Abstract:
A system is provided for increasing the brightness and color saturation of a liquid crystal display to permit direct sunlight viewing which includes the utilization of an array of diffractive color separation microlenses which serve both to spatially separate incoming white light into red, green and blue bands which do not overlap and to focus the bands onto a subpixel matrix such that each of the sub-pixels is illuminated with only one color. The diffractive color separation is made possible through the utilization of the iterative genetic algorithm which specifies the stepped surface of the lens that provide for exceptionally fine color separation. In one embodiment the genetic algorithm is applied iteratively to define the optimal stepped surfaces which are utilized to focus the various colors at different positions at the focal plane of the lens. The subject system improves the overall transmission efficiency of 5% for a standard liquid crystal display to in excess of 30% overall efficiency. This results in lower power requirements or alternatively a brighter display such that the displays are sunlight viewable and have application in lap top computers, cockpit displays, automobile instrument displays, ATM displays, projection displays, equipment displays, and in general any display of a color LCD nature which is to be viewed in direct sunlight.

Description:
This application claims benefit of provisional application No. 60/145,549 filed Jul. 23, 1999. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to liquid crystal displays and more particularly to a system for improving the brightness and color saturation of a color liquid crystal display to make it sunlight viewable. 
     BACKGROUND OF THE INVENTION 
     Liquid crystal displays have long been utilized for the display of information which is computer generated and which is to be viewable in direct sunlight, if possible. Such displays originated with the marine fishing industry in which so called super twist pixels were utilized to make a black and white display viewable in direct sunlight. This technology was extended for use in cockpit displays and indeed in other black and white displays in which the display was to have been used outdoors. 
     The problem with super twist crystals and the back and white displays was the amount of information that could be conveniently presented to the viewer. Many attempts have been made to adopt the super twist liquid crystal display technology for color liquid crystal displays in order to make them sunlight viewable. 
     The most recent attempts at such displays have been in the field of lap top commuters in which the lap top is provided with a liquid crystal display panel viewable from plus or minus 60 degrees for ease of usage. However, these displays wash out in bright sunlight primarily due to the reflection of the sunlight towards the viewer and lack of an ability to compensate for the reflection. 
     In the past, attempts to compensate for the reflection have centered around the utilization of so called anti-reflective coatings. However, the anti-reflective coating alone is insufficient to overcome the problem of daylight viewing given a limited power source. It will be appreciated that current liquid display stacks have an optical efficiency of only 5% when viewed from the point of view of the power in to the illuminator lamp verses illuminated power out. What this means is that while it may be possible to provide suitable daylight viewing liquid crystal displays, it is only at the cost of power consumption which in a portable application is not acceptable. 
     While in some applications power consumption is not the problem that it is portable applications, it is nonetheless important to be able to achieve the brightest, most highly visible color display possible to be able to counter the effects of direct sunlight and its reflection. 
     As illustrated in U.S. Pat. No. 5,600,486 issued to George Gal and Bruce Herman on Feb. 4, 1997 and assigned to the assignee thereof, color separation microlenses are described in which a single micro optical element is made up of a color separation grating integrated with a refractive lens. The color separation micro lens separates the spectrum into distinct color spots and focuses these spots into a common plain. These spots fall at the locations of different diffraction orders of the grating, with the color separation accomplished by the grating and the focusing being done by the lens. As mentioned in this patent, the color separation microlens can be fabricated as a monolithically integrated element or as a dual sided thin wafer. 
     While the color separation microlens described in U.S. Pat. No. 5,600,486 serves adequately for some applications, it has been found that the degree of color separation achievable with the stepped structure illustrated in this patent is insufficient to provide the necessary fineness of color separation required, for instance, for a 256×256 liquid crystal display. It will be appreciated that there are only a limited number of steps in the micro lens shown in the above identified patent with the steps being insufficient to provide sufficient color separation because the diffraction efficiency is determined by a number of factors including the number of steps. It can be demonstrated that the larger the number of steps the more fine will be the color separation and the more saturated will be each of the colors at the focal plane of the lens. Note that the fewer the number of steps in the microlens, the more the light spreads out which degrades the overall performance of the microlens. 
     It will also be appreciated that in this patent the color separation is in terms of spots or circles. With the step structure shown and the focusing properties of the lens it will be appreciated that what this patent describes is a means for providing focused spots of color as opposed to bands. However, as is common in color liquid displays the pixels are made up of three side by side rectangles which are separated by a mask. Thus the stepped structure and focusing described in this patent do not provide a pattern of colored bands which match to a rectilinear subpixel on the display. 
     Moreover, nowhere in the above mentioned patent is addressed the question of overall brightness of a display. It was sufficient for the Gal et al patent to be able to achieve color separation utilizing a microlens display. However, how a sunlight readable device is achievable using the Gal et al system it is not discussed within the patent. 
     However, as illustrated in U.S. Pat. No. 5,781,257 some of these issues are addressed, albeit with the same type of micro lens structure. In this patent it is pointed out that because of the color separation microlenses no color filters are required in the display which eliminates the light losses due to transmitting light through a color filter. It is however noted that the amount of brilliance of the display is directly proportional to the degree of color separation achievable and color saturation achievable by the microlens. The Gal et al device as described does not achieve maximal brightness or color saturation. More particularly, in a CIE color diagram while CRT displays in general conform to the best possible color saturation to generate the colors, and whereas color liquid crystal displays provide sufficient color saturation to permit portrayal of colored on-screen objects, the Gal et al patents and the microlens used therein do not permit depiction of a large number of colors, and more importantly, those colors normally utilized to portray colored on-screen objects. 
     By way of further background, it will be appreciated that in addition to the above mentioned patents which describe microlens structures, there are several methods in the prior art for fabricating microlenses. As can be seen in U.S. Pat. Nos. 5,310,623 and 5,482,800, photolithographic methods are described which permit the fabrication of microlenses utilizing a photoresist process, with a photoresist material replica used to reproduce the replica directly in a substrate material. Finally, a dispersive microlens is shown in U.S. Pat. No. 5,497,269 in which the dispersive microlens apparatus is used for detecting multiple different wavelengths or for combining a plurality of different emitted wavelengths into a bandwave of wavelengths. 
     SUMMARY OF THE INVENTION 
     Rather than utilizing the color filter techniques commonly used with color liquid crystal displays, and as a further improvement on the microlens separation techniques of Gal et al, in the subject system the microlenses are produced through the utilization of an iteratively applied genetic algorithm for providing optimal color separation and color saturation through the utilization of at least an order of magnitude more steps in the microlens than that described by Gal et al. In addition to the color saturation and separation being increased by the increased number of steps of the microlens, the iterative genetic algorithm also asks the computer to search for all allowable solutions to the color diffraction color separation problem, and provide an optimal solution based on the input parameters. The result is that not only is there finer color separation, to increase illumination of the subpixels and to minimize light incident on the mark as opposed to the subpixels, color saturation increases by an order of magnitude so as to permit the generation of all the colors required to depict on-screen graphical objects at the maximum brilliance. 
     ITERATIVE GENETIC ALGORITHM 
     The iterative algorithm for defining the stepped structure and the fresnel focusing is now described: 
     For purposes of this invention a genetic algorithm is an iterative method to design the surface profile of the color separator by defining several physical features of the surface profile as genes which are allowed to evolve to an optimal solution. For the present purposes the gene involved is the width of each of the optical elements. Other factors include the design wavelength and the focal plane as physical constraints. Each generation of the genetically defined surface function is scored with a testing function. High scoring surfaces are allowed to go on to the next generation, thus to provide a test of the fit of the surfaces to provide an ideal result. 
     In the present case the widths and heights of all portions of the design including the diffraction grating and the fresnel portion are provided in terms of a set of seed functions. The resulting surface profile is tested with the testing function, with the testing function giving an overall weight to the profile generated. Succeeding generations of the design are based on the initial seeds plus random elements to allow for genetic variation. Iteratively stepping through this process provides a maximal fit for optimal design. 
     In one embodiment, with physical constraints as to step width and the overall pixel size, a seed set is generated which includes a particular step width and a pattern of step heights for each element. In one embodiment the microlens is to have a 330 micron diameter. This is broken up into 1.2 micron elements. The seed set generates a surface which is tested using standard diffraction grating theory to ascertain the diffraction efficiency and focusing capability. Standard diffraction grating theory is described in a text entitled Optics by Hecht, p. 312-465 in a section entitled Diffraction. The surface profile of the microlens can be described as a transmission phase grating with non-uniform placement of elements. The test function analyzes the phase contribution from each element from first principles of Diffraction theory. 
     The test determines at a given off axis angle what the expected light intensity should be at a given color. The test also convolves the focusing merit figure, so that after a number of iterations in which random variations are added, an optimal solution is finally achieved. 
     This is accomplished by crossing for instance 5 seeds with each other. This means that the result of one seed is crossed with the result of another seed, with the results being tested. If 5 seeds are crossed one can obtain as many as 25 testable results. These results are tested and the worst 20 are discarded. The results are then crossed again along with a random seed input to permit the genetic change. 
     Thus, in general a genetic algorithm is one in which as number of seeds are used to create a result. The results are then crossed with each other to obtain multiple results which are then tested. Superior results are selected and crossed with each other along with a random seed factor and the results tested again. In this manner a large number of results can be tested to determine the optimal result. 
     EFFICIENCIES 
     In addition to the color separation and color saturation improvements, the system provided results in an overall efficiency of in excess of 30% over common color liquid crystal display technologies. The reason is not only the elimination of the color filters normally utilized in these displays which result in only a 5% efficiency, the utilization of the subject microlens permits the utilization of gradient index diffuser and anti-reflective coating to permit wide angle viewing while at the same time rejecting reflected sunlight. It will be appreciated that in the past, anti-reflective coatings have been traditionally utilized on liquid crystal displays but have been relatively ineffective because of the holographic diffusers normally utilized. Rather than utilizing a holographic diffuser, in the subject system a gradient index diffuser is useable which provides a wide angle of viewing suitable for the application requirements and is also capable of being coated with an anti-reflective coating due to the fact that its surface is smooth. 
     The result of utilizing the subject microlens array and the specific diffuser and anti-reflective coating is that it is now possible to provide sunlight viewable color liquid crystal displays in which all of the required colors can be generated. It is also important, due to the subject system, that power requirements are significantly reduced due to the 30% plus effective optical efficiency. This means battery life for portable devices such lap top computers will not suffer with the provision of the increased brightness and increased color saturation display. 
     In summary, a system is provided for increasing the brightness and color saturation of a liquid crystal display to permit direct sunlight viewing which includes the utilization of an array of diffractive color separation microlenses which serve both to spatially separate incoming white light into red, green and blue bands which do not overlap and to focus the bands onto a subpixel matrix such that each of the sub-pixels is illuminated with only one color. The diffractive color separation is made possible through the utilization of the iterative genetic algorithm which specifies the stepped surface of the lens that provide for exceptionally fine color separation. In one embodiment the genetic algorithm is applied iteratively to define the optimal stepped surfaces which are utilized to focus the various colors at different positions at the focal plane of the lens. The subject system improves the overall transmission efficiency of 5% for a standard liquid crystal display to in excess of 30% overall efficiency. This results in lower power requirements or alternatively a brighter display such that the displays are sunlight viewable and have application in lap top computers, cockpit displays, automobile instrument displays, ATM displays, projection displays, equipment displays, and in general any display of a color LCD nature which is to be viewed in direct sunlight. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features of the subject invention will be better understood in connection with the Drawings and conjunction with the Detailed Description, of which: 
     FIG. 1 is a diagrammatic illustration of a lap top application requiring an increased brightness, increased color saturation display suitable for direct sunlight viewing; 
     FIG. 2 is a cross-sectional and diagrammatic illustration of a prior liquid crystal display illustrating the utilization the absorptive color filters which, in combination with the losses across the liquid crystal display stack, result in only a 5% throughput; 
     FIG. 3 is a diagrammatic illustration of the losses incurred in the utilization of a prior color liquid crystal display stack illustrating that for a 47 watt input power only 130 lumens of light energy exits the display; 
     FIG. 4 is a CIE graph illustrating color saturation for various color displays, including that associated with the Gal et al patents; 
     FIG. 5A is a diagrammatic and exploded view of the subject system illustrating a light source, and a liquid crystal display panel which sandwich a microlens array in which each of the microlenses focuses and separates the incident light into colored bands which are focused respectively on the red, green and blue sub-pixels of the liquid crystal display; 
     FIG. 5B is a schematic diagram of the focusing of the red, green and blue bands onto the sub-pixels of a liquid crystal display; 
     FIG. 6 is a top view of the microlens of FIG. 5A showing the grating lines for the microlens as well as phase tears utilized in the focusing portion of the lens; 
     FIG. 7 is a diagrammatic illustration of the placement of the microlenses on the back of a glass substrate which spaces the lenses from the sub-pixels of the liquid crystal display such that the sub-pixels lie on the focal plane of the lenses; 
     FIG. 8 is a diagrammatic and cross-sectional view of the subject liquid crystal display stack illustrating the utilization of collimated light which impinges upon the microlenses and then through a polarizer, glass plate having an active pattern the matrix for driving the display, followed by the liquid crystal display panel, followed by a further glass plate to hold in the liquid crystal display, followed by a polarizer, followed by a diffuser, and finally out through the anti-reflective coating on the exterior surface of the diffuser; 
     FIG. 9 is a diagrammatic illustration showing the overall efficiency of the subject color liquid crystal display indicating the percentage transmission through each of the elements of the stack, illustrating a 32% efficiency; 
     FIG. 10 is a diagrammatic illustration of a portion of the microlens array of FIG. 5A indicating the ability to project onto rectangular sub-pixels the red, green and blue bands required for their illumination; 
     FIG. 11 is a diagrammatic illustration of the correspondence of the diffraction grating on the lens to a cross-sectional view of the lens itself; 
     FIG. 12 is a graph showing the surface structure of the microlens in phase space in which horizontal distances lie on the X axis and in which the vertical axis carries the phase information, with the phase information being one to one correlatable to the length design point; 
     FIG. 13 is a top view of a portion of the subject light crystal display having rectangularly masked sub-pixels, with the corresponding microlens being viewable therethrough; 
     FIG. 14 is a diagrammatic illustration of a prior art liquid crystal display mask in which the mask blocks out close to 40% of the incident light on the liquid crystal display; 
     FIG. 15 is a diagrammatic illustration of the ability to eliminate the effect of the mask on the system by the ability to exactly focus bands of different colors to corresponding different subpixel elements, thereby eliminating the mask illumination associated with the system of FIG. 14; 
     FIG. 16 is a diagrammatic illustration of one embodiment of a light collimator in which collimated light is collimated in the vertical direction to plus or minus one half a degree, thereby permitting the maximally fine focusing of the colored bands by the microlens assembly of FIG. 8; 
     FIGS. 17A-C are diagrammatic illustrations of the collimator of FIG. 1 showing the addition of top and bottom parabolically shaped portions of the waveguide to provide collation in a direction parallel to the axis of the fluorescent tube utilized to provide the lambertian light source; 
     FIG. 18 is a diagrammatic representation of the initial collimating elements showing the parabolic surfaces used therefor; 
     FIG. 19 is a side view of a collimating light source utilizing a collimating sheet as opposed to a collimating waveguide, showing the sheet being positioned between a fluorescent tube light source and the end of a reflective array with 45 degree stepped reflector elements and collimating lenses on the face thereof; 
     FIG. 20 is a diagrammatic illustration of the collimating sheet of FIG. 19 in which the sheet is provided with internal parabolic reflectors, each of which is focused on an edge of a slit which opposes the parabolic reflector; and, 
     FIG. 21 is a diagrammatic representation of a light source for use with the collimating sheet of FIG. 20 in which either a serpentine fluorescent tube is utilized or in which a plurality of parallel mounted fluorescent tubes are used to eliminate the need for the reflective array of FIG.  19 . 
    
    
     DETAILED DESCRIPTION 
     Referring now to FIG. 1, an individual 10 is depicted as viewing a liquid crystal display  12  of a laptop computer  14  which is bathed in sunlight through window  16 . It will be appreciated that it is only with difficulty that the individual can ascertain the graphical objects on the liquid crystal display due to the reflection of the sunlight towards the viewer of the display. While liquid crystal displays have been utilized routinely in darkened or semi-darkened surroundings to great effect, as mentioned hereinabove, the sunlight tends to wash out the screen making daylight viewing difficult. 
     One of the reasons that the prior art liquid crystal display panels were not sunlight viewable can be seen in connection with FIG. 2 in which a liquid crystal display stack  20  is illustrated as being illuminated with a light source  22 , in most cases a fluorescent light tube, which has its light redirected towards the display by a reflector  24 . The light from light source  22  is filtered by a polarizer  26  the purpose of which is to permit modulation of the light in a subpixel of a liquid crystal display  28 . Prior to modulation, absorptive color filters  30  are interposed between liquid crystal display  28  and polarizer  26 . The purpose of the absorptive color filters is to provide a pattern of red, green and blue light adjacent the subpixels of the liquid pixel display so that the white light from the light source is divided up into the primary red, green, blue colors and is made available immediately adjacent the corresponding red, green and blue subpixels. 
     In order to provide the appropriate modulation, a glass plate with addressing columns and rows  32  is interposed between absorptive color filters  30  and liquid crystal  28 , with a glass plate  34  utilized to contain the liquid crystal between itself and glass plate  32 . Polarizers  36  are provided on the outside of glass plate  34  to permit the aforementioned modulation of light passing through the subpixel elements in liquid crystal display  28 . As will be seen in connection with FIG. 3, the efficiency of such a prior art stack is only 5%, which requires either a very large power source to provide for adequate brightness or utilization of the device only in dim environments. 
     Referring now to FIG. 3, in one military night vision application assuming a 47 watt power input is illustrated at  40 , a power supply  42  has an efficiency of 85% which provides a 40 watt output as illustrated at  44 . This output is applied to a fluorescent lamp  22 , which in one case is a 65 lumens per watt lamp. The result is a 2600 lumen output as illustrated at  46 . This output impinges on divergence reduction filter  48  which has a transmissivity of 90%. It is the purpose of the divergence reduction filter to focus light into the required viewing angle. The output  50 , of this filter is 2340 lumens. This light impinges on NVIS filter  52  the purpose of which is to cut off wavelengths lower than a defined point for night vision viewing for military purposes. The output of filter  52 , as illustrated at  54 , is  2106  lumens which impinges upon a diffuser  56 , the purpose of which is to keep the light uniform so that when it bathes the liquid crystal display the liquid crystal display is uniformly illuminated. The output of such a diffuser as illustrated at  58  is 2000 lumens. This output is directed towards address cell assembly  60  which includes both the liquid crystal display and its associated polarizers. The address cell assembly includes the aforementioned colored filters, polarizers and active matrix, such that the output of this assembly is only 130 lumens. The efficiency of this so-called stack is on the order of 6.5%. The output light at 130 lumens compared to the light input of 2600 lumens provides an overall efficiency of only 5%. 
     If the 5% overall throughout efficiency of the prior color liquid crystal displays were not enough, even assuming one were to utilize the liquid crystal display systems of the aforementioned Gal et al patents, the color saturation as illustrated at  55  in FIG. 3 would be insufficient to provide the colors necessary for depiction of graphical objects. It will be appreciated that the CIE graph of FIG. 4 illustrates the desired color saturation at 100% for the depiction of colored objects, as illustrated at  57 . As illustrated by graph  59 , this graph corresponds to the color saturation for a normal color CRT display which indeed is quite adequate for the depiction of colored graphical objects. On the other hand, as illustrated by the inner graph  55  associated with the Gal et al patent, the color saturation is well below 50% of that required for adequate depiction of colored graphical objects. The reduced color saturation is that which results from the system described in the Gal et al patents and is due to the limited ability of the stepped surfaces of the lenses to be able to provide adequate color separation or indeed adequate intensity of the colored spots. Moreover, since the Gal et al patents refer to the focusing of colored spots on a liquid crystal display, it will be appreciated that round spots projected onto rectangular subpixels cannot create color saturation to the desired level. With the subject system as will be described the utilization of highly separated bands of color provides for increased color saturation so as to match that attainable with color CRT displays. 
     On the other hand, the color saturation associated with the subject system as illustrated at  61  provides substantial color saturation improvement as will be discussed due to the fine structure of the diffraction grating and the genetic algorithm used to generate it. 
     In contradistinction to the system illustrated in FIG. 2, and referring now to FIG. 5A, subject lens array  70  includes a number of microlenses  72  which is utilized to separate the white light from a collimated light source  74  and project it in columns or bands to subpixels  74 ,  76 , and  78  of a liquid crystal display  80 , with the subpixels generating respectively red, green and blue components for each pixel. As will be seen, it is the purpose of microlens  72  to be able to accurately separate the white light into the aforementioned columns or bands such that the particular colored band only is incident on its respective subpixel. Moreover, it is the purpose of the subject microlens that the color saturation at each of the subpixels exceeds 16 dB. This compares the amount of the color of the corresponding subpixel versus light leaking from other sources. 
     One possible structure of each microlens is illustrated in FIG. 6 in which the lens has a number of diffraction grating lines  82  across its face  84 , with the surface of the lens being provided with a fresnel pattern for focusing purposes, with the fresnel structure being diagrammatically illustrated by phase tears  86 . 
     Referring to FIG. 6, a number of microlenses  72  are arrayed on the back surface of a glass plate  88  which serves to space the lenses from the liquid crystal subpixel elements as illustrated in FIG.  7 . 
     Referring now to FIG. 7, collimated light in one embodiment illuminates the microlens array  72  as illustrated, with the lenses being supported by glass plate  88  such as illustrated in FIG.  6 . 
     Referring now to FIG. 8, between glass plane  88  and liquid crystal  90  is a polarizer  92  which serves the same purpose as that specified hereinabove. Glass plate  94  carries the active matrix addressing system for the subpixels, whereas the liquid is contained by another glass plate  96 . The drive for the liquid crystal display is illustrated at  98 . 
     The light output from the liquid crystal is passed through a polarizer  100  and thence through a diffuser  102  which is of the gradient index type and has a flat exterior surface. An anti-reflective coating  104  is applied across this flat surface, such that the overall efficiency of this stack, rather than being 5% is better than 32%. Note, that the particular flat surface diffuser permits use of an extremely effective anti-reflective coating to improve sunlight visibility while providing wide angle viewing. 
     The overall effect of the subject stack is to provide a brightness not heretofore possible, given the power constraints of a portable device while at the same time providing reflection of sunlight to a degree not heretofore possible. 
     Referring now to FIG.  9  and the overall efficiency of the subject stack, in one embodiment an efficient power supply  110  is provided, with the overall efficiency being 85%. A collimated light source is provided at  112  which provides 45 lumens per watt directed towards the interference based lens array  72  which itself has an efficiency of 85% as opposed to 17% for absorptive color filters. The focused and separated light bands here illustrated at  114 ,  116 , and  118  impinge upon a thin film transistor, liquid crystal and absorptive polarizer stack generally illustrated in FIG. 7 which has an efficiency of 40%. The output as illustrated at  120 ,  122 , and  124  impinges on the angle correcting gradient index diffuser  102  of FIG. 7 to provide an overall diffuse white image, with the angle correcting gradient index diffuser  102  having a transmission of 95%. It can therefore be seen that the overall efficiency of the subject system is in excess of 32% as opposed to 5% in the prior art. Thus, it will be appreciated that the subject system has at least a 5 to 1 efficiency improvement over that attainable over conventional color liquid crystal displays art. 
     Referring now to FIG. 10, a portion of array  72  is shown to illustrate the side by side microlens array in which each of the microlenses is responsible for triple subpixel elements here illustrated at  130 . The advantages of the subject microlens are due to the iterative genetic algorithm utilized in the generation of the surface of the lens. 
     Referring to FIG. 11, a cross sectional view of a microlens  72  is illustrated in which the lens surface  132  has ruled or etched diffraction steps or lines which are carried forward as illustrated in the top view as lines  134 . It is the position and configuration of these lines which provides for the aforementioned exceedingly fine color separation leading to not only enhanced color saturation but also the ability to focus the colored band or column directly and accurately onto a subpixel without having to illuminate the mask in between the subpixels. 
     The specific structure of the microlens surface is illustrated in FIG. 12, in which distance is displayed on the X axis, whereas phase space is depicted on the Y axis. It will be appreciated that were the graph to contain distance on the X axis and distance on the Y axis equally, the structure would not be visible for illustrative purposes. 
     What can be seen is that for each microlens there is central region by arrow  136 , the fresnel structure of which defines the focusing function of the lens. Each of the fraction lines here illustrated at  138  has a stepped structure  140  which is defined by the subject genetic algorithm. It is the purpose of the steps to separate the incident light into colored bands having sharply defined edges. Without these sharply defined edges, overlapping illumination would occur at each of the subpixels and light would be lost through illumination of the mask between the subpixels. 
     As can be seen phase tears  140  and  142  define the fresnel lens portion of the microlens. It will be appreciated that a fresnel configuration is utilized for the microlens structure to provide a relatively flat , with the lens curvature being provided by the fresnel structure. 
     MASK ILLUMINATION CONSIDERATIONS 
     Referring now to FIG. 13, a portion of the liquid crystal display  150  is shown with a mask  152  masking off separate regions  154 ,  156 , and  158  corresponding respectively to the blue, green and red regions to be illuminated. As pictured immediately under the mask illustrated at  152  is microlens  160 , with FIG. 12 being a top view looking through the liquid crystal display and mask towards the microlens. 
     Referring now to FIG. 14, and referencing to prior art liquid crystal displays, it will be appreciated that mask  152  has masked off regions between pixels  154 ,  156 , and  158 . Because the light from the color filters is incident upon not only the mask but also the subpixel regions, the mask blocks close to 40% of the light. The result is a throughput or efficiency of only 60% of the 17% of the light available at the liquid crystal display, leaving an efficiency of only 10.2%. 
     In contradistinction, and as illustrated at FIG. 15, microlens  72  provides exact and accurate illumination of subpixels  154 ,  156 , and  158  such that the mask blocks virtually none of the incident light. In one embodiment, the width of the subpixels is on the order of 80 microns whereas the space between the subpixels in on the order of 30 microns. It will be appreciated that it is the 30 micron space which heretofore has light incident on it, but from which losses occur. 
     LIGHT COLLIMATOR 
     What is now described is a collimator suitable for use with the subject microlens array and color liquid crystal display. Referring now to FIG. 16, a collimator  210  in one embodiment collimates the light from a lambertian light source  212  that in a preferred embodiment includes a fluorescent tube  214  which has a longitudinal axis therethrough. Tube  214  is surrounded by a diffuse reflector  216  which has an exit slit  218 , with the edges of exit slit  218  providing the focus for opposed parabolas of a waveguide, illustrated here at  220 . 
     It will be appreciated that waveguide  220  in one embodiment is made of a transparent material, conveniently acrylic or glass, in which sides  222  and  224  of the waveguide are parabolic. The parabolas for this waveguide have a focus at an opposed edge of the exit slit such that for instance, parabolic surface  222  has its focus  226  at the edge which is said to opposes this surface. Likewise parabolic surface  224  has its focus  228  at the indicated edge. 
     It is the purpose of the parabolic surfaces of waveguide  220  to redirect the light from the exit slit of the light source such that light which is normally dispersed in an arc of 180 degrees is redirected down the wave guide and exits exit aperture  230  of waveguide  220 , with a collimation of +/−3 degrees in the horizontal direction. The collimation of the light in the vertical direction is plus or minus  10  degrees, with the collimation being performed as illustrated in FIGS.  17  and  18  by top and bottom portions of the waveguide which also have parabolic surfaces. As used herein, this type of parabolic arrangement is referred to as a crossed parabolic collimator. 
     The light exiting aperture  230  is folded back on itself by 45 degree mirrors  232  and  234  into a reflective array  236  which functions to redirect the light down through the array at a direction normal to the light path for providing an extended panel of illumination, with the light being collimated in the horizontal direction to +/−½ degree. In order to collimate the light in the horizontal direction, reflective array  236  is provided with a number of cylindrical lenses  238  on the face thereof. These lenses serve to further collimate the +/−3 degree collimated light from waveguide  220  such that the +/−{fraction ( 1 / 2 )} degree collimation is achieved in the horizontal direction. 
     Note that the original collimation of +/−10 degrees for the vertical direction is somewhat degraded such that the collimation in the vertical direction is degraded to +/−15 degrees. However, mentioned above, the vertical collimation degradation is not important when the subject collimator is utilized for liquid crystal displays in which the sub-pixels are laid out in a horizontal direction. It will be appreciated that the degradation in the vertical direction is due to the emission of light from the array into free air. 
     This light is projected in one embodiment towards a color liquid crystal display here shown in dotted outline by reference character  240 , with the characteristic of this display being that it is provided with a microlens array between the light source and the liquid crystals themselves, with the liquid crystal display sub-pixels being arrayed as red, green, and blue sub-pixels in the horizontal direction. It is important in this type of liquid crystal display that the incoming light be collimated to a fairly high degree. If the incoming light is not collimated, as mentioned hereinbefore, there will be a smearing out of the colors, such that color separation is difficult to maintain. 
     Referring now to FIG. 17A, an exploded view of collimator  210  illustrates how the remainder of the parabolic collimator is provided. Here a top portion of waveguide  210  is illustrated at  242  which has a parabolic surface  244  that has as its focus the bottom edge of exit slit  218 . Likewise, a bottom portion of collimator  210 , here illustrated at  246 , carries with it a parabolic surface  248 , with the focus of this parabola being the top edge  250  of exit slit  218 . 
     Referring now to FIG. 17B, it will be appreciated that the entrance aperture  250  of parabolic surface  244  is moved down reflector  216 , with reflector  216  extending above edge  250 . It will be also appreciated that as illustrated in FIG. 17C, exit slit  218  in reflector  216  is spaced from top edge  254  by a distance illustrated by arrow  256 . 
     Referring now to FIG. 18 what is illustrated are the crossed parabolic elements of the collimator showing the generation of the parabolic surfaces based on the edges of exit slit  218 . Here it can be seen that a point P S  on surface  222  is generated as illustrated by line  260  from focus F S  which is on the opposed edge of exit slit  218 . 
     Likewise, a point P T  on the top parabolic surface  244  is, as illustrated by line  262 , focused on a point of F B  is on an edge  264  which is opposed to the top parabola. 
     Referring now to FIG. 19, while in FIGS. 16 through 18 an extended collimator is illustrated in which waveguide  220  typically is on the order  6  inches long, there are applications for which that amount of space is not available. In the embodiment illustrated in FIG. 19, light source  212  along with its reflector  216  is positioned to one side of a collimating sheet  270  placed at the entrance aperture of reflective array  236  which has the same cylindrical lens array  238  on the front surface thereof as described in connection with FIG.  16 . 
     Referring now to FIG. 20, in order for the collimator to be made compact, it is important that the entrance apertures for the collimator be exceedingly narrow. While in the embodiment of FIG. 16 the width of the exit slit was on the order of millimeters, in order to collapse the distance required for the collimator, the slit-like entrance apertures of sheet  270  must be in the micron range. One cannot go much smaller than the micron range because the structure produced will have diffractive qualities which are not intended. 
     As can be seen in FIG. 20, sheet  270  has a top surface  272  and a bottom surface  274 . The sheet generally is made of metal, silicon, or glass in which parabolic surfaces  274  and  276  are provided. In one embodiment the sheet is made of metal as illustrated at  278  and the surfaces are etched into the metal, leaving voids  280  therebetween. Alternatively voids  280  can be filled with transparent material such as glass or plastic to protect the reflective surfaces. 
     For each of the parabolas there is a slit-like aperture generally illustrated at  282  which is bounded by edges  284  and  286 , with the width of apertures  282  being in the micron range. The parabolas may have the crossed parabolic structure as described in FIGS. 16-18. Alternatively, the parabolas may be cylindrical symmetrical parabolas. 
     As illustrated, the space between apertures  282  of adjacent parabolas is provided with a reflective coating  288  to reflect back any light from light source  212  which does not enter the associated aperture. This light is reflected back towards the apertures by reflector  216  such that eventually all or nearly all the light from light source  212  is collimated and exits sheet  270 . 
     Referring now to FIG. 21, it will be appreciated that in order to eliminate the necessity of providing a reflective array to obtain a panel of collimated light a number of fluorescent tubes  290  can be provided, or the tube can be serpentine in nature. This in essence provides a panel of uncollimated light. This light is reflected by reflector  216  towards the collimating sheet  270  and thence, in this embodiment, rather than to a reflective array, directly to a sheet  292  carrying the cylindrical collimating lenses  238 . 
     It will be appreciated that either for the folded reflective array of FIG. 16 or for the directly illuminated array of FIG. 19, the interface between the reflective array and the cylindrical lens array is to be provided by an adhesive material which has an index of refraction less than either of the two interfaced elements. The purpose of this is to provide the required internal reflection. 
     In one embodiment, the precursors for the genetic algorithm are as follows, written in FORTRAN with special optical design calls through ASAP, Advanced System Analysis Program, available from Breault Research Corporation of Tucson, Arizona: 
     
       
         
               
             
           
               
                   
               
             
             
               
                 !***************************************************************** 
               
               
                 !** 
               
               
                 !** Initial setup for design of Diffractive color Separator 
               
               
                 !** testing for genetic algorithm components 
               
               
                 !** 
               
               
                 !** 
               
               
                 !***************************************************************** 
               
               
                 !!**************************************************************** 
               
               
                 $ECHO NONE 
               
               
                 $ERR bottom 
               
               
                 UNITS UM 
               
               
                 BEAMS COHERENT DIFFRACTIVE 
               
               
                 WLB=0.437 
               
               
                 COL=2 
               
               
                 WLC=0.540 
               
               
                 WLR=0.611 
               
               
                 GT=1100 
               
               
                 DCST=100 
               
               
                 EAT=100 
               
               
                 EBT=100 
               
               
                 POLT=100 
               
               
                 LCT=5 
               
               
                 VLW=17.5/2 
               
               
                 HLW=17.5/2 
               
               
                 TFTHW=17.5/2 
               
               
                 TFTHH=17.5/2 
               
               
                 VS=99.2 
               
               
                 HS=130 
               
               
                 HGRID=10 
               
               
                 VGRID=10 
               
               
                 RH1=0.0 
               
               
                 GH1=99.2 
               
               
                 BH1=−99.2 
               
               
                 RH2=(RH1)+3*99.2 
               
               
                 RH3=(RH1)−3*99.2 
               
               
                 GH2=(GH1)+3*99.2 
               
               
                 GH3=(GH1)−3*99.2 
               
               
                 BH2=(BH1)+3*99.2 
               
               
                 BH3=(BH1)−3*99.2 
               
               
                 PI=ACOS(−1) 
               
               
                 PARABASAL 8 
               
               
                 NB=1.500 
               
               
                 NG=1.496 
               
               
                 NR=1.491 
               
               
                 MEDIA; (NB) (NG) (NR) ‘ACRYLIC’ 
               
               
                 F=((DCST)+2*(GT)+(EAT)+(POLT)+(EBT)+100) 
               
               
                 D=4.5 
               
               
                 DIVERG=0.10 
               
               
                 WAVELENGTH (WLB) (WLG) (WLR) 
               
               
                 MEDIA; 1.500 1.498 1.496 ‘CORN_LCD_GLASS’ !!UNKNOWN 
               
               
                 MEDIA; 1.4872 1.4861 1.4859 ‘EPOXY_A’ !!UNKNOWN 
               
               
                 MEDIA; 1.4872 1.4861 1.4859 ‘EPOXY_B’ !!UNKNOWN 
               
               
                 MEDIA; 1.500 1.498 1.496 ‘DCF’ !!UNKOWN 
               
               
                 MEDIA; 1.4872 1.4861 1.4859 ‘LIQ_CRYS’ !!UNKNOWN 
               
               
                 MEDIA; 1.4872‘0 1.4861’0 1.4859‘0 ’POL_MAT‘!!’ORD‘ !!UNKNOWN 
               
               
                 !! 1.4872’5 1.4861‘5 1.4859’5 CRYSTAL 0 0 1 ORD ‘POL_MAT’ 
               
               
                 !!FRESNEL BOTH 
               
               
                 !!SPLIT 1 
               
               
                 !**************CT4040WCF GEOMETRY********************************* 
               
               
                 ! 
               
               
                 !  CORNING GLASS 
               
               
                 ! 
               
               
                 SURFACE !!corning 7059 lcd glass 
               
               
                 PLANE Z 0 RECTANG 500 450 
               
               
                 TUBE Z 0 500 450 (GT) 500 450 1 1 
               
               
                 PLANE Z (GT) RECTANG 500 450 
               
               
                 OBJECT; 0.3 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS ACRYLIC !!propogate only transmission 
               
               
                 OBJECT; 0.2 !!corning 7059 lcd glass 
               
               
                 OBJECT; 0.1 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS EPOXY_A !!propogate only transmission 
               
               
                 GROUP 0.3:0.1 
               
               
                 SHIFT Z (DCST) 
               
               
                 SURFACE !!corning 7059 lcd glass 
               
               
                 PLANE Z 0 0 RECTANG 500 450 
               
               
                 TUBE Z 0 500 450 (GT) 500 450 1 1 
               
               
                 PLANE Z (GT) RECTANG 500 450 
               
               
                 OBJECT; 0.3 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS EPOXY_B 
               
               
                 OBJECT; 0.2 !!corning 7059 lcd glass 
               
               
                 OBJECT; 0.1 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS LIQ_CRYS 
               
               
                 GROUP 0.3:0.1 
               
               
                 SHIFT Z ((DCST)+(GT)+(EAT)+(POLT)+(EBT)) 
               
               
                 SURFACE !!corning 7059 lcd glass 
               
               
                 PLANE Z 0 RECTANG 500 450 
               
               
                 TUBE Z 0 500 450 (GT) 500 450 1 1 
               
               
                 PLANE Z (GT) RECTANG 500 450 
               
               
                 OBJECT; 0.3 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS LIQ_CRYS 
               
               
                 OBJECT; 0.2 !!corning 7059 lcd glass 
               
               
                 OBJECT; 0.1 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS EPOXY_B 
               
               
                 GROUP 0.3:0.1 
               
               
                 SHIFT Z ((DCST)+2*(GT)+(EAT)+(POLT)+(EBT)+(LCT)) 
               
               
                 SURFACE !!corning 7059 lcd glass 
               
               
                 PLANE Z 0 RECTANG 500 450 
               
               
                 TUBE Z 0 500 450 (GT) 500 450 1 1 
               
               
                 PLANE Z (GT) RECTANG 500 450 
               
               
                 OBJECT; 0.3 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +0 CORN_LCD_GLASS EPOXY_A 
               
               
                 OBJECT; 0.2 !!corning 7059 lcd glass 
               
               
                 OBJECT; 0.1 !!corning 7059 lcd glass 
               
               
                 INTERFACE COATING +AR CORN_LCD_GLASS AIR 
               
               
                 GROUP 0.3:0.1 
               
               
                 SHIFT Z ((DCST)+3*(GT)+2*(EAT)+2*(POLT)+2*(EBT)+(LCT)) 
               
               
                 ! 
               
               
                 !  BIREFRIGNENT ABSORBITIVE POLARIZER 
               
               
                 ! 
               
               
                 SURFACE !!polarizer based on polaroid 
               
               
                 PLANE Z 0 RECTANG 500 450 
               
               
                 TUBE Z 0 500 450 (POLT) 500 450 1 1 
               
               
                 PLANE Z (POLT) RECTANG 500 450 
               
               
                 OBJECT; 0.3 !!polarizer based on polariod 
               
               
                 INTERFACE COATING +0 POL_MAT EPOXY_A !!propogate only transmission 
               
               
                 OBJECT; 0.2 !!polarizer based on polariod 
               
               
                 OBJECT; 0.1 !!polarizer based on polariod 
               
               
                 INTERFACE COATING +0 POL_MAT EPOXY_B !!propogate only transmission 
               
               
                 GROUP 0.3:0.1 
               
               
                 SHIFT Z ((DCST)+(GT)+(EAT)) 
               
               
                 SURFACE !!polarizer based on polaroid 
               
               
                 PLANE Z 0 RECTANG 500 450 
               
               
                 TUBE Z 0 500 450 (POLT) 500 450 1 1 
               
               
                 PLANE Z (POLT) RECTANG 500 450 
               
               
                 OBJECT; 0.3 !!polarizer based on polariod 
               
               
                 INTERFACE COATING +O POL_MAT EPOXY_B !!propogate only transmission 
               
               
                 OBJECT; 0.2 !!polarizer based on polariod 
               
               
                 OBJECT; 0.1 !!polarizer based on polariod 
               
               
                 INTERFACE COATING +0 POL_MAT EPOXY_A !!propogate only transmission 
               
               
                 GROUP 0.3:0.1 
               
               
                 SHIFT Z ((DCST)+3*(GT)+2*(EAT)+(POLT)+(EBT)+(LCT)) 
               
               
                 ! 
               
               
                 !  EPOXY COATINGS 
               
               
                 ! 
               
               
                 SURFACE !!epoxy based on 
               
               
                 TUBE Z 0 500 450 (EAT) 450 450 1 1 
               
               
                 OBJECT; 0.1 !!epoxy based on 
               
               
                 SHIFT Z ((DCST)+(GT)) 
               
               
                 SURFACE !!epoxy based on 
               
               
                 TUBE Z 0 500 450 (EAT) 450 450 1 1 
               
               
                 OBJECT; 0.1 !!epoxy based on 
               
               
                 SHIFT Z ((DCST)+3*(GT)+(EAT)+(POLT)+(EBT)+(LCT)) 
               
               
                 SURFACE !!epoxy based on 
               
               
                 TUBE Z 0 500 450 (EBT) 450 450 1 1 
               
               
                 OBJECT; 0.1 !!epoxy based on 
               
               
                 SHIFT Z ((DCST)+(GT)+(EAT)+(POLT)) 
               
               
                 SURFACE !!epoxy based on 
               
               
                 TUBE Z 0 500 450 (EBT) 450 450 1 1 
               
               
                 OBJECT; 0.1 !!epoxy based on 
               
               
                 SHIFT Z ((DCST)+3*(GT)+2*(EAT)+2*(POLT)+(EBT)+(LCT)) 
               
               
                 SURFACE !!LC 
               
               
                 TUBE Z 0 500 450 (LCT) 450 450 1 1 
               
               
                 OBJECT; 0.1 !!LC 
               
               
                 SHIFT Z ((DCST)+2*(GT)+(EAT)+(POLT)+(EBT)) 
               
               
                 SURFACE !!DCS MATERIAL 
               
               
                 TUBE Z 0 500 (D*50) (DCST) 500 450 1 1 
               
               
                 OBJECT; 0.1 !!DCS 
               
               
                 ! 
               
               
                 !  BLACK MATRIX 
               
               
                 ! 
               
               
                 BMH=((DCST)+2*(GT)+(EAT)+(POLT)+(EBT)−0.00001) 
               
               
                 BMV{ 
               
               
                 Q2=#1 
               
               
                 Q1=#2 
               
               
                 BMH=#3 
               
               
                 VLW=#4 
               
               
                 VS=#5 
               
               
                 HS=#6 
               
               
                 TFTHW=#7 
               
               
                 TVFHH=#8 
               
               
                 SURFACE 
               
               
                 PLANE Z (BMH) RECTANG (VLW) ((VS)/2) 
               
               
                 SHIFT Y (Q1)*(VS) 
               
               
                 $IF INT(((Q1)+5)/2) EQ INT[((QI)+5)/2]; SHIFT X ((Q2)*(HS)+(HS)/2) 
               
               
                 $IF INT(((Q1)+5)/2) NE INT[((Q1)+5)/2]; SHIFT X ((Q2)*(HS)) 
               
               
                 SURFACE 
               
               
                 PLANE Z (BMH) RECTANG (TFTHW) (TFTHH) 
               
               
                 SHIFT Y ((Q1)*(VS)+(VS)/2−(TFTHH)) 
               
               
                 $IF INT(((Q1)+5)/2) EQ INT[((QI)+5)/2]; SHIFT X ((Q2)*(HS)+(HS)/2+(TFTHW)) 
               
               
                 $IF INT(((Q1)+5)/2) EQ INT[((QI)+5)/2]; SHIFT X ((Q2)*(HS)+(TFTHW)) 
               
               
                 } 
               
               
                 BM{ 
               
               
                 Q1=#1 
               
               
                 BMH=#2 
               
               
                 VS=#3 
               
               
                 VLW=#4 
               
               
                 HS=#5 
               
               
                 TFTHW=#6 
               
               
                 TFTHH=#7 
               
               
                 HLW=#8 
               
               
                 SURFACE 
               
               
                 PLANE Z (BMH) RECTANG 700 (HLW) 
               
               
                 SHIFT Y ((Q1)*(VS)−(VS)/2+(VS)) 
               
               
                 LCOUNT=−3 
               
               
                 $BMV (LCOUNT) (Q1) (BMH) (VLW) (VS) (HS) (TFTHW) (TFTHH) 
               
               
                 LCOUNT=(LCOUNT)+1 
               
               
                 $IF (LCOUNT) LT 3; $GO −3 
               
               
                 OBJECT; 0.1 0 0.2 0 0.3 0 0.4 0 0.5 0 0.6 0 0.7 0 0.8 0 0.9 0.10 0 
               
               
                 INTERFACE 0 0 
               
               
                 OBJECT; 0.11 0 0.12 0 0.13 0 0.14 0 0.15 0 
               
               
                 INTERFACE 0 0 
               
               
                 } 
               
               
                 $DO 1 9 
               
               
                 { 
               
               
                 Q1=(?−5) 
               
               
                 $BM Q1 (BMH) (VS) (VLW) (HS) (TFTHW) (TFTHH) (HLW) 
               
               
                 } 
               
               
                 !!******************DCS DATA &amp; SOURCE BASE********************* 
               
               
                 WAVELENGTH 0.1 
               
               
                 $IF (COL) EQ 1; WL=(WLB); NM=NB 
               
               
                 $IF (COL) EQ 2; WL=(WLG); NM=NG 
               
               
                 $IF (COL) EQ 3; WL=(WLR); NM=NR 
               
               
                 H=SQRT((WL/8)*4*DIVERG/WL) 
               
               
                 W=(WL/8)/(H*0.455938) 
               
               
                 DCS { 
               
               
                 HT=#1 
               
               
                 BH1=#2 
               
               
                 GH1=#3 
               
               
                 RH1=#4 
               
               
                 BH2=#5 
               
               
                 GH2=#6 
               
               
                 RH2=#7 
               
               
                 BH3=#8 
               
               
                 GH3=#9 
               
               
                 RH3=#10 
               
               
                 F=#11 
               
               
                 WLB=#12 
               
               
                 WLG=#13 
               
               
                 WLR=#14 
               
               
                 WL=#15 
               
               
                 Q1=#16 
               
               
                 HGRID=#17 
               
               
                 VGRID=#18 
               
               
                 H=#20 
               
               
                 W=#19 
               
               
                 PI=#21 
               
               
                 CSN=0 
               
               
                 CSO=0 
               
               
                 X=0 
               
               
                 Q=−1 
               
               
                 Q=(Q)+1 
               
               
                 X0=(Q)/10 
               
               
                 BANG1=ATAN(((HT)−(BHI))/(F)) 
               
               
                 GANG1=ATAN(((HT)−(GH1))/(F)) 
               
               
                 RANG1=ATAN(((HT)−(RH1))/(F)) 
               
               
                 BANG2=ATAN(((HT)−(BH2))/(F)) 
               
               
                 GANG2=ATAN(((HT)−(GH2))/(F)) 
               
               
                 RANG2=ATAN(((HT)−(RH2))/(F)) 
               
               
                 BANG3=ATAN(((HT)−(BH3))/(F)) 
               
               
                 GANG3=ATAN(((HT)−(GH3))/(F)) 
               
               
                 RANG3=ATAN(((HT)−(RH3))/(F)) 
               
               
                 BBET1=(PI)*(D)*SIN(BANG1)/(WLB) 
               
               
                 GBET1=(PI)*(D)*SIN(GANG1)/(WLG) 
               
               
                 RBET1=(PI)*(D)*SIN(RANGI)/(WLB) 
               
               
                 BBET2=(PI)*(D)*SIN(BANG2)/(WLB) 
               
               
                 GBET2=(PI)*(D)*SIN(GANG2)/(WLG) 
               
               
                 RBET2=(PI)*(D)*SIN(RANG2)/(WLB) 
               
               
                 BBET3=(PI)*(D)*SIN(BANG3)/(WLB) 
               
               
                 GBET3=(PI)*(D)*SIN(GANG3)/(WLG) 
               
               
                 RBET3=(PI)*(D)*SIN(RANG3)/(WLB) 
               
               
                 CCB1=ATAN((0−(BH1))/(F)) 
               
               
                 CCG1=ATAN((0−(GH1))/(F)) 
               
               
                 CCR1=ATAN((0−(RH1))/(F)) 
               
               
                 CCB2=ATAN((0−(BH2))/(F)) 
               
               
                 CCG2=ATAN((0−(GH2))/(F)) 
               
               
                 CCR2=ATAN((0−(RH2))/(F)) 
               
               
                 CCB3=ATAN((0−(BH3))/(F)) 
               
               
                 CCG3=ATAN((0−(GH3))/(F)) 
               
               
                 CCR3=ATAN((0−(RH3))/(F)) 
               
               
                 PB1=(F)*(NB)/((WLB)*COS(CCB1)) 
               
               
                 PG1=(F)*(NG)/((WLG)*COS(CCG1)) 
               
               
                 PR1=(F)*(NB)/((WLR)*COS(CCR1)) 
               
               
                 PB2=(F)*(NB)/((WLB)*COS(CCB2)) 
               
               
                 PG2=(F)*(NG)/((WLG)*COS(CCG2)) 
               
               
                 PR2=(F)*(NB)/((WLR)*COS(CCR2)) 
               
               
                 PB3=(F)*(NB)/((WLB)*COS(CCB3)) 
               
               
                 PG3=(F)*(NG)/((WLG)*COS(CCG3)) 
               
               
                 PR3=(F)*(NB)/((WLR)*COS(CCR3)) 
               
               
                 RB1=((F)−(X0))*(NB)/((WLB)*COS(BANG1)) 
               
               
                 RG1=((F)−(X0))*(NG)/((WLG)*COS(GANG1)) 
               
               
                 RR1=((F)−(X0))*(NR)/((WLR)*COS(RANG1)) 
               
               
                 RB2=((F)−(X0))*(NB)/((WLB)*COS(BANG2)) 
               
               
                 RG2=((F)−(X0))*(NG)/((WLG)*COS(GANG2)) 
               
               
                 RR2=((F)−(X0))*(NR)/((WLR)*COS(RANG2)) 
               
               
                 RB3=((F)−(X0))*(NB)/((WLB)*COS(BANG3)) 
               
               
                 RG3=((F)−(X0))*(NG)/((WLG)*COS(GANG3)) 
               
               
                 RR3=((F)−(X0))*(NR)/((WLR)*COS(RANG3)) 
               
               
                 CB1=(X0)/(WLB) 
               
               
                 CG1=(X0)/(WLG) 
               
               
                 CR1=(X0)/(WLR) 
               
               
                 CB2=(X0)/(WLB) 
               
               
                 CG2=(X0)/(WLG) 
               
               
                 CR2=(X0)/(WLR) 
               
               
                 CB3=(X0)/(WLB) 
               
               
                 CG3=(X0)/(WLG) 
               
               
                 CR3=(X0)/(WLR) 
               
               
                 CSN1=(SIN(BBET1)*COS(2*(PI)*((PB1)−(RB1)−(CB1)))/(BBET1)) 
               
               
                 CSN1=(CSN1)+(SIN(GBET1)*COS(2*(PI)*((PG1)−(RG1)−(CG1)))/(GBET1)) 
               
               
                 CSN1=(CSN1)+(SIN(RBET1)*COS(2*(PI)*((PR1)−(RR1)−(CR1)))/(RBET1)) 
               
               
                 CSN2=(SIN(BBET2)*COS(2*(PI)*((PB2)−(RB2)−(CB2)))/(BBET2)) 
               
               
                 CSN2=(CSN2)+(SIN(GBET2)*COS(2*(PI)*((PG2)−(RG2)−(CG2)))/(GBET2)) 
               
               
                 CSN2=(CSN2)+(SIN(RBET2)*COS(2*(PI)*((PR2)−(RR2)−(CR2)))/(RBET2)) 
               
               
                 CSN3=(SIN(BBET3)*COS(2*(PI)*((PB3)−(RB3)−(CB3)))/(BBET3)) 
               
               
                 CSN3=(CSN3)+(SIN(GBET3)*COS(2*(PI)*((PG3)−(RG3)−(CG3)))/(GBET3)) 
               
               
                 CSN3=(CSN3)+(SIN(RBET3)*COS(2*(PI)*((PR3)−(RR3)−(CR3)))/(RBET3)) 
               
               
                 CSN=CSN1+CSN2+CSN3 
               
               
                 $IF (CSN) GT (CSO); X=(X0) 
               
               
                 $IF (CSN) GT (CSO); CSO=(CSN) 
               
               
                 $IF (Q) EQ 100; $GO stop 
               
               
                 $GO −70 
               
               
                 stop 
               
               
                 DT=(X) 
               
               
                 SURFACE 
               
               
                 PLANE Z −100+(DT) RECTANG 1E3 (D/2) 
               
               
                 SHIFT Y (D)*(Q1) 
               
               
                 TUBE Z −100+(DT) 1E3 (D/2) 0 1E3 (D/2) 1 1 
               
               
                 SHIFT Y (D)*(Q1) 
               
               
                 OBJECT; 0.1 0 0.2 0 
               
               
                 INTERFACE COATING +0 AIR ACRYLIC 
               
               
                 ST=(DT)−((DT/WL)−INT(DT/WL))*(WL) 
               
               
                 WAVELENGTH (WL) 
               
               
                 WIDTH (W) (H) 
               
               
                 GRID RECT Z −100.0+(ST) −1000 1000 −(D)/2 (D)/2 (HGRID) (VGRID) RANDOM 1.0 
               
               
                 SOURCE DIR 0 0 1 
               
               
                 SHIFT Y (D)*Q 
               
               
                 } 
               
               
                 $DO 0 INT(500/D) 
               
               
                 { 
               
               
                 HT=?*(D)−250 
               
               
                 Q1=?−INT(250/D) 
               
               
                 $DCS (HT) (BH1) (GH1) (RH1) (BH2) (GH2) (RH2) (BH3) (GH3) (RH3) (F) (WLB) (WLG) 
               
               
                 (WLR) (WL) (Q1), 
               
               
                 (HGRID) (VGRID) (D) (W) (H) (PI) 
               
               
                 A?=DT 
               
               
                 $REG A? 
               
               
                 C?=CSO 
               
               
                 $REG C? 
               
               
                 } 
               
               
                 $STO DEPTH A22 A90 
               
               
                 !! 
               
               
                 !!  DETECTOR 
               
               
                 !! 
               
               
                 SURFACE 
               
               
                 PLANE Z 0 RECTANG 200 150 
               
               
                 SHIFT Z ((DCST)+2*(GT)+(EAT)+(POLT)+(EBT)+(LCT)+0.01) 
               
               
                 OBJECT; 0.1 ‘DETECTOR’!! 
               
               
                 !!**********************ANALYSIS************************* 
               
               
                 WIN X Y 
               
               
                 PIXEL 140 
               
               
                 CONSIDER ALL 
               
               
                 TRACE 
               
               
                 !! ONLY DETECTOR 
               
               
                 WIN X −200 200 Y −150 150 
               
               
                 FIELD ENERGY ((DCST)+2*(GT) +(EAT)+(POLT)+(EBT)+0.0001) 
               
               
                 DISPLAY 
               
               
                 $IF (COL) EQ 0; WRITE BLUE 
               
               
                 $IF (COL) EQ 1; WRITE BLUE 
               
               
                 $IF (COL) EQ 2; WRITE GREEN 
               
               
                 $IF (COL) EQ 3; WRITE RED 
               
               
                 WIN X −200 200 Y −150 150 
               
               
                 PIXEL 140 
               
               
                 $IF (COL) EQ 0; DISPLAY BLUE 
               
               
                 $IF (COL) EQ 1; DISPLAY BLUE 
               
               
                 $IF (COL) EQ 2; DISPLAY GREEN 
               
               
                 $IF (COL) EQ 3; DISPLAY RED 
               
               
                 AVERAGE 4 5 
               
               
                 ISOMETRIC 
               
               
                 bottom 
               
               
                 END 
               
               
                   
               
             
          
         
       
     
     Having now described a few embodiments of the invention, and some modifications and variations thereto, it should be apparent to those skilled in the art that the foregoing is merely illustrative and not limiting, having been presented by the way of example only. Numerous modifications and other embodiments are within the scope of one of ordinary skill in the art and are contemplated as falling within the scope of the invention as limited only by the appended claims and equivalents thereto.