Optical substrate and method of making

[00002] This invention relates to optical substrates and, more specifically, to optical substrates having a surface performing at least two optical functions.

[00003] In backlight computer displays or other systems, films are commonly used to direct light. For example, in backlight displays, brightness enhancement films use prismatic structures to direct light along the viewing axis (i.e., normal to the display), which enhances the brightness of the light viewed by the user of the display and which allows the system to use less power to create a desired level of on-axis illumination. Films for turning light can also be used in a wide range of other optical designs, such as for projection displays, traffic signals, and illuminated signs.

[00004] Backlight displays and other systems use layers of films stacked and arranged so that the prismatic surfaces thereof are perpendicular to one another and are sandwiched between other optical films known as diffusers. Diffusers have highly irregular surfaces.

[00005] The invention features a multiple function optical substrate and a method of making the same. Under one aspect of the invention, the optical substrate includes a three-dimensional surface characterized by a function such as a correlation function, R(x,y), having a value of less than about 37 percent (1/e) of the initial value of R within a correlation length, l_c, of about 1 cm or less. The three-dimensional surface is defined by a first surface structure function modulated by a second, random, or at least pseudo-random, function. The properties of the first surface structure function produce a specular component from a first input beam of light, and this light turning behavior is retained in the three-dimensional surface. Generally, the pseudo-random function is a signal that modulates any combination of the frequency, height, peak angle or phase of the first surface structure function. A window is defined and points are randomly selected within the window thereby creating a modulation path connecting the randomly selected points. A master function is defined and a surface function is generated along the modulation path and repeatedly combined with a master function at successive locations within the master function. The resulting three-dimensional surface of the substrate retains the light turning characteristics of the first surface structure function, but also diffuses light to, for example, reduce Moiré artifacts.

[00006] In another aspect of the invention, the optical substrate is applied to one or more sides of a film used for brightness enhancement in a backlight panel light guide. The optical substrate also produces an on-axis increase in brightness of at least 30 percent in the brightness enhancement application. In addition, the three-dimensional surface produces diffused specular components of light with a power half angle of between about 0.1 and 60 degrees.

[00048] The embodiments of the invention provide an optical substrate for turning and diffusing light using the surface thereof. The substrate includes a surface defined by a first surface structure function for turning light and a second surface structure function for diffusing light. The combination of these two surface functions results in a single three-dimensional surface that both turns and diffuses light.

[00049] Embodiments of substrates will be described below with respect to brightness enhancing films for use in backlight displays or the like. The optical substrates, however, can be used in a wide variety of other applications as well.

[00050] FIG. 1 depicts in cross section a prior art film in which a series of prismatic structures 10 are used to turn light. In backlight displays, light enters surface 20 and exits surface 30. In the film of FIG. 1, a beam of light, A, having a zero degree angle of incidence to the light-entering surface 20 is directed off the prism structures 10 and is, essentially, reflected back toward the input. A second beam of light, B, having an angle of incidence of θ is turned by the prismatic structures 10 so that it is transmitted through the light-exiting surface 30 and exits substantially normal to the light-entering surface 20. Other beams (not shown) will turn or reflect at other angles. The bulk statistical properties of such a film are characterized by parameters such as optical gain and viewing angle.

[00051] In this prior art film, the surface 30 can be described as a function. If the height of the surface 30 relative to surface 20 is coordinate z and the coordinates across the page and normal to the page are x, y respectively, then the surface 30 can be defined by a function z=ƒ(x,y). In this case, ƒ(x) is a repeating triangular waveform, or sawtooth, with a constant offset relative to surface 20. In this case, the function defining surface 30 has a special geometry that both turns and reflects light as outlined above.

[00052] FIG. 2 is a top view of an optical substrate 40 according to a first embodiment of the invention. The embodiment of FIG. 2 shows a portion of a substrate 40 that has a length, l, of about 2,000 microns and a width, w, of about 2,000 microns. FIG. 3 is a top view of an embodiment of a portion of a substrate 42 that is about 500 microns by 500 microns in dimension, and FIG. 4 shows a perspective view of a portion of the substrate 42 of FIG. 3. The embodiments of FIGS. 3 and 4 have a three-dimensional surface that is more highly irregular than the three-dimensional surface of FIG. 2. Generally, the substrates shown in FIGS. 2-4 have an irregular three-dimensional surface structure on the light-exiting surface thereof. Because of its geometry, the irregular three-dimensional surface structure, turns light to produce output specular components, while at the same time diffusing light and having a low correlation length, l_c. Because the embodiments of the substrates can turn and diffuse light on a single surface, separate diffusion surfaces can be eliminated in some applications.

[00053] The substrates shown in FIGS. 2-4 have an irregular three-dimensional surface. This irregular surface, however, is not easily defined by well known mathematical functions, as is the case for the light exiting surface 30 of FIG. 1. Instead, this surface function is better defined as the result of modulating a first surface structure function by a second surface function, and in some cases by taking such modulated functions and superimposing them with other functions formed similarly. For example, the first function can be similar to that defined by the light exiting surface 30 of FIG. 1. The first function may also be that of a single prism. The second function can be a pseudo-random function of height, phase, frequency or peak angle. Moreover, the combination can be accomplished by way of modulating the first function by the second function so that the resulting function z=ƒ(x,y) of substrate 40 has a pseudo-randomly varying height, phase, frequency or peak angle along the “l” direction of the substrate 40 (FIG. 2). The first function provides the geometrical properties to turn or reflect light and the second function provides the geometrical properties to diffuse the turned light or reflected light. As will be discussed below, other functions can be substituted and other parameters can be relevant (e.g., the phase of an entity). If a prismatic surface function is used as the first function, the height, h, width, s, and peak angle, a, of the first surface function can vary depending on the intended use of the substrate. In addition, the first surface function need not be the symmetric structures as shown in FIG. 1.

[00054] In one embodiment, the first surface structure function is modulated in phase, frequency, peak angle or height by the second surface structure function. The second surface structure function defines the type of modulation, to produce the three-dimensional surface of the film on the light-exiting surface 41 (FIG. 2) of the substrate 40. The surface height of the light-exiting surface 41 of the substrate 40 is therefore defined by the combination of these two surface structure functions. For example, the height of the peak of one or more of the first surface structure functions, eg., prisms can be modulated along the length l of the substrate 40. The height can be randomly or pseudo-randomly modulated between certain limits at random or fixed intervals along the length, l, of the substrate 40. As best understood, the term random means true randomness or randomness to the extent possible when generated by human means, e.g., pseudo-randomness. In another example, the phase, i.e., the horizontal position along the width w of the substrate 40, of one or more of the first surface structure functions can be modulated, at least pseudo-randomly between certain limits along the length, l, of the substrate 40. In yet another example, the peak angle of the first surface structure function can be modulated along the length l of the substrate 40. Thus, a combination of modulation techniques can be used to create the three-dimensional surface of the substrate 40 so that the single three-dimensional surface turns and diffuses light. The specific modulation techniques used to produce the substrate 40 depicted in FIG. 2 will be described in greater detail below.

[00055] FIG. 5 is a graphical representation showing three cross-sections of a substrate 40 in different positions along the length “l” of FIG. 2. A first cross-section 50, taken at, for instance, the position of 400 microns along the “l” direction of FIG. 2, could extend for a portion of the width w of the substrate 40 (specifically, between about 200 and 500 microns in the “w” direction). The second cross-section 52 could be taken, for example, at the position of 800 microns along the “l” direction of FIG. 2, and the third cross-section 54 could be taken, for example, at the position of about 1400 microns along the “l” direction in FIG. 2. The vertical axis in FIG. 5 is meant to show only an amount of variation in the height of the surface of substrate 40 and not the actual height of the substrate 40. The horizontal axis in FIG. 5 shows the horizontal position along the w direction in FIG. 2. As can be seen in the cross-sections of FIG. 5, modulated sawtooth functions continue to exist at specific cross-sections 50, 52, and 54 of the substrate 40. Because the phase of these structures has been modulated, however, each cross-section 50, 52, 54 has peaks 56 that are not in alignment with the other cross-sections 50, 52, 54. This is also evident from the top view of FIG. 2, in which the modulated surface functions 46 extending the length l of the substrate 40, tend to sway, turn, combine or bifurcate, and cross in such a way that there are no discrete elements. In FIG. 5, the peak angles 58 of the sawtooth functions are about 90 degrees. Although FIG. 5 does not show modulated peak angles of the sawtooth functions, these peak angles could also vary from one peak to the next along the generally longitudinal direction “l” of FIG. 2 for a given optical element 46. The peak is the local height maxima on the resultant surface cross section in the w direction.

[00056] Even after the first surface structure function is modulated to produce the three-dimensional surface of the substrate 40, the characteristics of the first surface structure function that produce output specular components from input beams of light are largely retained in the resulting three-dimensional surface. The amount of specular behavior, or light turning behavior, is tunable by altering the amplitude and/or spatial frequency modulation applied to the first surface structure function. For instance, reducing the amount of modulation applied to the first surface structure function increases specular behavior. In contrast, an increase in the amount of modulation applied to the first surface structure function decreases specular behavior, but increases diffusion. Similarly, a reduction in the amount of modulation applied to the first surface structure function also decreases the diffuse behavior of the substrate, and an increase in the amount of modulation applied to the first surface structure function increases the diffuse behavior of the substrate.

[00057] FIG. 6 shows the turning and diffusing properties of an exemplary embodiment of an optical substrate 100 that can be used for brightness enhancement applications. For clarity in FIG. 6, the irregular three-dimensional surface 41 of FIG. 2 is not shown, but would be present if shown as light-exiting surface 102 with characteristic surface dimensions of from about 100 mm to about 1 nm. A first beam of light, 138, having a zero degree angle of incidence, θ, to the substrate 100 is directed back by the light-exiting surface 102 toward the input. The light is not only directed back, but it is diffused so that, instead of a single output beam being formed, there is a first diffusion ellipse formed by rays 136 and 134. Diffused light can, for instance, exist within the ellipse formed by rays 136 and 134 so that a solid ellipse is formed. A second input beam of light, 124 having an input angle of incidence of θ is directed by the substrate 100 so that it is transmitted through to the light-exiting surface 102 as exit beam 128 and is turned so that it exits generally normal to the substrate 100. Beam 128 is also diffused by light-exiting surface 102 so that a second diffusion ellipse is formed. The second diffusion ellipse is formed by the power half angle Φ between 128 and rays 130 or 132. The power half angle Φ, which can be used as one measure of the diffusion characteristics of the substrate 100, can vary between about 0.1 and 60 degrees. In other embodiments, by altering the type and/or amount of modulation, the power half angle Φ can be between about 1 and 5 degrees. FIG. 6 shows that at least one output beam 130, 132 of light is turned by the substrate 100 and deviates from its input angle of incidence θ.

[00058] The diffusion characteristics of the substrate 100 of FIG. 6 can vary widely. For example, the diffusion ellipses formed can be symmetric cones in one embodiment. In other embodiments, the diffusion can have no symmetry at all or can have very little symmetry. The random modulation can be controlled to effect diffusion in the w and l directions differently i.e., the amplitude, bandwidth and the modulation parameter is applied to can be one dimensional along either the w or l direction, or two dimensional with different parameters along w, l. Other coordinates could be used to change the orientation of the modulation function with respect to the first surface function, including other rotated or shifted Cartesian geometries, such as cylindrical, spherical or generally warped coordinate systems. These may be used when an asymmetric light pattern is desired.

[00059] The light directing characteristics of the substrate can also vary widely. Referring to FIG. 7, if used with a light guide 106 of a backlighting unit having a lamp 108 and lower reflective surface 109, substrates 112 and 114 can increase brightness substantially, while also diffusing light. In brightness enhancement embodiments, the substrates 112 and 114 can increase brightness as viewed on-axis by about 30 percent to about 300 percent. Prior art linear prism arrays as well as brightness enhancement films with randomized prism arrays, cannot be used, or it is undesirable to use such arrays, in parallel because of Moiré effects. With this invention two substrates can be used at any angle with respect to one another between crossed (orthogonal) and parallel, because of the lack or Moiré effects. This allows for greater flexibility in the light output pattern. In other embodiments, the substrate increases on-axis brightness by at least 50 percent and by perhaps as much as about 200 percent. In brightness enhancement embodiments, the two substrates 112, 114 can be arranged to be orthogonal to one another in order to turn and diffuse input beams of light from different directions. Because diffusion behavior is built into the substrates 112, 114, separate diffusion substrates need not be used to eliminate Moiré artifacts caused by the substrates 112, 114, although a diffusion substrate can be used within the scope of the invention for other reasons.

[00060] Prior art FIG. 7 shows diffusers 116 and 118. Diffuser 118 diffuses Mairé artifacts resulting from interference caused by any inherent regularity of substrates 112 and 114. Diffuser 116 diffuses Moiré artifacts due to the regularity of en extractor pattern on the underside 120 of light guide 106 and the regularity of LCD panel 122. Conventional brightness enhancement films 112 and 114 can be replaced with the current Invention possibly eliminating thereby diffusers 118 and 116.

[00061] The diffusion characteristics of the substrates of the present invention reduce or eliminate Moiré artifacts caused by many common light directing films, such as that shown in FIG. 1. Exemplary films incorporating the substrates of the present invention, therefore, can turn and diffuse light on one surface so that Moiré artifacts are reduced or eliminated.

[00062] The autocorrelation function, R(x,y), is a measure of the randomness of a surface that is used in surface metrology. Over a certain correlation length, l_c, however, the value of an autocorrelation function, R(x,y), drops to a fraction of its initial value. An autocorrelation value of 1.0, for instance, would be considered a highly or perfectly correlated surface. The correlation length, l_c, is the length at which the value of the autocorrelation function is a certain fraction of its initial value. Typically, the correlation length is based upon a value of 1/e, or about 37 percent of the initial value of the autocorrelation function. A larger correlation length means that the surface is less random than a surface with a smaller correlation length. A more detailed discussion of the autocorrelation function is provided in David J. Whitehouse, Handbook of Surface Metrology, IOP Publishing Ltd. (1994), p. 49-58.

[00063] In some embodiments of the invention, the value of the autocorrelation function for the three-dimensional surface of the optical substrate 100 drops to less than or equal to 1/e of its initial value in a correlation length of about 1 cm or less. In still other embodiments, the value of the autocorrelation function drops to 1/e of its initial value in about 0.5 cm or less. For the embodiment of the substrate 40, 100 shown in FIGS. 2 and 6, the value of the autocorrelation function along the length l drops to less than or equal to 1/e of its initial value in about 200 microns or less. For the same embodiment of FIGS. 2 and 6, the value of the autocorrelation function along the width w drops to less than or equal to 1/e of its initial value in about 11 microns or less.

[00064] The correlation length is related to the reduction of Moiré artifacts. As noted, smaller correlation length indicates a more random surface than a larger correlation length, and this smaller correlation length also relates to greater diffusion and the reduction of Moiré artifacts. Because the three-dimensional surface of the substrates 40, 100 are highly irregular, as indicated by the low correlation length, the substrates 40, 100 can be effective to reduce Moiré artifacts.

[00065] The following discussion is intended to provide some illustration of the anti Moiré properties of the present invention. In the following examples it will be shown that 1) the invention has much lower auto correlation than both straight prisms and randomized prism structures 2) auto correlation length is a good indicator as to the possibility that a structure will produce Moiré patterns in a system.

[00066] Consider the 20 um tall, 40 um pitch straight prism array 400 of FIG. 18 as a baseline. The auto-correlation function 402 of a horizontal profile taken through the prism structure 400 along the w direction is shown in FIG. 19. The attenuation of the auto correlation function 402 is an indicator of the randomness of the structure. The structure in FIG. 18 is completely ordered and therefore the only attenuation is due to the finite extent of the sample. We must consider this roll off of the envelope of the sinusoidal auto correlation function when comparing to other examples.

[00067] FIG. 20 shows a Moiré map 404. For the prism structure 400 of FIG. 18, the Moiré map in FIG. 20, is the image produced by multiplying the height (although, it doesn't have to be height that is modulated) maps of the structure of FIG. 18 by that of a reference prism structure of similar pitch. This is similar to what happens when two structures are placed in closed proximity in an optical system (or one is imaged onto another). The reference prism structure is a 50 um pitch prism array oriented parallel to that of the prism structure 400 of FIG. 18. This is the worst-case scenario for introducing Moiré.

[00068] A Moiré plot is shown in FIG. 21 at 406. This is a profile of the Moiré map 404 of FIG. 20 along the w direction. Note that for the 40 um pitch prism of FIG. 18, the Moiré map of FIG. 20 and the Moiré plot of FIG. 21 both show a strong beat pattern as a low frequency envelope.

[00069] Next consider the 40 um pitch prism array of FIG. 18 with +/−20% randomness introduced into the horizontal position (w direction) of the prism centers resulting in random variations along each prism in the vertical, or l direction as shown at 408 in FIG. 22.

[00070] Note now in FIG. 23, the somewhat more rapid attenuation of the auto correlation. This is due to the introduction of the randomness to the prism 40 um pitch prism array. In the Moiré map 412 of FIG. 24 and the profile 414 thereof in FIG. 25, the beat pattern is somewhat scrambled but still visible. As in FIG. 19, the attenuation of the autocorrelation in FIG. 23 is due to the finite extent of the sample.

[00071] Consider next one embodiment of the present invention as shown at 416 in FIG. 26. This structure has full cycle (e.g., greater than 100% of the “pitch”) randomization along with superimposed phase modulated “prism wave forms” with heights between 20 um and 10 um and slopes between 40 and 50 degrees. In this case that randomness and superposition used results in bifurcating (or splitting) and merging structures or elements.

[00072] Note that, as shown in FIG. 27, the auto-correlation function of a profile 418 of FIG. 26 drops very rapidly compared to those of FIGS. 19 and 23 (e.g., to less that 0.2 in under 100 um). Thus, it should be expected that the anti Moiré performance of FIG. 26 is better than in FIGS. 18 and 22. This is shown at 420 and 422 in FIGS. 28 and 29. The beat frequency is entirely absent and all that remains is areas of non-uniformity. As seen in FIG. 29, these small non-uniformities are associated with the local structure of the invention and not the result of a beat pattern. The consequence of this is illustrated in FIGS. 30, 31 and 32. Here the Moiré maps are produced by using a 44 um pitch reference prism array. Note that for the straight prism of FIG. 18 and the 20% randomized prism of FIG. 22, the beat pattern is at a lower spatial frequency (fewer cycles across the map).

[00073] In contrast the non-uniformities for the map of FIG. 26 are similar to those in FIG. 24. Since the non-uniformities are always on the same scale as the structure, they will not be visible in the display and are of no concern (if the design pitch is fine enough). Moiré in the former examples is far more problematic because the beat pattern can have a period that is a large multiple of the prism pitch and may result in easily visible artifacts.

[00074] In FIG. 33 the vertical (l direction) auto correlation 430 of FIG. 26 is shown. Here it is seen that the roll-off is much less than that of FIG. 27, due to the longer period of the modulation in the vertical direction. In this example the vertical modulation is set so that the period of the oscillations is between 300 um and 500 um. For the Prism Array of FIG. 22, the vertical modulation is set so that the period of the oscillations (run lengths) are between 10 um and 100 um. In this case the attenuation is faster than that of FIG. 31 (see 432 in FIG. 34).

[00075] The generation of a model for the surface of exemplary substrates will now be described in detail. It should be noted that a number of methods for the generation of a surface model can be used and that the following discussion is but one of these methods.

[00076] By way of example, the surface depicted in FIG. 2 can be generated using an iterative process of superimposition of randomly, or psuedo-randomly, modulated waveforms. In FIG. 2, a series of superimposed waveforms generally form the three-dimensional surface of the film. These “waveforms” in the resultant structure of FIG. 2 are not necessarily present as distinct waveforms, however. Instead, the resultant three-dimensional surface of FIG. 2 contains superimposed waveforms that cross over each other and/or combine into a single waveform at certain locations.

[00077] To begin the iterative process that generates a substrate 40, such as that shown in FIG. 2, a series of waveforms is defined. Each of the defined waveforms has the general cross sectional shape of a sawtooth with a height of about 20 micron (um) above a reference plane. This series of waveforms is the first surface structure function referred to above. Each waveform has geometrical properties to turn light. Each of the waveforms is modulated, as described earlier, in one or more of frequency, phase, peak angle (or height). For example, FIG. 8 shows a single waveform 140 that extends from one end to the other along the l direction of FIG. 2. This waveform 140 has been modulated in phase so that, as viewed in FIG. 8, the horizontal position of the peak of the waveform varies between −20 and +20 microns in the w direction from a center position 142. FIG. 9 shows the variation in phase of the waveform 140 as a function of position along the direction l of FIG. 8. In the embodiment of FIGS. 8 and 9, modulation is applied to the waveform in random intervals between about 300 and 500 microns along the length, l, of the waveform so that the phase of the peak changes every 300 to 500 microns as l varies.

[00078] The peak angle is the angle formed at the peak of a waveform and is shown in FIG. 5 as numeral 58. For the waveform of FIG. 8, the peak angle has also been modulated every 300 to 500 microns along l between 90 degrees and 92.8 degrees. FIG. 10 shows the variation in the peak angle of the waveform of FIG. 8 along the length l. The height of each waveform may also be modulated randomly between 15 and 20 microns along the length l.

[00079] Although only the phase and peak angle have been randomly modulated in the waveform shown in FIG. 8, the frequency and height can also be modulated in other embodiments. For instance, in one embodiment, the height of a single waveform could be randomly modulated along the length l. In another embodiment, the frequency of a single waveform could be randomly modulated along the length l. Thus, the waveform is thin in some locations and thicker in other locations. In still other embodiments, the height of different waveforms can be modulated differently. Thus, a variety of phase, frequency, peak angle and height modulation techniques can be used within the scope of the invention to form the three-dimensional surface structure of the substrates 40, 100. The amount of modulation can also vary widely in the in the various techniques.

[00080] To form the structure shown in FIG. 2, a first iteration of superimposition of waveforms is performed. In the depicted embodiment, each individual waveform (modulated as described above) is stepped or placed on the surface of the substrate 40, 100 at about 40 micron intervals along the width w of the substrate 40, 100. For the 2,000 micron wide surface shown in FIG. 2, fifty waveforms would be superimposed at about 40 micron intervals. The resulting surface structure model after this first iteration would appear as shown in FIG. 11.

[00081] A second iteration of the superimposition of modulated waveforms is then performed. This second iteration can be performed in a similar manner as the first iteration. For example, another series of waveforms can be created as described above and can be superimposed at about 40 micron intervals along the width w of the substrate. The resulting surface structure model is shown in FIG. 12.

[00082] Though not necessary, to form the surface structure model shown in FIG. 2 from that shown in FIG. 12, a third iteration can be performed in which a sawtooth function is superimposed. The sawtooth function may have an 8 micron height and be superimposed at 20 micron intervals along the width w of the film. This third iteration, which makes up a small portion of the resultant surface height map, can be used primarily to fill flat spots on the surface. The resulting three-dimensional surface has a random or pseudo-random structure in which the individual waveforms have been superimposed to form the surface. Due to the iterated method of superposition and the large height of the random phase modulating function the surface does not contain individual optical elements. Instead, the resultant surface is an integrated optical substrate that is formed by the convergence of multiple modulations and superimpositions by Boolean union.

[00083] Referring to FIGS. 14, 15 and 16, the method by which the substrate is randomized will now be explained. A first window 216 is defined in a coordinate system. Locations of control points 202, 204 are randomized to form a modulation path 206 in a second window 200. The second window 200 is wider than the cross section of a surface function 208, e.g., three times the width of the surface function 208. The surface function may be for example a sawtooth function or a triangular function. Starting with a first control point 202 at the top of the second window 200, at each control point location the following elements are randomized: the x position of the control point within a predetermined range such as +/−20 um; the y distance to the next control point within a predetermined range such as from 300 um to 500 um; the height of the surface function, e.g., either 0 um or 20 um.

[00084] The randomized control point locations 202, 204 are quantized to a predetermined interval such as 20 um in order to reduce diffraction effects. New control points are randomly added to the second window 200 along the modulation path 206 until the length of the second window 200 in the y (or l) direction is exceeded. However, the first control point 202, 204 falling outside of the second window 200 is retained.

[00085] The modulation path 206 is determined from the control points 202, 204 for example by using a combination of nearest neighbor or linear or cubic interpolation. Discontinuities along the modulation path 206 are introduced between any two consecutive control points 202 having a nonzero height when a control point 204 having zero height lies between the two consecutive control points 202 having a nonzero height.

[00086] A nonzero surface function 208 is generated along the modulation path between successive control points 202 having a nonzero height. The surface function 208 assumes a value of zero between control points 202 having a nonzero height when a control point 204 having zero height lies between the two consecutive control points 202 having a nonzero height. The surface function 208 may have for example a cross sectional profile of a saw tooth function.

[00087] The window 200, containing the randomized surface function 208 is aligned and overlayed at a first position with a master function 210, which is initially zero. A Boolean union operation is performed between the surface function 208 within the window 200 and the master function 210. This results in the surface function 208 on the master function 210. The window 200 is moved left to right along the master function 210 in a predetermined incremental step of for example 40 um. A new surface function 208 is now randomly generated within the window 200 in the manner described above and a Boolean union operation is performed between the new surface function 208 and the master function 210. The window is again moved the predetermined incremental step, a yet newer surface function 208 is again randomly generated within the window in the manner described above and yet a new Boolean union operation is performed between the newer first function 208 and the master function 210. This randomization, Boolean union and stepping process is repeated over the entire width of the master function 210. At the end of the master function 210, the window returns to the first position and the randomization, Boolean union and stepping process is repeated any number of times over the entire width of the master function 210 resulting the randomized substrate 152 of FIG. 13.

[00088] The surface function is a triangle with a width of approximately 40 um and a height of between 1 um and 200 um or more particularly a width of approximately 40 um and a height of approximately 18 um. The surface function may also be a triangle with a base to height ratio of between 40 to 1 and 1 to 10 or more particularly with a base to height ratio approximately 40 to 18.

[00089] Holes or areas of zero height in the randomized substrate are found using morphologic operators and a “skeleton mask” function is created (FIG. 40). This function is convolved with the surface function 208 and the result is combined by Boolean union with the master function 210. These sights or areas can also be use to create a sparse pattern of anti-wet-out (or Newton's rings) bumps or protrusions that have a height that is greater than the rest of the pattern. These bumps do not need to have the same form or function as the bulk of the surface. The final pattern 212 is taken by trimming away at least the outer 100 um from the master function 210. In FIG. 22, multiple copies of the final pattern 212 are then placed side-by-side to one another, or “tiled”, so as to create a substrate surface as a two dimensional array on a wafer 214 mirrored with respect to one another for first order continuity. The size of the tiles, i.e., the master, is larger than the correlation length of the resultant pattern.

[00090] Thus, in FIG. 16, a window is defined at 302 and points are randomly selected within the window 304 thereby creating a modulation path 306 connecting the randomly selected points. Heights are randomly assigned at 308 to the randomly selected points within the window. A master function is defined at 314 and a surface function is generated along the modulation path at 310 and repeatedly combined with a master function 312 at successive locations within the master function.

[00091] As best understood the surface of the substrate may not only be randomized in height, frequency, phase or peak angle, but also by refractive index. Any of these parameters may also be modulated as shown in FIGS. 35-39. Therein, a sinusoidal carrier waveform sin(x) may be modulated in amplitude, phase, or frequency by a random function r(x) yielding a randomized function R(x) according to any of the following equations:
R(x)=r(x)+sin(x/k)  (1)
R(x)=sin(x/k+c×r(x))  (2)
R(x)=sin(x/(k+c×r(x)))  (3)
R(x)=sawtooth(x²/(n+10r(x)))×(n)/(x+n)  (4)
R(x)=r′(x)+sawtooth(x^2/(k+m×r(x)) )×(n)/(x+n)  (5)
where r′(x) is a second random function (or third surface function) and c, k and n are constants. The sawtooth function generates a sawtooth wave as a function of time, t, or space, w, l, having a period of 2π. The sawtooth creates a wave similar to sin(t, w, l) having peaks of −1 and 1. The sawtooth wave is defined to be −1 at multiples of 2π and to increase linearly with time with a slope of 1/π at all other times. Generally a plurality of random functions may be used to modulate a plurality of parameters of the first surface function. The plurality of random functions, r(x), as seen in FIG. 39 may each be spatially constant or spatially varying, or any combination thereof.

[00098] The actual surface of the substrates, having characteristic dimensions of about 100 mm to 1 nm, can be generated in accordance with a number of processing techniques. These processing techniques include photolithograpy, gray-scale lithography, microlithography, electrical discharge machining and micromachining using hard tools to form molds or the like for the surface model described above.

[00099] For example, the method of making the substrates may be by mastering, electroforming and mold forming. Photolithographic Mastering may be used to direct laser write to a photoresist, a gray scale mask or a series of halftone masks that may be tiled. The photoresist may be directly removed by the laser photons or used as a precursor to an additional process step, such as reactive ion etching (RIE). Alternatively the geometry might be mastered using hard tools, such as a single point diamond tool on a five axis mill. The master will generally be made as a negative. The Substrate of the master may be glass, including fused silica, crystalline, metal or plastic (polycarbonate for example). The master may be used to mold plastic parts directly or used in electroforming.

[00100] Electroforming is in one or two stages. The master will be a positive if only one stage is used. The master may be coated with a thin metal coating (especially if the master is not conductive to begin with). A “father” electroform is created by electro-depositing nickel on the master. This replica is again electroformed to create a “daughter” that is used to mold the plastic parts.

[00101] The object that is used to mold the device (films) is referred to as the mold. The mold may be in the form or a belt, a drum, a plate, or a cavity. The mold may be tiles from a plurality of masters or electro forms. The mold may be used to form the structures on a substrate through hot embossing of the substrate, cold calendaring of the substrate or through the addition of an ultraviolet curing or thermal setting material in which the structures are formed. The mold may be used to form the film through injection molding or vacuum forming. The substrate or coating material may be any organic, inorganic or hybrid optically transparent material and may include suspended diffusion, birefringent or index of refraction modifying particles.

[00102] The optical substrate so formed may be formed with an optically transparent material with an index of refraction between of 1.1 and 3.0 and more particularly with an index of refraction of approximately 1.75.

[00103] In FIG. 41 a sectional view of a backlight display 500 device is shown. The backlight display device 500 comprises an optical source 502 for generating light 504. A light guide 506 guides the light 504 therealong. A reflective surface 508 reflects the light 504 out of the light guide 506. At least one optical substrate 510 is receptive of the light 504 from the reflective surface 510. The optical substrates 510 comprise a three-dimensional surface 512 defined by two surface structure functions, the first surface structure function has 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 has a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency, phase and peak angle along the length of the first surface structure function. The three-dimensional surface 512 has a correlation function value of less than about 37 percent of an initial in a correlation length of about 1 cm or less. In the backlight display device 500, one of the optical substrates 510 may include a first three-dimensional surface 512 and a second three-dimensional surface 514 opposing the first three-dimensional surface 512. The second three-dimensional surface 514 may also have a correlation function value of less than about 37 percent of an initial in a correlation length of about 1 cm or less. The second three-dimensional surface has two surface structure functions; a third 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 a fourth surface structure function having a geometry with at least pseudo-random characteristics to modulate the first surface structure function in one or more of frequency, phase and peak angle along the length of the first surface structure function.

[00104] In the backlight display device 500 the optical substrates 510 include first and second surface functions in a relative orientation from zero to ninety degrees with respect to one another, which may be parallel or perpendicular with respect to one another.

[00105] Aside from the use of the optical substrates described above in backlight displays for brightness enhancement, the substrates can be used in a wide variety of other applications as well. Embodiments of the substrates can be used in Fresnel lenses, holographic substrates or in combination with conventional lenses, prisms or mirrors. Such embodiments could be formed by modulating concentric circles or ellipses having fixed characteristics. The optical substrates can also be used in single or multi-order reflective, transmissive or partially transmissive, whether light absorbing or non light absorbing prisms, holographic optical elements, or diffraction gratings, and the output angles of the specular components can be tuned by changing the first surface structure function. The substrates can be used in other applications such as projection displays, illuminated signs, and traffic signals.

[00106] In the present discussion specular is defined to mean any component of reflected or transmitted light that that is not diffused on a macroscopic scale. The macroscopic is the bulk behavior that would be observed by interrogating the surface of the substrate with a beam of coherent light with a diameter of about 500 micron or greater. A classic multi-order grating would be considered to have multiple specular components.

[00107] Any references to front and back, right and left, top and bottom, upper and lower, and horizontal and vertical are, unless noted otherwise, intended for convenience of description, not to limit the present invention or its components to any one positional or spatial orientation. All dimensions of the components in the attached Figures can vary with a potential design and the intended use of an embodiment without departing from the scope of the invention.

[00108] While the invention has been described with reference to several embodiments thereof, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.