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An optical surface substrate. The optical substrate features a three-dimensional surface having a correlation length of about 1 cm or less. The optical substrate is defined by a first surface structure function modulated by a second surface structure function, the first surface structure function pr

An optical surface substrate. The optical substrate features a three-dimensional surface having a correlation length of about 1 cm or less. The optical substrate is defined by a first surface structure function modulated by a second surface structure function, the first surface structure function producing at least one specular component from a first input beam of light. The optical substrate is suitable for use in a variety of applications, including brightness enhancement and projection devices.

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1. A method of modeling a surface of an optical substrate, the method comprising:defining a first window in a coordinate system; defining a master function within the first window; defining a second window as a segment of the first window at a first location within the first window; selecting a set

1. A method of modeling a surface of an optical substrate, the method comprising:defining a first window in a coordinate system; defining a master function within the first window; defining a second window as a segment of the first window at a first location within the first window; selecting a set of points within the second window; defining a modulation path interconnecting the selected set of points; defining a surface function along the modulation path; modulating the surface function along the modulation path; combining the modulated surface function with the master function, generating thereby a three dimensional structural pattern over the extent of the modulation path. 2. The method as set forth in claim 1 wherein selecting a set of points within the second window includes randomly selecting a set of points within the second window.3. The method as set forth in claim 1 wherein modulating the surface function along the modulation path includes randomly modulating the surface function along the modulation path.4. The method as set forth in claim 1 further comprising moving the second window to a new location within the first window.5. The method as set forth in claim 4 further comprising repeatingselecting a set of points within the second window; defining a modulation path interconnecting the selected set of points; defining a surface function along the modulation path; modulating the surface function along the modulation path; combining the modulated surface function with the master function, generating thereby a three dimensional structural pattern over the extent of the modulation path until the second window has been coextensive with all of the points in the first window. 6. The method as set forth in claim 5 further comprising:returning the second window to the first location within the first window; and repeating selecting a set of points within the second window; defining a modulation path interconnecting the selected set of points; defining a surface function along the modulation path; modulating the surface function along the modulation path; combining the modulated surface function with the master function, generating thereby a three dimensional structural pattern over the extent of the first window until the second window has been coextensive with all of the points in the first window. 7. The method as set forth in claim 6 further comprising:generating a mask function from a set of morphologic operators; convolving the mask function with the surface function; and performing the Boolean union of the convolution of the mask function and the modulation function with the master function. 8. The method as set forth in claim 1 wherein combining the modulated surface function with the master function comprises performing the Boolean union of the modulated surface function with the master function.9. The method as set forth in claim 1 further comprising placing a plurality of three dimensional structural patterns generated over the extent of the first window side-by-side with one another to form an array of three dimensional structural patterns.10. An optical substrate generated by the method as set forth in claim 1, wherein the three-dimensional structural pattern has a surface, the surface of the three-dimensional structural pattern defined by a first surface structure function and a second surface structure function, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width.11. The optical substrate as set forth in claim 10 having a correlation function value of 1/e within a prescribed distance from a first location within the three dimensional structural pattern in a first direction in the coordinate system.12. The optical substrate as set forth in claim 11 wherein the correlation function is an auto correlation function.13. The optical substrate as set forth in claim 11 wherein the correlation function is a cross correlation function.14. The optical substrate as set forth in claim 11 having minimized Moir? patterns.15. The method as set forth in claim 1 wherein combining the modulated surface function with the master function comprises performing a boolean union of the modulated surface function with the master function.16. The optical substrate of claim 11, wherein the surface is characterized by a correlation function value of less than about 37 percent of an initial value within a correlation length of about 1 cm or less.17. The optical substrate as set forth in claim 10 wherein the optical substrate is generated by photolithograpy, gray-scale lithography, microlithography, electrical discharge machining or micromachining using hard tools to form molds.18. The optical substrate as set forth in claim 17 wherein the optical substrate includes a surface having characteristic dimension from 100 mm to 1 nm.19. The optical substrate as set forth in claim 10 wherein the first surface function is a triangle with a width of approximately 40 μm and a height of between 1 μm and 200 μm.20. The optical substrate as set forth in claim 10 wherein the first surface function is a triangle with a width of approximately 40 μm and a height of approximately 18 μm.21. The optical substrate as set forth in claim 20 wherein the surface of the optical substrate is formed with an optically transparent material with an index of refraction of approximately 1.75.22. The optical substrate as set forth in claim 10 wherein the first surface function is a triangle with a base to height ratio of between 40 to 1 and 1 to 10.23. The optical substrate as set forth in claim 10 wherein the first surface function is a triangle with a base to height ratio approximately 40 to 18.24. The optical substrate as set forth in claim 10 wherein the surface of the optical substrate is formed with an optically transparent material with an index of refraction of between 1.1 and 3.0.25. The optical substrate as set forth in claim 10 wherein the surface of the optical substrate is formed with an optically transparent material with an index of refraction of approximately 1.75.26. The method as set forth in claim 1, wherein the three-dimensional structural pattern is defined by a first surface structure function and a second surface structure function, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width.27. An optical substrate, comprising:a surface characterized by a correlation function value of less than about 37 percent of an initial value within a correlation length of about 1 cm or less, wherein the surface is defined by a first surface structure function modulated by a second surface structure function, the surface of the optical substrate producing specular and diffuse light from a first input beam of light, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width. 28. The optical substrate as set forth in claim 27, wherein the first surface structure function extends a length from a first end to a second end of the substrate.29. The optical substrate as set forth in claim 28, wherein the first surface structure function has a sawtooth or triangular cross section.30. The optical substrate as set forth in claim 27, wherein the surface of the optical substrate comprises a shape that turns and diffuses light to form a plurality of diffusion ellipses each with a power half angle between about 0.1 and about 60 degrees.31. The optical substrate as set forth in claim 30, wherein the power half angle is between about 1 and about 5 degrees.32. The optical substrate as set forth in claim 30, wherein first input beam of light has a first angle of incidence and the surface of the optical substrate is shaped so that the first input beam of light is transmitted through the optical substrate and turned by the surface of the optical substrate to an output angle different from the first angle of incidence.33. The optical substrate as set forth in claim 32, wherein the output angles of the specular components are determined by the first surface structure function.34. The optical substrate as set forth in claim 33, wherein a second input beam of light normal to the optical substrate is substantially reflected by the surface of the optical substrate and forms output specular components with a power half angle between about 0.1 and 60 degrees.35. The optical substrate as set forth in claim 27, wherein the correlation length of about 200 microns or less.36. The optical substrate as set forth in claim 27, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.37. The optical substrate of claim 27, wherein the optical substrate comprises a brightness enhancement film.38. A brightness enhancement film, comprising:surface characterized by a correlation length of about 1 cm or less, the surface having a shape to turn and diffuse incident light to produce at least a 30 percent brightness increase on-axis to a viewer, wherein the surface produces diffused components of light with a power half angle between about 0.1 and 60 degrees, the surface defined by a first surface structure function and a second surface structure function, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width. 39. The film as set forth in claim 38, wherein the surface is characterized by a correlation length of about 200 microns or less.40. The film as set forth in claim 38, wherein the brightness increase on-axis is about 30 percent to about 300 percent.41. The film as set forth in claim 38, wherein the brightness increase on-axis is about 50 percent to about 200 percent.42. The brightness enhancement film as set forth in claim 38, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.43. An optical substrate, comprising:a three-dimensional surface defined by a first surface structure function and a second surface structure function, the first surface structure function having a geometry with optical characteristics to produce at least one output specular component from an input beam of light; the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function; wherein the three-dimensional surface has a correlation function value of less than about 37 percent of an initial correlation function value in a correlation length of about 1 cm or less, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width. 44. The optical substrate as set forth in claim 43, wherein the surface is characterized by a correlation length of about 200 microns or less.45. The optical substrate as set forth in claim 43, wherein the first surface structure function is characterized by a series of first surface structure functions, each first surface structure function having a length, width and peak angle.46. The optical substrate as set forth in claim 45, wherein the phase modulation includes modulating a horizontal position of at least one of the first surface structure functions along the length of that first surface structure function.47. The optical substrate as set forth in claim 45, wherein the frequency modulation includes modulating the width of at least one of the first surface structure functions along the length of that first surface structure function.48. The optical substrate as set forth in claim 45, wherein the peak angle modulation includes modulating a peak angle of at least one of the first surface structure functions along the length of that first surface structure function.49. The optical substrate as set forth in claim 43, wherein the surface diffuses and turns the input beam of light to form a plurality of diffusion ellipses each with a power half angle between about 0.1 and about 60 degrees.50. The optical substrate as set forth in claim 49, wherein the power half angle is between about 1 and about 5 degrees.51. The optical substrate as set forth in claim 49, wherein the input beam of light has an angle of incidence and the surface is structured so that the input beam of light is transmitted through the optical substrate and turned by the surface to form output angles of the specular components that are different from the angle of incidence.52. The optical substrate as set forth in claim 51, wherein the output angles of the specular components are determined by the first surface structure function.53. The optical substrate as set forth in claim 43, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first structure function in one or more of frequency and peak angle along the length of the first surface structure function.54. A method for modeling a three-dimensional surface of an optical film, the method comprising:modulating a plurality of first surface structure functions with a second surface structure function to produce irregular, modulated waveforms, each one of the first surface structure functions having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width; placing a first set of the plurality of modulated waveforms at intervals on a work surface, each of the modulated waveforms of the first set being superimposed over adjacent modulated waveforms; and placing a second set of the plurality of modulated waveforms at intervals on the work surface, the second set of modulated waveforms being superimposed over the first set of modulated waveforms. 55. The method as set forth in claim 54, wherein the waveforms, prior to modulating, are shaped as sawtooth or triangular functions in cross section.56. The method as set forth in claim 55, wherein the plurality of sawtooth or triangular functions are modulated by one or more of phase, frequency, and peak angle modulation.57. The method as set forth in claim 54, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.58. A method of modeling a surface of an optical substrate, the method comprising:defining a first window in a coordinate system; defining a master function within the first window; defining a second window at a first location within the first window; randomly selecting a set of points within the second window; defining a modulation path interconnecting the selected set of points; defining a surface function along the modulation path; randomly modulating the surface function along the modulation path; combining the modulated surface function with the master function, generating thereby a three dimensional structural pattern over the extent of the modulation path; moving the second window to a new location within the first window and repeating selecting a set of points within the second window; defining a modulation path interconnecting the selected set of points; defining a surface function along the modulation path; modulating the surface function along the modulation path; and combining the modulated surface function with the master function, generating thereby a three dimensional structural pattern over the extent of the modulation path until the second window has been coextensive with all of the points in the first window. 59. An optical substrate, comprising:a surface characterized by a correlation function value of less than about 37 percent of an initial value within a correlation length of about 1 cm or less, wherein the surface is defined by a first surface structure function having a sawtooth or triangular cross section extending a length from a first end to a second end of the substrate modulated by a second function, the surface of the optical substrate producing specular and diffuse light from a first input beam of light, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width. 60. The optical substrate as set forth in claim 59, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.61. A brightness enhancement film, comprising:a surface characterized by a correlation length of about 1 cm or less, the surface having a shape to turn and diffuse incident light to produce a 50 percent to 200 percent brightness increase on-axis to a viewer, wherein the surface produces diffused components of light with a power half angle between about 0.1 and 60 degrees, the surface defined by a first surface structure function and a second surface structure function, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width. 62. The brightness enhancement film as set forth in claim 61, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.63. An optical substrate, comprising:a three-dimensional surface defined by a first surface structure function and a second surface structure function, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light; the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along a respective widths of the first surface structure functions; wherein the three-dimensional surface has a correlation function value of less than about 37 percent of an initial correlation function value in a correlation length of about 1 cm or less. 64. The optical substrate as set forth in claim 63, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.65. A method for modeling a three-dimensional surface of an optical film, the method comprising:modulating in at least a pseudo-random fashion at least a phase along respective lengths of a plurality of first surface structure functions shaped in cross section at sawtooth or triangular functions to produce irregular, modulated waveforms, the phase being a horizontal peak position along respective widths of the first surface structure functions; placing a first set of the plurality of modulated waveforms at intervals on a work surface, each of the modulated waveforms of the first set being superimposed over adjacent modulated waveforms; and placing a second set of the plurality of modulated waveforms at intervals on the work surface, the second set of modulated waveforms being superimposed over the first set of modulated waveforms. 66. The method as set forth in claim 65, wherein the modulating comprises modulating in a pseudo random fashion the plurality of first surface structure functions in one or more of frequency and peak angle along the length of the first surface structure functions.67. A method of making an optical substrate comprising a surface characterized by a correlation function value of less than about 37 percent of an initial value within a correlation length of about 1 cm or less, wherein the surface is defined by a first surface structure function modulated by a second function, the surface of the optical substrate producing specular and diffuse light from a first input beam of light, the method comprising:photolithographically mastering the surface of the optical substrate to a photoresist, a gray scale mask or a halftone mask; and forming a mold of the surface of the optical substrate from the master by hot embossing, cold calendaring, ultraviolet curing or thermal setting. 68. The method as set forth in claim 67 further comprising:electroforming the master with a metal coating forming thereby a parent electroform; electroforming the parent electroform forming thereby a child electroform. 69. The method as set forth in claim 68 wherein electroforming the parent and child electroforms includes electro-depositing nickel thereon.70. The method as set forth in claim 67 wherein the substrate comprises organic, inorganic or hybrid optically transparent material including suspended diffusion, birefringent or index of refraction modifying particles.71. The method as set forth in claim 67 wherein the master is a negative of the optical substrate.72. The method as set forth in claim 67 wherein the master comprises glass, crystalline metal or plastic.73. A method of making an optical substrate comprising a surface characterized by a correlation function value of less than about 37 percent of an initial value within a correlation length of about 1 cm or less, wherein the surface is defined by a first surface structure function modulated by a second function, the surface of the optical substrate producing specular and diffuse light from a first input beam of light, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width, the method comprising:hard tool mastering the surface of the optical substrate; and forming a mold of the surface of the optical substrate from the master by hot embossing, cold calendaring, ultraviolet curing or thermal setting. 74. The method as set forth in claim 73, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.75. A backlight display device comprising:an optical source for generating light; a light guide for guiding the light therealong including a reflective surface for reflecting the light out of the light guide; at least one optical substrate receptive of the light from the reflective surface, the optical substrate comprising: a three-dimensional surface defined by two surface structure functions, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light; the second surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width; wherein the three-dimensional surface has a correlation function value of less than about 37 percent of an initial correlation function value in a correlation length of about 1 cm or less. 76. The backlight display device as set forth in claim 75 wherein the at least one optical substrate comprises a plurality of optical substrates.77. The backlight display device as set forth in claim 76 wherein the plurality of optical substrates include first and second surface functions in a relative orientation from zero to ninety degrees with respect to one another.78. The backlight display device as set forth in claim 77 wherein the relative orientation of the first and second surface function is parallel or perpendicular with respect to one another.79. A backlight display device comprising:an optical source for generating light; a light guide for guiding the light therealong including a reflective surface for reflecting the light out of the light guide; and an optical substrate receptive of the light from the reflective surface, the optical substrate comprising: a first three-dimensional surface defined by first and second surface structure functions; the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light; the second surface structure function having a geometry with at least pseudo-random characteristic to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width of the first surface structure function; a second three-dimensional surface opposing the first three-dimensional surface and defined by a third surface structure function and a fourth surface structure function; the third surface structure having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light; the fourth surface structure function having a geometry with at least pseudo-random characteristics to modulate the third surface structure function in at least a phase along the length of the third surface structure function, the phase being a horizontal peak position along the width of the third surface structure function; wherein the first and second three-dimensional surface have a correlation function value of less than about 37 percent of an initial correlation function value in a correlation length of about 1 cm or less. 80. The backlight display device as set forth in claim 79 wherein the first and second surface structure functions are in a relative orientation from zero to ninety degrees with respect to one another.81. The backlight display device as set forth in claim 80 wherein the relative orientation of the first and third surface structure functions is parallel or perpendicular with respect to one another.82. The optical substrate as set forth in claim 79 wherein the second surface is optically smooth or planar.83. The optical substrate as set forth in claim 79 wherein the second surface has a matte or diffuse finish.84. The optical substrate as set forth in claim 83 wherein the second surface has diffusion characteristics that are anamorphic or anisotropic.85. The optical substrate as set forth in claim 79 wherein the second surface is optically smooth or planar including a pattern of protrusions formed either in the substrate or attached with an adhesive.86. The backlight display device as set forth in claim 79, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function, and wherein the fourth surface structure function has a geometry with at least pseudo-random characteristics to modulate the third surface structure function in one or more of frequency and peak angle along the length of the third surface structure function.87. An optical substrate, comprising:a surface characterized by a correlation function value of less than about 37 percent of an initial correlation function value within a correlation length of about 1 cm or less, wherein the surface is defined by a first surface structure function having a plurality of parameters modulated by a plurality of random functions, the first surface structure function having a length, width and peak angle with optical characteristics to produce at least one output specular component from an input beam of light, and the plurality of random functions each having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in at least a phase along the length of the first surface structure function, the phase being a horizontal peak position along the width. 88. The optical substrate as set forth in claim 87 wherein the plurality of random functions are spatially constant or spatially varying.89. The optical substrate as set forth in claim 87, wherein the second surface structure function has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency and peak angle along the length of the first surface structure function.