Patent Publication Number: US-2007097159-A1

Title: Methods for reducing die-to-die color inconsistances in a multi-die printing system

Description:
FIELD OF INVENTION  
      This invention relates generally methods of calibrating the performance of printing systems, and more specifically to methods of reducing die-to-die color inconsistencies in a multi-die printing system.  
     BACKGROUND  
      Inkjet printing systems are also are well known in the art. Small droplets of liquid ink, propelled by thermal heating, piezoelectric actuators, or some other mechanism, are deposited by a printhead on a print media, such as paper.  
      In scanning-carriage inkjet printing systems, inkjet printheads are typically mounted on a carriage that is moved back and forth across the print media. As the printheads are moved across the print media, the printheads are activated to deposit or eject ink droplets onto the print media to form text and images. The print media is generally held substantially stationary while the printheads complete a “print swath”, typically an inch or less in height; the print media is then advanced between print swaths. The need to complete numerous carriage passes back and forth across a page has meant that inkjet printers have typically been significantly slower than some other forms of printers, such as laser printers, which can essentially produce a page-wide image.  
      The ink ejection mechanisms of inkjet printheads are typically manufactured in a manner similar to the manufacture of semiconductor integrated circuits. The print swath for a printhead is thus typically limited by the difficulty in producing very large semiconductor chips or “die”. Consequently, to produce printheads with wider print swaths, other approaches are used, such as configuring multiple printhead dies in a printhead module, such as a “page wide array”. Print swaths spanning an entire page width, or a substantial portion of a page width, can allow inkjet printers to compete with laser printers in print speed.  
      One type of inkjet printing system utilizes multiple printhead modules that each print a substantial portion of a page width. The printhead modules in this type of system may include multiple printhead die linearly spaced across the print swath, such that each die prints a portion of the swath, typically one inch or less. Since the printhead die invariably differ slightly in their characteristics, such as drop weight, if corrections are not made for the slight differences between the die visible print quality defects may be introduced. For example, different die may print at slightly different densities. Since the print swaths of the individual die are immediately adjacent, such defects are readily discernible, particularly when attempting to reproduce high quality graphics and images. Banding in an area representing sky in a photograph, for example, is easily observed.  
      There is thus a need for methods of reducing die-to-die color inconsistances in a multi-die printing system.  
     SUMMARY  
      Exemplary embodiments of the invention include methods of reducing die-to-die color inconsistencies in a multi-die printing system. A die is linearized and becomes the reference die; density measurements are made for each pair of adjacent die, and the density comparisons are utilized to map the linearization data to each of the remaining die. The methods may utilize an optical sensor having good resolution as a densitometer, but which may lack stability.  
      Other aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  illustrates an exemplary printing system in which exemplary embodiments of the invention may be utilized;  
       FIG. 2  illustrates the paper path and printhead mechanisms of an exemplary inkjet printing system in which embodiments of the invention may be utilized;  
       FIG. 3  is a block diagram further illustrating a system in which embodiments of the invention may be employed;  
       FIG. 4  is a bottom perspective view of an exemplary compact optical sensor which may be used in embodiments of the invention;  
       FIG. 5  is a side elevational sectional view of the exemplary compact optical sensor of  FIG. 4 , shown monitoring a portion of a sheet of print media, such as paper;  
       FIG. 6  is an exploded view of the exemplary compact optical sensor of  FIG. 4 ;  
       FIG. 7  is a graph showing the relative specular reflectances and specular absorbances versus illumination wave length for cyan, yellow, magenta and black inks, and for blue, green, soft-orange and red illuminating Light emitting diodes (LEDs) used by the exemplary optical sensor of  FIG. 4  when monitoring images printed on white media, such as plain paper;  
       FIG. 8  illustrates in a simplified form how multiple printhead die are arrayed within an exemplary printhead assembly;  
       FIG. 9  illustrates how ramps of varying print density may be deposited on a print media by multiple printhead die;  
       FIG. 10  is a plot illustrating an exemplary linearization table for a printhead die; and  
       FIG. 11  is a flow chart further illustrating an embodiment of the present invention.  
    
    
     DESCRIPTION OF EMBODIMENTS OF THE INVENTION  
      Embodiments of the invention are described with respect to an exemplary inkjet printing system; however, the invention is not limited to the exemplary system, nor to the field of inkjet printing, but may be utilized as well in other systems.  
      In the following specification, for purposes of explanation, specific details are set forth in order to provide an understanding of the present invention. It will be apparent to one skilled in the art, however, that the present invention may be practiced without these specific details. Reference in the specification to “one embodiment” or “an exemplary embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearance of the phrase “in one embodiment” in various places in the specification do not necessarily refer to the same embodiment.  
       FIG. 1  illustrates an exemplary inkjet printing system  10  in which embodiments of the invention may be utilized. Intended for moderately high volume printing, the system may also include multiple other functions and may, for example, be connected to an office network to provide printing, scanning, and faxing capabilities to a workgroup. Methods of the invention may also be applied to other printing systems, such as those used for photo printing.  
       FIG. 2  illustrates the basic media path and printhead mechanisms  16  of an exemplary inkjet printing system  10  in which embodiments of the invention may be utilized. As shown in  FIG. 2 , print media  30 , such as a sheet of paper, is held to a rotating drum  18  by air suction. The print media  30  is rotated past printhead assemblies on print carriages  42 ,  52  that remain substantially stationary during a printing pass (although the carriages may be repositioned between passes, such as to allow printing of wider media using multiple passes). Multiple carriages with printhead assemblies may be utilized to span the page width as illustrated; one printhead assembly on a first carriage  42  may print a first portion  32  of the page width, and a second printhead assembly on a second carriage  52  may print a second portion  34  of the page width. Where the two portions of the printed page meet is a joint  36 , which ideally is not readily perceptible on the completed page.  
      The multiple printhead assemblies  42 ,  44  may in turn each comprise multiple separate printhead die, with each die positioned to print a portion of the total print swath, as further explained below. Print swath  34  is shown in  FIG. 2  as comprising four smaller swaths, such as would be produced by four separate die on printhead assembly  52 . The use of separate die may result in inconsistent color or tone across the complete print swath, a problem addressed by embodiments of the present invention, as also discussed below.  
      For multi-pass printing, the print media  30  may be held to the drum  18  by suction for more than one complete revolution of the drum, with printheads on the carriage assemblies  42 ,  44  depositing ink during each pass of the print media. The printer may include drying mechanisms (not shown) to accelerate the drying of the printed media, which may, for example, be placed near the bottom of the drum  18  such that the printed media may be at least partially dried between printing passes. The carriage assemblies  42 ,  52  permit the printheads to be moved side-to-side to different locations on the drum or off the drum entirely for servicing, or to reposition the printheads for different paper configurations.  
      Also positioned adjacent to print drum  18  is a compact optical sensor system  100 , described in detail below. In a similar manner to the printhead assemblies  42 ,  52 , the compact optical sensor system  100  is also configured to be repositioned at different locations across the printhead drum, such that, for example, the optical characteristics of printed samples from different printhead die may be sampled. In an actual printing system, the compact optical sensor  100  may be located on the same carriage mechanism as one of the printhead assemblies  42 ,  52  to reduce system cost and complexity. To allow for drying of the media and for making multiple measurements, the drum may make one or more rotations before or between sensor readings.  
       FIG. 3  is a schematic view of the exemplary inkjet printing system of  FIGS. 1 and 2 . Computing device  310  may be a computer directly connected to the printing system  300 , or there may be multiple computers accessing the printing system over a network, such as a Local Area Network (LAN). Alternatively, some processing capabilities may be incorporated into the printer itself, such as in a photo printer. Computing device  310  typically includes a processor  312  having access to memory  314  including image data  316 . The computing device  310  typically formats the image data in a form which may be utilized by printing system  300 .  
      Printing system  300  typically includes a controller  320  which includes a processor  322  having access to memory  324 . The memory may include the exemplary printhead calibration algorithms  326  of the present invention, together with other programs, parameters, and print data.  
      The controller  320  typically generates print data for each carriage assembly  342  of the printer, and also controls other printer mechanisms  332 , such as, for example, controlling the drum rotation, paper feeding mechanism, and media dryers (not shown). The controller also interfaces with the compact optical sensor  100 , controls it&#39;s positioning on the print drum and the optical stimulus generated by the sensor, and acquires measurements from the sensor, as discussed below.  
      Shown in  FIG. 4 , and in greater detail in  FIGS. 5 through 7 , is an exemplary compact optical sensor system  100 . The optical sensor  100  includes a housing or frame  102 . The sensor  100  also includes a printed circuit assembly (“PCA”)  105  (see  FIGS. 5 and 6 ), having a connector receptacle  106  that communicates with controller  320  via, for instance, conventional flexible cables ( 107 ). The PCA  105  includes two light-to-voltage converters, or photodiodes  108 ,  110  for receiving diffuse and specular reflected light, respectively. Preferably, each of the photodiode light-to-voltage converters  108 ,  110  are identical in construction to provide ease of manufacturing and a more economical, compact optical sensor  100 . The output voltage is an analog signal which is passed through an amplifier (not shown). This amplified signal is then passed to an analog-to-digital (“A/D”) converter which may be a portion of the printed circuit assembly  105 , or a portion of the controller  320 .  
      The PCA board  105  is constructed such that the specular and diffuse photodiodes  108 ,  110  receive light through incoming light passages  112 ,  114  defined by the housing  102 . To align the photodiodes  108 ,  110  with the light passages  124 ,  114 , the housing  102  includes a support surface  115 , which preferably has a lip, shown to the right of photodiode  110  in  FIG. 6 , under which the PCA board  105  is received. In the illustrated exemplary embodiment, the PCA board  105  defines an alignment hole  116  therethrough, which when assembled is received upon an alignment post  118  extending upwardly from the housing support surface  115 , as shown in  FIG. 6 .  
      The PCA board  105  of the exemplary compact optical sensor system includes four light emitting diodes (LEDs)  120 ,  122 , 124  and  126  which, in the illustrated embodiment are the colors, blue, green, red and soft-orange, respectively. The construction of the printed circuit assembly  105  advantageously uses a chip-on-board (“COB”) process where the bare silicon die for each component is wire bonded directly to the printed circuit board assembly. Thus, in the illustrated embodiment, the light emitting diodes (LEDs)  120 - 126  may be closely grouped together, in a space smaller than that occupied by a single-packaged LED. Note that the LEDs  120 - 126  and photodiodes  108 ,  110  have been drawn in  FIG. 7  to be about twice their normal size to better illustrate the concepts introduced herein. By clustering the light emitting diodes  120 - 126  so closely, a single outgoing optical light path  128  defined by the housing  102  may accommodate light generated by all of these LEDs.  
      The illustrated exemplary embodiment may also include two filter elements, one a diffuse filter element  130 , and the other a specular filter element  132 , preferably of colors selected to block long, infrared wavelengths, although in some implementations, other filters may be used to either filter or pass through more specific wavelength bands. In the illustrated embodiment, the filter elements  130 ,  132  are typically infrared wavelength blocking filters, such as those designed to block infrared wavelengths between 700 and 1000 nm (nanometers). Each of the filter elements  130 ,  132  are received within a recessed shelf portion  134 ,  136  defined by the housing  102 . The filter elements  130 ,  132  serve to limit the incoming light to the diffuse and specular photodiodes  108 ,  110  to light within the regions of the visible spectrum. In some embodiments, an upper portion of the incoming light passages  112 ,  114  is molded with a square diffuse stop, and a rectangular specular stop, with the longitudinal axis of the specular stop running perpendicular to the longitudinal axis of the housing  102 , that is, parallel with the X-axis. Again, the term “stop” refers to a window through which incoming light passes before it is received by in this case, the specular photodiode  110 .  
      The exemplary compact optical sensor  100  also includes a lens assembly  140 , which is received by a pair of lower extremities  142  of the housing  102 . In this manner, the filter elements  130 , 132  are held in place within recesses  134 ,  136  by the lens assembly  140 . The lens assembly  140  includes an outgoing LED lens  145 , and two incoming lenses, here, a diffuse lens  146  and a specular lens  148 . The lens elements  145 ,  146  and  148  are preferably selected to better focus and direct the light beams to follow the paths shown in  FIG. 6 , and as discussed further below after the remaining components of the optical sensor  100  have been introduced.  
      Preferably the exemplary sensor  100  includes an ambient light shield member  150 . The ambient light shield  150  slides over the lens assembly  140  and is attached to the housing  102 , for instance using various snap fitments, bonding elements, such as adhesives, fasteners or the like (not shown). The ambient light shield  150  has a pair of opposing slots  152  and  154  which are located to receive and secure a clear aerosol shield member  155 . The aerosol shield  155  in the illustrated embodiment is inserted through slot  152  then through slot  154 , with the forward insertion being limited by a stop  156  encountering a portion of the body of the ambient light shield  150  (see  FIG. 5 ). A snap fitment member  158  flexes upwardly during insertion of the aerosol shield  155 , then latches down over a lower portion of the slot  154  (see  FIG. 5 ) to hold the aerosol shield  155  in place within the ambient light shield  150 . Preferably, the aerosol shield  155  has an anti-reflection coating or property which allows light beams to pass therethrough without undue interference from the aerosol shield  155 .  
      Turning to the operation of the exemplary compact optical sensor  100 , as shown in  FIG. 5 , we see the Light emitting diodes (LEDs)  120 ,  122 ,  124 , and  126  emitting light beams through the outgoing passageway  128 , through the outgoing lens  145 , and emerging as light beams  160 ,  162 ,  164 , and  166 , respectively exiting through a light entrance/exit chamber portion  168  of the ambient light shield  150 . The emerging light beams  160 - 166  impact an upper exposed print surface of a sheet of print media  169 , such as, for example, a sheet of paper. Light beams  160 ,  162 ,  164 , and  166  are reflected directly off the media  169  as upwardly directed diffuse light beams  170 ,  172 ,  174 , and  176 , respectively. The term “diffuse” refers to light which is scattered (at any angle) when reflected from a surface. The portion of the diffuse light which is used in the illustrated embodiment are the perpendicular beams reflected off of the media  169 , as shown for the diffuse light beams  170 - 176  in  FIG. 5 . The incoming diffuse light beams  170 - 176  pass through lens  146 , through filter  130 , and through the incoming light chamber  112  and through a rectangular stop or window  178  where they are received by the diffuse photodiode  108 . The photodiode  108  is a light-to-voltage converter, as mentioned above, which interprets these incoming diffuse light beams  170 - 176  and produces a voltage signal proportionate to the intensity of these incoming light beams. This voltage signal is sent via receptical  106  and cable  107 , and ultimately to controller  320 , where this information may then be used by the controller to adjust various printing parameters.  
      Besides forming diffuse light beams  170 - 176 , the incoming light beams  160 ,  162 ,  164  and  166  reflect off of the media  169  to form incoming specular light beams  180 ,  182 ,  184  and  186 , respectively. The specular light beams  180 - 186  are reflected off of the media  169  at the same angle as the incoming light beams  160 - 166  impacted the media  169 , (i.e., the angle of incidence equals angle of reflection). In the illustrated embodiment, preferably the irradiance from each illuminating LED  120 - 126  strikes the print surface plane of the sheet of media  169  at an angle of about 45-65°, or more preferably at an angle of 45°, referenced from the print surface of the media  169 .  
      The specular reflectance light beams  180 - 186  pass through the light chamber  168  of the ambient light shield  150 , through the aerosol shield  155 , through the incoming specular lens  148 , through the specular filter element  132 , through the incoming light passageway  114 , then through a specular stop window  187 , after which they are received by the specular photodiode  110 . The photodiode  110 , which is a light-to-voltage converter, interprets the incoming light beams  180 - 186  and sends a signal to the controller  320 .  
      The use of four different colors of light emitting diodes  120 - 126  permits the exemplary compact optical sensor  100  to perform media type sensing, color calibration (specifically, color, hue and intensity compensation), automatic pen alignment and swath height error/linefeed calibration. In the illustrated embodiment, the diffuse reflectance beams  170 - 176  detect the presence of the primary inks used in inkjet printers, such as, cyan, light cyan, magenta, light magenta, yellow and black. The specular light beams  180 - 186  are used to determine the reflective and other surface properties of the media  169 , from which the type of media  169  may be determined, and the print routines then adjusted to match the type of media. Indeed, use of the four different colored Light emitting diodes (LEDs)  120 - 126  allows the compact optical sensor  100  to collect data which the controller  320  then may map to a three-dimensional color space which correlates to human perception of color. Moreover, while four light emitting diodes  120 - 126  are illustrated, it is apparent that other implementations may cluster additional LEDs above the outgoing light chamber  128 , or another cluster of LEDs may be provided in the region of the specular photodiode  110  on the printed circuit assembly  105 , foregoing media type determination in favor of additional color sensing capability.  
      A further advantage made use of in the optical sensor  100  is the arrangement of the colors of the LEDs  120 - 126 . In the illustrated embodiment, it is preferred to have LED  120  to be a blue color, LED  122  to be a green color, LED  124  to be a red color and LED  126  to be a soft-orange color, with LEDs  120  and  124  being furthest away from the diffuse photodiode  108 , and LEDs  122  and  126  being closer to the diffuse photodiode  108 . In the illustrated embodiment, using the particular types of LEDs  120 - 126  and lens  145  selected, this physical arrangement yields an economical and high performance sensor  100 .  
       FIG. 7  is a graph  200  illustrating the manner in which the colors for the LEDs  120 - 126  were selected, here based upon the colors of ink and their specular responses used in the printer  20 . In  FIG. 7 , the various wavelengths and percentage of reflectance and percentage of absorbance are shown for the four primary colors ejected by a typical printing unit  10  and for the four LEDs  120 - 126  of sensor  100 . For the inks, graph  200  shows a cyan colored ink trace  202 , a magenta colored ink trace  204 , a yellow colored ink trace  206  and a black color ink trace  208 . In the illustrated embodiment, graph  200  shows a blue LED ink trace  210  which is emitted by LED  120 , a green LED trace  212  which is emitted by LED  122 , a red LED ink trace  216  which is emitted by LED  124 , and a soft-orange LED ink trace  214  which is emitted by LED  126 .  
      The selection of the four LED colors was arrived at by an intensive study evaluating reflections from the interaction of a variety of different illuminating colors with each of the test colors. These interactions were either found through laboratory measurements, or by graphical comparisons of the spectral responses of the inks versus the illumination data provided by the manufacturers of the variety of LEDs available. When measuring any particular color sample, each of the four LEDs  120 - 126  may be illuminated in sequence, with the resulting diffuse light beams  170 - 176  then being interpreted by the diffuse light-to-voltage converter  108  to find the percentage of reflectance and/or absorbance. By comparing the reflectance values received when illuminated by the different LEDs  120 - 126 , the various shades may be distinguished by controller  320 . For instance, turning to  FIG. 7 , the cyan ink curve  202  may be distinguished from the other ink curves because the blue LED generates maximum reflectance, the green LED a medium reflectance, and the soft orange and red LEDs generate minimal reflectances. For the magenta ink curve  204 , the blue LED generates a small reflectance, the green LED generates a minimal reflectance, the orange LED generates a medium reflectance, while the red LED generates a high reflectance.  
      The sensor described with respect to  FIGS. 4 through 7  may provide relatively high resolution densitomer readings, but may be somewhat inadequate as spectrometer, in that noise in the sensor readings, sensor drift over time, and the contribution of the print media to the sensor readings may affect the resulting measurements. The minor inaccuracies due to sensor drift are typically not of concern when using the sensor to calibrate a single printhead die, since the small inaccuracies would not be readily observable when viewed in isolation. The inaccuracies may become a factor in a multi-die printing system, however.  
       FIG. 8  illustrates in simplified form how multiple printhead die  862 ,  864 ,  866 ,  868  are arrayed within a printhead assembly  842 . Each of the printhead die  862 ,  864 ,  866 ,  868  is shown having two linear arrays of print nozzles, such as might be used to print two different ink colors. A printhead assembly may include die for printing mutliple ink colors or printing fluids, such as, for example, cyan, magenta, yellow, black, and fixer. The individual die are arrange in a staggered pattern perpendicular to the direction of the media transport (indicated by the arrows). As indicated by the dashed lines, each printhead die overlaps the span of the adjacent dies by a small amount (i.e., there is a region near the ends of adjacent die where the rows of nozzles of the adjacent die overlap).  
      To produce the range of tonal values required for graphics and photographs, printhead die are typically calibrated, or “linearized”, such that the print densities of halftoned images substantially correspond to the densities of the continuous tone, or “contone” images, which are to be printed. Typically, measurements of the actual print density of the printhead die are made over the range of print densities, and a curve-fitting routine then “linearizes” the die (see e.g. Wu et al., U.S. Pat. No. 6,851,785, “Calibration Method and Apparatus Using Interpolation”). The linearization information may be stored in a non-volatile memory as a look-up-table (LUT) or as coefficients of an equation.  
      Independently linearizing each of the die in a multi-die system, however, may not adequately account for die-to-die variations. Assuming a linearized die has a density error equal to “α” then the difference between any two die is potentially 2α. If the two die are adjacent, a 2α density difference may be unacceptable.  
      Since all the die in an exemplary multi-die system have very similar physical characteristics, having been similarly manufactured, the shape of the linearization curves will also be similar, typically differing only by a constant adjustment, such a multiplication factor.  
       FIG. 9  illustrates how a “ramp” of varying print density may be deposited on a print media by each die of a multi-die printing system, such as the die  862 ,  864 ,  866 ,  868  of  FIG. 8 .  FIG. 9  is intended to be illustrative only, and does not necessarily represent ramps printed by a actual system.  FIG. 9  shows how density ramps  902 ,  904 ,  906 ,  908  may be printed in parallel for multiple printhead die. A ramp may, for example, include regions printed with sixteen discrete print densities equally spaced along the range of available “raw” print densities. After printing, the ramps may be repeatedly moved past the compact optical sensor  100 , as the drum  18  of the exemplary printing system rotates the media past the sensor.  
       FIG. 10  is a plot depicting an exemplary linearization table for a printhead die. The plot shows input level on the horizontal axis and output level on the vertical axis. The response curve  1002  represents the calibration necessary to cause the printhead to print tones linearly in the printer color space. For example, the input level may be an 8-bit value from 0 to 255, which is converted to a linearized output level, also an 8-bit value from 0 to 255. The curve may be stored in non-volatile memory as a table of values or as coefficients in a mathematical equation.  
      In exemplary embodiments of the invention, rather than performing a separate linearization of each die, a single “reference” die is linearized, with the resulting curve then adjusted for each of the remaining die based on a determination of the relative print densities produced by each adjacent die. Thus, potential print density differences between any two adjacent die may be significantly reduced from those which would result from independently linearizing each die.  
       FIG. 11  is a flow diagram further illustrating an exemplary method of the invention. The method begins  1102  and the “white” value of the unprinted media is determined. That is, the unprinted media is scanned past the compact optical sensor, and a determination is made of a baseline “white” value for the color channel being linearized (i.e., in an exemplary system, cyan, magenta, yellow, or black). The determination of the white baseline may include one or more measurements utilizing one or more of the measurement capabilities of the optical sensor; a statistical process may be performed to arrive at a baseline white value (e.g., multiple readings may be averaged to reduce measurement noise). The white value will be used to correct subsequent readings of the optical sensor to reduce the effects of media characteristics on the linearization process.  
      Ramps are then printed  1106  using all dies of the printhead assembly, as shown in  FIG. 9 . In an exemplary system, this may be accomplished by continuing to rotate the print drum retaining the print media a revolution as the print head dies deposit ink. The ramps that are printed are created using unlinearized values, and thus exhibit any of the non-linearity that is present in the printheads. As discussed above, each ramp may represent multiple discrete regions (in an exemplary system, sixteen) of print densities spaced along the range of potential densities.  
      In an exemplary method, one printhead die is then selected as a reference die. Typically, this will be one of the end die of the printhead module, such as, for example, die  862  or die  868  in  FIG. 8 . A density value is then determined  1110  for the “reference” die. Determining a reference value may include one or more measurements utilizing one or more of the measurement capabilities of the optical sensor; a statistical process may be performed to arrive at a baseline density value (e.g., multiple readings may be averaged to reduce measurement noise). In the exemplary printing system illustrated in  FIG. 2 , for example, more than 100 readings may be taken as a print sample is scanned past the compact optical sensor. In exemplary embodiments, determining the density value may entail averaging readings obtained from the optical sensor within a region of the printed ramp, such as the area shown at  912  in  FIG. 9 .  
      A corresponding density value is then determined  1112  for the next neighboring die adjacent to the reference die. The density determinations for the reference die and next neighboring die may be determined in close time proximity, such that any effects on the determinations due to sensor drift are obviated or minimized. A “white” value for the media, determined before the density ramps were deposited, may be used to correct the density values. The two density measurements thus provide a basis for accurately mapping the differences between any two adjacent die.  
      If all the density values for the printhead module have not been determined  1114 , the die that was the neighboring die in the previous step is now selected as the new “reference” die  1116 , and density determinations are made for the new reference die and the next die in line. The process thus essentially steps along the printhead assembly, and generates density comparison data for each adjacent set of die.  
      When all density values have been determined, linearization tables may be created for each of the printhead die. In an exemplary embodiment, a linearization table is first created  1122  for one of the die, such as the original end die with which the process began. The ramp data previously printed may be utilized to create a linearization table for the die using methods known in the art (see e.g. Wu et al., U.S. Pat. No. 6,851,785, “Calibration Method and Apparatus Using Interpolation”). In the exemplary embodiment, the linearization table for the original end die then becomes a basis for the linearization tables of the remaining die, as the die-to-die density comparison information between adjacent dies is used to remap  1124  the linearization table to each of the remaining die. Mapping may include adjusting the values in a linearization look-up-table (LUT) or the coefficients of a linearization equation, such as by multiplying the values or coefficients by a factor based on the relative measured densities; or mapping may include other operations, such as adjusting an offset value. The mapping function may be empirically determined to provide best results in a particular printing system.  
      When all linearization tables have been created  1126 , the exemplary method ends  1130 . The exemplary method illustrated in  FIG. 11  may be repeated for each color channel of the printhead module, such as, for example, cyan, magenta, yellow, and black. The exemplary method may also be extended to reduce color errors from printhead module to printhead module, such as, for example, between printhead modules  42  and  52  of  FIG. 2 , by continuing the process from the last printhead die of one module to the first printhead die of the next module.  
      An advantage of methods of the present invention is a significant decrease in the errors observed between adjacent print die. In comparison to an approach where each of the printhead die is separately linearized, embodiments of the invention have been determined to reduce the die-to-die error by roughly half.  
      The above is a detailed description of particular embodiments of the invention. It is recognized that departures from the disclosed embodiments may be within the scope of this invention and that obvious modifications will occur to a person skilled in the art. It is the intent of the applicant that the invention include alternative implementations known in the art that perform the same functions as those disclosed. This specification should not be construed to unduly narrow the full scope of protection to which the invention is entitled.  
      Embodiments of the invention include computer readable media containing program instructions for implementing the exemplary methods.  
      The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or acts for performing the functions in combination with other claimed elements as specifically claimed.