Patent Publication Number: US-7587117-B2

Title: Luminaire device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This is a continuation application of prior application Ser. No. 11/130,066, filed on May 16, 2005 now U.S. Pat. No. 7,209,628; which is a continuation application of prior application Ser. No. 10/641,304, filed on Aug. 14, 2003 now U.S. Pat. No. 6,993,242; which is a continuation of U.S. Ser. No. 09/995,497, filed on Nov. 27, 2001, now U.S. Pat. No. 6,671,452; which is a continuation of U.S. Ser. No. 09/533,043, filed Mar. 22, 2000, now U.S. Pat. No. 6,335,999; which is a continuation of U.S. Ser. No. 08/999,149, filed Dec. 29, 1997, now U.S. Pat. No. 6,044,196; which is a continuation of U.S. Ser. No. 08/783,212, filed Jan. 13, 1997, now U.S. Pat. No. 6,002,829; which is a continuation of Ser. No. 08/486,784, filed on Jun. 7, 1995, now U.S. Pat. No. 5,594,830; which is a continuation of Ser. No. 08/226,016, filed Apr. 11, 1994 now U.S. Pat. No. 5,528,720; which is a continuation-in-part of Ser. No. 08/029,883, filed Mar. 11, 1993, now U.S. Pat. No. 5,303,322; and which is a continuation-in-part of Ser. No. 07/855,838, filed on Mar. 23, 1992, now U.S. Pat. No. 5,237,641. 

   The present invention is concerned generally with a luminaire device for providing selected light illumination. More particularly, the invention is concerned with luminaires, such as a wedge, for backlighting by light output from a liquid crystal display layer and also by manipulating light polarization, recycling light of selected polarization and filtering selected light polarizations to enhance light illumination and image output. 
   A variety of applications exist for luminaire devices, such as, for liquid crystal displays. For flat panel liquid crystal displays, it is important to provide adequate backlighting while maintaining a compact lighting source. It is known to use wedge shaped optical devices for general illumination purposes. Light is input to such devices at the larger end; and light is then internally reflected off the wedge surfaces until the critical angle of the reflecting interface is reached, after which light is output from the wedge device. Such devices, however, have only been used to generally deliver an uncollimated lighting output and often have undesirable spatial and angular output distributions. For example, some of these devices use white painted layers as diffuse reflectors to generate uncollimated output light. 
   It is therefore an object of the invention to provide an improved optical device and method of manufacture. 
   It is another object of the invention to provide a novel three dimensional luminaire. 
   It is a further object of the invention to provide an improved multilayer tapered luminaire for optical purposes, such as for controlled utilization of light polarization. 
   It is still another object of the invention to provide a novel tapered luminaire device for controlled transmission or concentration of light. 
   It is an additional object of the invention to provide a novel optical device for providing collimated polarized light illumination from the device. 
   It is yet a further object of the invention to provide an improved tapered luminaire having a polarization filter layer. 
   It is still another object of the invention to provide a novel luminaire allowing conversion of polarized light to enhance illumination output from the invention. 
   It is yet a further object of the invention to provide an improved illumination system wherein a combination of a polarization filter layer and a light redirecting layer are utilized to provide improved light illumination over a controlled angular range of output to the viewer. 
   It is still a further object of the invention to provide a novel luminaire optical device wherein a combination of a polarization filter, polarization converting layer and a post LCD diffuser layer are used to enhance light illumination from the optical device. 
   It is yet a further object of the invention to provide an improved luminaire optical device wherein an LCD layer is disposed adjacent an overlying post LCD diffuser layer to enable control of light distribution over broader angles to viewers without loss of light output or image qualities. 
   It is also another object of the invention to provide an improved luminaire optical device having an internal polarization cavity for converting luminaire light to one polarization state for enhanced illumination gain. 
   It is yet an additional object of the invention to provide a novel luminaire optical device having a selected arrangement of a structured back reflector layer with a polarization beam splitter to enhance illumination efficiency. 
   It is still another object of the invention to provide an improved luminaire optical device having a polarization converting layer interacting with a structural back reflector layer to provide enhanced illumination efficiency. 
   It is also a further object of the invention to provide a novel luminaire optical device having a polarization beam splitter, a quarter wave converting layer and a microstructural back reflector layer to provide enhanced illumination gain. 
   It is yet another object of the invention to provide an improved luminaire optical device having a selectable arrangements of polarization splitting layers including one of (a) the splitting layer evaporated directly onto a base layer of the luminaire, and (b) evaporation of the splitting layer onto a separate glass plate. 
   It is also an additional object of the invention to provide a novel luminaire optical device including a quarter plate polarization converting element in one of a set of selectable arrangements of (a) disposed between a back reflector and luminaire base layer with air layers between, (b) coupled directly to a back reflector with an air layer between the luminaire base layer and the directly coupled layers, (c) coupled directly to the luminaire base layer with an air layer between the converting element and a metallic back reflector layer or a BEF type of back reflector, (d) coupled directly to the luminaire base layer on one side and a high efficiency mirror on the other side, and (e) coupled directly to the luminaire base layer on one side thereof and an air layer and back reflector on the other side of the base layer. 
   It is yet a further object of the invention to provide an improved luminaire optical device having a textured base layer for enhancing illumination properties. 
   It is still another object of the invention to provide a novel luminaire optical device utilizing a film based reflective polarizer in combination with a converter layer and BEF type back reflector. 
   It is also a further object of the invention to provide an improved luminaire optical device having a base layer separated by various air layers with polarized splitter, redirecting, converter, and back reflector layers disposed above and/or below the base layer. 
   It is yet an additional object of the invention to provide a novel luminaire optical device including a back reflector below a base layer and a redirecting layer adjacent the top surface of the base layer and a reflective polarizer and redirecting/diffuser layer positioned above the redirecting layer. 
   Other objects, features and advantages of the present invention will be readily apparent from the following description of the preferred embodiments thereof, taken in conjunction with the accompanying drawings described below. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a prior art wedge shaped device; 
       FIG. 2A  illustrates a multilayer tapered luminaire device constructed in accordance with the invention;  FIG. 2B  is a magnified partial view of the junction of the wedge layer, the first layer and the second faceted layer;  FIG. 2C  is an exaggerated form of  FIG. 2A  showing a greatly enlarged second faceted layer;  FIG. 2D  is a partial view of the junction of the three layers illustrating the geometry for brightness determinations;  FIG. 2E  is a multilayer wedge device with a light redirecting, internally transmitting layer on the bottom;  FIG. 2F  shows a wedge device with a lower surface translucent layer;  FIG. 2G  shows a wedge layer with a lower surface refracting faceted layer;  FIG. 2H  shows a wedge layer with a lower surface refracting layer and curved facets thereon;  FIG. 2I  shows a wedge layer with a refracting layer of facets having variable facet angles;  FIG. 2J  shows a single refracting prism coupled to a wedge layer;  FIG. 2K  shows a single refracting prism coupled to a wedge layer and with an integral lens;  FIG. 2L  shows a reflecting faceted layer coupled to a wedge device;  FIG. 2M  shows a reflecting faceted layer with curved facet angles and coupled to a wedge device;  FIG. 2N  shows a flat reflecting facet on a wedge layer and  FIG. 2O  shows a curved reflecting facet on a wedge layer; 
       FIG. 3A  illustrates a multilayer wedge device with curved facets on the ambient side of the second layer and  FIG. 3B  shows a magnified partial view of the junction of the various layers of the device; 
       FIG. 4A  shows calculated brightness performance over angle for an asymmetric range of angles of illumination;  FIG. 4B  shows calculated brightness distribution performance over angle for a more symmetric angle range;  FIG. 4C  illustrates calculated brightness performance over angle for the symmetry of  FIG. 4B  and adding an external diffuser element;  FIG. 4D  illustrates an output using flat reflecting facets, no parallel diffuser; full-width at half-maximum brightness (FWHM)=7 degrees;  FIG. 4E  illustrates an example of nearly symmetrical output distribution, measured using flat facets with parallel lenticular diffuser; FWHM=34 degrees;  FIG. 4F  illustrates an example of asymmetrical output distribution, measured using curved facets; FWHM=32 degrees;  FIG. 4G  illustrates an example asymmetrical output distribution, measured using curved facets; FWHM=26 degrees;  FIG. 4H  illustrates an example of a bimodal output distribution, measured using one faceted reflecting layer and one faceted refractive layer; and  FIG. 4I  illustrates an example of an output distribution with large “tails”, measured using a diffuse reflective bottom redirecting layer and a refracting/internally-reflecting top redirecting layer; 
       FIG. 5A  shows a top view of a disc shaped light guide and  FIG. 5B  illustrates a cross section taken along  5 B- 5 B in  FIG. 5A ; 
       FIG. 6A  shows a cross sectional view of a multilayer tapered luminaire device with an air gap layer included;  FIG. 6B  shows another tapered luminaire in cross section with a compound parabolic light source/concentrator;  FIG. 6C  illustrates another tapered luminaire in cross section with a variable parametric profile light source and a lenticular diffuser; and  FIG. 6D  shows another tapered luminaire in cross section with non-monotonic wedge layer thickness; 
       FIG. 7  illustrates a reflective element disposed concentrically about a light source; 
       FIG. 8  illustrates a reflective element disposed about a light source with maximum displacement between the reflector center of curvature and the center of the light source; 
       FIG. 9A  illustrates use of a redirecting layer to provide a substantially similar angular distribution emanating from all portions of the device and  FIG. 9B  illustrates use of a redirecting layer to vary angular distribution emanating from different portions of the device, and specifically to focus the various angular distributions to enhance their overlap at a selected target distance; 
       FIG. 10  illustrates one form of pair of lenticular arrays of a luminaire; and 
       FIG. 11  illustrates a lenticular diffuser array and curved facet layer of a luminaire; 
       FIG. 12A  illustrates a wedge shaped luminaire having a pair of diffraction gratings or hologram layers;  FIG. 12B  shows a wedge shaped luminaire with a pair of refracting facet layers and diffusers;  FIG. 12C  illustrates a wedge shaped luminaire with a pair of faceted layers;  FIG. 12D  shows a wedge shaped luminaire with two refracting single facet layers;  FIG. 12E  illustrates a wedge shaped luminaire with a refracting single facet layer and a bottom surface redirecting layer;  FIG. 12F  shows a luminaire with a top surface redirecting layer of a refracting faceted layer and a bottom surface refracting and internally reflecting layer;  FIG. 12G  illustrates a luminaire with a top surface refracting/internally reflecting faceted layer and a bottom surface refracting/internally reflecting faceted layer;  FIG. 12H  shows a luminaire with a top surface refracting faceted layer and a bottom surface refracting/internally reflecting faceted layer;  FIG. 12I  illustrates a luminaire with a bottom surface specular reflector and a top layer transmission diffraction grating or transmission hologram;  FIG. 12J  shows a luminaire with a bottom surface specular reflector and a top surface refracting faceted layer and diffuser;  FIG. 12K  illustrates a luminaire with a bottom layer specular reflector and a top layer refracting/internally reflecting faceted layer;  FIG. 12L  shows a luminaire with a bottom specular reflector and a top layer refracting/internally reflecting faceted layer;  FIG. 12M  illustrates a luminaire with an initial reflector section including an integral lenticular diffuser;  FIG. 12N  shows a luminaire with a roughened initial reflector section of a layer;  FIG. 12O  illustrates a luminaire with an eccentric light coupler and converging to the wedge shaped section;  FIG. 12P  shows a luminaire with an eccentric light coupler and a diffuser and roughened or lenticular reflector;  FIG. 12Q  illustrates a luminaire with a bottom specular or diffusely reflecting layer and a top refracting layer and  FIG. 12R  shows a luminaire for generating a “bat wing” light output; 
       FIG. 13  illustrates a combination of two wedge shaped sections formed integrally and using two light sources; 
       FIG. 14  shows a tapered disk luminaire including a faceted redirecting layer; 
       FIG. 15  illustrates a luminaire operating to provide a collimated light output distribution; 
       FIG. 16A  shows a prior art ambient mode LCD and  FIG. 16B  illustrates a prior art transflective LCD unit; 
       FIG. 17  shows a luminaire operative in ambient and active modes with a faceted redirecting layer and a lenticular diffuser; 
       FIG. 18A  illustrates a luminaire with an array of microprisms for a faceted surface disposed over a diffuse backlight and with the microprisms having equal angles on both sides, but each microprism having progressively changing facet angles across the face;  FIG. 18B  shows a microprism array as in  FIG. 18A  with the sides of each microprism having different angles varying again across the faceted surface; 
       FIG. 19A  illustrates a luminaire having a polarization filter layer;  FIG. 19B  shows a luminaire with a plurality of layers including a polarization filter layer; and  FIG. 19C  shows a variation on  FIG. 19B  with layer indices enabling output of both polarizations of light on one side of the luminaire; 
       FIG. 20A  illustrates a luminaire similar to  FIG. 19B  but further includes a reflector layer;  FIG. 20B  illustrates a luminaire as in  FIG. 20A  but a redirecting layer is disposed on the same side of the base layer and the polarization filter; and  FIG. 20C  is a variation on  FIG. 20B  with an additional redirecting layer and rearranged n 2 /filter/redirecting layers; 
       FIG. 21A  illustrates a luminaire having a polarization converting layer and polarization filter layer;  FIG. 21B  is a variation on  FIG. 21A  with the polarization filter layer and polarization converting layer on the same side of the base layer; 
       FIG. 22A  illustrates a luminaire with a polarization filter layer one side of the base layer and a polarization converting layer on the other side;  FIG. 22B  shows a variation on  FIG. 22A  with the filter and converting layers adjacent one another on the same side of the base layer;  FIG. 22C  shows a further variation of  FIGS. 22A  and B and with a reflector layer added;  FIG. 22D  illustrates a further variation on  FIG. 22C  with the converting layer moved to the other side of the base layer and  FIG. 22E  shows another variation on  FIG. 22D ; 
       FIG. 23A  illustrates a luminaire having plural layers including a polarization filter, a converting, a redirecting, a reflector and an LCD layer;  FIG. 23B  shows a variation on  FIG. 23A ; and  FIG. 23C  illustrates yet another variation on  FIG. 23A ; 
       FIG. 24A  illustrates a luminaire with two polarization filter layers for two polarization states;  FIG. 24B  shows a variation on  FIG. 24A  plus an added light redirecting layer;  FIG. 24C  is a further variation on  FIG. 24B  with a matching layer, a second redirecting layer and an LCD layer;  FIG. 24D  is yet another variation on  FIGS. 24B  and C;  FIG. 24E  is a variation on  FIG. 24D  with an added converting layer and two polarization filter layers and two redirecting layers and  FIG. 24F  is still another variation on  FIG. 24E  with LCD layers on both sides of the base layer; 
       FIG. 25A  illustrates a general construction utilizing two polarization filter layers and a polarization converting layer;  FIG. 25B  shows a variation on  FIG. 25A  with an added redirecting layer; 
       FIG. 26A  illustrates a multilayer luminaire with a light source coupled to a light angle transformer to control spatial uniformity of light output from the device;  FIG. 26B  is a variation on  FIG. 26A ; 
       FIG. 27A  illustrates a luminaire with a faceted redirecting layer and light polarization and polarization converting layers; and  FIG. 27B  is a variation on  FIG. 27A , wherein the redirecting layers includes a reflecting layer with curved facets for focusing light in a preferred viewing zone; 
       FIG. 28A  illustrates a luminaire including a polarization light filter, polarization converter and a faceted redirecting and diffusing layer;  FIG. 28B  shows a variation on  FIG. 28A  with two polarization filter layers and two faceted redirecting layer;  FIG. 28C  shows a light source coupled to a luminaire and is a variation on  FIG. 28A ;  FIG. 28D  is a variation on  FIG. 28C ; and  FIG. 28E  is yet another variation on  FIG. 28C ; 
       FIG. 29A  illustrates a luminaire with polarized light output in combination with an LCD layer and  FIG. 29B  is a variation on  FIG. 29A ; 
       FIG. 30A  illustrates a conventional LCD display system;  FIG. 30B  shows a polarization filter layer;  FIG. 30C  illustrates a multilayer thin film form of polarization filter;  FIG. 30D  shows a Brewster Stack form of polarization filter;  FIG. 30E  illustrates a birefringent plate and interacting polarized light;  FIG. 30F  shows Eulerian angles and optical vectors;  FIG. 30G  shows a backlight providing collimated light in the xz plane and  FIG. 30H  shows a detailed enlargement of a zone from  FIG. 30G ; 
       FIG. 31A  illustrates a luminaire with a coupled birefringent layer;  FIG. 31B  shows a luminaire and birefringent layer and an added light redirecting layer;  FIG. 31C  illustrates a luminaire system similar to  FIG. 31B  with an added light polarization converting layer;  FIG. 31D  is similar to  FIG. 31C  but the converting layer is on the same side of the base layer as the birefringent layer;  FIG. 31E  illustrates a variation on  FIG. 31C  with the converting layer coupled directly to the base layer;  FIG. 31F  is similar to  FIG. 31D  but the redirecting layer comprises a faceted layer;  FIG. 31G  is based on the embodiment of  FIG. 31F  but also includes a matching layer, an LCD layer and a diffuser layer; and  FIG. 31H  is a variation on  FIG. 31G ; 
       FIG. 32A  illustrates a luminaire system including an LCD layer and a post LCD diffuser layer for processing unpolarized light;  FIG. 32B  is a variation on  FIG. 32A ; and  FIG. 32C  is a variation on  FIG. 32B ; 
       FIG. 33  illustrates a luminaire system including a quarter wave converting layer and BEF based type of back reflector below the base layer and polarization splitter and redirecting layer above the base layer; 
       FIG. 34  illustrates another form of  FIG. 33  without the converting layer; 
       FIG. 35  illustrates a luminaire system including a BEF based type of back reflector below the base layer and a light redirecting layer above the base layer; 
       FIG. 36  illustrates another form of  FIG. 33  substituting a metallic back reflector for the BEF based type of back reflector layer; 
       FIG. 37  illustrates another form of  FIG. 36  except the polarization splitting layer is directly disposed onto the base layer; 
       FIG. 38  illustrates another form of  FIG. 35  except the back reflector layer is a metallic back reflector layer; 
       FIG. 39  illustrates another form of  FIG. 36  except the quarter wave plate converting layer is laminated to the base layer; 
       FIG. 40  illustrates a luminaire system with a polarization cavity formed by the base layer and a laminated converting layer; 
       FIG. 41  illustrates another form of  FIG. 40  but a polarization splitting layer is directly disposed onto the top surface of the base layer; 
       FIG. 42  illustrates a variation on  FIGS. 40 and 41  with a back reflector layer directly coupled to the converting layer laminated to the bottom surface layer of the base layer; 
       FIG. 43  illustrates a luminaire system having a polarization converting layer disposed above the top surface of the base layer; 
       FIG. 44  illustrates a variation of  FIG. 43  with the base layer made of a birefringent polarization converting material; 
       FIG. 45  illustrates a variation of  FIG. 39  with the back reflector layer being a BEF type back reflector; 
       FIG. 46  illustrates a variation on  FIG. 40  with the back reflector layer being a BEF type back reflector; 
       FIG. 47  illustrates a luminaire system having a polarization splitting layer disposed at the input to the base layer; 
       FIG. 48  illustrates a variation on  FIG. 47  with a polarization converting layer on the lamp cavity side of the polarization splitting layer; 
       FIG. 49  illustrates a variation on  FIG. 33 , not including a redirecting layer, the base layer being textured and a film based reflective polarizer substituted for the interference layer; 
       FIG. 50  illustrates a variation on  FIG. 49 , not having the textured base layer; 
       FIG. 51  illustrates a variation on  FIG. 49  with the metallic back reflector substituted for the BEF type back reflector; 
       FIG. 52  illustrates a variation on  FIG. 51  with the base layer not being textured; 
       FIG. 53  illustrates a variation on  FIG. 33  with the reflective polarizer layer substituted for the interference layer and the base layer is textured; 
       FIG. 54  illustrates a variation on  FIG. 53  except the redirecting layer is switched with the reflective polarizer layer; 
       FIG. 55  illustrates a variation on  FIG. 53  with the converting layer positioned above the base layer; 
       FIG. 56  illustrates a variation on  FIG. 53  with the converting layer laminated to the base layer; 
       FIG. 57  illustrates a variation on  FIG. 35  using a textured form of the base layer; 
       FIG. 58  illustrates a polarized luminaire system operated without use of a separate converter layer; 
       FIG. 59  illustrates a variation on  FIG. 58  with the polarizer layer positioned below the redirecting/diffuser layer; 
       FIG. 60  illustrates a variation on  FIG. 53  with polarization created by off-angle reflections; 
       FIG. 61A  illustrates a top view of a luminaire output measurement system and a luminaire device; and  61 B illustrates two half luminaires; 
       FIG. 62  illustrates a measured angle factor versus maximum brightness; and 
       FIG. 63  illustrates typical vertical distributions from a polarized and unpolarized luminaire using a standard backlight and a backlight using a coated plate polarization beam splitter. 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   A multilayer luminaire device constructed in accordance with one form of the invention is illustrated in  FIG. 2  and indicated generally at  10 . A prior art wedge  11  is shown generally in  FIG. 1 . In this wedge  11  the light rays within the wedge  11  reflect from the surfaces until the angle of incidence is less than the critical angle (sin −1 1/n) where n is the index of refraction of the wedge  11 . The light can exit equally from both top and bottom surfaces of the wedge  11 , as well as exiting at grazing angles. 
   The multilayer luminaire device  10  (hereinafter “device  10 ”) shown in  FIG. 2A  includes a base or wedge layer  12  which has a characteristic optical index of refraction of n 1 . The term “wedge layer” shall be used herein to include all geometries having converging top and bottom surfaces with wedge shaped cross sectional areas. The x, y and z axes are indicated within  FIGS. 2A and 2C  with the “y” axis perpendicular to the paper. Typical useful materials for the wedge layer  12  include almost any transparent material, such as glass, polymethyl methacrylate, polystyrene, polycarbonate, polyvinyl chloride, methyl methacrylate/styrene copolymer (NAS) and styrene/acrylonitrile. The wedge layer  12  in  FIG. 2A  further includes a top surface  14 , a bottom surface  16 , side surfaces  18 , edge  26  and a back surface  20  of thickness t o  spanning the top, bottom and side surfaces. A light source, such as a tubular fluorescent light  22 , injects light  24  through the back surface  20  into the wedge layer  12 . The light  24  is internally reflected from the various wedge layer surfaces and is directed along the wedge layer  12  toward the edge  26 . Other possible light sources can be used and will be described hereinafter. Generally, conventional light sources provide substantially incoherent, uncollimated light; but coherent, collimated light can also be processed by the inventions herein. 
   For the case where the surfaces  14  and  16  are flat, a single angle of inclination φ for a linear wedge is defined by the top surface  14  and the bottom surface  16 . In the case of nonlinear wedges, a continuum of angles φ are definable; and the nonlinear wedge can be designed to provide the desired control of light output or concentration. Such a nonlinear wedge will be described in more detail later. 
   In the embodiment of  FIG. 2A  a first layer  28  is coupled to the wedge layer  12  without any intervening air gap, and the first layer  28  has an optical index of refraction n 2  and is optically coupled to the bottom surface  16 . The first layer  28  can range in thickness from a few light wavelengths to much greater thicknesses and accomplish the desired functionality. The resulting dielectric interface between the wedge layer  12  and the first layer  28  has a higher critical angle than at the interface between the wedge layer  12  and ambient. As will be apparent hereinafter, this feature can enable preferential angular output and collimation of the light  24  from the device  10 . 
   Coupled to the first layer  28  is a second layer  30  (best seen in  FIG. 2B ) having an optical index of refraction n 3  which is greater than n 2 , and in some embodiments preferably greater than n 1 . This configuration then allows the light  24  to leave the first layer  28  and enter the second layer  30 . In the embodiment of  FIG. 2A  there are substantially no intervening air gaps between the first layer  28  and the second layer  30 . In the preferred form of the invention illustrated in  FIG. 2A , n 1  is about 1.5, n 2 &lt;1.5 and n 3 ≧n 1 . Most preferably, n 1 =1.5, n 2 &lt;1.5 (such as about one) and n 3 ≧n 1 . 
   In such a multilayer configuration for the device  10  shown in  FIG. 2 , the wedge layer  12  causes the angle of incidence for each cyclic time of reflection from the top surface  14  to decrease by the angle of inclination 2φ (relative to the normal to the plane of the bottom surface  16 ). When the angle of incidence with the bottom surface  16  is less than the critical angle characteristic of the interface between the wedge layer  12  and the first layer  28 , the light  24  is coupled into the first layer  28 . Therefore, the first layer  28  and the associated optical interface properties form an angular filter allowing the light  24  to pass when the condition is satisfied: θ&lt;θ c =sin −1  (n 2 /n 1 ). That is, the described critical angle is higher than for the interface between air and the wedge layer  12 . Therefore, if the two critical angles differ by more than 6φ, nearly all of the light  24  will cross into the interface between the wedge layer  12  and the first layer  28  before it can exit the wedge layer  12  through the top surface  14 . Consequently, if the two critical angles differ by less than φ, a substantial fraction, but less than half, of the light can exit the top surface  14 . If the two angles differ by more than φ and less than 6φ, then substantially more than half but less than all the light will cross into the wedge layer  12  and the first layer  28  before it can exit the wedge layer  12  through the top surface  14 . The device  10  can thus be constructed such that the condition θ&lt;θ c  is satisfied first for the bottom surface  16 . The escaping light  24  (light which has entered the layer  28 ) will then enter the second layer  30  as long as n 3 &gt;n 2 , for example. The light  24  then becomes a collimated light  25  in the second layer  30  provided by virtue of the first layer  28  being coupled to the wedge layer  12  and having the proper relationship between the indices of refraction. 
   In order to generate an output of the light  24  from the device  10 , the second layer  30  includes means for scattering light, such as a paint layer  33  shown in  FIG. 2E  or a faceted surface  34  shown in both  FIGS. 2B and 2C . The paint layer  33  can be used to preferentially project an image or other visual information. The paint layer  33  can comprise, for example, a controllable distribution of particles having characteristic indices of refraction. 
   By appropriate choice, light can also be redirected back through the wedge layer  12  and into ambient (see light  29  in  FIGS. 2A and 2C ) or output directly into ambient from the second layer  30  (see light  29 ′ in  FIG. 2F ). 
   In other forms of the invention a further plurality of layers with associated “n” values can exist. In one preferred form of the invention the index of the lowest index layer can replace n 2  in equations for numerical aperture and output angle (to be provided hereinafter). Such further layers can, for example, be intervening between the wedge layer  12  and the first layer  28 , intervening between the first layer  28  and the second layer  30  or be overlayers of the wedge layer  12  or the second layer  30 . 
   In certain embodiments the preferred geometries result in output of light into ambient without being reflected back through the wedge layer  12 . For example, in  FIG. 2F  the device  10  can include a translucent layer  37 . In another form of this embodiment shown in  FIG. 2G , a refracting layer  38  is shown. The refracting layer  38  can include flat facets  39  for providing a collimated output. Also shown in phantom in  FIG. 2G  is a transverse lenticular diffuser  83  which will be described in more detail hereinafter. The diffuser layer  83  can be used with any of the invention geometries, including above the wedge layer  12  as in  FIG. 6A . 
   In yet another example shown in  FIG. 2H , the refracting layer  38  can include curved facets  41  for providing a smoothly broadened output over a desired angular distribution. In a further example shown in  FIG. 2I , the refracting layer  38  includes variable angle facets  42 . These facets  42  have facet angles and/or curvature which are varied with position across the facet array to focus output light in a desired manner. Curved facets would enable producing a softly focused region within which the entire viewing screen appears to be illuminated. Examples of the application to computer screen illumination will be described hereinafter. In  FIGS. 2J and 2K  are shown, respectively, a single refracting prism element  43  and the prism element  43  with an integral lens  44  to focus the output light.  FIGS. 2L  and M show the faceted surface  34  with the facets angularly disposed to control the output distribution of light. In  FIGS. 2K and 2L  the light is output to a focal point “F”, while in  FIG. 2M  the output is over an approximate viewing range  45 .  FIGS. 2N and 2O  illustrate flat reflecting facets  48  and curved reflecting facet  49  for providing a collimated light output or focused light output, respectively. 
   As shown in  FIGS. 2A  and C the faceted surface  34  optically reflects and redirects light  29  through the second layer  30 , the first layer  28  and then through the wedge layer  12  into ambient. Only a fraction of each facet is illuminated, causing the output to appear alternately light and dark when viewed on a sufficiently small scale. Since this pattern is typically undesirable, for the preferred embodiment shown in  FIG. 2B  the period of spacing between each of the faceted surfaces  34  is preferably large enough to avoid diffraction effects, but small enough that the individual facets are not detected by the intended observing means. The spacing is also chosen to avoid forming Moiré interference patterns with any features of the device to be illuminated, such as a liquid crystal display or CCD (charge coupled device) arrays. Some irregularity in the spacing can mitigate undesirable diffraction Moiré effects. For typical backlighting displays, a spacing period of roughly 0.001-0.003 inches can accomplish the desired purpose. 
   The faceted surface  34  in  FIGS. 2B and 2C , for example, can be generally prepared to control the angular range over which the redirected light  29  is output from the device  10 . The minimum distribution of output angle in the layer  30  has a width which is approximately equal to:
 
Δθ=2φ[( n   1   2   −n   2   2 )/( n   3   2   −n   2   2 )] 1/2  
 
   Thus, since φ can be quite small, the device  10  can be quite an effective collimator. Therefore, for the linear faceted surface  34 , the exiting redirected light  29  has a minimum angular width in air of approximately:
 
Δθair= n   3 Δθ=2φ( n   1   2   −n   2   2 )/[1−( n   2   /n   3 ) 2 ] 1/2 .
 
As described hereinbefore, and as shown in  FIGS. 2H ,  2 I,  2 K,  2 L,  2 M, and  FIG. 3 , the facet geometry can be used to control angular output in excess of the minimum angle and also focus and control the direction of the output light.
 
   Fresnel reflections from the various interfaces can also broaden the output angle beyond the values given above, but this effect can be reduced by applying an anti reflection coating  31  on one or more of the internal interfaces, as shown in  FIG. 2B . 
   The brightness ratio (“BR”) for the illustrated embodiment can be determined by reference to  FIG. 2D  as well as by etendue match, and BR can be expressed as: 
               B   .   R   .     =         output   ⁢           ⁢   brightness       source   ⁢           ⁢   brightness       ⁢           ⁢   or       ,     
     ⁢       B   .   R   .     =     illuminated   ⁢           ⁢   area   ⁢     /     ⁢   total   ⁢           ⁢   area                     B   .   R   .     =         [     1   -       (       n   2     /     n   3       )     2       ]       1   /   2       =     0.4   -     0.65   ⁢           ⁢     (     for   ⁢           ⁢   most   ⁢           ⁢   transparent   ⁢           ⁢   dielectric   ⁢           ⁢   materials     )     .               
For example, the wedge layer  12  can be acrylic (n 1 =1.49), the first layer  28  can be a fluoropolymer (n 2 =1.28-1.43) or Sol-gel (n 2 =1.05-1.35, fluoride salts (n 2 =1.38-1.43) or silicone based polymer or adhesive (n 2 1.4-1.45); and the second layer  30  can be a faceted reflector such as polycarbonate (n 3 =1.59), polystyrene (n 3 =1.59) epoxy (n 3 =1.5-1.55) or acrylic (n 3 =1.49) which have been metallized at the air interface.
 
   The flat, or linear, faceted surfaces  34  shown, for example, in  FIGS. 2B and 2C  can redirect the incident light  24  to control direction of light output and also substantially preserve the angular distribution of light Δθ which is coupled into the second layer  30  by the angle-filtering effect (see, for example,  FIG. 4D ). For example, in one preferred embodiment shown in  FIG. 2L , the faceted surfaces  34  reflect light with the flat facet angles varied with position to focus the output light. In  FIG. 2M  the faceted surfaces  34  include curved facet angles which vary with position to produce a softly focused viewing zone  45  within which the entire screen appears to be illuminated (see also, for example  FIGS. 4F and 4G ). Also show in phantom in  FIG. 2M  is an exemplary liquid crystal display  47  usable in conjunction with the invention. As further shown in  FIGS. 3A  and B, curved facets  36  also redirect the incident light  24 , but the facet curvature increases the resulting range of angular output for the redirected light  29  (see for comparison for flat facets  FIG. 2D ). For example, it is known that a concave trough can produce a real image, and that a convex trough can produce a virtual image (see, for example,  FIG. 3B ). In each case the image is equivalent to a line source emitting light uniformly over the desired angular output range. Consequently, an array of such trough shaped facets  36  can redirect the incoming form of collimated light  25  from the first layer  28  (see  FIG. 2C ), and a plurality of such line source images then form the redirected light  29 . By arranging the spacing of the curved facets  36  to less than human eye resolution, the resulting array of line sources will appear very uniform to an observer. As previously mentioned, the choice of about three hundred to five hundred lines/inch or 0.002 to 0.003 inches for the period of facet spacing provides such a result. For a typical LCD display viewing distances of approximately twenty inches or greater are conventional. 
   Other useful facet shapes can include, for example, parabolic, elliptical, hyperbolic, circular, exponential, polynomial, polygonal, and combinations thereof. The user can thus construct virtually arbitrary distributions of averaged brightness of illumination using different facet designs. For example, polygon shaped facets can be used to produce output angular distributions having multiple peaks. 
   Examples of brightness distribution over various ranges of angular output using a curved-faceted reflector are illustrated in  FIGS. 4A-4C ,  4 F and  4 G.  FIGS. 4C and 4E  shows the brightness distribution in the case of a reflector having linear facets, and further including a diffuser element  40  (shown in phantom in  FIG. 2C ). The predicted performance output is shown for the various angular ranges (see  FIGS. 4A-4C ) and compared with the measured angular output of light for a commercially available source (labeled “Wedge”), such as a “Wedge Light” unit, a trademark of Display Engineering. The preferred angular range can readily be modified to accommodate any particular viewing and collimation requirements up to the minimum angle Δθ (air) described hereinbefore by the equation in terms φ, n 1 , n 2  and n 3 . This modification can be accomplished by progressively changing the curvature of the curved facets  36  in the manner shown in  FIG. 2M  and discussed hereinbefore. In addition to the illustrated control of the vertical viewing angular range, modification of the horizontal viewing range can also be accomplished by appropriate changes of the shape of the curved facets  36 . The above described angular distributions shown in  FIGS. 4A-4I  are representative when the device  10  is processing the light  24  within the numerical aperture NA=(n 1   2 −n 2   2 ) 1/2 . When light is outside this range, additional techniques can be applied to help control the angular output range. 
     FIGS. 9A and 9B  further illustrate the use of redirecting means to provide a tightly overlapping focused illumination output and a less overlapping focused illumination output, respectively. These concepts can be applied practically by considering that a typical portable computer screen  87  has a vertical extent “V” of about 150 mm, while a typical viewing distance, “D”, is 500 mm. A viewer at distance “D”, positioned normal to the vertical center of the computer screen  87  will view different areas of the screen  87  at angles ranging from −8.5° measured at the top of the screen  87  to +8.5° measured at the bottom of the screen  87 . This variation in viewing angle can, however, cause undesirable effects in use of a system having such screen illumination. Such a limited illumination angle for the screen  87  implies a limited range of positions from which a viewer can see a fully illuminated screen  87  (see  FIG. 9A ). Defining the viewer position in terms of the angle and distance from the center of the screen  87 , then the effective angular range is substantially reduced below the nominal illumination angle. For example, if the nominal illumination range is ±20° measured at each individual facet, then the effective viewing range is reduced to ±12° in the typical flat panel illuminator shown in  FIG. 9A . The resulting illumination between 12°-20°, either side of center for the screen  87 , will appear to be nonuniform to the viewer. 
   The invention herein can be used to overcome the above described nonuniformities by controlling the orientation of the faceted surface  34 . As illustrated, for example, in  FIG. 2M  both surfaces of the facets are rotated progressively such that the flat facet surface is varied from 35.6° to 33.3° relative to, or parallel to, the edges of the planes defining the various layers of the device  10 . This systematic variation from the top to the bottom of screen  89  (see  FIG. 9B ) results in the redirected output illustrated. The faceted surface  34  can further be combined with the diffuser  83  and the like to produce a variable, but controllable light illumination output distribution. A flat faceted surface  168  can further be combined with a diffuser  170 . Therefore, as shown in  FIG. 9B  the ability to rotate the angular distributions of light at different points on the screen  89  enable compensation for the variation in viewing angle with position. Systematic variations in the faceted surface  34  can further include variations in to focus the output of any faceted redirecting layer. Examples are shown in  FIGS. 2I and 2L . 
   In another example of overcoming nonuniformities of illumination, an array of micro-prisms for the faceted surface  34  can be laid over a conventional diffuse backlight  101  (see  FIG. 18A ). This faceted surface  34  operates by a combination of refraction and total internal reflection to permit only a limited angular range to be output through the layer into ambient. This angular range depends on the facet angles. For the case of acrylic film (n=1.49), highest brightness is typically achieved with a prism included angle of 90-100 degrees, resulting in a viewing angle of approximately ±35 degrees. Backlights using such a geometry show a sharp “curtaining” effect which is disconcerting to many viewers. This effect can be ameliorated by rotating the facets  38  from top to bottom of the screen to produce a focusing effect (see  FIG. 18B ). Simple ray-tracing shows that, for included angles in the range of 100°-110°, a facet rotated by an angle 3 will produce an angular distribution rotated by approximately 3/2. In the embodiment shown in  FIG. 18  the progressive variation of facet face angle can vary as position &gt; along the faceted surface  34  wherein, for example:
 
Ψ 1 =35°−(0.133°/mm)· x  
 
Ψ 2 =35°+(0.133°/mm)· x  
 
   This progressive facet angle change will produce an angular distribution which varies by approximately ten degrees across the screen  89 , and satisfies the generic constraints outlined above. 
   Whatever the desired facet shapes, the faceted surface  34  (see,  FIG. 2D ) is preferably formed by a conventional process such as molding or other known milling processes. Details of manufacture will be described hereinafter. 
   Nonlinear Wedges. 
   In another form of the invention the wedge layer  12 , which is the primary lightguide, can be other than the linear shape assumed hereinbefore. These shapes allow achievement of a wide variety of selected light distributions. Other shapes can be more generally described in terms of the thickness of the wedge layer  12  as a function of the wedge axis “z” shown in  FIGS. 2B  and C (the coordinate axis which runs from the light input edge to the small or sharp edge  26 ). For the linear shaped wedge,
 
 A ( z )= A   o   −C·z   (1)
         A o =maximum wedge thickness (see  FIG. 2A )   C=constant=tan φ       

   A large range of desired spatial and angular distributions can be achieved for the light output power (power coupled to the second layer  30 ). This light output power is thus the light available for output to the ambient by the appropriately faceted surfaces  34  or  36 , or even by the diffuse reflector  33  (see  FIG. 2E ) or other means. 
   For example, if L and M are direction cosines along the x and y axes, respectively, then L o  and M o  are the values of L and M at the thick edge (z=0). This initial distribution is Lambertian within some well-defined angular range, with little or no light outside that range. This distribution is especially important because ideal non-imaging optical elements have limited Lambertian output distributions. The key relationship is the adiabatic invariant, A(z)cos(θ c ) which is approximately equal to A 0 L 0  and which implicitly gives the position (z) of escape. To illustrate this concept, suppose we desire uniform irradiance so that dP/dz=constant. Suppose further that the initial phase space uniformly fills an elliptical area described by the following expression:
 
 L   o   2 /σ 2   +M   0   2 /τ 2 =1  (2)
 
where τ is the dimension of an ellipse along the M axis and σ is the dimension of the ellipse along the L axis.
 
   Then, dP/dL=const·[1−L 2 /σ 2 ] 1/2  but dA/dz=[A o /L c ]dL o /dZ where L c =cos θ c . Therefore, [1−(L c A) 2 /(A o σ) 2 ] 1/2 dA=constant times dz. Suppose σ=L c  in the preferred embodiment. This result can be interpreted by the substitution A/A 0 =sin u, so that A=A   sin u and u+½ sin (2u)=(π/2)(1−z/D) where D is the length of the wedge layer  12 . 
   If the desired power per unit length is dP/dz, more generally, then the desired shape of the wedge layer  12  is determined by the differential equation: 
   
     
       
         
           
             
               
                 
                   
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   Note that in all these cases the output distribution has only approximately the desired form because it is modified by Fresnel reflections. Note also that even when the wedge device  10  is curved, if the curvature is not too large, it may still be useful to define an average angle φ which qualitatively characterizes the system. 
   In another aspect of the invention the geometry of the above examples has an x,y interface between two refractive media with indices n 1  and n 2 . The components nM,nN are conserved across the interface so that n 1 M 1 =n 2 M 2 , n 1 N 1 =n 2 M 2 . The angle of incidence projected in the x,z plane is given by sin θ eff =N/(L 2 −N 2 ) 1/2 . Then using the above relations, sin θ 2eff /sin θ 1eff =(n 1 /n 2 )[1−M 1   2 ] 1/2 /[1−(n 1 /n 2 ) 2 M 1   2 ] 1/2 =(n 1 /n 2 ) eff . For example, for n 1 =1.49, n 2 =1.35, M 1 =0.5, the effective index ratio is 1.035(n 1 /n 2 ), which is only slightly larger than the actual index ratio. 
   Variation of Index of Refraction Over Spatial Parameters. 
   In the general case of tapered light guides, the wedge layer  12  is generally along the z axis with the narrow dimension along the x axis (see, for example,  FIG. 2A ). If we introduce optical direction cosines (nL,nM,nM where L,M,N are geometric direction cosines along x,y,z, then n is the refractive index which may vary with spatial position. For guided rays in the wedge layer  12 , the motion in x is almost periodic, and the quantity φnLdx for one period is almost constant as the ray propagates along z. This property is called adiabatic invariance and provides a useful framework for analyzing the lightguide properties. 
   In a first example the wedge device  10  shown in  FIG. 2A  has a uniform index in the wedge layer  12  and is linearly tapered in z with width A(z)=A 0 −C·z. Then, along the zigzag ray path, L(z)A(z) is approximately equal to a constant by adiabatic invariance. If a ray starts at z=0 with L=L 0 , then (A 0 −C·z)L(z) is approximately equal to L 0 A 0 . The ray will leak out of the wedge layer  12  when L=cos θ c  where θ c  is the critical angle=[1−(n 2 /n 1 ) 2 ] 1/2 . Thus, the condition for leaving the wedge layer  12  is A 0 −C·z=L 0 A 0 /cos θ c . This will occur at z=(A 0 /C)(1−L 0 /cos θ c ). Consequently, the density of rays emerging in z is proportional to the density of rays in the initial direction cosine L 0 . For example, the density will be uniform if the initial distribution in L 0  is uniform. 
   In a second example, the index profile is no longer uniform but falls off both in x and in z. If the fall-off in z is much slower than in x, the light ray path is still almost periodic, and the above adiabatic invariance still applies. Then, as the light ray  24  propagates in z, the path in x,nL space is almost periodic. Therefore the maximum value of L(z) increases and at some z may reach the critical value for escape. The z value for escape depends on the details of the index (n) profile. When this is specified, the analysis proceeds as in example one above. Thus, for a parabolic index profile, the index profile has the form n 2 (x)=n 2   0 [1−2Δ(x/ρ) 2 ] for −ρ&lt;xρ, =n 1   2 =n 2   0 [1−2Δ] for |x|&gt;ρ. Then, the critical angle at x=0 is still given by sin 2 θ c =2Δ=1−(n 1 /n 0 ) 2 . Then, if we have n 0  a slowly decreasing function of z, the slope θ at x=0 will slowly increase by the adiabatic invariance of φnLdx, while θ c  decreases so that light rays will escape. The details of the light ray distributions will depend on how the index (n) varies with z. 
   Nonwedge Tapered Geometries 
   In the most general case the light can be input into any shape layer (e.g., parallelepiped, cylinder or non-uniform wedge), and the principles described herein apply in the same manner, In addition, the index of refraction can be varied as desired in (x,y,z) to achieve the appropriate end result when coupled to means to output light to ambient. 
   For example, consider a disc-shaped light guide  46  which is tapered in the radial direction r shown in  FIG. 5 . The direction cosines in cylindrical polar coordinates are k r , k θ , k z . Light  48  propagating in this guide  46  satisfies the relationship:
 
φnk z dz˜constant.(adiabatic invariance)  (4)
 
 nrk   θ =constant.(angular momentum conservation)  (5)
 
   The adiabatic invariance condition is identical with that for the wedge device  10 , and the previous discussions pertinent to the wedge device  10  also thus apply to the light guide  46 . The angular momentum conservation condition requires that as the light streams outward from source  47  with increasing radius, the k θ  value decreases. Therefore, the light becomes collimated in the increasing radial direction. This makes the properties fundamentally like the wedge device  10 , and the light  48  can be made to emerge as light  52  at a selected angle to face  51 , collimated along the z direction. 
   For purposes of illustration we take the guide material to have a constant index of refraction n. For such geometries the light rays  48  along the two-dimensional cross sectional plane taken along  5 B- 5 B behave just as in the case of the wedge device  10  counterpart described hereinbefore. Similarly, various additional layers  54  and  56  and other means can be used to achieve the desired light handling features. For example, for the disc light guide  46  a preferred facet array  56  is a series of circles, concentric with the disk  46 . Thus, if the facets  56  are linear in cross section, the light rays  52  will emerge in a direction collimated within a full angle of 2φ times a function of the indices of refraction as in the device  10  described hereinbefore. 
   Tapered Luminaires with Two Low-Index Layers. 
   In another form of the invention shown in  FIG. 6A , the device  10  includes a first layer  61  having an optical index of refraction n 1  and a first or top layer surface  62  and a second or bottom layer surface  64  converging to establish at least one angle of inclination φ. The first layer  61  also includes a back surface  65  spanning the top layer surface  62  and the bottom layer surface  64 . 
   Adjacent the first layer  61  is layer means, such as a bottom transparent layer means, like a first intermediate layer  66  of index n 2  disposed adjacent to, or underlying, the bottom layer surface  64 . In addition, the layer means can embody a top transparent layer means, second intermediate layer  81  of index n 2  disposed adjacent to the top layer surface  62 . At least one of the layers  66  and  81  can be an air gap, or other gas or a transparent dielectric gap. 
   An air gap can be established by conventional means, such as by external supports, such as suspending the layers under tension (not shown) or by positioning spacers  68  between the first layer  61  and the adjacent light redirecting layer  70 . Likewise, the spacers  68  can be positioned between the first layer  61  and the second light redirecting layer  82 . Alternatively, solid materials can be used for the transparent dielectric to constitute layers  66  and  81  and can improve structural integrity, robustness and ease of assembly. Such solid materials can include, for example, sol-gels (n 2 =1.05-1.35), fluoropolymers (n 2 =1.28-1.43), fluoride salts (n 2 =1.38-1.43), or silicone-based polymers and adhesives (n 2 =1.40-1.45). Such solid materials for the transparent dielectric need no separate means to support or maintain it, but can result in lower N.A. acceptance since the index is higher than for an air gap. 
   The layers  66  and  81  allow transmission of light received from the first layer  61 . In this embodiment, part of the light will achieve θ c  first relative to the top layer surface  62 , and light will enter the layer  81  for further processing by the light redirecting layer  82 . The remaining light will thereby achieve θ c  first relative to the bottom layer surface  64 , thus entering the layer  66  for further processing by the light redirecting layer  70 . 
   In one preferred form of the invention (see  FIG. 6A ) both the layers  66  and  81  are present and can have similar, but significantly different indices n 2a  and n 2b , respectively. The indices are considered similar when they establish critical angles at the interfaces  62  and  64  which are similar in magnitude to the wedge angle φ, for example:
 
|arcsin( n   2a   /n   1 )−arcsin( n   2b   /n   1 )|&lt;6φ  (6)
 
   In this case significant, but unequal, fractions of light will enter each of the layers  66  and  81  for further processing by redirecting layers  70  and  82 , respectively. The larger fraction will enter the layer having the higher of the two indices n 2a  and n 2b . The redirecting layer  70  processes only the fraction which enters the layer  66 . Therefore, the influence of the redirecting layer  70  on the output angular distribution of light can be changed by varying the relationship between the indices n 2a  and n 2b . 
   In another preferred form of the invention the layers  66  and  81  can be the same transparent material of index n 2 &lt;n 1 . In general, lower values of n 2  will enhance the efficiency of the device  10  by increasing the numerical aperture at the light input surface  65 . Therefore, collection efficiency can be maximized when the layers  66  and  81  are gaps filled with air or other gases (with n 2 =1-1.01). 
   The thickness of the layers  66  and  81  can be selectively varied to control the output power spatial distribution of the device  10  or to enhance its visual uniformity. For example, increasing the thickness of the layer  81  by 0.002″-0.030″ sharply reduces non-uniformities which tend to appear at the thicker end of the device  10 . The thickness of layers  66  and  81  can also be smoothly varied with position to influence a desired spatial distribution of the light being output (see  FIG. 12L ). 
   In one preferred form of the invention shown in  FIG. 6A , the light redirecting layer  70  includes a reflective layer  71  which reflects the light back through the layer  66  and the first layer  61 . The light is then output into the first layer  61  through the top layer surface  62 , and ultimately through the light redirecting layer  82  for further processing. The reflective layer  71  can, for example, be any combination of a planar specular reflector, a partially or completely diffuse reflector, or a faceted reflector. 
   Use of a planar specular reflector leads to the narrowest angular distribution within the layer  81 . Therefore, the reflector can simplify design of the light redirecting layer  82  when the desired output angular distribution is unimodal. Diffuse or faceted reflectors can also be used for the layer  71  in order to achieve a large range of angular distributions (see  FIGS. 4H  and I) or to increase uniformity (see  FIG. 4N ). Diffuse reflectors are preferred if the desired angular distribution has large “tails” (see, in particular,  FIG. 4I ). Faceted reflectors can produce a bimodal angular distribution within the layer  81  (see  FIG. 4H ). Therefore, such faceted reflectors are preferred if the desired output angular distribution is bimodal. For example, a bimodal “batwing” distribution is preferred from luminaires for room illumination because it reduces glare. 
   In general each facet of the layer  71  can be shaped to control the angular distribution of the light reflected back through the layer  66  and the first layer  61  for further processing by the redirecting layer  82 . The angular distribution within the device  10  will in turn influence the angular distribution of the light output into ambient from the redirecting layer  82 . For example, curved facets can be used to smoothly broaden the angular distribution, as well as providing a diffusing effect to improve uniformity. The reflective layer  71  can also influence the output power spatial distribution as well as the angular distribution. The reflectivity, specularity, or geometry of the reflective layer  71  can be varied with position to achieve a desired output distribution. For example, as described hereinbefore, small variations in the slope (see  FIG. 12L ) of each element of the reflective layer  71  as a function of position significantly change the light output distribution. 
   The light redirecting layer  82  has an index n 3 &gt;n 2 , and is substantially transparent or translucent. The light in the low-index layer  81  enters the layer  82  and is redirected into ambient. The transmissive redirecting layer  82  also redirects the light which has been processed by reflection from the redirecting layer  71  then transmitted back through the low-index layer  66  and the first layer  61 . The transparency or geometry of the layer  82  can be varied with position to further influence the output spatial distribution of the device  10 . In one preferred form of the invention the redirecting layer  82  includes a faceted surface at the interface with the low-index layer  81 , as shown in  FIG. 6A . Light entering the layer  82  is refracted by one side  84  of each facet  85  as it enters, and then is totally internally reflected by second side  86  of each of the facets  85 . In one form of the invention the redirecting layer  82  can be a “Transparent Right-Angle Film” (hereinafter, TRAF), which is a trademark of 3M Corp., and this product is commercially available from 3M Corp. This TRAF operates by refraction and total internal reflection to turn incident light through approximately a ninety degree angle, as would be desired in a typical LCD backlighting application. The acceptance angle of the prior art TRAF is about twenty-one degrees, which is large enough to redirect a large fraction of light  75  which enters the low-index layer  81 . In a more preferred form of the invention, the facet angles are chosen to redirect more of the light  75  which enters the low-index layer  81  by the described mechanism of refraction plus total internal reflection. Either one or both of the facet surfaces  84  and  86  can be shaped to control the output angular distribution. For example, the use of curved facets smoothly broadens the distribution, as well as providing a light diffusing effect which can improve uniformity. 
   In another preferred embodiment, the facet angle surfaces of the redirecting layer  82  can be varied progressively to compensate for the variation in viewing angle with position, when viewed from typical viewing distances. The details of such a compensation effect were described earlier in reference to the design of the reflecting facet layer in the embodiment shown in  FIG. 2M . Similar principles can be applied to the design of any faceted redirecting layer, including refracting layers and refracting/internally-reflecting layers. Examples of embodiments which can, for example, make use of such progressively varied faceted layers are shown in  FIGS. 12E  (layer  140 ),  12 G (layer  152 ),  12 H (layer  166 ),  12 K (layer  186 ),  12 N (layer  210 ),  12 O (layer  228 ), and  12 P (layer  246 ). 
   In another form of invention the layers  66  and  81  can have similar but slightly different indices n 2  and n 2 ′, respectively. The operating principles of the device  10  will be substantially similar as long as the critical angles associated with interfaces between the first layer  61  and the two layers  66  and  81  do not differ by more than the first layer convergence angle:
 
|arcsin( n   2′   /n   1 )−arcsin( n   2   /n   1 )|&lt;φ  (7)
 
   Therefore, in this case approximately equal fractions of the light will enter layers  66  and  81 , for further processing by the redirecting layers  70  and  82 , respectively. 
   All forms of the invention can further include an output diffuser layer  40 , shown in phantom in  FIG. 2C  or transmissive or translucent diffuser layer  83  shown in  FIG. 6A . In general this diffuser layer  40  can be a surface diffuser, a volume diffuser, or at least one array of micro lenses having at least a section of a cylinder (known as a “lenticular array”). These layers  40  and  83  can increase light uniformity or broaden the angular distribution into ambient. Lenticular arrays are advantageous because they have low back-scattering in comparison to surface or volume diffusers, and because they have sharper output angle cut-offs when illuminated by collimated light. Lenticular arrays also preferentially diffuse only those features which would otherwise run in the general direction of the axis of each cylindrical micro lens. 
   In one preferred embodiment shown in  FIG. 10 , the light redirecting layer  10  makes use of flat facets  111  such that the output light is highly collimated. The desired output angular distribution is further controlled by including a lenticular diffuser  112  having an appropriate focal ratio, with its cylindrical micro lenses running approximately parallel to the y-axis. The lenticular diffuser  112  also diffuses non-uniformities which would otherwise appear to be running in the general direction of the y-axis. In this embodiment a second lenticular diffuser  113  can be included to diffuse non-uniformities which would otherwise appear running in the general direction of the z-axis. This second lenticular diffuser&#39;s micro lenses run approximately parallel to the z-axis (see  FIGS. 12H and 12N ). Note that the order of positioning of the diffusers  112  and  113  can be interchanged without loss of optical advantage. Similarly, the lenticular diffuser  112  and  113  can be inverted and can have concave contours rather than convex contours shown in  FIG. 10 . While such changes can affect the details of the performance, the diffuser layers  112  and  113  can still provide the general advantages described. 
   In another preferred embodiment shown in  FIG. 11 , the functions of the flat-faceted light redirecting layer  110  and the parallel lenticular diffuser  112  in  FIG. 10  can both be performed by a light redirecting layer  114  having curved facets (see also, for example,  FIGS. 2H ,  2 M and  3 A illustrating curved facets). These curved-facet layers redirect the light, control the angular output by having an appropriate facet curvature, and act as a diffuser for non-uniformities running in the general direction of the y-axis. By combining these functions in a single-layer the number of components is reduced, which improves thickness, cost, and manufacturability. In this embodiment, a single lenticular diffuser  115  can be included to diffuse the remaining non-uniformities which would otherwise appear running in the general direction of the z-axis. This type of lenticular diffuser micro lens runs approximately parallel to the z-axis. Note that the lenticular diffuser  115  can be inverted and can have concave contours rather than the convex contours shown in  FIG. 10 . Again, such changes can affect performance details, but the layers in  114  and  115  perform as intended. 
   In all embodiments using multiple micro-structured layers, the facet or lenslet spacings of these layers described hereinbefore can be chosen to have non-rational ratios, in order to avoid undesirable Moiré interaction between layers or with a liquid crystal display. 
   Similar lenticular diffusers can be used with non-wedge geometries having wedge shaped cross-actions, with similar advantages if the diffuser cross-sections are approximately as shown in  FIGS. 10 and 11 . One example is the tapered disk illustrated in  FIG. 5 . In this case the lenticular diffuser analogous to layer  112  in  FIG. 10  would have micro lenses whose axes run in concentric circles about the disk&#39;s axis of rotations. A diffuser analogous to the layer  113  in  FIG. 10 and 115  in  FIG. 11  would have micro lenses whose axes emanate radially from the disk&#39;s central axis. 
   Light Sources and Couplers 
   In a more preferred form of the invention shown in  FIGS. 2A  and B, a faceted layer  30  has been included for optically redirecting the light. The facets  34  can be integral to the layer  30  or a separate facet layer. Details of operation of such a faceted layer have been discussed hereinbefore. As shown further in  FIG. 6A  an input faceted layer  74  can also be disposed between a light source  76  and the first layer  61 . The faceted layer  74  can be a prismatic facet array which provides a collimating effect for input light  78  which provides brighter or more uniform output light  80  into ambient. 
   Linear prisms parallel to the y-axis can improve uniformity by adjusting the input angular distribution to match more closely the input numerical aperture. Linear prisms parallel to the x-axis can limit the output transverse angular distribution, and also improve output brightness when used with a fluorescent lamp light source. In other forms of the invention, diffusion of input light is desirable wherein a diffuser  79  is used to diffuse the light distribution to spread out the light to improve light uniformity. The diffuser  79  is preferably a lenticular array, with cylindrical lenslets parallel to the y-axis. The diffuser  79  can also be a standard surface or volume diffuser, and can be a discrete film or coupled integrally to the wedge layer  61 . Multiple prismatic or diffuser films can be used in combination. Such a film form of the diffuser  79  and the faceted film  74  can be interchanged in position to vary their effects. 
   In another preferred form of the invention, a portion of a dielectric total internally reflecting CPC portion  100  (compound parabolic concentrator) can be interposed between the light source  76  and the first layer  61  (see  FIGS. 2L ,  12 O and  12 P). The CPC portion  100  adjusts the input light to match more closely the input numerical aperture. The CPC portion  100  is preferably formed integrally with the first layer  61 . 
   Reflector elements  92  and  94  shown in  FIGS. 7 and 8 , respectively, can be shaped and positioned to maximize the throughput of light from the light source  76  to the light-pipe aperture. This is equivalent to minimizing the reflection of light back to the light source  76 , which partially absorbs any returned light. The light source  76  is typically cylindrical and is surrounded by a transparent glass envelope  93 , each having circular cross-sections as shown in  FIGS. 7 and 8 . Typical examples of such light sources include fluorescent tubes and long-filament incandescent lamps. The outer diameter of the light source  76  can be less than or equal to the inner diameter of the glass envelope  93 .  FIG. 7  shows a prior art U-shaped reflector  92  formed by wrapping a specular reflectorized polymer film around the light source  76  and making contact with the wedge layer  12  at each end of the film. The reflector element  92  typically is formed into a shape which is approximately an arc of a circle on the side of the light source  76  opposite the wedge layer  12 , with approximately straight sections connecting each end-point of the arc with the wedge layer  12 . This manner of coupling the reflector element  92  to the wedge layer  12  is most easily accomplished when the reflector element cross-section lacks sharp corners. In general the light source  76  is not permitted to touch either the wedge layer  12  or the reflectorized film, in order to minimize thermal and electrical coupling which can reduce lamp efficiency. 
   In one form of the present invention shown in  FIG. 8 , the reflector element  94  is advantageously designed and the light source  76  is advantageously placed to minimize the fraction of light returned to the light source  76 , and thereby increases efficiency. In one preferred embodiment, at least a section of the reflector element  94  is shaped such that a line drawn normal to the surface of the reflector element  94  at each point is tangent to the circular cross-section of the light source  76 . The resulting reflector shape is known as an involute of the light source  76 . 
   While an involute provides maximum efficiency, other shapes can generally be more easily manufactured. Polymer films can be readily bent into smooth curves which include almost semicircular arcs, as described above. It can be shown that when the cross-section of the light source  76  and semicircular section of the reflector element  92  are concentric as shown in  FIG. 7 , then the semicircular section of the reflector element  92  will return all incident rays to the light source  76 , leading to poor efficiency. Such inefficiency is a general property of self-absorbing circular sources and concentric semicircular reflectors. This general property can be derived from simple ray-tracing or the principal of skew invariance. Even if the reflector element  92  is not perfectly circular, each portion of the reflector element  92  will tend to return light to the light source  76  if the cross-section of the light source  76  is centered near the center of curvature of that reflector section. 
   In another preferred embodiment, the cross-section of the reflector element  94  in  FIG. 8  includes one or more almost semicircular arcs, and efficiency is increased by displacing the center of the light source  76  away from the center of curvature of the reflector element  94 . Ray-tracing and experiments have shown that such preferred embodiments can be determined using the following design rules: 
   1. The cross-section of the reflector element  94  has a maximum extent in the x-dimension equal to the maximum thickness of the wedge layer  12  (or light pipe); 
   2. The cross-section of the reflector element  94  has no optically sharp corners; 
   3. The radius of curvature of the reflector element  94  is as large as possible; and 
   4. The light source  76  is as far as possible from the wedge layer  12 , but is far enough from the reflector element  94  to avoid contact with worst-case manufacturing variations. 
     FIG. 8  shows an example of a coupler which satisfies these above described design rules for the light source  76  with inner diameter=2 mm, outer diameter=3 mm, thickness of the wedge layer  12  (or light pipe)=5 mm, and manufacturing tolerances which permit a 0.25 mm spacing between the reflector element  94  and the outer diameter of the glass envelope  93 . In this example of a preferred embodiment the radius of curvature of the reflector element  94  is 2.5 mm, and the center of the light source  76  is displaced by 0.75 mm away from the aperture of the wedge layer  12 . A coupler constructed according to this design was found to be 10-15% brighter than the comparable concentric coupler shown in  FIG. 7 . 
   The involute and the U-shaped reflector elements  92  and  94  previously described are designed to output light to the aperture of the wedge layer  12  with angles approaching ±90 degrees relative to the aperture surface normal. In another preferred embodiment, the reflector element  94  is shaped to output light with an angular distribution which is closer to the N.A. of the device  10 . As shown in  FIGS. 6B and 6C , such shapes as the reflector element  94  can include other geometries, such as, a compound parabolic source reflector  86  and a nonimaging illumination source reflector  88 . An example of the source reflector  88  is described in copending Ser. No. 07/732,982 assigned to the assignee of record of the instant application, and this application is incorporated by reference herein. 
   In another embodiment of the invention shown in  FIGS. 6D ,  12 L,  12 N, and  12 O, the wedge layer  90  has a non-monotonic varying wedge cross sectional thickness over various selected portions of the wedge shaped cross section. It has been determined that one can exert control over the light distribution being output by control of this cross section. Further, it has been determined that optical boundary effects, as well as intrinsic light source effects, can combine to give an output light distribution with unwanted anomalies. One can therefore also compensate for these anomalies, by providing a wedge cross section with nonlinear changes in the actual dimensions of the wedge layer  90 , for example, near the thicker end which typically receives the input light. By control of these dimensions one can thus have another degree of freedom to exert control over the light distribution, as well as provide virtually any design to compensate for any boundary effect or light source artifact. Furthermore, one can vary the index of refraction within the wedge layer  90  in the manner described hereinbefore to modify the distribution of light and also compensate for light input anomalies to provide a desired light distribution output. 
   Manufacture of Luminaire Devices 
   In one form of the invention, manufacture of the device  10  can be accomplished by careful use of selected adhesives and lamination procedures. For example, the wedge layer  12  having index n 1  can be adhesively bonded to the first layer  28  having index n 2 . An adhesive layer  60  (see  FIG. 3B ) can be applied in liquid form to the top surface of the first layer  28 , and the layer  28  is adhesively coupled to the bottom surface  16  of the wedge layer  12 . In general, the order of coupling the various layers can be in any given order. 
   In applying the layer  12  to the layer  28  and other such layers, the process of manufacture preferably accommodates the formation of internal layer interfaces which are substantially smooth interfacial surfaces. If not properly prepared such internal layers can detrimentally affect performance because each interface between layers of different indices can act as a reflecting surface with its own characteristic critical angle. If the interfacial surfaces are substantially smooth, then the detrimental effect of uneven surfaces is negligible. Therefore in effectuating the lamination of the various layers of the device  10 , the methodology should utilize adhesives and/or joining techniques which provide the above described smooth interfacial layers. Examples of lamination processes include, without limitation, joining without additional adhesive layers, coatings applied to one layer and then joined to a second layer with an adhesive and applying a film layer with two adhesive layers (one on each layer surface to be joined to the other). 
   In a preferred embodiment lamination of layers is done without any additional internal layer whose potential interfacial roughness will distort the light distribution. An example of such a geometry for the device  10  can be a liquid layer between the wedge layer  12  and the second layer  30 . This method works best if the first layer  29  (such as the liquid layer) acts as an adhesive. One can choose to cure the adhesive either before, partially or completely, or after joining together the various layers of the device  10 . The optical interface is thus defined by the bottom surface of the wedge layer  12  and the top surface of the second layer  30 . 
   In another embodiment wherein a coating is used with an adhesive layer, the first layer  28  can be the coating applied to the second layer  30 . Then, the coated film can be laminated to the wedge layer  12  in a second step by applying an adhesive between the coated film and the wedge layer  12 . It is preferable to apply the low index coating to the second layer  30  rather than directly to the wedge layer  12  since the second layer  30  is typically supplied in the form of continuous film rolls. In practice it is more cost effective to coat such continuous rolls than to coat discrete pieces. With this methodology it is more convenient to control thickness of the applied low index layer. 
   In another embodiment, the second layer  30  is manufactured in such a way that it adheres to the first layer  28  directly without use of additional adhesives. For example, the second layer  30  can be manufactured by applying a layer of polymer material to the first layer  28 , and then casting this material to have the desired second layer geometry. In another example, the first layer  28  can serve as a carrier film during the embossing of the second layer  30 . By use of appropriate temperatures during the embossing process, the second layer  30  can be heat-fused to the first layer  28 . Such heat-fusing can be accomplished using a conventional FEP first-layer film by embossing at almost five hundred degrees F or higher. 
   In a further embodiment using a film and two adhesives, the first layer  28  can be an extruded or cast film which is then laminated to the wedge layer  12 , or between the wedge layer  12  and the second layer  30  using adhesive between the two types of interfaces. In order to minimize the detrimental light scattering described hereinbefore, the adhesive layer should be flat and smooth. The film can be obtained as a low index material in commercially available, inexpensive forms. Such additional adhesive layers can increase the strength by virtue of the multi-layer construction having adhesive between each of the layers. 
   In the use of adhesive generally, the performance of the device  10  is optimized when the index of the adhesive between the wedge layer and the first layer is as close as possible to the index of the first layer  28 . When the critical angle at the wedge/adhesive interface is as low as possible, then the light undergoes a minimal number of reflections off the lower quality film interface before exiting the device  10 . In addition, the index change at the surface of the first layer film is minimized which decreases the effects of film surface roughness. 
   Manufacture of faceted surfaces can be accomplished by micro-machining a mold using a master tool. Machining can be carried out by ruling with an appropriately shaped diamond tool. The master tool can be replicated by known techniques, such as electroforming or casting. Each replication step inverts the shape of the desired surface. The resulting mold or replicates thereof can then be used to emboss the desired shape in the second layer  30 . A directly ruled surface can also be used, but the above described embossing method is preferred. Known “milling” processes can include chemical etching techniques, ion beam etching and laser beam milling. 
   In yet another method of mechanical manufacture, the faceted surface  34  (see  FIGS. 2B and 2M , for example) is manufactured by a welding process, such as embossing or casting, using a hard tool which has on one surface the inverse of the profile of the desired faceted surface  34 . Therefore, the manufacturing problem reduces to the matter of machining an appropriate tool. Usually the machined tool is used as a template to form the tools actually used in the casting or embossing process. Tools are typically replicated by electroforming. Since electroforming inverts the surface profile, and electroforms may be made from other electroforms, any number of such inversions can be accomplished and the directly machined “master” can have the shape of the faceted surfaces  3 A or its inverse. 
   The tooling for the faceted surface  34  can be manufactured by single-point diamond machining, wherein the distance between cutting tool and the work is varied to trace out the desired profile. The diamond cutting tool must be very sharp, but in principle nearly arbitrary profiles can be created. A given design can also require specific adaptations to accommodate the non-zero radius of the cutting tool. If curved facet surfaces are required, then circular arcs are preferred to facilitate fabrication. The cutting tool is moved through the cutting substrate and cuts a groove having the approximate shape of the tool. It is desirable to machine the entire piece using a single diamond tool. When this method is used for making a “focusing” type of the faceted surface  34 , the variable groove profile therefore should be designed such that the various groove profiles can be machined by the same tool. The required shape variations can still be accomplished by varying the angle of the tool, as well as the groove spacing and depth. 
   Design of the faceted surface  34  preferably satisfies a few general constraints: 
   1. Approximately linear variation in the center of the illumination angular distribution as a function of position. A variation of 11 degrees (±5.5°) from top to bottom of typical computer screens is effective; 
   2. The width of the variable angular distribution of light output should be approximately proportional to the local illuminance in order to achieve approximately uniform brightness to an observer. Examples given below show the spatial distribution is approximately uniform, so the angular cones have approximately uniform width; and 
   3. Spacing between grooves of the facets  38  should be large enough or irregular enough to avoid diffraction effects, but also be chosen to avoid Moiré patterns when used with an LCD panel. In practice these requirements limit the allowed spatial variations. 
   In the manufacture of the device  10 , for example, the viewing angle depends on the tilt and curvature of each of the facets  38 . Focusing is accomplished by rotating the facet structure as a function of position. Using the example of a 150 mm screen viewed from 500 mm away, the illumination cone can be varied by 17 degrees (i.e., ±8.5 degrees) from top to bottom. For typical materials, acrylic and FEP, this requires the facet structure to rotate by approximately 5.7 degrees from top to bottom of the screen  89  (see  FIG. 9B ). 
   Design constraints can result when limitations (1)-(3) are combined with the need to machine variable curved grooves with a single tool. For example, maintaining a constant angular width (Constraint #1) at a constant cutting depth requires a compensating variation in groove spacing or groove depth. Specifically, a linear change in groove spacing can reduce the brightness variation to a negligible level when the form tool which cuts the groove is shaped so that portions of each curved reflector facets (see  FIG. 2M ) are shadowed by the top edge of the adjacent facets. This spacing variation can be small enough to satisfy Constraint #3. 
   Further methods of manufacture can include vapor deposition, sputtering or ion beam deposition of the first layer  28  since this layer can be quite thin as described hereinbefore. Likewise, the second layer  30  can be controllably applied to form the faceted layer  30  shown in  FIG. 2B  (such as by masking and layer deposition). 
   Wedge Light Pipe as a Simple Collimator Device 
   In the most general embodiment the wedge layer  12  can function in the context of the combination as a simple collimating optical element. The substantially transparent wedge layer  12  has an optical index of refraction n 1  and the top surface  14  and the bottom surface  16  converge to establish at least one angle of inclination φ(see  FIG. 15 ). The wedge layer  12  also includes the back surface  20  spanning the top surface  14  and the bottom surface  16 . Adjacent to the wedge layer  12  is the transparent first layer  28  having index of refraction n 2  including an air gap. Adjacent to the first layer  28  is a specular reflective layer, such as the faceted surface  34  of the second layer  30 . 
   Substantially uncollimated light is introduced through the back surface  20  by the source  22 . The light propagates within the wedge layer  12 , with each ray decreasing its incident angle with respect to the top and bottom surfaces  14  and  16  until the incident angle is less than the critical angle θ c . Once the angle is less than θ c , the ray emerges into ambient. Rays which emerge through the bottom surface  16  are reflected back into the wedge layer  12  and then output into ambient. By virtue of the angle-filtering effect previously described, the output light is collimated within a cone of angular width approximately:
 
Δθ≅2φ 1/2 ( n   2 −1) 1/4   (8)
 
An area  99  to be illuminated lies beyond the end of the wedge layer  12  and substantially within the above-defined cone of width Δθ.
 
   In another preferred embodiment a light-redirecting means can be positioned beyond the end of the wedge layer  12  and substantially within the above-defined cone of width Δθ. The light-redirecting means can be a lens, planar specular reflector, or curved reflector. The light-redirecting means reflects or refracts the light to the area to be illuminated. Further details and uses of such redirecting means, such as lenticular diffusers, will be described hereinafter. 
   In the embodiments of  FIG. 6  having two air gaps or transparent dielectric layers, the light redirecting layers are independent, and thus one can construct devices having layers of different types. For example, the use of two transmissive redirecting layers is preferred when light is to be emitted from both sides of the device  10  or whenever maximum collimation is desired. Examples of the redirecting layer  82  in general for all inventions for two redirecting layers can include the examples in  FIG. 12  where the letter in parenthesis corresponds to the appropriate figure of  FIG. 12 : (a) diffraction gratings  120  or a hologram  122  in  FIG. 12A , (b) two refracting facet layers  124  with diffusers  126  in  FIG. 12B , (c) two faceted layers  128  with facets  130  designed to refract and internally reflect light output from the wedge layer  12 ; such facets  130  are capable of tuning the light output through a larger angle than is possible by refraction alone; (d) two refracting single facet layers  132  (prisms); (e) a top surface redirecting layer for the wedge layer  12  having a refracting single facet layer  134  with a curved output surface  136  for focusing. A bottom surface  138  includes a redirecting layer for refracting and internally reflecting light using a faceted layer  140 ; facet angles are varied with position to focus output light  142  at F; (f) a top surface redirecting layer  144  comprised of a refracting faceted layer  146  and a bottom redirecting layer comprised of a refracting/internally reflecting layer  148  with narrow angle output for the light, and a diffuser layer  150  can be added to smoothly broaden the light output angular distribution; (g) a top surface redirecting layer of refracting/internally reflecting faceted layer  152  with refracting surfaces  154  convexly curved to broaden the output angular distribution; the facet angles can be varied with position and thereby selectively direct the light output angular cones to create a preferred viewing region at a finite distance; this arrangement can further include a transverse lenticular diffuser  156  to diffuse nonuniformities not removed by the curved facet layer  152 ; the bottom redirecting layer comprises a refracting/internally reflecting faceted layer  158  with a reflecting surface  160  being concavely curved to broaden the light output angular distribution in a controlled manner; (h) a top redirecting layer, including a refracting faceted layer  162  with curved facets  164  to broaden the output angular distribution in a controlled manner and to improve uniformity; a bottom redirecting layer, including a refracting/internally-reflecting faceted layer  166  with flat facets  168  for narrow-angle output, with facet geometry varied with position to focus output light at a finite distance; a parallel lenticular diffuser  170  can be used to smoothly broaden the output angular distribution in a controlled manner and to improve uniformity; the transparent image shown in phantom can be printed on or adhesively based to a lenticular diffuser; a transverse lenticular diffuser  172  is used to diffuse non-uniformities not removed by the parallel lenticular diffuser  170 . The combination of a focused flat-faceted layer  166  and the diffuser  170  cooperate to create a preferred viewing zone at a finite distance, similar to using focused curved facets. Also shown is an LCD component  173  (in phantom) usable with this and any other form of the device  10  for illumination purposes. 
   In other architectures, one transmissive and one reflective redirecting layer can be combined. These are combinations of reflective redirecting layers with the various types of transmissive redirecting layers discussed above. Reflective redirecting layers can be specular, partially diffuse, diffuse, faceted or any combination thereof. These architectures are preferred when light emission is desired from one side only, or in some cases when minimum cost is paramount. Examples of such architectures are in  FIG. 12 : (i) a bottom surface specular reflector  174  combined with a top layer transmission diffraction grating or transmission hologram  176 ; (j) a bottom surface specular reflector  178  combined with a top surface refracting faceted layer  180 , with a diffuser  182  (shown in phantom in  FIG. 12J  and an intervening image-forming layer  171 ; (k) a bottom layer specular reflector  184  with a top layer refracting/internally-reflecting faceted layer  186 , with facet geometry being varied with position to focus output light at a finite distance; a diffuser  188  is shown in phantom; (l) a bottom layer specular reflector  190  with a top layer refracting/internally-reflecting faceted layer  192 , and curved facets  194  are used to smoothly broaden the angular output of light in a controlled manner and to improve uniformity. The thickness of the wedge layer  12  and of both top and bottom surface low-index layers  196  (e.g., air gaps) are varied to influence the light output spatial distribution; (m) a bottom reflector  198  is partially specular, partially diffuse to improve uniformity;  FIG. 12M  shows the initial reflector section made controllably diffuse by addition of an integral lenticular diffuser  200 ; the diffuser  200  is designed to selectively reduce nonuniformities which would otherwise appear in the output near the thicker end, and running in the general direction of the y-axis; also included is a top redirecting layer  202  which is refracting/internally-reflecting and has a reflecting surface which is curved; and (n) a bottom reflector layer  204  which is partially specular, partially diffuse to improve uniformity;  FIG. 12N  shows the initial reflector section  206  which is slightly roughened to reduce specularity, and thereby selectively reduces nonuniformities which would otherwise appear in the output near thicker end  208 ; a top redirecting layer  210  is used which is refracting/internally-reflecting with a flat-faceted layer  212 , and the facet geometry is varied to redirect light from each facet to a common focus at finite distance; a transverse lenticular diffuser  213  is shown in phantom; a parallel lenticular diffuser  214  is used to smoothly broaden the output angular distribution in a controlled manner, converting the focal zone of the flat-faceted layer  212  to a wider preferred viewing zone; the lenticular diffuser  213  also improves uniformity; an LCD display  216  or other transparent image is show in phantom; (o) in a preferred embodiment an eccentric coupler  218  uses a uniformity-enhancing lenticular diffuser  220  shown in phantom in  FIG. 12O . A converging tapered section  222  or CPC (integral to the wedge layer) transforms the output angular distribution to match more closely the input N.A. of the wedge layer  12 . The wedge layer  12  thickness is smoothly varied to influence output spatial distribution and improve uniformity; a bottom redirecting layer  224  is a specular or partially diffuse reflector; a top redirecting layer  226  is a refracting/internally-reflecting faceted layer  228  with reflecting surfaces  230  convexly curved to smoothly broaden output angle in a controllable manner; facet geometry is varied with position to selectively direct the angular cone of light from each face to create a preferred viewing zone  232  at a finite distance; a transverse lenticular diffuser  234  is shown in phantom; an LCD display  236  or other transparent image is also shown in phantom; the more converging N.A.-matching section is advantageous in combination with the faceted redirecting layers, because the redirecting and low-index layers do not need to overly the more converging section; therefore, the input aperture (and thus efficiency) of the device  10  is increased with minimum increase in total thickness of the device; (p) another preferred embodiment for LCD backlighting uses an eccentric coupler with a uniformity-enhancing diffuser shown in phantom in  FIG. 12P ; a converging half-tapered section  240  or half-CPC (integral to the wedge layer  12 ) transforms a coupler output angular distribution to match more closely the input N.A. of the wedge layer  12 . A diffuser  239  (in phantom) can also be interposed between light source  217  and the wedge layer  12 . The sufficiently truncated half-CPC  240  is just a simple tapered section. A bottom reflector  242  which is partially specular; partially diffuse is used to improve uniformity;  FIG. 12P  further shows an initial reflector section  244  which is slightly roughened to reduce specularity, or alternatively shaped into a series of parallel reflective grooves, which thereby selectively reduces nonuniformities which would otherwise appear in the output near the thicker end; a top redirecting layer  246  is a refracting/internally-reflecting faceted layer  248 , with refracting surfaces  250  convexly curved to smoothly broaden output angle in a controllable manner; facet geometry is varied with position to selectively direct angular cones of light from each facet to create a preferred viewing zone at a finite distance; a transverse lenticular diffuser  252  is shown in phantom. Also included is an LCD display  254  or other transparent image shown in phantom. 
   The more converging N.A.-matching section (such as half tapered section  240 ) is advantageous in combination with the faceted redirecting layers, because the redirecting and low-index layers do not need to overly the more converging section; therefore, the light-accepting aperture of the device  10  is increased without increasing the total thickness. The advantage is also conferred by the fully-tapered section  222  shown in  FIG. 12O ; but in comparison the half-tapered section  240  in  FIG. 12P  provides greater thickness reduction on one side, at the expense of being longer in the direction of taper for equivalent N.A.-matching effect. It can be desirable to concentrate the thickness reduction to one side as shown, because the top surface low-index layer can be made thicker to improve uniformity. This configuration can be more easily manufactured because the bottom reflector layer can be integral to the coupler reflector cavity, without need to bend a reflective film around a corner; (q) a bottom specular or diffusely reflecting layer  256  can be combined with single-facet refracting top layer  258  in yet another embodiment (see  FIG. 12Q ); and (r) in cases for interior lighting usage, a bimodal “bat-wing” angular light distribution  260  is preferred; in  FIG. 12R  is shown a top refracting layer  262  with facets  264  and has a curved front surface  266  to smoothly broaden angular output and improve uniformity, with output light directed primarily into a forward quadrant; a bottom reflecting layer  268  reflects light primarily through a back surface of a top redirecting layer, with output directed substantially into a backwards quadrant. 
   As understood in the art the various elements shown in the figures can be utilized with combinations of elements in tapered luminaire devices. Examples of two such combination geometries are shown in  FIGS. 13 and 14 , each figure also including features specific to the geometry shown. As illustrated in  FIG. 13 , two wedges  276  can be combined and formed integrally. This combination can provide higher brightness than a single wedge having the same extent because it permits two light sources to supply light to the same total area. While brightness is increased for this device, efficiency is similar because two sources also require twice as much power as one source. A redirecting film  272  with facets  274  can be a single, symmetric design which accepts light from both directions as shown. Alternatively, the redirecting film  272  can have a different design for each wing of the butterfly. 
   In  FIG. 14  is shown a three dimensional rendition of a tapered disk  270 , such as shown in  FIG. 5 , and is sectioned to show the appearance of the various layers. A faceted redirecting layer  280  comprises concentric circular facets  282  overlying a tapered light-pipe portion  284 . Directly over a light source  288 , overlying the gap at the axis of the light-pipe portion  284 , the redirecting layer  280  takes the form of a lens (a Fresnel lens  280  is shown, for example). Directly below the light source  288  is a reflector  290  positioned to prevent light from escaping and to redirect the light into the light-pipe portion  284  or through the lens. At least one opening is provided in the reflector to permit passage of elements, such as wires or light-pipes. 
   Use of Imaging or Colored Layers 
   All embodiments of the invention can incorporate one or more layers which have variable transmission to form an image, or which impart color to at least a portion of the angular output. The image-forming layer can include a static image, such as a conventional transparent display, or a selectively controlled image, such as a liquid crystal display. The image-forming or color-imparting layer can overlay one of the redirecting layers, or alternatively it can comprise an intermediate layer between one of the low-index layers and the associated redirecting layer, or an internal component of a redirecting layer. For example, overlying image-forming layers  129  are shown in phantom in  FIGS. 12C and 12G . Examples of an internal image-forming layer  171  are shown in  FIGS. 12H and 12J . 
   In one preferred embodiment, the image-forming layer (such as  129  and  170 ) is a polymer-dispersed liquid crystal (PDLC) layer. By proper arrangement of the layers, the image or color may be projected from the device within selected portions of the output angular distribution. The image or selected color can be substantially absent in the remaining portions of the output angular distribution. 
   Bi-Modal Reflective Wedge for LCD Panel Illumination 
   In some applications it is desired to illuminate a single LCD panel selectively with either ambient light or by active back-lighting. In these applications ambient illumination is selected in well-lit environments in order to minimize power consumption by the display. When available environmental illumination is too low to provide adequate display quality, then active backlighting is selected. This selective bi-modal operating mode requires a back-illumination unit which can efficiently backlight the LCD in active mode, and efficiently reflect ambient light in the alternative ambient mode. 
   The most widespread prior art bi-modal liquid crystal display is the “transflective display”  101 , such as is shown in  FIG. 16B . This approach uses a conventional backlight  102  and a transmissive LCD panel  103 , with an intervening layer  104  which is partially reflective and partially transmissive. In order to achieve adequate ambient mode performance, it is typically necessary for the intervening layer  104  to be 80-90% reflective. The resulting low transmissivity makes the transflective display  101  inefficient in the active mode of operation. 
   Another embodiment of the invention is shown in  FIG. 17 . This embodiment outperforms prior art transflective displays in the active mode, and demonstrates comparable performance in the ambient mode. In this embodiment the wedge layer  12  (index=n 1 ) having the bottom surface  16  is coupled to a transparent layer  28  of index n 2 &lt;n 1 , which can be an air gap. The n 2  layer is coupled to a partially diffuse reflector layer  105 . This reflector layer  105  is, for example, preferably similar to the reflectors used in conventional LCD panels used in ambient mode only, as shown in  FIG. 16A . Overlaying the wedge layer top surface  14  is a faceted redirecting layer  106 , such as a lenticular diffuser with micro lenses approximately parallel to the y-axis. A liquid crystal display panel  107  overlays the faceted redirecting layer  106 . The back surface  20  of the wedge layer  12  is coupled to the light source  22 . 
   The lenticular redirecting layer  106  and the wedge-layer  12  are substantially transparent to the incident and reflective light, so that in ambient mode the device  10  operates in a manner similar to conventional ambient-mode-only displays. When an active mode is selected, the light source  22  is activated, and the multiple layers act to spread the light substantially uniformly over the device  10  by virtue of the relationship between the indices of refraction and convergence angles of the layers, as described before. The resulting uniform illumination is emitted through the top surface  14  of the wedge layer  12 . In a preferred embodiment, the reflector layer  105  is nearly specular in order to maximize ambient-mode performance. In this preferred embodiment the light emitted from the top surface is emitted largely at grazing angles, unsuitable for transmission by the LCD display panel  107 . The redirecting layer  106  redirects a fraction of this light by a combination of refraction and total internal reflection, as described hereinbefore. The redirecting layer  106  is preferably designed such that at least 10-20% of the light is redirected into angles less than 30 degrees from the LCD normal, because typically the LCD transmission is highest in this angular range. It is sufficient to direct only a fraction of the back-illumination into suitable angles, because the prior art transflective display is quite inefficient in the active mode of operation. 
   Processing Polarized Light 
   In another aspect of the invention, the light being processed by the optical device  10  has an inherent polarization (such as, linear, circular and elliptical) that can be used to advantage in improving the illumination from a liquid crystal display (“LCD”) system or other output which depends on using polarized light. In a system which employs an LCD, it is necessary to remove one type of polarized light  308  and pass to the LCD layer only the other type of polarized light. For example in  FIG. 30  a conventional polarization layer  312  preferentially absorbs one polarization of light amounting to about one-half the input light from light source  306 , with the preferred polarization light being transmitted to LCD layer  316 . The polarized light of the proper polarization is processed by the liquid crystals and a second polarizer  314  in the desired manner to provide the displayed feature of interest. In such a conventional system about half the light from the light source is “unwanted” and thus is lost for purposes of providing an LCD output of interest. Consequently, if a means could be found to utilize both types of polarized light (not removing light of an unwanted polarization), a substantial gain in efficiency and brightness can result for the liquid crystal display. The subject invention is directed in part to that end, and the following embodiments are preferred structures and methods for accomplishing that goal. 
   In the most general explanation of a polarization filter, referring to  FIG. 30B , the function of a polarization filter layer  307  is to take the input light  308  consisting of two polarization states of type  1  and  2  and create transmitted light  309  consisting of polarization states  3  and  4  and reflected light  311  consisting of polarization states  5  and  6 . This can be related to our specific references hereinafter to a “first” and “second” state as “states”  1 , 3  and  5  as the “first polarization light  218 ” and  2 , 4  and  6  as the “second polarization” light  220 . Thus, we assume that the form of states  3  and  5  are chosen so that they alone specify the light that is transmitted and reflected due to the light portion incident in polarization state  1 , and let states  4  and  6  be associated with polarization state  2 . However, the form of the polarization states need not be related in any more specific way. For some range of incident angles over some spectral wavelength range and for some specific selection of input polarization states, the polarization filter layer  307  processes the input light  308  and produces output light  309  with a specific total power relationship. If we define the powers (P i ) in each of the polarization states (i, where i=1, 2, 3, 4, 5, 6), the condition is: 
   
     
       
         
           
             
               P 
               3 
             
             
               P 
               1 
             
           
           &gt; 
           
             
               P 
               4 
             
             
               P 
               2 
             
           
         
       
     
   
   By definition, any layer which exhibits the above characteristics over a suitable angular and spectral range is a form of the polarization filter layer  307 . Generally, the polarization states considered can be of arbitrary type such as linear, circular, or elliptical. In later sections we will quantify the performance of the polarization filter layer  307  by a degree of polarization (P T ) defined as: 
             P   T     =         T   31     -     T   42           T   31     +     T   42                   where                 T   31     =       P   3       P   1         ,           ⁢       T   42     =       P   4       P   2               
For lossless layers, the transmittance is related to the reflectance, R, by
   T   31 =1− R   51   ,T   42 =1− R   62    where   R   51   =P   5   /P   1  and  R   62   =P   6   /P   2    
   There are a variety of implementations of a layer medium which has the properties described above for the polarization filter layer  307 . These include, but are not restricted to, implementations containing one or more of the following types of layers: (1) thin-film layers produced by coating, extrusion, or some other process which are either non-birefringent or birefringent and are designed to operate as optical interference coatings; (2) “thick” film layers which are more than a single quarter wavelength optically thick somewhere in the spectral band of interest and may be produced by stacking, coating, extrusion, lamination, or some other process and are designed to operate as a Brewster Stack even when the angles and indexes do not exactly match the Brewster angle conditions; (3) a combination of the thin-film and thick film approaches; (4) correlated, partially correlated, or uncorrelated surface roughness or profile which results in polarization dependent scattering and produced by any method including etching, embossing, micro-machining, or other method; (5) and layers based on dichroic material. In general, an aggregate layer formed by one or more the above layer types is a suitable form of the polarization filter layer  307  layer if it satisfies the general functional specifications described above for polarization filter layers. 
   The implementations of the polarization filter layer  307  can consist of either thin-film or thick-film birefringent or non-birefringent layers. Particular examples and discussion of birefringent layers will be provided in a labeled subsection presented hereinafter. 
   One example embodiment of a thick film form of the polarization filter layer  307  is based on a specific design center wavelength ( 6   o ) and a specific design operating angle 
   (3 inc ) as shown in  FIG. 30C  and based on isotropic planar layers. Layers  313  in this design example consist of two types of alternating layers, called high (H) layer  314  and low (L) layer  315  of optical refractive index n H  and n L  respectively. From Snell&#39;s law, we know the angle with respect to the surface normals (3 L ,3 H ) at which the light  317  are traveling in any of the layer  313  in terms of the refractive indexes of the layers (n inc , n L , n H ) if we know the incidence angle. This implies:
 
n inc  sin θ inc =n L  sin θ L  
 
n inc  sin θ inc =n H  sin θ H  
 
For p-polarized form of the light  317  incident on an interface between two optically isotropic regions, there is an angle called the Brewster&#39;s Angle at which the reflectivity of the interface is zero. This angle measured to the surface normal (θ H/L , θ L/H ) is:
 
             tan   ⁢           ⁢     θ     H   /   L         =       n   L       n   H                     tan   ⁢           ⁢     θ     L   /   H         =       n   H       n   L             
The reflectivity of the interfaces to s-polarized light at Brewster&#39;s Angle can be significant. The layers  313  which preferentially transmits the p-polarization state is designed by spacing these interfaces by quarter-wave optical thicknesses. Such quarter wavelength thicknesses (t L , t H ) are given by:
 
             t   L     =       λ   o       4   ⁢     n   L     ⁢   cos   ⁢           ⁢     θ   L                       t   H     =       λ   o       4   ⁢     n   H     ⁢   cos   ⁢           ⁢     θ   H               
One can show that the H and L indexes of refraction are related by the design equation:
 
               (       n   L       n   H       )     2     =           (       n   inc       n   H       )     2     ⁢     sin   2     ⁢     θ   inc         1   -         (       n   inc       n   H       )     2     ⁢     sin   2     ⁢     θ   inc                 
As an example, consider the specific case of:
 n H =1.5,n inc =1.0,θ inc =80°,λ o =500 nm 
This implies that the design index of refraction of the low index layer and the physical thicknesses of the low and high index layers  314  and  315  should be respectively n L =1.31,t L =145 nm, t H =110 nm. These can be achieved by using sputtered glass and vacuum deposited lithium chloride for n H =1.5 and n L =1.31, respectively. Assuming that the design is a matched design as in  FIG. 30C , with the layers  313  surrounded by an index of refraction of 1.5, the reflectivity can be easily calculated with the well-known Rouard&#39;s Method. This matching assumption is quite general as the outer surfaces could always be anti-reflection coated. The reflectivity for a variety of basic layer counts for the layers  313  is shown in Table 1 below:
 
   
     
       
         
             
           
             
               TABLE 1 
             
           
          
             
                 
             
             
               Performance data for the polarization filter layer 307 
             
          
         
         
             
             
             
          
             
               Layer Count 
               s-Reflectivity 
               P T   
             
             
                 
             
          
         
         
             
             
             
          
             
               1 
               0.069 
               0.036 
             
             
               5 
               0.45 
               0.29 
             
             
               11 
               0.85 
               0.75 
             
             
               15 
               0.95 
               0.90 
             
             
               21 
               0.99 
               0.98 
             
             
                 
             
          
         
       
     
   
   There are a variety of similar alternative designs. More than a single refractive index may be used as part of the thin-film structure of the layers  313 . The surrounding layers need not be air and the exact number of low and high index layers is variable. The carrier or substrate could have other refractive index values. The layers  313  can be varied from their quarter-wave thickness at the design angle and the wavelength so as to improve spectral and angular bandwidths. In fact, the operability of the layers  313  can be quite broad band and the Brewster angle design, does not have to be followed with great precision in index and angle. For example, you can trade off s-reflectivity with p-transmission by changing refractive indexes. The whole system can be flipped without changing its function. 
   A variety of preferred embodiments include at least two layers of different indices. Such arrangements have the n H  and n L  such that n H /n L &gt;1.15 in order to minimize the number of layers required for high polarization selectivity. Further, optical interference is most preferably used to enhance performance by using at least one layer with index n and thickness t such that 50 nm (n 2 −1) 1/2 &lt;t&lt;350 nm/(n 2 −1) 1/2 . This relationship derives from the equations provided hereinbefore regarding t L  and t H , by noting that the wavelength is in the visible light range 400 nm to 700 nm, that the incident light is near the critical angle so that n sin θ≈1 and optical interference effects are promoted by layers with an optical thickness between ⅛ and ½ of the light wavelength. Materials and methods for fabricating such layers are well-known in the art of multi-layer dielectric coatings. 
   The Brewster Stack approach is similar to the thin-film approach described above except that the layers are many wavelengths thick and tend to function largely on the basis of the incoherent addition of the waves rather than the coherent effect that occurs in optical interference coatings. The design of this form of the polarization filter layer  307  is the same as the design of the thin-film polarized described above except that layer thicknesses are not important as long as they are at least several wavelengths thick optically. The lack of optical thickness effects suggests that the performance of the Brewster Stack implementation should generally be less sensitive to spectral wavelength and angular variations. The transmission ratio defined in terms of the transmission of the s and p polarized light (T S ,T p ) of the set of N layer pairs in the geometry of  FIG. 30D  can be estimated using the approximate formula: 
               T   s     /     T   p       ≈       [       4   ⁢     (       n   H   2     -   1     )         n   H   4       ]       2   ⁢   N             
The results of applying this formula to a geometry with varying numbers of layer pairs is shown in Table 2 below:
 
                   TABLE 2                  Performance data for a Brewster Stack Form of the Filter Layer 307                         Layer Pairs   T s /T p     P T                                   1   0.9755   —       20   0.61   —       50   0.29   0.55       100   0.08   0.85                    
Generally speaking, this type of the polarization filter layer  307  requires much larger index differences and many more layers for the same reflectivities. There is no sharp dividing line between the thin-film design and the Brewster stack approach. As thickness increases, coherence effects slowly decrease and beyond some point which is dependent on the spectral bandwidth of the light signal, the coherence effects become small compared to incoherent effects. These examples described herein are simply the extreme of cases of the coherent and incoherent situations.
 
   In  FIG. 19  are shown variations on one form of a polarized light luminaire system  204 . In particular, in  FIG. 19B , the system  204  includes a base layer  206  having a wedge-shaped, cross-sectional area with optical index of refraction n 1 , and a first surface  208  and second surface  210  converging to define at least one angle of inclination Φ. The base layer  206  further includes a back surface  211  spanning the first surface  208  and the second surface  210 . Light  212  injected by a source (not shown) through the back surface  211  reflects from the first and second surfaces and exits the base layer  206  when the light  212  decreases its angle of incidence relative to a normal to the first and second surfaces with each reflection from the surfaces  208  and  210  until the angle is less than a critical angle  3   c  characteristic of an interface between the base layer  206  and a first layer means, such as a layer  214 . This layer  214  includes at least a layer portion having index n 2  less than n 1  disposed beyond the second surface  210  relative to the base layer  206 . The first layer  214  enables the light  212  to enter the first layer  214  after output from the base layer  206  when the light  212  in the base layer  206  achieves the angle of incidence less than the critical angle  3   c  characteristic of an interface between the base layer  206  and the layer portion having index n 2  in the layer  214 . 
   The system  204  also includes a layer means for preferential processing of polarized light of one state relative to another state, such as a polarization filter layer  216  (see previous generic description of the polarization filter layer  307 ). In addition to the samples described for the filter layer  307 , a further example of the polarization filter layer  216  is a birefringent material which will be described hereinafter in the context of particular embodiments in a separate subsection. In  FIG. 19 , the injected light  212  includes light  218  of a first polarization and light  220  of a second polarization. The filter layer  216  then interacts with the light  212  to preferably output the light  218  of a first polarization state compared to the light  220  of a second polarization state. This filter layer  216  is disposed beyond the second surface  210  relative to the base layer  206 , and this filter layer  216  is also able to reflect at least part of the light  220 . This reflected light  220  is then transmitted through both the first layer  214  and the base layer  206  and into a medium  207  having index n 3  (such as air). The light  218  on the other hand is output from the system  204  on the side of the base layer  206  having the polarization filter layer  216 . In  FIG. 19B , the light  218  is shown being output into a media  221  having index n 4 . In this embodiment in  FIG. 19B , the relationship among indices is:
 
n 4 ≧n 2  and
 
arcsin( n   2   /n   1 )−2Φ&lt;arcsin( n   3   /n   1 )&lt;arcsin( n   2   /n   1 )+2Φ  (9)
 
In this preferred embodiment n 2  and n 3  can be air layers with “n” being approximately one.
 
   This same index relationship can apply to  FIG. 19A  which is a variation on  FIG. 19B , but the first layer  214  of index n 2  is disposed further from the base layer  206  than the polarization filter layer  216 . In the embodiment of  FIG. 19B , the first layer  214  is closer to the base layer  206  than the polarization filter layer  216 . 
   In another embodiment shown in  FIG. 19C , the indices are such that Equation (10) below is followed and this results in the light  220  of second polarization state continuing to undergo internal reflection, rather than exiting through the first surface  208  as shown in  FIGS. 19A and 19B . The angle of incidence made relative to the polarization filter layer  216  decreases with each cyclic reflection. The index n 3  can thus be made small enough such that the light  220  will decrease its angle beyond the range where the filter layer  216  exhibits its preferred reflectivity of the light  220 . Consequently, at least part of the light  220  can pass through the second surface  210 , but is separated in angle of output relative to the light  218  of first polarization state. In the embodiment of  FIG. 19C  the indices have the following relationship:
 
 n   4   ≧n   2  and arcsin( n   3   /n   1 )&lt;arcsin( n   2   /n   1 )−4Φ  (10)
 
   The polarization filter layer  216  most preferably outputs the light  218  and reflects the light  220  when the angle of incidence is greater than:
 
θ p =arcsin [−4Φ(( n   1   /n   2 ) 2 −1) 1/2 ]  (11)
 
When light is incident at angles less than 3p, the filter layer  216  can therefore be substantially transparent to light of both polarization states (i.e., the light  218  and the light  220 ).
 
   In another embodiment of the invention shown in, for example,  FIGS. 20A-C , the system  204  includes light redirecting means, such as a light reflector layer  222  in  FIG. 20A , or more generically, a light redirecting layer  224  as shown in  FIGS. 20B and 20C . In general for the inventions of the device  10  (system  204  in  FIG. 20 ), we can define light redirecting means in terms of the propagation directions of light rays incident on, and departing from, the light redirecting layer  224 . Consider the case of a light ray propagating parallel to a unit vector  r   i  in an optical medium having an index of refraction n i . If ū is a unit vector perpendicular to the redirecting layer  224  at the point of light ray incidence and directed away from the redirecting layer  224  toward the side from which the incident light ray originates, then the incident light ray interacts with the light redirecting layer  224  to produce light rays which depart from the region of interaction. If the departing light rays propagate parallel to a distribution of unit vectors  r   c  in an optical medium having index of refraction n c , then light redirecting means includes any layer which processes the incident light ray such that the departing light ray has one of the following properties with respect to incident light rays throughout the operative angular range:
 
(1)n c (  r   c ×ū) is not equal to n i (  r   i ×ū) for at least 25% of the departing light rays;  (12)
 
(2)   r     c   =  r     i −2( ū·  r     i ) ū  for at least 90% of the departing light rays.  (13)
 
   The light redirecting layer  224  can redirect light according to condition (1) in Equation (12) if (a) the light interacts with optical surfaces which are rough, (b) if the light interacts with optical surfaces which have a different slope from the incident surface, or (c) if the redirecting layer  224  diffracts the light into appropriate angles. For example, light redirecting means according to condition (1) may be any combination of transmissive or reflective, diffusive or non-diffusive, and prismatic or textured layer. In addition, the light redirecting means can be a diffraction grating, a hologram, or a binary optics layer. 
   A light redirecting means which redirects light in accordance with condition (2) of Equation (13) is a specular reflector. Examples of such a specular reflector can be a metallic coating (e.g., the light reflector layer  222  in  FIG. 20A  can be a metallic coating), a multi-layer dielectric coating or a combination of these. In each case, the internal and external surfaces are preferably smooth and mutually parallel. 
   In  FIG. 20A  one of the preferred embodiments includes light reflecting, redirecting means in the form of the reflector layer  222  which reflects the light  220 . The reflector layer  222  is disposed beyond, or underlying, the first surface  208  of the base layer  206  and preferably is a flat, specular reflector, such as a metallic coating. Also shown is an intervening layer  223  of index n 3  disposed between the base layer  206  and the reflector layer  222 . This intervening layer  223  can be considered to be part of the base layer  206 , or a separate layer, depending on the functional interaction between the base layer  206  and the intervening layer  223 . The index of refraction n 3  of this intervening layer  223  can be adjusted to controllably affect the resulting spatial and angular distribution of the light  212  after encountering the layer  223 . 
   As can be seen, for example, in  FIGS. 20B and 20C  the light redirecting layer  224  can be positioned at different locations, and each layer  224  can also have different characteristics enabling achievement of different light output characteristics as needed for a particular application. Further examples of light redirecting means and uses, as well as specific embodiments, are illustrated in the remaining figures and will be described in detail hereinafter. 
   In another embodiment of the polarized light luminaire system  204 , light converting means is included and is illustrated as a polarization converting layer  226  in  FIGS. 21 and 22 , for example. In these illustrated embodiments, the indices have n 4 ≧n 2  and the conditions of Equation (9) must in general be met. In these embodiments, a light converting means includes a layer which changes at least part of one polarization state (such as the light  220 ) to another polarization state (such as the light  218 , or even light  227  of a third polarization state, which can be, for example, a combination of the first and second state). 
   The polarization converting layer  226  has the function of changing the polarization state to another state, such as rotating polarization by 90° (π/2). Moreover, such conversion is most preferably done for oblique incidence. As one example we describe the nature of such conversion for a uniaxial birefringent material where the index of refraction perpendicular to the optic axis is independent of direction. Many preferred materials, such as stretched fluoropolymer films are of this type. More general birefringent materials where the index of refraction is different in all directions can also be used following the general methods described herein. To understand the polarization conversion process, we first review the case for normal incidence. 
   As shown in  FIG. 30E , a plate  229  of birefringent material has its transverse axis along vector K and the optic axis is along vector I (see vectors in  FIG. 30F ). For a stretched birefringent film, the direction of stretch would be along vector I. Vectors I, J, K are an orthogonal triad of unit vectors along the x,y,z axes. For normal incidence, the wave normal is along vector K. We can describe the polarization of the electromagnetic wave by its displacement vector D. Let D′ be the polarization of the ordinary ray, and D″ the polarization of the extraordinary ray. Let n′ be the ordinary index of refraction, and let n″ be the extraordinary index of refraction. We can orient the optic axis of the birefringent plate  229  so that it makes an angle of 45° (π/4) to the incident polarization vector D 0 . This vector has two components D 0 x=(1/√2)D 0  cos ωt and D 0 y=(1/√2)D 0  cos ωt. Upon emerging from the birefringent plate  229 , the D vector has components D 0 x=(1/√2)D 0  cos (ωt−δ″) and D 0 y=(1/√2)D 0  cos (ωt−δ′), where δ′=(2π/λ)n′h and δ″=(2π/λ)n″h, where h is the plate thickness. Hence the phase difference introduced is δ′−δ″=|(2π/λ)(n″−n′)|h. In particular, if the emergent light has polarization vector D at right angles to the initial polarization vector D′, we need δ′−δ″=π (or more generally δ′−δ″=(2m+1)π, where m is any integer). This means the thickness h should be chosen as h=|(2m+1)/(n″−n′)|λ/2. 
   In summary, we choose the thickness h in accordance with the above relation and orient the optic axis at 45° to the incident polarization. In a preferred form of the invention such as in  FIG. 26B , the light traverses the converting layer  226  birefringent plate  229  twice, so that the actual thickness should be one-half of that specified above. In other words, the thickness is the well known λ/4 plate. Any reflections from a metallic mirror  231  introduces an additional phase shift of approximately π to both components and does not change the conclusions. 
   In an embodiment wherein the light has oblique incidence with the converting layer  226  (see  FIG. 26B ), it is first necessary to show that splitting of the incident beam into two beams (the well-known birefringent effect) does not cause difficulties. The reason this is not a problem is that the two beams emerge parallel to the initial direction, but slightly displaced from one another. The two beams are coherent with each other and the displacement is &lt;λ. The angular splitting is Δθ≈tan θ c Δn/n where θ c  is the critical angle and Δn=(n″−n′), n=(n″+n′)/2. The displacement is ≈hΔθ/cos θ c =hΔn/n tan θ c /cos θ c . But, we will choose hΔn/cos θ≈λ/4, so automatically the displacement is &lt;λ and the two light beams can be treated as one. 
   The geometry of oblique incidence on a uniaxial form of the birefringent plate  229  is somewhat complicated, and thus to simplify matters, we introduce the Eulerian angles as shown in  FIG. 30F . The relations between the (i,j.k) vector triad and the (I,J,K) ventor triad can be read from Table 3. 
                                   TABLE 3                       I   J   K                                                    i   −sin φ sin ψ + cos   cos φ sin ψ + cos   sin θ cos ψ           θ cos φ cos ψ   θ sin φ cos ψ       j   −sin φ cos ψ − cos   cos φ cos ψ − cos θ sin φ   sin θ sin ψ           φ cos θ sin ψ   sin ψ       k   sin θ cos φ   sin θ sin φ   cos θ                    
Let the normal to the air/plate interface=K, the direction of the incident wave normal=k, and the optic axis of the plate  229 =I. We wish to rotate the incident polarization D 0  by 90°. Since the incident polarization D 0  is in the interface plane, it is consistent to let D 0  be along i 0  so that ψ 0 =π/2. The polarization D′ of the ordinary ray is perpendicular to both I and k. Therefore, let D′ be along i′. Now i′ x =0. From Table 3 we conclude that tan ψ′=cot φ cos θ. The polarization of the extraordinary ray D″ is perpendicular to both D′ and k. Therefore, ψ″=ψ′±π/2. We choose ψ″=ψ′−π/2, and then tan ψ″=tan φ/cos θ. To achieve the desired output, we can appropriately orient the birefringent plate  229 . Just as in the normal incidence case, we let ψ 0  to be at 45° to the D′ and D″ directions. Therefore, we chose ψ′=π/2, and then tan φ=cos θ. For a typical case, where θ is close to θ c ≈40°, φ≈37°. In practice, for a range of incidence angles and wavelengths one would readily adjust φ experimentally to get the most complete polarization conversion, using the above formulae as a starting point and guide. We next determine the thickness, h, of the birefringent plate  229 . As in the case of normal incidence, the condition is: h=|(2m+1)/(n″−n′)|λ/2. However, the extraordinary index of refraction n″ now depends on the angle of incidence θ and must be read off the index ellipsoid: (1/n″) 2 =(1/n 0 ) 2  sin 2  θ+(1/n e ) 2  cos 2  θ where n 0  is the ordinary index of refraction and n e  is the extraordinary index of refraction. Also note that n′=n o . Typically, the index of refraction differences are small, &lt;0.1 and approximately, (n″−n′)≈(n e −n c )cos 2 θ. In addition, the light path length for oblique incidence is greater than that for normal incidence. The length h for oblique incidence is greater than the thickness of the plate  229  by a factor of 1/cos θ. Therefore, since the effective index difference is reduced by cos 2  θ, but the path length is increased by 1/cos θ, it follows that the thickness required for oblique incidence is larger than for normal incidence by ≈1/cos θ. In practice, for a range of incidence angles and wavelengths one would adjust h experimentally to obtain the most complete polarization conversion. In practice, for a range of incidence angels and wavelengths, one can adjust φ experimentally to obtain the most complete polarization conversion, using the above formulae as a starting point and guide.
 
   In another ex ample embodiment, the conversion of light of one polarization into another polarization state can be considered as involving three steps: (1) separation of different polarization states into substantially distinct beams at every point on the system  204 , (2) polarization conversion without affecting the desired polarization and (3) light diffusion into an appropriate angular distribution without depolarization of the light output. 
   As described herein, a variety of methods can be used to separate the different polarization states in the system  204 . For example, the low index layer  214  can be birefringent, as shown, for example, in  FIGS. 31A-C . The layer  214  can be, for example, an oriented fluoropolymer convertor layer which creates two light beams  218  and  220  of orthogonal polarization emerging from every point along the system  204 . This can be used provided two conditions are met. The first condition requires that the birefringence of the layer  214  is large enough to significantly prevent substantial overlap between the two polarized beams  218  and  220 . This condition is summarized by Equations (15)-(17) where C is at least 1 and preferably greater than 4. The second condition is that the direction of birefringence orientation (direction of stretch) of the first layer  214  is substantially parallel to the y axis. 
   For φ=1-1.5 degrees, the birefringence must be at least 0.03-0.05 to satisfy Equations (15)-(17). Measurements of the birefringence of various commercial fluoropolymer films yielded the following data (average index, birefringence): 
   Tefzel 250 zh: (1.3961, 0.054) 
   Tefzel 150 zm: (1.3979, 0.046) 
   Teflon PFA 200 pm: (1.347, 0.030) 
   The wedge layer  206  laminated with the 250 zh material produced just-separated polarized beams where even the Fresnel reflected parts did not overlap. 
   In another embodiment, one can achieve even greater angular separation of polarization by using a faceted redirecting layer comprised of a highly birefringent material. 
   A third approach for separation of polarization states uses a sheet of polymeric beam splitters consisting of an alternating structure of birefringent/transparent layers  427  shown in  FIGS. 30G  and H. Such an array of the layers  427  can rest on top of a collimated backlight  428  and polarizes by selective total internal reflection. The index of the film of polymeric layers  429  parallel to the plane of light incidence is lower than that of a transparent layer  430 , and the index perpendicular to the plane of light incidence is closely matched to the transparent layer  430 , so that an incoming collimated light beam  431  from the backlight  428  (inclined to the beam splitter layers  427 ) is split: the parallel polarized beam  431  is totally internally reflected, but the perpendicular component is transmitted. 
   One example of his arrangement can be Mylar/Lexan layers. Mylar indexes are: (1.62752, 1.6398, 1.486). The Lexan index is: 1.586. The complement of the critical angle is twenty degrees; therefore, the beam splitter layer  427  will function as long as the complement of the incidence angle is less than twenty degrees (in the Lexan). However, at glancing angles, Fresnel reflection causes reduction in the degree of polarization. For example, for thirteen degrees the Fresnel reflected perpendicular component is 9%. 
   Another example of this arrangement of the layer  427  is uniaxial Nylon/Lexan. Nylon indexes are: (1.568, 1.529, 1.498). Here there are two critical angles, the complements of which are nine and nineteen degrees for perpendicular and parallel, respectively. So, the obliquity must be inside this angular range for polarization to be operative. Taking the same case for Fresnel reflection as for Mylar (thirtee degree angle), the Fresnel reflected perpendicular component is only 5%, because the index matching is better. 
   For either of these examples, each beam splitter layer  427  needs to have the appropriate aspect ratio such that all rays of the beam  431  have exactly one interaction with the film/Lexan interface. 
   In one embodiment, once the light of different polarization states is separated into two orthogonally polarized beams at every position along the backlight  428 , there must be a means of converting the undesired polarization to the desired one, such as the polarization converting layer,  346  in  FIG. 31C and 429  in  FIG. 30G . 
   One method of performing the polarization conversion is by an alternating waveplate combined with a lens or lens array. In the single lens method, a light beam  218  and  220  will fall upon lenses focused to two nonoverlapping strips of light of orthogonal polarization at the focal plane. The alternating wave plate acts to rotate the polarization of only one of the beams ( 220 ) by ninety degrees, the emergent light will be completely converted to light  218 . This can be effected by the presence of a half-wave retarder placed to capture only the light  220  of one polarization. This has been demonstrated visually with a large lens, a plastic retardation plate, and Polaroid filters (Polaroid is a registered trademark of Polaroid Corporation). 
   In a second approach using a lenticular array, one uses a thin sheet of lenses and an alternating waveplate structure (with the frequency equal to the lens frequency), where the retardation changes by 180 degrees for each lens. For a lenticular array 1 mm thick, each image can be of the order of 5 thousandth of an inch in size so the registration of the lenticular array with the waveplate would have to be exact enough to prevent stack-up errors of less than one thousandth of an inch. 
   Another method of performing the polarization conversion is by use of a double Fresnel rhombus (“DFR”) which is another embodiment of a converting layer, such as the layer  346  in  FIG. 31C and 429  in  FIG. 30G . The DFR avoids registration problems by selectively retarding according to angle instead of position. Such a DFR causes the light of first polarization state to suffer from total internal reflection events corresponding to 4×45°180° of phase shift, while the other polarization state light is only transmitted, so that the output light is completely polarized to the light of first polarization in one plane in the end. The DFR can be constructed, for example, by having four acrylic or Lexan films each embossed with 45 degree prisms, all nested. For the DFR to cause retardation the two orthogonal plane polarized beams L and R (by a ¼-wave plate). If the L is transmitted by the DFR then the R beam will get converted to the L beam by the DFR. Finally the L beam is converted to plane polarized by another ¼-wave plate, the orientation of which determines the final plane of polarization. 
   In a preferred embodiment shown in  FIG. 21A , the converting layer  226  is disposed on the opposite side of the base layer  206  relative to the polarization filter layer  216 . In the embodiment of  FIG. 21B , the converting layer  226  is disposed on the same side as the polarization filter layer  216 . As can be seen by reference to  FIGS. 21A  and B, the converting layer  226  can even convert the light  218  and  220  to the light of  227  of another third polarization state. This light  227  can be, for example, the light of a third polarization state or even a variation on, or combinations of, the first or second polarization states discussed hereinbefore. The resulting light polarization is dependent on the response characteristics of the converting layer  226 . The converting layer  226  can therefore be designed to respond as needed to produce a light of desired output polarization state; and in combination with appropriate positioning of the layer  226 , one can produce an output light in the desired direction having the required polarization characteristics. 
   In another form of the invention illustrated in  FIGS. 22A-E , the converting layer  226  is utilized for other optical purposes.  FIGS. 22 ,  23 ,  24  E-F,  25 - 27 ,  28 A and C, and  29  all illustrate use of the converting layer  226  to change the light  220  of the second polarization state to the light  218  of the first polarization state. In addition, the elements of the luminaire system  204  are arranged such that the light being processed will pass through, or at least encounter, one or more of the polarization filter layer  216  at least once after passing through the converting layer  226 . For example, in the case of processing the light  220 , the arrangement of elements enables return of the light  220  to pass through the polarization filter layer  216  after passing through the converting layer  226 . In some instances, the light  220  can encounter the polarization filter layer  216  two or more times before being output as the light  218  of the first polarization state.  FIGS. 22A-E  illustrate examples of a variety of constructions to achieve a desired output. In  FIG. 22A , after the light  212  encounters the polarizing filter layer  216 , the reflected light  220  passes through the converting layer  226 , and is converted to the light  218 . The light is then returned to the polarization filter layer  216  via internal reflection. In addition, in  FIG. 22B , the light  220  also passes through the converting layer  226 , is converted to the light  218 , and is then returned again to the filter layer  216  after internal reflection. In these cases, n 3  is low enough such that the relationship among n 1 , n 2  and n 3  in Equation (10) is met. 
   In the embodiments of  FIGS. 22C-E , a redirecting means in the form of the light reflector layer  222  is added to return the light  220  to the polarization filter layer  216 . As described hereinbefore for the embodiment of  FIG. 20A , the intervening layer  223  has an index of refraction n 3  which can be adjusted to affect the spatial and angular distribution of light encountering the layer  224 . In a preferred form of the invention shown in  FIGS. 22C-E , the layers of index n 2  and n 3  can include air gaps, and in the most preferred form of the invention the layers of index n 2  are air gaps. 
     FIGS. 24A-F  illustrate a sequence of constructions starting with use of one of the polarization filter layer  216  in  FIG. 24A  and continuing construction of more complex forms of the luminaire system  204 . In  FIGS. 24C-F , there is added one or more of the light redirecting layer  224 , at least one liquid crystal display (“LCD”) layer  230  and light matching means, such as a matching layer  232 . The matching means acts to convert the light output by the assembly of the other layers to a particular polarization state preferred by a target device or additional layer, such as the LCD layer  230 . The matching layer  232  is thus a special case of the converting layer  226 . 
   In  FIGS. 23A-C  are illustrated other forms of the polarized light luminaire system  204  in combination with the LCD layer  230 . In one general form of the embodiment of  FIG. 23A , a layer  234  is included. In more particular forms of the inventions, for example as in  FIG. 23 , the preferred value of n 2  is about 1 (see, for example,  FIGS. 23B  and C). In certain forms of  FIG. 23A , n 2 &gt;1 can also be utilized. Alternatively, preferably choices for the relationship among indices of refraction are set forth in Equation (9) and (10). 
   Further examples of preferred embodiments are shown in  FIGS. 26A  and B, and in  FIG. 26A  is included a cold cathode fluorescent tube (“CCFT”) light source  236 . This embodiment further includes an angle transformer layer  238  which operates to change the angular distribution of the light. This angle transformer layer  238  can, for example, change the distribution in the xz-plane to control the spatial uniformity of light output from the device  10 . In the preferred embodiment, the distribution of the output light  250  is substantially uniform in its spatial distribution over at least 90% of the output surface. In addition, the angular distribution of the light  212  in the xz-plane is approximately ±θ max  with respect to the normal to the back surface  211 , where 
                     π   2     -     θ   c     +     6   ⁢   Φ       ≥     θ   max     ≥       π   2     -     θ   c               (   14   )               
and the back surface  211  is about perpendicular to at least one of the first surface  208  and the second surface  210 . The angle transformer layer  238  can be a tapered light-pipe section, a compound parabolic concentrator (a “CPC”), a micro-prismatic film ( FIG. 28C ) a roughened-surface layer, or a hologram. The angle transformer layer  238  is most preferably optically coupled to the base layer  206  without an intervening air gap. The angle transformer layer  238  can also operate to change, and preferably narrow, the light distribution in the yz-plane to improve brightness, LCD image quality, and viewer privacy as well. In addition, in  FIG. 26A , an output diffuser layer  248  has been added before the LCD layer  230  to broaden the angular distribution and enhance uniformity of output light  242  provided to the LCD layer  230 .
 
   In another preferred embodiment of  FIG. 26B , a CPC  239  is coupled to a light source  244  operating to help maintain output light  250  within the proper angular distribution in the xz plane. In addition, one can control the range of angular output by use of a light redirecting means, such as a prismatic redirecting layer, such as the layer  246 , using flat prismatic facets, such as the facets  247 . See, for example, this type of layer and prismatic facets in  FIGS. 28C , D and E and  FIGS. 29A  and B and the description in detail provided hereinafter. This embodiment as shown in  FIG. 28E  refers to the prismatic layer  251  and facets  253 , and this embodiment also adds after the LCD layer  302  a light diffuser layer  304  for broadening light distribution in a specific plane. In a most preferred form of this embodiment, for example, shown in  FIG. 28E , the light  242  is directed to pass through the LCD layer  302  within a narrow angular range in the xz-plane. The elements of the luminaire system  204  are therefore constructed to assist in providing transmission of the light  242  through the LCD layer  302  at an angle where the image forming properties are optimized. With the diffuser layer  304  positioned on the other side of the LCD layer  302  relative to the base layer  206 , the diffuser layer  304  can broaden the angular distribution of viewer output light  250  without diffusing the light  250  in the xy-plane. For example, the diffuser layer  304  can be a “parallel” diffuser which can take the form of a holographic diffuser or lenticular diffuser with grooves substantially parallel to the y-axis. Viewers at a wide range of angles can then see the image which is characteristic of the optimal angle for the light  242  which is subsequently transmitted through the LCD layer  302  to form the light  250 . Example configurations utilizing this form of general construction are thus shown in  FIGS. 28D  and E and  FIGS. 29A  and B. Further,  FIGS. 28D  and E and  FIG. 29A  also include a transverse diffuser layer  252  which diffuses the output light  242  provided to the LCD layer  302  only in the xy-plane in order to improve uniformity without broadening the distribution of the light  242  in the xz-plane. For example, the transverse diffuser  252  can be a holographic diffuser or a lenticular diffuser with grooves substantially parallel to the z-axis. Further details will be described hereinafter. 
   In  FIGS. 27A  and B are additional preferred embodiments wherein the first layer means of index of refraction n 2  is most preferably not air. These embodiments show different examples of the light redirecting layer  224 . Further, in  FIG. 27A  medium  254  having index n 3  need not be air, but the various indices of the system  204  must meet the requirements of Equation (10) to achieve the total internal reflection illustrated. In  FIG. 27B  the medium  254  is air, the light redirecting layer  224  has curved facets  256 , and the light  245  is focused within a preferred viewing zone  258 . 
   The embodiments of  FIGS. 28 and 29  preferably utilize an air gap layer  260  as the first layer means. The layer  260  enables light to enter the layer  260  after the light  212  has achieved an angle of incidence less than the critical angle  3   c  characteristic of an interface between the base layer  206  and the air gap layer  260 . The embodiment of  FIG. 28B  includes a first redirecting layer  262  between the base layer  206  and a diffuser layer  264  and a second redirecting layer  265  on the other side of the base layer  206 . This first redirecting layer  262  includes refracting/internally reflecting prisms  266  while the second redirecting layer  265  includes refracting prisms  268 . Two of the polarization filter layer  216  are disposed either side of the base layer  206 , each transmitting the appropriate light  218  or  220  which is passed through the associated light redirecting layer,  262  and  265 , respectively. In  FIG. 28C  is a more preferred embodiment wherein the light redirecting layer  246  comprises a refracting/internally reflecting layer having the relatively small prisms  247 . The surface angles of each of the prisms  247  can vary across the illustrated dimension of the redirecting layer  246  in a manner described hereinbefore. This variation in angle enables focusing different cones of light coming from the prisms  247  onto the preferred viewing zone  258  (see  FIG. 27B ). The light reflector layer  222  can be a metallic coating as described hereinbefore. 
   The reflector layer  222  can be applied to the converting layer  226  by conventional vacuum evaporation techniques or other suitable methods. The other layers, such as the redirecting layer  246  can be formed by casting a transparent polymeric material directly onto the matching layer  232  (see  FIGS. 24  C-F and  28 C and D). The polarization filter layer  216  can likewise be manufactured by conventional methods, such as deposition of multiple thin layers directly onto the base layer  206 . Also included is an angle transformer layer  274  coupled to the back surface  211  (see  FIG. 28C ). This angle transformer  274  includes prisms  276  which broaden the angular distribution of input light  212  to the base layer  206  to help provide a more spatially uniform form of the output light  218  to the LCD layer  230 . Other forms of the angle transformer layer  274  can be a roughened layer and a hologram (not shown) coupled to the back surface  211  (or other input surface) without an intervening air gap. 
   In the preferred embodiment of  FIG. 28D , a first prismatic light redirecting layer  249  is disposed between the base layer  206  and the polarization filter layer  216 . This redirecting layer  249  reduces the angle of incidence of light  280  incident on the polarization filter layer  216 . A second prismatic light redirecting layer  282  then redirects light  284  output from the filter layer  216  to an LCD layer  302  with a post diffuser layer  304 , operable as a parallel diffuser as described hereinbefore. This embodiment further includes the CCFT light source  236  with a reflector  290  having a position following at least a portion of an involute of the light source  236  inner diameter. Another portion of the reflector  290  directly opposite the back surface  211  is convexly curved or bent. 
   In the preferred embodiment of  FIG. 28E  a light redirecting layer  251  comprises refracting micro prisms  253 . A polarization filter layer  296  is disposed adjacent a converting layer  298 , and the transverse diffuser layer  252  is positioned between the redirecting layer  251  and the LCD layer  302 . A parallel diffuser  304  is disposed on the light output side of the LCD layer  302  with the light  242  directed through the LCD layer  302  at a preferred angle to optimize output light  301  for best image-forming quality of the LCD layer  302  (contrast, color fidelity and response time). 
   The embodiments of  FIGS. 29A  and B show some of the advantages of some forms of the invention over a conventional LCD polarizer system  304  shown in  FIG. 30A . In  FIG. 30A , a prior art backlight  306  emits light  308  of both polarizations in nearly equal proportions. A typical prior art LCD layer arrangement  310  includes a first form of polarization filter  312  and a second form of polarization filter  314  with the liquid crystal layer  316  sandwiched therebetween. In this LCD layer arrangement  310 , the first polarization filter  312  must provide a high polarization ratio, that is, it must have an extremely low transmission of light of the second polarization state which is unwanted for input to the liquid crystal layer  316  in order for the LCD layer arrangement  310  to provide adequate LCD contrast. In practice, the polarization filter  312  has a high optical density for the desired light of the first polarization state as well. The resulting losses therefore further degrade the LCD light transmission and image output. In contrast to this prior art arrangement  310 , the invention provides a much higher percentage of light which is preferred by the LCD layer arrangement  316  thereby making use of a substantial portion of the light of the unwanted second polarization and also minimizing loss of the desired light of the first polarization state. 
   In the embodiment of  FIG. 28A  this advantageous processing of the light  218  and the light  220  for the LCD layer  316  is accomplished by positioning the converting layer  226  adjacent the base layer  206 . Disposed adjacent the converting layer  226  is the polarization filter layer  216 . The light redirecting layer  224  includes curved microprismatic facets  318  to broaden the angle of light distribution in the xz plane and improve the uniformity of light distribution output from the luminaire system  204 . A transverse diffuser  320  is preferably laminated to the light redirecting layer  224  or can be formed on opposite sides of a single polymeric layer (not shown). The polarizing filter layer  216  can be laminated or is disposed directly onto the converting layer  226  which in turn is laminated or deposited directly onto the first surface  208 . 
   In the preferred embodiment of  FIG. 29A  the advantageous processing of the light  218  and the light  220  for the LCD layer  302  is accomplished by using a first polarization filter layer  324  and a second polarization filter layer  322 . The first filter  324  can, however, have a relatively low polarization ratio compared to the prior art polarization filter  312 . For example, the polarization filter layer  324  can have a lower dye concentration than the prior art filter  312 . This difference enables higher LCD light transmission and improved image-forming properties described hereinbefore. This preferred embodiment utilizes a post diffuser layer  328  which is coupled to an LCD system  330  (the combination of the layer  324 , the liquid crystal layer  302  and the layer  322 ). Preferably the post diffuser layer  328  is laminated to, or integrally formed with, the second polarization filter layer  322 . 
   In the preferred embodiment of  FIG. 29B , the advantages are achieved by using only one polarization filter layer  248  which results in reduced cost for the luminaire system  204  and increased light transmission. In this embodiment the light output through the matching layer  232  is preferably at least 90% composed of light  218  of the LCD preferred polarization state. A coupled angle transformer  334  coupled to the back surface  211  reduces the angular width of light distribution in the yz plane, and this reduced angular distribution further improves quality of the output light  250  making up the LCD image from the luminaire system  204 . 
   In another preferred form of the invention shown in  FIG. 33 , the device  10  embodies a base layer  400  for receiving input light  402  from a light cavity  404  having lamp  406 . The base layer  400  is most preferably an acrylic wedge as explained hereinbefore. The input light  402  is comprised of two polarization states “a” and “b” as shown in  FIG. 33 . The general terminology “a” and “b” is used throughout to cover all different polarization combinations, such as linear “s” and “p”, left and right circular, and elliptical polarization with the second state being orthogonal to the first. As described hereinafter the “a” and “b” states are preferably operated on by a polarization beam splitter, referred to hereinafter as interference layer  411  or reflective polarizer layer  480 . Light  405  is thus output from the base layer  400  into an air layer  407  under selected optical conditions in accordance with requirements explained hereinbefore in detail. Some of the light  405  with polarization “a” is further transmitted as light  409  into and through interference layer  411  disposed on glass plate  412 , passes through air layer  414  and is acted upon by redirecting layer  416 . Preferably this layer  416  is a prismatic layer described hereinbefore and is used to control the angle of output of the light  409  of polarization state “a”. The redirecting layer  416  is designed preferably to act on light centered at about 74° from the normal which is a typical exit angle from the base layer  460 , thereby changing the light direction to one substantially perpendicular to the particular exit face of the base layer  400 . This layer  416  can also be diffractive in nature such as a hologram layer in other embodiments. The output light  409  from the redirecting layer  416  can be further processed with post diffuser layers (not shown) and other appropriate layers described in great detail hereinbefore. 
   Regarding polarization splitting, two basic types of polarization splitting layers (the interference layer  411 ) were used. One type of the layer  411  was based on vacuum deposition of thin inorganic films (for example, an interference layer (or “polarization filter”) described hereinbefore as alternating layer of high index n H  and low index n L  material, to create a polarization selective beam splitter which could be used in non-normal incidence, specifically in the neighborhood of seventy-four degrees. Beam splitters of this type were created by vacuum depositing the layers on 1 mm thick glass plate using standard thin film physical vapor deposition techniques. 
   The second type of the layer  411  used consisted of a multi-layer polymer film. For example, the polymer film can be a well known DBEF (a trademark of 3M Co.) layer manufactured by 3M Co. Details concerning this commercially available product can be found in PCT publication WO95/17303 and WO96/19347. This film has the advantage that it could be used for normal incidence of the light as well as at wide incidence angles, has a film defined polarization axis, and can potentially be produced by high volume continuous manufacturing processes. These attributes allowed us to experiment with additional angles other than normal incidence type systems or a narrowly defined oblique angle, and various orientations of the pass axis of the film. 
   There are a number of other well known approaches that can produce polarization splitting effects used in these embodiments, including but not limited to scattering (such as dipole scattering), double refraction, reflection from collesteric liquid crystals, and thick film Brewster splitters. 
   As stated above, some of the light  405  has polarization state “b” and is reflected from the interference layer  411  (the polarization splitter) as light  418 , passing through the air layer  411 , the base layer  400 , air layer  420 , a converting layer  422  (for example, a quarter wave plate layer), air layer  424  and is reflected by a reflector that could be a silver film, such as Silverlux (a trademark of 3M Co.) or a dielectric reflector such as a BEF (a trademark of 3M Co.) type back reflector layer  426 . This BEF layer  426  can also be disposed against white paper  425  (shown in phantom) to diffusely reflect the small amount of light that has passed through the layer  426 . The reflector layer  426  may contribute to the polarization process or behave as a simple reflector. The reflected light  418  returns through the above-recited layers; but instead of being reflected by the interference layer  411 , the light  418  has been converted by the converting layer  422  to light  423  of polarization state “a” which is transmitted, and the output angle is controlled by the redirecting layer  416 . 
   As noted above, the preferred polarization converting layer  422  included commercially available quarter-wave stretched, birefringement polymer films and were designed for 550 nm light wavelength at normal incidence. This form of converting medium was not necessarily the design optium, but the materials were readily available; thus, many of the prototypes built used these available films at non-normal incidence and the retardation was not strictly of the quarter-wave type. For example, many of the surfaces of the device  10  show various compensation effects off angle. The optimal compensation film to be paired with these components is not necessarily a quarter-wave type film oriented at 45° to the system symmetry axis as evaluated herein. However, the embodiments illustrate the operability of the basic designs of the devices  10 . 
   These films of the converting layer  422  were used in a number of configurations. Since the film was supplied with adhesive, it was laminated either to triacetate cellulose (“TAC”) film which had low birefringence when it was necessary to use it as a free “unlaminated” film. To reduce reflections, improve performance, and stability, many architectures can be constructed where the film was directly laminated to other components of the device  10 . 
   Other light  423  of both polarization states “a” and “b” is reflected by top surface  432  of the base layer  400 , then passes through the base layer  400 , the air layer  420 , the converting layer  422 , the air layer  424 , and reflected by the BEF back reflector layer  426  back through the layers until striking the interference layer  411 . This light  423  therefore acts in a manner similar to the light  405  upon output from the base layer  400  producing an output light  434  of polarization state “a” and reflecting light  436  of polarization state “b”. This light  436  also acts in the manner as the light  418  of polarization state “b”, resulting in output of light  438  of polarization state “a” (like the light  428 ). It should be noted that throughout the specification only certain important example light ray paths are shown to illustrate operation of the many embodiments of the device  10 . To quantify the performance of the devices  10  studied, a series of gain parameters were developed which reflect increase of efficiency due to brightness and solid angle changes. Therefore, the performance of the embodiment of  FIG. 33  is shown in Table 4 (the parameters are defined in the Example), and the measurement system and method are described in detail in the Example and in  FIGS. 61-63 . 
   The above-described device  10  therefore includes an assembly of layers which act as a “cavity” containing an internal polarization conversion and recycling mechanism. The term “cavity” can include, for example, a light waveguide wherein the light is moving between layers. Due to the “cavity” or waveguide nature of the device  10 , the light ray paths can be numerous in type and combination. The requirement is that there be sufficient polarization conversion in the cavity so that light is converted from the state “b”, which preferentially reflects from the interference layer  411 , to the state “a” which is transmitted efficiently to avoid substantial internal losses. Consequently, multiple Fresnel reflections and non-ideal conversion mechanisms from “b” to “a” states within the cavity are permissible. 
   
     
       
         
             
           
             
               TABLE 4 
             
           
          
             
                 
             
             
               Comparison of Various Architectures to Basic Tapered Luminare with 
             
             
               a Metallic Based Back Reflector 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
          
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               g Total (Usable 
             
             
                 
               Redirecting 
                 
               Base 
                 
                 
                 
               g Luminance 
               g Range 
               Gain-product of 
             
             
                 
               Layer 
                 
               Layer 
               Back 
               Reflective 
                 
               (Brightness 
               (Range 
               brightness gain 
             
             
               FIG. 
               Display Side 
               Diffuser 
               (B. Layer) 
               Reflector 
               Polarizer 
               Rotator 
               Gain) 
               Gain) 
               and range gain) 
             
             
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
          
             
               33 
               Yes 
               No 
               Smooth 
               Structured 
               Evaporated 
               Yes 
               1.04 
               1.26 
               1.31 
             
             
               34 
               Yes 
               No 
               Smooth 
               Structured 
               Evaporated 
               No 
               1.06 
               1.20 
               1.27 
             
             
               35 
               Yes 
               No 
               Smooth 
               Structured 
               None 
               No 
               1.07 
               1.09 
               1.17 
             
             
               36 
               Yes 
               No 
               Smooth 
               Metallic 
               Evaporated 
               Lam to BRefl 
               1.12 
               1.21 
               1.35 
             
             
               37 
               Yes 
               No 
               Smooth 
               Metallic 
               Evap on Pipe 
               Lam to BRefl 
               1.10 
               1.06 
               1.17 
             
             
               38 
               Yes 
               No 
               Smooth 
               Metallic 
               None 
               None 
               1.00 
               1.00 
               1.00 
             
             
               39 
               Yes 
               No 
               Smooth 
               Metallic 
               Evaporated 
               Lam to Pipe 
               1.16 
               1.12 
               1.30 
             
             
               40 
               Yes 
               No 
               Smooth 
               Metallic 
               None 
               Lam to Pipe 
               0.97 
               1.02 
               .99 
             
             
               45 
               Yes 
               No 
               Smooth 
               Structured 
               Evaporated 
               Lam to Pipe 
               1.13 
               1.19 
               1.35 
             
             
               46 
               Yes 
               No 
               Smooth 
               Structured 
               None 
               Lam to Pipe 
               1.06 
               1.11 
               1.18 
             
             
               47 
               Yes 
               No 
               Smooth 
               Structured 
               At Pipe Input 
               None 
               1.16 
               0.99 
               1.15 
             
             
               48 
               Yes 
               No 
               Smooth 
               Structured 
               At Pipe Input 
               At Pipe Input 
               1.08 
               1.01 
               1.09 
             
             
                 
             
          
         
       
     
   
   To investigate the polarization conversion mechanisms in the device  10 , a variety of components were evaluated regarding converting light in TE(s) and TM(p) states, and 45° incident linear polarization of the light into the orthogonal linear polarization state. To make this measurement a 623.8 nm laser and a polarizer analyzer pair were used. Each sample was illuminated at seventy-four degrees incidence which is near the center of the ray distribution leaving the base layer  400 . For the prismatic form of the redirecting film  414 , transmitted light was measured, and for all other parts reflected light was measured. The results in Table 5 illustrate these conversion effects. 
   
     
       
         
             
             
             
             
           
             
               TABLE 5 
             
             
                 
             
             
               System 
               TE 
               TM 
               45° 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
          
             
               BEF Only 
               17% 
               18% 
               30% 
             
             
               BEF and Separate Converter 
               27% 
               35% 
               56% 
             
             
               BEF with Laminated Converter 
               29% 
               39% 
               42% 
             
             
               Metallic Reflector Only 
               0% 
               0% 
               29% 
             
             
               Metallic Reflector with Separate Converter 
               35% 
               37% 
               49% 
             
             
               Metallic Reflector with Laminated Converter 
               52% 
               59% 
               33% 
             
             
               Light Pipe, Specular 
               1% 
               6% 
               69% 
             
             
               Prismatic Redirecting Film 
               2% 
               5% 
               54% 
             
             
                 
             
          
         
       
     
   
   Generally, conversion of light in a light pipe type of geometry can originate from a number of mechanisms and that the effect of the various interactions in the system depends on the specific polarization state at that point, for example, TE, TM, 45°, circular, etc. Hence, the polarization conversion effect can result, for example, from total internal reflection, reflection beyond the Brewster&#39;s angle from dielectric interfaces, and material birefringence. 
   Since every transmission or reflection has the potential of changing polarization depending on the exact circumstances, there are a variety of ways that compensation/polarization conversion films can be used to advantageously improve performance by increasing the conversion and specifically control polarization beyond the natural effect of various elements. In addition, the angle of the polarization splitting layer can be used as an important parameter to enhance polarization conversion in the manner intended. 
   Example architectures chosen to study were either (1) the central rays of the luminaire of TE or TM polarization with respect to the system which makes the base layer  400  and redirecting layer  414  have low conversion and have good control over the polarization, or (2) at 45° where nearly every interaction converts polarization, and the net effect of all of the separate conversions is some total amount of conversion or depolarization of the light recycles through the polarization cavity. It also should be readily understood that one can control the light polarization conversion process in the 45° architecture, as is done in other cases. 
   In an additional embodiment of the invention shown in  FIG. 34 , the layer structure is like that of the embodiment of  FIG. 33  except the converting layer  422  is removed. The polarization recycling cavity is still substantially formed by the combination of the interference layer  411  and the back reflector layer  426 . As a result of removing the converting layer  422 , the light  418  of polarization “b” is transmitted through the base layer  400 , the air layer  420  and is reflected as light  440  of polarization “b” and “a”, with some of the “b” state being converted to the “a” state. Polarization conversion now relies on conversion from reflections from the various elements, such as the back reflector layer  426  and residual birefringence of the various layers of the device  10  to output light  442  preferably of polarization state “a”. The performance of this embodiment is shown in Table 4. 
   In a further embodiment in  FIG. 35 , the converting layer  422  and the interference layer  440  have been removed as compared to the embodiment of  FIG. 33 . This embodiment includes an unpolarized form of the light  402  input from the lamp cavity  404 . This embodiment thus shows a polarization level of only about 6% above random with a high brightness direction being along the direction of propagation of the light in the base layer  400 . The performance of this embodiment is shown in Table 4. 
   In another preferred embodiment shown in  FIG. 36 , the arrangement of layers is quite similar to the embodiment of  FIG. 33  and generally results in processing the same family of light rays of particular polarization with the various polarization cavity elements. The principal distinction is the reflector layer is now a metallic back reflector layer  446  which is laminated to the converting layer  422  with no intervening air layer. Preferably this layer  446  comprises a commercially available, silver coated polymer film (Silverlux, for example, referred to hereinbefore) laminated to a substrate, such as aluminum or other suitable support. The performance of this embodiment is shown in Table 4. 
   In an additional preferred embodiment shown in  FIG. 37 , the arrangement is quite similar to the embodiment of  FIG. 36  except the polarization splitting interference layer  411  is directly disposed onto the base layer  400 . This layer  411  is preferably deposited by evaporation although any other conventional thin film deposition technique can be used to produce an operative layer. This layer  411  can also be obtained by lamination of reflective polymers or other polarization splitter layers which are of low loss and do not significantly attenuate light rays in the base layer  400 . The relative performance of this embodiment is illustrated in Table 4. 
   In yet another embodiment shown in  FIG. 38 , the arrangement of layers is quite similar to that of  FIG. 35  except the back reflector layer is the metallic back reflector layer  446 . The light ray paths are also quite similar to those in  FIG. 35 . The degree of polarization is about 4% which is also very similar to the device  10  of  FIG. 35 . The performance of this embodiment of  FIG. 38  is shown in Table 4. 
   In yet a further preferred embodiment in  FIG. 39 , the arrangement of layers is similar to that of  FIG. 36  except that the converting layer  422  is laminated to the base layer  400  instead of being laminated to the metallic back reflector layer  446 . Instead, there is an air layer  448  between the converting layer  422  and the metallic back reflector layer  446 . The light ray paths are also quite similar to those of  FIG. 36 , except that additional polarization of unpolarized light occurs and polarization conversion also occurs before the light exits the base layer  400 . These additional polarization and conversion steps will be described hereinafter in reference to the embodiment of  FIG. 40 . The resulting output is light  452  suitably controlled in angle by the redirecting layer  416 . A portion of the light  450  has been reflected by the interference layer  411  as light  453  of polarization state “b” which is her processed and converted to the light  438  of state “a” and output. The performance of this embodiment of  FIG. 39  is shown in Table 4. 
   In a yet another preferred embodiment in  FIG. 40 , a different polarization recycling and conversion arrangement is shown. In this embodiment the polarization recycling cavity is formed by the base layer  400  and a laminated form of the converting layer  422  which confines light by total internal reflection (hereinafter, “TIR”). In this device  10 , the input light  402  is continuously converted in polarization by the converting layer  422  as the light  402  travels down the diminishing thickness of the wedge shaped base layer  400 . These components of the light  402  which are p-polarized (“a” state for this embodiment) with respect to the top surface  432  are then preferentially coupled from the base layer  400  due to the lower reflectivity of the “a” state light as compared to s-polarized (“b” state); and as the light ray angles pass θ c  (see discussion hereinbefore concerning critical angle), the light  402  begins to escape the base layer  400 . Various example light ray paths are shown in the figure. In one case, the light  402  of polarization “a” and “b” is reflected from the top surface  432  and bottom surface  454  until θ c  has been achieved. The light  456  of polarization “a” is then output through the air layer  407  and through the redirecting layer  416  with a controlled angular range toward the viewer. A remaining component of light  458  of polarization state “b” is reflected and passes through the base layer  400 , and the light  458  is coupled out into the converting layer  422 . Upon reflection and traversal again of the layer  422 , the light  458  has become light  460  of polarization state “a” and is output through the air layer  407  and the redirecting layer  416 . A further example of the process is the light  458  passes once through the converting layer  422 , is outcoupled into air layer  448 , reflected by the metallic reflector layer  446 , passes again through the converting layer  422  to become light  462  of polarization “a” which is then output toward the viewer. The generally preferred output is still, however, light of “a” polarization. Therefore, the difference between the reflectivities of the “a” and “b” states enables improved polarization efficiency. In addition, the resulting polarization produced was about thirteen percent. The performance of this embodiment is shown in Table 4. 
   In yet another embodiment shown in  FIG. 41 , the arrangement of layers is similar to  FIG. 40 , but the limited difference between reflectivities of the “a” and “b” states are further enhanced by depositing a polarization splitting layer  464  directly onto the top surface  432  of the base layer  400 . 
   In another variation related to the embodiments of  FIGS. 40 and 41 ,  FIG. 42  shows a back reflector layer  466  directly coupled to the converting layer  422  which is also laminated to the bottom surface layer  454  of the base layer  400 . 
   In yet another embodiment shown in  FIG. 43 , the converting layer  422  can be disposed on the other side of the base layer  400  above the top surface  432 . This arrangement also accomplishes the purpose of confining the light as it travels along the base layer  400 . Several example light ray paths are shown with the primary difference being the light  402  of polarization state “a” and “b” is outcoupled from the top surface  432 , and then the “b” state component is converted to light  468  of “a” state by the quarter wave plate converting layer  422 . 
   In a further variation on the embodiment of  FIG. 43 , the base layer  400  in  FIG. 44  is made of a birefringement polarization converting material which functionally operates to include with the base layer  400  the polarization converting function of the converting layer  422  of  FIG. 43 . As shown in  FIG. 44 , the light  402  is outcoupled into the air layer  407  as the light  468  of polarization state “a”. 
   In considering the performance measurements in Table 4, it was noted that increased polarization efficiency did not necessarily result in systematic gain increase. This was believed to arise from scattering and absorption losses from the type and quality of the adhesive bond used to couple various layers and also on the attached quarter wave film. 
   In a further variation on the embodiment of  FIG. 39 , the back reflector layer in  FIG. 45  is the BEF type back reflector layer  426  rather than the metallic back reflector  446 . The light ray paths between layers are quite similar, and the performance is shown in Table 4. 
   In a further variation on the embodiment of  FIG. 40 , the back reflector layer in  FIG. 46  is the BEF type back reflector layer  426  rather than the metallic back reflector  446 . The light ray paths are quite similar, and the performance is shown in Table 4. 
   Another form of the invention is shown in  FIG. 47 , in which a polarization splitting layer  470  is disposed at the input to the base layer  400 . In this embodiment, the polarization recycling “cavity” is formed by the lamp cavity  404  and the polarization splitting layer  470 . The input light  402  thus is processed by the light cavity  404  and the polarization splitting layer  470  to produce light  476  of polarization state “a”. In order to achieve this result, the polarization splitting layer  470  most preferably is positioned to have its pass axis either substantially parallel, or perpendicular to the direction of the symmetry axis of the base layer  400 . This arrangement keeps light in the base layer  400  substantially in one polarization state as it travels down the base layer  400 . Therefore, the input light  402  (the light emitted by the lamp  406 ), leaves the lamp  406  in an unpolarized state and ultimately encounters the polarization splitting layer  470 . A substantial part of the light  402  is transmitted as light  476  of polarization state “a”, while the remainder of polarization state “b” is reflected or recycled back into the lamp cavity  404  for eventual conversion and output as the light  476  of polarization “a”. The performance of this device  10  is shown in Table 4. 
   In a variation on the embodiment of  FIG. 47 , the arrangement of  FIG. 48  further includes the feature of a polarization converting layer  478  on the lamp cavity side of the polarization splitting layer  470 . The light ray paths in this embodiment are quite similar to the paths shown in  FIG. 46 . The performance results are shown in Table 4. 
   In another variation on the embodiment of  FIG. 33 , the device  10  of  FIG. 49  does not include the redirecting layer  416 , the base layer  400  is a textured light pipe, rather than one having optically smooth surfaces, and a film based reflective polarizer layer  480  is substituted for the interference layer  410  to split and reflect the light polarization states. The effect of the texture on (or equivalently within) the base layer  400  is to diffuse (or misdirect) the light  402  as it travels down the base layer  400  and also as it exits and is recycled through the base layer  400 . The textured base layer  400  can, for example, be created by spraying a curable coating onto a smooth version of the base layer  400  or by using a textured mold to create the textured form of the base layer  400 , or by dispersing submicron to micron size scattering centers within the layer  400 . These textures operate such that any ray path undergoes small misdirection. This interaction involves a weak scattering event and while changed by this, the ray path is not changed drastically. In this context, the texture refers either to slope variations on its surface of the base layer  400  or refractive index variations on or within the base layer  400 , either of which will deviate the ray path by an amount on the order of fractions of a degree to degrees from its path in the absence of such texture. This embodiment was directed to evaluation of the losses arising from the redirecting layer  416  processing broad angle illumination provided by the polarization elements of the device  10 . As can be noted by reference to Table 6, the elimination of the redirecting layer  416  results in improved efficiency. The light ray paths followed are quite similar to the paths in  FIG. 33  except the light rays exit the device  10  at wider angles without use of the redirecting layer  416 . 
   In another form of the embodiment of  FIG. 49 , the device  10  of  FIG. 50  does not include the textured form of the base layer  400  described previously. The comparative performance is shown in Table 6, and the light ray paths are quite similar to that of  FIG. 49 . It should be noted that the data of Tables 4 and 6 cannot directly be compared because a different reference architecture was used in each table. One can roughly compare the data of one table to another by multiplying the data of Table 4 by 1.17 to compare with Table 6 data. 
   In another form of the embodiment of  FIG. 49 , the device  10  of  FIG. 51  uses the metallic back reflector  446  rather than the BEF-type back reflector layer  426 . In addition, the layer  426  is laminated to the converting layer  422  without an air layer. The light ray paths are quite similar to those in  FIG. 49 , and the comparative performance is shown in Table 6. 
   In a variation on the embodiment of  FIG. 51 , the device  10  of  FIG. 52  does not use a textured form of the base layer  400 . The light ray paths are very similar, and the comparative performance is shown in Table 6. 
   In another form of the embodiment of  FIG. 33 , the device  10  of  FIG. 53  uses the reflective polarizer layer  480  rather than the interference layer  411 ; and a textured form of the base layer  400  is used. The light ray paths are quite similar, and the comparative performance is illustrated in Table 6. 
   In another form of the invention shown in  FIG. 54  the device  10  is similar to the one shown in  FIG. 53  except the redirecting layer  416  is switched with the reflective polarizer layer  480  (a polarization splitter like the interference layer  411 ). As a result of this rearrangement, the light ray paths are quite 
                   TABLE 6                  Comparison of Various Architectures to Basic Tapered Luminare with a Structured Back Reflector.                                                         Base               g Luminance   g Range   g Total           Redirecting   Layer   Back   Reflective       (Brightness   (Range   (Usable       FIG.   Layer   (B. Layer)   Reflector   Polarizer   Rotator   Gain)   Gain)   Gain)                                                         49   No   Textured   Structured   Over B. Layer   Under B. Layer   0.71   1.92   1.37       50   No   Smooth   Structured   Over B. Layer   Under B. Layer   0.68   2.02   1.38       51   No   Textured   Specular   Over B. Layer   Under B. Layer   0.67   2.41   1.62       52   No   Smooth   Specular   Over B. Layer   Under B. Layer   0.77   2.36   1.81       53   Yes   Textured   Structured   Over B. Layer   Under B. Layer   1.10   1.09   1.2       54   Yes   Textured   Structured   Over Nfilm   Under B. Layer   0.97   1.13   1.1       55   Yes   Textured   Structured   Over B. Layer   Under Refle   0.96   1.16   1.11       56   Yes   Textured   Structured   Over B. Layer   Laminated to   1.06   1.14   1.21       57   Yes   Textured   Structured   None   None   1.00   1.00   1.00       58   Yes &amp;   Textured   Structured   Over   None   1.08   1.1   1.19           Dfilm           Dfilm @ 45       59   Yes &amp;   Textured   Structured   Over   None   1.04   1.08   1.12           Dfilm           Nfilm @ 45       60   Yes &amp;   Textured   Structured   Over   None   1.15   1.09   1.25           Dfilm           Wedge @ 45                    
different. The input light  402  to the base layer  400  can, as in the embodiment of  FIG. 53 , be coupled out through the top surface  432  of the base layer  400  with some of the light  405  of polarization “a” output through the redirecting layer  416  and the reflective polarizer layer  480 . Some of the light  405  of polarization state “b” is reflected as light  482 , passing through the base layer  400 , the air layer  420 , the converting layer  422 , the air layer  424  and is reflected by the BEF type back reflector layer  426 . Upon return passage through the converting layer  422 , the light  482  changes to light  484  of polarization state “a” and output to the viewer through the base layer  400 , the redirecting layer  416  and the reflective polarizer layer  480 . The exchanged position of the redirecting layer  416  and the reflective polarizer layer  480  also results in the redirecting layer  416  operating on wide angle light traveling in both the forward and reverse directions as shown in  FIG. 54 . The forward traveling light passes through the base layer  400  in a manner like that shown in  FIG. 52 , but the reverse traveling light passes backward through the base layer  400 . Ultimately, some of this light will even recycle through the lamp cavity  409 . Several example overlapping light paths are illustrated in  FIG. 54 , but numerous other light paths also exist. The performance of this device  10  is shown in Table 6.
 
   In another variation on the embodiment of  FIG. 53 , the device  10  in  FIG. 55  places the converting layer  422  above the base layer  400 . The light ray paths are similar to those of  FIG. 53  except the polarization conversion occurs above the base layer  400 . For example, the light  402  is coupled out of the top surface  432  as the light  405  passes through the converting layer  422  to reverse polarization states, and the light  409  of polarization state “a” is output through the reflective polarizer layer  480  and the redirecting layer  416 . Of more interest is light  482  of polarization state “b” reflected by the reflective polarizer layer  480  which passes through the air layer  407 , the converting layer  422 , the air layer  485 , the base layer  400 , the air layer  420 , reflected by the BEF type back reflector layer  426  and returns through these layers to be converted by the converting layer  422  to light  484  of polarization state “a” for output. The comparative performance of the device  10  is shown in Table 6. 
   In another variation on the embodiment of  FIG. 53 , the device  10  of  FIG. 56  has the converting layer  422  laminated to the base layer  400 . The light ray paths are thus quite similar, and the performance of this embodiment is shown in Table 6. 
   In another form of the embodiment of  FIG. 35 , the device  10  of  FIG. 57  uses a textured form of the base layer  400 . The light ray paths are quite similar and the performance is shown in Table 6. 
   In another form of the invention illustrated in  FIGS. 58-60 , operation of the device  10  as a polarized luminaire is shown without use of a separate form of the converting layer  422 . This is accomplished by light reflection past the Brewster angle, polarization conversion upon off-angle metallic reflection events, polarization due to total internal reflection and internal birefringence in a stretched film base layer of the primitive redirecting layer  416  and the BEF type back reflector layer  426 . Each of these mechanisms can contribute to polarization conversion when we position the reflective polarizer layer  480  at the same angle to the symmetry axis of the device  10 . For simplicity, a 45° angle is chosen for the pass axis of the polarizer layer  480 . 
   In  FIG. 58  is shown the device  10  having substantially unpolarized light  486  traveling along the base layer  400  until its angle increases to exceed θ c  at one of the top surface  432  or the bottom surface  457 . The light  486  then passes through the air layer  407 , the prismatic redirecting layer  416  which changes the angle of the light  486 ; and after passing through air layer  487 , another redirecting/diffuser layer  488  broadens the angular distribution of the light  486 . The light  486  then passes through air layer  489  and encounters a reflective polarizer layer  490  which acts as a polarization splitting layer. This polarizer layer  490  is oriented so that the pass-axis is at 45° to the symmetry axis of the device  10  which in this particular case is the primary propagation direction of the device  10 . The polarizer layer  490  splits the light  486  into two components: light  492  of one state “a” is preferably passed and light  494  of state “b” is preferably reflected. The light  494  is thus recycled back in a broad angular distribution by passing through the redirecting/diffuser layer  488 . This broad angular distribution of the light  494  has a variety of recycling paths. For example, some of the light  494  will recycle through the redirecting/diffuser layer  488  in the general manner shown in  FIG. 54 . Polarization conversion in this case can occur by interaction through Fresnel reflection from the faces of the base layer  400 , total internal reflections in the redirecting/diffuser layer  488 , conversion due to birefringence in the redirecting/diffuser layer  488 , metallic reflection effects and diffuse scattering in the lamp cavity  404 . The light  494  traveling this path can ultimately recouple through the redirecting/diffuser layer  488  and back through the other components of the device  10 . The wide variety of recycled rays ultimately reach the polarizer layer  490  with some polarization conversion accumulated resulting in system gain. The performance of this device  10  is shown in Table 6. 
   In a variation on the embodiments of  FIG. 58 , the device  10  in  FIG. 59  has the polarizer layer  490  positioned below the redirecting/diffuser layer  488  so that light rays recycle in the general manner similar to those in the embodiment of  FIG. 54  without the broad angle diffusion effects present in the embodiment of  FIG. 58 . This embodiment in  FIG. 59  also takes advantage of off-angle reflections and scattering to convert polarization state of the light  486  rather than the explicit polarization converting layer  422  of  FIG. 54 . The performance of this embodiment is shown in Table 6. 
   In another embodiment similar to that of  FIG. 53 , the device  10  of  FIG. 60  accomplishes polarization conversion by off-angle reflections since the reflective polarizer layer  480  is at a 45° angle relative to the symmetry axis of the device  10 . The device  10  thus does not include the converting layer  422  and does add the redirecting/diffuser layer  488  with an intervening air layer  491 . The performance of this device  10  is shown in Table 6. 
   Birefringent Layers in Luminaire Systems 
   A birefringent material can be used to advantage in the polarized light luminaire system  204  discussed hereinbefore. In the embodiment illustrated in  FIG. 31A , the first layer  214  can be a birefringent material of index n 2  with two different optical indices n 2α  and n 2β  for the light  212  of two different polarization states “a” and “b”, both indices being less than one. This light  212  encounters the layer  214  near the respective critical angles for these two polarization states,
 
θ cα =arcsin( n   2α   /n   1 )  (15)
 
and
 
θ cβ .=arcsin( n   2β   /n   1 )  (16)
 
The conditions of Equation (10) must be satisfied for n 2  equal to both n 2α  and n 2β , independently. The light  212  of both polarization states decreases its angle of incidence by an angle  2 Φ for each cyclic reflection from the first surface  208  and the second surface  210  as described previously. In this embodiment n 2α &gt;n 2β  and therefore θ cα &gt;θ cβ . As the incidence angle for both polarization states decreases, the light  212  of both polarization states can encounter the interface with the birefringent first layer  214  with the light having an incidence angle less than the first critical angle θ cα , but exceeding the second critical angle θ cβ . Therefore, light  218  of the first polarization state is at least partially transmitted through the birefringent first layer  214 , while the light  220  of the second state is preferentially reflected by total internal reflection. This reflected second-state light  220  and the residual first-state light  218  continue to decrease their angles of incidence with successive reflections. The light  218  of the first polarization state is transmitted at each successive encounter with the interface between the first layer  214  and the base layer  206 . The light  220  of the second state continues to undergo total internal reflection at this interface until its angle of incidence becomes less than the second critical angle θcβ, at which point this second-state light  220  also is at least partially transmitted through the birefringent first layer  214 . By virtue of this mechanism and of the difference in indices n 2α  and n 2 β, the light exiting the birefringent first layer  214  has a different angle distribution for the two polarization states “a” and “b”.
 
   Birefringent materials can in general include crystalline materials having an anisotropic index of refraction. A preferred material is a stretched polymeric film such as stretched fluorinated film. The stretching orients the film and makes the index of refraction different along that direction. Elsewhere we give birefringence values of these stretched fluoropolymer film with Δn ranging from 0.030-0.054. Other films are PVA (Polyvinylalcohol). Polypropylene, Polyolefin or even Polyester (Mylar). Mylar is actually biaxial, but may still be used to rotate polarization. More traditional uniaxial birefringent materials are: Calcite and Quartz. These are not as practical as the stretched films. In practice the two polarization states are well-separated only if the two indices are sufficiently different. This condition may be expressed as,
 
θ cα ≧θ cβ sφ  (17)
 
where s must be at least 1 and is preferably greater than four. This condition may be achieved, for example, using uniaxially oriented fluoropolymer material for the birefringent layer, acrylic polymer for the base layer  206  and reasonable values of Φ (between one and one-and-a-half degrees is typical for notebook computer LCD backlighting).
 
     FIG. 31B  is like  FIG. 31A , but the redirecting layer  224  has been added; and the preferred embodiment uses air for the layer  207  having index n 3 . The light  218  and the light  220  are output from the system  204  at different angles. 
     FIG. 31C  illustrates another variation on  FIGS. 31A  and B, but the redirecting layer  224  comprises a flat faceted reflective layer  340 . The light  218  and also the light  220  are directed to a converting layer  346  which transmits the light  218  without substantially changing its polarization state; however, the converting layer  346  does convert the light  220  to the light  218  of the desired first polarization state. The converting layer  346  shown in  FIG. 31C  has a construction that operates to convert the light polarization only within the angular range occupied by the light  220 . The converting layer  346  thus utilizes the schematically illustrated angular separation of the light  218  and the light  220  to carry out the conversion of the light  220  to the light  218  without converting the light  218  to the light  220 . 
   In the embodiments of  FIGS. 31D  and E, the reflected form of the light  220  is returned to the interface of the base layer  206  with the birefringent first layer  214 . This is accomplished by virtue of total internal reflection of the light  220  together with passing at least twice through the converting layer  346 , which results in at least partially converting the light  220  into the light  218  of the first polarization state. Since this light  218  has an incidence angle less than the first critical angle θ cα , the light  218  is transmitted through the interface between the base layer  206  and the first layer  214 . This light  218  can then be reflected or transmitted by the redirecting layer  224 , depending on the particular nature of the redirecting layer  224 . The alternatives of transmitted and reflected light are shown in phantom in  FIGS. 31D  and E. Further, in the embodiment of  FIG. 31D , the converting layer  346  is on the same side of the base layer  206  as the birefringent first layer  214 . The converting layer  346  is also disposed between the base layer  206  and the birefringent first layer  214 . The embodiment of  FIG. 31E  shows another variation on  FIG. 31D  with the converting layer  226  and the birefringent first layer disposed on opposite sides of the base layer  206 . 
   In the embodiment of  FIG. 31F  the system  204  is similar to the embodiment of  FIG. 31D , but the redirecting layer  224  comprises a layer of facets  311 . In the embodiment of  FIG. 31G , the system  204  further includes the LCD layer  302 , the matching layer  232 , and the diffuser layer  304  is disposed in a spatial position after the light  218  has passed through the LCD layer  302 . The redirecting layer  224  comprises the layer of microprisms  251  having flat faces and a metallic coating  342  for high light reflectivity. Also shown is the angle transformer layer  238  to control the spatial distribution of the light  253  output from the system  204 . The embodiment of  FIG. 31H  is similar to the embodiment in  FIG. 31G , but the system  204  uses curved facets  345  for the redirecting layer  224  with facet angles adjusted at different spatial locations to focus the output light  250  onto a preferred viewing zone. The angle transformer  238  is illustrated as a CPC. 
   Light Diffuser after LCD Layer Processing 
   In the embodiments shown in  FIGS. 12N and 12O  the LCD display  216  or  236  provides an output light to the viewer. In a further improvement of these embodiments a post diffuser layer  350  is disposed in the path of the light  250  output from the LCD layer  302  (see  FIGS. 32A  and B). In the preferred embodiments shown in these figures, the general operation is similar to the embodiments illustrated in  FIGS. 26B ,  28 D and E;  29 A and B and  31 G, but without any of the polarization filter layers  216 . As described hereinbefore, it is advantageous to provide light to the LCD layer  302  in a collimated angular range, preferably substantially perpendicular to the LCD layer  302  to optimize the image output therefrom. The use of the post diffuser layer  350  allows the output light  253  to provide an image to viewers over a wide angular range without compromising light contrast and color fidelity. 
   One aspect which is preferably controlled in a system including the post diffuser layer  350  is the width in the xz-plane of the angular distribution transmitted through the LCD layer  302 . The output angular distribution preferably has a full width less than 
                   Δθ     ρ   ⁢           ⁢   d       =     2   ⁢       n     ℓ   ⁢           ⁢   cd       ⁡     (     1   d     )                 (   18   )               
and a full width less than half of this value is even more preferred. In this equation Δθ pd  is in radians, N LCD  is the average index within the LCD layer  302 , □ is the repetition period of display pixel rows in the z-direction, and d is the thickness of the LCD layer  302 . For a typical LCD used in notebook computers, n LCD  is approximately 1.5, l=0.3 mm, and d=3 mm. For this example, Δθ pd  is preferably less than 18 degrees, and a full-width of nine degrees or less is even more preferred. By comparison, Equation (8) can be used to calculate the output angular width of the current invention using a flat-facet prismatic redirecting layer, such as is shown in  FIG. 32A  (layer  359 ) or in  FIG. 28B  (layer  262 ). For a typical notebook computer backlighting system, Φ=1.3 degrees and n=1.49. In this example, Equation (8) gives an output angular distribution of eighteen degrees.
 
     FIG. 32A  shows a preferred arrangement of the system  204  having a parallel form of the post diffuser  350  disposed overlying the LCD layer  302 . Also included is a holographic angle transformer  364  disposed on the back surface  211 . 
   In another embodiment shown in  FIG. 32B  a refracting/internally reflecting layer  360  includes curved facets  362  in order to narrow the angular distribution in the xz-plane of light  364  directed through the LCD layer  302 , and thereby to improve image-quality by reducing parallax at the post diffuser layer  350 . The embodiment has the curved reflecting facets  362 , but flat refracting facets can achieve the desired function as well, as shown in  FIG. 32C . In either case, the curved facets  362  preferably have a focal length less than the repetition period between each of the facets  362 . The angular distribution in the xz-plane is preferably narrowed beyond the width given in Equation (8), and is most preferably narrowed beyond the width given in the equation above. In addition, the facet angles of the redirecting layer  224  are arranged to focus the light output from different portions of the system  204  onto a preferred viewing zone. This figure also shows the micro-prismatic angle-transforming layer  274 . 
   In  FIG. 32C  is shown a variation on the embodiment of  FIG. 32B . In the system  204  an LCD layer arrangement  370  differs from the prior art LCD layer arrangement  310  illustrated in  FIG. 30 . In particular, a parallel light diffuser layer  372  (such as a holographic diffuser) is disposed between the LCD layer  302  (layer  316  in  FIG. 30 ) and the second polarization filter layer  322  (layer  314  in  FIG. 30 ). This arrangement enables the second polarization filter layer  322  to reduce the glare which can otherwise be caused by ambient light being reflected by the diffuser layer  372 .  FIG. 32C  further shows a light redirecting layer  374  having curved refracting facets  376  which perform the same angle narrowing function as the curved reflecting facets  362  shown in  FIG. 32B . 
   The following example illustrates a measurement system and method for various ones of the device  10 . 
   Example 
   The performance of the various devices  10  was quantified by introducing a concept of useful system gain. The light output distribution from the devices  10  can be approximated by the sum of a diffuse Lambertian background and a one dimensionally collimated beam consisting of a limited angle Lambertian distribution. In this model, the illuminance emitted into a limited angle (I imited ) from the luminaire device  10  can be expressed in terms of the peak luminance (L max ) of the total distribution, fraction of the illuminance in the diffuse Lambertian background (α), and the width of the limited angle Lambertian distribution specified by the limiting angles (θ + ,θ − ) in the form 
   
     
       
         
           
             I 
             Limited 
           
           = 
           
             
               
                 
                   sin 
                   ⁡ 
                   
                     [ 
                     
                       θ 
                       + 
                     
                     ] 
                   
                 
                 - 
                 
                   sin 
                   ⁡ 
                   
                     [ 
                     
                       θ 
                       - 
                     
                     ] 
                   
                 
               
               
                 1 
                 + 
                 
                   
                     1 
                     2 
                   
                   ⁢ 
                   
                     α 
                     
                       ( 
                       
                         1 
                         - 
                         α 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         sin 
                         ⁡ 
                         
                           [ 
                           
                             θ 
                             + 
                           
                           ] 
                         
                       
                       - 
                       
                         sin 
                         ⁡ 
                         
                           [ 
                           
                             θ 
                             - 
                           
                           ] 
                         
                       
                     
                     ) 
                   
                 
               
             
             ⁢ 
             
               L 
               Max 
             
           
         
       
     
   
   This is a useful quantity as it represents the total illuminance that can be redistributed using various redirecting layers, such as angle transforming films and diffusers. Although the fraction of the total illuminance in the diffuse background can be quite large, the majority of the peak brightness is typically due to the limited angle light emitted by the device  10  due to the much smaller solid angle covered by the illuminance in the limited angular range case. 
   This idea was applied to a real device  10  by assuming that the +/−angles specified in the formula were the half-luminance points measured using a spot-photometer  498 . For each set of measurements we measured the maximum brightness, and the angular location of the half-luminance points. The system  500  used to perform the measurements is shown in  FIGS. 61A  and B. A few different diffusers were tried to vary location of the half-luminance points while maintaining the same illuminance. Fitting this model to the data yielded a value for the fraction of power in the diffuse background. We found this value to be 60.1% for the basic form of the device  10  used in our experimental work.  FIG. 62  shows the measured data and fitted curves for a basic form of the device  10 . 
   In the remainder of our work we quantified the performance of the device  10  by developing a set of gain factors based on the illuminance estimate above. These gain factors were the total system gain (g total ), the brightness gain (g luminance ), and the gain due to an increase in the solid angle of the illumination leaving the luminaire (g range ). These were given in terms of the measured luminance (L ref ), and an angular range factor (R u ) defined below. The highly restricted angle of illumination was only in a single direction of the device  10 , so we used the one-dimensional formulas shown as the basis of our analysis. In particular we defined: 
   
     
       
         
           
             g 
             total 
           
           = 
           
             
               g 
               luminance 
             
             ⁢ 
             
               g 
               range 
             
           
         
       
     
     
       
         
           
             g 
             luminance 
           
           = 
           
             
               L 
               sample 
             
             
               L 
               ref 
             
           
         
       
     
     
       
         
           
             g 
             range 
           
           = 
           
             
               R 
               sample 
             
             
               R 
               ref 
             
           
         
       
     
     
       
         
           
             R 
             u 
           
           = 
           
             
               
                 sin 
                 ⁡ 
                 
                   [ 
                   
                     θ 
                     u 
                     + 
                   
                   ] 
                 
               
               - 
               
                 sin 
                 ⁡ 
                 
                   [ 
                   
                     θ 
                     u 
                     - 
                   
                   ] 
                 
               
             
             
               1 
               + 
               
                 
                   1 
                   2 
                 
                 ⁢ 
                 
                   α 
                   
                     ( 
                     
                       1 
                       - 
                       α 
                     
                     ) 
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           θ 
                           u 
                           + 
                         
                         ] 
                       
                     
                     - 
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           θ 
                           u 
                           - 
                         
                         ] 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
   
   Operationally, these measurements were made by dividing a luminaire device in two halves  502  and  504  (See  FIG. 61B ), both driven by the same CCFT lamp, and with the sample light-pipe. For those measurements that required coatings on or laminations to the light pipe, were laminated or coated only to half of the light-pipe. This method was adopted for stability reasons, especially stability in the output of the CCFT lamp. We believe that the effect, if any, of this half-luminaire measurement approach was to penalize our gain values. Since our goal was to demonstrate attainable gains, such a potential penalty was acceptable. 
   To obtain the final gain values reported in the tables, the observed values were collected by the gains measured by making both the half-luminaires  502  and  504  of the same construction. This was to correct for a small side to side dependence that we observed. These corrected gains (g corrected ) were calculated from gains of measured samples (g measured ) and calibration gains (g calibration ) measured with sides of the half-luminaire  502  in the reference configuration by just
 
 g   corrected   =g   measured   /g   calibration  
 
   Using this approach, a variety of luminaires were measured using a Photo Research Pritchard Spot Photometer. To do the measurement, the device  10  was placed on a stand equipped with a rotation stage aligned so that during the rotation our measurement spot was stationary (see  FIG. 61A ). Once the lamp in the luminaire at the center of each of the half-luminaires  502  and  504  (see  FIG. 61B ). For each measurement, a linear polarizer was used in front of the photometer  498  aligned to pass the maximum amount of light. For most of the measurements, this direction was horizontal or vertical with respect to the device  10  and instrument, so the internal polarizers were used in the instrument for these cases. For each of these halves, found the maximum brightness was formed and then the angular locations of the half-brightness points by rotating the device  10  about a rotation axis. 
   While preferred embodiments of the inventions have been shown and described, it will be clear to those skilled in the art that various changes and modifications can be made without departing from the invention in its broader aspects as set forth in the claims provided hereinafter.