Abstract:
A method for estimating an effective luminance pattern representing a distribution of projected light in a display apparatus involves determining driving values for one or more light sources arranged to project light. The light sources are solid-state light sources such as light-emitting diodes in some embodiments. The method determines an effective luminance pattern for the projected light by determining contributions to the effective luminance pattern for different components of a point spread function and then combining the contributions of the components the effective luminance pattern to yield an estimated effective luminance pattern.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 13/466,065 filed on 7 May 2012 and entitled RAPID IMAGE RENDERING ON DUAL-MODULATOR DISPLAYS, which is a continuation of U.S. patent application Ser. No. 11/627,936 filed on 26 Jan. 2007 now issued as U.S. Pat. No. 8,217,970 and entitled RAPID IMAGE RENDERING ON DUAL-MODULATOR DISPLAYS, which is a continuation of PCT International Application No. PCT/CA2005/000807 filed on 27 May 2005 and entitled RAPID IMAGE RENDERING ON DUAL-MODULATOR DISPLAYS, which claims priority from U.S. Patent Application No. 60/591,829 filed on 27 Jul. 2004 and entitled RAPID FRAME RENDERING FOR HIGH DYNAMIC RANGE DISPLAYS. For purposes of the United States of America, this application claims the benefit under 35 U.S.C. §119 of U.S. Patent Application No. 60/591,829 filed on 27 Jul. 2004 and entitled RAPID FRAME RENDERING FOR HIGH DYNAMIC RANGE DISPLAYS. 
    
    
     TECHNICAL FIELD 
     This invention pertains to systems and methods for displaying images on displays of the type that have two modulators. A first modulator produces a light pattern and a second modulator modulates the light pattern produced by the first modulator to yield an image. 
     BACKGROUND 
     International patent publication WO 02/069030 published 6 Sep. 2002 and international patent publication WO 03/077013 published 18 Sep. 2003, both of which are incorporated by reference herein, disclose displays which have a modulated light source layer and a modulated display layer. The modulated light source layer is driven to produce a comparatively low-resolution representation of an image. The low-resolution representation is modulated by the display layer to provide a higher resolution image which can be viewed by an observer. The light source layer may comprise a matrix of actively modulated light sources, such as light emitting diodes (LEDs). The display layer, which is positioned and aligned in front of the light source layer, may be a liquid crystal display (LCD). 
     If the two layers have different spatial resolutions (e.g. the light source layer&#39;s resolution may be about 0.1% that of the display layer) then both software correction methods and psychological effects (such as veiling luminance) prevent the viewer from noticing the resolution mismatch. 
     Electronic systems for driving light modulators such as arrays of LEDs or LCD panels are well understood to those skilled in the art. For example, LCD computer displays and televisions are commercially available. Such displays and televisions include circuitry for controlling the amount of light transmitted by individual pixels in an LCD panel. 
     The task of deriving from image data signals to control a light source layer and display layer can be computationally expensive. Deriving such signals can be executed by a processor of a computer&#39;s video/graphics card, or by some other appropriate processor integral to a computer, to the display itself or to a secondary device. Performance limitations of the processor can undesirably limit the rate at which successive image frames can be displayed. For example, if the processor is not powerful enough to process incoming video data at the frame rate of the video data then an observer may detect small pauses between successive frames of a video image such as a movie. This can distract the observer and negatively affect the observer&#39;s image viewing experience. 
     There is a need for practical, cost effective and efficient systems for displaying images on displays of the general type described above. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The appended drawings illustrate non-limiting embodiments of the invention. 
         FIG. 1  graphically depicts segmentation of a point spread function (PSF) into narrow and wide base Gaussian segments. 
         FIGS. 2A ,  2 B and  2 C graphically depict the splitting of a 16-bit point spread function (PSF) into two 8-bit (high and low byte) segments. 
         FIG. 3  graphically depicts the transitional behaviour of 8-bit high and low byte point spread function values relative to a 16-bit range. 
         FIG. 4  graphically depicts high and low byte point spread functions corresponding to the point spread function depicted in  FIG. 1 . 
         FIG. 5  graphically depicts application of an iteratively-derived interpolation function to derive an interpolated effective luminance pattern (ELP) closely approximating an actual effective luminance pattern (ELP). 
         FIG. 6  is a schematic diagram of a display. 
         FIG. 7  is a flowchart illustrating a method for displaying an image on a display having a controllable light source layer and a controllable display layer. 
         FIG. 8  is a flowchart illustrating a method for determining an effective luminance pattern. 
         FIG. 9  is a flowchart illustrating a method for determining an effective luminance pattern or a component of an effective luminance pattern. 
     
    
    
     DESCRIPTION 
     Throughout the following description, specific details are set forth in order to provide a more thorough understanding of the invention. However, the invention may be practiced without these particulars. In other instances, well known elements have not been shown or described in detail to avoid unnecessarily obscuring the invention. Accordingly, the specification and drawings are to be regarded in an illustrative, rather than a restrictive, sense. 
     The invention may be applied in a wide range of applications wherein an image is displayed by producing a light pattern that is determined at least in part by image data, and modulating the light pattern to yield an image. The light pattern may be produced by any suitable apparatus. Some examples include:
         A plurality of light sources driven by driver circuits that permit brightnesses of the light sources to be varied.   A fixed or variable light source combined with a reflection type or transmission type modulator that modulates light from the light source.
 
The following description relates to non-limiting example embodiments in which the light pattern is produced on one side of an LCD panel by an array of light-emitting diodes and the LCD panel is controlled to modulate the light of the light pattern to produce a viewable image. In this example, the array of LEDs can be considered to constitute a first modulator and the LCD panel constitutes a second modulator.
       

     In general, rendering image frames or a frame set for display on an LED/LCD layer display entails the following computational steps:
     1. Obtaining image data (which may be full screen or partial screen image data).   2. Deriving from the image data appropriate driving values for each LED of the first modulator, using suitable techniques well known to persons skilled in the art (e.g. nearest neighbour interpolation which may be based on factors such as intensity and colour).   3. The derived LED driving values and the point spread functions of LEDs on the LED layer as well as the characteristics of any layers between the LED layer and the LCD layer are used to determine the effective luminance pattern which will result on the LCD layer when the LED driving values are applied to the LED layer.   4. The image defined by the image data is then divided by the effective luminance pattern to obtain raw modulation data for the LCD layer.   5. In some cases, the raw modulation data is modified to address issues such as non-linearities or other artifacts arising in either of the LED or LCD layers. These issues can be dealt with using suitable techniques well known to persons skilled in the art (e.g. scaling, gamma correction, value replacement operations, etc.). For example, creating the modified modulation data may involve altering the raw modulation data to match a gamma correction curve or other specific characteristics of the LCD layer.   6. Final modulation data for the LCD (which may be the raw modulation data or the modified modulation data) and the driving data for the LEDs are applied to drive the LCD and LED layers to produce the desired image.   

     Various ways to reduce the computational cost of (i.e. to speed up) generating the final modulation data for use in displaying images are described herein. These include:
         Performing at least some parts of the computation in a lower precision domain (for example, by performing computations in the 8-bit domain instead of in the 16-bit domain); and,   Implementing one or more of the options for efficiently establishing an effective luminance pattern that are described herein.
 
While these techniques may be implemented individually, any suitable combinations of the techniques described herein may be used.
 
Effective Luminance Pattern Determination
       

     The point spread function of each LED in an LED layer is determined by the geometry of the LED. A simple technique for determining an LED layer&#39;s total effective luminance pattern is to initially multiply each LED&#39;s point spread function (specifically, the point spread function of the light which is emitted by the LED and passes through all optical structures between the LED and LCD layers) by a selected LED driving value and by an appropriate scaling parameter to obtain the LED&#39;s effective luminance contribution, for that driving value, to each pixel on the LCD layer. 
     In this way, the luminance contributions of every LED in the LED layer can be determined and summed to obtain the total effective luminance pattern, on the LCD layer, that will be produced when the selected driving values are applied to the LED layer. However, these multiplication and addition operations are very computationally expensive (i.e. time consuming), because the effective luminance pattern must be determined to the same spatial resolution as the LCD layer in order to facilitate the division operation of step 4 above. 
     The computational expense is especially great if the LED point spread function has a very wide “support.” The “support” of an LED point spread function is the number of LCD pixels that are illuminated in a non-negligible amount by an LED. The support can be specified in terms of a radius, measured in LCD layer pixels, at which the LED point spread function becomes so small that is perceptually irrelevant to an observer. The support corresponds to a number of LCD pixels that are illuminated in a significant amount by each LED. 
     For example, consider a hexagonal LED array in which the centre of each LED is spaced from the immediately adjacent LEDs by a distance equal to 50 of the LCD layer&#39;s pixels. If each LED has a point spread function having a support of 150 LCD pixels then each pixel in the center portion of the LCD layer will be illuminated by light from approximately 35 of the LEDs. Calculation of the effective luminance pattern for this example accordingly requires 35 operations for each pixel of the LCD layer, in order to account for the light contributed to each pixel by each relevant LED. Where the LCD layer has a high spatial resolution, this is very computationally expensive (i.e. time consuming). 
     Resolution Reduction 
     The time required to determine the effective luminance pattern produced on the LCD can be reduced by computing the effective luminance pattern at a reduced spatial resolution that is lower than that of the high resolution image which is to appear on the LCD layer. This is feasible because the point spread functions of individual light sources are generally smoothly varying. Therefore, the effective luminance pattern will be relatively slowly varying at the resolution of the LCD. It is accordingly possible to compute the effective luminance pattern at a lower resolution and then to scale the effective luminance pattern up to a desired higher resolution, without introducing significant artifacts. 
     The scaling may be done using suitable linear, Gaussian or other interpolation techniques. Such spatial resolution reduction yields an approximately linear decrease in the computational cost of establishing the effective luminance pattern. Many available interpolation methods that can be used to scale up an effective luminance pattern computed at a lower resolution are computationally inexpensive as compared to the computational cost of computing the effective luminance pattern at the resolution of the LCD or other second light modulator. 
     Using the foregoing example, a 10-times resolution reduction in both the width and height directions yields an approximate 100-times reduction in computational cost. This is because the total number of pixels in the reduced resolution image is 100-times fewer than the total number of pixels in the high resolution image which is to appear on the LCD layer. Each pixel in the reduced resolution image still receives light from 35 LEDs, necessitating 35 computational operations per pixel—but those operations are applied to 100-times fewer pixels in comparison to a case in which the computations are performed separately for every pixel in the actual high resolution image which is to appear on the LCD layer. 
     Point Spread Function Decomposition 
     The computational cost of image rendering can also be reduced by decomposing the point spread function of each light source (e.g. each LED) into several components (e.g. by performing a Gaussian decomposition) in such a way that the recombination of all of the components yields the original point spread function. An effective luminance pattern can then be determined separately for each component. Once an effective luminance pattern has been determined for each component, those effective luminance patterns can be combined to produce a total effective luminance pattern. The combination may be made by summing, for example. 
     Computing the effective luminance patterns contributed by the components may be performed at the resolution of the LCD layer or at a reduced resolution, as described above. 
     A speed benefit is attained even if the effective luminance pattern for each component is computed at the resolution of the LCD layer since hardware components specially adapted to perform rapid computations based upon standard point spread functions (e.g. Gaussian point spread functions) are commercially available. Such hardware components are not normally commercially available for the typically non-standard point spread function of the actual LEDs in the display&#39;s LED layer—necessitating resort to considerably slower computational techniques using general purpose processors. 
     A greater speed benefit is attained if the resolution reduction technique described above is used to determine an effective luminance pattern for each component. Moreover, different spatial resolutions can be applied to different components of the point spread functions to yield even greater speed benefits. For example,  FIG. 1  depicts (solid line) an example LED point spread function having a steep central portion  10  and a wide tail portion  12 . In this situation, the actual point spread function can be decomposed into a narrow base Gaussian component  14 A and a wide base Gaussian component  14 B, as depicted. 
     The wide base Gaussian component  14 B (dotted line) contributes relatively little image intensity, in comparison to narrow base Gaussian segment  14 A (dashed line). Further, wide base Gaussian component  14 B is more slowly varying than narrow base Gaussian component  14 A. Accordingly, an effective luminance pattern for narrow base Gaussian component  14 A may be determined at a moderately high spatial resolution while an effective luminance pattern for the wide base Gaussian component  14 B can be computed at a significantly lower spatial resolution. This preserves a substantial portion of the image intensity information contained in narrow base Gaussian component  14 A and is still relatively fast since the effective support of the narrow base Gaussian segment is small and thus few LCD pixels are covered by that component. By contrast, since wide base Gaussian component  14 B contains relatively little image intensity information, that component can be processed relatively quickly at low resolution without substantially degrading the resolution of the total effective luminance pattern produced by combining the patterns derived for each component. 
     8-bit Segmentation 
     Image data is typically provided in 16-bit word form. High-end (i.e. more expensive) graphic processors typically perform computations in the 16-bit domain. Such processors may have dedicated 16-bit or floating point arithmetic units that can perform 16-bit operations quickly. The need for a high-end processor capable of performing 16-bit operations quickly can be alleviated by computing the effective luminance pattern in the 8-bit domain. Such computations can be performed reasonably quickly by less expensive processors. 
     Each LED&#39;s point spread function is a two dimensional function of intensity versus distance relative to the center of the LED. Such a point spread function may be characterized by a plurality of 16-bit data words. Where the point spread function is represented by a look up table, many 16-bit values are required to define the point spread function; for example, one value may be provided for every LCD pixel lying on or within a circle centered on the LED and having a radius corresponding to the support of the point spread function. 
     Each one of those 16-bit data words has an 8-bit high byte component and an 8-bit low byte component (any 16-bit value A can be divided into two 8-bit values B and C such that A=B*2 8 +C, where B is the “high byte” and C is the “low byte”). The 8-bit values are preferably extracted only after all necessary scaling and manipulation operations have been applied to the input 16-bit data.  FIG. 2A  depicts a 16-bit point spread function;  FIGS. 2B and 2C  respectively depict the 8-bit high and low byte components of the  FIG. 2A  16-bit point spread function. 
     A 16-bit data word is capable of representing integer values from 2 0 -1 to 2 16 -1 (i.e. from 0 to 65535). An 8-bit byte is capable of representing integer values from 2 0 -1 to 2 8 -1 (i.e. from 0 to 255). The “support” (as previously defined) of a point spread function characterized by an 8-bit high byte component is much smaller (narrower) than the support of the point spread function as a whole. This is because the 8-bit high byte component reaches the lowest value (zero) of its 255 possible values, when the 16-bit data word characterizing the point spread function as a whole reaches the value 255 out of its range of 65535 possible values. The remaining 255 values are provided by the low byte component with the high byte component&#39;s value equal to zero. The effective luminance pattern corresponding to the narrow base 8-bit high byte component can accordingly be rapidly determined, without substantial loss of image intensity information. The resolution reduction and/or other techniques described above may be used to further speed up the determination of the effective luminance pattern for the 8-bit high byte component. 
     The support of a point spread function characterized by an 8-bit low byte component is comparatively wide. Specifically, although the 8-bit low byte component has only 255 possible values, those values decrease from 255 to 0 (out of 65535 values for the point spread function as a whole) and those 255 values correspond to the 255 lowest intensity levels (i.e. levels at which the value of the high byte component is equal to zero). Those 255 levels represent the value of the point spread function in its peripheral parts. 
     The low byte component can be separated into two regions. A central region, lying within the boundary on which the point spread function characterized by the high byte component reaches zero. In the central region the low-byte component typically varies in an irregular saw-tooth pattern (as depicted in  FIG. 3 ) if the original 16-bit point spread function is reasonably smooth. This is because, in the central region, the portion of the point spread function characterized by the low byte component augments the portion of the point spread function characterized by the high byte component. 
     For example, consider a transition from the 16-bit value 10239 to the 16-bit value 9728. The 16-bit value 10239 has a high byte component value of 39 and a low byte component value of 255 (i.e. 39*256+255=10239). Consequently, the low byte component&#39;s contribution to the point spread function is initially 255 and the high byte component&#39;s contribution is initially 39. The value of the high byte component&#39;s contribution remains at 39, while the value of the low byte component&#39;s contribution smoothly decreases from 255 to 0—the point at which the original 16-bit point spread function has the value 9984 (i.e. 39*256+0). The value of the high byte component&#39;s contribution to the point spread function then changes smoothly from 39 to 38, but that change is accompanied by an abrupt change (from 0 to 255) in the value of the low byte component&#39;s contribution to the point spread function. 
     As seen in  FIG. 4 , inside a radius R of the original point spread function (and where the value of the high byte component&#39;s contribution to the point spread function is non-zero) the resulting saw-tooth pattern of the low byte component&#39;s contribution to the point spread function is characteristic of the original point spread function. Outside the radius R, the value of the high byte component&#39;s contribution to the point spread function is zero, and the value of the low byte component&#39;s contribution changes smoothly. 
     The contributions from the low-byte component of the point spread function can be processed differently in these two regions (i.e. the regions inside and outside the radius R) to avoid unwanted artifacts. For example, to preserve a substantial portion of the image intensity information contained in the region inside the radius R, the effective luminance pattern for that region is preferably determined using the same relatively high resolution used to determine the effective luminance pattern for the high byte component&#39;s contribution to the point spread function, as previously described. By contrast, the effective luminance pattern for the region outside the radius R can be determined using a much lower resolution, without substantial loss of image intensity information. 
     After the three point spread function segments (i.e. the high byte component, the region of the low byte component inside the radius R, and the region of the low byte component outside the radius R) have been processed as aforesaid, the results are individually up-sampled to match the resolution of the LCD layer, then recombined with appropriate scaling factors being applied. Recombination typically involves summation of the values for the two low byte component regions and the value for the high byte component, after the value for the high byte component has been multiplied by 256. 
     Interpolation 
     If an effective luminance pattern value is determined using a resolution lower than the resolution of the LCD layer, it is necessary to up-sample that value to match the resolution of the LCD layer. Interpolation techniques for up-sampling low resolution images into high resolution images are well known, with both linear and Gaussian based techniques being common. Although such prior art techniques can be used in conjunction with the above described techniques, accuracy, or speed, or both may be improved by utilizing an interpolation technique which is optimized for a particular display configuration. Optimization facilities higher resolution image compression, minimizes introduction of unwanted interpolation artifacts, and reduces the image rendering time. In extreme cases, an interpolation technique can be used to reduce the resolution of the effective luminance pattern resolution to match the resolution of the LED layer. 
     Prior art interpolation techniques are often restricted to use with specific pre-interpolation data, or to use with specific interpolation functions. The interpolation techniques used to match the resolution of the effective luminance pattern to that of the LCD display do not need to satisfy such restrictions, provided convolution of the pre-interpolation data with the selected interpolation function will yield an effective luminance pattern having adequate similarity to the actual effective luminance pattern. 
     The required degree of similarity depends on the display application. Different applications require different degrees of similarity—in some applications relatively small deviations may unacceptably distract an observer, whereas larger deviations may be tolerable in other applications (such as applications involving television or computer game images in which relatively large deviations nonetheless yield images of quality acceptable to most observers). Consequently, it is not necessary to apply the interpolation technique directly to the actual LED driving values or to the actual LED point spread function. 
     For example,  FIG. 5  depicts the result obtained by using an iteratively-derived interpolation technique to reduce the resolution of the effective luminance pattern to match the resolution of the LED layer. The pixel values at the LED layer&#39;s resolution are not the LED driving values—they are the luminance values of the effective luminance pattern before interpolation. The interpolation function can be determined using standard iteration methods and a random starting condition. As seen in  FIG. 5 , convolution of the iteratively-derived interpolation function with the effective luminance pattern values yields results which are reasonably close to the actual effective luminance pattern. 
     Many different interpolation techniques can be used. There need not be any correlation between the interpolation function and the LEDs&#39; point spread function, the LED driving values, or any other characteristic of the display, provided the selected interpolation function and the input parameters selected for use with that function yields a result reasonably close to the actual effective luminance pattern. 
     EXAMPLE EMBODIMENTS 
       FIGS. 6 to 9  show some example embodiments of the invention.  FIG. 6  shows a display  30  comprising a modulated light source layer  32  and a display layer  34 . Light source layer  32  may comprise, for example:
         an array of controllable light sources such as LEDs;   a fixed-intensity light source and a light modulator disposed to spatially modulate the intensity of light from the light source;   some combination of these.
 
In the illustrated embodiment, light source layer  32  comprises an array of LEDs  33 .
       

     Display layer  34  comprises a light modulator that further spatially modulates the intensity of light incident on display layer  34  from light source layer  32 . Display layer  34  may comprise an LCD panel or other transmission-type light modulator, for example. Display layer  34  typically has a resolution higher than a resolution of light source layer  32 . Optical structures  36  suitable for carrying light from light source layer  32  to display layer  34  may be provided between light source layer  32  and display layer  34 . Optical structures  36  may comprise elements such as open space, light diffusers, collimators, and the like. 
     In the illustrated embodiment a controller  40  comprising a data processor  42  and suitable interface electronics  44 A for controlling light source layer  32  and  44 B for controlling display layer  34  receives image data  46  specifying images to be displayed on display  30 . Controller  40  drives the light emitters (e.g. LEDs  33 ) of light source layer  34  and the pixels  35  of display layer  34  to produce the desired image for viewing by a person or persons. A program store  46  accessible to processor  42  contains software instructions that, when executed by processor  42  cause processor  42  to execute a method as described herein. 
     Controller  40  may comprise a suitably programmed computer having appropriate software/hardware interfaces for controlling light source layer  32  and display layer  34  to display an image specified by image data  48 . 
       FIG. 7  shows a method  50  for displaying image data on a display of the general type shown in  FIG. 6 . Method  50  begins by receiving image data  48  at block  52 . In block  54  first driving signals for light source layer  32  are derived from image data  48 . Suitable known methods may be applied to obtain the first driving signals in block  54 . 
     In block  56  method  50  computes an effective luminance pattern. The effective luminance pattern may be computed from the first driving signals and known point spread functions for the light sources of light source layer  32 . Block  56  computes the effective luminance pattern at a resolution that is lower than a resolution of display layer  34 . For example, block  56  may compute the effective luminance pattern at a resolution that is a factor of 4 or more smaller in each dimension (in some embodiments a factor in the range of 4 to 16 smaller in each dimension) than the resolution of display layer  34 . 
     In block  60  the effective luminance pattern computed in block  58  is upsampled to the resolution of display layer  34 . This may be done through the use of any suitable interpolation technique for example. In block  62  second driving signals for the display layer are determined from the upsampled effective luminance pattern and the image data. The second driving signals may also take into account known characteristics of the display layer and any desired image corrections, colour corrections or the like. 
     In block  64  the first driving signal obtained in block  54  is applied to the light source layer and the second driving signals of block  62  are applied to the display layer to display an image for viewing. 
       FIG. 8  shows a method  70  for computing an effective luminance pattern. Method  70  may be applied within block  56  of method  50  or may be used in other contexts. Method  70  begins by computing an ELP for each component of the point spread function for the light sources of light source layer  32  (blocks  72 A,  72 B and  72 C—collectively blocks  72 ). Blocks  72  may be performed in any sequence or may be performed in parallel with one another.  FIG. 8  shows three PSF components  73 A,  73 B and  73 C and three corresponding blocks  72 . The method could be practised with two or more PSF components  73 . 
     The components of the point spread function (PSF) will typically have been predetermined. A representation of each component is stored in a location accessible to processor  42 . Each of blocks  72  may comprise, for each light source of light source layer  32 , multiplying values that define a component of the point spread function by a value representing the intensity of the light source. In block  74  the effective luminance patterns determined in blocks  72  are combined, for example by summing, to yield an overall estimate of the effective luminance pattern that would be produced by applying the first driving signals to light source layer  32 . 
       FIG. 9  illustrates a method  80  that may be applied for computing effective luminance patterns. Method  80  may be applied to:
         computing the effective luminance pattern in block  56  of method  50 ; or   computing the effective luminance patterns for individual components of a point spread function in blocks  72  of method  70 ; or   applied in other contexts.       

     Method  80  begins in block  82  with data characterizing a point spread function (or a PSF component) for a light source of light source layer  32  and data indicative of how intensely the light source will operate under the control of the first driving signals. Method  80  combines these values (e.g. by multiplying them together) to obtain a set of values characterizing the contribution of the light source to the effective luminance pattern at various spatial locations. 
     Block  84  obtains high-order and low-order components of the resulting values. In some embodiments, the resulting values are 16-bit words, the high-order component is an 8-bit byte and the low-order component is an 8-bit byte. 
     Contributions to the ELP are determined separately for the high-order and low-order components in blocks  86  and  88 . For each light source, the area of support for which values are included in the high-order contribution of  86  is typically significantly smaller than the area of support for which values are included in the low-order contribution of block  88 . 
     Block  88  typically computes the low-order contribution for points located within the area of support of the high-order contribution (block  90 ) separately than for points located outside of the area of support of the high-order contribution (block  92 ). Blocks  86 ,  90  and  92  may be performed in any order or simultaneously. 
     In block  94  the contributions from blocks  86 ,  90  and  92  are combined to yield an overall ELP. The computations in blocks  86 ,  90  and  92  may be performed primarily or entirely in the 8-bit domain (i.e. using 8-bit operations on 8-bit operands) in the case that the high-order and low-order components are 8-bit bytes or smaller. 
     Certain implementations of the invention comprise computer processors which execute software instructions which cause the processors to perform a method of the invention. For example, one or more processors in a computer or other display controller may implement the methods of  FIG. 7 ,  8  or  9  by executing software instructions in a program memory accessible to the processors. The invention may also be provided in the form of a program product. The program product may comprise any medium which carries a set of computer-readable signals comprising instructions which, when executed by a data processor, cause the data processor to execute a method of the invention. Program products according to the invention may be in any of a wide variety of forms. The program product may comprise, for example, physical media such as magnetic data storage media including floppy diskettes, hard disk drives, optical data storage media including CD ROMs, DVDs, electronic data storage media including ROMs, flash RAM, or the like or transmission-type media such as digital or analog communication links. The computer-readable signals on the program product may optionally be compressed or encrypted. 
     Where a component (e.g. a member, part, assembly, device, processor, controller, collimator, circuit, etc.) is referred to above, unless otherwise indicated, reference to that component (including a reference to a “means”) should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e., that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention. 
     As will be apparent to those skilled in the art in the light of the foregoing disclosure, many alterations and modifications are possible in the practice of this invention without departing from the spirit or scope thereof. For example,
         The light source layer may comprise a number of different types of light source that have point spread functions different from one another;   The display may comprise a colour display and the computations described above may be performed separately for each of a number of colours.       

     While a number of example aspects and embodiments have been discussed above, those of skill in the art will recognize certain modifications, permutations, additions and sub-combinations thereof. It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions and sub-combinations as are within their true scope.