Patent Publication Number: US-7708362-B2

Title: Printhead error compensation

Description:
BACKGROUND 
   It may be desirable, in some printer applications to have high alignment accuracy between printhead nozzles to improve print quality. However, manufacturing variations frequently result in misalignment of printhead nozzles. For example, columns of nozzles are frequently curved and the spacing between columns of nozzles may be irregular. These errors are known as scan axis directionality (SAD) errors. In other instances, a column of nozzles may be straight but tilted. This may be the result of the entire printhead being tilted about an axis perpendicular to the medium as a result of the individual column of nozzles being tilted relative to other columns of nozzles on the same printhead. These errors are commonly known as THETA Z errors. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic illustration of a printing system configured to provide horizontal printhead error compensation according to an exemplary embodiment 
       FIG. 2  is a bottom plan view of a first printhead with image forming points having no horizontal errors according to an exemplary embodiment. 
       FIG. 3  is a bottom plan view of a second printhead having image forming points having a first horizontal error characteristic according to an exemplary embodiment. 
       FIG. 4  is a bottom plan view of a third printhead having image forming points having a second horizontal error characteristic according to an exemplary embodiment. 
       FIG. 5  is a bottom plan view of a fourth printhead with image forming points having a third horizontal error characteristic according to an exemplary embodiment. 
       FIG. 6  is a diagram illustrating two columns of image forming points and the horizontal error distances associated with distinct portions of the columns according to an exemplary embodiment. 
       FIG. 7  is a schematic diagram illustrating alignment of a first portion of the second printhead of  FIG. 4  with a print medium and printing of reference images upon the print medium using the first portion according to an exemplary embodiment. 
       FIG. 8  is a schematic diagram illustrating alignment of the reference diagnostic images with a second portion of the second printhead of  FIG. 4  and printing of diagnostic images with the second portion according to an exemplary embodiment. 
       FIG. 9  is a graph illustrating an inverse of optical density versus various offset distances between the pairs of reference and diagnostic images of  FIG. 9  according to an exemplary embodiment. 
       FIG. 10  illustrates two pairs of reference and diagnostic images printed upon a medium for determining a horizontal printhead error compensation value for portions of image forming points of a printhead that are tilted in opposite directions according to an exemplary embodiment. 
       FIG. 11  is a timing diagram illustrating the printing of a vertical line using portions of the printhead shown in  FIG. 2  according to an exemplary embodiment. 
       FIG. 12  is a timing diagram illustrating the printing of a vertical line using portions of the printhead shown in  FIG. 3  according to an exemplary embodiment. 
       FIG. 13  is a timing diagram illustrating the printing of a vertical line using portions of the printhead shown in  FIG. 4  according to an exemplary embodiment. 
       FIG. 14  is a timing diagram illustrating the printing of a vertical line using portions of the printhead shown in  FIG. 5  according to an exemplary embodiment. 
       FIG. 15  is a schematic diagram illustrating a first portion of a first column of image forming points in alignment with a print medium and a reference image formed upon the medium using the first portion of image forming points according to an exemplary embodiment. 
       FIG. 16  is a schematic diagram illustrating the medium of  FIG. 15  moved to align the reference image with a second portion of a second column of image forming points and a diagnostic image printed upon the medium using the second portion of image forming points according to an exemplary embodiment. 
   

   DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
     FIG. 1  is a schematic illustration of a printing system  12  configured to provide horizontal printhead error compensation. Printing system  12  is generally configured to print diagnostic images  18  upon a print medium  20 , to analyze such images to determine an error compensation value and to modify printing based upon such error compensation values. System  12  includes printer  22  and print cartridges  24 ,  26  and  28 . Printer  22  includes carriage  30 , carriage drive  32 , media feed device  34 , sensor  37  and controller  38  and computer readable media  39 . Carriage  30  generally comprises a structure configured to be moved back and forth across medium  20  along a scan axis  40  while supporting at least one print cartridge. In the particular embodiment illustrated, carriage  30  includes print cartridge locations  42 ,  44  and  46 . Print cartridge locations  42 ,  44  and  46  generally comprise structures along carriage  30  that are configured to hold or retain an individual print cartridge. Print cartridge locations  42 ,  44  and  46  are configured such that each of print cartridges  24 ,  26  and  28  is interchangeable with one another. Carriage  30  may alternatively be configured to specifically support a particular one of print cartridges  24 ,  26  and  28 . The exact configuration of such print cartridge locations may be varied depending upon the exact configuration of the ink print cartridge to be held or retained at the print cartridge location, as well as the type of connecting or supporting arrangement employed at each print cartridge location. 
   Carriage drive  32  is shown schematically and generally comprises an actuator configured to move carriage  30  along scan axis  40  across medium  20  in response to control signals from controller  38 . Media feed device  34 , schematically shown, comprises one or more mechanisms, such as belts, pulleys, drive rollers and motors, configured to feed and move medium  20  relative to carriage  30  and whatever print cartridges are supported at print cartridge locations  42 ,  44  and  46 . The exact configuration of media feed device  34  may be varied depending upon the characteristics of medium  20  being fed past carriage  30 . For example, media feed device  34  may have different configurations depending upon the particular dimensions of medium  20 . 
   Sensor  37  comprises a mechanism configured to detect optical densities of diagnostic images  18  upon print medium  20 . Sensor  37  generates electrical signals that are processed by controller  38 . In the particular embodiment illustrated, sensor  37  is coupled to carriage  30  and is configured to be moved by carriage drive  32  along scan axis  40  across diagnostic images  18 . In other embodiments, sensor  37  may be coupled to one or more of print cartridge locations  42 ,  44 ,  46 , may be coupled to one of print cartridges  24 ,  26  or  28 , may be movably coupled to another structure of printer  22  so as to move across or relative to diagnostic images  18  or may be stationarily coupled to a frame or other structure of printer  22 , wherein media feed device  34  moves diagnostic images  18  relative to the sensor. For purposes of this disclosure, the term “coupled” shall mean the joining of two members directly or indirectly to one another. Such joining may be stationary in nature or movable in nature. Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate member being attached to one another. Such joining may be permanent in nature or alternatively may be removable or releasable in nature. 
   Controller  38  generally comprises a processor unit configured to generate control signals which are transmitted to carriage drive  32 , media feed device  34  and whatever print cartridges  24 ,  26 ,  28  that are mounted to carriage  30 . Controller  38  may comprise a processing unit that executes sequences of instructions contained in a memory (not shown). Execution of the sequences of instructions causes the processing unit to perform steps such as generating control signals. The instructions may be loaded in a random access memory (RAM) for execution by the processing unit from a read only memory (ROM), a mass storage device, or some other persistent storage. In other embodiments, hard-wired circuitry may be used in place of or in combination with software instructions to implement the functions described. Controller  38  is not limited to any specific combination of hardware circuitry and software, nor to any particular source for the instructions executed by the processing unit. Although controller  38  is illustrated as being physically incorporated as part of printer  22 , controller  38  may alternatively be physically incorporated as part of another device such as a distinct computing device to which printer  22  is connected. In other embodiments, portions of controller  38  may be physically incorporated into distinct electronic devices, wherein such portions cooperate with one another. For example, a first portion of controller  38  may be located in printer  22  while a second portion of controller  38  is incorporated as part of a distinct computer. 
   Controller  38  receives data representing an image to be printed from a media reader, a computer, or directly from memory of a device, such as a video camera, digital camera, scanner and the like. Controller  38  further receives information from sensors (not shown) indicating the characteristics and locations of print cartridges  24 ,  26 ,  28  or other print cartridges mounted to carriage  30 . Based upon such information, controller  38  controls carriage drive  32  to move carriage  30  along scan axis  40 , controls media feed device  34  to move medium  20  relative to carriage  30  in directions generally perpendicular to scan axis  40 , and controls the application of inks or other printing material from one or more of print cartridges  24 ,  26 ,  28  supported by carriage  30 . 
   Computer readable media  39  generally comprises any form of media containing executable instructions that are readable by a computing device. Examples of computer readable media containing executable instructions that are readable by a computing device include: optical disks, magnetic disks or tape, and digital memory hardwired circuitry. The instructions contained by media  39  are used by controller  38  to generate control signals to achieve printhead horizontal error compensation. In particular, the instructions contained on media  39  direct controller  38  to generate control signals such that the following steps are performed in response to control signals generated by controller  38 . 
   Initially, media feed device  34  positions media  20  in a first position relative to print cartridges  24 ,  26 ,  28 . A diagnostic reference image  18  is printed upon medium  20  using a portion of a total of image forming points of printhead  62  of one of cartridges  24 ,  26  or  28 . For purposes of the disclosure, the term “image forming points” shall mean any distinct point that causes an image to be formed upon a medium. In the particular embodiment illustrated, printhead  62  includes the plurality of individual image forming points which comprise nozzles configured to dispense fluid ink or other fluid printing material upon a medium. For purposes of this disclosure, the term “image” shall mean any mark or point or series of marks or points created upon a medium by either depositing a material upon the medium or interacting with the medium to activate materials within or on the medium. 
   Next, media feed device  34  moves media  20  relative to print cartridges  24 ,  26 ,  28  so as to vertically align a second portion of a total of image forming points of one of print cartridges  24 ,  26 ,  28  with the diagnostic reference image. For purposes of this disclosure, the term “vertical” refers to a direction perpendicular to scan axis  40 . Likewise, the term “horizontal” refers to a direction parallel to scan axis  40 . A diagnostic alignment image is printed upon print medium  20  using the second portion of image forming points. Sensor  37  scans a combination of the first diagnostic reference image  18  and the second diagnostic alignment image  18  to produce an electrical signal corresponding to an optical density of the combined first diagnostic image and second diagnostic image. 
   This process is repeated. Each time the process is repeated, the particular printhead used to print the second diagnostic image is horizontally repositioned relative to the previous position of the printhead by a horizontal offset. As a result, multiple optical densities representing different locations of the printhead used to print the second diagnostic image are detected. Based on these differing optical densities and their corresponding horizontal offsets, controller  38  determines a printhead horizontal error compensation value. This horizontal error compensation value is then used by controller  38  to calibrate and properly position the second portion of image forming points along scan axis  40  during printing. 
   Print cartridges  24 ,  26  and  28  (schematically shown) are substantially identical to one another, except for different inks or ink combinations contained within the print cartridges. In particular, each of print cartridges  24 ,  26  and  28  generally comprises an inkjet print cartridge having a printhead  62  and a plurality of distinct chambers  64  which communicate with the printhead  62 . Printhead  62  includes a plurality of individual image forming points, such as nozzles, wherein each chamber  60  is in communication with one or more of the plurality of nozzles. Based upon control signals from controller  38 , image forming material, such as ink, is dispensed from the chambers  64  through the nozzles of printhead  62  onto print medium  20 . 
   In the particular embodiment illustrated, each of print cartridges  24 ,  26  and  28  includes three chambers  64  in communication with printhead  62 . An example of a three chambered ink jet print cartridge that may be employed is disclosed in U.S. Pat. No. 5,969,739 by Altendorf et al. which issued on Oct. 19, 1999, the full disclosure of which is hereby incorporated by reference. In other embodiments, one or more of print cartridges  24 ,  26  and  28  may only include a single chamber carrying a single ink or other printing material. Although printer  22  is illustrated for use with three print cartridges, printer  22  may alternatively be configured for use with a greater or fewer number of such single or multi-chamber print cartridges. 
   In other embodiments, printing system  12  may utilize other sources of ink or printing material besides cartridges  24 ,  26  and  28 . For example, printing system  12  may alternatively utilize an off-axis ink supply fluid delivery system. In still other embodiments, printing system  12  may omit cartridges  24 ,  26  and  28  and may alternatively be configured to form images upon a medium using other image forming points other than nozzles of an ink jet printing system. For example, printing system  12  may alternatively use dye-sublimation, wherein printhead  62  includes image forming points comprising heating elements that vary in temperature. Printing system  12  may alternatively comprise a thermal wax printing system wherein printhead  62  includes image forming points comprising heated pins. In other embodiments, printing system  12  may comprise a thermal autochrome printing system in which printhead  62  has image forming points comprising individual heating elements that vary in temperature to activate different colors in the print medium. 
     FIGS. 2-5  illustrate four columns  200 ,  202 ,  204  and  206  of image forming points  208  located upon one or more printheads  62  and positioned relative to surface  210  of medium  20 . Although each of columns  200 ,  202 ,  204  and  206  are illustrated as including a total of 24 image forming points  208  for purposes of illustration, the actual number of image forming points  208  in a single column may be larger or smaller depending upon the particular kind of image forming points employed upon printhead  62  and the printing resolution achievable by printhead  62 . 
   For purposes of discussion, the total number of image forming points  208  of each of columns  200 ,  202 ,  204  and  206  are illustrated as being divided into four segments or portions  212 ,  214 ,  216  and  218 . Each portion  212 ,  214 ,  216  and  218  includes six image forming points and is mutually exclusive with respect to image forming points of the other portions. Although portions  212 ,  214 ,  216  and  218  are illustrated as being bounded by rectangular boxes, such boxes are solely used in the figures to distinguish and identify portions  212 ,  214 ,  216  and  218 . Furthermore, although portions  212 ,  214 ,  216  and  218  are illustrated as including six image forming points, the actual number of portion and number of image forming points within each portion may alternatively be larger or smaller in number. 
     FIG. 2  schematically illustrates one example of a printhead  62  having a column  200  of image forming points  208 . Column  200  of image forming points  208  is illustrated in alignment with no horizontal errors. In particular, there are no SAD errors in that image forming points  208  along an entire length of column  200  are aligned with one another so as to extend along a single axis  220 . No THETA Z errors exist in that axis  220 , along which image forming points  208  extend, is not tilted about an axis perpendicular to medium  20 . In the particular embodiment shown, when no horizontal errors exist, axis  220  extends perpendicular to scan axis  40 . 
     FIGS. 3-5  illustrate various horizontal errors that may occur as between image forming points of a single printhead or of multiple printheads.  FIG. 3  illustrates printhead  62  in which image forming points  208  do not have a SAD error but have a THETA Z error. Although image forming points  208  all extend along a common axis  224 , axis  224  is tilted about an axis perpendicular to the surface  210  of media  20 . Although column  202  is illustrated as being tilted such that each of portions of  212 ,  214 ,  216  and  218  are sloped in a leftward-leaning direction. Alternatively, portions  212 ,  214 ,  216  and  218  may be tilted and sloped in a rightward-leaning direction. 
   As shown by  FIG. 4 , column  204  includes SAD horizontal errors. In particular, image forming points  208  of column  204  are horizontally offset from one another by varying horizontal distances and in varying directions such that column  204  is curved. In the particular example illustrated in  FIG. 4 , portions  212  and  214  are each generally sloped in a leftward-leaning direction, while portions  216  and  218  are each generally sloped in a rightward-leaning direction as seen in  FIG. 4 . In an alternative example, column  204  may be curved or bowed in an opposite direction wherein portions  212  and  214  are sloped in a rightward-leaning direction while portions  216  and  218  are sloped in a leftward-leaning direction as seen in  FIG. 4 . 
   As shown by  FIG. 5 , image forming points  208  are horizontally offset from one another such that column  206  includes multiple SAD errors or multiple curved portions. In particular, portion  212  is leftward-leaning, portion  214  is rightward-leaning, portion  216  is rightward-leaning and portion  218  is leftward-leaning such that column  206  has a general S shape. 
     FIGS. 2-5  illustrate but a few examples of various horizontal errors that may occur along a single column of image forming points  208 , between portions of distinct columns on a single printhead or between portions of image forming points  208  of distinct columns on distinct printheads  62 . Such errors may be due to several factors, including manufacture and placement of the image forming points  208  on printhead  62  and the positioning of the one or more printhead  62  relative to medium  20  by a printhead supporting structure. For example, in printing system  12  shown and described with respect to  FIG. 1 , print cartridge location  42  of carriage  30  may undesirably support printhead  62  of cartridge  24  in a tilted orientation so as to introduce THETA Z errors. This may be the result of manufacturing tolerances or manufacturing errors. Sensor  37 , controller  38  and computer readable media  39  function as a diagnostic system to identify such errors and to also take remedial steps to correct for such errors during printing. 
     FIG. 6  is a diagram illustrating horizontal error distances resulting from image forming points being horizontally offset from their intended locations during printing either as a result of manufacturing tolerances or errors occurring during the manufacture of one or more of printheads  62  or as a result of one or more of printheads  62  being improperly supported in position relative to medium  20 .  FIG. 6  illustrates columns  200 ,  202  and  207  of image forming points  208 . As discussed above with respect to  FIG. 2 , column  200  is illustrated as having no horizontal errors. As discussed above with respect to  FIG. 3 , column  202  is illustrated as having a THETA Z error in that column  202  extends tilted in a leftward-leaning direction. Column  207  is similar to column  202  except that column  207  has a THETA Z error in which column  207  is tilted in a rightward-leaning direction. In the example shown, column  207  is tilted with an angle Θ 1  while column  202  is tilted with an angle of Θ 2 . Even though top end  240  of portions  212  of columns  202  and  207  are illustrated as being in horizontal alignment with nominal axis  241  along which each of image forming points  208  are intended to be located during printing, the lower ends  242  of portion  212  and the upper ends  242  of portion  214  are horizontally spaced from nominal axis  241  by horizontal error distances E 21  and E 11 , respectively. Such horizontal error distances E 21  and E 11  each equal to L sine Θ, wherein L is the linear length of the particular portion of the column. For example, horizontal error distance E 21  is equal to the linear length L of portion  212  sine Θ 2 . 
   As shown in the example diagram of  FIG. 6 , each succeeding portion has a larger horizontal error distance as compared to the preceding portions. Portion  214  of column  202  has an upper end  242  with a horizontal error distance E 21  and a lower end  244  with a horizontal error distance E 22 . As a result, images created by image forming points  208  from portion  214  of column  202  will be horizontally offset from images created by corresponding image forming points  208  from portion  212  of column  202  by a horizontal error distance of E 22  minus E 21 . Absent horizontal errors, portions  212  and  214  would both extend along nominal axis  241 . 
     FIGS. 7-9  illustrate the method by which sensor  37 , controller  38  and an optional computer readable media  39  diagnose a horizontal printhead error and determine a horizontal printhead error compensation value. As shown by  FIG. 7 , controller  38  generates control signals which cause media feed  34  to position medium  20  perpendicular to and in alignment with scan axis  40 . Controller  38  further generates control signals causing carriage drive  32  to move carriage  30  along scan axis  40  while portion  212  of column  202  of printhead  62  prints or forms a series of reference images  230 ,  232 ,  234 ,  236  and  238 . Each reference image  230 ,  232 ,  234 ,  236  and  238  includes a plurality of horizontally spaced individual marks  240 . Although each image  230 ,  232 ,  234 ,  236 ,  238  is illustrated as having two marks  240 , as indicated by broken lines  241 , each image  230 ,  232 ,  234 ,  236 ,  238  has a pattern of greater than two marks  240 . In one embodiment, each image  230 ,  232 ,  234 ,  236 ,  238  has at least twenty marks  240 . In other embodiments, a greater or fewer number of marks  240  may be formed. 
   In one embodiment, each of marks  240  is in the form of vertical line. In other embodiments, each mark  240  may have other configurations. Each mark  240  has a width W, and is spaced from an adjacent mark  240  of the same diagnostic image by a distance D 1 . 
   In the particular example shown, each mark  240  is formed by a single image-forming actuation of each of image-forming points  208  along portion  212 . In other examples, each mark  240  may be formed by multiple image-forming actuations of each image-forming point  208  and portion  212 . In addition, consecutive marks  240  of a particular diagnostic image  230 ,  232 ,  234 ,  236  or  238  may be horizontally spaced from one another by varying distances so long as the same non-uniform spacing of marks is employed during the formation of a second of a series of second diagnostic alignment images as described hereafter. 
   As shown by  FIG. 8 , controller  38  (shown in  FIG. 1 ) generates additional signals in response to reading instructions from computer readable media  39  or another source, to cause media feed  34  to move medium  20  so as to reposition medium  20  relative to printhead  62 . In particular, media feed  34  repositions medium  20  such that the horizontal series of reference images  230 ,  232 ,  234 ,  236  and  238  move into vertical alignment with portion  214  of image-forming points  208  of column  202  (i.e., horizontally across from or directly beneath portion  214 ). Control signals generated by controller  38  further cause carriage drive  32  to move carriage  30  along scan axis  40  as image-forming points  208  of portion  214  print or form a series of diagnostic alignment images  250 ,  252 ,  254 ,  256  and  258 . Diagnostic images  250 ,  252 ,  254 ,  256  and  258  correspond with and at least partially overlie reference images  230 ,  232 ,  234 ,  236  and  238 , respectively. Each pair of corresponding diagnostic images and reference images are referred to as patches. Each diagnostic image  250 ,  252 ,  254 ,  256  and  258  includes a plurality of horizontally spaced marks  260 . Although each image  250 ,  252 ,  254 ,  256 ,  258  is illustrated as having two marks  260 , as indicated by broken lines  261 , each image  250 ,  252 ,  254 ,  256 ,  258  has a pattern of greater than two marks  260 . In one embodiment, each image  250 ,  252 ,  254 ,  256 ,  258  has at least twenty marks  260 . In other embodiments, a greater or fewer number of marks  260  may be formed. 
   In the example shown, each of marks  260  of a particular diagnostic image  250 ,  252 ,  254 ,  256  and  258  are horizontally spaced from one another by a distance D 2 . Each of marks  260  has a width W 2 . In one embodiment, width W 2  is substantially equal to width W 1  and distance D 2  is substantially equal to distance D 1  with respect to marks  240 . The horizontal spacing between consecutive marks  260  of a particular diagnostic image  250 ,  252 ,  254 ,  256  and  258  may vary so long as the overall spacing pattern between marks  260  of a particular diagnostic image  250 ,  252 ,  254 ,  256  and  258  is identical to the overall spacing pattern of marks  240  of an underlying corresponding diagnostic image  230 ,  232 ,  234 ,  236  and  238 . 
   As further shown by  FIG. 8 , the marks  260  of diagnostic images  250 ,  252 ,  254 ,  256  and  258  are horizontally offset from their corresponding underlying marks  240  of reference images  230 ,  232 ,  234 ,  236  and  238 , respectively, by differing degrees. In particular, marks  240  of diagnostic image  234  are printed upon medium  20  with a zero offset value. Absent horizontal errors between image-forming points  208  of portions  212  and  214 , marks  260  of diagnostic image  254  printed with portion  214  will substantially horizontally overlap and align with the underlying marks  240  of reference image  234  when diagnostic image  254  is printed with a zero offset. In other words, the leftward edge and rightward edge of each mark  260  of image  254  will substantially align with the leftward edge and the rightward edge of its corresponding underlying mark  240  of reference image  234 . This would be the result had images  234  and  254  been printed using portions  212  and  214  of column  200  of printhead  62  (described above with respect to  FIG. 2 ) which does not include horizontal errors. However, because reference image  234  and diagnostic image  254  are printed utilizing portions  212  and  214  of column  202  of image-forming points  208  which have horizontal errors, marks  260  of diagnostic image  254  do not substantially overlap and align with the underlying marks  240  of reference image  234 . In particular, each of marks  260  printed by image-forming points  208  of portion  214  is horizontally misaligned with the corresponding underlying marks  240  of reference image  234  printed by image-forming points  208  of portion  212  by the horizontal error distance E 22  minus horizontal distance E 21  (explained in greater detail with respect to  FIG. 6 ). The slope or tilt of marks  240  and  260  of images  234  and  254  as well as the horizontal distance by which marks  260  of image  254  are horizontally misaligned with the corresponding underlying marks  240  of image  240  depends on the angle θ by which the particular column of image-forming points  208  is spaced from the nominal axis  241  (shown in  FIG. 6 ). For example, because column  202  has a leftward-leaning tilt, each of marks  234  and  260  is also leftward-leaning and each of marks  260  has a rightward-most edge  262  that extends to the right of the rightward-most edge  264  of the underlying mark  240 . 
   To determine a compensation value, multiple patches of corresponding reference and diagnostic images are printed across a range of varying offsets between the reference images and the corresponding diagnostic images. In other words, diagnostic images  230 ,  232 ,  236  and  238  are printed with respect to their underlying reference images  250 ,  252 ,  256  and  258 , respectively, at different offset values. Diagnostic image  250  has an offset value of −2, wherein each of marks  260  of image  250  is printed while the printhead providing portion  214  of column  202  is horizontally offset by two units of distance to the left from the horizontal position of the printhead when the corresponding marks  240  of the reference image  230  were printed. Diagnostic image  232  is printed with an offset value of −1, wherein each of marks  260  of image  252  is printed while the printhead providing portion  214  of column  202  is at a horizontal position 1 unit of distance to the left of portion  212  of column  202  when the corresponding underlying marks  240  of reference image  232  were printed. Diagnostic image  254  has an offset value of +1, wherein each mark  260  of image  254  is printed while the printhead providing portion  214  of column  202  is positioned 1 unit of distance to the right as compared to the location of portion  212  of column  202  when the corresponding underlying marks  240  of reference image  236  were printed. Diagnostic image  258  has an offset value of +2, wherein each of marks  260  of image  258  is printed while the printhead providing portion  214  of column  202  is horizontally offset two units of distance to the right of the horizontal position of portion  212  of column  202  when each of the corresponding underlying marks  240  of reference image  238  were printed. 
   As shown by  FIG. 9 , controller  38  (shown in  FIG. 1 ) further generates control signals which cause carriage drive  32  to move sensor  37  (shown in  FIG. 1 ) across each pair of diagnostic images printed at each of the offset distances (−2, −1, 0, 1, 2). In the particular embodiment illustrated, sensor  37  is moved across each of the pairs of diagnostic images after all of the diagnostic images have been printed. In alternative applications, sensor  37  is scanned or moved across each pair of diagnostic images at each offset value immediately following the actual printing of the individual pair of diagnostic images. 
   As sensor  37  is moved across each of the pairs of diagnostic images, sensor  37  detects an optical density of each pair of diagnostic images. Electrical signals representing the sensed optical density are transmitted to controller  38 . Based upon such sensed optical densities, controller  38  determines an horizontal printhead offset error compensation value. In particular, as shown in  FIG. 8 , as the extent to which each pair of diagnostic images align and overlap with one another is increased, the surface area of medium  20  which is not printed upon (i.e., the amount of white space) increases. A perfect alignment of a pair of diagnostic images which is the result of no horizontal errors would result in the greatest white space and the lowest optical density. 
   In the particular example, the inverse of each of the sensed optical densities  301 ,  302 ,  303 ,  304 ,  305  at each of the different offset distances (−2), (−1), zero, (+1) and (+2), respectively, are then fit to a smooth curve  306 . A maximum  307  of this curve is interpolated as shown in  FIG. 9 . The offset value corresponding to a maximum of the smooth fit curve is identified as the optimum horizontal printhead error compensation value for each of image forming points  208  of portion  214  of column  202 . 
   In lieu of forming a smooth fit curve to identify an optimum horizontal printhead error compensation value, controller  38  may alternatively identify the horizontal printhead error compensation value for portion  214  of column  202  based upon the sensed optical densities using other calculation techniques. For example, controller  38  may alternatively fit sensed optical density values to a smooth fit curve of optical density versus offset distances, wherein the offset value corresponding to the minimum of the curve is interpolated to determine the horizontal printhead error compensation value. In some other applications, the horizontal printhead error compensation value may be deemed to be the particular offset distance which corresponds to the lowest optical density without any interpolation being performed. Although the method illustrated in  FIG. 8  depicts five pair of diagnostic images having substantially uniformly varied offset distances with an equal number of diagnostic image pairs being printed in both directions relative to the zero offset, the method may alternatively include a greater or fewer number of such diagnostic pairs having non-uniformly spaced offset distances and having a total number of diagnostic image pairs that are non-symmetrically centered about a zero offset. 
   The overall process for identifying an optimum horizontal printhead error compensation value for portion  214  of column  202  with respect to portion  212  of column  202  is repeated for each of portions  216  and  218  with respect to portion  212  of column  202 . Likewise, horizontal printhead error compensation values may also be determined for each of portions  214 ,  216  and  218  with respect to portion  212  of columns  204  and  206 . These horizontal printhead error compensation values are utilized by controller  38  to calibrate the positioning of printhead  62  during printing. Controller  38  generates control signals based upon such horizontal printhead error compensation values which cause carriage drive  32  to move printhead  62  along scan axis  40  in such a way so as to account for the identified horizontal errors. 
     FIG. 10  illustrates the determination of a printhead error compensation value for image forming points by comparing two portions tilted in opposite directions such as with those portions of columns  204  and  206  (shown in  FIGS. 4 and 5 ). In the illustrated example, the horizontal error compensation value is determined for image forming points  208  of portion  218  of column  204  by comparing diagnostic images printed using portion  218  of column  204  with reference diagnostic images printed using portion  212  of column  204 . Controller  38  (shown in  FIG. 1 ) generates control signals which cause a reference diagnostic image  310  having marks  312  to be printed using portion  212  of column  204  (shown in  FIG. 4 ) upon a print medium. Controller  38  further generates control signals which cause media feed  34  to move medium  20  to position image  310  across from portion  218  of column  204  (shown in  FIG. 4 ). Thereafter, a diagnostic image  316  having marks  318  is printed using image forming points  208  of portion  218  of column  204 . This is done while portions  212  and  218  of printhead  62  are positioned at the same horizontal position along a nominal vertical axis by carriage drive  32 . 
   This process is repeated in an identical fashion except that a diagnostic image printed by portion  218  of column  204  is printed while the printhead  62  is horizontally offset from the first position or from the nominal axis by varying offset distances and directions with respect to a zero offset. For example,  FIG. 10  illustrates a second pair of diagnostic images including a third diagnostic image  320  having marks  322  printed by portion  212  of column  204  while printhead  62  is in a third horizontal position and a fourth diagnostic image  326  having marks  328  printed by portion  218  of column  204  while printhead  62  is at a third position horizontally offset from the first horizontal position. Because portions  212  and  218  are tilted in opposite directions, marks printed by portions  212  and  218  can never perfectly align and overlap with one another. However, as shown by  FIG. 10 , at a certain offset value, the extent of overlap and the extent of alignment between the pair of diagnostic images is maximized. This offset distance corresponds to or may be used to interpolate an optimum horizontal printhead compensation value for image forming points  208  of portion  218  with respect to the location of image forming points  208  of portion  212  which is used as a reference. 
     FIGS. 11-14  are timing diagrams illustrating printing of an image upon medium  20  using columns  200 ,  202 ,  204  and  206  of printhead  62  after the movement of printhead  62  by carriage  32  has been calibrated based upon the determined horizontal error compensation values for each of portions  214 ,  216  and  218  with respect to portion  212  of each of columns  200 ,  202 ,  204  and  206 .  FIGS. 11-14  illustrate the timing at which image forming points  208  of portions  212 ,  214 ,  216  and  218  of columns  200 ,  202 ,  204  and  206 , respectively, are actuated to an image forming state to form identical images.  FIG. 11  illustrates the creation of the image using column  200 . As noted above, column  200  is ideal in that it avoids THETA Z or SAD errors. As a result, the horizontal printhead error compensation values for each of portions  214 ,  216  and  218  is zero. In the particular illustration, image forming points  208  of portions  212 ,  214 ,  216  and  218  are simultaneously actuated to image forming states to form horizontally aligned vertical marks. 
     FIG. 12  illustrates the timing diagram for printing a vertical image using image forming points of column  202 . As described above, a negative offset distance and a negative horizontal error compensation value was determined for each of the image forming points  208  of portion  214  with respect to portion  212 . In this particular instance, the horizontal error compensation value corresponded to a horizontal distance of −1 unit of distance (shown in  FIG. 8 ). This negative horizontal error compensation value results in image forming points  208  of portion  214  being actuated to image forming state to form images upon medium  20  prior to the actuation of image forming points  208  of portion  212  of column  202 . Based upon this horizontal error compensation value, controller  38  (shown in  FIG. 1 ) generates control signals such that printing by image forming points  208  of portion  214  will occur at horizontal location X and that any printing by image forming points  208  of portion  212  will occur when printhead  62  is at horizontal location X plus one unit of distance.  FIG. 12  further illustrates either the relative timing at which image forming points  208  of portions  216  and  218  are actuated to an image forming state or the relative positioning of printhead  62  supporting portions  216  and  218  during printing of an image.  FIGS. 13 and 14  illustrate the same timing or relative horizontal location of printhead  62  for portions  212 ,  214 ,  216  and  218  of columns  204  and  206 . 
   Although the method described with respect to  FIGS. 2-10  involves printing a pair of diagnostic images using portions of a column of image forming points on a single printhead  62  to determine a horizontal error compensation value for one of the portions using the other of the portions as a reference, the method may also be applied by printing a pair of diagnostic images using distinct portions of image forming points from two distinct columns of a single printhead or of two distinct columns of different printheads.  FIGS. 15 and 16  illustrate the determination of a horizontal error compensation value for a first portion of image forming points  208  with reference to a second portion of image forming points contained in a distinct column. As shown by  FIG. 15 , controller  38  generates control signals which cause media feed  34  to position medium  20  across from columns  402  and  406  of image forming points  208 . For purposes of illustration only, columns  402  and  406  are illustrated as being divided into four portions  212 ,  214 ,  216  and  218 . Once medium  20  has been properly positioned, control signals generated by controller  38  (shown in  FIG. 1 ) cause carriage drive  32  to move columns  402  and  406  along scan axis  40  as a reference diagnostic image  430  having marks  432  is printed by image forming points  208  of portion  212  of column  402 . In particular applications, carriage drive  32  stationery positions column  402  opposite medium  20  as image forming points  208  of portion  212  are actuated to an image forming state. This temporary halting of movement carriage  30  by carriage drive  32  is extremely short in nature and is many times imperceptible. In other applications, carriage drive  32  may be configured to continuously transport column  402  along scan axis  40  as image forming points  208  are actuated to an image forming state. 
   Once diagnostic image  430  has been formed, controller  38  (shown in  FIG. 1 ) generates control signals that cause media feed  34  to reposition medium horizontally across from portion  216  of column  406 . Control signals generated by controller  38  further cause carriage drive  32  to move column  406  of image forming points  208  and to print second alignment diagnostic image  436  having marks  438 . In the particular example being illustrated in  FIGS. 15 and 16 , columns  402  and  406  are designed to extend along nominal axes  442  and  444 , respectively, separated by a nominal horizontal design distance D 3 . For example, distance D 3  may be the spacing between two columns on a single printhead or may be the spacing between two columns on two distinct printheads. When determining a horizontal error compensation value for portion  216  of column  406  with portion  212  of column  402  as a reference, controller  38  is configured to generate control signals for controlling movement of carriage drive  32  and positioning of the one or more printheads  62  providing columns  402  and  406  based upon distance D 3 . In the particular example, each mark  432  is printed while the one or more printheads is located at horizontal position X. Controller  38  generates control signals such that for each mark  432  printed by portion  212  of column  406 , a corresponding alignment mark  438  is printed by portion  216  while the one or more printheads is at a horizontal location X minus distance D 3 . 
   This overall process of printing a pair of diagnostic images (a reference diagnostic image and a alignment diagnostic image) is repeated at one or more additional offset distances from the zero offset. As described above, an optical density is detected for each of the combined pair of diagnostic images. Based on these optical densities, an optimal horizontal error compensation value is determined and is utilized by controller  38  to general control signals when printing non-diagnostic images using image forming points  208  of portion  216  of column  406 . 
   In the particular example described, each segment or portion of each pen is calibrated relative to a single reference segment or portion of a single pen for every print speed and every print direction. In the particular example described, the reference diagnostic image for the single reference segment is printed using a color having high contrast with LED colors employed. According to one example in which the image forming points are configured to dispense ink, a reference diagnostic image is formed or is printed using a portion of image forming points of a printhead that dispenses black ink. For calibrations between different printheads, the light emitting diode of sensor  37  has a high contrast with the color of the image formed by the second portion of image forming points which are being calibrated. When a column being calibrated which has nozzles that are interlaced relative to a reference column, a change in dot overlap with horizontal offsets is maximized while the impact of vertical trajectory errors is minimized. This is achieved by printing a second series of reference diagnostic images and alignment diagnostic images offset vertically to provide a vertical line to provide a series of vertical lines that are fully filled with no gaps. Alternatively, a vertical offset may be introduced so that the interlaced image forming points of the first portion of image forming points are in a vertically aligned relationship with a second portion of image forming points. 
   Overall, embodiments of the present method as carried out by printing system  12  following instructions from optional computer readable media  39  may be configured to align all portions or portions of all cartridges in all print directions and speeds to compensate for cartridge-to-cartridge, column-to-column, THETA Z, SAD shape and bidirectional errors at each print speed. Although embodiments of the method have been described with reference to printing system  12  which employs image forming points comprising nozzles of inkjet printhead  62 , the described embodiments may also be employed in other printing systems having other configurations or other types of image forming points. Although the method has been described for compensating for each of pen-to-pen, column-to-column, THETA Z, SAD shape and bi-directional errors, the method may alternatively be employed to compensate for fewer than all of these occurrences. 
   Although the present invention has been described with reference to example embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. For example, although different example embodiments may have been described as including one or more features providing one or more benefits, it is contemplated that the described features may be interchanged with one another or alternatively be combined with one another in the described example embodiments or in other alternative embodiments. Because the technology of the present invention is relatively complex, not all changes in the technology are foreseeable. The present invention described with reference to the example embodiments and set forth in the following claims is manifestly intended to be as broad as possible. For example, unless specifically otherwise noted, the claims reciting a single particular element also encompass a plurality of such particular elements.