Method and apparatus for fabricating optical substrates

Abstract

In one embodiment, an optical substrate that includes a prism structure modulated along a path in a lateral direction. The path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and frequency.

1 . An optical substrate comprising a prism structure that was modulated along a path in a lateral direction, wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random, or pseudorandom parameters selected from the group consisting of amplitude, phase, and frequency. 
   
   
       2 . The optical substrate as set forth in  claim 1 , wherein the mathematical function is defined by the equation
     y   i   =A   i  sin {Ψ i   }+S   i      wherein i is an integer indicative of the number of the path, y i  is the instantaneous displacement relative to C on the i th  path, A i  is the maximum displacement relative to C, Ψ i  is the phase of y i  and S i  is a shift in the starting position of y i .   
   
   
       3 . The optical substrate as set forth in  claim 2 , wherein 
     
       
         
           
             
               Ψ 
               i 
             
             = 
             
               
                 φ 
                  
                 
                   ( 
                   
                     
                       λ 
                       i 
                     
                     - 
                     
                       
                         q 
                         
                           i 
                           + 
                           k 
                         
                       
                       2 
                     
                   
                   ) 
                 
               
               - 
               
                 Φ 
                 i 
               
             
           
         
       
       where φ is a number between zero and 2π inclusive, 
     
     
       
         
           
             
               λ 
               i 
             
             = 
             
               
                 2 
                 × 
                 C 
               
               N 
             
           
         
       
     
     where N is a nonrandom, random, or pseudo random positive or negative integer, 
     
       
         
           
             
               q 
               
                 i 
                 + 
                 k 
               
             
             2 
           
         
       
     
     is an additive factor modifying λ i  on a k th  subsequent path and Φ i  is a nonrandom, random, or pseudo random number between zero and 2π inclusive. 
   
   
       4 . The optical substrate as set forth in  claim 2 , wherein, for a k th  path subsequent to the i th  path, a starting point of the mathematical function is shifted a distance S i  from the starting point of the mathematical function on the i th  path. 
   
   
       5 . The optical substrate as set forth in  claim 4 , wherein a width w k  of the k th  path is different than for the i th  path. 
   
   
       6 . The method as set forth in  claim 5 , wherein the difference in the width w k  of the k th  path with respect to the i th  path is a gradient over all path. 
   
   
       7 . The method as set forth in  claim 5 , wherein the difference in the width Wk of the k th  path with respect to the i th  path is random or pseudo random. 
   
   
       8 . The optical substrate as set forth in  claim 2 , wherein the value of A i  is nonrandom, random, or pseudo random. 
   
   
       9 . The optical substrate as set forth in  claim 2 , wherein 
     
       
         
           
             
               Ψ 
               i 
             
             = 
             
               
                 φ 
                  
                 
                   ( 
                   
                     
                       λ 
                       i 
                     
                     - 
                     
                       
                         q 
                         
                           i 
                           + 
                           k 
                         
                       
                       2 
                     
                   
                   ) 
                 
               
               - 
               
                 Φ 
                 i 
               
               - 
               
                 
                   a 
                   i 
                 
                  
                 sin 
                  
                 
                   { 
                   
                     φ 
                      
                     
                       ( 
                       
                         
                           
                             λ 
                             i 
                           
                           
                             b 
                             i 
                           
                         
                         - 
                         
                           Ω 
                           i 
                         
                       
                       ) 
                     
                   
                   } 
                 
               
             
           
         
       
       where φ is a number between zero and 2π inclusive, 
     
     
       
         
           
             
               λ 
               i 
             
             = 
             
               
                 2 
                 × 
                 C 
               
               N 
             
           
         
       
     
     where N is a nonrandom, random, or pseudo random positive or negative integer, 
     
       
         
           
             
               q 
               
                 i 
                 + 
                 k 
               
             
             2 
           
         
       
     
     is an additive factor modifying λ i  on a k th  subsequent path and Φ i  is a random or pseudo random number between zero and 2π inclusive, a i  and b are scalar quantities and Ω i  is a nonrandom, random, or pseudo random number between zero and 2π inclusive. 
   
   
       10 . The optical substrate as set forth in  claim 9 , wherein, for a k th  path subsequent to the i th  path, a starting point of the mathematical function is shifted a distance S i  from the starting point of the mathematical function on the i th  path 
   
   
       11 . The optical substrate as set forth in  claim 9 , wherein the value of A i  is nonrandom, random, or pseudo random. 
   
   
       12 . The optical substrate as set forth in  claim 1 , wherein the mathematical function is selected from the group of mathematical functions consisting of triangular function, sawtooth function, and square wave function. 
   
   
       13 . A backlight display device comprising:
 an optical source capable of generating light;   a light guide capable of guiding the light therealong;   a reflective device positioned along the light guide capable of reflecting the light out of the light guide;   an optical substrate capable of receiving the light from the light guide, the optical substrate comprising a prism structure that was modulated along an i th  path in a lateral direction, wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase, and frequency.   
   
   
       14 . A backlight display device comprising:
 an optical source capable of generating light;   a light guide capable of guiding the light therealong; and   a reflective device positioned along the light guide and capable of reflecting the light out of the light guide;   wherein the light guide includes a surface that includes a prism structure that was modulated along an i th  path in a lateral direction;   wherein the path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random, or pseudo random parameters selected from the group consisting of amplitude, phase, and frequency.   
   
   
       15 . The display device as set forth in  claim 14 , wherein for a k th  path, subsequent to the i th  path, a width Wk of the k th  path is different than the i th  path. 
   
   
       16 . The display as set forth in  claim 15 , wherein the difference in the width Wk of the k th  path with respect to the i th  path is a gradient over all paths. 
   
   
       17 . The display as set forth in  claim 15 , wherein the difference in the width Wk of the k th  path with respect to the i th  path is random or pseudo random. 
   
   
       18 . A method of machining a surface of a workpiece, wherein the workpiece comprises a rotating drum, the method comprising:
 bringing a cutting tool into contact with the surface of the workpiece; and   for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece in a direction parallel to an axis of the drum;   wherein causing relative movement between the cutting tool and the surface of the workpiece comprises   bandpass filtering a noise signal;   providing the bandpass filtered noise signal to a function generator;   generating a randomly or pseudorandomly modulated mathematical function from the function generator; and   directing the relative movement between the cutting tool and the surface of the workpiece in response to the randomly or pseudorandomly modulated function.   
   
   
       19 . A method of machining a surface of a workpiece, wherein the workpiece comprises a flat plate moving at a velocity v, the method comprising:
 bringing a cutting tool into contact with the surface of the workpiece; and   for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece in a direction across the plate;   wherein causing relative movement between the cutting tool and the surface of the workpiece comprises   bandpass filtering a noise signal;   providing the bandpass filtered noise signal to a function generator;   generating a randomly or pseudorandomly modulated mathematical function from the function generator; and   directing the relative movement between the cutting tool and the surface of the workpiece in response to the randomly or pseudorandomly modulated function.