Abstract:
A method for manufacturing a collimating device is disclosed herein. In one embodiment the method includes a step of constructing a reflective layer. After the reflective layer is constructed, a step of constructing an optical element layer follows, including a step of forming an array of microstructures in the optical element layer. Next, the array of microstructures is abutted against the reflective layer. Heat and pressure are then applied to the optical element layer to puncture the reflective layer and penetrate a predetermined distance through the reflective layer. Sub-assemblies are also defined, wherein optical elements are coupled to prevent light loss.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application is a continuation-in-part of U.S. application Ser. No. 11/194,360 filed on Aug. 1, 2005, now U.S. Pat. No. 7,345,824, which is a continuation-in-part of U.S. application Ser. No. 10/108,296 filed on Mar. 26, 2002, now abandoned, a continuation-in-part of U.S. application Ser. No. 10/688,785 filed on Oct. 17, 2003, now U.S. Pat. No. 7,428,367, and claims the benefit of priority of U.S. Provisional Application No. 60/600,272 filed on Aug. 10, 2004. 

   FIELD OF INVENTION 
   The present application relates to both (1) transflective structures and (2) light collimating structures. In particular, the present application relates to a method of making a reflective layer for transflective films and light collimating films. 
   BACKGROUND 
   Light collimating films, sometimes known as light control films, are known in the art. Such films typically have opaque plastic louvers lying between strips of clear plastic. U.S. Pat. No. Re 27,617 teaches a process of making such a louvered light collimating film by skiving a billet of alternating layers of plastic having relatively low and relatively high optical densities. After skiving, the high optical density layers provide light collimating louver elements which, as illustrated in the patent, may extend orthogonally to the surface of the resulting louvered plastic film. U.S. Pat. No. 3,707,416 discloses a process whereby the louver elements may be canted with respect to the surface of the light collimating film. U.S. Pat. No. 3,919,559 teaches a process for attaining a gradual change in the angle of cant of successive louver elements. 
   Such light collimating films have many uses. U.S. Pat. No. 3,791,722 teaches the use of such films in lenses for goggles to be worn where high levels of illumination or glare are encountered. Such films also may be used to cover a backlit instrument panel, such as the dashboard of a car, to prevent undesired reflections in locations such as the windshield, or a backlit electronic device (e.g., a LCD computer screen or LCD TV). 
   U.S. Pat. No. 5,204,160 discloses light collimating films that are formed from a plastic film with a series of grooves formed therein. The grooves are filled with a light absorbing material or the sides and bottoms of the grooves may be painted with a light absorbing ink. 
   U.S. Patent Application Publication No. 2005/0259198 discloses light collimating devices and transflecting devices that include a layer having a plurality of three dimensional optical elements and a reflective layer. The reflective layer has apertures corresponding to the position and shape of the ends of the three dimensional optical elements. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings, structures are illustrated that, together with the detailed description provided below, describe exemplary embodiments of the claimed invention. 
     In the drawings and description that follows, like elements are identified with the same reference numerals. The drawings are not to scale and the proportion of certain elements may be exaggerated for the purpose of illustration. 
       FIG. 1  is a depiction of a vertical plane cross-section of one embodiment of an optical element; 
       FIG. 2  is a three-dimensional depiction of another embodiment of an optical element; 
       FIG. 3  is a three-dimensional depiction of one embodiment of an array of optical elements defined by cross channels; 
       FIG. 4  is a three-dimensional depiction of one embodiment of an array of optical elements defined by lenticular channels; 
       FIGS. 5A and 5B  are a perspective view and an exploded perspective view, respectively, of one embodiment of a light collimating device; 
       FIGS. 6A and 6B  are vertical plane cross-sections of one embodiment of a light manipulating device; 
       FIG. 7  is a front plan view of one embodiment of a micro-milling tool; 
       FIG. 8  is a front plan view of an alternative embodiment of a micro-milling tool; 
       FIG. 9  is a vertical plane cross-section of an alternative embodiment of a light manipulating device having a first and second immersion layer; 
       FIG. 10  is a vertical plane cross-section of an alternative embodiment of a light manipulating device having a spacing layer; 
       FIG. 11  is a vertical plane cross-section of an alternative embodiment of a light manipulating device with no immersion layer; 
       FIGS. 12A and 12B  are vertical plane cross-sections of alternative embodiments of a light manipulating device; 
       FIG. 13  is a three-dimensional depiction of one embodiment of an array of optical elements defined by lenticular channels and having additional shallow cuts in a top surface; 
       FIG. 14  is a simplified side view of one embodiment of a light collimating assembly; 
       FIG. 15  is a simplified side view of an alternative embodiment of a light collimating assembly; 
       FIG. 16  is a simplified side view of one embodiment of a light transflecting sub-assembly; 
       FIG. 17  is a simplified side view of an alternative embodiment of a light transflecting sub-assembly; 
       FIG. 18  is a simplified side view of one embodiment of a light transflecting and collimating sub-assembly; and 
       FIG. 19  is a simplified side view of an alternative embodiment of a light transflecting and collimating sub-assembly. 
   

   DETAILED DESCRIPTION 
   The following includes definitions of selected terms employed herein. The definitions include various examples and/or forms of components that fall within the scope of a term and that may be used for implementation. The examples are not intended to be limiting. Both singular and plural forms of terms may be within the definitions. 
   “Horizontal plane cross-section” as used herein, refers to a cross-section taken along a plane perpendicular to the direction in which light travels through the element. 
   “Tapered” as used herein, refers to a narrowing along either a linear or curved line in the vertical plane cross-section direction, such that horizontal plane cross-sections taken at different locations will have different areas. In other words, a tapered object will have a small area end and a large area end. 
   “Vertical plane cross-section” as used herein, refers to a cross-section taken along a plane parallel to the direction in which light travels through the element. 
   The present application relates to both (1) transflective devices and (2) light collimating devices. Light collimation is defined as taking the given angular distribution of a light source and increasing the peak intensity, which may be on-axis, by the process of narrowing that given angular distribution. 
   Light collimating effects can be accomplished by using an optical layer formed by a series of discrete tapered optical elements in combination with a reflecting layer having openings or apertures disposed therein, corresponding to the position and shape of the tapered ends of the optical elements. To perform a light collimating function, the optical element is tapered towards a light source, such that the optical element has a large area end and a small area end. In a light collimating device, the small area ends are light input ends and the large area ends are light output ends. 
   Transflecting devices and collimating devices are more fully described in U.S. patent application Ser. No. 11/194,360 (“the &#39;360 application”), now published as U.S. Publication No. 2005/0259198 and incorporated herein by reference. The &#39;360 application discloses light collimating devices and transflecting devices that include a layer having a plurality of three dimensional optical elements and a reflective layer. The reflective layer has apertures corresponding to the position and shape of the ends of the three dimensional optical elements. The present application discusses methods for making the three dimensional optical elements and aligning the optical elements with the apertures of the reflective layer. 
     FIG. 1  illustrates a vertical plane cross-section of one embodiment of an optical element  100 . The optical element  100  may be used as part of a light collimating device or as part of transflecting device. The optical element  100  includes a tapered end  110  and a broad end  120 . The optical element further includes sidewalls  130  configured to reflect and/or guide light. In the illustrated embodiment, the sidewalls are curved. The curved lines may be parabolic, circular, or defined by other known curves, or a combination thereof. In alternative embodiments, the sidewalls may be defined by straight lines or a plurality of straight and curved lines. 
   In one embodiment, light L enters the optical element  100  at one end and exits from the opposite end. Some light rays L strike the sidewalls  130  and are reflected. Other light rays (not shown) pass directly through the optical element  100  without striking a sidewall  130 . 
   When the optical element  100  is used as a collimator, light L enters the optical element  100  at the narrow end  110  from multiple directions. As the light L travels through the optical element  100 , it may impinge on the sidewall  130 . The sidewall  130  reflects the light L and focuses it an angle such that the light L emerges from the broad end  120  as a substantially uniform sheet. 
   When the optical element  100  is used as a transflector, light from a first source enters the optical element  100  at the broad end  120 . As the light travels through the optical element  100 , it may impinge on the sidewall  130 . The sidewall  130  reflects the light such that it emerges from the tapered end  110 . As is described more fully below and in the &#39;360 application, the optical element is used in combination with a reflective layer that reflects light traveling from a second source opposite the first source. 
     FIG. 2  illustrates a perspective view of one embodiment of an optical element  200  having a tapered end  210  and a broad end  220 . In this embodiment, the optical element is a discrete post and the tapered end  210  is a flat square. The broad end  220  of the optical element  200  is also square and the optical element has a square horizontal plane cross-section. In other embodiments (not shown), the ends and the horizontal plane cross-section may be a circle, a rectangle, or any curved or polygonal shape. 
     FIG. 3  illustrates one embodiment of an optical element array  300  (also referred to as an optical element layer). The illustrated optical element array is an exemplary 10×10 array of optical elements having square horizontal plane cross-sections, such as the optical element  200  illustrated in  FIG. 2 . In other embodiments, an optical element array can be of any desired size or include any desired number or arrangement of optical elements. As shown, the square cross-section allows for a high packing density of optical elements. As will be explained in more detail below, in one embodiment the optical element array  300  is made by micro-milling a first set of substantially parallel lenticular channels, then micro-milling a second set of substantially parallel lenticular channels that are substantially perpendicular to the first set of lenticular channels. 
     FIG. 4  illustrates an alternative embodiment of an optical element array  400 . In this embodiment, a plurality of optical elements  410  are defined by a plurality of lenticular channels  420 . The lenticular channels are substantially parallel to each other. In one embodiment, the lenticular channels  420  are formed by micro-milling. 
     FIGS. 5A and 5B  show exploded and assembled views, respectively, of a light collimating device that includes a light manipulating device  500 . The light manipulating device  500  includes an optical element layer  510  and a reflecting layer  520 . In the illustrated embodiment, the reflecting layer  520  is formed on an immersing layer  530 . In the illustrated embodiment, the optical element layer  510  is an array of optical elements formed by cross-channels, such as the optical element array  300  shown in  FIG. 3 . In an alternative embodiment, the optical elements of the optical element layer are formed by lenticular channels, such as the optical element array  400  shown in  FIG. 4 . 
   The reflecting layer  520  includes apertures (or openings)  540  which match the tapered ends of optical elements in the optical element layer  510 . In the illustrated embodiment, the apertures  540  are square shaped to correspond with square-shaped tapered ends of the optical elements. In alternative embodiments (not shown), the apertures are polygonal, circular, or any combination of curved and/or straight lines that correspond to the shape of the tapered ends of the optical elements. For example, in the case of optical elements formed by lenticular channels, the apertures of the reflecting layer would be elongated rectangles. 
   In one embodiment, the reflecting layer  520  is constructed of metal, such as nickel, gold, aluminum, silver, or other suitable metal. In other embodiments (not shown), the reflecting layer may be constructed of any reflecting substance. 
   Also shown in  FIGS. 5A and 5B  is a backlight B (such as one used in a LCD TV) having a surface S that simultaneously acts as an emitting and reflecting surface. Those familiar with the state of the art will recognize that this is a standard feature in LCD backlights. The reflecting feature allows for light recycling, a property that enhances performance. In the illustrated embodiment, the tapered ends of the optical elements are facing the backlight B, and thus light manipulating device  500  acts as a light collimator. As will be described further below, if the light manipulating device  500  is reversed, it acts as a transflector. 
     FIG. 6A  illustrates a vertical plane cross-sectional view of one embodiment of the light manipulating device  600 . In the illustrated embodiment, the light manipulating device  600  includes an optical element layer  610  having a plurality of optical elements  620 . Each optical element  620  has a tapered end  630  and a broad end  635 . The tapered end  630  has a width W e  and the broad end  635  has a width W 0 . In one embodiment, the width W e  of the tapered end  630  and/or the width W 0  of the broad end  635  are pre-selected. In another embodiment, described in more detail below, other dimensions are pre-selected and the width W e  of the tapered end  630  and/or the width W 0  of the broad end  635  are a function of those dimensions. In one embodiment, the width W e  of the tapered end  630  is selected to be 5 μm. In alternative embodiments, the width W e  of the tapered end  630  may be any dimension. 
   The optical elements  620  are defined by a plurality of channels  640 . Each channel has a bottom surface  650  and a pair of sidewalls  660 . In one embodiment, the channels  640  are formed by micro-milling. In the illustrated embodiment, the optical elements  620  may be formed by cross-channels, forming an array such as shown in  FIG. 3  or the optical elements  620  may be formed by lenticular channels, forming an array such as shown in  FIG. 4 . In one embodiment, the optical elements are formed by micro-milling a plurality of substantially parallel channels  640  by a tool. 
     FIG. 7  illustrates a front plan view of one embodiment of a tool  700  for micro-milling channels. In one embodiment, the tool has a bit  710  with a tip  720 . In one embodiment, the tool bit  710  is a diamond tool bit. In one embodiment, the tool bit  710  has a width W t  and a sidewall  730  having a shape defined by the equation:
 ( x+k   1 ) 2 +( y+k   2 ) 2 =( k   3 ) 2   (1) 
here x is the horizontal distance from a predetermined point external to the bit  710  and y is the vertical distance measured from the tip  720 . For exemplary purposes, the X-Y axes defining the curve of the bit  710  are as shown in  FIG. 7 . In one embodiment, k 1 =596.2 μm, k 2 =3.8 μm, and k 3 =622.26 μm. All dimensions are cited in microns for convenience. In alternative embodiments, other dimensions may be used.
 
   In an alternative embodiment, the above selected k values are scaled proportionally upwards. In one known embodiment, the k values are scaled proportionally upwards by a factor of 5 or less. In another alternative embodiment, the above selected k values are scaled proportionally downwards. In one known embodiment, the k values are scaled proportionally downwards by a factor of 5 or less. In an alternative embodiment, other values may be selected for k 1 , k 2 , and k 3 . 
   In one embodiment, the bit  710  has a circular horizontal plane cross-section. In this embodiment, the sidewalls  730  of the drill bit are symmetrical about a central radius. In an alternative embodiment, the bit  710  has a polygonal horizontal plane cross-section. 
     FIG. 8  illustrates an alternative embodiment of a tool bit  810 . In the illustrated embodiment, the tool bit  810  has a main body portion  820  having curved sidewalls. In one embodiment, the curved sidewalls are defined by equation (1) above. 
   In the illustrated embodiment, the tool bit  810  further includes a lower linear end  830  and an upper linear end  840 . The lower and upper linear ends  830 ,  840  each have sidewalls defined by a straight line. Linear ends limit the vertical angle of the sidewall, which has manufacturing benefits. In an alternative embodiment (not shown) the tool bit includes a lower linear end, but not an upper linear end. In another alternative embodiment, the tool bit includes an upper linear end, but not a lower linear end. 
   In one embodiment, the bit  810  has a circular horizontal plane cross-section. In this embodiment, the sidewalls of the drill bit are symmetrical about a central radius. In an alternative embodiment, the bit  810  has a polygonal horizontal plane cross-section. 
   Returning to the light manipulating device  600  of  FIG. 6A , the channels  640 , when milled with the tool  700 , will have the same dimensions as the tool  700 . In other words, the bottom surface  650  of the channel  640  will have a width equal to the width W t  of the tip  710  and each sidewall  660  will be a curve defined by equation (1) above. 
   In this embodiment, the origin of the X-Y axes is shown at the center of the broad end  635  of an optical element  620 . We may refer to the left and right sidewalls  660  of an optical element  620 , rather than refer to the sidewalls of a channel. It should be understood that an optical element may include more than a left and right sidewall. The number of sidewalls of an optical element is determined by the shape of the horizontal plane cross-section of the element. 
   Under the above stated conventions, we may use a modified equation (1) to define both the left and right sidewalls  660  of an optical element  620 . Equation (1) may be modified as such:
 
(| x|+k   1 ) 2 +( y+k   2 ) 2 =( k   3 ) 2   (2)
 
This modification expresses the symmetry of the optical elements  620  about the Y-axis. As with the tool, in one embodiment, W t =2.5 μm, k 1  =596.2 μm, k 2 =3.8 μm, and k 3 =622.26 μm.
 
   In an alternative embodiment, the above selected k values are scaled proportionally upwards. In one known embodiment, the k values are scaled proportionally upwards by a factor of 5 or less. In another alternative embodiment, the above selected k values are scaled proportionally downwards. In one known embodiment, the k values are scaled proportionally downwards by a factor of 5 or less. In an alternative embodiment, other values may be selected for k 1 , k 2 , and k 3 . 
   As shown in  FIG. 6A , the channel  640  has a depth defined as y d . At the top of the sidewall  660 , x has a value defined as x d  (or −x d ). The width of the tapered end W e  of the optical element  620  is therefore defined as:
 
W e =2x d   (3)
 
   With continued reference to  FIG. 6A , at the bottom of the sidewall  660 , y=0 and x has a value defined as x 0  (or −x 0 ). The width W 0  of the optical element  620  at the broad end  635  is therefore defined as:
 
W 0 =2x 0   (4)
 
   In one embodiment, the channels  640  are micro-milled such that the optical elements  620  form a regular array having a periodicity P. The periodicity P is defined as the horizontal distance between any point on an optical element, and an identical point on the adjacent optical element. In  FIG. 6A , the periodicity P is shown as measured from the right side of the broad end  635  of an optical element  620  to the right side of the broad end of the adjacent optical element. It should be understood that because the optical elements  620  have substantially the same dimensions and are arranged in a regular array, the periodicity P is constant, no matter what point is chosen as a measuring point. 
   When P is measured from the right side of the broad end  635  of an optical element  620  as described above, it follows that:
 
 P=W   t   +W   0   (5)
 
Substituting equation (4) into equation (5), it follows that:
 
 P=W   t +2 x   0   (6)
 
   As can be seen from above, the periodicity P, the width W t  of the channel  640  (or the width of the tip  710  of the tool  700 ), the half-width x 0  of the broad end  635  (or the width W 0  of the broad end  635 ), the half-width x d  of the tapered end  630  of the optical element  620  (or the width W e  of the tapered end  630  of the optical element  620 ), and the depth y d  of the channel  640  are all dependent variables. In one embodiment the width W t  of the channel  640 , the half-width x 0  of the broad end  635 , and the half-width x d  of the tapered end  630  of the optical element  620  are pre-selected. Additionally, in one embodiment, the width W t  of the channel  640  is selected as 2.5 μm, the half-width x 0  of the broad end  635  is selected as 26.05 μm, and the half-width x d  of the tapered end  630  of the optical element  620  is selected as 2.5 cm. In this embodiment, from equation (6) it follows that the periodicity P is 54.6 μm. Further, it follows from equation (2), when k 1 =596.2 μm, k 2 =3.8 μm, and k 3 =622.26 μm, then the depth y d  of the channel  640  is 165.8 μm. 
   In alternative embodiments, other values for the constants and the dependent values may be selected. In another alternative embodiment, the depth of the channels and/or the periodicity may be pre-selected in combination with other dependent variables. In such an embodiment, the remaining dependent variables could be determined based on equations (2)-(6). 
   After the optical elements  620  are formed in the optical element layer  610  of the light manipulating device  600 , a separate reflective layer  670  is formed. In one embodiment, the reflective layer  670  is less than 1 μm. In one known embodiment, the reflective layer  670  is thinner than 0.2 μm, just sufficient thickness and optical density to maximize reflectivity.  FIG. 6A  shows the reflective layer  670  separate from the optical element layer  610  to show that the reflective layer  670  may be formed separately before it is combined with the optical element layer  610 . 
   In one embodiment, the reflective layer  670  is formed on an immersion layer  680 . In one embodiment, the reflective layer  670  is formed directly on the immersion layer  680  by a sputtering process. In alternative embodiment, the reflective layer  670  is formed directly on the immersion layer  680  by a chemical vapor deposition process or any other known forming process. In another alternative embodiment, the reflective layer  670  is a thin, solid layer of reflecting material formed by a rolling process. 
   In one embodiment, after the reflective layer  670  is formed, it is placed in contact with the tapered ends  630  of the optical elements  620  of the optical element layer  610 . Then, a combination of heat and/or pressure of sufficient amounts is used to puncture the optical elements  620  through the reflective layer  670 , pushing aside portions of the reflective layer  670  that block or partially block either the sidewall  660  or the tapered end  630  of the optical element layer  610 , as shown in  FIG. 6B . 
   In this embodiment, the result is a light manipulating device  600  that (1) reflects light where the reflective layer  670  is intact and (2) transmits light through the optical elements  620  where the optical elements  620  have punctured the reflective layer  670 . 
   In the embodiment illustrated in  FIG. 6B , the reflective layer  670  is disposed on an immersion layer  680 . Because the reflective layer  670  is thin, the immersion layer  680  provides stability to and helps maintain the integrity of the reflective layer  670  during the piercing process. The immersion layer  680  is softer than the optical elements  620 . In one embodiment, the immersion layer  680  is a polymer film. In one embodiment, the immersion layer  680  is a pressure sensitive adhesive (PSA). In an alternative embodiment, the immersion layer  680  is a polymer with a low glass transition temperature (T g ) or a polymer that could be hardened after penetration by exposure to, for example, UV light. 
   In one embodiment the immersion layer  680  has an index of refraction equal to that of the optical element layer  610 . In another embodiment, the immersion layer  680  has an index of refraction lower than that of the optical element layer  610 . In yet another embodiment, the immersion layer  680  has an index of refraction higher than that of the optical element layer  610 . It should be understood that both the optical element layer  610  and the immersion layer  680  are light transmitting layers. 
   With continued reference to  FIG. 6B , the optical elements  620  puncture the reflective layer  670  and extend through the combined reflective layer  670  and into the immersion layer  680  a specified distance, defined as the penetration depth D. In the illustrated embodiment, the reflective layer  670  is located a vertical distance y r  above the bottom surface  650  of the channel  640 . This vertical distance y r  may be any distance less than the depth y d  of the channel  640 . Once the vertical distance y r  is selected, a corresponding half-width x r  of the optical element  620  at y r  can be determined from equation (2). In one embodiment, the vertical distance y r  is selected as 150 μm. From equation (2), when k 1  =596.2 μm, k 2 =3.8 μm, and k 3 =622.26 μm, it follows that the corresponding half-width x r  of the optical element  620  is 6.75 cm. 
   Additionally, a width W a  of the aperture of the reflective layer  670  can be determined. The width W a  of the aperture is defined as:
 
W a =2x r   (7)
 
Therefore, when the half-width x r  of the optical element  620  at y r  is 6.75 μm, it follows that the width W a  of the aperture of the reflective layer  670  is 13.5 μm.
 
   In one embodiment, the combined thickness of the reflective layer  670  and the immersion layer  680  exceeds the penetration depth D of the optical element  620 . In an alternative embodiment, the combined thickness of the reflective layer  670  and the immersion layer  680  does not exceed the penetration depth D of the optical elements  620 . In other words, in this embodiment, the tapered ends  630  of the optical elements  620  extend beyond the immersion layer  680 . The thickness of the immersion layer is limited only by manufacturing constraints of total penetration depth. 
     FIG. 9  illustrates a vertical plane cross-section of an alternative embodiment of a light manipulating device  900  having an optical element layer  910  and a reflective layer  920 . In the illustrated embodiment, an immersion layer  930  includes a first immersion layer  940  disposed on the reflective layer  920  and second immersion layer  950  disposed on the first immersion layer  940 , opposite the reflective layer  920 . In this embodiment, the first immersion layer  940  is softer than the optical element layer  910 , thereby facilitating penetration of the optical element layer  910  into the first immersion layer  940 . The second immersion layer  950  is constructed of a material sufficiently hard to stop the penetration. In one embodiment the second immersion layer  950  is as hard as the optical element layer  910 . In an alternative embodiment, the second immersion layer  950  is harder than the optical element layer  910 . In these embodiments, the thickness of the first immersion layer  940  is equal to the penetration depth of the optical element layer  910 . 
     FIG. 10  illustrates a vertical plane cross-section of an alternative embodiment of a light manipulating device  1000  having an optical element layer  1010 . In the illustrated embodiment, the light manipulating device  1000  includes a reflective layer  1020  and an immersion layer  1030 , similar to the reflective layer  670  and immersion layer  680  of the light manipulating device  600  illustrated in  FIG. 6 . In an alternative embodiment (not shown), the light manipulating device includes a first and second immersion layer, similar to the light manipulating device  900  illustrated in  FIG. 9 . 
   With continued reference to  FIG. 10 , the light manipulating device further includes a spacing layer  1040  disposed on the reflective layer  1020  on the side opposite the immersion layer  1030 . The spacing layer  1040  assists in pushing aside the reflective layer to maintain the integrity of the reflective layer  1020  during the piercing process. In one embodiment the spacing layer  1040  is constructed of a polymer. In one specific embodiment, the spacing layer  1040  is constructed of the polymer used to construct the immersion layer  1030 . 
   In one embodiment, the spacing layer  1040  has an index of refraction lower than that of the optical element layer  1010 . In one known embodiment, the spacing layer  1040  has an index of refraction sufficiently lower than the optical element layer  1010  such that total internal reflection occurs inside the optical element layer  1010 . 
   In one embodiment, the optical element layer  1010 , the immersion layer  1030 , and the spacing layer  1040  are all light transmitting layers. In an alternative embodiment, the spacing layer  1040  is not a light transmitting layer. 
   In one embodiment, the combined thickness of the reflective layer  1020 , the immersion layer  1030 , and the spacing layer  1040  exceeds the penetration depth D of the optical element layer  1010 . In an alternative embodiment, the combined thickness of the reflective layer  1020 , the immersion layer  1030 , and the spacing layer  1040  does not exceed the penetration depth D of the optical element layer  1010 . In other words, in this embodiment, the tapered ends of the optical elements in the optical element layer  1010  extend beyond the immersion layer  1030 . In all embodiments, the penetration depth exceeds the combined thickness of the reflective layer  1020  and the spacing layer  1040 . If the penetration depth did not exceed this combined thickness, the reflective layer  1020  would not be pierced. 
     FIG. 11  illustrates a vertical plane cross-section of an alternative embodiment of a light manipulating device  1100  having an optical element layer  1110 . In the illustrated embodiment, a reflective layer  1120  is disposed on a spacing layer  1130 . The optical element layer  1110  then punctures the combined reflective layer  1120  and spacing layer  1130 , such as described with relation to  FIGS. 6A and 6B . 
   In one embodiment, the light manipulating device  1100  is employed as illustrated in  FIG. 11 . In an alternative embodiment, an immersion layer (not shown) is added to the device  1100 , such that the device resembles the light manipulating device  1000  illustrated in  FIG. 10 . The immersion layer may be a liquid polymer that is poured on the device  1100  and then hardens, a semi-solid polymer that is formed around the ends of the optical element layer  1110 , or a solid polymer that is preformed to cover both the optical element layer  1110  and the reflective layer  1120 . 
   In one embodiment, the spacing layer  1130  has an index of refraction lower than that of the optical element layer  1110 . In one known embodiment, the spacing layer  1130  has an index of refraction sufficiently lower than the optical element layer  1110  such that total internal reflection occurs inside the optical element layer  1110 . 
   In one embodiment, the optical element layer  1110  and the spacing layer  1130  are both light transmitting layers. In an alternative embodiment, the spacing layer  1130  is not a light transmitting layer. 
     FIG. 12A  illustrates a vertical plane cross-section of an alternative embodiment of a light manipulating device  1200  having an optical element layer  1210 . In the illustrated embodiment, a reflective layer  1220  is disposed between an immersion layer  1230  and a spacing layer  1240 . The optical element layer  1210  then punctures the combined reflective layer  1220 , immersion layer  1230 , and spacing layer  1240 , such that the tapered ends of the optical elements extend beyond the immersion layer  1230  and are exposed. 
   In one embodiment, the light manipulating device  1200  is employed as illustrated in  FIG. 12A . In an alternative embodiment, a second immersion layer  1250  is added to the device  1200 , such as illustrated in  FIG. 12B . The second immersion layer  1250  may be a liquid polymer that is poured on the device  1200  and then hardens, or it may be a solid polymer that is preformed to cover both the optical element layer  1210  and the immersion layer  1230 . In one embodiment, the second immersion layer  1250  has the same index of refraction as the immersion layer  1230 . In an alternative embodiment, the second immersion layer  1250  has a different index of refraction from the immersion layer  1230 . 
   In one embodiment, the spacing layer  1240  has an index of refraction lower than that of the optical element layer  1210 . In one known embodiment, the spacing layer  1240  has an index of refraction sufficiently lower than the optical element layer  1210  such that total internal reflection occurs inside the optical element layer  1210 . 
   In one embodiment, the optical element layer  1210  and the spacing layer  1240  are both light transmitting layers. In an alternative embodiment, the spacing layer  1240  is not a light transmitting layer. 
   While the above descriptions applies to both arrays of optical elements formed by cross-channels (such as the array  300  illustrated in  FIG. 3 ) and arrays of optical elements formed by lenticular channels (such as the array  400  illustrated in  FIG. 4 ), in one embodiment, additional steps may be taken with arrays formed by lenticular channels to aid in the piercing of a reflective layer. As is understood in the art, a smaller surface area is more effective at piercing an object. Therefore,  FIG. 13  illustrates an array  1300  of optical elements  1310  defined by lenticular channels  1320 , wherein the optical elements  1310  further include shallow cross cuts  1330  defining square tops  1340 . A common term to describe this shallow cross cut is “nicking”. In alternative embodiments, the cross cuts define circular or polygonal tops or any top defined by curved and/or straight lines. 
   In one embodiment, the periodicity and depth of the cross cuts  1330  are calculated such that the piercing process will not leave unpierced regions in the remainder of the channel while simultaneously totally penetrating the immersion layer and the reflective layer. Unpierced regions are undesirable because they act as dead spots in the collimating device. An appropriate choice of these parameters allows the use of the piercing technique for manufacturing the reflective layer in a lenticular-channeled device. 
   With continued reference to  FIG. 13 , the cross cuts  1330  in the optical elements  1310  define a plurality of 5 μm square tops  1340 . In order for the cross cut region of the lenticular channels to penetrate the reflective layer, the vertical distance y c  between the base of the cross cut  1330  and the bottom surface of the lenticular channel  1320  must be greater than the vertical distance y r  between the reflective layer (as shown in  FIG. 6 ) and the bottom surface of the lenticular channel  1320 :
 
y c &gt;y r   (8)
 
   In one embodiment, the lenticular channel  1320  has a depth y d  of 165.8 μm, the vertical distance y r  between the reflective layer (not shown) and the bottom surface of the lenticular channel  1320  is 150 μm, and the vertical distance y c  between the bottom surface of the cross cut  1330  and the bottom surface of the lenticular channel  1320  is 160.8 μm. Further, instead of defining the vertical distance y c  between the bottom surface of the cross cut  1330  and the bottom surface of the lenticular channel  1320 , we may define a nicking depth D n  as the vertical distance from the bottom surface of the cross cut  1330  to the top surface of an optical element  1310 . In alternative embodiments, other values of y r  and y c  may be used. 
   In one embodiment, a cross cut of  1330  having a vertical depth of 160.8 μm relative to the cross channel  1330  is formed by using the tool  700  of  FIG. 7  at a depth 5 μm from the tip  720  of the bit  710 . In other words, the cross cut  1330  has a nicking depth D n  of 5 μm. To determine the periodicity of the cross cuts  1330 , the width of the tool at the nicking depth D n  must be calculated. The width of the tool at a specified distance above the tip  720  can be determined since the change in width is simply twice the difference in the values of x from the tip  720  to the nicking depth D n  of the cross cut  1330 . The difference between the two values of x can be calculated by substituting the values of y into equation (2) and subtracting the results. This difference when added to the width of the tool  700  at the tip  710  is equal to the width of the tool at the nicking depth D n . Therefore, when the nicking depth D n  is 5 μm, the two values of x are 26.05 μm and 26.0 μm. Thus the width of the of the cross cut  1330  at the top of the optical element  1320  is 5.1 μm. Accordingly, the cross cuts  1330  have a periodicity 10.1 μm when the depth of cut is 5 μm. 
   In another embodiment a tool of different shape. For example, the edge of the tool could be chosen to optimize the edge of the penetrator shape that is orthogonal to the channel in the lenticular design. 
   While the processes described thus far are directed to a method for micro-milling an optical element array, it should be understood that in manufacturing, other methods of making an optical element array may be employed. In one embodiment, the above described process is used to manufacture a master array. The master array is then used to create a negative mold. The negative mold may be used as an impact mold, an injection mold, or a blow mold to form optical element arrays. The master array may be constructed of metal, a hard polymer, or other known material of sufficient hardness to create a negative mold. Similarly, the negative mold may be constructed of metal, a hard polymer, or other known material. 
   In one embodiment, the negative mold is used to form a second master. The second master is then used to form a second negative mold. The second negative mold may be used as an impact mold, an injection mold, or a blow mold to form optical element arrays. In an alternative embodiment, the process is repeated for several generations and the final negative mold may be used as an impact mold, an injection mold, or a blow mold to form optical element arrays. 
   In an alternative embodiment, the optical element layer is formed by an electroforming process. In another alternative embodiment, a negative mold is formed by an electroforming process. 
     FIGS. 14-17  illustrate light manipulating devices, such as those illustrated in FIGS.  6  and  9 - 13 , in use as a collimator or transflector. 
     FIG. 14  illustrates a collimating device  1400  positioned adjacent a backlight B. The collimating device  1400  is one of a light manipulating device  600 ,  900 ,  1000 ,  1100 ,  1200 , or  1300  as shown in FIGS.  6  and  9 - 13 . The collimating device  1400  includes a reflecting layer having apertures formed therein to both transmit light from the backlight B and recycle light back to the backlight B. In this embodiment, the reflecting layer is formed on the side of an immersing layer facing an optical element layer. A more detailed description of collimators is included in the &#39;360 application and is incorporated herein by reference. 
   In one embodiment, the collimating device  1400  is optically coupled to the backlight B, thereby creating a sub-assembly with no air gaps between the collimating device  1400  and the backlight B. Optically coupling the elements eliminates unwanted loss of light. In an alternative embodiment (not shown), for manufacturing purposes, the collimating device  1400  is positioned adjacent the backlight B such that there is an air gap. 
     FIG. 15  illustrates an alternative embodiment of a collimating assembly  1500 . In this embodiment, a diffusing layer  1510  is positioned between a collimating device  1520  and a backlight B. In one embodiment, one side the diffusing layer  1510  is optically coupled to the collimating device  1520  and the opposite side of the diffusing layer  1510  is optically coupled to the backlight B, thereby creating an assembly  1600  with no air gaps. In an alternative embodiment (not shown), the diffusing layer  1510  is positioned between the collimating device  1520  and the backlight B such that air gaps exist. 
     FIG. 16  illustrates a transflective device  1600  positioned between a backlight B and an ambient light source A. The transflective device  1600  is one of a light manipulating device  600 ,  900 ,  1000 ,  1100 ,  1200 , or  1300  as shown in FIGS.  6  and  9 - 13 . The transflective device  1600  includes a reflecting layer having apertures formed therein to transmit light from the backlight B while reflecting light from the ambient light source A. In this embodiment, the reflecting layer is formed on the side of an immersing layer facing an optical element layer. A more detailed description of transflectors is included in the &#39;360 application and is incorporated herein by reference. 
   In one embodiment, the transflective device  1600  is optically coupled to the backlight B, thereby creating a sub-assembly with no air gaps between the transflective device  1600  and the backlight B. Such an embodiment eliminates unwanted loss of light. In an alternative embodiment (not shown), for manufacturing purposes, the transflective device  1600  is positioned adjacent the backlight B such that there is an air gap. 
     FIG. 17  illustrates an alternative embodiment of a transflective assembly  1700 . In this embodiment, a diffusing layer  1710  is positioned between a transflective device  1720  and a backlight B. In one embodiment, one side the diffusing layer  1710  is optically coupled to the transflective device  1720  and the opposite side of the diffusing layer  1710  is optically coupled to the backlight B, thereby creating an assembly  1700  with no air gaps. In an alternative embodiment (not shown), the diffusing layer  1710  is positioned between the transflective device  1720  and the backlight B such that air gaps exist. 
     FIGS. 18 and 19  illustrate sub-assemblies that combine both a collimator and a transflective device.  FIG. 18  illustrates one embodiment of a sub-assembly  1800  that includes the collimating device  1400  of  FIG. 14 , adjacent to a backlight B. The collimating device  1400  is also adjacent to a transflective device  1810 . The transflective device  1810  is one of a light manipulating device  600 ,  900 ,  1000 ,  1100 ,  1200 , or  1300  as shown in FIGS.  6  and  9 - 13 . In an alternative embodiment (not shown), the sub-assembly includes a collimating device having a diffusing layer, as illustrated in  FIG. 15 . 
   In the illustrated embodiment, the sub-assembly components are optically coupled such that there are no air gaps. In an alternative embodiment (not shown), for manufacturing purposes, the collimating device  1400  is positioned adjacent the backlight B such that there is an air gap. In another alternative embodiment (not shown), for manufacturing purposes, the transflective device  1810  is positioned adjacent the collimating device  1400  such that there is an air gap. In yet another alternative embodiment (not shown), for manufacturing purposes, the components are positioned such that there is an air gap between each component of the sub-assembly. 
     FIG. 19  illustrates one embodiment of a sub-assembly  1900  that includes the transflective device  1600  of  FIG. 16 , adjacent to a backlight B. The transflective device  1600  is also adjacent to a collimating device  1910 . The collimating device  1910  is one of a light manipulating device  600 ,  900 ,  1000 ,  1100 ,  1200 , or  1300  as shown in FIGS.  6  and  9 - 13 . In an alternative embodiment (not shown), the sub-assembly includes a transflective device having a diffusing layer, as illustrated in  FIG. 17 . 
   In the illustrated embodiment, the sub-assembly components are optically coupled such that there are no air gaps. In an alternative embodiment (not shown), for manufacturing purposes, the transflective device  1600  is positioned adjacent the backlight B such that there is an air gap. In another alternative embodiment (not shown), for manufacturing purposes, the collimating device  1910  is positioned adjacent the transflective device  1600  such that there is an air gap. In yet another alternative embodiment (not shown), for manufacturing purposes, the components are positioned such that there is an air gap between each component of the sub-assembly. 
   While the present application illustrates various embodiments, and while these embodiments have been described in some detail, it is not the intention of the applicant to restrict or in any way limit the scope of the claimed invention to such detail. Additional advantages and modifications will readily appear to those skilled in the art. Therefore, the invention, in its broader aspects, is not limited to the specific details, the representative apparatus, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the spirit or scope of the applicant&#39;s claimed invention.