Color correction methods for electronic displays

The present invention features methods and apparatus for the correction of spatial non-uniformities in color only, and color and brightness combined, that arise from materials, manufacturing, and operational variations in tiled, color flat-panel displays. Such uniformities can introduce gradual or abrupt color and brightness variations in monolithic and tiled displays. Correction methods are based on control of the manufacturing and assembly process, and/or remapping of the colors of the display to match uniformity requirements of the average human observer. Correction methods can be implemented using serial and parallel versions using electronic circuits commonly used in video signal processing. Apparatus for a self-calibration method are also described.

FIELD OF THE INVENTION
 This invention pertains to the field of electronic, color displays, and,
 more particularly, details methods and apparatus that are designed for
 correcting spatial nonuniformities in color and/or color and luminance on
 flat-panel displays that are constructed from a single display unit or a
 multiplicity of display tiles.
 BACKGROUND OF THE INVENTION
 Images on electronic displays are derived from a two-dimensional array of
 pixels, each of which represents one small element of the image. The
 resulting image is presented to the observer in a 1:1 size in direct-view
 displays, while projection displays magnify the image size, using an
 optical lens system. In black-and-white displays, each pixel displays one
 of two colors, black or white; in a gray-tone display, pixels can produce
 a specified number of gray tones between black and white. Since colors can
 be formed by combining primary colors red (R), blue (B) and green (G)
 light, in specified ratios, electronic color displays use primary-color
 elements in each pixel, in order to form a desired image via additive
 color mixing. In order to show still images, pixels can carry the same
 information all of the time; for moving images, the content of each pixel
 must be redefined periodically. Depending on the application, full-motion
 images are usually required to be redrawn 30 to 75 times per second.
 Pixels can be accessed by using several techniques, including scan-, grid-,
 shift-, matrix- and direct-addressing. If, for example, the display
 carries an array of N.times.M pixels, and it has to be redrawn n times
 each second, the data sent to each pixel must be provided in 1/(n*N*M)
 seconds and then held constant for (N*M-1)/(n*N*M) seconds, as other
 pixels are being defined. In the current American television (TV) standard
 (NTSC), each frame has about 250,000 pixels, with an aspect ratio of
 4.times.3, which are refreshed at the rate of 30 frames/second. One of the
 new picture formats proposed to the Federal Communications Commission
 (FCC) for American high-definition television (HDTV) has an aspect ratio
 of 16.times.9 and a refresh rate of 60 frames/second. Pixels are arranged
 into 1280 horizontal and 720 vertical lines or, alternatively, 1920
 horizontal and 1080 vertical lines (I. Gorog, "Displays for HDTV: Direct
 View CRTs and Projection Systems", Proceedings of the IEEE, vol. 82, no.
 4, pp. 520-536, 1994). The typical, low-resolution computer display (VGA)
 has 480 rows of 640 pixels, or, a total of 307,200 pixels at a refresh
 rate of 72 frames/second.
 Electronic displays can be implemented by using a multitude of different
 technologies, including, for example, the cathode-ray tube (CRT),
 electroluminescent displays (ELDs), light-emitting diode displays (LEDs)
 and liquid-crystal displays (LCDs). While a CRT display has a depth
 comparable to the height of the screen, ELDs and LCDs belong to that class
 of flat-panel displays (FPDs), the dimension of which, in their direction
 perpendicular to the image plane, is much smaller than that of the CRT.
 With the CRT, either one (gray-tone) or three (color) electron beams scan
 along horizontal lines in order to access each pixel. All color signals
 are thus carried to the pixels via the electron beam flux. FPDs (such as
 the LCDs) use matrix-addressing, in which each pixel is accessed via row
 and column lines. The column lines usually carry the color signals, while
 row lines are used for control signals. The pixel at the cross-point of a
 specific row and column line can be selected via passive or active
 techniques. In the passive case, the non-linearity of the pixel's element
 is used for the selection. For example, in LCDs the non-linearity of the
 liquid-crystal material is used. Active, matrix-addressed LCDs (AMLCDs),
 on the other hand, require a device (e.g., a transistor) for the selection
 of the pixel. In active matrix-addressing, a row of pixels is usually
 selected at once by placing a specific, control signal on the row line
 (usually a voltage on a transistor's gate electrode). Pixel color data is
 then made available via column lines to each of the pixel elements in the
 selected row (usually a voltage on a transistor's drain). An entire row of
 pixels can be accessed in parallel in active matrix-addressing. Coupling
 between pixels and row and column lines is one of the disadvantages of
 matrix-addressing.
 The size of an electronic display is usually specified by the length of the
 diagonal of the pixel array. Computer displays generally have sizes of
 between 10" and 21"; home television displays generally have sizes of
 between 19" and 31". Large public displays (e.g., used in sports arenas)
 generally feature sizes that range between 200" and 700".
 The resolution of the image on an electronic display is determined by the
 pitch of the pixels, i.e., the smaller the pixel pitch, the finer the
 details that can be displayed. Typical computer displays have pixel
 pitches on the order of 0.25 to 0.3 mm, and they can be viewed from
 distances as close as 30 cm without the human eye having to resolve the
 mosaic structure of the pixels. Large-screen, public displays have pixel
 pitches as large as 30 mm [see, e.g., Panasonic Astrovision, AZ-3000
 Series High Density Fluorescent Displays, Panasonic Corporation, Japan,
 1995]. Viewing distances of at least 10 meters are required for such
 displays.
 A duty cycle is defined as the time spent for turning on individual pixels
 or a row of pixels. With a CRT, each pixel is accessed individually and
 sequentially by sweeping the electron beam. Thus, for example, in a VGA
 display with N.times.M=640.times.480 and n=72 Hz, the dwell time of the
 electron beam on each pixel is 46 ns. By definition this equals the duty
 cycle of this CRT. In an FPD VGA display with the same frame rate, the
 dwell time is 640 times longer or 29 .mu.s, due to parallel
 matrix-addressing.
 The brightness of an image on an electronic display is characterized by
 using the photometric quantity of luminance measured in candelas per unit
 area (cd/m2=1 nit). The luminous efficiency is used to describe how much
 light the display produces per the amount of electrical energy provided to
 the display. LCDs operate with highly efficient backlights (such as
 fluorescent lamps) with a luminous efficiency as high as 55 lm/W and a
 typical light transmittance of about 4%. This gives a typical luminous
 efficiency of 2.2 lm/W for AMLCDS, which exceeds the performance of all
 other display technologies. The brightness of LCDs can be increased by
 simply turning up the intensity of the backlight.
 The contrast in a display is another important attribute. It describes the
 achievable light intensity modulation in the image between the brightest
 and dimmest pixels. An image having a greater contrast is more sparkling
 in appearance. The best AMLCDs achieve contrast ratios as large as 100:1.
 Ambient illumination affects the contrast of the displayed image. The
 component of the ambient illumination that is reflected from the display's
 surfaces will be added to the emitted intensity of the image to be
 displayed. The higher the contrast, the more tolerant the display is to
 ambient light. Of all displays, AMLCDs have the highest tolerance to
 ambient light, because of the presence of polarizers, and the ability of
 AMLCDs to independently adjust the intensity of the backlight.
 The viewing characteristics of electronic displays are specified by the
 viewing distance and viewing angle ranges. The minimum viewing distance is
 related to the pixel pitch via the resolution ability of the observer's
 retina. Displayed images are usually best viewed at normal incidence.
 Maximum horizontal and vertical viewing angles away from the normal are
 determined by the type of the display, and the layout and the optical
 design of the pixels. Viewing angle ranges of .+-.30.degree. horizontal
 and .+-.15.degree. vertical are average for typical AMLCD displays.
 Full-color displays are expected to be able to display 256 (8-bit) shades
 of each of the highly saturated primary colors red, blue and green. This
 results in a total of 256.sup.3 or 16,777,216 colors that (in principle)
 can be displayed. Full-color capability has been available on CRTs for
 quite some time via the selection of the R, B and G phosphor materials, as
 well as the control of the electron beam. Full color was demonstrated for
 the first time with LCDs in 1993 by developing 8-bit data driver circuits
 [G. H. Henck Van Leeuven et al., "A Digital Column Driver IC for AMLCDs",
 Euro-Display, pp. 453-456, 1993; see also H. Okada, K. Tanaka, S. Tamai
 and S. Tanaka, "An 8-Bit Digital Data Driver for AMLCDs", Society for
 Information Display International Symposium Digest of Technical Papers,
 vol. XXV, pp. 347-350, 1994]. To date, several manufacturers have
 demonstrated full-color AMLCDs by using amorphous silicon (a-Si),
 thin-film transistors (TFT) as the switches. Saturated primary colors are
 defined by using a uniform "white" backlight in combination with three
 color filters. Driver electronics is used to provide an optimal
 linearization of the liquid-crystal response, in order to facilitate the
 additive mixing of colors.
 Direct-view electronic displays with diagonals up to about 31" are usually
 manufactured in monolithic form, with the entire pixel array fabricated on
 a single continuous medium. The size of a commercial color CRT is limited
 by the deflection optics and the weight of the unit to about 35".
 Commercial, monolithic AMLCDs are currently limited to sizes less than 12"
 because of manufacturing yield and cost. Commercial, 16" AMLCD displays
 are in product development. AMLCD sizes of up to 21" have been
 demonstrated in research [M. Hijikigawa and H. Take, "Future Prospects of
 Large-Area Direct View LCDs", Society for Information Display
 International Symposium Digest of Technical Papers, vol. XXVI, pp.
 147-149, 1995]. Very large electronic displays cannot be made in a
 monolithic fashion. Rather, each pixel is separately fabricated, and then
 the display array is assembled by accurately arranging pixels into rows
 and columns. The alignment process is difficult and cannot be made with
 high precision over large areas. As a consequence, the pixel pitch in
 large-screen displays usually is on the order of at least 30 mm.
 Intermediate-sized electronic displays with pixel pitches from about 0.6 to
 3 mm, can, in principle, be assembled from smaller monolithic pieces, with
 each carrying many pixels [see, e.g., N. Mazurek, T. Zammit, R. Blose and
 J. Bernkopf, "A 51-in Diagonal Tiled LCD VGA Monitor", Society for
 Information Display International Symposium Digest of Technical Papers,
 vol. 24, pp. 614-617, 1993]. These monolithic pieces are then arranged
 into a regular, tiled array to form the full display. In tiled displays,
 the pixel pitch on all tiles is, preferably, the same. Because of the
 small size of the tiles, this can be achieved with a tightly-controlled
 manufacturing process. The seams between adjacent tiles must be large
 enough to facilitate assembly. The seams will be visible to the human
 observer, unless the pixel spacing across the seam is the same as the
 pixel spacing on the tiles. This is very difficult to achieve.
 Consequently, to date, commercial-prototype, tiled displays have had
 visible seams between the tiles. The minimum achievable pixel pitch in
 tiled displays is, therefore, determined by the available assembly
 technology.
 SUMMARY OF THE INVENTION
 This invention describes methods and apparatus for the correction of
 spatial non-uniformities in chromaticity that arise from materials,
 manufacturing, and operational parameter variations (e.g. backlight) in
 tiled, color, flat-panel displays (FPDs). Such uniformities can introduce
 gradual or abrupt variations of color and brightness. Displays composed of
 a multitude of display tiles, each carrying a single pixel or an array of
 pixels, tend to exhibit abrupt non-uniformities at the edges of the tiles,
 while displays with monolithic construction tend to exhibit gradual
 non-uniformities. Combinations of abrupt and gradual non-uniformities may
 also exist. The objective of the color correction methods is to remove all
 variations irrespective of their origin to a level below the detection
 threshold of the average human observer.
 The methods for correcting color variations cover the following cases:
 control of materials and manufacturing parameters to a predefined
 precision; remapping of color coordinates for non-uniform primary colors
 using electronic means; remapping of color coordinates for non-uniformly
 defined color coordinates using electronic means; remapping of color
 coordinates for simultaneously varying color coordinates and primary
 colors using electronic means; and remapping of colors for simultaneously
 varying color and brightness using electronic means. These color
 correction methods can be implemented using the electronic circuits
 commonly used in video processing electronics and electronic color
 displays. The circuit implementations can generally be performed in a
 serial fashion by operating on the video signal stream or by operating in
 the parallel mode on the data for a row of pixels at a time.
 The application of these color correction methods allows the design and
 manufacture of monolithic and tiled electronic, color, flat-panel displays
 of superior uniformity or, alternatively, significant increases in the
 manufacturing yield to meet uniformity specifications.

DESCRIPTION OF THE PREFERRED EMBODIMENT
 Generally speaking, this invention features methods and an apparatus for
 correcting color variations across the pixels of electronic displays,
 whether these variations arise from the primary colors themselves, their
 additives mixed to produce other colors from the primary colors, or other
 components of a display (such as backlight sources).
 Color Classification, Definition and Uniformity
 Every color has three basic characteristics: hue, lightness and chroma. Hue
 is the property that distinguishes and gives each color its name.
 Lightness measures the amount of light reflected from the hue. Chroma
 measures the amount of saturation or concentration thereof. There are two
 common ways to classify colors by using these characteristics. The Munsell
 system was devised by the American portrait painter Albert Munsell in the
 early 1900s (D. Nickerson, "History of the Munsell System, Company and
 Foundation, 1-111", Color Research Applications, vol. 1, pp. 7-10, 69-77,
 121-130, 1976). The Munsell system classifies each color (hue) according
 to value (which is related to lightness) and chroma. Munsell's
 classification is subjective due to the differences between individuals in
 perception of colors. The CIE system of colors was developed by the
 International Commission on Illumination, or, CIE (see, e.g., G. Wyszecki
 and W. S. Stiles, Color Science, 2nd edition, Wiley, New York, 1982). The
 CIE system is based on the use of spectrophotometers and the concept of a
 standard observer, expressed in color tables, and, thus, independent of a
 specific observer.
 Display colors are usually formed by additively combining three, primary,
 saturated colors, for example, red (R), green (G) and blue (B). A
 specified number (for example: 2.sup.8 =256 shades) of each primary color
 is generated by the respective color element in each pixel of the display.
 In this case each pixel must carry the R, G and B colors in three color
 elements. For example, in a CRT, when hit by the electron beam, the
 selected element of a color pixel emits light with its intensity
 approximately proportional to the electron beam flux. The same happens in
 the other primary color elements of the same pixel. The actual sensation
 of color occurs when light, emitted from each of the primary color
 elements within a pixel, blends in the eye and the visual cortex of the
 viewer. Because of this, human factors are significant in the perception
 of displayed colors. A specific, illustrative model for the definition of
 colors is hereinafter discussed. The invention is not limited to this
 illustrative color combination model, but, rather, applies to all possible
 ways of combining additively primary colors.
 Referring now to FIG. 1, assume that the red (R), green (G) and blue (B)
 primary colors have been defined. This definition includes the tabulation
 of the intensity-wavelength dependence for each of the primaries, or,
 alternatively, specifying the CIE tristimulus values for each primary.
 According to standard color theory, any other color C within the color
 triangle 10 formed by the primaries R, G and B can be expressed as a
 linear combination of the primaries
EQU C=RR+GG+BB, (1)
 where the coefficients R, G and B are the color coordinates. Linear color
 coordinates are used throughout this disclosure without regard to the
 gamma corrections and other compression techniques used to preprocess
 color signals in some displays. Such compressions can always be undone to
 recover linear color coordinates. The color defined in Equation (1) can
 also be specified by using the R,G,B-based chromaticity coordinates (r,g)
 defined by
EQU r=R/(R+G+B)
EQU g=G/(R+G+B). (2)
 In this model, each color C is uniquely defined by specifying the three
 color coordinate (R,G,B) values for each pixel. These color coordinates
 are mapped on suitable drive signals (for example, voltages, currents or
 pulse trains) in all electronic displays. The primaries R, G and B are
 usually chosen so that the white point of the display is given by
 (R,G,B)=(1,1,1). The complete set of colors formed in this fashion, via
 Equation (1), are called the gamut of colors for the chosen primaries. By
 specifying these three color coordinate values for each pixel in the
 N.times.M array of the display, the entire image has been defined. The
 color coordinate values correspond to electronic drive signals that
 control each color element. These signals include voltage, current,
 frequency-multiplexed and time-multiplexed, coded forms. For example, the
 drive signals in an AMLCD are voltages applied to the liquid-crystal
 cells, in order to modulate their optical rotation and thus change the
 optical transmission.
 Although the RGB, primary-based color representation given in Equation (1)
 is most often used in the discussion of electronic displays, CIE-based
 specifications are better suited for quantitative comparisons of colors.
 The transformation from a particular RGB system to the CIE XYZ tristimulus
 values is a matrix equation of the form
 ##EQU1##
 The 3.times.3 transformation matrix A depends, of course, on the chosen
 primaries R, G and B. For example, for the RGB system specified in Rec.
 709, with the white point D65, the transformation matrix A reads
 ##EQU2##
 Once the CIE tristimulus values (X,Y,Z) are known, the CIE chromaticity
 coordinates (x,y) can be computed from
 ##EQU3##
 In this representation the tristimulus value Y alone stands for the
 luminance. Therefore, there is always a simple correspondence between a
 color defined with the color coordinates (R, G, B) and the CIE
 chromaticity/luminance representation (x,y,Y).
 The uniformity of chromaticity and luminance describes the ability of the
 display to define uniformly all colors and brightness across the entire
 pixel array of the display for any predefined combination of the
 primaries. This requires very good control over both the primaries and the
 color coordinate values. There are many potential sources of
 nonuniformities. Electron beam deflection and spot size are the primary
 sources of nonuniformities in CRTs, while materials, manufacturing- and
 backlight-related issues are the most common factors responsible for
 nonuniformities in AMLCD displays. Another mechanism giving rise to
 nonuniformity originates in the additive color formation process, given
 the display's viewing conditions. For example, an ambient light gradient
 may introduce a nonuniformity into the additive color sum, when the
 reflected light interferes with the emitted light. This phenomenon limits
 the use of electronic displays in bright ambient light.
 Perception tests with human observers have shown that tristimulus value
 differences as small as 2 to 4% are observable under the most demanding
 viewing conditions. Perception tests also show that gradual color
 nonuniformities occurring continuously over many pixels are less
 perceptible, because the observer loses the reference over the area of the
 display screen. In fact, gradual color coordinate value changes as large
 as 10 to 20% over the size of the display screen may not be disturbing to
 an average viewer. Under normal viewing conditions, both brightness and
 color uniformities are more observable when viewed from a greater
 distance, rather than from up close.
 Color and brightness nonuniformities in monolithic electronic displays are
 caused by process variations, which tend to cluster into gradual changes
 over large sections of the display. Therefore, monolithic displays can be
 manufactured with relatively large process tolerances. On the other hand,
 abrupt changes in brightness or color between adjacent color pixels, or
 groups of pixels, are disturbing. Such abrupt non-uniformities arise in
 displays where each pixel, or array of pixels, has been manufactured
 separately and then assembled to form a complete, tiled, pixel array.
 Materials, manufacturing- and design-related factors introduce abrupt
 nonuniformities in tiled displays. Another possible source of
 nonuniformities in tiled displays arises from the possibility that pixels
 close to the edge of a tile have different characteristics than do the
 interior pixels. If uncorrected, this effect may either cause scalloped
 luminance or chromaticity gradients close to the edge of tiles.
 Referring now to FIG. 2, the combination of both gradual and abrupt
 nonuniformities on a tiled display is illustrated. The upper portion of
 FIG. 2 depicts a portion of a row of a tiled, color FPD, consisting of
 three adjacent tiles, shown generally at reference numeral 18. Luminance
 and the two chromaticity values are measured at a number of positions
 along the line 12, placed at an arbitrary position on each of the adjacent
 tiles 18a, 18b and 18c. The lower portion 20 of FIG. 2 is a graphical
 representation of luminance or one of the two chromaticity values measured
 along line 12. Segments 22, 24 and 26 correspond to luminance or other
 values of tiles 18a, 18b and 18c, respectively. In this example, abrupt
 transitions in luminance or the tristimulus value occur at the boundaries
 between the tiles. Gradual variations occur within the tiles, as indicated
 by the respective, sloped-line portions.
 This invention covers methods and an apparatus that correct for color
 nonuniformities (or combinations of color- and brightness nonuniformities)
 in electronic displays. While the methods work both for gradual and abrupt
 nonuniformities, they are most useful for the latter, especially for
 displays that are assembled from single pixels or are tiled from
 rectangular arrays of pixels.
 Description of Color Correction Methods
 In order to accurately match colors on electronic displays, the perceived
 brightness and color have to match within the human eye's discrimination
 threshold. "Brightness" describes the appearance of the radiant flux of an
 object. The brightness of an object depends on the viewing conditions of
 the display and the adaptation of the observing eye. The psychophysical
 equivalent to brightness is luminance, which is, of course, independent of
 viewing and observation conditions. Luminance is quantified by using the
 concept of luminous flux per projected area of the source of light. The
 ability of the human eye to discriminate between two luminances is
 measured using Weber's fraction. Assume that two objects are viewed side
 by side, with one object having the luminance of B, and the other
 B+.DELTA.B. Assume further that .DELTA.B is increased from 0 to a value
 that makes the brightness of the two objects detectably different. The
 discrimination threshold value, then, for .DELTA.B defines Weber's ratio
 as .DELTA.B/B. According to extensive visual discrimination studies,
 Weber's fraction is not a constant (i.e., Weber's original law), but,
 rather, depends on the luminance B [S. Hecht, "The Visual Discrimination
 of Intensity and the Weber-Fechner Law", Journal of General Physiology,
 vol. 7, p. 214, 1924]. However, for the luminance range from 1 to 1000
 cd/m.sup.2 (nit) desirable for electronic displays, .DELTA.B/B is
 approximately constant, and has the value on the order of 0.04 for a dark
 surround. Weber's fraction increases rapidly for reducing brightness
 levels, when the eye of the observer goes from photopic to scotopic
 vision. For example, at 1.times.10.sup.-6 nit .DELTA.B/B is 0.14.
 In terms of physical quantities, luminance is defined as:
 ##EQU4##
 where: K.sub.m, V(.lambda.), P(.lambda.), .omega. and .alpha. cos .theta.
 denote the maximum luminous efficiency (683 lm/W), the relative efficiency
 or luminosity function, radiant flux, solid angle and projected source
 area, respectively [see, e.g., Television Engineering Handbook Featuring
 HDTV Systems, McGraw-Hill, edited by K. B. Benson, revised by J. C.
 Whittaker, 1992]. The international standard for luminance is determined
 by blackbody radiation at 2042 K and is set at 60 nit. Quantities related
 to luminance that are often used include luminous flux, defined as
EQU F=K.sub.m.intg.V(.lambda.)P(.lambda.)d.lambda.
 and measured in lumens (lm), and luminous intensity, defined as I=F/.omega.
 and measured in lm/steradian.
 As can be seen from Equation (6), luminance is an additive quantity.
 Therefore, the luminance of a color field additively mixed from three
 components can be written as
EQU L=R L.sub.R +G L.sub.G +B L.sub.B, (7)
 where L.sub.R, L.sub.G and L.sub.B denote the luminance unit amounts of the
 primaries R, G and B. Linear, primary excitations are assumed. As an
 example, for the commonly used CRT phosphors (Rec. 709), the relative
 primary luminances are L.sub.R =0.2125, L.sub.G =0.7154 and L.sub.B
 =0.0721. The unit luminances are usually adjusted so that, when they are
 combined in equal amounts, they will produce the display white, e.g., the
 CIE illuminant D65 [International Commission of Illumination]. Therefore,
 in order to make an electronic color display uniform in terms of
 luminance, the resultant luminance must be controlled within the luminance
 band given by Weber's fraction .DELTA.L/L. Resultant luminance variations
 in violation of this condition may arise from color coordinate or color
 element unit luminance variations.
 Several different methods for keeping the resultant luminance constant have
 been described in the co-pending patent application, Ser. No. 08/636,604,
 filed on Apr. 23, 1996, now abandoned in favor of Ser. No. 09/173,068,
 filed Oct. 14, 1998, and herein incorporated by reference.
 Colors in electronic displays are usually defined by specifying a "gray"
 level for each primary color, and then combining the three primaries
 additively as expressed by Equation (1). If, for example, each color has
 2.sup.8 =256 gray levels, there will a total of 256.sup.3 =16,777,216
 different color coordinate combinations. This is the 3.times.8=24-bit
 color scheme, which is usually considered to provide "full color". A
 smaller number of gray levels per primary (7, 6, 5, 4, 3) and 2 bits will
 give a total of 2,097,152; 262,144; 32,768; 4,096; 512; and 64 different
 color coordinate combinations, respectively.
 The number of colors that can be distinguished under certain viewing
 conditions depends upon the tristimulus values of the primaries and the
 threshold for color difference perception. Many different studies of
 equally perceptible color differences have been made over the entire range
 of visible colors. Perhaps the best-known study has been done by MacAdam
 [D. L. MacAdam, "Visual Sensitivities to Color Differences in Daylight",
 Journal of Optical Society of America, vol. 32, pp. 247-274 (1942)].
 According to these studies, the threshold for color difference perception
 depends upon the color. The human eye is most and least sensitive to
 variations among the blue and green colors, respectively. The threshold
 sensitivity to red colors is in the middle range.
 In order to maintain faithful chromaticity reproduction across an
 electronic display, both primary colors and the color coordinates must be
 maintained from pixel to pixel. As with luminance, an observer can best
 spot chromaticity nonuniformities at sharp boundaries between uniform
 color patches. Gradual color variations across a significant distance on
 the screen are much less perceptible. Chromaticity variations can be
 characterized with Weber's fractions .DELTA.R/R.sub.o, .DELTA.G/G.sub.o,
 and .DELTA.B/B.sub.o, where R.sub.o, G.sub.o and B.sub.o denote the center
 color coordinates and .DELTA.R, .DELTA.G and .DELTA.B, the variations.
 Local, (i.e., pixel-to-pixel) color control on the order of 1 to 5% must
 be achieved, while gradual global variations as large as 10-20% are
 tolerable under many viewing conditions.
 According to Equation (1), chromaticity nonuniformities arise either from
 the primary colors or the color coordinates. In CRTs, primary colors are
 produced by fluorescent phosphors (relatively well-controlled materials
 characteristic of monolithic screens), while color coordinates are defined
 by the electron flux hitting each color stripe through the shadow mask at
 each pixel. In a monolithic AMLCD, primaries are formed by light
 transmitted through a patterned color filter layer with R, G and B
 stripes. Color coordinates are determined by the backlight and the LCD
 cell for each color element (including the liquid-crystal layer, the
 thin-film transistor and the polarizers). As with luminance, chromaticity
 nonuniformities arising from materials, manufacturing, structural or
 operational parameters in monolithic electronic displays tend to be
 gradual over the display area. In tiled displays, abrupt changes will
 arise at the tile boundaries.
 This invention includes several different methods for keeping the resultant
 chromaticity either alone or together with the luminance of selected
 display pixels that are substantially constant, using active control
 means. Strictly speaking, the chromaticity threshold applies only to
 adjacent pixels, or to two adjacent groups of pixels having a sharp
 boundary. For more distant pixels, or groups of pixels, gradual luminance
 variations as large as 10 to 20% may be permissible. This range of
 variations is known as the gradient rule. For gradual variations, the
 gradient of the chromaticity is the key parameter to control. Chromaticity
 may be held constant in many ways by adjusting the three components and
 their sum in Equation (1). This property will be demonstrated hereinafter
 to correct the chromaticity or luminance so that the remaining variations
 will be below the detection threshold, as shown in FIG. 3. The upper
 portion of this FIGURE shows a row of tiles 18 and the lower portion 20'
 the luminance or chromaticity as a function of position along the line 12
 across the tiles 18. Segments 22, 24 and 26 show the non-uniform
 characteristics of the display before correction, and segments 22', 24',
 and 26' show the corrected characteristics that meet the criteria set for
 the detection threshold. It is assumed for illustrative purposes that the
 display described hereinbelow is of the normally dark type. In such a
 display, the drive signals control positive chromaticity and luminance
 contributions from each color element to form the desired color and
 brightness for each pixel. However, the methods apply equally well to
 normally bright displays, in which the drive signals reduce the
 contributions of each pixel from the display white.
 The methods described in this invention assume that the pixels selected for
 correction are active, i.e., that their gray levels can be fully modulated
 to all levels between white and black. Completely inactive pixels (which
 can be stuck in the black, white or intermediate states) will not be
 considered. However, if the faulty pixels are partially active and can
 reach a subset of the levels between white and black, the present methods
 can be used to set these pixels in real time into states closest to the
 chromaticity and luminance of adjacent pixels, and thus make them less
 disturbing to the observer in the displayed image.
 (i) Color Correction Method for Case With Uniform Color Coordinates and
 Uniform Primary Colors
 In this case R, G and B color coordinates and the primary colors R, G and B
 are kept uniform within the chromaticity and luminance tolerances. In this
 embodiment, this is achieved by tightly controlling materials, design,
 manufacturing and operational parameters individually to tolerances that
 do not exceed the threshold for the additive sum in the sense of Equation
 (1). In monolithic displays with clustered nonuniformities, the gradient
 rule is met, since the parameters tend to vary smoothly. For tiled
 displays, the tolerance threshold between pixels on adjacent tiles should
 not be exceeded. Sorting operations and tile clustering may be used to
 enhance yields, when assembling tiled displays. Nevertheless, this
 embodiment requires very tight control of all parameters, and may lead to
 an impractical situation for tiled displays.
 (ii) Color Correction Method for Case with Uniform Color Coordinates and
 Non-Uniform Primary Colors
 Assume that uniform color coordinates are supplied to each pixel, but that
 primary colors vary from pixel to pixel. Consider, as an example, two
 pixels, 1 and 2, with different primaries, the first one producing the
 color C.sub.1, and the other, C.sub.2 :
EQU C.sub.1 =RR.sub.1 +GG.sub.1 +BB.sub.1 (8)
EQU C.sub.2 =RR.sub.2 +GG.sub.2 +BB.sub.2 (9)
 Here, C.sub.1 and C.sub.2 are approximately the same, but not quite
 identical, colors. Since both Equations (8) and (9) can approximately
 represent a full gamut of colors, each of the primaries in one system can
 be represented as a linear combination in the other. Hence, if the
 primaries of the first system are expressed in terms of the second system,
 one obtains:
EQU R.sub.1 =a.sub.11 R.sub.2 +a.sub.12 G.sub.2 +a.sub.13 B.sub.2 (10)
EQU G.sub.1 =a.sub.21 R.sub.2 +a.sub.22 G.sub.2 +a.sub.23 B.sub.2 (11)
EQU B.sub.1 =a.sub.31 R.sub.2 +a.sub.32 G.sub.2 +a.sub.33 B.sub.2. (12)
 Then,
EQU C.sub.1 =R(a.sub.11 R.sub.2 +a.sub.12 G.sub.2 +a.sub.13 B.sub.2)+G(a.sub.21
 R.sub.2 +a.sub.22 G.sub.2 +a.sub.23 B.sub.2)+B(a.sub.31 R.sub.2 +a.sub.32
 G.sub.2 +a.sub.33 B.sub.2), (13)
 or
EQU C.sub.1 =(R a.sub.11 +G a.sub.21 +B a.sub.31)R.sub.2 +(R a.sub.12 +G
 a.sub.22 +B a.sub.32)G.sub.2 +(R a.sub.13 +G a.sub.23 +B a.sub.33)B.sub.2.
 (14)
 This is equivalent to the color coordinate transformation of:
EQU R'=(R a.sub.11 +G a.sub.21 +B a.sub.31) (15)
EQU G'=(R a.sub.12 +G a.sub.22 +B a.sub.32) (16)
EQU B'=(R a.sub.13 +G a.sub.23 +B a.sub.33) (17)
 or:
 ##EQU5##
 for color C.sub.1 in the second primary system R.sub.2, G.sub.2 and
 B.sub.2.
 Therefore, if the transformation matrix a in Equation (18) can be stored,
 and the multiplications and summations performed in real time, then the
 colors C.sub.1 and C.sub.2 can be accurately matched for all colors in the
 union of the two color gamuts 28 and 30 (see FIG. 4). Colors outside the
 union cannot be expressed in one system or the other. However, since only
 relatively small, color nonuniformities are addressed in this disclosure,
 any color lying outside the union of the gamuts 28' and 30' (FIG. 5) can
 be replaced by the closest color therein.
 Since the color transformation matrix a is defined by 9 elements, nine
 numbers per pixel need to be stored, and 9 multiplications and 8
 summations performed, in order to perform the transformation. Thus, for a
 display with a resolution of 1024.times.768, there will be 7,707,888
 numbers to be stored. The precision of the color coordinates in the worst
 case is only 8 bits and, therefore, both storage and arithmetical
 operations can be performed at a precision that is only a few digits
 higher, making sure that the end results are to correct to 8 bits.
 Therefore, these operations can be performed either in the integer domain
 combined with linear scaling, or in the fixed-point decimal domain.
 Referring now to FIG. 6, an embodiment 40 of the color correction method
 expressed in Equation (18) is shown. A single color transformation unit 50
 receives video input 44, clock input 46, and synchronization input 48 from
 a video source, usually a video card, not shown. The coefficients of the
 transformation matrix of the selected pixels are stored in a memory
 sub-system 42. The color transformation unit 50 operates on the pixel
 data, one pixel at a time, and passes the corrected color coordinates, R',
 G', and B', to the display controller 52, which interacts with the row
 drivers 54 and column drivers 56 in a conventional fashion to distribute
 the pixel data to the LCD array unit 53.
 The computational time required for the arithmetical operations in Equation
 (18) can be minimized by performing color transformations in parallel for
 each row of pixels. A parallel embodiment of the color correction method
 expressed in Equation (18) is depicted in FIG. 7. Multiple color
 transformation units 50 and memory units 42 for storing color
 transformation data are used. The implementation in FIG. 7 uses one color
 transformation unit 50 per column driver 56 as an illustrative example
 only. Uncorrected pixel data (R, G, and B) is passed from the column
 decoder 57 to each of the color transformation units 50. They perform the
 color transformations in parallel for an entire row of pixels and pass the
 corrected data, R', G', and B', to the column driver circuits 56. These
 arithmetical operations can also be integrated into the column driver
 circuits. These operations can be pipelined, as well. For tiled displays
 having uniform color offsets (compared to other tiles), only one
 transformation matrix per tile needs to be stored. All pixels on each tile
 will be subjected to the same transformation. This simplifies the
 electronics and reduces the storage cost dramatically. If color variations
 follow a simple, spatial form, e.g., linear vs. position in the pixel
 array, the elements of the transformation matrix can be interpolated
 linearly. While this will further reduce storage requirements, it will
 simultaneously require further real-time computations.
 In practical embodiments, the color transformations defined in Equation
 (18) must be performed with respect to a suitably chosen reference system
 (R.sub.ref, G.sub.ref and B.sub.ref), which should be chosen so that it is
 contained within the union of the color gamuts formed by all of the pixels
 that have been selected for matching from over the entire area of the
 display. The reference system should also be color-balanced, so that
 equal-strength primaries result in the desired white point (e.g., the CIE
 illuminant D65). If these conditions are not met, small regions of colors
 cannot be represented, because of the non-overlapping nature of the gamuts
 (see, e.g., FIG. 5). The amount of color compression that has to be
 accepted, when pixel colors are transformed into the union of all gamuts,
 is relatively small and, under typical viewing conditions, unobservable.
 However, the total number of colors that can be displayed can be reduced.
 The color gamuts produced by each pixel can best be characterized by
 determining the CIE tristimulus values (X,Y and Z) or the CIE chromaticity
 coordinates (x,y) and luminance value Y, via pixel-to-pixel measurements.
 The measurements can be performed by scanning each selected pixel, using
 commercially available calorimeters (e.g., Tektronix Lumacolor JXX).
 Either single pixels or a group of pixels can be measured by selectively
 turning on the primaries and the local white point. Measurements are best
 performed under computer control and data stored in memory. Based on this
 information, the color gamuts and their union can be computed, and the
 reference system chosen. After that, the transformation matrices can be
 determined by using the mathematics described in Equations (8)-(18). All
 of these operations can be best performed during the final testing of the
 display by scanning selected pixels, e.g., on an x-y table, on which both
 the lateral position (x,y) and the distance of the calorimeter head from
 the pixel plane (z) can be accurately controlled. Once the transformation
 matrices are known, they can be stored into the display's non-volatile
 memory.
 (iii) Color Correction Method for Case with Uniform Primary Colors and
 Non-Uniform Primary Color Coordinates
 In this case, it is assumed that the primary R, G and B colors are uniform
 across the screen, but that the color coordinates vary somewhat in a known
 way across the pixels. The color coordinates R, G and B must be adjusted
 so that the relative weights of the primaries become correct in the sense
 of Equation (1), if correct additive colors are to be reproduced. Here it
 is assumed that the variations of the color coordinates can expressed in
 function form, for example,
EQU R'=f.sub.R (R)
EQU G'=f.sub.G (G)
EQU B'=f.sub.B (B), (19)
 where (R', G', B') and (R, G, B) denote the correct and actual color
 coordinates at an arbitrary pixel, respectively. The functions f.sub.R,
 f.sub.G and f.sub.B are assumed to be independent of the values of R, G,
 and B but dependent on the pixel. The functional form can be established
 by performing a set of optical measurements on each color element of the
 selected pixels over a predetermined number of color coordinate values.
 Examples of simple functional forms include
EQU R'=R+R.sub.o (20)
 and
EQU R'=R+R.sub.o +u(R-R.sub.ref) (21)
 with similar equations holding for other color coordinates. Above R.sub.o,
 R.sub.ref, and u denote a constant off-set, reference color coordinate
 value, and a linear multiplier, respectively. Given sufficiently simple
 forms for the functions f.sub.R, f.sub.G, and f.sub.B, they can
 parameterized, the parameters stored in memory, and then evaluated in real
 time for pixels selected for correction. Storage requirements depend on
 the form and parametrization of the functions. Dramatic reduction of
 storage may be achieved in cases where the functions change in a simple
 way from pixel to pixel and interpolation techniques can be employed to
 compute parameters for a significant fraction of the pixels. The
 implementations of this method are similar to those shown in FIGS. 6 and 7
 except for the fact that the color transformer unit(s) is (are) replaced
 with units capable of performing the mathematics described in this section
 including any interpolation required.
 (iv) Color Correction Method for Case with Non-Uniform Color Coordinates
 and Non-Uniform Primary Colors Method
 In this case both color coordinates and primary colors are non-uniform due
 to parameters related to design, materials, manufacturing, or operational
 issues. If as before, both color coordinate and primary color variations
 are predictable across the pixel array, they can be corrected in much the
 same way as described above. Now one needs to combine the procedures in
 (ii) and (iii). The storage requirements are on the order of the sum of
 cases (ii) and (iii).
 (v) Color and Brightness Correction Method for Case with Simultaneous
 Non-Uniform Color and Non-Uniform Brightness
 In the most general case both chromaticity and luminance of a display may
 simultaneously exhibit sufficiently large variations that must be
 corrected in order to meet predefined uniformity goals. Now the primaries
 R.sub.i, G.sub.i, and B.sub.i at the pixels i do not necessarily even have
 a well defined white point. In such a case we first measure the
 tristimulus values of the primaries with the result given in Table 1. Both
 commonly used CIE representations, (X,Y,Z) and (x,y,Y), are given in this
 table. With all color coordinates normalized to 0.ltoreq.R.sub.i.ltoreq.1,
 0.ltoreq.G.sub.i.ltoreq.1 and 0.ltoreq.B.sub.i.ltoreq.1, the true color
 and brightness for pixel i will be given in Table 2.
 TABLE 1
 Tristimulus values for primaries R.sub.i, G.sub.i, and B.sub.i at the pixel
 i.
 Primary CIE X CIE Y CIE Z CIE x CIE y CIE Y
 R.sub.i X.sub.1i Y.sub.1i Z.sub.1i x.sub.1i y.sub.1i Y.sub.1i
 G.sub.i X.sub.2i Y.sub.2i Z.sub.2i x.sub.2i y.sub.2i Y.sub.2i
 B.sub.i X.sub.3i Y.sub.3i Z.sub.3i x.sub.3i y.sub.3i Y.sub.3i
 TABLE 1
 Tristimulus values for primaries R.sub.i, G.sub.i, and B.sub.i at the pixel
 i.
 Primary CIE X CIE Y CIE Z CIE x CIE y CIE Y
 R.sub.i X.sub.1i Y.sub.1i Z.sub.1i x.sub.1i y.sub.1i Y.sub.1i
 G.sub.i X.sub.2i Y.sub.2i Z.sub.2i x.sub.2i y.sub.2i Y.sub.2i
 B.sub.i X.sub.3i Y.sub.3i Z.sub.3i x.sub.3i y.sub.3i Y.sub.3i
 In terms of this result uniformity requires that
EQU R.sub.i x.sub.1i +G.sub.i x.sub.2i +B.sub.i x.sub.3i =constant (22)
EQU R.sub.i y.sub.1i +G.sub.i y.sub.2i +B.sub.i y.sub.3i =constant (23)
 for chromaticity and
EQU R.sub.i Y.sub.1i +G.sub.i Y.sub.2i +B.sub.i Y.sub.3i =constant (24)
 for luminance. Notice that Equation (24) essentially restates Equation (7).
 For a perfectly uniform display the color coordinates (R.sub.i, G.sub.i,
 B.sub.i), primary chromaticities (x.sub.1i, y.sub.1i),
 (x.sub.2i,y.sub.2i), and (x.sub.3i, y.sub.3i), and primary luminances
 Y.sub.1i, Y.sub.2i, and Y.sub.3i are independent of i. Therefore the
 expressions (22)-(24) are by construction constant for the same video
 signal. If on the other hand, primaries vary from pixel to pixel, both
 chromaticity and luminance tend to be nonuniform at the same time.
 In the most general case Equations (22)-(24) can be satisfied by picking a
 reference point (j) and then matching all other points to it. This will
 require the solution of the linear system
EQU R.sub.i x.sub.1i +G.sub.i x.sub.2i +B.sub.i x.sub.3i =C.sub.1j (25)
EQU R.sub.i y.sub.1i +G.sub.i y.sub.2i +B.sub.i y.sub.3i =C.sub.2j (26)
EQU R.sub.i Y.sub.1i +G.sub.i Y.sub.2i +B.sub.i Y.sub.3i =C.sub.3j (27)
 for the color coordinates (R.sub.i, G.sub.i, B.sub.i). When this solution
 (R.sub.i ', G.sub.i ', B.sub.i ') is used to replace the nominal color
 coordinates (R.sub.i, G.sub.i, B.sub.i), the display will be fully
 uniform. However, a new solution will be needed for each combination color
 coordinates (R.sub.i, G.sub.i, B.sub.i) and as a consequence the
 transformations corresponding to the solutions are difficult to store, but
 should be computed in real time, which leads to much more computation.
 Consider next a more restrictive case, for which the chromaticity and
 luminance uniformities are small. Then
EQU x.sub.1i =x.sub.1i0 +.DELTA.x.sub.1i (28)
EQU y.sub.1i =y.sub.1i0 +.DELTA.y.sub.1i (29)
EQU Y.sub.1i =Y.sub.1i0 +.DELTA.Y.sub.1i. (30)
 Substituting these equations in Equations (25)-(27) and realizing that the
 center value contributions on both sides cancel, one obtains
EQU R.sub.i.DELTA.x.sub.1i +G.sub.i.DELTA.x.sub.2i +B.sub.i.DELTA.x.sub.3i =0
 (31)
EQU R.sub.i.DELTA.y.sub.1i +G.sub.i.DELTA.y.sub.2i +B.sub.i.DELTA.y.sub.3i =0
 (32)
EQU R.sub.i.DELTA.Y.sub.1i +G.sub.i.DELTA.Y.sub.2i +B.sub.i.DELTA.Y.sub.3i =0.
 (33)
 By expressing color coordinates also in difference form, or R.sub.i
 =R.sub.io +.DELTA.R.sub.i with similar equations holding for other
 components, Equations (31)-(33) can be rewritten as
EQU .DELTA.R.sub.i.DELTA.x.sub.1i +.DELTA.G.sub.i.DELTA.x.sub.2i
 +.DELTA.B.sub.i.DELTA.x.sub.3i =-(R.sub.i0.DELTA.x.sub.1i
 +G.sub.i0.DELTA.x.sub.2i +B.sub.i0.DELTA.x.sub.3i) (34)
EQU .DELTA.R.sub.i.DELTA.y.sub.1i +.DELTA.G.sub.i.DELTA.y.sub.2i
 +.DELTA.B.sub.i.DELTA.y.sub.3i =-(R.sub.i0.DELTA.y.sub.1i
 +G.sub.i0.DELTA.y.sub.2i +B.sub.i0.DELTA.y.sub.3i) (35)
EQU .DELTA.R.sub.i.DELTA.Y.sub.1i +.DELTA.G.sub.i.DELTA.Y.sub.2i
 +.DELTA.B.sub.i.DELTA.Y.sub.3i =-(R.sub.i0.DELTA.Y.sub.1i
 +G.sub.i0.DELTA.Y.sub.2i +B.sub.i0.DELTA.Y.sub.3i) (36)
 This shows that even small corrections are interdependent in a similar
 fashion as Equations (25)-(27) unless the determinant in Equations
 (31)-(33) (alternatively Equations (34)-(36)) is zero. In that case the
 solution for the correction is independent of the particular color being
 displayed. Therefore the solution for the small differences in Equations
 (31)-(33) or (34)-(36) leads to a very similar mathematical problem as
 that of Equations (25)-(27).
 From the practical point of view it is advantageous to solve for the small
 corrections from Equations (31)-(33) or (34)-(36). The primary reason for
 this is that then the original color coordinates (R.sub.i, G.sub.i,
 B.sub.i) at pixel i can be used, if the correction mathematics fails in
 isolated cases because of numerical instabilities or near linear
 dependencies. Note also that an accurate solution is not needed, because
 the corrections need to reduce chromaticity and luminance nonuniformities
 only below the detection threshold for the average observer. As a
 consequence, fast approximate techniques, including adaptive, neural
 network, or fuzzy logic-type solutions are possible. Also, the solutions
 can again be implemented one pixel row at a time, using parallel real time
 processing, rather than serial processing using a single centralized
 correction processor operating on the entire pixel stream. The required
 reference primaries (R.sub.ref, G.sub.ref, B.sub.ref) can be chosen to be
 one of the pixels, or alternatively it can be a virtual one specified
 e.g., via the CIE chromaticity and luminance of its primaries (x.sub.ref,
 y.sub.ref, Y.sub.ref). In order to set up the linear equations, for
 example as listed in Equations (25)-(27), the CIE chromaticities and
 luminances for each pixel and the reference system need to be stored. This
 requires nine numbers per pixel. Equation set-up will take 9
 multiplications and 6 sums. The CIE chromaticity coordinates are confined
 into the range 0&lt;x.sub.i, y.sub.i &lt;1 and the luminances typically less
 than 100 to 200 nits for typical FPDs. Therefore computations can be
 performed using fixed point arithmetic at a precision sufficient to
 guarantee a final result precise to 8 bits. This would be determined by
 the condition number of the corresponding matrix. Among the number of fast
 solution methods that can be applied to this problem include the
 LU-decomposition method. The coefficients on the left hand side of
 Equations (25)-(27) will always be the same for each pixel. This can be
 further used to speed up the computations by sharing some of the
 computational start-up cost involved in the solution. Once the equations
 have been solved, the solution (R.sub.i, G.sub.i, B.sub.i) can directly be
 sent to pixel i for display.
 A serial implementation of this method is shown in FIG. 8. A single pixel
 color processor unit 50' receives video input 44', clock input 46', and
 synchronization input 48' from a video source, usually a video card, not
 shown. The chromaticity and luminance data for the primaries of the
 selected pixels and the reference pixel are stored in a memory sub-system
 42'. The pixel color processor unit 50' operates on the pixel data, one
 pixel at a time, computes the corrections in accordance with Equations
 (25)-(27) or the equivalent equations (31)-(33) or (34)-(36), and passes
 the corrected color coordinates, R', G', and B', to the display controller
 52, which interacts with the row drivers 54 and column drivers 56 in a
 conventional fashion to distribute the pixel data to the LCD array unit
 53.
 With a resolution of 640.times.480 pixels and 30 frames/sec there would be
 108 ns to solve the linear system of equations, assuming that corrections
 are done for every pixel. With a column parallel implementation shown in
 FIG. 9, this time increases to 52 .mu.s. In this parallel embodiment,
 multiple pixel color processors 50' operate in parallel on an entire row
 of pixels. Multiple memory units 42' are used for storing chromaticity and
 luminance data for pixels. The implementation in FIG. 9 uses one color
 processor 50' per column driver 56 as an illustrative example only.
 Uncorrected pixel data (R, G, and B) is passed from the column decoder 57
 to each of the color processors 50'. They perform the color
 transformations in parallel for an entire row of pixels and pass the
 corrected data, R', G' and B', to the column driver circuits 56. The
 latter send the corrected pixel data to the row of pixels selected by the
 row driver circuits, not shown. More time for the computations may be
 available, if corrections are done only to selected pixels only. However,
 it is evident that the fastest dedicated hardware implementations need to
 be considered in order to able to perform the computations required for
 this most general case color correction method in real time at full video
 rates.
 Equations (25)-(26) can be considered as an example of set of rules that
 are applied to the color coordinates (R, G and B) in order to arrive at
 the corrected set (R', G' and B'). Since the latter do not necessarily
 need to have mathematically unique values, but rather meet the uniformity
 perception thresholds of the average human observer as defined above, many
 other ways for arriving at approximately correct color coordinates can be
 envisioned. Sequential iterative techniques provide another example and
 neural network algorithms a third one. Therefore all rule sets that have
 the objective of matching color or color and brightness in the present
 sense are considered to be covered.
 (vi) Method for Self-Calibration of Color or Color and Brightness Combined
 The characterization procedures for all the above correction methods can
 also be performed in the field at end user sites after the display has
 been in use for some time. Thus, non-uniform aging effects can be
 compensated for in the same fashion. The same methods can further be used
 for implementing an automatic self-calibration feature into the display
 for faithful color or color and brightness reproduction. In that case,
 referring to FIG. 10, a colorimeter head 35 is mounted on an arm 33 with
 the scan motion covering the entire pixel array of the display. For
 example, the calorimeter head 35 can be designed to move along the arm 33
 in the horizontal direction, arrows 36, while the arm 33 can be made to
 move in the vertical direction, arrows 38. The colorimeter arm 33 can be
 designed to be parked outside the viewable area of the display 34 inside
 the frame, not shown, when not in use. Using such a movable colorimeter
 head 35, selected pixels of the display 34 can be turned on and their
 color element and full pixel characteristics scanned and measured, the
 reference system selected, color or color and brightness correction
 parameters computed, and all correction data stored into the memory 42 or
 42' (FIGS. 6, 7 and 8) of the display under computer control. Such a
 self-calibration apparatus can be activated periodically by the display
 unit itself or initiated by the user to ensure uniform and faithful color
 or color and brightness characteristics. It should be understood that the
 apparatus 32 is only one of a number of devices that can be used to
 perform this calibration function; other devices are therefore to be
 considered within the scope of the present invention.
 Since other modifications and changes varied to fit particular operating
 requirements and environments will be apparent to those skilled in the
 art, the invention is not considered limited to the examples chosen for
 purposes of disclosure, and covers all changes and modifications which do
 not constitute departures from the true spirit and scope of this
 invention.
 Having thus described the invention, what is desired to be protected by
 Letters Patent is presented in the subsequently appended claims.