Abstract:
A method for aligning a printhead to compensate for printhead roll when an image receiving member moves laterally during printing has been developed. The method includes generating at different times a plurality of marks in a process direction with different inkjets in a printhead and identifying relationships between marks in each plurality. Lateral motion is thereby detected and removed from the analysis identifying the magnitude of the roll corresponding to the locations of the marks in the pluralities of marks.

Description:
TECHNICAL FIELD 
       [0001]    The present disclosure relates to imaging devices that utilize inkjet printheads to form images on media, and, in particular, to the alignment of such printheads in printers. 
       BACKGROUND 
       [0002]    Ink jet printing involves ejecting ink droplets from orifices in a printhead onto an image receiving member to form an ink image. Inkjet printers commonly utilize either direct printing or offset printing architecture. In a typical direct printing system, ink is ejected from the inkjets in the printhead directly onto the final substrate. In an offset printing system, the printhead jets the ink onto an intermediate transfer surface, such as a liquid layer on a drum. The final substrate is then brought into contact with the intermediate transfer surface and the ink image is transferred to the substrate before being fused or fixed to the substrate. 
         [0003]    Alignment among multiple printheads may be expressed as the position of one printhead relative to the image receiving member, such as a media substrate or intermediate transfer surface, or another printhead within a coordinate system of multiple axes. For purposes of discussion, the terms “cross-process direction” and “X-axis direction” refer to a direction or axis perpendicular to the direction of travel of an image receiving member past a printhead within the plane of the image receiving member. The terms “process direction” and “Y-axis direction” refer to a direction or axis parallel to the direction of an the image receiving member, the term “Z-axis” refers to an axis perpendicular to the X-Y axis plane. 
         [0004]    One particular type of alignment parameter is printhead roll. As used herein, printhead roll refers to clockwise or counterclockwise rotation of a printhead about an axis normal to the image receiving member, i.e., the Z-axis. Printhead roll may result from mechanical vibrations and other sources of disturbances on the machine components that may alter printhead positions and/or angles with respect to the image receiving member. As a result of roll, the rows of nozzles may be arranged diagonally with respect to the process direction movement of the image receiving member. This roll may cause horizontal lines, image edges, and the like to be skewed relative to the image receiving member. If the printer controls for this skew using timing adjustments, roll can increase the magnitude of the adjustments required, potentially causing the system to run out of actuation latitude. Depending upon the arrangement of nozzles in the printhead, roll error may also produce cross-process direction uniformity defects in image areas of uniform ink density. 
         [0005]    Various methods are known to measure printhead roll and to calibrate the printhead to reduce or eliminate the effects of printhead roll on images generated by the printhead. The known methods include printing selected marks or test patterns onto the image receiving member from the printhead to identify printhead roll. In some imaging systems, the image receiving member moves in the cross-process direction while the printhead generates the test pattern. Even comparatively small movements in the image receiving member can result in errors in printed test patterns that reduce the effectiveness of known methods for detecting printhead roll. Thus, improvements to printhead measurement and calibration procedures for detecting printhead roll are desirable. 
       SUMMARY 
       [0006]    In one embodiment, a method of aligning a printhead has been developed. The method includes ejecting a first plurality of ink drops from a first inkjet in the printhead to form a first plurality of marks arranged in a process direction on an image receiving member, ejecting a second plurality of ink drops from a second inkjet in the printhead to form a second plurality of marks arranged in the process direction on the image receiving member, the ejection of the second plurality of ink drops beginning at a time that is later than a time at which the ejection of the first plurality of ink drops began, generating image data corresponding to the first plurality of marks and the second plurality of marks, identifying with reference to the image data a cross-process location of each mark in the first plurality of marks and each mark in the second plurality of marks on the image receiving member, identifying a first relationship between a relative cross-process location of each mark in the first plurality of marks with reference to a first mark in the first plurality of marks and a time at which each mark in the first plurality of marks was formed, identifying a second relationship between a relative cross-process location of each mark in the second plurality of marks with reference to a first mark in the second plurality of marks and a time at which each mark in the second plurality of marks was formed, the first mark in the second relationship having a relative cross-process direction location that corresponds to a relative cross-process direction location in the first relationship at a time at which the first mark in the second plurality of marks was formed on the image receiving member, generating an estimate of a cross-process direction offset of the image receiving member over time with reference to the first relationship and second relationship, identifying a relative cross-process direction offset of the image receiving member corresponding to each of the first plurality and second plurality of marks with reference to the estimate of the cross-process direction offset of the image receiving member over time and a time at which each mark was formed on the image receiving member, generating a corrected cross-process direction location for each mark in the first plurality of marks and the second plurality of marks with reference to the identified cross-process location of each mark and the identified cross-process direction offset of the image receiving member corresponding to each mark, identifying with reference to the corrected cross-process direction location of each mark in the first plurality of marks and second plurality of marks a plurality of cross-process direction distances between the first plurality of marks formed by the first inkjet and the second plurality of marks formed by the second inkjet, and identifying a difference between an angular orientation of the printhead and the cross-process direction with reference to the plurality of identified cross-process direction distances. 
         [0007]    In another embodiment, a method of operating a printer has been developed. The method includes generating with an optical sensor in the printer image data corresponding to an array of marks formed a plurality of inkjets in the printhead on an image receiving member that moves in a process direction, the array of marks including a plurality of series of marks arranged in a cross-process direction on the image receiving member, each series of marks being arranged in the process direction on the image receiving member and being formed by one inkjet in the plurality of inkjets that each form a first mark in the corresponding series of marks at a different time, identifying a relationship between relative cross-process locations of successive marks in each series of marks in the plurality of series of marks in the image data with reference to predetermined times at which each mark in each series of marks in the plurality of series of marks was formed, and generating an estimate of a cross-process direction movement of the image receiving member over time with reference to the identified relationships between the marks in each series of marks in the plurality of series of marks in the image data. 
         [0008]    In another embodiment, an inkjet printer has been developed. The printer includes a media transport configured to move a media web through a print zone in a process direction, a printhead positioned in the print zone and having a plurality of inkjets configured to eject ink drops onto the media web, a plurality of optical detectors configured in a cross-process direction across the image receiving member, each optical detector in the plurality of optical detectors being configured to detect light reflected from the image receiving member, and a controller operatively connected to the printhead and the plurality of optical detectors. The controller is configured to operate the plurality of inkjets in the printhead to form an array of marks on the media web, each inkjet in the plurality of inkjets forming one series of marks in the array of marks extending in the process direction and the array of marks including a plurality of series of marks extending in the cross-process direction, each inkjet in the plurality of inkjets commencing formation of a corresponding series of marks in the plurality of series of marks at a time that is different from a time at which at least one other inkjet commences formation of another one of the plurality of series of marks, generate image data corresponding to the array of marks with the plurality of optical detectors, identify a cross-process direction location of each mark in the array of marks with reference to the image data, identify a relationship between relative cross-process locations of successive marks in each series of marks in the plurality of series of marks in the image data with reference to predetermined times at which each mark in each series of marks was formed, generate an estimate of a cross-process direction movement of the media web over time with reference to the relationship for each series of marks in the plurality of series of marks in the image data, generate a corrected cross-process direction location for each of the series of marks in the array of marks with reference to the identified cross-process location of each mark and an estimated cross-process direction offset of the media web at a time at which each mark was formed with reference to the estimate of cross-process direction movement of the media web, identify with reference to the corrected cross-process direction location of each mark in the array of marks a cross-process direction distance between a first series of marks and at least one other series of marks, and identify a difference between an angular orientation of the printhead and the cross-process direction with reference to the identified cross-process direction distance. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    The foregoing aspects and other features of a printer that detects and compensates for roll in one or more printheads in the printer are explained in the following description, taken in connection with the accompanying drawings. 
           [0010]      FIG. 1A  is a view of a printhead with a plurality of inkjets aligned with a cross-process direction. 
           [0011]      FIG. 1B  is a view of the printhead of  FIG. 1A  with an exaggerated angular offset from the cross-process direction. 
           [0012]      FIG. 2  is a schematic view of a direct printer that includes a plurality of printheads. 
           [0013]      FIG. 3  is a depiction of a plurality of printheads in the direct printer of  FIG. 1  including a test pattern formed by one printhead in the plurality of printheads. 
           [0014]      FIG. 4  is a block diagram of a process  400  for identifying and correcting cross-process direction motion of a media web and for identifying printhead roll. 
           [0015]      FIG. 5  is a diagram depicting relative cross-process direction offsets over time between dashes in a test pattern formed by a plurality of inkjets in a printhead. 
           [0016]      FIG. 6  is a diagram depicting one series of cross-process direction offsets from one inkjet that are arranged in series with the cross-process direction offsets of another inkjet where portions of the dashes formed by both inkjets are formed during a common time period. 
           [0017]      FIG. 7  is a diagram depicting the cross-process direction offsets from each inkjet in  FIG. 5  arranged in a single series. 
           [0018]      FIG. 8  is a diagram depicting cross-process direction error compared to the nominal position of inkjets in a printhead. 
       
    
    
     DETAILED DESCRIPTION 
       [0019]    For a general understanding of the present embodiments, reference is made to the drawings. In the drawings, like reference numerals have been used throughout to designate like elements. As used herein, the terms “printer” generally refer to an apparatus that applies an ink image to print media and may encompass any apparatus, such as a digital copier, bookmaking machine, facsimile machine, multi-function machine, etc., which performs a print outputting function for any purpose. As used in this document, “ink” refers to a colorant that is liquid when applied to an image receiving member. For example, ink may be aqueous ink, ink emulsions, melted phase change ink, and gel ink that has been heated to a temperature that enables the ink to be liquid for application or ejection onto an image receiving member and then return to a gelatinous state. “Print media” can be a physical sheet of paper, plastic, or other suitable physical substrate suitable for receiving ink images, whether precut or web fed. A printer may include a variety of other components, such as finishers, paper feeders, and the like, and may be embodied as a copier, printer, or a multifunction machine. An ink image generally may include information in electronic form, which is to be rendered on print media by a marking engine and may include text, graphics, pictures, and the like. 
         [0020]    The term “printhead” as used herein refers to a component in the printer that is configured to eject ink drops onto the image receiving member. A typical printhead includes a plurality of inkjets that are configured to eject ink drops of one or more ink colors onto the image receiving member. The inkjets are arranged in an array of one or more rows and columns. In some embodiments, the inkjets are arranged in staggered diagonal rows across a face of the printhead. Various printer embodiments include one or more printheads that form ink images on the image receiving member. 
         [0021]    As used herein, the term “dash” refers to a mark formed on an image receiving member that includes a series of ink drops extending in the process direction formed by a single inkjet in a printhead. A dash can be formed from ink drops located in adjacent pixels in the process direction on the image receiving member and can include a pattern of on/off adjacent pixels in the process direction. As used herein, the term “pixel” refers to a location on the image receiving member that receives an individual ink drop from an inkjet. Locations on the image receiving member can be identified with a grid-like pattern of pixels extending in the process direction and cross-process direction on the image receiving member. As used herein, the term “test pattern” refers to a predetermined arrangement of markings formed on an image receiving member by one or more printheads in the printer. In some embodiments, a test pattern includes a predetermined arrangement of a plurality of dashes formed by some or all of the inkjets in the printheads arranged in the print zone. 
         [0022]      FIG. 1A  depicts a printhead  100  including a plurality of inkjets exemplified by inkjets  1 - 16 . The inkjets are formed in a plurality of diagonal rows, with  FIG. 1  depicting a group of sixteen inkjets in the printhead  100  with one diagonal row including even-numbered inkjets  2 ,  4 ,  6 ,  8 ,  10 ,  12 ,  14 , and  16  and another diagonal row including odd numbered inkjets  1 ,  3 ,  5 ,  7 ,  9 ,  11 ,  13 , and  15 . In one configuration, each inkjet in the printhead  100  is configured to eject ink having a single color onto an image receiving member. In another configuration, the printhead  100  is a multi-color printhead where selected groups of inkjets emit ink drops having different colors of ink. In one configuration of a multi-color printhead, the even-numbered inkjets  2 - 16  eject ink having one color and the odd numbered inkjets  1 - 15  eject ink having a different color. While printhead  100  is depicted with sixteen inkjets for illustrative purposes, alternative printheads include hundreds or thousands of inkjets. In one embodiment, a printhead includes 880 inkjets and in one operating mode groups of sixteen inkjets in the printhead similar to the configuration of  FIG. 1A  form test patterns on the image receiving member. The inkjets  1 - 16  in the printhead  100  are operated in a predetermined order to form a test pattern with a plurality of dashes on an image receiving member. 
         [0023]    In the printhead  100 , the inkjets arranged along each diagonal are separated from each other by a predetermined distance in the process direction  224  and another predetermined distance in the cross-process direction. For example, inkjets  3  and  13  are separated by a predetermined process direction distance  120 , and cross-process direction distance  122 . The structure of the printhead  100  and density of the inkjets in the printhead determine the cross-process and process direction distances between the inkjets. In the embodiment of the printhead  100 , all of the inkjets are formed with uniform separation in the cross-process direction  122  between the inkjets. 
         [0024]      FIG. 1B  depicts the printhead  100  of  FIG. 1A  with an angular orientation that alters the distance between inkjets in the cross-process direction. In the configuration of  FIG. 1B , the printhead  100  is said to have a printhead roll. The printhead roll is depicted by an angle of rotation  132  between the printhead  100  and the cross-process direction  128 . The magnitude of the angle  132  is typically measured in degrees or radians. The direction of the angle  132  refers to whether the printhead  100  rolls in a clockwise or counter-clockwise direction, which can also be expressed as positive or negative values of the sign of the angle  132 . 
         [0025]    In  FIG. 1B , the printhead  100  rotates in a counter-clockwise direction. The cross-process direction distance between the inkjets  3  and  13  in the orientation of  FIG. 1B  is depicted by distance  126 . A second distance  127  depicts a difference between the cross-process distance  126  and the nominal cross-process distance  122  between the inkjets  3  and  13  from  FIG. 1A  where there printhead  100  is aligned in the cross-process direction. In the configuration of  FIG. 1B , the cross-process distance  126  is smaller than the predetermined cross-process distance  122  of the aligned printhead. In orientations where the printhead  100  experiences roll in a clockwise direction, the cross-process distance between corresponding inkjets is larger than the predetermined distance  122 . Printhead roll affects the cross-process direction distance between any two inkjets in the printhead  100 . As described in more detail below, both the magnitude and direction of the printhead roll are identified with reference to the measured cross-process distance between two or more inkjets compared to the predetermined cross-process distance between the inkjets when the printhead is aligned with the cross-process direction. 
         [0026]    The magnitude of the printhead roll depicted in  FIG. 1B  is exaggerated for illustrative purposes. In a typical printer embodiment, the printhead roll is on the order of approximately 0.001 to 0.01 radians. The systems and method described herein are suitable for identifying and correcting printhead roll over a wide range of angular displacements and printhead resolutions. 
         [0027]      FIG. 2  depicts an exemplary embodiment of a printer  200  that is configured to identify and correct printhead roll. Printer  200  is a continuous web printer that includes six print modules  202 ,  204 ,  206 ,  208 ,  210 , and  212 ; a media path configured to accept a print medium  214 , and a controller  228 . The print modules  202 ,  204 ,  206 ,  208 ,  210 , and  212  are positioned sequentially along the media path and form a print zone in which ink images are formed on a print medium  214  as the print medium  214  moves past the print modules in a process direction  224 . In the embodiment of the printer  200 , the print medium  214  is an elongated medium, such as a roll of paper, which unrolls through the media path in a web-like configuration and is commonly known as a media web. The print modules  202 - 212  print ink drops directly on the media web  214  as the media web  214  moves through the print zone, and the media web is the image receiving member in the embodiment of printer  200 . 
         [0028]    In printer  200 , each print module  202 ,  204 ,  206 ,  208 ,  210 , and  212  in this embodiment provides an ink of a different color. In all other respects, the print modules  202 - 212  are substantially identical. Print module  202  includes two print sub-modules  240  and  242 . Print sub-module  240  includes two print units  244  and  246 . The print units  244  and  246  each include an array of printheads that may be arranged in a staggered configuration across the width of both the first section of the web media and second section of web media. Each of the printheads includes a plurality of inkjets in a configuration similar to the printhead  100  depicted in  FIG. 1 . In a typical embodiment, print unit  244  has four printheads and print unit  246  has three printheads. The printheads in print units  244  and  246  are positioned in a staggered arrangement to enable the printheads in both units to emit ink drops in a continuous line across the width of media path at a predetermined resolution. 
         [0029]    Print sub-module  242  is configured in a substantially identical manner to sub-module  240 , but the printheads in sub-module  242  are offset by one-half the distance between the inkjets in the cross-process direction from the printheads in sub-module  240 . The arrangement of sub-modules  240  and  242  enables a doubling of linear resolution for images formed on the media web  214 . For example, if each of the sub-modules  240  and  242  ejects ink drops at a resolution of 300 drops per inch, the combination of sub-modules  240  and  242  ejects ink drops at a resolution of 600 drops per inch. 
         [0030]    The printer  200  includes an optical sensor  238  that generates image data corresponding to light reflected from the media web  214  after the media web  214  has passed through the print zone. The optical sensor  238  is configured to detect, for example, the location, intensity, and/or location of ink drops jetted onto the receiving member by the inkjets of the printhead assembly. The optical sensor  238  includes an array of optical detectors mounted to a bar or other longitudinal structure that extends across the width of the media web  214  in the cross-process direction. 
         [0031]    In one embodiment in which the media web  214  is approximately twenty inches wide in the cross process direction and the print modules  202 - 212  print at a resolution of 600 dpi in the cross process direction, over 12,000 optical detectors are arrayed in a single row along the bar to generate a single scanline across the imaging member. The optical detectors are configured in association with one or more light sources that direct light towards the surface of the image receiving member. The optical detectors are arranged in the optical sensor  238  in a predetermined configuration in the cross-process direction. Consequently, the cross-process location of light reflected from the media web  214  can be identified with reference to the optical detector that detects the reflected light. For example, if two optical detectors in the optical sensor  238  detect light reflected from two different ink drops on the media web  214 , then the predetermined distance that separates the optical detectors in the optical sensor  238  corresponds to the cross-process distance between the two ink drops on the media web  214 . 
         [0032]    The optical detectors receive the light generated by the light sources after the light is reflected from the image receiving member. The magnitude of the electrical signal generated by an optical detector in response to light being reflected by the bare surface of the image receiving member is larger than the magnitude of a signal generated in response to light reflected from a drop of ink on the image receiving member. This difference in the magnitude of the generated signal can be used to identify the locations of ink drops on an image receiving member, such as a paper sheet, media web, or print drum. The magnitudes of the electrical signals generated by the optical detectors are converted to digital values by an appropriate analog/digital converter. The digital values are denoted as image data in this document and a processing device, such as controller  228  executing programmed instructions, analyzes the image data to identify location information about dashes formed by ink drops on the image receiving member. 
         [0033]    During operation, the media web  214  moves through the media path in process direction  224 . The media web  214  unrolls from a source roller  252  and passes through a brush cleaner  222  and a contact roller  226  prior to entering the print zone. The media path moves the media web  214  through the print zone past the print modules  202 - 212  with various rollers including a pre-heater roller  218 , backer rollers, exemplified by backer roller  216 , apex roller  219 , and leveler roller  220 . The media web  214  then passes through a heater  230  and a spreader  232  after passing through the print zone. The media web passes an exit guide roller  234  and then winds onto a take-up roller  254 . The media path including the rollers  216 - 220  depicted in  FIG. 2  is exemplary of one media path configuration in a web printing system, but various different configurations also lead the web past different rollers and other components. Alternative embodiments use media path configurations that include a duplexing unit that enables the printer  200  to form ink images on both sides of the media web  214 . 
         [0034]    The media web  214  may experience oscillations in the cross-process direction as the media web moves through the printer  200 . During a printing operation, the web  214  oscillates on the apex roll  219  due to axial and/or radial run out of the apex roll  219 . Run out refers to any deviation in the rotational motion of the apex roll  219  from a uniformly circular rotation about a longitudinal axis of the roller. Consequently, cross-process direction position of the web  214  changes as the media web  214  moves past the print modules  202 - 212 . In one configuration, the media web oscillates in the cross-process direction with a frequency of approximately 8 Hz and a magnitude of 30 μm. The oscillations can reduce the accuracy of absolute location measurements made with reference to the image data generated by the optical sensor  238  because the optical sensor  238  remains stationary while the media web  214  oscillates. 
         [0035]    Controller  228  is configured to control various subsystems, components and functions of printer  200 . The controller  228  is operatively connected to each of the printheads in the print modules  202 - 212  to control ejection of ink from each of the print modules  202 - 212 . The controller  228  is connected to each of the printhead roll actuators, and adjusts the roll of each printhead in a clockwise or counterclockwise direction by operating a corresponding actuator. The controller  228  is also connected to optical sensor  238  and the controller  228  receives digital image data that the optical sensor  238  generates from light reflected from the media web  214 . 
         [0036]    In various embodiments, controller  228  is implemented with general or specialized programmable processors that execute programmed instructions. These components can be provided on a printed circuit card or provided as a circuit in an application specific integrated circuit (ASIC). Each of the circuits can be implemented with a separate processor or multiple circuits can be implemented on the same processor. Alternatively, the circuits can be implemented with discrete components or circuits provided in VLSI circuits. Also, the circuits described herein can be implemented with a combination of processors, ASICs, discrete components, or VLSI circuits. 
         [0037]    Controller  228  is operatively coupled to the print modules  202 - 222  and controls the timing of ink drop ejection from the print modules  202 - 212  onto the media web  214 . The controller  228  generates a plurality of electrical firing signals for the inkjets in each of the print modules  202 - 212 . The controller  228  is configured to generate a predetermined sequence of firing signals for at least one of the printheads in the print modules  202 - 212  to generate test pattern ink marks on the media web  214 . Various configurations of test patterns formed on the media web  214  enable the controller  228  to identify printhead roll of the printheads in the print modules  202 - 212 . 
         [0038]      FIG. 3  depicts the print units  244  in the printer  200  including one printhead  300  that experiences printhead roll. The printhead  300  is rotated in a counter-clockwise direction about an axis  340  that is perpendicular to the surface of the media web  214 . Printhead  300  shares the same configuration as the printhead  100  and includes the arrangement of inkjets  1 - 16  depicted in  FIG. 1A  and  FIG. 1B .  FIG. 3  depicts a top view of the printhead  300  printing downward onto the media web  214 . The controller  228  operates inkjets in the printhead  300  to form a test pattern  320  on the media web  214  as the media web  214  moves in the process direction  224 . 
         [0039]    The test pattern  320  includes five groups of dashes  322 A- 322 E. Each series of dashes in the test pattern  320  is formed by one of the inkjets in the printhead  300 . In the test pattern  320  each inkjet forms a series of ten dashes extending in the process direction  224 , although alternative test patterns including a different number of dashes in each series of dashes can be used. In the exemplary configuration of  FIG. 3 , the group of dashes  322 A includes dashes formed by four inkjets while the groups  322 B- 322 E each include dashes formed by three inkjets. One alternative test pattern includes four groups of dashes that are each formed by four different inkjets. Various other test patterns can be used that provide sufficient spacing between the dashes to enable an optical sensor to detect and distinguish each of the separate dashes in the test pattern. 
         [0040]    Inkjets that form each group of dashes  322 A- 322 E are operated at different times to form the dashes in a series of rows that are substantially parallel with the cross-process axis  316 . Referring to both  FIG. 1A ,  FIG. 1B , and  FIG. 3 , the inkjets  1 - 16  in the printhead  300  are arranged in a diagonal direction and operate at different times to form each group of dashes  322 A- 322 E in the test pattern  320 . The firing order of each of the inkjets  1 - 16  is depicted in parenthesized numbers in  FIG. 1A  and  FIG. 1B . In the example of  FIG. 3 , the inkjets operate to form the test pattern  320  in the following order:  1 ,  9 ,  2 ,  10 ,  12 ,  11 ,  4 ,  6 ,  14 ,  3 ,  13 ,  16 ,  5 ,  7 ,  15 ,  8 . During the time that each inkjet forms each series of dashes, at least one other inkjet also ejects ink drops onto the media web  214  to form part of another series of dashes. For example, after inkjet  1  begins forming a first series of dashes in the group of dashes  322 A, inkjet  9  begins forming a series of dashes in the group of dashes  322 D. Even though the two series of dashes are not in the same group of dashes, both of the inkjets  1  and  9  operate at approximately the same time while forming some of the dashes in each respective series of dashes. Inkjet  1  begins forming dashes before inkjet  9  begins forming dashes, and inkjet  9  ends forming dashes after inkjet  1  ends forming dashes. Similarly, inkjet  2  begins forming dashes after inkjet  9  has started forming dashes and ends after inkjet  9  finishes forming dashes, and the remaining inkjets continue printing in a similar manner. Thus, the time period during which each inkjet forms dashes on the media web  214  overlaps a portion of the time period during which at least one other inkjet in the printhead  300  forms dashes on the media web  214 . 
         [0041]    The media web  214  moves past the printhead  300  in the process direction  224  as the printhead  300  prints the test pattern  320 . As described above, the media web  214  can oscillate in either direction along the cross-process direction axis  316  while the inkjets  1 - 16  in the printhead  300  print the dashes in the test pattern  320 . The oscillation of the media web  214  produces an apparent offset of the cross-process location of dashes within each series of dashes and between different series of dashes that are printed on the media web  214 .  FIG. 3  depicts an exaggerated set of apparent cross-process direction offsets that the oscillation of the media web  214  induces in the test pattern  320 . While the inkjets in the printhead  300  do not move appreciably during formation of the test pattern  320 , the movement of the media web  214  changes the actual cross-process distance that separates each series of dashes in the test pattern. In one embodiment, the magnitude of the oscillation of the media web is approximately 30 μm. Since each series of dashes begins printing at a different time, the magnitude and direction of the cross-process error is often different for each series of dashes. In the example of  FIG. 3 , the first series of dashes ( 1 ) formed by inkjet  1  has an apparent drift to the right on the image receiving member  214  generated by movement of the image receiving member to the left on the cross-process axis  316 . The twelfth series of dashes ( 12 ) formed by inkjet  16  begins printing a later time after the media web  214  has started to oscillate to the right on the cross-process axis  316 , and the series of dashes ( 12 ) appears to drift to the left on the cross-process axis  316 . The oscillation of the media web  214  introduces different offset errors to each series of dashes in the test pattern  320  that varies over time as the printhead  300  prints the test pattern  320 . Since the identification of printhead roll is based on the difference between a predetermined cross-process direction distance between inkjets in the printhead and the measured cross-process direction distance between dashes formed by two or more inkjets in the printhead, the oscillation of the media web  214  can produce measurements of the distance differences that affect the accurate identification of the printhead roll. 
         [0042]      FIG. 4  depicts a process  400  for identifying cross-process direction movement of the media web  214  using image data generated from the test pattern  320  and for correcting errors introduced by varying offsets of the oscillating media web  214  during identification of printhead roll. Process  400  is described with reference to the printer  200 , printhead  300 , and test pattern  320  depicted in  FIG. 2-FIG .  3 . Process  400  begins by operating a printhead to form a test pattern on an image receiving member with a plurality of inkjets in a single printhead (block  404 ). In the printer  200 , one of the printheads, such as printhead  300 , prints a test pattern, such as test pattern  320 , on the media web  214 . The printer then generates image data of the printed test pattern (block  408 ). In the printer  200 , the optical sensor  328  generates a two-dimensional arrangement of image data corresponding to the test pattern  320  on the media web  214 . The image data include pixel locations of each mark in the test pattern, including each of the dashes in the test pattern  320 . 
         [0043]    Process  400  identifies the series of dashes in the image data corresponding to the first inkjet in the printhead that started printing the test pattern (block  412 ). In the printhead  300 , inkjet  1  begins printing the test pattern  320  with a first series of dashes ( 1 ) in the dash group  322 A. Since each series of dashes in the test pattern is generated with a predetermined sequence of firing signals, the controller  228  in printer  200  associates the image data of each series of dashes in the test pattern  320  with the corresponding inkjet that formed the series of dashes, including the first inkjet. Process  400  also uses the time at which the first inkjet begins printing marks on the image receiving member as a reference for identifying the relative time at which the other inkjets in the printhead  300  begin forming marks in the test pattern. 
         [0044]    Once the first series of dashes are identified in the image data, process  400  identifies differences in the cross-process direction locations of the dashes in the series of dashes formed by the first inkjet (block  416 ). In  FIG. 3 , the first inkjet  1  in the printhead  300  prints a series of dashes beginning with dash  332  and ending with dash  334 . The controller  228  identifies the cross-process direction location of each dash with reference to the image data corresponding to the first dash  332 . The relative change in cross-process location of the successive dashes in the first series of dashes corresponds to cross-process direction movement of the media web  214  during the time when the first inkjet formed the first series of dashes. Process  400  identifies a relationship through the relative cross-process direction locations of the dashes in the first series of dashes starting from the first dash  332  (block  420 ). In the printer  200 , the controller  228  identifies the relationship as a curve fit through the identified cross-process direction location of each dash in the first series of dashes in the image data. In one embodiment, the curve fit is plotted as a function of relative error in the cross-process direction with reference to the first dash in the series with reference to time.  FIG. 5  depicts the relative cross-process direction errors for each series of dashes in the test pattern  320 , with relationship  501  indicating the cross-process error for the series of dashes formed by inkjet  1 . The first dash  332  is plotted at time zero with zero relative cross-process direction error as a reference for each of the other dashes in the test pattern. Process  400  can identify various relationships through the dashes using one or more methods known to the art, including, but not limited to, linear regressions, linear and polynomial interpolations, and splines. 
         [0045]    Process  400  continues in an iterative manner through image data corresponding to each series of dashes in the image data of the test pattern  320 . Process  400  identifies a next series of dashes in the image data from the next inkjet to operate in the printhead when forming the test pattern  320  (block  424 ), identifies the difference in the cross-process direction locations of the dashes in the next series of dashes (block  428 ), and identifies a relationship of the relative error in the cross-process locations of the next series of dashes (block  432 ). Process  400  continues with the processing of blocks  424 - 432  being performed for the next series of dashes in substantially the same manner as blocks  412 - 420 , respectively, were performed. In the test pattern  320 , the next series of dashes refers to the dashes formed by the next inkjet to begin printing dashes on the image receiving member with reference to time. In the example of printhead  300 , after the first inkjet  1  begins printing dashes, the next inkjet to begin printing is inkjet  9 , which is then followed by inkjet  2 , etc., as described above.  FIG. 5  depicts the curve fits for each series of dashes in the test pattern  320  arranged according to the time at which each inkjet in the printhead  300  begins forming dashes in the test pattern  320 . Curves  501 ,  509 ,  502 ,  510 ,  512 ,  511 ,  504 ,  506 ,  514 ,  503 ,  513 ,  516 ,  505 ,  507 ,  515 , and  508  correspond to inkjets  1 ,  9 ,  2 ,  10 ,  12 ,  11 ,  4 ,  6 ,  14 ,  3 ,  13 ,  16 ,  5 ,  7 ,  15 , and  8  in the printhead  300 , respectively. 
         [0046]    After identifying the curve fit for the next series of dashes, process  400  moves the identified curve fit of the next series of dashes with reference to the relative cross-process direction error of the previous curve fit (block  436 ). For example, in  FIG. 5  the curve fit  501  for the relative cross-process direction errors for dashes from inkjet  1  and the curve fit  509  for the relative cross-process direction errors for dashes from inkjet  9  are the previous and next curve fits, respectively. Inkjet  9  begins printing after inkjet  1  but before inkjet  1  completes printing the first series of dashes. As indicated in  FIG. 5 , some of the dashes formed by inkjet  9  are formed at approximately the same time as dashes formed by inkjet  1 . Process  400  adds the relative cross-process error identified in the curve fit  501  to the curve fit  509  to adjust the relative cross-process direction error for dashes formed by inkjet  9  with reference to the dashes formed by inkjet  1 .  FIG. 6  depicts the curve  509  after the relative cross-process direction error from the curve fit  501  is added to the curve  509 . 
         [0047]    Process  400  continues in an iterative manner through blocks  424 - 436  for each additional dash series in the image data (block  440 ). For example, after performing blocks  424 - 436  for the series of dashes formed by inkjet  9 , process  400  continues for the series of dashes formed by inkjet  2  using the curve fit  509  identified for the dashes formed by inkjet  9  as the previous series of dashes. The curve fit identified for each series of dashes is added to the sum of the identified cross-process direction errors for all of the preceding dash series. 
         [0048]    After processing each series of dashes in the image data corresponding to the test pattern (block  440 ), process  400  identifies a function that estimates the varying offset of the media web in the cross-process direction during the time that the printer printed the test pattern on the media web (block  444 ). As used herein, the term “function” in the context of estimating the cross-process direction offset of the media web refers to a mathematical relationship that assigns a single value of a dependent variable to a range of values of an independent variable. In some embodiments of process  400 , the independent variable in a function represents a range of time and the dependent variable represents the cross-process direction offset of the media web  214 . The function generates a single value of the cross-process direction offset of the media web  214  for a given value of time. Other functions can include multiple dependent variables, each of which has a single value for a given value of an independent variable. 
         [0049]    In one embodiment, process  400  identifies a polynomial function, such as a third-order polynomial function that estimates the cross-process direction motion of the media web over time.  FIG. 7  depicts a curve  704  corresponding to a polynomial fit through the adjusted curves for each series of dashes beginning with the curve  501  corresponding to the image data of the dash series formed by inkjet  1 . The curve  704  depicts the cross-process motion of the media web  214  over time as the test pattern  320  is printed on the media web  214 . The exemplary polynomial curve  704  depicts a situation in which the media web  214  is moving in one cross-process direction as the printhead  300  begins to print the test pattern  320 , and then reverses direction prior to completion of the test pattern. In various situations the cross-process direction offset of the media web may change at a comparatively constant rate, at an accelerating or decelerating rate, or reverse one or more times while the test pattern is printed. 
         [0050]    Process  400  continues by generating corrected cross-process direction locations for one or more dashes in the image data of the test pattern  320  (block  448 ). Since each dash in the test pattern  320  is printed at a predetermined time, the correction process subtracts the relative error identified in the curve  704  from the cross-process direction location of the dash at the predetermined time when the dash was formed. Referring to the example of  FIG. 7 , if inkjet  1  ejects dash  334  formed by inkjet  1  in the test pattern  320  at a relative time of approximately 7.5 milliseconds, then the curve  704  estimates that the cross-process direction offset error of the media web is approximately 12 μm. The identified error of 12 μm is subtracted from the cross-process direction location of the dash  334  in the image data to generate a corrected location for the dash. The sign of the error indicates the direction in which the media web oscillates, with positive values indicating that the media web  214  oscillates in one direction on the cross-process axis  316 , and negative values indicating that the media web  214  oscillates in the opposite direction. The first dash in the test pattern, which is dash  332  in the test pattern  320 , is a reference dash and is not corrected. The cross-process direction locations of the remaining dashes in the test pattern  320  are corrected with reference to the first dash  332  using the curve  704 . In one embodiment, process  400  identifies the cross-process direction location of an inkjet as the average cross-process direction location of the corrected series of dashes printed by the inkjet to reduce or eliminate the effect of media web oscillation. 
         [0051]    While  FIG. 7  depicts an estimated polynomial function that generates a curve to estimate the cross-process direction offset of the media web  214  with respect to time, other embodiments of process  400  produce estimates of the media web offset using non-polynomial functions. For example, a Fourier expansion generates a series of sinusoidal (sine and cosine) functions that estimate the periodic cross-process direction offset of the media web  214 . The Fourier expansion generates an estimate of the oscillation of the media web  214  as a linear combination of a plurality of sinusoidal functions. Still other functions estimate the cross-process direction motion of the media web  214  in the frequency domain where the frequency of motion of the media web  214  is the independent variable in a function instead of time. Another estimation technique generates a spline fit through the cross-process direction position of the dashes in the test pattern with respect to time. In one embodiment of a spline fit, a least-squares cubic spline method generates a function that estimates the motion of the media web  214  with reference to the identified cross-process direction locations of the dashes in the image data. In one embodiment, the controller  228  in the printer  200  generates numerical estimates of the motion of the media web  214  with respect to time that correspond to one or more of the functions described above. The controller  228  corrects the identified cross-process direction locations for the dashes in the test pattern  320  with reference to the numerical estimates and the predetermined time of formation for each dash on the media web  214 . 
         [0052]    After generating the corrected cross-process direction locations for the dashes in the test pattern  320 , process  400  identifies a magnitude and direction of the angular roll of the printhead  300  (block  452 ). One exemplary process for identifying printhead roll is described in commonly-assigned U.S. patent application Ser. No. 12/413,817, which is entitled “Method and System for Detecting Print Head Roll,” and was filed on Mar. 30, 2009, the contents of which are expressly incorporated herein by reference. Process  400  identifies the magnitude and angular direction of the printhead roll from the average slope of the linear relationships generated for the measured errors in each printhead. The magnitude of the roll error angle θ is identified with the equation θ=arctan(m) where m is the identified average slope of the relationship between the measured cross-process direction error between two inkjets and the nominal process direction separation between the inkjets. Intuitively, the slope of the error line can be thought of as an angle of deviation from the expected slope of the diagonally arranged inkjets depicted in  FIG. 1A . Various alternative methods for identifying printhead roll are also suitable for use with the corrected cross-process direction locations identified for the dashes in the test pattern. One method identifies the printhead roll with reference to a difference between an average cross-process direction spacing between dashes formed by a series of odd numbered jets and dashes formed by a next even numbered jet in the printhead. Another method identifies the printhead roll with reference to a difference between an average cross-process direction spacing between dashes formed by a series of even numbered jets and dashes formed by a next odd numbered jet in the printhead. 
         [0053]      FIG. 8  depicts a plot of points  806 A- 806 D corresponding to a plot of the identified locations of corrected cross-process locations of inkjets in the printhead  300  compared to the expected cross-process direction distance between the inkjets in a printhead that is aligned in the cross-process direction.  FIG. 8  plots the deviation in cross-process direction distances between four inkjets, but alternative configurations use two or more inkjets to identify the printhead roll. Process  400  identifies the printhead roll from the slope m of the line  812 . As depicted in dashed lines, the uncorrected apparent locations of the inkjets  804 A- 804 D fit a second line  810  with a different slope m′. The difference between the slopes m and m′ represents the error in printhead roll measurement introduced by the oscillation of the media web  214  while the test pattern is printed. Process  400  reduces or eliminates the effect of the media web oscillation to enable accurate identification of the printhead roll. 
         [0054]    Process  400  identifies the direction of the rotation based on the direction of the average measured errors, which also corresponds to the sign of the average slope. In the example of  FIG. 3 , the printhead rolls in a counter-clockwise direction that reduces the measured cross-process distance between the selected inkjets, while a clockwise printhead roll increases the cross-process distance between the selected inkjets. Thus, the direction of errors, indicating either an increased or decreased distance between inkjets in the printhead, identifies the direction of the printhead roll. Since the sign of the slope of the linear error relationship  812  is generated based on the direction of the errors, a positive or negative sign of the slope indicates the direction of the printhead roll. The selected arrangement of inkjets in the printhead determines whether increases or decreases in the cross-process distance between inkjets indicate clockwise or counter-clockwise rotation of the printhead. 
         [0055]    Process  400  optionally corrects the identified roll of the printhead (block  456 ). In the printer  200 , an actuator  335  is operatively connected to the printhead  300  and selectively rotates the printhead  300  around the axis  340 . In some embodiments, the actuator  335  is an electrical stepper motor. The controller  228  operates the actuator to rotate the printhead  300  in an opposite direction of the identified roll. For example, if the controller  228  identifies that the printhead  300  is rotated 0.005 radians in the counterclockwise direction during process  400 , then the controller operates the actuator  335  to rotate the printhead by 0.005 radians in the clockwise direction to correct the roll. 
         [0056]    During operation, the printer  200  can perform process  400  periodically to identify and correct for printhead roll in one or more printheads in the print zone. In some configurations, the printer  200  performs process  400  for different printheads in the print zone concurrently, where each printhead prints a test pattern on a different area of the media web  214 . 
         [0057]    While process  400  is directed to identification and correction of printhead roll, the estimation of media web oscillation can be used to monitor the operation of various components in the printer as well. For example, the magnitude and frequency of the oscillation of the media web  214  provides an indication of the degree of run out in the apex roller  219 . In one embodiment, process  400  identifies the frequency and magnitude of the periodic motion of the rollers with a power spectral density (PSD) function in the frequency domain. 
         [0058]    The controller operating the printer identifies whether the magnitude or frequency of the identified oscillation exceeds predetermined operating parameters for the printer. For example, if the magnitude of the oscillation exceeds a certain value, such as 50 μm, then the oscillation may generate an unacceptable degradation in image quality. The controller  228  generates a visual or audible alert to inform an operator that the run out of the apex roller  219  exceeds a predetermined tolerance range. The apex roller  219  is subsequently serviced or replaced to eliminate the excessive run out and media web oscillation. 
         [0059]    It will be appreciated that various of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems, applications or methods. Various presently unforeseen or unanticipated alternatives, modifications, variations or improvements therein may be subsequently made by those skilled in the art, which are also intended to be encompassed by the following claims.