. 
     As discussed above, the diffuser and its facets will often be configured for diffusing light of various wave lengths. For example, the facets may be engineered to provide the predefined light distribution (particular scattering or diffusing of light) for white light as well as specific ranges of wavelengths for various applications such as IR, lower wave lengths, and the like. In the same or other examples, the design programming can be done for touchless screens and so forth. In other words, the diffusers can be made to work at very specific wavelengths as taught herein and understood by ready extension by those skilled in the arts. 
     In some embodiments, the diffusers are configured as metallized reflective diffusers, and a thin film or layer of reflective metal is provided upon the planar surface of the diffuser and the output light from the light source first passes through the surface containing the facets prior to reflection with light scattering as described herein. The diffusers described herein may be manufactured in a number of ways as discussed above and further including via molded glass and injection molded plastics processes.