Patent Publication Number: US-2007099478-A1

Title: Polymer sheet having surface relief features

Description:
BACKGROUND  
      1. Field of the Invention  
      The present invention relates to the manufacture of polymer sheets having surface relief features.  
      2. Description of the Related Art  
      Polymer sheets can be employed in a wide variety of applications including optical elements. Polymer sheets may be used, for example, in displays such as liquid crystal displays (LCDs) for computers, cell phones, personal digital assistants (PDAs), games, automobile and navigational instrumentation, and for other applications. Such displays may include a liquid crystal spatial light modulator to produce an image pattern. These displays may further comprise a system for backlighting the spatial light modulator. To control the direction of light propagating from the spatial light modulator, the display may also include prismatic films between the spatial light modulator and the backlighting system. Such a prismatic film comprises plastic having a surface that includes a plurality of grooves that form facets of small prisms. These small prisms or micro-prisms limit the angle of light transmitted through the prismatic film and can be used to establish the field-of-view of the display. The array of micro-prisms may also increase the brightness of the display by recycling light back toward the backlighting system if the light is directed outside the desired field-of-view. However, when a prismatic film comprising rows or columns of prisms structures is used with a spatial light modulator comprising pixels also arranged in rows and columns, the rows or columns of prisms can interfere with the rows and columns of the spatial light modulator and produce a Moiré pattern, an interference pattern seen when viewing the display screen. Adding a diffuser can help to reduce the Moiré effect. Similarly, introducing diffusing surface features on the surface of the prismatic film can also attenuate the Moiré effect.  
      Polymer prismatic films may be fabricated using a metal master having surface relief structure disposed thereon. The surface relief structure may be used to mold, extrude, emboss, or otherwise form prismatic surface structure in a polymer sheet. The surface relief structure on the master may be formed by cutting grooves in the master using diamond turning. Diamond turning, however, has limitations. Diamond turning techniques are not able to provide diffusing relief structures having certain shapes, such as diffusing features that are elliptical, in a random fashion superimposed on prismatic surface structure. This limitation in the formation of the master extends to the product produced by the master. Accordingly, a diamond turned master has difficulty forming randomized and elliptical surface features on prismatic films.  
      What is needed therefore are alternative methods for manufacturing surface relief structures in polymer sheets.  
     SUMMARY  
      One embodiment of the invention comprises a method of manufacturing a polymer sheet having surface relief features. This method comprises depositing a layer of fluid over a first surface. The fluid comprises a pre-polymer material comprising monomers, oligomers, or a mixture of monomers and oligomers. The method further comprises first exposing a plurality of spatially separated locations on the fluid to light such that the pre-polymer material locally cures and substantially solidifies at the locations. A portion of the monomers, oligomers, or monomers and oligomers in the pre-polymer material migrates to the locations from regions outside the locations. The method also comprises a second exposure of the fluid comprising pre-polymer material such that the regions outside the locations are cured and substantially solidified. The curing produces the polymer sheet having the surface relief features. The surface relief features are at the locations.  
      Another embodiment of the invention comprises a method of manufacturing a polymer sheet having surface relief features. This method comprises providing a layer of fluid comprising curable material. This layer of fluid has a surface. The method further comprises altering the height of the surface of the layer of fluid at spatially separated locations relative to the surrounding surface such that the locations correspond to the position of the surface relief features. The altering comprises curing the curable material at the locations differently than the surrounding surface.  
      Another embodiment of the invention comprises a method of manufacturing a polymer sheet having a contoured surface. This method includes providing a layer of curable material. A first set of surface relief structures is formed in the layer by contact. A second set of surface relief features is produced in the layer by optically curing the curable material. The curing of material at locations corresponding to the surface relief features is different than the curing outside of the locations. The first set of surface relief structures and the second set of surface relief features are selected to provide different optical effects when corresponding surface relief structures and surface relief features are formed in a transmissive medium or reflective surface.  
      Another embodiment of the invention comprises a method of manufacturing a polymer sheet having surface relief features. This method comprises providing a layer of curable material, first exposing a plurality of spatially separated locations on the curable material to electromagnetic radiation such that the material locally cures at the locations, and second exposing the curable material such that regions outside the locations are cured. The curing produces the polymer sheet having the surface relief features. The surface relief features are at the locations.  
      Another embodiment of the invention comprises a method of manufacturing a polymer sheet having surface relief features. The method comprises providing a layer of curable material having a surface and altering the height of the surface of the layer at spatially separated locations relative to the surrounding surface. The locations correspond to the position of the surface relief features. The altering comprises curing the material at the locations differently than the surrounding surface. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIGS. 1A and 1B  are schematic drawings that illustrate a photo-polymerization process wherein a pre-polymerized material is cured with light to obtain a polymer sheet.  FIG. 1C  shows a free volume region produced by a reduction in volume of the pre-polymerized material with polymerization.  
       FIGS. 2A-2D  are schematic drawings that illustrate a two-stage photo-polymerization process wherein first, a localized portion of a pre-polymerized material is cured by propagating light through an aperture in a mask, and second, surrounding portions of the pre-polymerized material are cured with the mask removed to obtain a surface feature.  
       FIG. 3  is a surface plot on x, y, and z axes showing the profile of a surface feature produced by the photo-polymerization process shown in  FIGS. 2A-2D  as modeled for a mask having a circular aperture.  
       FIGS. 4A-4C  are schematic drawings that illustrate a photo-polymerization process involving contacting a pre-polymerized material with a surface having surface relief structure thereon and curing the pre-polymerized material with light to obtain a polymer sheet having surface structure thereon.  
       FIGS. 5A-5C  are schematic drawings that illustrate a two-stage photo-polymerization process that involves first propagating light through a mask to polymerize localized regions of the pre-polymer material while contacting the pre-polymerized material with a surface having surface relief structure thereon and removing the mask and further curing the pre-polymerization material.  
       FIGS. 6A-6C  are schematic drawings that illustrate a photo-polymerization process similar to that shown in  FIGS. 5A-5C  used to form elliptical surface features disposed on a faceted surface.  
       FIGS. 7A and 7B  are schematic drawings that illustrate a replication process wherein the faceted surface structure having elliptical features thereon is used to form a prismatic structure with elliptically shaped diffusing features thereon.  
       FIG. 8  is a schematic drawing showing the prismatic structure in a display further comprising a spatial light modulator that is backlit.  
       FIG. 9A  is a schematic drawing that illustrates sandwiching a pre-polymerized liquid between a carrier and a rigid surface using a roller.  
       FIG. 9B  is a schematic cross-sectional view that shows light propagating through a mask to cure the pre-polymerized material sandwiched between the carrier and the rigid surface depicted in  FIG. 9A .  
       FIG. 9C  is a cross-sectional view schematically depicting a blanket UV exposure with the mask removed to cure the pre-polymerized material sandwiched between the carrier and the rigid surface thereby forming a polymer layer.  
       FIG. 9D  is a cross-sectional view that schematically illustrates separating the carrier and polymer layer formed thereon from the rigid surface.  
    
    
     DETAILED DESCRIPTION OF CERTAIN PREFERRED EMBODIMENTS  
      A polymer sheet may be fabricated by curing curable material using light or electromagnetic radiation. This curable material may comprise a pre-polymerized material and the light may be used to polymerize this pre-polymerized material. This pre-polymer material may comprise a fluid or liquid.  
       FIG. 1A  shows an exemplary photo-polymerization process wherein a pre-polymerized material  10  is exposed to electromagnetic radiation (represented by arrow  12 ) to cure the pre-polymerized material. The electromagnetic radiation may comprise, for example, ultraviolet (UV) light or actinic light. The pre-polymer material  10  may comprise monomers, oligomers, or a mixture of monomers and oligomers. The pre-polymer material  10  also includes a photo-initiator.  FIG. 1  shows a blanket exposure of the pre-polymer material  10  to ultraviolet (UV) light. A surface  14  of the pre-polymer material  10  is completely exposed to the UV light. Exposure of this pre-polymerized material  10  to ultraviolet light causes the monomer and oligomer molecules to crosslink to form a polymer network.  
       FIG. 1B  shows a polymerized sheet  16  produced by exposing the pre-polymerized material to UV light to cure the pre-polymerized material. This polymerized sheet  16  may comprise a plastic sheet in some embodiments.  FIG. 1B  is a schematic drawing that shows the polymerized sheet  16  as thick and relatively narrow. This sheet  16  may, however, be thinner and wider. More generally this sheet  16  may have any shape and any dimensions. The sheet  16  may comprise, for example, a film, a plate, or a thicker component and may be curved or shaped.  
      The polymer sheet  16  may have a smaller volume than the pre-polymerized material. In general, polymerization results in the shrinkage of volume.  FIG. 1C  illustrates this shrinkage and the resultant generation of a free volume region  18 .  
      The photo-polymerization process may be different. in different embodiments. For example, a wide variety of pre-polymer materials can be employed. Different photo-intiators that are responsive to different wavelengths of light may also be used. Accordingly, different wavelengths of light may be used to cure the pre-polymerized material  10 .  
      In another embodiment shown in  FIGS. 2A and 2B , a mask  20  is used to expose a portion  22  of the surface  14  of the pre-polymerized material  10  formed on a substrate  11  to UV radiation. The mask  20  may comprise a material that is substantially opaque to the UV light and thus blocks the UV light. The mask  20  has an aperture  24  therein through which some of the UV light passes. The aperture  24  may comprise a physical opening in the mask  20  or may comprise material that is substantially optically transmissive to the UV light. The mask  20  thereby provides spatial modulation of the UV light. In  FIGS. 2A and 2B , the aperture  24  and the exposed portion  22  of the pre-polymer material are shown as square, however, the aperture and the exposed portion may have any shape. The mask  20  may comprise, for example, a lithographic films formed, e.g., by a photographic process that yields patterned black portions that block light or a photomask comprising, e.g., a glass or quartz plate with patterned chrome, aluminum, or other metal portions that block light, although other types of masks may be used.  
      The exposed portion  22  of the pre-polymerized material  10  is polymerized. As described above, monomers and/or oligomers in the pre-polymerized material  10  are cross-linked to form polymer. In various embodiments wherein the pre-polymerized material  10  comprises a fluid or a liquid, the exposed portions  22  of the material  10  solidifies. A localized surface relief feature  26  is thereby formed.  
      As depicted in  FIG. 2C , the mask  20  is removed and the surface  14  of the pre-polymerized material  10  is again exposed to UV light (as represented by arrow  12 ′). Both the previously exposed portion  22  and area surrounding  28  the previously exposed portion are further exposed to UV light in this “blanket” exposure. In other embodiments, the surrounding area  28  may be exposed without exposing the localized surface relief feature  26  although a blanket exposure may be easier to perform.  
      The surrounding area  28 , here the remaining portions of the pre-polymerized material  10 , are polymerized with the blanket exposure as illustrated in  FIG. 2D . In various embodiments wherein the pre-polymerized material  10  comprises a fluid or a liquid, the surrounding area  28  also solidifies. The result is a polymer sheet  16  having a surface  14  that includes the localized surface relief feature  26  disposed thereon. As described above,  FIG. 2D  is a schematic drawing that shows the polymerized sheet  16  as thick and narrow. This sheet  16 , however, may be relatively thin. More generally, this sheet  16  may have any shape and any dimensions. The sheet  16  may comprise, for example, a film, a plate, or a thicker component, which may be curved or shaped.  
      In other embodiments, the mask  20  may be above or below (on either side of) the pre-polymerized material  10  and substrate  11  and the UV light can be directed from either side as well. Similarly, the UV light used in the second exposure may be from either side (e.g., above or below) the pre-polymerized material  10  and the substrate  11 . Accordingly, in some embodiments, the substrate  11  is substantially optically transmissive to the light used to cure the pre-polymerized material  10 . In some embodiments, the mask may contact the pre-polymerized material.  
      Advantageously, the localized surface relief feature  26  is formed by exposing the pre-polymerized material  10  to light, which in certain preferred embodiments, creates a hardened surface feature without the need for an added step of developing, for example, without exposure to a solvent such as an alkaline solution to remove un-exposed pre-polymerized material  10  prior to the second exposure. Similarly, the surrounding area  28  is exposed and hardened by exposing the pre-polymerized material  10  in the surrounding area to light, again without the need for an additional step of developing, for example, without the need for rinsing with a solvent such as an alkaline solution. Moreover, in certain preferred embodiments, the hardened polymer sheet  16  is formed without the additional step of baking, for example, to solidify and/or harden the pre-polymerized mixture in the localized surface relief feature  26  or the surrounding area  28 .  
      Without subscribing to any particular scientific theory, one possible explanation of this process is that with the mask  20  in place, exposure of the localized portion  22  of the pre-polymerized material  10  causes polymerization of monomers and/or oligomers in the localized portion and draws additional monomers and/or oligomers from the surrounding area  28 . This migration of monomers and/or oligomers from the surrounding area  28  into the localized exposed region  22  is represented by arrows  30 .  
      The shape of the surface  14  may not be exactly the same as illustrated in  FIGS. 2C and 2D . In certain embodiments, the shape and size of the localized surface relief feature  26  is correlated to parameters, such as the size and shape of the aperture  24  in the mask  20 , the mobility of monomers and/or oligmers, the thickness of the pre-polymerized material  10 , and the UV radiation. For example, the height of the surface relief structure  26  can be dependent on these parameters.  
      According to one theory, during the first exposure, a polymer network as well as free volume forms in the localized exposed portion  22 . A chemical potential gradient is generated between the localized exposed portion  22  and the surrounding unexposed area  28 . As a result, the monomer and/or oligomer molecules migrate to the localized exposed area  24  through a diffusion process and the free volume counter-diffuses to the surrounding unexposed area  28 . After the first photo-polymerization, the localized exposed area  22  may have a higher weight per unit area as molecules migrated to the localized exposed area and free volume is produced in the surrounding unexposed area  28 . With the second exposure, wherein the mask  10  is removed, the unreacted monomer and/or oligomer mixture polymerizes and the surrounding region  28  shrinks producing more free volume. Consequently, the surface relief structure  26  formed with the first exposed area is higher than the surrounding area  28 .  
      The photo-polymerization and polymer migration process can be modeled using reaction-diffusion equations:  
                 ∂     ϕ   m         ∂   t       =         -   γ     ⁢           ⁢     I   α     ⁢     ϕ   m       +     ∇     ·     [     D   ⁢     ∇     ϕ   m         ]                   (   1   )                   ∂     ϕ   p         ∂   t       =       (     1   -   β     )     ⁢   γ   ⁢           ⁢     I   α     ⁢     ϕ   m               (   2   )             
 
 where φ m  is the concentration of monomers and/or oligomers, t is time, γ is the reaction rate, which depends on the concentration of photo-initiator and reactivity of monomers and/or oligomers, I is the local light intensity, α is the exponential component for polymerization, D is the effective diffusion constant, φ p  is the polymer concentration, and β is the shrinkage factor. In this model, the migration of polymer is neglected since the molecular weight of polymer is much higher than that of monomers and/or oligomers and, consequently, the migration of polymer is much slower than that of monomers and/or oligomers. 
 
       FIG. 3  is a plot of the localized surface relief feature  26  calculated using the diffusion equations (1) and (2) for a mask having a circular aperture  24 . The surface relief feature  26  is plotted on x, y, and z axes which correspond to lateral spatial location (x, y) and surface height (z) in arbitrary units. The plot shows the portion  22  exposed by light propagating through the aperture  24  as well as the surrounding area  28 . Inner and outer regions  32 ,  34  of the surrounding area  28  close to and farther away, respectively, from the localized surface relief feature  26  are shown. In this plot, the height of the localized surface relief feature  26  is higher than both regions  32  and  34  of surrounding area  28 . The height of the inner region  32  of the surrounding area  28  is lower than that height in the z direction of the outer region  34 . This profile may indicate that during the photo-polymerization, the monomer and/or oligomer migrates from the surrounding area  28  to the locally exposed portion  22  to form the surface relief feature  26 .  
      Migration of the monomer and/or oligomer is one theory for explaining the formation of the surface relief feature  26  as a result of the photo-polymerization process shown in  FIGS. 2A-2D , which involved two exposure steps. Other scientific explanations, however, are also possible.  
      As shown in  FIGS. 4A-4C , a tool  50  having surface relief structure  52  (see  FIG. 4B ) formed thereon can be used to form a polymer sheet  54  that consequently also has surface relief structure  56  (see  FIG. 4C ). The surface relief structure  56  in the polymer sheet  54  will be the negative or inverse of the surface relief structure  52  of the tool  50 .  
       FIG. 4A  shows a pre-polymerized material  58  disposed on the tool  50 . Injection gravier coating, slot die coating, or other methods may be used to introduce the pre-polymerized material  58  to the tool  50  such that the tool contacts the pre-polymerized material. A carrier substrate  59  is disposed over the pre-polymerized material  58 . The pre-polymerized material  58  is exposed to ultraviolet light, represented by arrow  60 , to cure the pre-polymerized material. The pre-polymerized material  58  is thereby polymerized to form the polymer sheet  54 .  
      In the embodiment shown in  FIG. 4A , the UV is propagated through the carrier substrate  59  and to the pre-polymerized material  58 . Accordingly, the carrier substrate  59  may be substantially optically transmissive to UV light or any other light used to cure the pre-polymerized material  59 . In other embodiments, the light may be propagated through the tool  50  to cure the pre-polymerized material  58 . In such cases, the tool  50  may be substantially optically transmissive to the wavelength of light used to cure the pre-polymerized mixture  58 .  
      The polymer sheet  54  can be separated from the tool  50  as shown in  FIG. 4B . The tool  50  may comprise metal that has been diamond turned to provide the surface relief structure  52  therein. Other types of tools  50 , which may comprise other materials and may be fabricated by other methods including photolithography and holography, may also be used. In the example shown, the tool  50  is corrugated. The tool  50  has a plurality of grooves formed therein. As a result, the surface relief structure  52  has peaks  62  and valleys  64 , ridges and depressions, highs and lows.  
      Similarly, the polymer sheet  54  fabricated from the tool  50  comprises a plurality of grooves; see  FIG. 4C . This surface relief structure  56  too has peaks  66  and valleys  68 , ridges and depressions, highs and lows. The peaks  66  and valleys  68  of the polymer sheet  54 , however, respectively match the valleys  64  and peaks  62  of the tool  50  from which these peaks  66  and valleys  68  were formed. As described above, the surface relief structure  56  on the polymer sheet  54  is the inverse or negative of the surface relief structure  52  on the tool  50 .  
      This process is referred to as a replication process even though the negative or inverse of the surface relief structure  52  of the tool  52  are formed in the polymer sheet  54 . The process can be repeated using the polymer sheet  54  as a tool in the formation of a second polymer sheet (not shown) having surface relief structure. The surface relief structure of this second polymer sheet (not shown) will be the same as the original tool  50  and not the inverse. Accordingly, virtually exact copies of the tool  50  can be made by the replication process. The replication process can be repeated any number of times alternately producing negatives (inverse) and positives (identical copies) of the tool  50 . Any of the copies may be used as a tool or master to produce a plurality of polymer sheets (e.g. product). In other embodiments, for example, this first polymer sheet  54  can be used as a tool, a master, to produce a plurality of polymer sheets (e.g., product) that are replicas of the original tool  50 . In still other embodiments, the second polymer sheet (not shown) can be used as a tool, a master, to produce a plurality of polymer sheets (e.g., product). Either or both of the first polymer sheet  54  or the second polymer sheet (not shown) or any other copies may be metalized in certain embodiments.  
      The double exposure process shown in  FIGS. 2A-2D  may be used to provide the ability to further modify the surface relief structure  56  on the polymer sheet  54  shown in  FIG. 4C . A more a sophisticated surface relief structure can thereby be formed.  
       FIGS. 5A-5C  illustrates one embodiment of such a process. As shown in  FIG. 5A , a mask  70  is used to expose spatially separated locations  78  (see  FIG. 5B ) on a pre-polymerized material  72  to UV radiation (represented by arrow  71 ). As shown, a carrier substrate  73  is disposed over the pre-polymerized material  72 .  
      As discussed above, the mask  70  may comprise a material that is substantially opaque to the UV light and thus blocks the UV light. The mask  70  includes a plurality of separate apertures  74  through which some of the UV light passes. The apertures  74  may comprise a physical opening in the mask  70  or may comprise material that is substantially optically transmissive to the UV light. The mask  70  thereby provides spatial modulation of the UV light. In  FIGS. 5A and 5B , the apertures  74  are shown as elliptical. Similarly, the exposed portions  78  (shown in  FIG. 5B ) of the pre-polymer material are also elliptical. The aperture  74  and the exposed portions  78  may have any shape. The mask  70  may comprise, for example, lithographic films or photo-masks, although other types of masks may be used.  
      The exposed portions  78  of the pre-polymerized material  72  (shown in  FIG. 5B ) are polymerized. As described above, monomers and/or oligomers in the pre-polymerized material  72  are cross-linked to form polymer.  
      In the embodiment depicted in  FIG. 5A , the UV light is propagated through the carrier substrate  73  and to the pre-polymerized material  72 . Accordingly, the carrier substrate  73  may be substantially optically transmissive to UV light or any other light used to cure the pre-polymerized material  72 . In other embodiments, the mask  70  may be below the tool  75 . Accordingly, the tool  75  may be between the mask  70  and the pre-polymerized material  72 . The light may be propagated through the mask  70  and the tool  75  to cure the pre-polymerized material  72 . In such cases, the tool  75  may be substantially optically transmissive to the wavelength of light used to cure the pre-polymerized material  72 . The mask  70  may contact the carrier substrate  73 , pre-polymerized material  72  or tool  75  depending on the configuration.  
       FIGS. 5A and 5B  show the pre-polymerized material  72  formed over a tool  75 . As described above, a carrier substrate  73  is disposed over the pre-polymerized material  72 . Gravier coating, slot die coating, or other methods may be used to introduce the pre-polymerized material  72  to the tool  50  such that the tool contacts the pre-polymerized material.  
      The tool  75  has surface relief structures  80 . In particular, the tool  75  shown in  FIGS. 5A and 5B  has an undulating surface  82 . The tool  75  may comprise, for example, metal that has been cut using, e.g., diamond turning such as single point diamond turning, as described above. Other methods of forming the tool, such as lithography and holography, may also be used.  
      The mask  70  is removed, as shown in  FIG. 5B , and the polymer and remaining pre-polymerized material  72  is exposed to UV light (as represented by arrow  71 ′). Both the previously exposed portions  78  and area  84  surrounding the previously exposed portions are further exposed to UV light in this “blanket” exposure. In other embodiments, the surrounding area  84  may be exposed without exposing the previously exposed portions  78  although a blanket exposure may be easier to perform.  
      The surrounding area  84 , here the remaining portions of the pre-polymerized material  72 , are polymerized with the blanket exposure. The result is a polymer sheet  86  shown in  FIG. 5C  having a surface  88  that includes the localized surface relief features  90  disposed thereon.  FIG. 5C  shows the polymer sheet  86  separated from the tool  75 .  
      In other embodiments, the light represented by arrow  71 ′ is propagated through the tool  75  to the pre-polymerized material  72 . In such embodiments, the tool  75  may be substantially optically transmissive to UV light or any other wavelength used to cure the material  72 .  
      As described above, the tool  75  is corrugated in the embodiment shown; see  FIG. 5A . In particular, the tool  75  has a plurality of grooves formed therein. The surface relief structure  80  in the tool  75  includes a plurality of peaks  92  and valleys  94 , ridges and depressions, highs and lows; see  FIG. 5B .  
      Similarly, the polymer sheet  86  fabricated from the tool  75  comprises a plurality of grooves; see  FIG. 5C . The surface  88  has surface relief structure  93  comprising peaks  96  and valleys  98 , ridges and depressions, highs and lows. The peaks  96  and valleys  98  of the polymer sheet  86 , however, respectively match the valleys  94  and peaks  92  of the tool  75  from which these peaks  96  and valleys  98  were formed. As described above, the surface relief structure  93  on the polymer sheet  86  is the inverse or negative of the surface relief structure  80  on the tool  75 . Accordingly, in this process, the negative or inverse of the surface relief structure  80  of the tool  75  are formed in the polymer sheet  86 .  
      Additionally, the surface relief features  90  are formed on the surface  88  of the polymer sheet  86 . In the embodiment shown in  FIG. 5C , the surface relief features  90  comprise a plurality of elliptically shaped features, however, the shape may be different. For example, circular features may be used. Also, different shaped features may be included on the same sheet  86 . The shapes may be irregular. The size (e.g., height and/or lateral dimensions) and orientation may also vary from that shown in  FIG. 5C . The distribution of the surface relief features  90  may be different as well. The features  90  are spatially separated from each other. In certain embodiments, at least a portion of the surface relief features  90  are touching. (In some embodiments, most of the surface  88  is exposed using the mask  70  whereas only a portion is unexposed in the initial exposure step. After subsequent exposure the remainder may be exposed. The result is that the surface  88  includes a plurality of regions with reduced size in comparison with the remainder of the surface.)  
      The process can be repeated using the polymer sheet  86  as a tool in the formation of a second polymer sheet (not shown) having surface relief structure. The replication process can be repeated any number of times alternately producing negatives (inverse) and positives (identical copies) of the second polymer sheet. In some embodiments, one of these negative or positive replicas may be used as a master for producing additional sheets (e.g. product). In other embodiments, this first polymer sheet (not shown) can be used as a tool, e.g., a master, to produce a plurality of polymer sheets (e.g. product). In still other embodiments, this second polymer sheet (not shown) can be used as a tool, e.g., a master, to produce a plurality of polymer sheets (e.g. product). Either or both of the first polymer sheet  86  or the second polymer sheet (not shown), as well as any copies thereof, may be metalized in certain embodiments. Accordingly, the processes herein may be used to form tools or products as well as intermediate structures.  
      As described above,  FIG. 5C  is a schematic drawing that shows the polymerized sheet  86  as thick and narrow. This sheet  86 , however, may be thinner and wider. More generally this sheet  86  may have any shape and any dimensions. The sheet  86  may comprise, for example, a film, a plate, or a thicker component, which may be curved or shaped.  
      The processes described herein can be used to fabricate diffraction gratings and diffractive optical elements. Holograms and holographic optical elements may be formed. Diffusers, lens including microlenses, and other optical components may be fabricated. The optical components may be transmissive, reflective, or both transmissive and reflective. The optical components can reflect, refract, scatter, and/or diffract light. In some embodiments, the components produced by these processes are opaque. These processes need not necessarily be used to form optical components but can be used for other applications including those yet to be realized.  
       FIGS. 6A-6D  illustrate how this multiple exposure process can be employed to fabricate a prismatic film for controlling propagation of light, for example, in an optical display. As discussed above, prismatic films may be used in displays such as LCD displays to control the direction of light propagating from the display. Such displays may include a liquid crystal spatial light modulator to produce an image pattern. These displays may further comprise a system for backlighting the spatial light modulator. The prismatic film may be disposed between the spatial light modulator and the backlighting system. The prismatic film may comprise plastic having a surface that includes a plurality of grooves that form facets of small prisms. These small prisms or micro-prisms limit the angle of light transmitted through the prismatic film and can be used to establish the field-of-view of the display. The array of micro-prisms may also increase the brightness of the display by recycling light back toward the backlighting system if the light is directed outside the desired field-of-view. However, when a prismatic film comprising rows or columns of prisms structures is used with a spatial light modulator comprising pixels also arranged in rows and columns, the rows or columns of prisms structures can interfere with the rows and columns of the spatial light modulator and produce a Moiré pattern, an interference pattern seen when viewing the display screen. Introducing diffusing surface features on the surface of the prismatic film can attenuate the Moiré effect. Accordingly, a prismatic film that in addition to grooves that form facets of the prisms may further include diffusing features that scatter or diffuse the light.  
      As shown in  FIG. 6A , a mask  100  is used to expose spatially separated locations on a pre-polymerized material  102  to UV radiation (represented by arrow  101 ). As discussed above, the mask  100  may comprise a material that is substantially opaque to the UV light and thus blocks the UV light. The mask  100  includes a plurality of separate apertures  104  through which some of the UV light passes. In  FIG. 6A and 6B , the apertures  104  are shown as elliptical. Similarly, exposed portions  108  (shown in  FIG. 6B ) of the pre-polymer material  102  are also elliptical. The apertures  104  and the exposed portions  108  (shown in  FIG. 6B ) may have any shape (including but not limited to circular).  
      In other embodiments, the light used to cure the pre-polymerized material  102  may be propagated through the tool  105 . Accordingly, the mask  100  may be located on the other side of the pre-polymerized material  102  and the tool  105  may be substantially optically transmissive to UV light. Additionally, in certain embodiments where wavelengths other than UV are used for curing, the mask  100  may comprise material substantially opaque to the wavelength of light employed. Likewise, the mask  100  includes optical apertures through which the wavelengths may pass. The tool  105  may also be substantially optically transmissive to the light depending on the configuration.  
      The exposed portion  108  of the pre-polymerized material  102  is polymerized. As described above, monomers and/or oligomers in the pre-polymerized material  102  are cross-linked to form polymer.  
       FIGS. 6A and 6B  show the pre-polymerized material  102  formed over a tool  105  having surface relief structures  110  suitable for the formation of prismatic films. Gravier coating, slot die coating, or other methods may be used to introduce the pre-polymerized material  102  to the tool  50  such that the tool contacts the pre-polymerized material. A substrate carrier  103  is formed on the pre-polymerized material  102 . In embodiments where the light is propagated through the substrate carrier  103  to cure the pre-polymerized material  102 , the substrate may be substantially optically transmissive to the wavelengths used for curing.  
      The tool  105  shown in  FIGS. 6A and 6B  has a grooved surface  112  comprising sloped or inclined substantially planar faces. The tool  105  may comprise, for example, metal that has been cut using, e.g., diamond turning such as single point diamond turning, as described above. Methods including lithography and holography may also be used in the formation of the tool  105 . Other types of tools  105  may also be used, e.g., when light is to be propagated through the tool.  
      The mask  100  is removed, as shown in  FIG. 6B , and the polymerized and pre-polymerized material  102  are exposed to UV light (as represented by arrow  101 ′). Both the previously exposed portions  108  and area  114  surrounding the previously exposed portions are exposed to UV light in this “blanket” exposure. In other embodiments, the surrounding area  114  may be exposed without exposing the previously exposed portions  108  although a blanket exposure may be easier to perform.  
      The surrounding area  114 , here the remaining portions of the pre-polymerized material  102 , are polymerized with the blanket exposure as illustrated in  FIG. 6B . The result is a polymer sheet  116  shown in  FIG. 6C  having a surface  118  that includes the localized surface relief features  120  disposed thereon.  FIG. 6C  shows the polymer sheet  116  separated from the tool  105  and disposed on the carrier substrate  103 .  
      As described above, the tool  105  is corrugated in the embodiment shown; see  FIG. 6B . In particular, the tool  105  has a plurality of grooves formed therein. The surface relief structure  110  includes a plurality of peaks  122  and valleys  124 , ridges and depressions, highs and lows.  
      Similarly, the polymer sheet  116  fabricated from the tool  105  comprises a plurality of grooves; see  FIG. 6C . The grooves are defined by sloping or inclined substantially planar faces. The surface  118  of the polymer sheet  116  has surface relief structure  123  comprising peaks  126  and valleys  128 , ridges and depressions, highs and lows. The peaks  126  and valleys  128  of the polymer sheet  116 , however, respectively match the valleys  124  and peaks  122  of the tool  105  from which these peaks  126  and valleys  128  were formed. As described above, the surface relief structure  123  on the polymer sheet  116  is the inverse or negative of the surface relief structure  110  on the tool  105 . Accordingly, in this process, the negative or inverse of the grooves of the tool  105  are formed in the polymer sheet  116 .  
      Additionally, the surface relief features  120  are formed on the surface  118  of the polymer sheet  116 . In the embodiment shown in  FIG. 6C , the surface relief features  120  comprise a plurality of elliptically shaped features, however, shape may be different. For example, circular features may be used. Also, different shaped features may be included on the same sheet  86 . The shapes may be irregular. The size (e.g., height and/or lateral dimensions) and orientation may also vary from that shown in  FIG. 6C . The distribution of the surface relief features  120  may also be different as well. The features  120  are spatially separated from each other. In certain embodiments, at least a portion of the surface relief features  120  are touching. (In some embodiments, most of the surface  118  is exposed using the mask  100  whereas only a portion is unexposed in the initial exposure step. After subsequent exposure, the remainder may be exposed. The result is that the surface  118  includes a plurality of regions with reduced size in comparison with the remainder of the surface.)  
      As shown in  FIGS. 7A and 7B , the photo-polymerization process can be repeated using the polymer sheet  116  as a tool in the formation of a second polymer sheet  130  comprising a prismatic film for use, for example, in a display.  FIG. 7A  depicts the first polymer sheet  116  and a pre-polymerized material  132  in contact with the first polymer sheet. Pre-polymerized material  132  is disposed on a substrate  135 . The surface  118  of the first polymer sheet  116  having surface relief structure  123  and localized surface relief features  120  is contacted to the pre-polymerized material  132 .  
      The pre-polymerized material  132  is exposed to ultraviolet light, represented by arrow  131  to cure the pre-polymerized material. The pre-polymerized material  132  is thereby polymerized to form the second polymer sheet  130 . In the embodiment shown, the first polymer sheet  116  including the carrier layer  103  is optically transmissive to wavelengths corresponding to the UV light such that the UV light can be transmitted through the first polymer sheet to expose the pre-polymerized material  132 . In alternative embodiments, the pre-polymerized material  132  may be cured without directing light through the polymer sheet  116 , for example, the light may be propagated from an opposite direction. The light may, for instance, be passed through the substrate  135  to the pre-polymerized material  132 .  
       FIG. 7B  shows the second polymer sheet  130  separated from the first polymer sheet  116 . The second polymer sheet  130  has a surface having surface relief structure  133 . The surface relief structure  133  of this second polymer sheet  130  will be the same as the surface relief structure  110  on the original tool  105  and not the inverse. In addition, the second polymer sheet  130  will have the inverse of the surface relief features  120  that are on the first polymer sheet  116 . In particular, the surface relief structure  133  on the second polymer sheet  130  comprises a plurality of grooves defined by sloping or inclined substantially planar faces. These substantially planar faces comprise the facets of micro-prisms in the prismatic film. The facets of the micro-prisms will totally internally reflect a portion of the light incident on and propagating through the second polymer sheet  130 . Conversely, another portion of the light that is incident on the second polymer sheet  130  is transmitted through the prismatic film and refracted by the facets of the micro-prisms into a limited range of angles as discussed more fully below. The surface relief structure  133  also has peaks  134  and valleys  136 , which are the inverse of the valleys  128  and peaks  126  on the first polymer sheet  116 .  
      The surface  138  of the second polymer sheet  130  further comprises surface relief features  140 . These surface relief features  140  comprise diffusing structure that diffuses light transmitted through the second polymer sheet as discussed more fully below. In the embodiment shown in  FIG. 7B , the surface relief features  140  comprise a plurality of elliptically shaped features, however, shape may be different. For example, circular features may be used. Also, different shaped features may be included on the same sheet  86 . The shapes may be irregular. The size (e.g., height and/or lateral dimensions) and orientation may also vary from that shown in  FIG. 7B . The distribution of the surface relief features  140  may also be different as well. The features  140  are spatially separated from each other. In certain embodiments, at least a portion of the surface relief features  140  are touching. (In some embodiments, most of the surface of the polymer sheet  130  includes regions with reduced size in comparison with the remainder of the surface.)  
      This first polymer sheet  116  can be used as a tool (e.g., a master) to produce a plurality of polymer sheets  130 . These polymer sheets  130  may be product that is used, for example, in displays, as discussed more fully below. In other embodiments, the second polymer sheet  130  can be used as a tool (e.g., a master) to produce a plurality of polymer sheets. These polymer sheets may also be product that is used, for example, in displays, as discussed more fully below. In other embodiments, the replication process can be repeated any number of times producing surface relief structure that is the alternately negative (inverse) of and positive (identical copies) of the surface relief structure  110  on original tool  105 . For example, the second polymer sheet  130  can be used to fabricate a sheet which is used to fabricate yet another sheet and so on. In some embodiments, one of these negative or positive replicas may be used as a master for producing additional sheets (e.g. product). Either or both of the first polymer sheet  116  or the second polymer sheet  130 , as well as any copies thereof, may be metalized in certain embodiments. Accordingly, the processes herein may be used to form tools or products as well as intermediate structures.  
      As discussed above,  FIG. 7B  is a schematic drawing that shows the first and second polymerized sheets  116 ,  130  are thick and narrow. These sheets  116 ,  130 , however, may be thin. More generally these first and second sheets  116 ,  130  may have any shape and any dimensions. The polymer sheets  116 ,  130  may comprise, for example, a film, a plate, or a thicker component and may be curved or shaped.  
      The second polymerized sheet  130  may be substantially optically transmissive to visible wavelengths and may be used as an optical component for controlling the propagation of light.  FIG. 8  shows an embodiment of a display  142  comprising a spatial light modulator  144  for viewing by a viewer  146 . The spatial light modulator  144  may comprise, for example, a liquid crystal display (LCD). The spatial light modulator  144  is backlighted by a backlighting system as represented by arrow  147 . The display  142  further comprises a prismatic film  148  that controls the propagation of light to the spatial light modulator  144 . This prismatic film  148  may comprise the second polymer sheet  130  shown in  FIG. 7B . As described above, this second polymer sheet  130  comprises a plurality of sloping or inclined faces that form the facets of micro-prisms. These facets totally internally reflect a portion of the light incident on and propagating through the prismatic film  148 . These facets also transmit another portion of light incident on and propagating through the prismatic film  148 . As shown, the facets refract a substantial portion of the light that is transmitted through the prismatic film  148  into a range of angles, θ. This range of angles does not exceed a maximum angle θ max . Accordingly, the prismatic film  148  limits the angle at which a substantial portion of the light is directed propagated through the spatial light modulator  144  to the viewer  146  and thereby substantially limits the field-of-view of the display  142 .  
      Also, as described above, this second polymer sheet  130  comprises a plurality of localized surface relief features  140  that diffuse light transmitted through the prismatic film  148 . In the embodiment shown, the surface relief features  140  are elliptically shape and may diffract light into an elliptically shaped divergent beam. The spatial light modulator  144  comprises a plurality of pixels arranged in rows and columns. The juxtaposition of plurality of linear grooves with respect to the rows and columns of pixels may produce a Moiré pattern. The diffusing surface relief features  140 , which may scatter and diffract the light, reduce this effect. The diffusing surface relief features  140  may have different sizes, shapes, orientations, and distributions and may be arranged or configured differently. These surface relief features  140  form a diffusing texture that is superimposed on the surface relief structure  133  that form the micro-prisms of the prismatic film  148 .  
      The photo-polymerization process may be implemented in a wide variety of ways.  FIG. 9A  shows one embodiment wherein a pre-polymerized liquid  150  is disposed over a rigid surface  152 . This rigid surface  152  may be substantially smooth or may have a surface relief texture (e.g. roughened, patterned, etc.). In some embodiments this surface  152  comprises glass. The pre-polymer liquid  150  comprises monomers, oligomers, or a combination of monomers and oligomers.  
      A substrate carrier  154  is rolled out over the rigid surface  152  with the pre-polymerized liquid  150  therebetween. The substrate carrier  154  may comprise, e.g., polyethylene terephthalate (PET). The pre-polymerized liquid  150  is also rolled out by action of rolling out the substrate carrier  154 . A roller  156  is shown in  FIG. 9A  rolling out the substrate carrier  154 . The pre-polymerized liquid  150  and the substrate carrier  154  are between the rigid surface  152  and the roller  156 . Other configurations are possible.  
      A mask  158  is disposed over the substrate carrier  154  as shown in  FIG. 9B . The pre-polymerized liquid  150  is exposed by UV light represented by arrow  160  to cure the pre-polymerized liquid. The UV light passes through apertures (not shown) in the mask  158 . The substrate carrier  154  is optically transmissive to the UV light that is used to cure the pre-polymerized liquid  150 . Although the mask  158  is shown separated from the pre-polymerized liquid  150 , the mask may contact the liquid in some embodiments. Such a configuration may provide higher resolution patterning in some embodiments.  
      As shown in  FIG. 9C , the mask  158  is removed and the pre-polymerized polymerized liquid  150  is again exposed by UV light represented by arrow  160 ′ to cure the remaining uncured pre-polymerized liquid. The pre-polymerized liquid  150  is thereby transformed into a polymer layer  162  shown in  FIG. 9D . Although the pre-polymerized liquid  150  is shown as being illuminated from above, the UV light may be directed from below as well regardless of whether the preceding expose with the mask  158  was from above or below. In some embodiments, UV light may be directed from both sides at different times or simultaneously. In cases where the light is to be propagated through the rigid surface, the rigid surface is preferably substantially optically transmissive to the wavelength of light used to cure the pre-polymerized material. Also, although the mask  158  is shown above the pre-polymerized liquid  150 , the mask may alternatively be located below the pre-polymerized liquid. Similarly, UV light  160  can be directed from below the pre-polymerized liquid, through the rigid surface  152 . In such embodiments, the rigid surface  152  may be substantially optically transmissive to UV light.  
       FIG. 9D  shows the polymer layer  162  together with the substrate carrier  154  being separated from the rigid surface  152 . The polymer layer  162  contains surface relief structure corresponding to the texture (if present) in the rigid surface  152 . The polymer layer  162  also contains surface relief features corresponding to the apertures in the mask  158  as described above. The height of the surface features can be increase by washing the surface with a chemical wash comprising, for example, a solvent such as methanol. Other washes can also be used to enhance the modulation effect. These surface relief features may range in height from 10 nanometers to 1 millimeter in some embodiments although values outside this range are possible.  
      Certain parameters, such as the thickness of layer of pre-polymerized liquid  150  can affect the height of the surface relief features. Increased thickness of the pre-polymerized liquid  150  permits more monomer and oligomer molecules to migrate. The sharpness of the edges that define the surface relief features can also be influenced by certain parameters such as the length of time the pre-polymerized liquid is exposed to the UV light, the thickness of the substrate carrier  154 , the thickness of the pre-polymerized liquid  150 , as well as the material properties (for example, some formulations may include monomers and oligmers that migrate more or less than others).  
      As described above, UV light is not necessary for curing the curable material. Other wavelengths, for example, may be used. Other types of curable material may also be used.  
      The configuration may vary. For example, the curable material may be disposed on the tool or the tool may be disposed over the curable material. In some embodiments, first and second tools may be disposed over and under the curable material. The tool may be substantially optically transmissive to the electromagnetic radiation used to cure the curable material and the electromagnetic radiation may be passed through the tool to expose the curable material. The curable material may also be cured from the opposite side of the curable material such that the electro-magnetic material need not propagate through the tool and the tool need not be optically transmissive to the wavelength of light used for curing. Likewise, surface relief structure formed in one or more tools may be on one or both sides of the polymer sheet. Similarly, surface relief features in one or more masks may be on one or both sides of the polymer sheet.  
      As discussed above, a surface having surface relief structures may contact the curable material to introduce surface relief structure into the polymer sheet. In some embodiments, one or more surfaces that are substantially devoid of surface relief structure, e.g., are substantially flat, may contact the curable material. The electromagnetic radiation may propagate through this surface in some embodiments, and thus this surface may be substantially optically tranmissive to the electro-magnetic radiation. Pressure of this surface against the polymer sheet after the curing has been completed may suppress the formation surface features until the surface separated from the polymer sheet. After separation, the topographical changes may occur. If the surface is not removed, as in the case of the substrate carrier  154  depicted in  FIGS. 9A-9D , the surface features will not form on the side of the polymer layer  162  with the surface of the substrate carrier  154  remaining in contact with the polymer sheet. In the embodiment, shown in  FIGS. 9A-9D , the surface features may form on the side of the polymer layer  162  opposite to the substrate carrier  154  after the polymer layer is separated from the rigid surface  152 . Similarly, the tool may apply pressure to the polymer sheet and suppress the formation of the surface features until removal of the tool.  
      Although a two stage photo-polymerization process has been described above, wherein curable material is exposed to UV light with and without a photomask, other embodiments may employ additional exposure steps. For example, a first mask may be disposed with respect to the cureable material and electromagnetic radiation transmitted therethrough. The first mask may be removed and a second mask may be disposed with respect to the curable material and the electromagnetic radiation may be transmitted therethrough. A third blanket exposure may follow. In other embodiments more masks and more exposures may be used.  
      Still other arrangements for exposing localized portions of the curable material are possible. In other embodiments, for example, an imaging system that projects an image may be employed instead of the mask. A laser may also be used as a light source. In some embodiments, laser scanning may be employed. In various embodiments, a laser can be used not for the interference properties of the coherent light produced but as a highly controlled bright light source (e.g., non-interferometrically). Still other configurations are possible.  
      More generally, the methods described herein may vary. One or more steps may be added or removed. The order of the steps may be changed.  
      Similarly, the structures produced may be different. The surface relief structures and localized surface relief features may have different configurations, patterns, or arrangements. The dimensions may also be different. Also as describe above, polymer surfaces, layers, films, sheets, or other structures may be formed using the processes described herein. Additional surfaces, layers, films, or components may be added. Items may be removed as welt or ordered, positioned, oriented, or arranged differently. For example, the carrier substrate may be excluded in certain embodiments. Similarly one ore more layers may be disposed between any of the layers, e.g., carrier substrate, pre-polymerized material, tool, described above. Other variations are also possible.  
      As described above, the processes described herein may be used to fabricate optical elements such as diffusers and prismatic films. Diffraction gratings and diffractive optical elements as well as holograms and holographic optical elements may be fabricated. For example, the processes described herein may be used to form surface relief structure and surface relief features that diffract light to produce the desired diffractive and/or holographic effects. Such diffractive or holographic optical elements may be transmissive or reflective. The processes described herein may also be used to fabricate total internal reflection elements.  
      In one exemplary embodiment, a prismatic film that includes diffusing features may be formed to provide control over the properties of a display. For example, the field-of-view may be restricted. Additionally, the brightness of the display may be enhanced for a range of angles. Such optical components may be used, e.g., for computers, televisions cell phones, personal digital assistants (PDAs), games, automobile and navigational instrumentation, and for other applications. For example, the processes describe herein can be used for micro-electro-mechanical systems (MEMS) and microfluidics. Still other applications are possible. In some embodiments the polymer sheet produced is not an optical element.  
      Various embodiments of the invention have been described above. Although this invention has been described with reference to these specific embodiments, the descriptions are intended to be illustrative of the invention and are not intended to be limiting. Various modifications and applications may occur to those skilled in the art without departing from the true spirit and scope of the invention as defined in the appended claims.