Patent Publication Number: US-9888153-B2

Title: Observer metameric failure compensation method and system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation of U.S. application Ser. No. 13/559,638 filed Jul. 27, 2012 (Allowed), the entire contents of which is hereby incorporated by reference. 
     Reference is also made to commonly assigned, co-pending U.S. patent application Ser. No. 13/559,647 filed Jul. 27, 2012 (allowed), entitled “Observer Metameric Failure Reduction Method”; and to commonly assigned U.S. Pat. No. 8,941,678 issued Jan. 27, 2015, entitled “Display System Providing Observer Metameric Failure Reduction,” each of which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to the field of digital display systems with narrow-band primaries, and more particularly to methods for reducing the experience of observer metameric failure. 
     BACKGROUND OF THE INVENTION 
     The motion picture industry is presently transitioning from traditional film based projectors to digital or electronic cinema. This trend is accelerating due to the popularity of 3-D movies. Even as digital cinema projection has matured and succeeded, largely based on the use of the well-known Digital Light Projection (DLP) technology, the promise of a further evolution to laser-based projection has been hovering in the background. Laser projection, whether for digital cinema, home projection, or other markets, has long been held back due to the cost and complexity of the laser sources, particularly in the green and blue spectral bands. As the necessary lasers are now becoming increasingly mature and cost competitive, the potential benefits expected from laser projection, including the larger color gamut, more vivid, saturated and brighter colors, high contrast, and low cost optics are increasingly being realized. An exemplary system is described in the paper “A Laser-Based Digital Cinema Projector”, by B. Silverstein et al. (SID Symposium Digest, Vol. 42, pp. 326-329, 2011). 
     Additionally, other commonly recognized laser projection problems, including the reduction of the visibility of laser speckle and the management of laser safety to reduce eye exposure risk or hazard potential, are increasingly being addressed in a satisfactory manner. As these issues are resolved, other less recognized issues will become increasingly important. As one example, image displays with narrow-bandwidth light sources, including lasers, can suffer from observer metameric failure, such that individual viewers can perceive significantly different colors. 
     In the field of color science, metamerism is the visual perception of color matching for color stimuli having different spectral power distributions. Two stimuli that have the same broadband spectral power distribution are said to be isomers, and will generally be seen as identical color matches by all observers. Whereas, two colors that appear identical to an observer but which have different spectral power distributions are called metamers. Due to differences in spectral sensitivity among observers, a metamer for one observer may not be a metamer for all observers. The greater the spectral differences between a pair of metameric stimuli, the more sensitive the color perception of that metameric pair will be to any changes in the illuminant, material compositions, observers, or field of view. 
     As can then be anticipated, there are various circumstances in which the spectral differences of a nominal metameric pair can lead to metameric failure, in which the expected color match is no longer perceived. As a first example, observer metameric failure (sometimes referred to as observer color perception variability) occurs when the color of two objects, or two elements in a displayed image, are perceived differently by two or more observers in the same viewing conditions. Observer metameric failure occurs because the optical system of the eyes, the color receptor response, and neural color processing varies among individuals. As another example, illuminant metameric failure occurs when colors match under one light source, but not another. For example, two color patches with different reflectance spectra can appear to be identical, providing the same color appearance when viewed under daylight illumination. However, then when viewed under fluorescent illumination, the color patches can appear differently, even to a single observer. Conditions of metameric failure are further defined to include field-size metameric failure and geometric metameric failure. Field-size metameric failure occurs because the relative proportions of the three cone types in the retina vary from the center to the periphery of the visual field. This is exemplified by the differences observed in the CIE standard observer color matching functions for 2° and 10° viewing fields (see  FIG. 1B ). Therefore, colors that match when viewed as very small, centrally fixated areas can appear different when presented over large color areas. Geometric metameric failure can occur when two samples match when viewed from one angle, but fail to match when viewed from a different angle. For the purposes of the present invention, observer metameric failure and illuminant metameric failure are of predominant interest. 
     One method to prevent metameric failure from occurring is to construct color imaging systems based on spectral color reproduction. Such systems would be based on the principle of isomers, with the relative spectral power distribution of scene color being carefully captured and then reproduced. A famous example is the Lippmann two-step method of photography introduced in 1891, in which color images were made and viewed essentially using spectral color reproduction, or regeneration of the captured scene&#39;s wavelength spectrum. However, such systems are complex, radiometrically inefficient, and sensitive to viewing angles. Therefore they have never come into wide use. 
     The fact that the human visual system has only three types of cone photoreceptors makes it possible for two stimuli to match in perceived color without having identical spectral power distributions, and thus metameric color matching occurs. In particular, each type of cone, red (long), green (medium), or blue (short), responds to the cumulative or integrated energy from a broad range of wavelengths. As a result, different combinations of light across all wavelengths can produce an equivalent receptor response. As long as the integrated responses of the three cone types are equal, for one spectrum compared to another, the stimuli will represent a metameric match, and will have the same perceived color to the observer. 
     Most practical color imaging systems use a limited set of colorants (typically three or four) and rely on the phenomenon of metamerism to produce color images having the desired color appearance, even though the reproduced color spectra will generally not match the original color spectra. The comparative amounts of the colorants provided by the color imaging system are adjusted to produce a color which will appear to closely match the original scene color. Modern color imaging systems are optimized to provide close color matches between the original and the reproduction for as many important colors as possible, relative to a standard observer, or set of observers. 
     As suggested previously, the phenomenon of metamerism, in which color matches occur despite spectral differences, is prone to failure. In general, metamerism depends on the interaction of the light source spectrum with the spectral reflectance/transmittance properties of the materials illuminated with the light, and the spectral response of the observer (or the camera sensor). Color perception among color normal observers varies depending on pre-retinal filtering in the optical media (cornea, lens, and humors), macular photo pigment density, cone distribution differences, color neural processing differences, and differences in cone spectral sensitivity. Human color perception can be measured using color matching functions (CMFs), which vary among individuals and are known to change with age.  FIG. 1A  illustrates twenty sets of color matching functions  300  measured for a set of different individuals having “normal” color vision, for 10° observational fields, using data from Table I (5.5.6) in the book “Color Science” by Wyszecki and Stiles (2 nd  Ed., John Wiley &amp; Sons, New York, pp 817-822, 1982). In particular,  FIG. 1A  shows that color sensitivity can vary significantly among individual observers, with significant local variations of 5-10% or more at many wavelengths. 
     The Commission International de l&#39;Eclairage (CIE) has documented color matching functions for two different standard observers: a 2° 1931 CIE standard observer and a 10° 1964 CIE standard observer.  FIG. 1B  compares the CIE 2° color matching functions  300   a  and CIE 10° color matching functions  300   b . It is noted that the CIE 10° color matching functions  300   b  deviate from the CIE 2° color matching functions  300   a  in each of the red, green, and blue portions of color space, but the biggest differences occur in blue portion of color space. In particular, the largest differences occur in the blue (&lt;500 nm), as the blue (short) color matching function response peaks ˜10% higher for the CIE 10° color matching functions  300   b  compared to the CIE 2° color matching functions  300   a . Additionally, both the green (middle) and red (long) color matching functions crosstalk into the blue spectral range, and the color response differences between the respective CIE 2° color matching functions  300   a  and the CIE 10° color matching functions  300   b  are larger in the blue than in many portions of the red and green color spectra. In particular, above 540 nm, the blue color matching function lacks significant response with only two color matching functions (red and green) contributing significantly to the perception of color samples, the color differences between these cones being comparatively smaller. Also, the presence of the short wavelength “blue” cones is very small in the fovea and increases on the periphery. These differences reflect the fact that metameric color perception differences can be observed for different observational field sizes and can vary with wavelength. 
     Under normal circumstances, for example in daylight viewing conditions, the most common source of observer metameric failure is colorblindness (i.e., impaired color vision) among one or more observers. However, as the spectral properties of a light source or an object&#39;s reflectivity narrow and become more complex, and lack spectral color diversity, significant observer metameric failure can occur even amongst individuals who are considered to have normal color vision. 
     Systems (e.g., displays) that utilize narrow-band color primaries are most susceptible to observer metameric failure effects. Therefore, it can be anticipated that viewers of laser based displays, including digital laser projectors, and other displays with narrow spectrum primaries (such as LEDs), may experience observer metameric failure. While the expanded color gamut that laser displays can offer has been eagerly anticipated, in reality, it will include many wide-gamut colors that are not only outside of a conventional film or CRT display color gamut, but which are also seldom seen in nature. As a result, differences in color perception among observers of such very saturated colors at or near the gamut boundary may be hard to describe or quantify. On the other hand, color perception differences among observers for gamut colors of typical devices, and particularly for memory colors, such as sky blue, skin tones, or grass greens, which occur minimally with broadband light sources, can occur more frequently and dramatically with narrow-band light sources like lasers. 
     In the case of digital cinema, significant differences in color perception among expert observers viewing content involving memory colors in a color suite or screening room, may lead to significant dissatisfaction. For example, one expert observer may state that a displayed skin tone looks too green, while another may state that it looks too red. In such settings, problems can also emerge when comparing the narrow-band or laser displays to a broadband display that is an accepted standard. Moreover, even if a group of expert observers are satisfied, some members of a broader audience may not be, and such experiences may lead to dissatisfaction that may ultimately affect marketplace success of a narrow-bandwidth display technology. 
     Some approaches to mitigate the problem of observer metameric failure have been previously suggested or demonstrated. As an example, Thornton and Hale, in the paper “Color-imaging primaries and gamut as prescribed by the human visual system” (Proc. SPIE, Vol. 3963, pp. 28-35, 2000), consider the problem of observer metameric failure reduction for an additive color display systems having three narrow-band primaries (Δλ˜10 nm full-width-half-maximum (FWHM)). The authors proposed that to reduce the effects of observer metameric failure, the color primaries should preferentially be close to the so-called “prime wavelengths” (450, 540, and 610 nm) which are at or near the peaks of the three spectral sensitivities of the normal human visual system. Thornton et al. are not clear about how much improvement their method would be expected to yield. The Thornton prime wavelength primaries are overlaid on the color matching functions  300  in  FIG. 1A  as Thornton red laser primary  432 , Thornton green laser primary  434  and Thornton blue laser primary  436 . Also shown for comparison are a typical set of laser primaries for the exemplary laser projection system described in the aforementioned paper by Silverstein et al., including red laser primary  422 , green laser primary  424  and blue laser primary  426 . 
     In a more recent paper, “Minimizing observer metamerism in display systems,” by Ramanath, (Color Research and Application, Vol. 34, pp. 391-398, 2009), observer metameric failure for different types of displays having three primaries is examined. In particular, Ramanath explores the comparative occurrence of observer metameric failure among different electronic display devices, including CRT displays, LCD, DLP and LED based displays, a CCFL (cold cathode fluorescent lamp) based display, and a laser display. Ramanath concludes that observer metameric failure can occur more frequently, and provide greater perceived color differences, as the display spectrum narrows (smaller FWHM) or the number of modes in the display spectrum increases. As a result, the laser display and CCFL display, which lack spectral color diversity due to narrow or multi-modal spectra, have a high propensity to cause observer metameric failure. By comparison, the CRT and lamp based DLP displays, which have broad primaries (Δλ≈60-70 nm FWHM), exhibit low potential for observer metameric failure. In the case of laser displays, where the spectral bandwidths can easily be 2 nm or less in width, a small expansion of the lasing bandwidths, at the cost of a small color gamut decrease, would provide a reasonable trade-off if observer metameric failure is significantly decreased. However, Ramanath found that spectral distributions with moderate FWHM bandwidths (Δλ˜28 nm), such as LED illuminated displays, can still produce significant perceptible observer metameric failure, suggesting that reductions in observer metameric failure may not come quickly with increases in spectral bandwidth. 
     Ramanath also builds on the work of Thornton, and provides a modeled “ideal” set of primary spectral power distributions (SPDs) for a three primary display having primaries with spectral peaks close to the Thornton primaries, that may reduce the difference between the colors seen by a reference observer and a non-reference observer. In particular, Ramanath proposes that three broadband color channels or primaries, a blue primary with peak power at 450 nm and a bandwidth of Δλ˜49 nm, a green primary with peak power at 537 nm and a bandwidth of Δλ˜80 nm, and a red primary with peak power at 615 nm and a bandwidth of Δλ˜56 nm, will provide the least susceptibility to observer metameric failure. However, taken together, these two papers suggest that a three primary display having color spectra with preferential locations per Thornton, but moderate bandwidths (e.g., Δλ˜30 nm) will still exhibit significant metameric failure among observers. Thus, the guidance for minimizing observer metameric failure in a system with three narrow-bandwidth primaries is even less clear. 
     Other researchers have suggested that observer metamerism can be reduced by using more than three color primaries or color channels. In the paper “A multiprimary display: discounting observer metamerism” (Proc. SPIE, Vol. 4421, pp. 898-901, 2002), Konig et al. describe an image display system having six primaries that is used to display metamers and reduce observer metameric failure. This paper states that imaging systems having only three color signals as input (e.g. RGB values or L*a*b* values) cannot produce color reproductions that are precise for all human observers, as information is not available on how different observers perceive the original color. That is, the color vision response of the human visual system for an observer cannot be directly measured to determine how the primaries can be optimized. By comparison, the authors propose that a multiprimary display having more than three primaries introduces additional degrees of freedom for displaying a given color, such that perceptual color differences can be reduced for each observer. In particular, Konig et al. find that a multispectral display having more than three broadband primaries can provide both a large color gamut and the spectral control to reproduce color for each pixel by spectral color reproduction, such that observer metameric failure is minimized. An exemplary multi-spectral display is described, using two LCD projectors that provided overlapped images to a screen, that together provide an extended color gamut. This display has six broad bandwidth (Δλ˜40-100 nm FWHM) primaries, where one projector provides RGB images, and the second provides CMY images. 
     Fairchild and Wyble, in their paper “Mean observer metamerism and the selection of display primaries”, (Proc. 15th Color Imaging Conference, pp. 151-156, 2007), express concern about observer metameric failure occurring during the use of narrow-band primary displays, such as laser digital cinema projectors, causing consternation among filmmakers during “image proofing”. This paper models and compares differences in color perception for a display having broad bandwidth RGB primaries approximated by Gaussians having FWHM bandwidths of Δλ˜100 nm, and a second display with narrow-band primaries having FWHM bandwidths of Δλ˜5 nm, where the peak wavelengths of the color primaries were selected to be close to Thornton&#39;s prime wavelengths (450, 540, and 610 nm). After modeling age- and field-dependent color perception differences in terms of color matching functions (CMFs) and ΔE* color differences, Fairchild and Wyble conclude that color errors with displays having only three narrow-band primaries, such as laser projector, will be too large to be acceptable for critical color applications. The authors then suggest that display manufacturers, in developing displays capable of wider color gamut and greater luminance contrast, should abandon development of such narrow-band primary systems and redirect their efforts to systems that support spectral color reproduction. In particular, the authors suggest that emergent displays with large color gamut and enhanced luminance contrast should use multiple (N&gt;3) wide-band primaries. 
     The paper “Display with arbitrary primary spectra” (SID Digest, Vol. 39, pp. 783-786, 2008), by Bergquist, provides an example of a multi-spectral display that attempts to reduce observer metameric failure. A field-sequential color display is described having a temporally-averaged, modulated array of N=20 Gaussian light sources (such as LEDs), each having FWHM bandwidths of Δλ˜30 nm, to approximate the spectrum of a color to be reproduced on the display. In this way, Bergquist provides a spectral reproduction system that synthesizes an approximation of the physical signal rather than emulating the sensation of color using superposition of a reduced set of narrowband primaries. Observer metameric failure is then reduced as compared to colorimetric matching, as a given observer would find the original scene and its reproduction to be identical (as the original and reproduced spectra are essentially identical). As a result, good agreement would be found among most observers, including many with color vision deficiencies, regardless of their interpretation of the sensation and the name they would give to a scene color. While the method is successful at reducing observer metameric failure, it requires many additional channels (N&gt;&gt;3) of color information at the capture stage (multispectral capture), and increased complexity in signal processing and display. None of this additional complexity is readily compatible with the image capture, processing, and display infrastructure of today or of the foreseeable future. 
     As another approach, Sarkar et al., in the paper “Toward reducing observer metamerism in industrial applications: colorimetric observer categories and observer classification” (Proc. 18th Color Imaging Conference, pp. 307-313, 2010), analyzed the Wyszecki and Stiles data and identified seven distinct groupings or categories of observers, for whom color vision, as measured by the respective CMFs, is statistically similar. With the goal of reducing observer metameric failure when using wide gamut displays, the authors suggest that a method for observer-dependent color imaging can be developed wherein the color workflow is tuned to match one of several observer classes. Of course, application of this method requires the classification of observers based on their color vision. While this approach might work for personalized color processing or small groups of people, it would not be extensible to helping the random assemblage of people present in a cinematic audience. 
     U.S. Pat. No. 6,816,284 to Hill et al., entitled “Multispectral color reproduction system with nonlinear coding,” provides a system that alters the color data captured by a multi-spectral camera using an encoding method that reduces the large amount of data required to represent the spectral information without causing a noticeable loss of the color information visible to an observer. As such, this patent is enabling data friendly spectral color reproduction as a means for reducing observer metameric failure when using N≧4 multi-primary displays. 
     Commonly assigned U.S. Pat. No. 7,362,336 to Miller et al., entitled “Four color digital cinema system with extended color gamut and copy protection,” discloses a multi-primary display having N≧4 narrow-band color channels that uses metameric matching to provide copy protection. In particular, it provides that selective rendering of portions of an image or image sequence can provide metameric matches by using the different combinations of primaries to provide the same color, but with varying spectral compositions, on a frame to frame basis. As such, the altered image portions can look similar to the human observers, but will look different to cameras that can be used to illicitly capture images from a projection or video screen. This approach exploits a special case of “observer” metameric failure that occurs between people and cameras to achieve the desired effect of copy protection, rather than reducing the occurrence of observer metameric failure among human observers. 
     In summary, while observer metameric failure has been identified as a problem that can affect display systems using narrow-band primaries, adequate solutions have not yet been suggested, particularly for displays having three primaries. The primaries used for the laser projection systems have narrow spectral bands. This leads to an increased color gamut and capacity to display highly saturated colors. At the same time, compared with existing reference displays, metameric mismatches are more frequent. Similarly, issues related to observer metameric failure in laser projection displays have also been documented. 
     The solutions offered to date are either incomplete, or require larger numbers of primaries (N&gt;3) that preferentially have much wider spectra than lasers have, or require observer color matched displays. Thus, there remains a need for design approaches or operational methods that significantly reduce observer metameric failure for displays using narrow-band primaries without requiring observer-dependent color tuning or more than three primaries. 
     SUMMARY OF THE INVENTION 
     The present invention represents a method for color correcting a color image to account for color vision characteristics associated with a set of target observers in preparation for displaying the color image on a color display device having a plurality of device color primaries, at least one of the device color primaries being a narrow-band primary, comprising: 
     receiving an input color image in an input color space, the input color image having input color values and being adapted for display on a reference color display device having a plurality of input color primaries having associated input color primary spectra; 
     using a data processing system to apply a metamerism correction transform to the input color image to determine an output color image having output color values in an output color space appropriate for display on the color display device, the output color image having a plurality of output color channels, each of the output color channels being associated with one of the device color primaries, wherein the metamerism correction transform modifies colorimetry associated with the input colors to provide output color values such that an average observer metameric failure is reduced for a distribution of target observers; and 
     storing the output color image in a processor accessible memory. 
     This invention has the advantage that observer metameric failure associated with color display devices using narrow-band primaries can be substantially reduced for a set of target observers. 
     It has the additional advantage that digital images adapted to be displayed on conventional display devices using wide-band primaries can be corrected for display on color display devices using narrow-band primaries to compensate for average perceived color shifts that result from observer metameric failure. 
     It has the further advantage that color dithering can be used to provide color diversity to further reduce observer metameric failure artifacts. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  depicts color matching function data for 20 observers; 
         FIG. 1B  depicts the 1931 CIE 2° color matching functions and the 1964 CIE 10° color matching functions; 
         FIG. 2  depicts an audience of observers viewing a projected image; 
         FIG. 3  depicts an exemplary optical system for a laser projector; 
         FIG. 4  depicts a data path for a laser projector system; 
         FIG. 5  depicts exemplary projection spectra; 
         FIG. 6  depicts exemplary device color primaries and color gamuts; 
         FIGS. 7A, 7B, 7C and 7D , provide plots indicative of perceived color differences resulting from observer metameric failure for a set of observers viewing white, sky blue, grass green and skin tone image content, respectively; 
         FIG. 8A  is a data flow diagram for a conventional color management method; 
         FIGS. 8B-8D  are data flow diagram for color management methods providing observer metameric failure correction in accordance with embodiments of the present invention; 
         FIG. 9A  depicts a method for determining a metamerism correction in accordance with an embodiment of the present invention based on a distribution of perceived color shifts associated with metamerism correction for a set of target observes; 
         FIG. 9B  depicts a method for determining a metamerism correction in accordance with an embodiment of the present invention based on a distribution of matching colors for a set of target observes; 
         FIG. 10A  shows an exemplary distribution of perceived color shifts determined relative to the CIE 2° color matching functions for a magenta input color; 
         FIG. 10B  shows average perceived color shifts determined for a set of different input colors relative to the CIE 2° color matching functions; 
         FIG. 10C  shows a contour plot for color differences corresponding to the average magnitudes of the perceived color shifts in  FIG. 10B ; 
         FIG. 11A  shows an exemplary distribution of perceived color shifts determined relative to the CIE 10° color matching functions for a magenta input color; 
         FIG. 11B  shows a contour plot for color differences corresponding to the average magnitudes of the perceived color shifts determined relative to the CIE 10° color matching functions; 
         FIG. 12  shows a transition zone between an inner color gamut and an extended color gamut zone; 
         FIG. 13  is a flow chart of a method for determining a corrected output color in accordance with the present invention; 
         FIG. 14  illustrates exemplary transition functions useful for the method of  FIG. 13 ; 
         FIGS. 15A and 15B  depict frame and sub-frame timing diagrams, respectively; 
         FIG. 16  illustrates a set of dithering colors arranged on a dithering locus around a target color; 
         FIG. 17  depicts a set of target colors, each having an associated set of dithering colors; 
         FIGS. 18A-18D  illustrate exemplary sets of dithering colors arranged around white, sky blue, grass green and skin colored target colors, respectively; and 
         FIG. 19  depicts exemplary wide color gamuts for projection of images in accordance with the present invention. 
     
    
    
     It is to be understood that the attached drawings are for purposes of illustrating the concepts of the invention and may not be to scale. 
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following description, some embodiments of the present invention will be described in terms that would ordinarily be implemented as software programs. Those skilled in the art will readily recognize that the equivalent of such software may also be constructed in hardware. Because image manipulation algorithms and systems are well known, the present description will be directed in particular to algorithms and systems forming part of, or cooperating more directly with, the method in accordance with the present invention. Other aspects of such algorithms and systems, together with hardware and software for producing and otherwise processing the image signals involved therewith, not specifically shown or described herein may be selected from such systems, algorithms, components, and elements known in the art. Given the system as described according to the invention in the following, software not specifically shown, suggested, or described herein that is useful for implementation of the invention is conventional and within the ordinary skill in such arts. 
     The invention is inclusive of combinations of the embodiments described herein. References to “a particular embodiment” and the like refer to features that are present in at least one embodiment of the invention. Separate references to “an embodiment” or “particular embodiments” or the like do not necessarily refer to the same embodiment or embodiments; however, such embodiments are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to the “method” or “methods” and the like is not limiting. It should be noted that, unless otherwise explicitly noted or required by context, the word “or” is used in this disclosure in a non-exclusive sense. 
     For a variety of reasons, including improving light efficiency, expanding color gamut, increasing light source lifetime and reducing ongoing replacement costs, there is increasing impetus to replace the traditional lamps (such as xenon arc, tungsten halogen and UHP lamps) with solid state light sources (such as lasers or LEDs) in projectors and displays. Until recently, the desire for laser-based projection systems has been unfulfilled, in part as compact, robust, low-to-moderate cost, visible wavelength laser technologies had not emerged in a commercializable form, particularly for green and blue. However, with the recent emergence of blue diode lasers and compact green SHG lasers, low cost, laser based, pico-projectors from companies such as Microvision (Redmond, Wash.) are reaching the market place. 
     In parallel, similar obstacles for compact high power visible lasers capable of supporting digital cinema projection have also started to disappear, as companies such as Laser Light Engines (Salem, N.H.) and Necsel (Milpitas, Calif.) have demonstrated prototype or early product laser devices. For example, Necsel (previously known as Novalux) offers green (532 nm) and blue (465 nm) laser arrays, each of which provides 3-5 Watts of optical output power. At these power levels, and allowing for system efficiency losses, a modest sized projector (˜1200 lumens output) for a large conference room or a home theatre, can be achieved using a single laser device per color. However, in the case of cinema, the on-screen luminance can require 10,000-40,000 lumens or 40-170 Watts or more of combined optical power (flux) incident to the screen, depending on screen size and screen gain. Presently, these power levels are achieved by optically combining the output of multiple laser arrays in each color channel. 
     In order to better understand the present invention, it is instructive to describe the overall context within which apparatus and methods of the present invention can be operable. As shown in  FIG. 2 , an audience of observers  60  in a theater  50  views an image  195  formed with image light  175  from projector  100  that is imaged onto a display surface  190 . The projected image typically comprises a 2-D array of image pixels (not shown), each having a specified color and luminance for a frame time. As the color perception is variable among the observers  60 , as for example described by the different sets of color matching functions  300  of  FIG. 1A , then observer metameric failure can occur as the projected images are viewed. This is particularly true if projector  100  uses three narrow-bandwidth spectral primaries based on lasers, LEDs, or other narrow-band light sources. Within the context of the present invention, narrow-band light sources are considered to be light sources having full-width half-maximum (FWHM) spectral bandwidths of not more than ˜30 nm. Likewise, wide-band light sources are considered to be light sources having full-width half-maximum (FWHM) spectral bandwidths of at least ˜45 nm, where the spectral bandwidths of wide-band displays generally fall in a range ˜45-90 nm. Displays with intermediate bandwidth light sources (with spectral bandwidths of ˜25-50 nm) can still benefit from the methods of the present invention for reducing the impact of observer metameric failure, although to a lesser extent. The intermediate bandwidth range can partially overlap with either the narrow bandwidth or wide bandwidth spectral ranges, as the metameric failure susceptibility can depend on the details of the spectral structure (e.g., spectral mode structure). 
     The schematic diagram of  FIG. 3  shows an exemplary arrangement for a projector  100  in accordance with the present invention having three narrow-band primaries (λ b , λ g , λ r ). Red, green and blue illumination assemblies  110   r ,  110   g  and  110   b  are shown, providing red, green and blue (RGB) primary colors from respective red, green and blue laser light sources  120   r ,  120   g  and  120   b . This system is similar to that described in the aforementioned Silverstein et al. paper. Each of the red, green and blue laser light sources  120   r ,  120   g  and  120   b  will include one or more light source devices, which are typically multi-emitter laser array devices. For example, the red laser light source  120   r  can comprise multiple (for example 12) semiconductor laser arrays, which are assembled to provide a narrow-band primary (λ r ) for a red color channel. In some embodiments, the red laser light source  120   r  can use multiple Mitsubishi ML5CP50 laser diodes, each emitting ˜6 Watts of optical flux at ˜638 nm from an array of 12 laser emitters. Similarly, the green laser light source  120   g  and the blue laser light source  120   b  can each comprise a plurality of laser devices. For example, in some embodiments, the green laser light source  120   g  can use a NECSEL-532-3000 green visible array package that nominally emits 3-4 Watts of 532 nm light in 48 beams, distributed as 24 beams from each of two rows of beams. Similarly, in some embodiments, the blue laser light source  120   b  can use a NECSEL-465-3000 blue visible array package that nominally emits 3-4 Watts of 465 nm light, also in 48 beams, distributed as 24 beams from each of two rows of beams. In each case, the respective laser light source assemblies can include lenses, mirrors, prisms, or other components (not shown) to provide laser beam shaping and directional control to fashion an array of emergent beams that exit an aperture of a housing, as input into the rest of the illumination system. 
     It should be understood that at present, the power levels needed for digital cinema can be accomplished cost effectively by optically combining the output of multiple laser arrays in each color channel, using free space optics or fiber coupling, to provide a system such as that of  FIG. 3 . Eventually, laser technology may advance such that a few, modest cost, compact laser devices can drive each color. Fiber lasers may also be developed that are appropriate for this application. Of course, each approach has its advantages and disadvantages, relative to trade-offs of simplicity, cost, and vulnerability to laser failure. 
     In a given color channel, the light beams emerging from a laser light source assembly encounter further portions of the respective red, green and blue illumination assemblies  110   r ,  110   g  and  110   b , which can include various illumination lenses  145 , a light integrator  150 , one or more mirrors  155 , and other illumination optics  140  such as filters, polarization analyzers, wave plates, apertures, or other elements as required. A polarization switching device (not shown), or other optics, to enable 3D projection, can also be included with the projector. 
     As then shown in  FIG. 3 , illumination light  115  from the light source assemblies is directed onto respective spatial light modulators  170  by redirection with one or more mirrors  155 . Modulated image light  175 , bearing image data imparted into the transiting light by the addressed pixels of the spatial light modulators  170  is combined using a combiner  160  (such as a dichroic combiner) to traverse a common optical axis  185  passing through imaging optics  180  and onto display surface  190  (such as a projection screen). The display surface  190  is typically a white matte screen that approximates a Lambertian diffuser, or a gain screen that back reflects light in a narrower cone (e.g., with a gain of g˜2.4). Gained screens can be curved, fabricated with complex surface structures, can maintain polarization to aid 3-D projection, and have a white or neutral (slightly gray) spectral reflectance. In the illustrated embodiment, the combiner  160  comprises a first combiner  162  and a second combiner  164 , each of which is a dichroic element or filter having appropriate thin film optical coatings that selectively transmits or reflects light according to its wavelength. 
     It should be understood that mirrors  155  need not lie in the plane of the optical system. Thus the mirror  155  in the optical path for the green channel can be out of plane, and not obstructing image light  175  passing to imaging optics  180 , as might be otherwise implied by  FIG. 3 . Additionally, while combiner  160  is shown as a pair of tilted glass plates, other exemplary constructions can be used, including X-prisms, V-prisms, or Philips (or Plumbicon) type prisms. In other embodiments, mirrors  155  can also be provided in the form of prisms, such as the widely used TIR (total internal reflection) prism that is often used in combination with the Philips prism and DLP devices. 
     In  FIG. 3 , the imaging optics  180  are depicted symbolically by a single lens element. In practice, the imaging optics  180  are a multi-element assembly comprising multiple lens elements that directs and focuses image light  175  such that it images spatial light modulators  170  at their respective object planes along optical axis  185  to an image plane (display surface  190 ) at high magnification (typically 100×-400×). Imaging optics  180  can be fixed focus or zooming optics, and can wholly comprise transmissive elements (e.g., lenses) or reflective elements (e.g., imaging mirrors), or can be catadioptric, including both transmissive and reflective elements. The imaging optics  180  typically comprise projection optics (e.g., a projection lens including a plurality of lens elements) that form an image of the modulators onto the screen. In some embodiments, imaging optics  180  can also include relay optics (e.g., a relay lens including a plurality of lens elements) that creates a real aerial image at an intermediate image plane, which is then subsequently imaged to the screen by the projection optics. In some embodiments, a de-speckling device, to reduce the visibility of laser speckle, can be provided in the optical path. In some configurations, it is advantageous to locate the de-speckling device at or near the intermediate image plane. 
     In a preferred embodiment, the spatial light modulators  170  of projector  100  are Digital Light Processor (DLP) or Digital Micro-mirror Devices (DMDs), developed by Texas Instruments, Inc., Dallas, Tex. The DLP device uses pulse width modulation (PWM) control of the pixels or micro-mirrors to impart image data information to the transiting light. However, in other embodiments, other technologies can also be used for the spatial light modulators  170 , including transmissive liquid crystal displays (LCDs) or reflective liquid crystal on silicon (LCOS) devices, which typically alter polarization states of the transiting light to impart the image data information therein. 
       FIG. 4  shows an exemplary schematic of a data path  200  that provides image data to projector  100 , and which enables the metameric failure reduction method of the present invention. An image file package  210  can be delivered in a memory to the theatre or other venue, as a set of data files that are compressed, encrypted and packaged for distribution. This image file package  210  can also include audio files and sub-title files, provided according to the Digital Cinema Distribution Master (DCDM) specifications, or in other formats. These files are accessed by data input interface  220 , and subsequently decrypted and decompressed as appropriate, by data decryption  230  and data decompression  235  processors. Image processor  240  can prepare the image data files for display by applying various processing operations, including image corrections provided by image corrector  245  and metameric color corrections provided by metameric color corrector  250 . The image corrections applied by the image corrector  245  can include operations such as uniformity corrections, and color/tone scale corrections. The image processor  240  will generally perform its processing operations in response to appropriate parameters and look-up tables (LUTs) that are provided as inputs. 
     The resulting processed images are stored in a frame buffer  260  or some other processor accessible memory, which then provides the image data to the projector  100  to be projected to the display surface  190 . The projector  100  includes combiner  160  for combining imaging light from the different color channels and imaging optics  180  for projecting the imaging light onto the display surface  190 , as well as other components such as light sources that are not shown in  FIG. 4 . (Refer to  FIG. 3  for more details of other components typically included in projector  100 .) 
     On a per frame or sub-frame basis, synchronized by modulator timing control  265 , image data is fed from the frame buffer  260  to the spatial light modulators  170  to provide image modulation on a per pixel basis. In some embodiments, the data path  200  can reside in whole, or in part, within the housing of projector  100 . 
     With respect to color perception, including color gamut and metameric failure, the center or peak wavelengths and the spectral bandwidths in each color channel are important parameters. In accordance with the presently available laser technology, the nominal projector wavelengths used in projector  100  are commonly 465 nm, 532 nm and 638 nm (see red laser primary  422 , green laser primary  424  and blue laser primary  426  in  FIG. 1A ), which are significantly offset from the potentially optimal Thornton primaries of 450 nm, 540 nm and 610 nm (see Thornton red laser primary  432 , Thornton green laser primary  434  and Thornton blue laser primary  436  in  FIG. 1A ) that were discussed earlier. 
     Depending on the technology, given laser devices have a device specific bandwidth (Δλ 2 ), and a collection of devices of that type will have in a larger bandwidth range (Δλ 1 ). Referring to the red laser light source  120   r  in  FIG. 3 , in some embodiments, individual red laser devices are used having peak emission wavelengths in the spectral range from λ˜632-645 nm, or Δλ 1 ˜13 nm, with 640 nm being the typical wavelength, while the typical spectral band width for a given laser is Δλ 2 ˜2 nm FWHM. Similarly, in some embodiments the green laser light source  120   g  in  FIG. 3  uses Novalux Extended Cavity Surface Emitting Laser (NECSEL™) green lasers, which have center wavelengths in the range of λ˜527-537 nm (quoted Δλ 1 ˜6 nm), with a given device having a typical peak wavelength of 532 nm and a typical FWHM spectral bandwidth of Δλ 2 ˜0.2 nm. Likewise, in some embodiments the blue laser light source  120   b  in  FIG. 3  uses NECSEL™ blue lasers having center wavelengths in the range of 460-470 nm (quoted Δλ 1 ˜6 nm), with a typical peak wavelength of 465 nm and a typical FWHM spectral bandwidth of Δλ 2 ˜0.2 nm. 
       FIG. 5  shows three spectral power distributions: an exemplary laser projection spectrum  420 , an exemplary film projector spectrum  400 , and an exemplary digital cinema projector spectrum  410 . The laser projection spectrum  420  depicts a set of representative laser sources useful in projector  100  including spectra for the red laser primary  422  provided by the red laser light source  120   r  which corresponds to a red color channel, the green laser primary  424  provided by the green laser light source  120   g  which corresponds to a green color channel, and the blue laser primary  426  provided by the blue laser light source  120   b  which corresponds to a blue color channel. (The exemplary set of laser primary spectra in  FIG. 5  is not necessarily intensity balanced to produce a particular color or white point, but rather primarily indicate spectral location.) For each color channel, the laser primary spectra associated with illumination assemblies including a plurality of individual laser devices will typically have a FWHM bandwidth within a range of Δλ 1 ˜5-15 nm, with individual laser devices having much narrower emission bandwidths (e.g., Δλ 2 ˜0.2-2 nm). 
     The larger bandwidth associated with use of multiple laser devices per color channel, can help to reduce both observer metameric failure and speckle perception. In exchange for these benefits, a modest color gamut loss results. However, in practice, the lasers can have a statistical distribution of center wavelengths that is appreciably narrower than this potential spectral range Δλ 1  (e.g., about 3-7 nm). Additionally, as noted previously, Ramanath has suggested that even the yet wider spectral bandwidths typical of LEDs (Δλ˜30 nm FWHM) can still cause significant observer metameric failure. Thus, relying on using an ensemble of lasers having a distribution of peak emission wavelengths will likely not reduce the occurrence of observer metameric failure sufficiently to be satisfactory, particularly for projectors or displays with only three color primaries (i.e., three color channels). Moreover, methods for reducing the occurrence or magnitude of observer metameric failure for observers  60  can be valuable for displays having one or more color primaries having spectral bandwidths of Δλ˜30 nm or less. 
     Also shown for comparison on  FIG. 5  are an exemplary film projector spectrum  400  which represents the illumination to the print film from a xenon arc lamp that was filtered to remove both UV and IR light. In a film based projector, this spectrum is subsequently modulated on a localized image content basis by the transmission spectra of the red, green, and blue film dyes. The illustrated digital cinema projector spectrum  410  is associated with a conventional projector having a xenon arc lamp light source, which is dichroically split to form red, green, and blue color primaries, which together comprise spectrum  410 . The digital cinema projector spectrum  410  is typical of that provided a Barco digital cinema projector, such as the model DP-1500 projector. Each color primary has a broadband spectrum (e.g., Δλ˜68 nm FWHM, or Δλ˜89 nm FW 1/e 2 ). The light in each of these color primaries is directed to an associated spatial light modulator that imparts image data into the light associated with that color channel. It can be seen that the film projector spectrum  400  and the digital cinema projector spectrum  410  do not include the narrow spectral peaks associated with the laser projector spectrum  420 , and will therefore not suffer from the high susceptibility to observer metameric failure. 
     One common way to represent color is using a CIE x,y chromaticity diagram  320 , as depicted in  FIG. 6 . In this diagram, colors are plotted using x,y chromaticity coordinates, which can be calculated from CIE XYZ tristimulus values using the following equations: 
                     x   =     X     X   +   Y   +   Z         ⁢     
     ⁢     y   =     Y     X   +   Y   +   Z                 (   1   )               
The theory of the CIE XYZ system is that if two colors have the same XYZ values (and the same viewing conditions), the patches will visually match if the XYZ values match. Since the x,y chromaticity coordinates represent only two color dimensions, they are not capable of fully describing a color. In particular, while the x,y chromaticity coordinates can provide an indication of the hue and saturation of a color, they do not provide any indication of luminance. Typically, the Y tristimulus value, which represents perceived luminance, is used together with the x,y chromaticity coordinates to fully specify a color as a set of x,y,Y color coordinates. Other color spaces that are commonly used to represent color are the well-known CIELAB and CIELUV color spaces.
 
     In  FIG. 6 , the outer curved boundary is the “horseshoe-shaped” spectrum locus  325 , which corresponds to the pure monochromatic colors of the visible spectrum. As shown by the labeled wavelengths, the spectrum locus  325 , proceeds from blue colors at the lower left corner through green colors at the top to red colors at the lower right corner. The spectrum locus  325  represents the boundary of the color gamut of the human visual system, and encompasses the entire range of colors that are visible to a human observer. The straight edge on the lower part of the gamut boundary is called the line of purples  327  or the purple boundary. (These colors are not part of the spectrum locus  325  and are not provided by monochromatic emitters.) 
     One characteristic of the CIE x,y chromaticity diagram  320  is that a color that is formed by a mixture of two colors will have chromaticity coordinates that fall along the straight line that connects the chromaticity coordinates for the two colors that are being mixed. Since additive color imaging devices, such as CRTs and laser projectors, produce images by forming mixtures of a set of color primaries, the color gamuts of these devices will be given by a triangle on the CIE x,y chromaticity diagram  320 , with the color primaries being located at the corners of the triangle. A wide-band color gamut  330  is shown on  FIG. 6 , corresponding to a set of wide-band color primaries (i.e., red primary  331 , green primary  332  and blue primary  333 ). These primaries and their associated color gamut are typical of those provided by the phosphors used in a typical CRT monitor or television. Similarly, a laser primary color gamut  335  is also shown in  FIG. 6 , which corresponds to the set of typical laser projector color primaries that were discussed earlier (i.e., red laser primary  422 , green laser primary  424  and blue laser primary  426 ). 
     As expected, both the laser primary color gamut  335 , and the smaller conventional wide-band color gamut  330  are contained within spectrum locus  325 . As accustomed as people are to using CRT displays, few are aware of the limited color gamut they have. For example, while important memory colors like neutrals (e.g., white color coordinate  340 ), sky blues (e.g., sky blue color coordinate  342 ) and skin tones (e.g., skin tone color coordinate  346 ) can be rendered, greens are limited, and many grass green colors (e.g., grass green color coordinate  344 ) cannot be reproduced. (With modern LCD displays, the available color gamut can be of comparable size to the wide-band color gamut  330 , or a bit larger, but may be somewhat shifted, allowing grass green type colors to be rendered.) 
     It has been estimated that the gamut of colors present in natural scenes is about 30% of the theoretical maximum of ˜2.3 million discernible colors for all of color space. However, when the lightness (Y) dimension is ignored, there are only about 26,000 naturally-occurring perceptually-different colors. The number of memory colors is much smaller. They are colors, like the colors of grass, sky and autumn leaves, which are processed by the human visual system (HVS) and stored as memories. 
     By comparison, the spectrum locus  325  comprises monochromatic colors, which can only be produced by lasers, or an arc lamp, such as a mercury-vapor lamp with selected narrow emission spectra, or a light source filtered with narrow spectral bandpass filters. In the case of the representative laser primary color gamut  335 , these monochromatic colors occur at the corners, where the laser primaries (e.g., 465 nm, 532 nm, and 638 nm) intersect the spectrum locus  325 . The perceived colors along the spectrum locus  325 , including those corresponding to the red, green, and blue laser primaries  422 ,  424  and  436 , are seldom seen in nature and are not memory colors. The most prominent exception is in the yellows, where some naturally occurring yellow colors are very close to the spectrum locus  325 . However, in general, differences in perception of these highly saturated monochromatic colors along the spectrum locus  325  are less likely to cause angst among observers  60 , in part because a language to precisely describe or compare these colors is lacking Other colors that are near the spectrum locus  325 , though not actually on it, such as a green near the 520 nm spectrum locus point, but having a very small blue or red additive color contribution, are spectrally impure or polychromatic, but can still be very saturated wide gamut colors that are also not memory colors. However, as the additive contributions of the three primaries tend to equalize, the colors tend to move towards center, and critical or widely recognized colors (such as turquoise, cranberry red or pumpkin orange), including memory colors such as sky blue, grass green, and skin tones are produced. So while a group of observers  60  ( FIG. 2 ) viewing a display that can produce a wide color gamut (e.g., laser primary color gamut  335 ) can experience significant observer metameric failure when viewing colors at or near the spectrum locus  325 , high levels of dissatisfaction are most likely to occur when the observers  60  view commonly experienced colors or memory colors. 
     As discussed previously, prior approaches for reducing observer metameric failure in displays with narrow-bandwidth primaries feature preferential spectral locations for the primaries, or the use of a multi-primary (N&gt;3) display, preferentially having at least moderately broad bandwidths (≧30 nm) in the N color channels. As the multi-primary display infrastructure for capturing image content, transmitting the resulting data, and displaying it is not well-established, and as three-primary laser-based projectors and displays are developing rapidly, there is a need for solutions for reducing observer metameric failure for such N=3 primary displays. 
     A comparative analysis of color perception for observers viewing a conventional digital cinema projector and a laser projector  100  further illustrates the problem of observer metameric failure. A set of target colors, including sky blue, grass green, skin tone, gray and white, was defined having specified CIE x,y chromaticity coordinates which are shown in Table 1, together with corresponding Digital Cinema Initiative Distribution Master (DCDM) code values. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Target color values. 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Patch 
                 x 
                 y 
                 Y 
                 DCDM X′ 
                 DCDM Y′ 
                 DCDM Z′ 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 White 
                 0.314 
                 0.351 
                 0.880 
                 3612 
                 3770 
                 3803 
               
               
                 Gray 
                 0.314 
                 0.351 
                 0.113 
                 1637 
                 1709 
                 1679 
               
               
                 Sky Blue 
                 0.225 
                 0.265 
                 0.184 
                 1939 
                 2066 
                 2658 
               
               
                 Skin 
                 0.403 
                 0.377 
                 0.281 
                 2494 
                 2431 
                 1973 
               
               
                 Grass Green 
                 0.227 
                 0.464 
                 0.085 
                 1166 
                 1534 
                 1311 
               
               
                   
               
            
           
         
       
     
     The projectors were modeled using both the wide-bandwidth digital cinema projector spectrum  410  and the narrow-bandwidth laser projector spectrum  420  shown in  FIG. 5 . The color values associated with each of the target colors were translated into corresponding light intensities that would produce the desired color values for a standard observer for the respective color primaries for the conventional digital cinema projector and the laser projector. The resulting intensity modulated spectra for both projectors were then analyzed for individual color perception using a set of observer-specific color matching functions  300  to determine corresponding perceived XYZ tristimulus values for each individual observer. 
     Color difference values between the perceived colors for the two projectors were calculated for each individual observer in terms of chromaticity differences:
 
Δ x   i   =x   i,n   −x   i,b  
 
Δ y   i   =y   i,n   −y   i,b    (2)
 
where (x i,n , y i,n ) are chromaticity values for the narrow-bandwidth laser projector for the ith observer, (x i,b , y i,b ) are chromaticity values for the conventional wide-bandwidth digital cinema projector for the ith observer, and (Δx i , Δy i ) are the chromaticity differences for the ith observer. (In some embodiments, a luminance difference ΔY i =Y i,n −Y i,b  can also be defined to account for any differences in the luminance perception.) By definition, the CIE standard observer should perceive colors having the same CIE colorimetry XYZ input color values, no matter whether the spectral source providing the colors has a broadband spectrum (e.g.,  410 ) or a narrow band spectrum (e.g.,  420 ). Thus, if a particular observer perceived the colors in the same way as the standard observer, then the resulting color differences would be zero. A non-zero color difference value for a particular observer provides an indication of the magnitude and direction of the perceived color shift, resulting from observer metameric failure that occurs when the particular observer views the nominally identical color pair provided by wide-bandwidth and narrow-bandwidth projectors.
 
       FIGS. 7A-7D  show chromaticity difference plots  350  for the white, sky blue, grass green and skin target colors from Table 1, respectively. The set of observer-specific color matching functions used in this analysis included the 10° color matching functions  300  from the Wyszecki and Stiles data shown in  FIG. 1A , as well as a set of 2° color matching function data from Stiles and Burch, published in detail by Trezona in the article “Individual observer data for the 1955 Stiles-Burch 2° pilot investigation” (J. Opt. Soc. Am. A., Vol. 4, pp. 769-782, 1987). The aim chromaticity difference  370  would be Δx=0, Δy=0, corresponding to the case where there is no observer metamerism failure, and therefore the colors produced by the two projectors would appear to have the identical chromaticities to the observers. Each of the plotted data points corresponds to the chromaticity difference for a particular observer. An average chromaticity difference  352  is shown on each of the chromaticity difference plots  350 , corresponding to an average color shift  355  of the perceived laser projector color relative to the perceived conventional digital cinema projector color. In general, the 2° observer data points cluster closer to the origin (the aim chromaticity difference  370 ) than do the 10° observer data points. 
     Considering the results shown in  FIGS. 7A-7D , it can be seen that there is a significant amount of variation in the observer metamerism failure characteristics for each of the different observers. However, in each case, there is a systematic bias to the cloud of data points, suggesting that most observers would tend to view the laser projector colors as being more yellow-green than the corresponding conventional digital cinema projector color having the identical colorimetry (e.g., identical CIE XYZ values) if they were viewed side by side. This is consistent with experimental observations made by the inventors using the projector described in the aforementioned article by Silverstein et al. This suggests that the average amount of observer metemaric failure can be significantly reduced by introducing color corrections (i.e., color shifts in the blue-magenta direction) to the displayed colors on the laser projector to compensate for the average color shift  355 . While this will not reduce the size of the differences between the responses of the different observers, it can eliminate the systematic bias that has been observed between the perceived colors on a laser projector and a conventional digital cinema projector. 
       FIGS. 8A-8D  illustrate a framework within which color corrections can be applied to image data originally prepared for use with a wide-band display device to adapt it for use with a narrow-band display device such that an average observer metameric failure is reduced for a distribution of target observers. 
       FIG. 8A  shows a conventional color management method  440  to transform input color values  450  (R W , G W , B W ) adapted for display on a wide-band display device to provide output color values  454  (R W , G W , B W ) adapted for display on a narrow-band display device. 
     An input device model  451  (D W ) for the wide-band display device is used to transform the input color values  450  to corresponding device-independent color values  452 . Methods for forming such device models are well-known in the color management art. Typically the device-independent color values  452  will be in a standard CIE color space such as the well-known CIE XYZ or CIELAB color spaces. In some embodiments, the input device model  451  includes a set of one-dimensional nonlinear functions (e.g., “gamma functions”) that are applied to the input color values  450 , and a 3×3 phosphor matrix transformation that is used account for the colors of the input device color primaries. Such models generally work well for additive display devices such as conventional wide-band digital projection systems. In some embodiments, the input device model  451  may include other types of transform elements such as a multi-dimensional look-up table (LUT) or a parametric model such as a polynomial function. 
     An inverse output device model  453  (D N   −1 ) for the narrow-band display device is used to determine the output color values  454  needed to produce the device-independent color values  452  on the narrow-band display device. In some embodiments, the inverse output device model  453  includes a 3×3 inverse phosphor matrix transformation that is used account for the colors of the output device color primaries, and a set of one-dimensional nonlinear functions (e.g., “inverse gamma functions”). Such models generally work well for additive display devices such narrow-band laser projection systems. In some embodiments, the inverse output device model  453  may include other types of transform elements such as a multi-dimensional look-up table (LUT) or a parametric model such as a polynomial function. In some embodiments, the input device model  451  and the inverse output device model  453  are embodied using the well-known ICC color management profile format for use in an ICC color management system. 
     In some embodiments, the input device model  451  and the inverse output device model  453  can be combined to form a composite color transform  455 . In some embodiments, the composite color transform  455  can be embodied as an ICC device link profile. 
       FIG. 8B  shows a color correction method  442  in accordance with an embodiment of the present invention that incorporates a metamerism correction transform  460 . The metamerism correction transform  460  is used to transform the device-independent color values  452  to determine corrected device-independent color values  461  (X C , Y C , Z C ). As will be described later, the metamerism correction transform  460  is adapted to provide a reduced average observer metameric failure for a distribution of target observers (for example by applying inverse color shifts to compensate for the average color shifts  355  shown in  FIGS. 7A-7D ). 
     The corrected device-independent color values  461  are transformed using the inverse output device model  453  to determine corrected output color values  462  (R NC , G NC , B NC ). In some embodiments, the input device model  451 , the metamerism correction transform  460  and the inverse output device model  453  can be combined to form a composite metamerism correction transform  463 . 
       FIG. 8C  shows a color correction method  444  in accordance with an alternate embodiment of the present invention that incorporates a metamerism correction transform  465 . In this case, a conventional color management process (e.g., the color management method  440  shown in  FIG. 8A ) is used to determine output color values  454 . The metamerism correction transform  465  is then used to make appropriate adjustments to the output color values  454  to determine the corrected output color values  462 . In some embodiments, the input device model  451 , the inverse output device model  453  and the metamerism correction transform  465  can be combined to form a composite metamerism correction transform  466 . 
     In some embodiments, images may be provided to the display system (e.g., projector  100  in  FIG. 2 ) in a device-independent color encoding rather than a color encoding associated with a particular display device. For example, digital motion pictures are commonly distributed in the form of digitally encoded tristimulus values as specified by the DCDM digital cinema specification. In this case, color transforms are used to transform the input digital image data to the form that is appropriate for the particular projector.  FIG. 8D  illustrates an embodiment of the present invention where the input image data is received as device-independent color values  452  (XYZ). When the image is projected using a conventional wide-band display device, a conventional color management method  446  applies an inverse output device model  456  (D W   −1 ) for the wide-band display device is used to determine the output color values  457  needed to produce the device-independent color values  452  on the wide-band display device. When the image is projected using a narrow-band display device, a color correction method  448  is applied in accordance with the present invention where the metamerism correction transform  460  and the inverse output device model  453  are used to determine the appropriate corrected output color values  462  as was discussed earlier with respect to  FIG. 8B . 
       FIG. 9A  illustrates an exemplary perceived color shift determination method  540  for determining a metamerism correction  530  for an input color  500  (e.g., a pixel color for an image pixel) that reduces average observer metameric failure for a set of target observers. The metamerism correction  530  corrects for observer metamerism failure between images displayed on a conventional wide-band display system using a set of wide-band primaries  502  (e.g., the primaries shown in the digital cinema projector spectrum  410  of  FIG. 5 ) and. images displayed on a narrow-band display system using a set of narrow-band primaries  504  (e.g., the red laser primary  422 , the green laser primary  424  and the blue laser primary  426  in the laser projector spectrum  420  of  FIG. 5 ). This method can be used in the process of defining the metamerism correction transform  460  in  FIG. 8B  or the metamerism correction transform  465  in  FIG. 8C . 
     In the exemplary embodiment, the input color  500  is represented by a set of CIE XYZ tristimulus values. However, in other embodiments the input color  500  can be represented in any appropriate color space, including a device dependent color space (e.g., device dependent input color values  450  in  FIGS. 8A-8C ). 
     A determine wide-band spectrum step  552  is used to determine a wide-band spectrum  508  corresponding to the input color  500 . In embodiments where the input color is specified in a device-independent color space such as CIE XYZ, the determine wide-band spectrum step  552  determines the magnitudes of each of the wide-band primaries  502  that are required to provide the specified input color  500 . Likewise, a determine narrow-band spectrum step  510  is used to determine a narrow-band spectrum  512  corresponding to the input color  500 . The wide-band spectrum  508  and the narrow-band spectrum  512  will have matching CIE colorimetry, and would therefore match for an observer having color matching functions (CMFs) that exactly match those of the CIE standard observer. However, as was discussed relative to  FIGS. 7A-7D , it has been found that populations of real observers then to perceive the wide-band spectrum  508  as having a shifted color relative to the narrow-band spectrum  512  as a result of observer metameric failure. 
     To determine an appropriate metamerism correction  530 , a set of target observers is defined for which the average observer metameric failure is to be reduced. In a preferred embodiment, a set of target observer color matching functions  514  is specified to characterize the visual response of the set of target observers, where CMFs i  is the set of color matching functions for the i th  target observer. In some embodiments, one or both of the aforementioned set of 10° color matching functions  300  from Wyszecki and Stiles or the aforementioned set of 2° color matching functions from Stiles and Burch that were discussed earlier can be used to define the set of target observers. In other embodiments, a particular set of persons that is representative of a target audience can be specified for use as the set of target observers. In the limiting case, the set of target observers can be one particular person so that the system performance can be personalized to reduce observer metamerism effects for that particular person. For example, if the display system is used in a home environment, the system performance can be personalized for the homeowner, or for the set of family members in the home. In some embodiments, the color matching functions for a plurality of target observers can be averaged to determine a single set of color matching functions corresponding to an “average observer” that is representative of the set of target observers. In this case the set of target observer color matching functions  514  can include only the averaged color matching functions. 
     A determine perceived color step  516  is used to determine a target observer perceived wide-band color  518  (XYZ W,i ) corresponding to the wide-band spectrum  508  for each of the target observers. In a preferred embodiment, the determine perceived color step  516  determines tristimulus values (XYZ W,i ) using the following equations:
 
 X   W,i   =∫S   W (λ)   x     i (λ) dλ 
 
 Y   W,i   =∫S   W (λ)   y     i (λ) dλ 
 
 Z   W,i   =∫S   W (λ)   z     i (λ) dλ   (3)
 
where S W (λ) is the wide-band spectrum  508 , ( x   i (λ), y   i (λ), z   i (λ)) are the target observer color matching functions for the i th  target observer, and (X W,i , Y W,i , Z W,i ) are tristimulus values for the target observer perceived wide-band color  518 . Similarly, a determine perceived color step  520  is used to determine a target observer perceived narrow-band color  522  (XYZ N,i ) corresponding to the narrow-band spectrum  512  for each of the target observers.
 
     In general, due to observer metameric failure, the target observer perceived wide-band colors  518  will not match the target observer perceived narrow-band colors  522  for any particular target observer. A determine perceived color shift step  524  is used to determine a target observer perceived color shift  526  for each of the target observers. In some embodiments, the target observer perceived color shift  526  is represented as a difference between tristimulus values for the target observer perceived wide-band colors  518  and the target observer perceived narrow-band colors  522 :
 
Δ X   i   =X   N,i   −X   W,i  
 
Δ Y   i   =Z   N,i   −Z   W,i  
 
Δ Z   i   =Z   N,i   −Z   W,i   (4)
 
where (X N,i , Y N,i , Z N,i ) are tristimulus values for the target observer perceived narrow-band color  522  and (ΔX i , ΔY i , ΔZ i ) is the target observer perceived color shift  526  for the ith target observer.
 
     In other embodiments, the target observer perceived color shifts  526  can be represented using some other color space besides differences of tristimulus values. For example, the tristimulus values can be converted to chromaticity values (x, y, Y), L*a*b* values or L*u*v* values using well-known equations, and the target observer perceived color shift  526  can be determined relative to that color space (e.g., ΔE*). For embodiments where color spaces that determine color values relative to a reference white point (e.g., L*a*b* or L*u*v*), an appropriate white point can be defined corresponding to a particular white spectrum (e.g., a white spectrum associated with a specified white point associated with the wide-band primaries  502 ). 
     The determine metamerism correction step  528  determines an appropriate metamerism correction  530  responsive to the target observer perceived color shifts  526 . In a preferred embodiment, the metamerism correction  530  is determined to counteract an average of the target observer perceived color shifts  526 : 
                       C   X     =       -       Δ   ⁢           ⁢     X   i       _       =       -     1   N       ⁢       ∑     i   =   1     N     ⁢     Δ   ⁢           ⁢     X   i               ⁢     
     ⁢       C   Y     =       -       Δ   ⁢           ⁢     Y   i       _       =       -     1   N       ⁢       ∑     i   =   1     N     ⁢     Δ   ⁢           ⁢     Y   i               ⁢     
     ⁢       C   Z     =       -       Δ   ⁢           ⁢     Z   i       _       =       -     1   N       ⁢       ∑     i   =   1     N     ⁢     Δ   ⁢           ⁢     Z   i                       (   5   )               
where N is the number of target observers, and (C X , C Y , C Z ) is the metamerism correction  530 .
 
       FIG. 9B  is a flowchart showing a matching color determination method  545 , which represents an alternate method for determining an appropriate metamerism correction  530  for the narrow-band primaries  504  according to another embodiment. In this example, input color  550  is specified in terms of control values (RGB W ) for the wide-band display device, where the control values are used to control the amplitudes of the corresponding wide-band primaries  502 . 
     A determine wide-band spectrum step  552  determines a wide-band spectrum  508  corresponding to the input color  550 . Generally the determine wide-band spectrum step  552  determines the wide-band spectrum by forming a weighted combination of the spectra for the wide-band primaries  502 , where the weights are specified by the control values for the input color  550 . 
     As was discussed relative to  FIG. 9A , the determine perceived color step  516  determines target observer perceived wide-band colors  518  for the set of target observers responsive to the corresponding target observer color matching functions  514 . 
     A determine matching color step  554  determines a matching output color  556  for each of the target observers. In a preferred embodiment, the matching output color  556  is specified by a set of corrected narrow-band control values (RGB NC,i ) for the narrow-band display device which will produce a narrow-band spectrum that the target observer will perceive to be a match to the corresponding target observer perceived wide-band color  518 . The narrow-band spectrum is determined by forming a weighted combination of the spectra for the narrow-band primaries  504 , where the weights are specified by the narrow-band control values. The CIE colorimetry associated with the input color  540  and the matching output color  556  will generally be different from each other, reflecting the fact that the target observers will generally have different color matching functions than the CIE standard observer. The magnitude of the differences in the CIE colorimetry will typically be color dependent, and will be closely related to the target observer perceived color shifts  526  discussed with reference to the perceived color shift determination method  540  of  FIG. 9A . 
     In a preferred embodiment, the determine matching color step  554  determines the matching output color  556  responsive to the target observer color matching functions  514 . In some implementations, a nonlinear optimization technique can be used to iteratively adjust the amounts of the narrow-band primaries  504  until corresponding target observer perceived narrow-band colors (XYZ N,i ) are equal to the target observer perceived wide-band colors  518  (XYZ W,i ) to within a predefined tolerance (e.g., 0.00001). In other implementations, a phosphor matrix can be determined for the narrow-band primaries  504  for each set of target observer color matching functions  514 . Methods for determining a phosphor matrix given a set of color matching functions and a set of color primary spectra are well-known in the art. Once determined, the phosphor matrixes can be used to directly determine the matching output color  556  that will match the target observer perceived wide-band colors  518 . 
     In an alternate embodiment, the determine matching color step  554  can be performed by performing a visual matching experiment using the set of target observers. A first color patch having the input color  550  can be displayed on a screen using the wide-band primaries  502 . A second color patch can be displayed on the screen using the narrow-band primaries  504 . User controls can be provided that enable a target observer to adjust the amounts of the narrow-band primaries  504  until the target observer perceives the second color patch to visually match the first color patch. The resulting amounts of the narrow-band primaries  504  are used to define the matching output color  556 . This method, for example, might be practiced by a colorist or cinematographer in preparing content for distribution. 
     A determine metamerism correction step  558  is then used to determine the metamerism correction  530 . The metamerism correction  530  can be represented in many different forms. For example, if the color correction method  444  of  FIG. 8C  is used to provide the observer metamerism failure correction by adding offsets (R N =R NC +C R , G N =G NC +C G , B NC =B N +C B ) to the output color values  454 , then the offsets (ΔR, ΔG, ΔB) for a particular input color  550  can be determined by determining averaging observer-specific offsets: 
                       Δ   ⁢           ⁢   R     =       -       Δ   ⁢           ⁢     R   i       _       =       -     1   N       ⁢       ∑     i   =   1     N     ⁢     Δ   ⁢           ⁢     R   i               ⁢     
     ⁢       Δ   ⁢           ⁢   G     =       -       Δ   ⁢           ⁢     G   i       _       =       -     1   N       ⁢       ∑     i   =   1     N     ⁢     Δ   ⁢           ⁢     G   i               ⁢     
     ⁢       Δ   ⁢           ⁢   B     =       -       Δ   ⁢           ⁢     B   i       _       =       -     1   N       ⁢       ∑     i   =   1     N     ⁢     Δ   ⁢           ⁢     B   i                       (   6   )               
where (ΔR i , ΔG i , ΔB i ) are the observer-specific offsets for the ith target observer given by:
 
Δ R   i   =R   NC,i   −R   N  
 
Δ G   i   =G   NC,i   −G   N  
 
Δ B   i   =B   NC,i   −B   N   (7)
 
and ( ΔR i   , ΔG i   , ΔB i   ) are the average offsets. The offsets determined in this manner correspond to the centroid of the observer-specific offsets. In some embodiments, a different type of central tendency measure can be used to combine the observer-specific offsets. For example, a geometric mean of the observer-specific offsets can be determined, a median offset can be determined, or a weighted averaging process can be used to weight some target observers more highly than others.
 
     The metamerism correction  530  can be converted to any other appropriate form depending on the method used to implement the observer metamerism failure correction in a particular embodiment (e.g., the methods described with respect to  FIGS. 8B-8D ). The methods shown in  FIGS. 9A-9B  describe how an appropriate metamerism correction  530  can be determined for a particular input color  500 ,  550 . These methods can be repeated for a plurality of different input colors  500 ,  550  to form the metamerism correction transform  460 ,  465  ( FIGS. 8B-8D ). 
     The set of input colors used in the formation of the metamerism correction transform  460 ,  465  are preferably a set of colors spanning the range of colors that are important to a particular application. In some cases, the set of input colors includes important memory colors, such as those shown in Table 1. In some cases, the set of input colors can include a set of colors representing the 11 basic color names that are present in most human languages: white, black, grey, red, green, blue, yellow, brown, purple, orange, and pink. Additionally, a collection of multimedia content can be analyzed to determine frequently occurring color categories using image analysis algorithms, such as for example, a k-means clustering algorithm, the identified clusters can be included in the set of input colors. In yet another embodiment, a list of colors can be chosen based on audience preferences, or other criteria useful in particular circumstances, such as proofing or calibration with standardized color targets. By such methods, the collection of corrected colors can be expanded. 
     In some cases the set of input colors can include a lattice of input colors that systematically samples the wide-band color gamut  330  of the wide-band primary display device. It can also be useful to provide project specific input colors, including specific wide gamut colors, for particular image content that are important for realizing the intended “look” of that content. 
     In some embodiments, the metamerism correction transform  460 ,  465  is a parametric function having a plurality of parameters (e.g., a multi-dimensional polynomial, or parameters defining a series of matrices and 1-D LUTs). In this case, metamerism corrections can be determined for a set of different input colors, and a mathematical fitting process (e.g., a well-known least-squares regression process) can be used to determine the parameters for the parametric function by fitting the set of input color  500 ,  550  and the corresponding set of metamerism corrections  530  or output colors  556 . 
     In other embodiments, the metamerism correction transform  460 ,  465  is a multi-dimensional LUT that stores output color values (or metamerism correction values) corresponding to a lattice of input color values. In this case, the lattice of input color values can be used for the input colors  500 ,  550  and the stored output color values can be determined in accordance with the present invention (for example, using one of the methods shown in  FIGS. 9A-9B ). Alternately, the values stored in the multi-dimensional LUT can be determined by applying a fitting process to fit a smooth function to the set of input color  500 ,  550  and the corresponding set of metamerism corrections  530  or output colors  556 . For example, commonly assigned U.S. Pat. No. 4,941,039 to D&#39;Errico, entitled “Color image reproduction apparatus having a least squares look-up table augmented by smoothing” teaches a method for using a least-squares fitting process to provide a smooth multi-dimensional LUT. 
     Consider the case where the perceived color shift determination method  540  of  FIG. 9A  is used to determine the metamerism correction  530 . A set of input colors  500  can be evaluated corresponding to a lattice of input color values for the wide-band primaries  502 .  FIG. 10A  shows perceived color shift plot  560  including a set of target observer color vectors  565  corresponding to the target observer perceived color shifts  526  ( FIG. 9A ) for an input color  500  ( FIG. 9A ) in the magenta region of color space. An input color coordinate  562  is shown corresponding to the L*a*b* color of the input color  500  determined using the 1931 CIE 2° color matching functions  300   a  ( FIG. 1B ), indicating how the CIE standard observer would see this color. The tails of the target observer color vectors  565  correspond to the target observer perceived wide-band colors  518  ( FIG. 9A ) determined using the target observer color matching functions  514  ( FIG. 9A ). (The target observer color matching functions  514  used in the calculations were the aforementioned set of 10° color matching functions  300  ( FIG. 1A ) from Wyszecki and Stiles.) The heads of the target observer color vectors  565  (shown using diamond symbols) correspond to the target observer perceived narrow-band colors  522  ( FIG. 9A ) determined using the target observer color matching functions  514 . 
     From  FIG. 10A , it can be seen that there is a substantial amount of variability in the way that the target observers perceive the colors produced using the wide-band and narrow-band primaries, but that, with only a few exceptions, there is a general agreement that perception of the narrow-band colors are shifted in the yellow-green direction (i.e., in a negative a* and positive b* direction). It is noted that there are several outlier color vectors  564  having color shifts that are significantly different from the majority of the target observers. In some embodiments, it may be desirable to remove any outlier target observers from the set of target observers in order to avoid biasing the determined metamerism corrections  530 . An average color vector  568  is shown corresponding to the average magnitude and direction of the target observer color vectors  565 . (The position of average color vector  568  is offset from the set of target observer color vectors  565  for clarity.) It can be seen that both the tails and heads of the target observer color vectors  565  are shifted relative to the input color coordinate  562 , indicating that none of the target observer color matching functions  514  are very close to the standard 1931 CIE 2° color matching functions  300   a  ( FIG. 1B ). 
     As mentioned earlier, in some embodiments, the metamerism correction  530  can be determined with respect to an average of the color shifts determined for the set of target observers, while in other embodiments it can be determined for an “average observer” having a set of combined color matching functions corresponding to an average of the target observer color matching functions  514 . An average observer color vector  566  is shown corresponding to the color shift determined for this average observer. It can be seen that the magnitude and direction of the average observer color vector  566  is consistent with the general trend observed for the target observer color vectors  565 . In many cases, it has been found that similar results can be obtained by either averaging the color shifts determined for the set of target observers to determine the average color vector  568 , or by determining the average observer color vector  566  using the combined “average observer” color matching functions. 
       FIG. 10B  shows an example of a perceived color shift plot  570  in CIELAB color space that includes a set of color vectors  575  representing average perceived color shifts determined in this manner, where the heads of the vectors are shown using diamond symbols. The tails of the color vectors  575  correspond to the input colors  500 , and the magnitude and direction of the color vectors  575  correspond to the average of the target observer perceived color shifts  526  ( FIG. 9A ). The wide-band primaries  502  used in this example were those associated with the Barco model DP-1500 digital cinema projector, and the narrow-band primaries  504  were laser primaries having wavelengths of 465, 532, and 637 nm. 
     Also shown for reference are several memory colors represented by sky blue color coordinate  342 , grass green color coordinate  344  and skin tone color coordinate  346 . Significant perceived color shifts were observed for these memory colors were observed (i.e., sky blue≈4.4 ΔE*, grass green≈2.1 ΔE* and skin≈2.0 ΔE*). Even more dramatic color shifts were observed for many saturated colors including saturated greens (≈3-4 ΔE*), saturated blues (≈4-6 ΔE*), and saturated magentas/violets (≈4-9 ΔE*). Color differences determined for many other colors were more modest (≈1-1.5 ΔE*), including many low saturations reds, yellows and greens. 
     It is seen that the color shifts indicated by color vectors  575  are generally directed to the upper left, indicating a shift in the perceived color towards a yellow-green direction. The magnitude of the color vectors  575  is generally larger in the negative b* portion of color space, indicating that the perceived color shifts are color dependent and are larger in the cyan-blue-magenta color regions than elsewhere. To compensate for these perceived color shifts, thereby reducing the average amount observer metameric failure, color-dependent compensating color shifts can be defined for the metamerism correction  530 . In a preferred embodiment, the color-dependent compensating color shifts will have the same magnitude as the color vectors  575 , but will be directed in the opposite direction (i.e., in a generally blue-magenta direction). 
       FIG. 10C  shows a perceived color difference plot  580  corresponding to the perceived color shift plot  570  of  FIG. 10A . A target color gamut  585  is shown which is preferably slightly smaller than the range of colors that can be produced using the wide-band primaries  502  ( FIG. 9A ) to insure that all of the enclosed colors can be produced using both the wide-band primaries  502  and the narrow-band primaries  504 . Within the target color gamut  585 , a series of color difference contour lines  590  are shown indicating the average magnitudes of the color vectors  575  for the perceived color shifts in  FIG. 10A  as a function of a* and b*. It can be seen that the magnitude of the perceived color shifts are color-dependent and range from about 1 ΔE* to 5 ΔE*. 
     Taken together,  FIGS. 10A-10C  show that color dependent differences in color perception resulting from observer metameric failure can be reduced on average for an audience of observers  60 , by applying metamerism corrections  530  ( FIG. 9A ) comprising color-dependent compensating color shifts to the input image colors that are to be displayed by projectors  100  that include one or more narrow-band primaries  504 . These compensating color shifts would be greatest for blue, violet and magenta colors, and still significant for many green colors, but less significant (and perhaps unnecessary) for many red, yellow, and orange colors. These compensating color shifts can then be applied using many different arrangements, including those discussed with respect to  FIGS. 8B-8D . 
     As noted earlier, neither both the tails and heads of the target observer color vectors  565  in  FIG. 10A  are shifted relative to the input color coordinate  562 , reflecting the fact that none of the target observer color matching functions  514  (which in this example were the set of 10° color matching functions  300  ( FIG. 1A ) from Wyszecki and Stiles) are very close to the standard 1931 CIE 2° color matching functions  300   a  ( FIG. 1B ). This is not totally surprising because of the difference in the fields of view (2° vs. 10°). While the 1931 CIE 2° color matching functions  300   a  are generally used for digital cinema applications since the DCI digital cinema specification is based upon the 1931 CIE system of colorimetry, in some cases it may be appropriate to consider basing the metamerism correction calculations on the 1964 CIE 10° color matching functions  300   b  ( FIG. 1B ). For example, depending on the distance from the viewer to the screen, the contrast of the content being viewed, and the angular size of that content, often times a viewer&#39;s attention will perceive a field much larger than a 2° field. Therefore, the 1964 CIE 10° color matching functions  300   b  may represent an appropriate metric in some cases. 
     Considering the 1931 CIE 2° color matching functions  300   a  and 1964 CIE 10° color matching functions  300   b , in greater detail, as shown in  FIG. 1B , important differences emerge. It is noted that the CIE 10° color matching functions  300   b  deviate from the CIE 2° color matching functions  300   a  in the red, green, and blue regions of the wavelength spectrum, but the largest differences occur in blue region. In particular, it can be seen that the short wavelength color matching function peaks ˜10% higher for the CIE 10° color matching functions  300   b  compared to the CIE 2° color matching functions  300   a . Additionally, it can be seen that the location of the left edges of the main lobe of the long wavelength color matching functions are shifted between the respective CIE 2° color matching functions  300   a  and the CIE 10° color matching functions  300   b . These differences in the color matching functions will result in different metameric characteristics. 
     Further, it is observed that the short wavelength color matching function is both spectrally narrower by ˜2× (55 nm FWHM for blue, vs. 110 nm for green, and 90 nm for red) and higher gained (≈1.68× greater for 1931 color matching functions; ≈2× greater sensitivity with 1964 color matching functions) compared to the medium and long wavelength color matching functions. Alternately stated, the short wavelength (blue) color matching function slope sensitivity is much higher, and therefore small variations in the spectra of a narrow-band blue primary, or in an observer color matching function, in the short wavelength region can cause larger perceptual differences than in other regions. Indeed, the modeling indicates that small changes in the short wavelength color matching functions have ˜2× the contribution to the perceived color shifts relative to changes in the medium or long wavelength color matching functions. The comparatively high gain for the short wavelength (blue) cones likely compensates for their scarcity, as red and green cones predominate, with only ˜5% of retinal cones being of the short wavelength (blue) variety. In general, human perception of blue is inferior to that for red and green image content, relative to resolution, flicker sensitivity, and many other criteria. 
     In further considering the color matching functions  300  shown in  FIG. 1A , it is also notable that perception of many bluish colors depends on responses of all the three color matching functions, whereas for the perception of many green and red colors, the response of the short wavelength color matching function is a non-factor. Color perception can be thought of as a differencing mechanism, as represented by opponent models of color vision. In particular, the sensation of “blueness” can be described as the contribution of the short (S) wavelength cones exceeding the sum of the middle (M) and long (L) wavelength cones [S&gt;L+M]. In this context, the color matching functions  300  suggest that differential blue light perception can occur because of significant cone response variations among observers for all three cones, whereas for red and green light color perception above 540 nm, essentially only two cone responses are involved, and they may therefore exhibit smaller perceived color difference variations. 
       FIG. 11A  shows a target observer color vectors  565  analogous to that shown in  FIG. 10A , where in this case the wide-band spectrum  508  ( FIG. 9A ) and the narrow-band spectrum  512  ( FIG. 9A ) were determined to provide the input color  500  ( FIG. 9A ) relative to the 1964 CIE 10° color matching functions  300   b  ( FIG. 1B ). As with  FIG. 10A , the target observer color matching functions  514  used in the calculations were the aforementioned set of 10° color matching functions  300  ( FIG. 1A ) from Wyszecki and Stiles. 
     Comparing  FIG. 10A  to  FIG. 11A , it can be seen that the tails and heads of the target observer color vectors  565  are shifted closer to the input color coordinate  562 , reflecting the fact that the target observer color matching functions  514  are closer to the standard 1964 CIE 10° color matching functions  300   b . However, it can be seen that most of the target observers still observe a similar color shift in the yellow-green for the narrow-band colors relative to the wide-band colors that have the same CIE colorimetry. Therefore the metamerism corrections  530  ( FIG. 9A ) determined in this case would be similar to those determined using the data in  FIG. 10A .  FIG. 11B  shows a perceived color difference plot  580  analogous to that shown in  FIG. 10C , where the color perception differences were calculated for input colors that match relative to the 1964 CIE 10° color matching functions  300   b . It can be seen that the average size of the perceived color differences is somewhat smaller, but that there is still a substantial amount of average perceived color difference due to the observer metameric failure. The largest color perception differences are again present for magenta colors. Thus, it has been established that observer metameric failure, as characterized by color-dependent color perception differences, exists regardless of the CIE standard observers is used as reference. 
     The particular set of standard observer color matching functions ( 300   a  or  300   b ) and the particular set of target observer color matching functions  514  that are used to determine the metamerism correction  530  can be application dependent. In cases where the input colors are specified with respect to the 1931 CIE system of colorimetry, it will generally be appropriate to use the 1931 CIE 2° color matching functions  300   a  to determine the colorimetrically matching colors. The most appropriate set of target observer color matching functions  514  can be dependent on the target audience. In some embodiments, several different metamerism corrections can be determined using different combinations of standard and target observers, and the results can be evaluated using a set of observers to select the preferred amount of correction. For example, as human color matching functions can with observer age (e.g., due to yellowing of the eye lenses), having sets of target-observer color matching functions  514  that are demographically broad and others that are filtered by age (e.g., ≦28 years old, ≧55 years old) may be relevant. Thus, for example, sets of target-observer color matching functions  514  can be developed for demographic sub-groups of target observers, such as youth, and then used when displaying content that is predominately watched by such as an audience. As another example, measurement or assembly of a set of target-observer color matching functions  514  optimized for cinema equivalent viewing conditions can also account for characteristics such as viewing distances and field size. 
     The above calculations were performed using the nominal laser primaries (i.e., red laser primary  422  at 637 nm, green laser primary  424  at 532 nm and blue laser primary  426  at 465 nm) shown in  FIG. 1A . It is noted that these analyses were also repeated using the alternate Thornton primaries shown in  FIG. 1A  (i.e., Thornton red laser primary  432  at 610 nm, Thornton green laser primary  434  at 530 nm and Thornton blue laser primary  436  at 450 nm). From  FIG. 1A , it is seen that the Thornton green laser primary  434  and the nominal green laser primary  424  are quite similar, (530 nm vs. 532 nm), but that both the Thornton blue laser primary  436  and the Thornton red laser primary  432  are shifted to lower wavelengths compared to the exemplary blue laser primary  426  and red laser primary  422  (450 nm vs. 465 nm, and 610 nm vs. 637 nm, respectively). Although the Thornton primaries align more closely with the peaks of the three spectral sensitivities of the normal human visual system, they also line up comparatively at or near the peaks or maximum difference in observer variation in color matching functions, compared to the nominal primaries. As a result, for the analysis using the Thornton primaries for the narrow-band primaries  504 , it was found that color perception differences followed the same general trends as those of  FIG. 10B , but the magnitudes were about 2-3× larger. This suggests that the use of the Thornton primaries would actually provide greater observer metameric failure. 
     The metamerism corrections  530  determined using the methods discussed above are based on determining target observer perceived color shifts  526  ( FIG. 9A ) between colorimetrically matching colors displayed using the different sets of primaries, or determining narrow-band matching output colors  556  ( FIG. 9B ) that match wide-band input colors  550 . These processes can only be applied to input colors  500  and  550  that are within the color gamuts of both the wide-band primaries  502  and the narrow-band primaries  504 . 
     There are many colors that are within the narrow-band color gamut (e.g., the laser primary color gamut  335  of  FIG. 6 ) that are outside of the wide-band color gamut. Therefore, projectors  100  that employ narrow-band primaries may be called on to display input colors that cannot be reproduced with conventional systems using wide-band primaries. As a result, the metamerism correction transform  460  ( FIG. 8D ) should be adapted to process colors both inside and outside of the color gamut associated with the wide-band primaries. 
     The color shifts applied for input colors that are outside of the wide-band primary color gamut can be determined in a variety of ways. It will generally be preferable that there be no abrupt changes in the applied color shifts to avoid contouring artifacts where small differences in the input color produce large perceived differences in the displayed color. In some embodiments, the metamerism corrections  530  determined for colors inside of the wide-band primary color gamut can be extrapolated to those colors that are outside of the wide-band primary color gamut. Methods for extrapolating a function are well-known in the art. 
       FIG. 12  shows a cross-section through CIELAB color space, including an inner color gamut  358 , an extended color gamut zone  362  and a transition zone  360 . Preferably, the inner color gamut  358  is a conventional color gamut corresponding to a particular set of wide-band primaries  502  ( FIG. 9A ). For example, the inner color gamut  358  can correspond to the wide-band color gamut  330  of  FIG. 6  (translated to CIELAB). In other cases, inner color gamut  358  can be smaller or larger than the conventional color gamut. In a preferred embodiment, color shifts to be applied for colors inside the inner color gamut  358  are determined using a method such as those discussed with respect to  FIGS. 9A-9B  to determine appropriate metamerism corrections  530 . 
     For highly saturated colors in the extended color gamut zone  362 , no color shifts are applied. Such colors are not generally seen in nature, and therefore people typically lack expectations of their color appearance, or even language or metrics to describe their differential color perceptions. As such, differences in color perception of such colors among observers  60  can be acceptable. Furthermore, since these colors cannot be produced by the conventional systems, there will be no need to correct for color perception differences. 
     Transition zone  360  is preferably provided between the inner color gamut  358  and the extended color gamut zone  362  to provide continuity between the color regions. Within the transition zone  360 , the color shifts are smoothly transitioned from the metamerism corrections  530  determined for the colors within the inner color gamut  358  down to no color shifts in the extended color gamut zone. The use of the smooth transition avoids introducing contouring artifacts where colors that are very close to each other in an input image are mapped to colors that are far apart in the displayed image, resulting in a visual discontinuity. Such artifacts would be particularly objectionable for pixels contiguously describing an object (e.g., a ball) locally within the image content. Such artifacts would be more likely for colors in the blue/magenta/violet portions of color space, where large color dependent color perception difference values (ΔE*) have been found (see  FIGS. 10C, 11B ). 
     In some embodiments, the transition zone  360  can extend out a fixed distance (e.g., 10 ΔE*) from the surface of the inner color gamut  358 . In other embodiments, the width of the transition zone  360  can be adjusted according to the characteristics of the metamerism corrections  530  applied near the surface of the inner color gamut  358 . In some embodiments, the width of the transition zone can be set to be a multiple (M) of the magnitudes of the color shifts being applied at the corresponding location on the surface of the inner color gamut  358 . For example, the width of the transition zone  360  can be M×(ΔE*), where M=4. Accordingly, if the color shift at the surface of the inner color gamut  358  in a blue hue direction is 5 ΔE*, then the width of the transition zone can be set to 4×5 ΔE*=20 ΔE*. 
       FIG. 13  provides an exemplary metameric failure compensation method  600  for determining a corrected output color  660  by providing compensating color shifts to an input color  610 . The input color  610  is typically a color value associated with an image pixel an image which is to be displayed by the projector  100  ( FIG. 3 ). In a preferred embodiment, the input color  610  is specified such that it has the desired color appearance on a display having conventional wide-band primaries  502  ( FIG. 9A ). 
     In some embodiments, the metameric failure compensation method  600  of  FIG. 13  can be performed by a data processing system within the projector data path  200  ( FIG. 4 ) of projector  100  (e.g., by the metameric color corrector  250 ). In other embodiments, the method is performed ahead of time during the formation of a color transform (e.g., metamerism correction transform  460  in  FIG. 8B ), which is stored for application to the image data at a later time. 
     Metamerism correction data  605  provides an indication of appropriate metamerism corrections  530  ( FIG. 9A ) determined for colors inside the conventional color gamut test  615  in accordance with the present invention using methods such as those described in  FIGS. 9A-9B . An inside conventional color gamut test  615  determines whether the input color  610  is inside the inner color gamut  358  ( FIG. 12 ). If so an apply full metamerism correction step  620  applies the appropriate metamerism correction color shift from the metamerism correction data  605  and applies it to the input color  610  to determine the corrected output color  660 . 
     The apply full metamerism correction step  620  can apply the metameric corrections by various mathematical and processing approaches. For example, in Section 3.5, of the book  Computational Color Technology  (Society of Photo-Optical Engineers, Bellingham, Wash., 2006) by H. R. Kang, several methods for applying metameric correction functions are mathematically described. Although Kang does not provide a theory or model for determining appropriate metameric corrections, as compared to the present invention which provides methods for determining such metameric corrections, Kang does provide an architecture for applying color corrections to input color data. One of the methods is additive correction. In accordance with Kang, the additive correction is performed in L*a*b* space, where the correction in each color channel is specified as a color difference vector (ΔL*, Δa*, Δb*). Alternately, Kang provides that a multiplicative correction that can be performed in CIE XYZ tristimulus space. In that case, tristimulus values of the input colors are multiplied by a set of ratios. Any of these methods can be used to apply the metamerism corrections of the present invention. 
     If the image content only includes input colors  610  within the inner color gamut  358 , the corrected image data would consist of pixel data solely determined using the apply full metamerism correction step  620 . If however, the image content includes input colors  610  outside the inner color gamut  358 , then image pixels having such colors can be subjected to further analysis. If the inside conventional color gamut test  615  determines that a particular input color  610  is not inside the inner color gamut  358 , an inside transition zone test  625  determines whether the input color  610  is in the transition zone  360  ( FIG. 12 ). If not, it can be assumed that the input color  610  is in the extended color gamut zone  362  ( FIG. 12 ). In this case, an apply no metamerism correction step  640  sets the corrected output color  660  to be equal to the input color  610 . 
     If the inside transition zone test  625  determines that the input color  610  is in the transition zone  360 , an apply partial metamerism correction step  630  is used to apply a fraction of the metamerism correction at a corresponding point in the surface of the inner color gamut  358 . The partial metamerism correction is then applied to the input color  610  to determine the corrected output color  660 . A transition function  635  is used to specify an appropriate fraction of the metamerism function that should be applied as a function of the relative position of the input color  610  within the transition zone  360 . In a preferred embodiment, the transition function  635  linearly tapers the amount of metamerism correction from 100% at the surface of the inner color gamut  358  down to 0% at the outer surface of the transition zone  360 , where the outer edge is given by the previously defined transition zone width. In this way, continuity is preserved so that there are no abrupt changes in the corrected output color  600 . 
       FIG. 14  shows an example of a linear transition function  670  than can be used for the transition function  635  ( FIG. 13 ). The input to the transition function  635  is the distance of the input color from the neutral axis of the color space. If the input color is expressed in terms of L*a*b* values, the radius is given by the C* value where (C*=(a* 2 +b* 2 ) 0.5 ). The radius of the inner color gamut  358  at the corresponding hue and lightness is given by C* G , and the outer radius of the transition zone  360  is given by C* T . The output of the transition function  635  is the correction fraction, which ranges from 0% to 100%. In other embodiments, the transition function  635  can apply other types of transition functions, such as a sigmoid transition function  675 . 
     In some embodiments, a continuity function  650  can help maintain visual color continuity within discrete objects provided locally within the image content. For example, image content analysis can analyze the pixel values of the digital image to identify object areas having similar colors (e.g., a red ball, for example). Care can then be taken to apply consistent metameric shifts within each object area. In some embodiments, the continuity function  650  can specify that the same metamerism correction be applied to all image pixels within an object area. In some embodiments, the continuity function can apply a constraint that avoids applying metamerism corrections that cause a hue shift out of a colors range that is generally recognized by a given color name. Such hue shifts are most likely to occur at hue boundaries or for hues that occupy small portions of color space (e.g., yellow). 
     In some embodiments, rather than applying no metamerism correction to colors in the extended color gamut zone  362 , it may be found to be desirable to define metameric corrections based on some other criterion besides that is not based on reducing color appearance differences between specified sets of wide-band primaries  502  and narrow-band primaries  504 . In this case, the apply no metamerism correction step  640  can be replaced with a step that applies the desired metamerism correction. The apply partial metamerism correction step  630  can then be used to transition between the metamerism corrections applied inside the inner color gamut  358  and the extended color gamut zone  362 . 
     In an alternate embodiment, the method described in commonly-assigned U.S. Pat. No. 5,583,666 to Ellson et al., entitled “Method for cross-device color calibration and enhancement using explicit constraints,” can be used to provide the smooth transition within the transition zone  360 . Accordingly, a first subset of input colors is defined including input colors within the inner color gamut  358 , and a second subset of input colors is defined including input colors within the extended color gamut zone  362 . A first color transform in accordance with the metamerism corrections  530  is assigned to the first subset of input colors, and a second transform that preserves the input colors is assigned to the second subset of input colors. A third subset of input colors is formed including the input colors that are not included in the first and second subsets. The third subset of input colors will contain the input colors in the transition zone  360 . A color transform for the input colors in the third subset is defined which preserves continuity with the transforms assigned to the first and second subsets. In some embodiments, the color transform for the input colors in the third subset is determined using an appropriate interpolation method. 
     In some embodiments, rather than applying the full metamerism corrections throughout the entire inner color gamut  358 , the metameric corrections can be applied selectively to localized color regions, such as for memory colors like sky blue, skin tones, grass green, white, grays, and other critical or widely recognized colors. Selective metameric color corrections may also be applied to certain target colors that are particularly important for a given production or film. Transition zones  360  can then be defined around each of the localized color regions to provide for smooth transitions of the metameric corrections. 
     In some embodiments, rather than applying no metamerism correction to colors in the extended color gamut zone  362 , it may be desirable to define metameric corrections based on some other criterion than on reducing color appearance differences between specified sets of wide-band primaries  502  and narrow-band primaries  504 . In this case, the apply no metamerism correction step  640  can be replaced with a step that applies the desired metamerism correction. The apply partial metamerism correction step  630  can then be used to transition between the metamerism corrections applied inside the inner color gamut  358  and the extended color gamut zone  362 . 
     The method of the present invention has been described with the reference to correcting observer metameric failure artifacts between a first display having wide-band primaries  502  and a second display using narrow-band primaries  504 . However, the described method can also be applied to correcting observer metameric failure artifacts between two displays both of which use narrow-band primaries. For example, a first narrow-band display system using a first set of narrow-band primaries can be a studio or screening room reference system, and a second narrow-band display system using a second set of narrow-band primaries can be deployed in cinematic or residential distribution. As the display systems evolve with newer technologies, use of a standard or reference system having specified standard primaries can provide a standard distribution encoding and can enable archival storage, but without providing observer metameric failure correction, the colors would not have the desired appearance if they were directly displayed on a system having a different set of primaries. Thus, it should be understood that a similar process can be applied to adapt input data that was previously prepared for viewing by a particular display with a first set of narrow-band primaries for viewing by an alternate display with a second set of narrow-band primaries. In this case, the wide-band primaries  502  in the above-described methods can simply be replaced with the first set of narrow-band primaries, and the second set of narrow-band primaries can be used for the narrow-band primaries  504 . 
     As noted previously, digital cinema image content is commonly distributed as data files encoded according to the DCDM digital cinema specification. Today, these images are optimized for projection by a projector having three broad bandwidth primaries (e.g., using filtered xenon lamp light, as represented by digital cinema projector spectrum  410 , in  FIG. 5 ). As shown in  FIG. 4 , after file decryption and decompression, any necessary projector specific image corrections are applied via image processor  240 , before the data is passed forward for projection. For example, these corrections can further optimize the incoming image data for projection by a DLP or LCOS based projector, as appropriate. However, for the purposes of the present invention, projector  100  can further include metameric color corrector  250  that alters the color reproduction to optimize the incoming image data for projection by a narrow-bandwidth primary projector for the purpose of reducing the occurrence of observer metameric failure. As an example, metameric color corrector  250  can provide CIEXYZ space multiplicative scaling corrections or CIELAB additive corrections to compensate for the metameric failure induced color shifts shown in  FIGS. 7A-7D and 10A-10B . In particular, the incoming data can be altered to apply metamerism corrections  530  ( FIG. 9A-9B ) to compensate for to the average perceived color shifts, so that the observers  60  ( FIG. 2 ) will tend to view the displayed colors on the narrow-band projection system as being closer to the colors that they would see if the image were displayed on a conventional wide-band projection system. 
     As the present invention has been described thus far, the image processor  240  and metameric color corrector  250  reside within the projector data path  200  and provide the image analysis that identifies image content or colors that can benefit from metameric failure color correction, and then provide the appropriate color corrections. Metameric color corrector  250  can use matrices, look-up tables (LUTs), parametric functions or algorithms, or combinations thereof, to apply appropriate metamerism corrections  530 . Metameric color corrector  250  can also be enabled using a programmable logic device, such as a FPGA device. A memory or frame store can be included with image processor  240 , to compile the altered image frame, including both normal image quality corrections provided by image corrector  245  and metameric failure reduction image corrections provided by metameric color corrector  250 . The resulting image frames can then be passed to frame buffer  260 . 
     Alternately, the data processing system that applies metameric failure color corrections can be operated at the content source (including studios, post-house, cinematographer, or colorist) or other location, such that pre-corrected image data files or image data altering files can be delivered to the exhibitor. For example, when it is determined or known that the image content will be viewed on a display with narrow-band primaries, whether in a cinema, home theatre, or other venue, pre-color corrected image content can be provided or pre-determined, and accompanying metadata or data files with the DCDM content files can enable or provide the metameric color corrected image content. 
     In summary, the previously discussed papers by Konig et al., Fairchild et al., and J. Bergquist, suggested that observer metameric failure can only be effectively reduced by displays using N&gt;3 nominally intermediate- to wide-band (e.g., 30-100 nm) primaries. However, the present invention provides a method applicable to displays having N=3 narrow-band primaries by which color-dependent metamerism corrections  530  are determined and applied to reduce the average magnitude of observer metameric failure for a set of target observers. In particular, the exemplary metameric correction modeling methods of  FIGS. 9A-9B  are used to calculate appropriate metamerism corrections  530 . These metamerism corrections  530  can then be applied via the exemplary metameric failure compensation method  600  of  FIG. 13  to provide at output corrected output colors  660  as appropriate on a pixel-wise basis. However, while this method primarily corrects for the predominant shifts in color perception (e.g., the yellow-green color shifts observed in the exemplary color perception difference plots of  FIGS. 7A-7D ), other approaches for reducing observer metameric failure can complement or extend this method. 
     The displays and projectors  100  of the present invention have been nominally described as being three primary (N=3) systems, where the three primaries are each provided by narrow-band light sources (e.g., lasers or LEDs). However, it will be obvious to one skilled in the art that the inventive method can also be used in displays having mixed primaries, where some primaries are narrow-band and other are wide-band. As one example, a display system having two narrow-band primaries (e.g., red and green) and one wide-band primary (e.g., blue) can still apply metameric corrections determined in accordance with the present invention to compensate for the observer metameric failure contributions from the use of the narrow-band primaries. 
     The discussion to this point has assumed that the input color is adapted for display on a conventional wide-band display, and has generally been directed at reducing color perception differences between the wide-band display and a narrow-band display that result from observer metameric failure. However, observer metameric failure will also cause perceived color differences between two narrow-band displays having different sets of narrow-band primaries. For example, an input image can be optimized to be displayed on a narrow-band display having a first set of narrow-band primaries, and it can be desired to apply appropriate metemaric corrections in order to display the image on a narrow-band display having a second set of narrow-band primaries. The method of the present invention can also be used to compensate for these color differences. In this case, the wide-band primaries  502  in  FIGS. 9A-9B  can be replaced with the first set of narrow-band primaries, and the second set of narrow-band primaries can be used for the narrow-band primaries  504 . 
     As another example, a six primary projection system could be constructed where three wide-band primaries (R W G W B W ) define a conventional color gamut and three narrow-band primaries (R n G n B n ) define an extended color gamut. In operation, the three wide-band primaries principally provide colors within the conventional color gamut, while the three narrow-band primaries principally provide colors extending to the boundaries of the extended color gamut, but not the colors inside the conventional wide-band color gamut  330 . In such an example, the color perception difference modeling method described herein can be used to determine perceived color difference values and corresponding metamerism corrections  530  for pixels having colors that are displayed using the narrow-band primaries, or with combinations of the wide-band and narrow-band primaries. Scaled color corrections and transitions zones  360  can be used for colors near the boundary of the conventional wide-band color gamut  330 , and can overlap with the conventional wide-band color gamut  330  produced by the wide-band primaries (RwGwBw). This approach has the disadvantage that two complete projectors are essentially required, which likely have many significantly different optical components as the light sources are so different. However, it has the advantage of providing an expanded color gamut, while reducing the occurrence of observer metameric failure artifacts. 
     The invention can also be applied to display systems having more than three narrow band primaries (e.g., N=6). Such systems can be useful for expanding spectral color diversity so as to reduce observer metameric failure among the observers  60 , while using a common optical design with mostly identical components. For example, such a display system can have two blue laser primaries (e.g., 445 nm and 465 nm), two green laser primaries (e.g. 532 nm and 560 nm), and two red laser primaries (e.g. 632 nm and 650 nm). In some embodiments, a first projector  100  ( FIG. 4 ) can display an image using one set of primaries (e.g., 445 nm, 560 nm, and 650 nm) onto the display surface  190 , and a second projector  100  can display an overlapping image using the second set of primaries (e.g. 465 nm, 532 nm, and 632 nm) onto the same display surface  190 . As a result, a color provided for a pixel, unless it is on or very near the spectrum locus  325 , can be rendered using primaries provided by both projectors  100 . As both the white point color balance and the primary color coordinates of the two projectors  100  will not be identical, the data signals provided to the spatial light modulators  170  are not identical between common (e.g., blue) color channels for the two projectors  100 . This display system, per the present invention, can use the color perception difference modeling method and the metameric failure correction method described above to provide metamerism corrections  530  appropriate for the image data provided by each projector  100 . 
     This approach bears some similarity to the projection technology of Infitec GmbH, Ulm, Germany, which uses wavelength multiplexing with two sets of color primaries to provide 3-D imagery to observers  60  who are wearing appropriate viewing glasses. The Infitec approach provide channel separation for stereo projection by filtering broadband light sources to match left and right eye color band filter glasses (e.g., left eye: red=629 nm, green=532 nm, blue=446 nm, and right eye: red=615 nm, green=518 nm, blue=432 nm). In contrast, although the exemplary N=6 laser primary projector may provide 3-D imagery, it mainly provides reduced observer metameric failure with narrow primaries by increasing spectral color diversity providing while providing metamerism corrections  530  per the method of the present invention, thus addressing a distinct and separate problem. 
     As a variation on N=6 laser primary projection, one projector  100  can be used instead, where each spatial light modulator  170  receives illumination light from both types of laser sources for that color. In that case, white point balancing can essentially work with a wavelength averaged color channel. While the greater spectral color diversity is still present, and only one projector  100  is required, controlling color reproduction can be more difficult. 
     Alternately, each color channel can use the two laser wavelengths per color in a sequentially time multiplexed fashion (e.g., scrolling color), using both sets of primaries within a frame time to render the pixel colors. Such spectral color time multiplexing depends on the modulation capabilities within the display or projector  100 . In the case of digital cinema systems, the base projection frame rate is typically 24 fps (or 24 Hz), which corresponds to a frame time of 41.67 ms. In a film projector, a shutter effectively doubles the frame rate to reduce flicker perception by providing two pulses of illuminating light to a film frame. Digital or electronic projectors can have similar frame replication effects. 
     Consider the timing diagram of  FIG. 15A , in which an image frame  700  is projected during a frame time  710  that includes a blanking time  725  and a frame ON time  705 . The blanking time  725  is an OFF state, during which light is nominally not sent to the display surface  190  ( FIG. 2 ), and other activities occur (e.g., the loading of image data). The frame ON time  705  is the portion of the frame time  710  during which the projector  100  ( FIG. 2 ) provides image light to the  190  with the light intensity in spatial and temporal accordance with the image content. 
     At present, to enable 3-D image presentation, DMD or DLP projectors typically utilize “Triple Flash” projection, where six sub-frames  730 , having sub-frame ON times  735 , are presented per frame time  710 , as depicted in  FIG. 15B . In the case of 3-D image projection, the left eye and right eye images are each presented to the eye in an alternating fashion three times per frame. In the case of 2-D projection, the identical frame content is presented in each of the six sub-frames, for an effective frame rate of 144 Hz (which corresponds to a 6.94 ms sub-frame time). Within each of the sub-frames  730 , whether for 2-D or 3-D image projection, DMD projection uses a temporal or pulse-width modulation (PWM) scheme on a pixel-wise basis to present the image content according to the corresponding pixel code values. The sub-frames  730  typically have a high duty cycle (˜95%), with short blanking times  725  between the sub-frames  730 . During the blanking times  725 , various periodic timing events, such as polarization switching or DMD global reset functions, can occur without causing on-screen image artifacts. The frame ON time  705  (or the sub-frame ON times  735 ) represents the time that a particular set of image data are projected to the display surface  190 . 
     In this example, the color required for a given projected image pixel during a particular frame time  710  can be created by projecting with the first set of laser primaries during the odd sub-frames  730  (e.g.,  1 ,  3 ,  5 ) and projecting with the second set of laser primaries during the even sub-frames  730  (e.g.,  2 ,  4 ,  6 ). The metamerism corrections  530  determined in accordance with the present invention would be different for each set laser primaries. In summary, these exemplary N=6 laser primary projection approaches provide increased spectral color diversity and metameric observer failure image artifact reduction, while only modestly reducing the color gamut and aiding speckle reduction. 
     It is also noted that spectral color diversity can be increased, and therefore observer metameric failure reduced, by effects applied external to the projector  100  having narrow-bandwidth primaries. In particular, commonly assigned U.S. Pat. No. 8,085,467 to Silverstein et al., entitled “Projection display surface providing speckle reduction”, which is incorporated herein by reference, provides a projection screen sparsely coated with fluorescing materials that provide visible fluorescence at wavelengths near or around the visible stimulating light. For example, incident red laser light can cause a visible red fluorescence where the fluorescing bandwidth can be, for example, Δλ˜30 nm. While the principal advantage of this screen is to aid speckle reduction, the increase in spectral color diversity that it provides can also reduce the occurrence or magnitude of observer metameric failure among observers  60  of images projected onto the fluorescently enhanced projection screen. Depending on the fluorescing bandwidth Δλ, created, the wide color gamut provided by such a laser based projector  100 , can be only modestly reduced. 
     The previous discussion described methods for reducing observer metameric failure by increasing spectral color diversity using more than three narrow-band primaries, including with the use of spectral color multiplexing, where the same color is generated by different sets of narrow-band primaries. In some embodiments, a spectral color “dithering” aspect can be added, where primaries from the two sets are used in an intermingled fashion to generate the same color within a frame time  710  by changing primary combinations by sub-frame  730  (e.g., sub-frame # 1 : λ b1 , λ g2 , λ r2 ; sub-frame # 2 : λ b2 , λ g1 , λ r2 ). 
     Although adding more primaries can help reduce the occurrence of observer metameric failure in displays having narrow-band primaries by increasing spectral diversity, this option complicates the optical design. Thus, it would be desirable to find other opportunities for reducing observer metameric failure effects in three primary systems. As an alternative, color diversity can be provided by performing color dithering about a target color  750  as illustrated in  FIG. 16 . In particular, for a given target color  750 , the intensities of the laser primaries can be modulated in rapid succession on a pixel-wise basis, or group-of-pixels basis, to “dither” the displayed color in a color neighborhood around the target color  750 . (Within the context of the present invention, the term “dither” refers to rapidly varying between a series of different states or colors to introduce variation.) Preferably, the target color  750 , around which color dithering occurs, is the corrected output color  660  ( FIG. 13 ) determined using the previously described methods. The color dithering can be a random, periodic, or aperiodic modulation of a set of dithering colors  762 ,  764 ,  766  arranged on a color dithering locus  760  about the color center (i.e., target color  750 ). The dithering colors  762 ,  764 ,  766  are selected so that they temporally average to provide the colorimetry of the target color  750 . The rapid projection of the series of dithering colors  762 ,  764 ,  766  will appear to the observers  60  as the target color  750 . This mechanism provides display color diversity compared to displaying the target color  750  directly with constant intensity primaries, thereby increasing the likelihood that they can report seeing a common color. As discussed earlier, the magnitude of the perceptual color shifts associated with observer metamerism failure can be substantially different in different parts of color space. Therefore, in some embodiments it can be desirable to adjust the size of the color dithering locus  760  as a function of location in color space in accordance with the magnitude of the associated perceptual color shifts. 
     This mechanism provides display color diversity compared to displaying the target color  750  directly with constant intensity primaries. As individual observers  60  are stimulated with a larger color space area inclusive of the dithering colors  770 , these color space areas will overlap among at least some observers  60 , thereby increasing the likelihood that they can report seeing a common color. The color perception averaging aspect of temporal color dithering can be compared to scrolling color projectors that project colored images in rapid sequence; e.g., a red image, followed by a green image and a blue image. In such projectors, if the frame refresh rate is fast enough, the observer does not perceive a sequence of flickering colored images, but rather perceives a temporally integrated multicolored image. By comparison, with temporal color dithering, a projector  100  having a single set of narrow-band primaries (λ b , λ g , λ r ) can assemble the designated target color  750  for a particular image pixel in a particular frame time  710  ( FIG. 15B ), by projecting the dithering colors  762 ,  764  and  766  in sequential sub-frames  730  ( FIG. 15B ). For example, for a given pixel in a particular image frame  700  ( FIG. 15A ), the projector  100  can provide sub-frames # 1  and # 4  with the dithering color  762 , sub-frames # 2  and # 5  with the dithering color  764 , and sub-frames # 3  and # 6  with the dithering color  766 . Dithering color  762  can be greener than the target color  750 , dithering color  764  can be bluer than the target color  750  and dithering color  762  can be redder than the target color  750 . Nonetheless, experiments have shown that observers  60  can perceive a color patch projected with this type of temporal color dithering as color matched to an adjacent color patch that is displayed a constant target color  750 . 
     Temporal color dithering is further illustrated in  FIG. 17 , which depicts a CIE x,y chromaticity diagram  320  outlined by spectrum locus  325 , and a laser primary color gamut  335  corresponding to red laser primary  422 , green laser primary  424  and blue laser primary  426 . Four exemplary target colors  750  ( FIG. 16 ) are indicated by white target color  751 , sky blue target color  752 , grass green target color  753 , and skin tone target color  754 . 
     About each target color, a color dithering locus  760  is depicted, which includes a set of distinct dithering colors that can be presented in a temporal sequence and temporally average to appear as the corresponding target color. The dithering colors in each color dithering locus  760  are formed by an appropriate combination of the laser primaries. 
     To expand on this,  FIGS. 18A-18D  depict enlarged views of sub-portions of the CIE x,y chromaticity diagram  320  in  FIG. 17 , that zoom in on the color regions including the white target color  751  ( FIG. 14A ), the sky blue target color  752 ( FIG. 14B ), the grass green target color  753  ( FIG. 14C ), and the skin tone target color  754  ( FIG. 14D ), respectively. About each of the respective target colors, are a series of exemplary color dithering loci  771 ,  772 ,  773  and  774  including dithering colors  770 . 
     The dithering colors  770  can be defined by the magnitude and direction of color shift relative to the respective target color, and the modulation criteria amongst the dither colors. In some embodiments, the well-known MacAdam ellipses can be used as a benchmark in the definition of the dithering colors. The MacAdam ellipses indicate color regions in CIE x,y chromaticity space that contain colors which are indistinguishable to the typical human observer from the color at the center of the ellipse. In particular, colors within the MacAdam ellipses are perceived as being less than 1 JND different from the central color, while colors outside the ellipses are &gt;1 JND different from the central color. In some embodiments, the dithering colors can be defined to lie on a color dither locus corresponding to an ellipse in CIE x,y chromaticity space centered on the respective target color, where the size and orientation of the ellipse is defined based on the MacAdam ellipses to provide a desired number of JNDs of color difference (e.g., 4 JNDs). More generally, the dithering colors  770  by defining appropriate color dithering loci in CIE XYZ, CIELAB, or other color spaces, using a variety of scales or units, including ΔE*, Δa*, Δb*, JNDs, or x-y vector lengths, as appropriate. 
       FIGS. 18A-18D  illustrate color dithering loci  771 ,  772 ,  773  and  774  that are defined according to various criteria. Color dithering locus  774  is a circle centered on the associated target color with a radius of 0.01 in x-y chromaticity coordinate space, with exemplary dithering colors  770  shown as points distributed around the circle. 
     While the circular color dithering locus  774  is convenient to define, it has the disadvantage that it is defined based on the CIE x-y chromaticity space, which is known to be perceptually non-uniform. In a preferred embodiment, the color dithering loci is defined such that the dithering colors  770  are at equivalent visual distances from the target color. The CIELAB color space (i.e., L*a*b*) was designed to be approximately visually uniform so that equal distances approximately correspond to equal visual differences. In some embodiments, the color dithering loci can be defined to be a circle in CIELAB having a radius which is a specified number of ΔE* units. The dithering points can be defined in terms of their L*a*b* coordinates, and then translated back to corresponding chromaticity coordinates. The color dithering loci  771 ,  772  and  773  in  FIGS. 18A-18D  were defined in this manner, with color differences of 1, 2, and 4 ΔE*, respectively. (A color shift of 1 ΔE* can be considered to be approximately equivalent to a 1 JND color change). As  FIGS. 18A-18D  show, the color dithering loci  771 ,  772  and  773  are approximately elliptical in shape in the x,y chromaticity space, but of comparable size to the circular color dithering locus  774 . Once the color dithering loci are defined, the dithering colors  770  can be distributed around color dithering locus so that they average to provide the corresponding target color. 
     In considering the color dithering plots  FIGS. 18A-18D , for each exemplary color dithering locus  771 ,  772  and  773  arranged about the corresponding target color, the dithering colors  770  can be distributed in various ways. In some embodiments, they are spaced at certain angles in color space (e.g., equally spaced angles in L*a*b* space or in x-y chromaticity space). For example, they can be positioned at 0°, 60°, 120°, 180°, 240° and 300° relative to the target color. Alternately, the choice of the dithering colors  770  can be based on other considerations, such as whether they lie parallel to the axes of a color space that represents underlying physiological mechanisms of color vision, such as cone contrast or opponent modulation color spaces or other color spaces suggested in the literature. Cone contrast or opponent modulation color spaces are described by Brainard in “Cone contrast and opponent modulation color spaces” (in  Human Color Vision,  2 nd  edition, Ed. Kaiser and Boynton, Optical Society of America, Washington, D.C., pp. 563-579, 1996). 
     In some embodiments, the dithering colors  770  are distributed such that they can be achieved by increasing or decreasing the amount of one of the color primaries. That is, colors that are slightly more red (R + ), slightly more green (G + ), slightly more blue (B + ) slightly less red (R − ) (equivalent to more cyan (C + )), slightly less green (G − ) (equivalent to more magenta (M + )), or slightly less blue (B − ) (equivalent to more yellow (Y + )), than the target color (T). Other variants are possible, such as using two slightly more red colors (R 1   + , R 2   − ) that are different from each other. The same holds for the green, blue, cyan, magenta or yellow colors. 
     In some embodiments, the dithering colors  770  are chosen so that they have the same luminance (Y) as the target color. (This will generally require adjusting all three primaries so that the increase in one primary is compensated by decreases in at least one of the other primaries. In some embodiments, the dithering colors  770  can include colors that vary in luminance (Y), either being brighter or dimmer, such as R + G 1   + B + G 2   + , where G 1   +  is brighter than G 2   + . In this case, the dithering colors should be chosen such that their average luminance matches the luminance of the target color. 
     Care is required in choosing the dithering colors  770  in order to ensure that the cumulative result of averaging the color shifts gives the same tristimulus values as the target color T. In the case that the dithering colors  770  are equidistant from the target color in ΔE* units, averaging to match the target color T can be straightforward. However, dithering colors  770  in a color set can be defined with different shift amounts, such as 4 ΔE* units and 2 ΔE* units. Small luminance (Y) adjustments can be used to help the temporal color averaging of the dithered colors provide a color match to the target color. 
     Temporal color dithering can be applied in various sequences, including R + G + B + , or R + B + G + , R + G + B + R − G − B − , or R + G + B + T, or C + M + Y + , or C − M + Y + T, or R 1   + R 2   + G 1   + G 2   + B 1   + B 2   + , and so on. The temporal color dithering using a given color set, such as R − G + B + , can be repeated or sequenced about the target color, cyclically R + G + B + R + G + B + R + G + B +  . . . , as long as the appropriate image content is present at the display surface. 
     Projection experiments have validated the averaging aspect of temporal color dithering. In particular, a set of observers was shown a first color patch of a static target color (T), and a second color patch comprising a set of temporal sequence of dithering colors  770 , such as R + G + B +  or C + M + Y +  modulated at a 48 fps effective rate. The dithering colors  770  were temporally cycled, to appear in two non-adjacent sub-frames  730  ( FIG. 12B ) per frame time, which provided color changes without noticeable flicker for most observers. These experiments were performed separately with a broad spectrum Barco digital cinema projector and a laser digital cinema projector having the laser projector spectrum  420  shown in  FIG. 5 . In both cases, the individual observers generally considered the static color patches and the dithered color patches to be color matched. This was the case even if the dithering colors  770  were shifted by 4 ΔE* units from the target color, such that the individual dithering colors  770  had enough color difference to be individually distinctive. 
     In terms of color averaging to synthesize the target color, the preferred amount of color noise can vary with the target color T. For example, for sky blue, whites and grays, experiments indicated that the desired color noise is preferably 3 or 4 ΔE* units, while for the grass green color, 5 ΔE* units of color noise was preferred. In these experiments, a color dithering locus  760  having a color set of just three dithering colors  770 , such as R + G + B +  or C + M + Y + , seemed most effective for creating the perception of the target color using nearby colors. 
     To help in reducing observer metameric failure, the dithering colors  770  should be sufficiently visually distinct from the target color T, so as to provide adequate color variation or display color diversity. Thus, color noise or dithering colors  770  include values preferably altered by 3-5 ΔE* or more, and the offsets can be scaled to at least encompass areas of the scatter plot ( FIGS. 7A-7D ) that include a majority of observers. 
     The temporal color dithering can be supplied by various methods, including via metameric color corrector  250  ( FIG. 4 ). When colors, which are to be corrected for observer metameric failure, are determined, the metameric color corrector  250  can determine offset colors using an algorithm, a color dependent look up table, or other approaches (for example, random selection from within the color dithering locus  760 ) and provide the dithering colors  770  as a sequence of color noise on a frame or sub-frame basis. Alternately, metameric color corrector  250  can alter the incoming or original image data using a color noise generator, which pseudo randomly generates dithering colors  770  within a bounded color space that is constrained by rules for the sequence and amount (ΔE*, Δa*, Δb*, JNDs, H, L) of color shifting or differencing applied. While dithering colors  770  can be applied to every frame, computational or image processing requirements can be managed by applying changes in a common way for image data for a sequence of frames with similar image content (e.g., a scene). 
     In some embodiments, the correction or compensation of observer metameric failure among observers  60  ( FIG. 2 ) viewing an image  195  provided by projector  100  having three narrow-bandwidth primaries or color channels is achieved by using the two approaches in combination (i.e., both providing compensating metamerism corrections  530  and temporal color dithering with dithering colors  770 ). Other methods, such as the previously mentioned fluorescent screen, can be used in combination with one or both of these methods. 
     It should be understood that the yellow-green shifts shown in  FIGS. 7A-7D  were determined based on using the Barco DP-1500 projector as an exemplary standard for explaining the present invention. However, in practice, industry participants, including studios, post production houses, directors, cinematographers, and colorists, may use particular displays as a reference standard for determining metamerism corrections  530  and dithering colors  770 . For example, Digital Projection Inc. (Kennesaw, Ga.) offers a “Reference Series” of DLP-based projectors for use in critical viewing conditions including post-production houses and screening rooms. It can be expected that the metamerism corrections  530  and dithering colors  770  may be different if a different display or projector is used as the standard. 
     As represented by  FIG. 2  and  FIG. 3 , the primary emphasis has been on reducing the occurrence of observer metameric failure for observers of a laser-based digital cinema projector. However, it should be understood that the described method for reducing observer metameric failure can be applied more broadly. For example, this method can be applied in laser projectors for other markets, including residential, special event (concert), or museums (planetariums), and for either front screen or rear screen projection geometries. This method is particularly adaptable to projection displays having narrow or moderate bandwidth primaries, including displays using lasers, LEDs, filtered LEDs, visible emitting super luminescent diodes (SLEDs), lamps, or combinations thereof The method of the present invention can also be applied to projection displays where only some of the primaries or color channels have narrow or moderate spectral bandwidths, while the other primaries have wide spectral bandwidths. Additionally, this method can be applied to electronic displays more generally, including backlit displays, and displays suitable to computer monitors, televisions, and video gaming and other markets. When the temporal color dithering approach is employed, it is required that the display can be modulated fast enough to support the required temporal variations. 
     The projector  100  of  FIG. 3  is a three primary display, having red, green, and blue color primaries. However, it should be understood that the method of the present invention for reducing observer metameric failure is extensible to displays having N primaries, and particularly to displays having N&gt;3 narrow-bandwidth primaries. While displays with many primaries, such as N=20, that use the method of the present invention are possible, multi-primary displays having N=4 or N=5 narrow-band primaries are of particular interest for expanding the accessible color gamut. In addition to extending the color gamut, displays with N=4 or N=5 narrow-band primaries can also provide spectral color diversity to reduce observer metameric failure, as discussed previously.  FIG. 19  shows a CIE x,y chromaticity diagram  320  depicting two exemplary N=4 primary extended color gamuts: a yellow-enhanced wide color gamut  337  that includes a yellow primary  310 , and a cyan-enhanced wide color gamut  338  that includes a cyan primary  312 . 
     The use of a yellow-enhanced wide color gamut  337  is often considered valuable as it includes pure yellows. As noted previously, there are some naturally occurring yellow colors that are very close to the spectrum locus  325  of monochromatic colors. Thus an N=4 primary display that includes a yellow primary may not seem to add much color gamut area as seen in an CIE x,y chromaticity diagram, but there are important colors there, which other color spaces better represent. 
     Cyan is a common and important color in nature that can be minimally supported by even many wide color gamut displays. Thus, enhancing a display to have N=4 primaries, including a cyan primary  312 , to provide a cyan-enhanced wide color gamut  338 , can be particularly valuable. In such instances, even if these primaries are narrow-band sources, such as lasers, observer metameric failure can be reduced in creating a target color (T), such as turquoise, by using all 4 primaries at once, or using different combinations of 3 primaries. However, the methods of the present invention, including those for providing compensating metamerism corrections  530  and temporal color dithering with dithering colors  770 , can be used with such displays to further reduce the occurrence or magnitude of observer metameric failure. Similarly, an N=5 primary display that includes both a yellow color primary and a cyan color primary can provide both a further extended color gamut and reduced observer metameric failure when using the methods of the present invention. 
     Selective application of the method for reducing observer metameric failure can also depend on usage dependent circumstances. As an example, television displays are bright and typically viewed in a bright environment, compared to cinema projectors, which typically have a peak luminance that is ˜2× dimmer, and which are viewed in dimmer conditions. While both displays can provide viewable images under normal photopic viewing conditions, both can also provide images in dark (mesopic) viewing conditions. This is particularly true for cinema viewing, where the light levels can often slip into the mesopic range, such as when viewing films stylized with many dark scenes. Under such mesopic conditions, the human visual system adapts over time to increase sensitivity, with cone (color) sensitivity diminishing, while rods become increasingly important. As a result, typically human color perception changes dramatically, with the relative perceived brightness of colors experiencing a blue shift that favors perception of blue light relative to the perception of green or red light. Thus, human perception of yellow, orange, and red colors becomes less accurate. Human perception of blue and low green colors also suffers, but less dramatically. In the commonly-assigned U.S. Patent Application Publication 2011/0175925, to Kane et al., entitled “Adapting display color appearance for low luminance conditions”, which is incorporated herein by reference, a method is provided for color correcting a display that is being viewed in low luminance conditions to provide a better color appearance for human observers who are experience adaptation shifts. This approach provides display color adjustments based on detected light levels and analysis of the time course of adaptation, but does not provide corrections for observer metameric failure when the display has a narrow or moderate bandwidth primaries. The metameric failure compensation methods of the present invention can be used in combination with the mesopic color correction method. For example, as the viewing conditions become increasingly mesopic, metamerism corrections  530  can be modified to include mesopic viewing color corrections. 
     It is again noted that various analysis results have been presented using the exemplary embodiments of the present invention where the 1931 CIE 2° standard observer or the 1964 CIE 10° standard observer were used as the reference observer. Additionally, the 10° color matching functions data for the twenty Wyszecki and Stiles observers has been used to represent a set of target observers. In the decades since these data sets have been published, the data has been occasionally criticized, but mostly validated, and not replaced. In particular, even though the 1931 CIE 2° standard observer is relevant as the assumed reference within the DCDM standard, and though the 1964 CIE 10° standard observer may actually be more relevant for cinema viewing conditions, in reality a perfect standard observer model is unlikely to be developed. It is perhaps more likely that color matching functions may be measured for an alternate set of target observers that can replace the WS observers, or alternately, be more relevant for cinema viewing conditions. As a set of target observers, the twenty Wyszecki and Stiles observers represent reasonable demographics as far as age and gender are concerned, although males, Caucasians, and people of ages 16-50 were perhaps over represented. For example, as it was previously noted that human color matching functions vary among individuals are somewhat correlated with observer age, due to yellowing of the eye lenses with age, a broader age demographic may be relevant. 
     The methods of the present invention can be used with alternate sets of reference observer color matching functions, should appropriate alternatives be developed. As one example, a set of standard observer color matching functions and a set of target observer color matching functions can be developed for demographic sub-groups of target observers, such as youth, and then used when displaying content that is predominately watched by such as an audience. As another example, measurement or assembly of a set of human color matching functions for target observers encountering cinema equivalent viewing conditions can also account for different viewing distances and the simultaneous presence of wide field of view illumination into the eye. In summary, the present inventive methods for reducing observer metameric failure, can benefit from efforts to determine additional color matching functions for one or more sets of relevant target observers. 
     It is noted that other visual effects aside from observer metameric failure can also occur with narrow-bandwidth primary displays. In particular, these include the Helmholtz-Kohlrausch (H-K) effect and the Bezold-Brücke (B-B) effect. The H-K effect describes perceived changes in brightness that can occur when humans experience highly saturated light near the spectrum locus  325 , while the B-B effect describes perceived changes in hue that humans can experience when viewing bright light of particular wavelengths. For example, due to the B-B effect, high intensity long-wavelength red light (such as 660 nm) can appear to be tinged with yellow. These effects will generally have minimal impact for cinema, due to the typical light levels, the distant position of the audience to the screen, and the typical color content of images. The wavelength or bandwidth of the primaries can also impact the occurrence of these effects. However, these effects are more likely to occur when viewing high luminance displays that provide image content having large areas with bright saturated colors. While such conditions tend to be less critical for color viewing, the observer metameric failure reduction methods of the present invention, or variations thereof that also correct for these effects, can also be applied for these viewing conditions, as is appropriate. For example, when the displayed image content includes large image areas having spectral colors that stimulate the H-K effect, the color signals can be corrected by locally modifying the effective brightness or the displayed color gamut. 
     A computer program product for implementing the present invention can include one or more non-transitory, tangible, computer readable storage medium, for example; magnetic storage media such as magnetic disk (such as a floppy disk) or magnetic tape; optical storage media such as optical disk, optical tape, or machine readable bar code; solid-state electronic storage devices such as random access memory (RAM), or read-only memory (ROM); or any other physical device or media employed to store a computer program having instructions for controlling one or more computers to practice the method according to the present invention. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
     PARTS LIST 
     
         
           50  theater 
           60  observers 
           100  projector 
           110   b  blue illumination assembly 
           110   g  green illumination assembly 
           110   r  red illumination assembly 
           115  illumination light 
           120   b  blue laser light source 
           120   g  green laser light source 
           120   r  red laser light source 
           140  illumination optics 
           145  illumination lens 
           150  light integrator 
           155  mirror 
           160  combiner 
           162  first combiner 
           164  second combiner 
           170  spatial light modulator 
           175  image light 
           180  imaging optics 
           185  optical axis 
           190  display surface 
           195  image 
           200  data path 
           210  image file package 
           220  data input interface 
           230  data decryption 
           235  data decompression 
           240  image processor 
           245  image corrector 
           250  metameric color corrector 
           260  frame buffer 
           265  modulator timing control 
           300  color matching functions 
           300   a  CIE 2° color matching functions 
           300   b  CIE 10° color matching functions 
           310  yellow primary 
           312  cyan primary 
           320  CIE x,y chromaticity diagram 
           325  spectrum locus 
           327  line of purples 
           330  wide-band color gamut 
           331  red primary 
           332  green primary 
           333  blue primary 
           335  laser primary color gamut 
           337  yellow-enhanced wide color gamut 
           338  cyan-enhanced wide color gamut 
           340  white color coordinate 
           342  sky blue color coordinate 
           344  grass green color coordinate 
           346  skin tone color coordinate 
           350  chromaticity difference plot 
           352  average chromaticity difference 
           355  average color shift 
           358  inner color gamut 
           360  transition zone 
           362  extended color gamut zone 
           370  aim chromaticity difference 
           400  film projector spectrum 
           410  digital cinema projector spectrum 
           420  laser projector spectrum 
           422  red laser primary 
           424  green laser primary 
           426  blue laser primary 
           432  Thornton red laser primary 
           434  Thornton green laser primary 
           436  Thornton blue laser primary 
           440  color management method 
           442  color correction method 
           444  color correction method 
           446  color management method 
           448  color correction method 
           450  input color values 
           451  input device model 
           452  device-independent color values 
           453  inverse output device model 
           454  output color values 
           455  composite color transform 
           456  inverse output device model 
           457  output color values 
           460  metamerism correction transform 
           461  corrected device-independent color values 
           462  corrected output color values 
           463  composite metamerism correction transform 
           465  metamerism correction transform 
           466  composite metamerism correction transform 
           467  composite metamerism correction transform 
           500  input color XYZ 
           502  wide-band primaries 
           504  narrow-band primaries 
           506  determine wide-band spectrum step 
           508  wide-band spectrum 
           510  determine narrow-band spectrum step 
           512  narrow-band spectrum 
           514  target observer color matching functions 
           516  determine perceived color step 
           518  target observer perceived wide-band color 
           520  determine perceived color step 
           522  target observer perceived narrow-band color 
           524  determine perceived color shift step 
           526  target observer perceived color shift 
           528  determine metamerism correction step 
           530  metamerism correction 
           540  perceived color shift determination method 
           545  matching color determination method 
           550  input color 
           552  determine wide-band spectrum step 
           554  determine matching color 
           556  matching output color 
           558  determine metamerism correction 
           560  perceived color shift plot 
           562  input color coordinate 
           564  outlier color vectors 
           565  target observer color vectors 
           566  average observer color vector 
           568  average color vector 
           570  perceived color shift plot 
           575  color vectors 
           580  perceived color difference plot 
           585  target color gamut 
           590  color difference contour lines 
           600  metameric failure compensation method 
           605  metamerism correction data 
           610  input color 
           615  inside conventional color gamut test 
           620  apply full metamerism correction step 
           625  inside transition zone test 
           630  apply partial metamerism correction step 
           635  transition function 
           640  apply no metamerism correction step 
           650  continuity function 
           660  corrected output color 
           670  linear transition function 
           675  sigmoid transition function 
           700  frame 
           705  frame ON time 
           710  frame time 
           725  blanking time 
           730  sub-frames 
           735  sub-frame ON time 
           750  target color 
           751  white target color 
           752  sky blue target color 
           753  grass green target color 
           754  skin tone target color 
           760  color dithering locus 
           762 ,  764 ,  766  dithering colors 
           770  dithering colors 
           771 ,  772 ,  773 ,  774  color dithering locus