Patent Publication Number: US-2017355189-A1

Title: Printing method with multiple aligned drop ejectors

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Reference is made to commonly assigned, U.S. patent application Ser. No. ______, entitled: “Inkjet Printhead with Multiple Aligned Drop Ejectors”, by Mu et al. filed concurrently herewith, which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention pertains to the field of inkjet printing and more particularly to a drop ejector arrangement for high speed, high reliability, high resolution printing. 
     BACKGROUND OF THE INVENTION 
     Inkjet printing is typically done by either drop-on-demand or continuous inkjet printing. In drop-on-demand inkjet printing ink drops are ejected onto a recording medium using a drop ejector including a pressurization actuator (thermal or piezoelectric, for example). Selective activation of the actuator causes the formation and ejection of a flying ink drop that crosses the space between the printhead and the recording medium and strikes the recording medium. The formation of printed images is achieved by controlling the individual formation of ink drops, as is required to create the desired image. 
     Motion of the recording medium relative to the printhead during drop ejection can consist of keeping the printhead stationary and advancing the recording medium past the printhead while the drops are ejected, or alternatively keeping the recording medium stationary and moving the printhead. This former architecture is appropriate if the drop ejector array on the printhead can address the entire region of interest across the width of the recording medium. Such printheads are sometimes called pagewidth printheads. A second type of printer architecture is the carriage printer, where the printhead drop ejector array is somewhat smaller than the extent of the region of interest for printing on the recording medium and the printhead is mounted on a carriage. In a carriage printer, the recording medium is advanced a given distance along a medium advance direction and then stopped. While the recording medium is stopped, the printhead carriage is moved in a carriage scan direction that is substantially perpendicular to the medium advance direction as the drops are ejected from the nozzles. After the carriage has printed a swath of the image while traversing the print medium, the recording medium is advanced; the carriage direction of motion is reversed; and the image is formed swath by swath. 
     A drop ejector in a drop-on-demand inkjet printhead includes a pressure chamber having an ink inlet for providing ink to the pressure chamber, and a nozzle for jetting drops out of the chamber. Two side-by-side drop ejectors are shown in prior art  FIG. 1  (adapted from U.S. Pat. No. 7,163,278) as an example of a conventional thermal inkjet drop on demand drop ejector configuration. Partition walls  20  are formed on a base plate  10  and define pressure chambers  22 . A nozzle plate  30  is formed on the partition walls  20  and includes nozzles  32 , each nozzle  32  being disposed over a corresponding pressure chamber  22 . Ink enters pressure chambers  22  by first going through an opening in base plate  10 , or around an edge of base plate  10 , and then through ink inlets  24 , as indicated by the arrows in  FIG. 1 . A heater  35 , which functions as the actuator, is formed on the surface of the base plate  10  within each pressure chamber  22  and is configured to selectively pressurize the pressure chamber  22  by rapid boiling of a portion of the ink in order to eject drops of ink through the nozzle  32 . 
       FIG. 2  shows a prior art configuration of drop ejectors  60  disposed as a linear array  52  along an array direction  54  on a printhead  50 . For simplicity, only the pressure chamber  22  and the nozzle  32  are shown for each drop ejector  60 . The spacing between drop ejectors  60  in linear array  52  along array direction  54  is D y . Recording medium  62  and printhead  50  are moved relative to each other along scan direction  56 , and drop ejectors  60  are controllably fired to eject drops of ink toward recording medium  62 . Dots are formed on recording medium  62  where ink drops land. Allowable image dot locations  66  are defined by a pixel grid  64  including pixel rows  68  and pixel columns  70 . The spacing of pixel columns  70  from each other along the array direction is D y , which is the same as the spacing between drop ejectors  60  in linear array  52 . The spacing D x  of pixel rows  68  from each other along the scan direction  56  is related to the timing of firing of drop ejectors  60 . For recording medium  62  and printhead  50  moving at constant velocity V relative to each other along scan direction  56 , D x =Vt=V/f, where t is the time interval between consecutive firings of drop ejectors  60  and f is the drop ejection frequency. For many types of printheads  50 , drop ejectors  60  cannot be all fired simultaneously due to excessive electrical current requirements. In such cases, the linear array  52  is typically not actually a straight line. Rather the drop ejectors  60  are offset as needed in order to compensate for firing at different times so that the ink drops land along substantially straight pixel rows  68  on recording medium  62 . 
     Image resolution R x  along the scan direction  56  is equal to 1/D x =f/V. In other words, the print speed V=f/R x . For a desired image resolution along the scan direction, R x  is proportional to the drop ejector frequency f and inversely proportional to print speed. There are physical limitations to the drop ejection frequency f. For example, the pressure chamber  22  needs to refill with ink before a subsequent drop can be fired. 
     Image resolution R y  along the array direction  54  is equal to 1/D y . For a linear array  52 , in order to have a high resolution R y , the drop ejector spacing D y  needs to be small. Drop ejectors  60  of various types need to have a certain size to eject sufficiently large drops in order to provide good ink coverage on the recording medium  62 . A typical achievable drop ejector spacing D y  for a thermal inkjet drop ejector is 42.3 microns, equivalent to 600 nozzles per inch. By contrast, a typical achievable drop ejector spacing for a piezo inkjet printhead is approximately 254 microns, equivalent to 100 nozzles per inch. Conventional thermal inkjet printheads can provide 1200 spot per inch resolution R y  by providing two staggered linear arrays  52  of drop ejectors  60 . 
     In order to enable high resolution printing for larger drop ejectors, such as piezo drop ejectors, multiple offset rows of drop ejectors can be provided on a printhead, as seen in prior art  FIG. 3  adapted from U.S. Pat. No. 7,300,127. Rows of drop ejectors extend horizontally along array direction  54  in  FIG. 3 . Each drop ejector in the figure includes a pressure chamber  102  and a nozzle  100 - kl , where l indicates the row number with the first row (l=1) being at the bottom, and k indicates the position within each row and increases toward the right. A first row of drop ejectors includes nozzles  100 - 11 ,  100 - 21 ,  100 - 31 . A second row of drop ejectors includes nozzles  100 - 12 ,  100 - 22  (not labeled) and  100 - 32  (not labeled). The second row is offset along the array direction  54  from the first row by a distance P. There are a total of six rows, so the spacing in the array direction  54  between nozzle  100 - 11  and  100 - 21  is 6 P. By appropriately timing the firing of drop ejectors as the recording medium is moved relative to the printhead, the drops can be made to land on the recording medium to form dots in a horizontal line along the array direction  54  as shown. The leftmost dot in  FIG. 3  was ejected by nozzle  100 - 11 . The adjacent dot to the right (shown as being located a distance P to the right of the leftmost dot) was ejected by nozzle  100 - 12 . Using such a two-dimensional “staggered lattice” of drop ejectors, high resolution printing can be provided even though individual drop ejectors are large compared to the dot spacing P. As the recording medium is moved relative to the staggered lattice of drop ejectors in the scan direction  56 , additional horizontal lines of dots can be printed. 
     Even for compact types of drop ejectors such as thermal inkjet drop ejectors, it can be beneficial to arrange the drop ejectors in multiple offset rows in order to provide room for ink feeds and electrical circuitry, as shown in prior art  FIG. 4  adapted from U.S. Pat. No. 8,118,405. Printhead module  210  (shown in a top view in  FIG. 4 ) is one of a plurality of printhead modules  210  that are assembled together end to end at butting edges  214  in order to extend the printhead length. Arrays  211  of drop ejectors  212  are inclined relative to the non-butting edges  209  of printhead module  210 . Ink can be fed from the back side of printhead module  210  through segmented ink feeds  220  including slots  221  that extend from the back side to the top side. Ink then flows from slots  221  to ink inlets  24  ( FIG. 1 ) to enter pressure chambers  22  ( FIG. 1 ) of the drop ejectors  212 . The segmented ink feeds  220  are disposed adjacent to arrays  211  of drop ejectors  212 . Also disposed between arrays  211  and near butting edges  214  is electrical circuitry  230  that can include driver transistors to provide electrical pulses for firing drop ejectors  212 , as well as logic electronics to control the driver transistors so that the correct drop ejectors  212  are fired at the proper time. Electrical contacts  240  extend along one or both non-butting edges  209  for providing electrical signals to the electrical circuitry  230 . Recording medium (not shown) is advanced relative to printhead module  210  along scan direction  56 . 
     A plurality of printheads having corresponding nozzles that are aligned to each other can be used to form dots having multiple ink drops per dot, as shown in  FIGS. 5A and 5B  adapted from Japanese Patent Application Publication No. 10-151735 (JP &#39;735). Printheads  2  and  4  are mounted on a common carriage (not shown) that is moved along scan direction  56 . Corresponding nozzles  18  in printheads  2  and  4  are aligned along the scan direction  56 . The drop ejectors are sized such that ejected drops have half the drop volume required to form a dot of the desired size on the recording medium.  FIG. 5A  shows half-sized dots  40  that are printed by only the nozzles  18  in printhead  2 .  FIG. 5B  shows overlapping dots formed by nozzles  18  on both printheads  2  and  4 . A more generalized example disclosed in Japanese Patent Application Publication No. 10-151735 is the use of three or more printheads having aligned nozzles  18 , where the drop ejectors are sized to provide drop volumes that are inversely proportional to the number of printheads. An advantage stated is that the printing speed can be increased. 
     A plurality of printheads having corresponding nozzles that are aligned to each other is also disclosed in Japanese Patent Application Publication No. 10-157135 (JP &#39;135). In JP &#39;135 two printheads each having a single row of drop ejectors are arranged in similar fashion to  FIG. 5A  adapted from JP &#39;735. In JP &#39;135 aligned drop ejectors of the two printheads are controllably fired to form dots on a scan line from each printhead in order to compensate for drop volume nonuniformity of drop ejectors on the two printheads. 
     Drop ejectors can fail during the life of a printer. For example there can be electrical failure of the actuator, such as a failed resistive heater in a thermal inkjet drop ejector. Alternatively a drop ejector nozzle can become plugged. For inkjet printheads (such as those in  FIGS. 2 through 4 ) that print in a single pass and that have a single drop ejector responsible for printing all pixels on a line along the scan direction  56 , a non-recoverable failure of a single drop ejector results in an objectionable white streak in the image along the scan direction  56 . Carriage printers can disguise the effects of failed drop ejectors through multi-pass printing where each printed line of dots along the carriage scan direction is printed by multiple drop ejectors during the multiple print passes where the recording medium is advanced along the scan direction between each pass. However, multi-pass printing reduces printing throughput dramatically. 
     Despite the previous advances in drop ejector configurations on inkjet printheads, what is still needed are printhead and printing system designs, as well as printing methods, that provide high resolution printing with high reliability and image uniformity, even if high speed single-pass printing is used and even if one or more drop ejectors fail. 
     SUMMARY OF THE INVENTION 
     According to an aspect of the present invention, a method is provided for printing an image on a recording medium by an inkjet printing system having a transport mechanism for providing relative motion along a scan direction between the recording medium and a printhead that has a two-dimensional array of drop ejectors that are in fluidic communication with a first ink source. The two-dimensional array is configured as a plurality of columns each having a plurality of banks each having a plurality of N 2  groups each having a plurality N 1  drop ejectors, such that the N 1  drop ejectors within each group are aligned substantially along the scan direction and such that the groups within each column are offset from each other along a cross-track direction perpendicular to the scan direction. The method for printing includes providing image data to the printhead, and using the image data to control whether or not a drop ejector is fired when it is enabled. Firing of a first endmost drop ejector of a first group in each bank in each column is enabled during a first cycle of a first stroke. Firing a second drop ejector of the first group in each bank in each column is enabled during a second cycle of the first stroke. The second drop ejector of the first group is a nearest neighbor of the first endmost drop ejector of the first group. Firing of successive nearest neighbor drop ejectors of the first group in each bank in each column is sequentially enabled during successive cycles of the first stroke until all N 1  members of the first group in each bank in each column have had opportunity to eject a drop of ink. Firing of a first endmost drop ejector of a second group in each bank in each column is enabled during an N 1 +1 cycle of a first stroke. Firing a second drop ejector of the second group in each bank in each column is enabled during an N 1 +2 cycle of the first stroke. The second drop ejector of the second group is a nearest neighbor of the first endmost drop ejector of the second group. Firing of successive nearest neighbor drop ejectors of the second group in each bank in each column is sequentially enabled during successive cycles of the first stroke until all N 1  members of the second group in each bank in each column have had opportunity to eject a drop of ink. Firing the drop ejectors of any additional groups in each bank in each column is sequentially enabled during successive cycles of the first stroke until all drop ejectors in the two-dimensional array have had opportunity to eject a drop of ink. Firing the drop ejectors in the two-dimensional array is enabled in a series of subsequent strokes similar to the first stroke as the recording medium is moved relative to the printhead, thereby printing dots on the recording medium by ejected drops of ink, until printing of the image according to the image data is completed. 
     According to another aspect of the present invention, a method is provided for printing an image on a recording medium by an inkjet printing system having a transport mechanism for providing relative motion along a scan direction between the recording medium and a printhead that has a two-dimensional array of drop ejectors that are in fluid communication with a common ink source. The two-dimensional array includes spatially offset groups of drop ejectors, each group having a plurality of drop ejectors that are aligned substantially along the scan direction. The method for printing includes providing image data to the printhead and using the image data to control whether or not a drop ejector is fired when it is enabled. The recording medium is continuously advanced relative to the printhead along the scan direction. Simultaneous firing of drop ejectors that are corresponding members of a first set of groups is enabled. Sequential firing of individual drop ejectors within each group of the first set of groups is enabled until each member of each group has had opportunity to fire. Simultaneous firing of drop ejectors that are corresponding members of a second set of groups is enabled. Sequential firing of individual drop ejectors within each group of the second set of groups is enabled. Likewise firing of any additional groups in the two-dimensional array is successively enabled until all drop ejectors in the two-dimensional array have had opportunity to fire during a first stroke. Firing of the drop ejectors of the two-dimensional array is enabled in subsequent strokes similar to the first stroke as the recording medium is moved relative to the printhead along the scan direction until printing of the image with the common ink according to the image data is completed. 
     This invention has the advantage that each line in the scan direction is printed by multiple drop ejectors, thereby providing high printing throughput and multi-pass image quality in single pass printing. 
     This invention has the further advantages of a variety of print modes, including a non-interlaced print mode having a higher scan direction resolution than the number of drop ejectors per inch along the scan direction; interlaced print modes for even higher scan resolution or addressability, a multiple drop per pixel mode for extended color gamut, a redundant drop ejector mode for compensating for defective drop ejectors, and a print mode having a lower scan resolution than the number of drop ejectors per inch along the scan direction for lower ink usage. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a perspective of a prior art drop ejector configuration; 
         FIG. 2  shows a prior art printhead including a linear array of drop ejectors and also a recording medium with a pixel grid of allowable dot locations; 
         FIG. 3  shows a prior art printhead having multiple offset rows of drop ejectors; 
         FIG. 4  shows a prior art printhead module having inclined arrays of drop ejectors; 
         FIGS. 5A and 5B  show a prior art configuration of two printheads having aligned nozzles plus the dot patterns that they print; 
         FIG. 6  is a schematic representation of an inkjet printing system according to an embodiment; 
         FIG. 7  is a top view of a printhead die having a two-dimensional array of drop ejectors including groups of drop ejectors that are aligned along the scan direction according to an embodiment; 
         FIG. 8  is similar to  FIG. 7  and shows spatial relationships of the drop ejectors in the two-dimensional array; 
         FIG. 9  is similar to  FIG. 7  and further shows electrical features; 
         FIG. 10  is a schematic of driver circuitry and addressing circuitry according to an embodiment; 
         FIGS. 11A through 11E  schematically show snapshots at successive times that occur during a first printing stroke according to an embodiment; 
         FIGS. 12A through 12D  schematically show snapshots at successive times during a second print stroke following the first print stroke according to an embodiment; 
         FIGS. 13A through 13D  schematically show snapshots at successive times during a third print stroke following the second print stroke according to an embodiment; 
         FIG. 14  shows a portion of a pixel grid with solid circles representing dots that are enabled for printing during the first three printing strokes shown in  FIGS. 11A through 13D  according to an embodiment; 
         FIGS. 15A through 15D  illustrate four printing strokes for double-interlaced printing according to an embodiment; 
         FIGS. 16A through 16E  illustrate five printing strokes for triple-interlaced printing according to an embodiment; 
         FIGS. 17A through 17D  illustrate the printing of up to two drops per pixel according to an embodiment; 
         FIGS. 18A through 18D  illustrate printing with a reversed firing order relative to  FIGS. 11A through 11E  according to an embodiment; 
         FIG. 19  shows a top view of a printhead die having a pair of two-dimensional arrays of drop ejectors that are separated along the scan direction according to an embodiment; 
         FIG. 20  shows a prior art drop ejector configuration for color printing; 
         FIG. 21  shows a pair of butted printhead die according to an embodiment; 
         FIG. 22  shows a pair of printhead die that are in fluidic communication with different ink sources according to an embodiment; 
         FIG. 23  shows a pair of butted printhead die each having a pair of two-dimensional arrays of drop ejectors according to an embodiment; 
         FIG. 24A  shows a pair of butted printhead die where corresponding drop ejectors in each column are aligned along the array direction as in  FIG. 7 ; 
         FIG. 24B  shows a pair of butted printhead die where adjacent columns of drop ejectors are displaced along the scan direction by one unit of drop ejector spacing according to an embodiment; 
         FIG. 25  shows a pair of butted printhead die where adjacent butting edges include steps that are positioned in complementary fashion; 
         FIG. 26  schematically represents a roll-to-roll inkjet printing system that can be used in some embodiments; 
         FIG. 27  schematically represents a carriage printing system that can be used in some embodiments; 
         FIG. 28A  shows two groups of drop ejectors that are perfectly aligned along the scan direction; 
         FIG. 28B  shows a group of drop ejectors that is perfectly aligned and a group of drop ejectors that is not perfectly aligned along the scan direction; and 
         FIG. 28C  shows a pair of drop ejectors and a best-fit line along the scan direction. 
     
    
    
     It is to be understood that the attached drawings are for purposes of illustrating the concepts of the invention and may not be to scale. Identical reference numerals have been used, where possible, to designate identical features that are common to the figures. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The invention is inclusive of combinations of the embodiments described herein. References to “a particular embodiment” and the like refer to features that are present in at least one embodiment of the invention. Separate references to “an embodiment” or “particular embodiments” or the like do not necessarily refer to the same embodiment or embodiments; however, such embodiments are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to the “method” or “methods” and the like is not limiting. It should be noted that, unless otherwise explicitly noted or required by context, the word “or” is used in this disclosure in a non-exclusive sense. 
     The present invention will now be described with reference to  FIG. 6 , which includes a schematic representation of inkjet printing system  1  together with a perspective of printhead die  215 . Image data source  2  provides data signals that are interpreted by a controller  4  as commands for ejecting drops. Controller  4  includes an image processing unit  3  for rendering images for printing. The term “image” is meant herein to include any pattern of dots directed by the image data. It can include graphic or text images. It can also include patterns of dots for printing functional devices if appropriate inks are used. Controller  4  also includes a transport control unit for controlling transport mechanism  6  and an ejection control unit for ejecting ink drops to print a pattern of dots corresponding to the image data on the recording media  62 . Controller  4  sends output signals to an electrical pulse source  5  for sending electrical pulses to an inkjet printhead  50  that includes at least one inkjet printhead die  215 . Transport mechanism  6  provides relative motion between inkjet printhead  50  and recording medium  62  along a scan direction  56 . Transport mechanism  6  is configured to move the recording medium  62  while the printhead  50  is stationary in some embodiments. Alternatively, transport mechanism  6  can move the printhead  50 , for example on a carriage, past stationary recording medium  62 . In a carriage printer, the scan direction  56  during drop ejection can reverse as successive swaths of the image are printed. 
     Various types of recording media for inkjet printing include paper, plastic, and textiles. In a 3D inkjet printer, the recording media include flat building platform and thin layer of powder material. In addition, in various embodiments recording medium  62  can be web fed from a roll or sheet fed from an input tray. 
     Printhead die  215  includes a two-dimensional array  150  of drop ejectors  212  formed on a top surface  202  of a substrate  201  that can be made of silicon or other appropriate material. Ink is provided to drop ejectors  212  by first ink source  290  through ink feed  220  which extends from the back surface  203  of substrate  201  toward top surface  202 . Ink source  290  is generically understood herein to include any substance that can be ejected from an inkjet printhead drop ejector. Ink source  290  can include colored ink such as cyan, magenta, yellow or black. Alternatively ink source  290  can include conductive material, dielectric material, magnetic material, or semiconductive material for functional printing. Ink source  290  can alternatively include biological or other materials. For simplicity, location of the drop ejectors  212  is represented by the circular nozzle. Not shown in  FIG. 6  are the pressure chamber  22 , the ink inlet  24 , or the actuator  35  ( FIG. 1 ). Ink inlet  24  is configured to be in fluidic communication with first ink source  290 . The pressure chamber  22  is in fluidic communication with the nozzle  32  ( FIG. 1 ) and the ink inlet  24 . The actuator  35  is configured to selectively pressurize the pressure chamber  22  for ejecting ink through the nozzle  32 . 
     Two-dimensional array  150  is configured according to a prescribed organizational structure. The basic building block of the organizational structure is the group  120 . Each group  120  includes a plurality N 1 &gt;1 of drop ejectors  212 . In the example shown in  FIG. 6 , each group  120  includes four drop ejectors  212 . The drop ejectors  212  within each group  120  are substantially aligned along a first direction that is parallel to scan direction  56 . The next higher level building block is the bank  130 . Each bank includes a plurality N 2 &gt;1 of groups  120 . Groups  120  within each bank  130  are spaced from each other along the scan direction  56  and are offset from each other along a second direction, which is called the array direction  54  herein. In the example shown in  FIG. 6 , each bank  130  includes four groups  120 . The next higher level of the organizational structure is the column  140 . Each column  140  includes a plurality N 3 &gt;1 of banks  130 . The banks  130  in each column  140  are spaced from each other along the scan direction  56  and are offset from each other along the array direction  54 . Columns  140  are offset from each other along the array direction  54 . Two-dimensional array  150  includes a plurality N 4 &gt;1 of columns  140 . In the example shown in  FIG. 6  there are nine columns  140  and each column  140  includes two banks  130 . The total number of drop ejectors in the two-dimensional array  150  is N 1 *N 2 *N 3 *N 4 , where * is the multiplication operator. In the example shown in  FIG. 6  there are a total of 4*4*2*9=288 drop ejectors  212 . 
     Two-dimensional array  150  has a width W along the scan direction  56  and a length L along the array direction  54 , where L is greater than W. Typically the array direction  54  is perpendicular to the scan direction  56 . In the figures included herein the size of the two-dimensional array is relatively small for simplicity. In an actual printhead die  215  there can be thousands of drop ejectors  212 , and the length L is typically much greater than the width W. It is advantageous for the length L along a direction perpendicular to scan direction  56  to be long in order to allow printing a large area of the recording medium  62  in a single pass or in a single swath. It is advantageous to keep the area of printhead die  215  relatively small in order to reduce manufacturing costs. Therefore, it is advantageous for width W of the two-dimensional array  150  to be somewhat smaller than L, while still accommodating multiple drop ejectors  212  in each group  120  aligned along the scan direction  56  along which the width W extends. 
       FIG. 7  is a top view of a portion of a printhead die  215  (also called a die herein) and shows a portion of a two-dimensional array  150 . In the example of  FIG. 7 , four columns ( 141 ,  142 ,  143  and  144 ) are shown. The sides of printhead die  215  are illustrated as jagged lines, indicating that there can be more than four columns. Each column includes two banks  131  and  132 . Bank  131  includes two groups  121  and  122 , and bank  132  includes two groups  123  and  124 . Each group includes four drop ejectors, such as drop ejectors  111 ,  112 ,  113  and  114 . The numbering convention in  FIG. 7  is that the drop ejectors in each bank are numbered consecutively. For example, in column  141  and bank  131 , the drop ejectors in group  121  are numbered  111 ,  112 ,  113  and  114  from lowest member of group  121  to the highest member. In group  122  the drop ejectors are numbered  115 ,  116 ,  117  and  118 . Drop ejectors in a group are substantially aligned along scan direction  56 . In the example shown in  FIG. 7 , N 1 =4, N 2 =2, N 3 =2 and N 4 ≧4. 
       FIG. 8  is similar to  FIG. 7  and shows the spatial relationships of the drop ejectors in the two-dimensional array  150 , where X is the scan axis having coordinates along the scan direction  56 , and Y is the array axis having coordinates along the array direction  54 . The center to center distance between the substantially evenly spaced drop ejectors within a group along the scan direction  56  is X 1 , as seen in the bottom right corner of two-dimensional array  150  (i.e. between drop ejectors  111  and  112  in bank  131  in column  144 ). The center to center distance between nearest neighbor drop ejectors of adjacent groups within a bank along the scan direction  56  is X 1 , as seen between drop ejector  114  in group  121  and drop ejector  115  in group  122  in bank  131  in column  144 . As a result, the center to center distance between corresponding drop ejectors in two adjacent groups in a bank is equal to X 2 =N 1 X 1 . For example, in bank  131  of column  141  the spacing between bottom-most drop ejector  111  in group  121  and bottom-most drop ejector  115  in group  122  is X 2 =4X 1 . 
     Adjacent groups within each bank are substantially evenly spaced by a first offset Y 1  along the array direction  54 . Reference lines  57  are parallel to the scan direction  56  and pass through the centers of drop ejectors in each group in the example shown in  FIG. 8 . In bank  132  of column  141 , for example, a first reference line  57   a  passes through the centers of drop ejectors  115 ,  116 ,  117  and  118  of group  124 , and a second reference line  57   b  passes through the centers of drop ejectors  111 ,  112 ,  113  and  114  of group  123 . The distance between first reference line  57   a  and second reference line  57   b  is equal to first offset Y 1  along the array direction  54 . 
     The spacing along the scan direction  56  between nearest neighbor drop ejectors of a first bank and an adjacent second bank in a column is equal to X 5 , which is greater than or equal to X 1 . For example, in column  144 , drop ejector  118  in group  122  of bank  131  has a nearest neighbor drop ejector  111  along the scan direction  56  in group  123  in adjacent bank  132 . The distance along the scan direction  56  between these two drop ejectors is X 5 , which is greater than X 1  in the example shown in  FIG. 8 . The distance X 5  is the spacing between nearest neighbor drop ejectors of first bank  131  and adjacent second bank  132  for all four columns  141 ,  142 ,  143  and  144 . As a result, the center to center distance between corresponding drop ejectors in corresponding groups in adjacent banks is equal to X 3 =N 2 *X 2 +X 5 −X 1 . This expression reduces to X 3 =N 2 *N 1 *X 1  if X 5 =X 1 . For example, in column  141  the spacing between bottom-most drop ejector  111  in bottom-most group  121  of bank  131  and bottom-most drop ejector  111  in bottom-most group  123  of bank  132  is X 3 =7X 1 +X 5 . 
     Nearest adjacent groups in adjacent banks in each column are spaced apart by the first offset Y 1  along array direction  54 . In column  141 , for example, second reference line  57   b  passes through the centers of drop ejectors  111 ,  112 ,  113  and  114  of group  123  in bank  132 . The nearest adjacent group in adjacent bank  131  is group  122 . Third reference line  57   c  passes through the centers of drop ejectors  115 ,  116 ,  117  and  118  of group  122  in adjacent bank  131 . The distance between second reference line  57   b  and third reference line  57   c  is equal to first offset Y 1  along the array direction  54 . 
     A smallest spacing along array direction  54  between a group in a first column and a group in an adjacent second column is also equal to first offset Y 1 . For example, the groups that have the smallest spacing along array direction  54  in columns  141  and  142  are group  124  of column  141  and group  121  of column  142 . First reference line  57   a  passes through the centers of the drop ejectors of group  124  of column  141 . Fourth reference line  57   d  passes through the centers of the drop ejectors of group  121  of column  142 . The distance between first reference line  57   a  and fourth reference line  57   d  is equal to first offset Y 1  along the array direction  54 . 
     In other words, in two-dimensional array  150 , successive groups (from left to right in  FIG. 8 ) are equally spaced by first offset Y 1  along array direction  54 . If recording medium  62  ( FIG. 6 ) is moved relative to printhead die  215  along scan direction  56 , and if the firing of drop ejectors in different groups is appropriately timed, the allowable adjacent dot locations  66  ( FIG. 2 ) within rows  68  along array direction  54  will be spaced evenly by first offset Y 1 . Dot spacing along the array direction  54  is analogous to prior art  FIGS. 2 and 3 . As described in more detail below in connection with the method of printing, dot formation along the scan direction  56  is different from the prior art. The differences in printing along the scan direction  56  are enabled by having groups of drop ejectors that are aligned along scan direction  56 . A printhead configuration that includes a plurality of drop ejectors aligned along the scan direction  56  in each group in two-dimensional array  150  enables dots that are disposed linearly along the scan direction  56  on the recording medium  62  to be cooperatively printed in a single pass by a plurality of different drop ejectors. If a single drop ejector in a group fails, it does not result in a white streak along the scan direction  56  as is the case for prior art printheads used in single-pass printing. 
     As described above relative to prior art  FIG. 4 , it can be beneficial to arrange the drop ejectors in multiple offset rows in order to provide room for ink feeds and electrical circuitry. As shown in  FIGS. 8 and 9 , offset groups of drop ejectors provide a similar advantage. With reference to  FIG. 8 , the distance Y 4  along the array direction  54  between corresponding groups in adjacent columns is equal to 4Y 1  for the case where there are N 2 =2 groups in a bank and N 3 =2 banks in a column. More generally speaking, the distance between corresponding groups in adjacent columns is equal to N 2 *N 3 *Y 1 . As shown in the example of  FIG. 9 , driver circuitry  160  can thus be fit into the spaces between corresponding groups in adjacent columns. The actuator of each drop ejector is electrically connected to the driver circuitry  160  for energizing the actuator. Also schematically shown in  FIG. 9  is addressing circuitry  170  for selectively energizing the actuators of the drop ejectors by the driver circuitry  160 . For example, the driver circuitry  160  can include driver transistors  161  ( FIG. 10 ) that are connected to each actuator. The addressing circuitry  170  can include data input lines, clock lines and logic elements such as shift registers and latches in order to turn on the driver transistors of the driver circuitry  160  for energizing the actuators in the proper sequence and timing for printing the image according to image data source  2  ( FIG. 6 ). 
       FIG. 10  shows an example of driver circuitry  160  and addressing circuitry  170  that can be included in a printhead die  215  similar to the example of  FIG. 9 . For simplicity in  FIG. 10 , each group  121 ,  122 ,  123  and  124  has two drop ejectors  212  rather than the four drop ejectors per group in the example of  FIG. 9 . There are N 4  columns ( 141 ,  142  up to N 4 ) in  FIG. 10  and each column has two banks  131  and  132 . Address circuitry  170  includes a plurality of address lines  171 ,  172 ,  173  and  174 . More generally speaking, the number of address lines is equal to the number of drop ejectors per bank (the product of the number of drop ejectors per group and the number of groups per bank, i.e. N 1 *N 2 ). Each drop ejector in a bank is connected to a different address line. By that it is meant that the driver transistor  161  connected to the actuator (not shown) of each drop ejector  212  in a bank is connected to a different address line. For example, in bank  131  address line  171  is connected to the driver transistor  161  corresponding to the lower drop ejector  125  in group  121 ; address line  172  is connected to the driver transistor  161  corresponding to the upper drop ejector  126  in group  121 ; address line  173  is connected to the driver transistor  161  corresponding to the lower drop ejector  125  in group  122 ; and address line  174  is connected to the driver transistor  161  corresponding to the upper drop ejector  126  in group  122 . Similarly, in bank  132 , address line  171  is connected to the driver transistor  161  corresponding to the lower drop ejector  125  in group  123 ; address line  172  is connected to the driver transistor  161  corresponding to the upper drop ejector  126  in group  123 ; address line  173  is connected to the driver transistor  161  corresponding to the lower drop ejector  125  in group  124 ; and address line  174  is connected to the driver transistor  161  corresponding to the upper drop ejector  126  in group  124 . Each address line of the addressing circuitry  170  is connected to one drop ejector  212  in a corresponding location in each group in each bank. For example, address line  171  is connected to the driver transistor  161  corresponding to the lower drop ejector  125  in the lower group  121  in bank  131 , and address line  171  is also connected to the driver transistor  161  corresponding to the lower drop ejector  125  in the lower group  123  in bank  132 . In addition, each address line is connected to drop ejectors in corresponding locations in each column. For example, address line  171  is connected to the driver transistor  161  corresponding to the lower drop ejector  125  in group  121  in column  141 , to the driver transistor  161  corresponding to the lower drop ejector  125  in group  121  in column  142 , and to the driver transistor  161  corresponding to the lower drop ejector  125  in group  121  in column N 4 . As a result of this address line configuration, when a signal pulse is sent along address line  171 , for example, the lower drop ejector  125  in corresponding groups in each bank in each column can be fired simultaneously. Whether an ejector will actually be fired depends on the image date from image data source  2  ( FIG. 6 ). The maximum number of drop ejectors  215  that can be fired simultaneously by the addressing configuration of  FIG. 10  is the product of the number of banks per column and the number of columns, i.e. N 3 *N 4 . 
     Also associated with addressing circuitry  170  is a sequencer  175  that determines the order in which signals are sent by address lines  171 ,  172 ,  173  and  174 . For example, signals can be sent successively by address lines in a first sequence  171 ,  172 ,  173  and  174  or in a second sequence  174 ,  173 ,  172  and  171  that is opposite to the first sequence. In other words, the addressing circuitry  170  is configured to selectively address the driving circuitry  160  for energizing the actuators in either a first sequence or a second sequence that is opposite to the first sequence. 
     In the examples described herein, the number N 1  of drop ejectors in each group is an even number. An even number of drop ejectors in a group can be preferable for addressing, but it is also contemplated that there can be configurations having an odd number of drop ejectors in each group. 
     In the example shown in  FIG. 8  the spacing along the scan direction  56  between nearest neighbor drop ejectors of a first bank and an adjacent second bank in a column is equal to X 5 , which is greater than or equal to X 1 . For X 5  greater than X 1 , proper dot spacing can be achieved by causing different position drop ejectors in different banks to eject the drops to land on the recording medium  62  in the appropriate positions. In some embodiments, as shown in  FIG. 9 , it can be advantageous to have X 5  greater than X 1  in order to place an electrical lead  180  between first bank  131  and adjacent second bank  132 . This is especially true for types of drop ejectors such as thermal inkjet drop ejectors that require relatively high electrical currents. In order to avoid excessive voltage drops along the current-carrying leads, it can be useful to provide additional leads such as electrical lead  180  in the space provided between adjacent banks. 
     Further embodiments of printheads and printing systems will be described below, but it is instructive to consider methods of printing using the printhead configuration embodiments described above.  FIGS. 11A through 11E  schematically show snapshots at successive times during a first print stroke. A stroke is defined as a plurality of print cycles during which drop ejectors  212  in the two-dimensional array  150  ( FIG. 6 ) are fired, such that during one stroke all drop ejectors  212  in the two-dimensional array  150  ( FIG. 6 ) are fired once.  FIGS. 11A to 11C  show snapshots at three times t 1 , t 2  and t 4  as drop ejectors  111  to  114  from groups  121  and  123  in a single column eject drops of ink while the recording medium  62  ( FIG. 6 ) is moved relative to printhead die  215  along scan direction  56 . Note: relative motion of the recording medium  62  and the printhead along scan direction  56  is sometimes referred to herein as moving relative to the printhead, or to the printhead die, or to the drop ejectors. All of these expressions are understood to be equivalent herein. The relative motion during drop ejection can consist of transporting the recording medium past the stationary printhead or transporting the printhead past the stationary recording medium. For simplicity, the recording medium  62  ( FIG. 6 ) is not shown in  FIG. 11  but just the dot locations. Numbering of drop ejectors, groups and banks is similar to that used in  FIGS. 7 and 8 . Allowable pixel locations  300  are shown as unfilled circles, while already enabled print dots are shown as filled circles. In  FIG. 11A  at an initial time t 1 , endmost drop ejector  111  from group  121  in bank  131  and corresponding endmost drop ejector  111  from group  123  in bank  132  are simultaneously enabled to fire during a first printing cycle to form first dots  301  at first positions  311  on the recording medium that are aligned with drop ejectors  111  at time t 1 . Whether or not drops of ink will actually be ejected by drop ejectors  111  to form first dots  301  is controlled according to image data from image data source  2  ( FIG. 6 ). 
     The recording medium is moved relative to the drop ejectors along scan direction  56  at a substantially constant velocity V, so that at a second time t 2  shown in  FIG. 11B , the recording medium has moved a distance VΔt relative to first position  311  where Δt=t 2 −t 1 , or more generally Δt=t n −t n-1 , where t n  is the time at the start of the nth printing cycle. First dot  301  has moved a distance VΔt from first position  311  at t 1  to second position  312  at t 2 . As shown in  FIG. 11B , after waiting for time delay Δt after firing the first drop ejector of the first group, second drop ejectors  112  from group  121  in bank  131  and from group  123  in bank  132  are enabled to be fired simultaneously in a second printing cycle. Drops that are fired during the second printing cycle form second dots  302  that are aligned with drop ejectors  112  at time t 2 . Second drop ejectors  112  are nearest neighbors of the first endmost drop ejectors  111  in their respective groups. The distance (also called the scan direction pitch p) between first dot  301  and second dot  302  is equal to the spacing between drop ejectors  111  and  112  minus the distance that the recording medium has moved along scan direction  56  relative to the printhead die  215  during the time interval between t 1  and t 2 , i.e. p=X 1 −VΔt. In this embodiment, the direction  127  between the first drop ejector  111  enabled for firing in a group and the second drop ejector  112  enabled for firing in the group is in the same direction as the recording medium travel direction (scan direction  56 ) relative to the printhead die. In such embodiments, the scan direction pitch p is less than the spacing X 1  between drop ejectors. This can be advantageous for achieving higher resolution printing (spots per inch) along the scan direction  56  than the number of drop ejectors per inch formed on the printhead. 
     Printing cycles are repeated in similar fashion, where the time interval from the start of a printing cycle to the start of the next printing cycle is Δt=(X 1 −p)/V. Although a third printing cycle where drop ejectors  113  (nearest neighbors of drop ejectors  112 ) print third dots  303  at time t 3 =t 1 +2Δt is not shown, a fourth printing cycle where drop ejectors  114  (nearest neighbors of drop ejectors  113 ) print fourth dots  304  at time t 4 =t 1 +3Δt is shown in  FIG. 11C . The recording medium has traveled a distance VΔt since the third printing cycle, so the scan direction pitch p between third dot  303  and fourth dot  304  is again p=X 1 −VΔt. Relative to initial position  311 , the recording medium has moved relative to the printhead by a total distance of 3VΔt and all four drop ejectors in each of groups  121  and  123  have been fired by time t 4  for this example where there are N 1 =4 drop ejectors per group. More generally, all N 1  drop ejectors in the first groups in each bank are fired by time t N1  and the recording medium has moved relative to the printhead by a total distance of (N 1 −1)* VΔt.  FIGS. 11A to 11C  show only the printing of dots by a single column of drop ejectors. Similar printing is simultaneously enabled for each column  140  in the two-dimensional array  150  ( FIG. 6 ). In other words, firing of successive nearest neighbor drop ejectors of a first group in each bank in each column is sequentially enabled during N 1  successive cycles of a first stroke until all N 1  members of the first group in each bank in each column have had opportunity to eject a drop of ink. 
     In a similar way, firing of endmost drop ejectors  115  of second groups  122  and  124  in banks  131  and  132  of each column is enabled during an N 1 +1 cycle of the first stroke. Then, firing of drop ejectors  116  (nearest neighbors of drop ejectors  115 ) of second groups  122  and  124  in banks  131  and  132  of each column is enabled during an N 1 +2 cycle of the first stroke. Then, successive nearest neighbor drop ejectors of the second group in each bank in each column is enabled during successive cycles of the first stroke until all N 1  members of the second group in each bank in each column have had opportunity to eject a drop of ink.  FIG. 11D  shows the dots that have been enabled for printing at t 8 , after drop ejectors  115 - 118  in second groups  122  and  124  have been successively fired following the firing of drop ejectors  111 - 114  that was illustrated in  FIGS. 11A to 11C . Consecutive printing cycles within the first stroke are spaced evenly in time by time interval Δt, so that (since X 1  and V are substantially constants), the scan direction pitch p=X 1 −VΔt is substantially constant. The distance between dot  301  printed by drop ejector  111  and dot  118  printed seven printing cycles later is 7 p. The distance the recording medium has moved relative to the drop ejectors from first position  311  to eighth position  318  is 7VΔt, as shown in  FIG. 11D . 
     In this example, the number of groups in a bank is N 3 =2. If the number of groups in a bank were greater than 2, firing of the drop ejectors of additional groups in each bank in each column would be sequentially enabled in similar fashion until all drop ejectors in the two-dimensional array  150  have had opportunity to eject a drop of ink. 
     In  FIG. 11D , the recording medium is not yet in position to start printing the second stroke. In order for the pitch p to remain constant along the scan direction  56 , the recording medium must move a total distance of N 1 *p between the start of the first stroke at time t 1  and the start of the next stroke at time t S , as illustrated in  FIG. 11E  where N 1 *p=4p. In  FIG. 11D  at t=t 8 , the recording medium has moved by 7VΔt=(N 1 *N 2 −1)*VΔt relative to the first position  311 . The extra distance that the recording medium needs to move between t 8  ( FIG. 11D ) and t S  ( FIG. 11E ) is N 1 *p−(N 1 *N 2 −1)VΔt=N 1 *p−(N 1 *N 2 −1)*(X 1 −p) Thus there needs to be a delay time τ 1 =t S −t 8 =(N 1 *p−(N 1 *N 2 −1)*(X 1 −p))/V after all N 1 *N 2  drop ejectors in each bank have been fired in a first stroke before the second stroke begins. 
       FIGS. 12A through 12D  schematically show snapshots at successive times during a second print stroke following the first print stroke. Dots that are printed during the second stroke are shown as filled triangles in order to distinguish them from dots that are printed during the first stroke.  FIG. 12A  is at t 1 =t S +Δt, after the first dot  301  of the second stroke is printed by drop ejector  111 .  FIG. 12B  shows the fourth printing cycle of the second stroke where drop ejectors  111 ,  112 ,  113  and  114  have successively fired during the second stroke, and the fourth dot  304  of the second stroke is aligned with drop ejector  114 .  FIG. 12B  is analogous to  FIG. 11C . The distance the recording medium has traveled relative to the drop ejectors between  FIG. 12A and 12B  is 3VΔt.  FIG. 12C  shows the eighth printing cycle of the second stroke where drop ejectors  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  117  and  118  have successively fired during the second stroke, and the eighth dot  308  of the second stroke is aligned with drop ejector  118 .  FIG. 12C  is analogous to  FIG. 11D . The distance the recording medium has traveled relative to the drop ejectors between  FIG. 12A and 12C  is 7VΔt. 
       FIG. 12D  is analogous to  FIG. 11E . The distance between drop ejector  111  in group  121  and drop ejector  111  in group  123  is equal to X 5 +7X 1 , or more generally X 5 +(N 1 *N 2 −1)*X 1 . Because drop ejector  111  in bank  132  is fired at the same time as drop ejector  111  in bank  131 , in order to provide an integer number n of equally spaced dots with pitch p between them, it follows that 
         X   5 +( N   1   *N   2 −1)* X   1   =np.    (1)
 
     In other words, the spacing between corresponding drop ejectors of adjacent banks in each column in the scan direction is an integer multiple of p. By counting the dot spacings between drop ejector  111  in bank  131  and drop ejector  111  in bank  132  in  FIG. 12D  or  FIG. 13A  it can be seen that in this example, equation 1 reduces to X 5 +7X 1 =13p. 
       FIGS. 13A through 13D  schematically show snapshots at successive times during a third print stroke following the second print stroke. Dots that are printed during the third stroke are shown as filled squares in order to distinguish them from dots that are printed during the first and second strokes.  FIGS. 13A through 13D  are analogous to  FIGS. 12A through 12D  respectively, and the dot positions and timing will not be described in detail.  FIGS. 13A through 13D  illustrate the formation of lines  351 ,  352 ,  353  and  354  of printed dots that extend linearly along the scan direction  56 . As shown in  FIG. 13C , adjacent lines of dots are separated along the array direction  54  by first offset Y 1 , which is the offset distance between adjacent groups of drop ejectors in the array direction  54 . 
     The Y axis (parallel to array direction  54 ) on the recording medium is sometimes called the cross-track direction. Dots that are printed along the scan direction  56  at a particular cross-track location on the recording medium are cooperatively printed by the N 1  drop ejectors of a corresponding group. With reference to  FIGS. 8 and 13D , the dots in line  351  were cooperatively printed by drop ejectors  111 ,  112 ,  113  and  114  in group  121  in bank  131  of column  141 , for example. No one single drop ejector is responsible for printing all the dots in a line. Therefore, if one drop ejector fails in a group of N 1  drop ejectors, the other (N 1 −1) drop ejectors print the remaining dots in the line, so it does not appear as a white streak. Similarly, the dots in line  352  were cooperatively printed by drop ejectors  115 ,  116 ,  117  and  118  in group  122  in bank  131  of column  141 . The dots in line  353  were cooperatively printed by drop ejectors  111 ,  112 ,  113  and  114  in group  123  in bank  132  of column  141 . The dots in line  354  were cooperatively printed by drop ejectors  115 ,  116 ,  117  and  118  in group  124  in bank  132  of column  141 . 
     Drop ejectors in the two-dimensional array  150  are enabled to be fired in a series of subsequent strokes similar to the first stroke as the recording medium is moved relative to the printhead, as has been described for the second stroke in  FIGS. 12A through 12D  and for the third stroke in  FIGS. 13A through 13D . As a result, dots are printed on the recording medium by ejected drops of ink until printing of the image according to the image data from image data source  2  ( FIG. 6 ) is completed. 
       FIG. 14  shows a portion of a pixel grid  250  with solid circles representing dots that are enabled for printing during the first three strokes as in  FIG. 13D . Allowable image dot locations formed by ink drops ejected onto the recording medium are defined by pixel grid  250 . The printed dots in  FIG. 13D  represent printing of lines of dots  351 ,  352 ,  353  and  354  by one column such as column  141  of  FIG. 8 . Pixel grid  250  also shows dots enabled for printing by columns  142 ,  143 ,  144  and several other columns of drop ejectors during the first three strokes. The pixel spacing along scan direction  56  is scan direction pitch p, while the pixel spacing along the cross-track direction Y is first offset Y 1 . Because groups of drop ejectors within each column are offset from each other by first offset Y 1  along the cross-track direction as shown in  FIG. 8 , and because the smallest spacing along array direction  54  between a first group in a first column and a second group in an adjacent second column is also equal to the first offset Y 1  ( FIG. 8 ), the pixel grid  250  has a uniform cross-track pitch equal to the first offset Y 1 . Because of the relative movement of the recording medium and the printhead during printing, it is generally true that scan direction pitch p is different from the drop ejector spacing X 1  along scan direction  56 . In the example described above relative to  FIGS. 11-13 , p=(X 1 −VΔt) is less than X 1 . 
       FIGS. 13D and 14  illustrate the filling of pixel grid  250  during the first three successive strokes as the recording medium is advanced along the scan direction  56  relative to the drop ejectors. As seen in  FIG. 13D , in a particular line such as line  351 , the pixels (represented by filled squares) printed during the third stroke are located below the pixels (represented by filled triangles) printed during the second stroke, which are below the pixels (represented by filled circles) printed during the first stroke. In other words, pixel grid  250  is filled from below on successive strokes as the recording medium moves upward relative to the printhead. In line  351 , for example, no dot can be printed above dot  304  ( FIG. 11C ) that was printed by the topmost drop ejector  114  in group  121  during the first stroke, because the relative motion of the recording medium has moved that portion of the recording medium beyond the last drop ejector  114  at the corresponding position in the array direction  54 . More generally, in  FIG. 14 , pixel locations above boundary line  251  can never be printed. Therefore, at the lead edge of an image, the image processing unit  3  and controller  4  ( FIG. 6 ) will arrange the print data and the firing sequences such that drops will not be ejected corresponding to the dots above boundary line  251 . Another way to think about this is that if recording medium  62  is a sheet of paper, at time t 1  in  FIG. 11A  when drop ejectors  111  in bank  131  and  132  are enabled to be fired, if the lead edge of the paper has just reached drop ejector  111  in bank  131 , there would be no paper under drop ejector  111  in bank  132 , so image processing unit  3  and controller  4  would not allow drop ejector  111  in bank  132  to fire at the lead edge. In general, image processing unit  3  and controller  4  format the print data and the firing sequences such that drops will land in the appropriate locations to form the desired image on the recording medium  62 . 
     In the example described above with reference to  FIGS. 11A through 13D  consecutive dots printed in a line along scan direction  56  are printed by consecutive drop ejectors in a group. For example, in  FIG. 11C , dot  301  is printed by drop ejector  111 , adjacent dot  302  is printed by adjacent drop ejector  112 , next adjacent dot  303  is printed by next adjacent drop ejector  113  and next adjacent dot  304  is printed by next adjacent drop ejector  114 . In this type of printing, which will be called non-interlaced printing herein, the scan direction pitch p is less than X 1 , but cannot be made arbitrarily small. The time between printing cycles in a stroke is Δt=(X 1 −p)/V. Since there are N 1 *N 2  printing cycles in a stroke, the time required to print all the drop ejectors in the two dimensional array  150  is N 1 *N 2 *Δt=N 1 *N 2 *(X 1 −p)/V, and the distance moved by the recording medium moving at velocity V relative to the two dimensional array printhead is N 1 *N 2 *(X 1 −p). This distance needs to be less than or equal to N 1 *p. In other words, the travel distance between the recording medium and the printhead along the scan direction  56  during a time used to complete each stroke is less than or equal to a spacing along the scan direction  56  between a first dot formed on the recording medium by ejecting a drop of ink from a drop ejector in a group within a bank and a second dot formed on the recording medium by ejecting a drop of ink from a corresponding drop ejector in an adjacent group within the bank. If the distance relatively moved by the recording medium is greater than N 1 *p, then there would be a gap between a cluster of dots printed along the scan direction  56  during the first stroke and a cluster of dots subsequently printed along the scan direction  56  during the second stroke. In other words, the delay time τ 1  described above with reference to  FIG. 11E  needs to be greater than or equal to zero. Therefore, 
         N   1   *N   2 *( X   1   −p )≦ N   1   *p , so that  N   2 *( X   1   −p )≦ p.    (2)
 
     As a result, the minimum value of scan direction pitch for non-interlaced printing in the example of  FIGS. 11A through 13D  is 
         p   min   =N   2   *X   1 /( N   2 +1).   (3)
 
     In the non-interlaced printing example of  FIGS. 11A through 13D  where the number of groups in a bank N 2 =2, the minimum scan direction pitch p is two-thirds of the drop ejector spacing X 1  along the scan direction  56 . For example, a two-dimensional array of 400 drop ejectors per inch along the scan direction could print non-interlaced dots on a pixel grid where the scan direction resolution is 600 dots per inch. 
     In order to print at even higher scan direction resolution with the drop ejector array arrangement described above with reference to  FIG. 7 , it is necessary to use interlaced printing as described below.  FIGS. 15A through 15D  illustrate a method of double-interlaced printing at higher resolution by using double the number of strokes. Successive double-interlaced strokes are called odd strokes and even strokes below.  FIGS. 15A through 15D  show only the drop ejectors and dot locations corresponding to groups  121  and  122  of bank  131  for simplicity. For the double-interlaced example, p 2  is the scan direction pitch.  FIG. 15A  is analogous to  FIG. 11A . In  FIG. 15A  at an initial time t 1 (O 1 ) for a first odd stroke, drop ejector  111  from group  121  is enabled to fire during a first printing cycle to form first odd dot  411  on the recording medium. Unfilled circles represent allowable odd dot positions  401  that have not yet been enabled for printing. Spacing between allowable dot positions printed by the first odd stroke is 2p 2 , i.e. twice the scan direction pitch p 2 . During the printing of the first odd stroke, the recording medium moves at velocity V in the scan direction  56  relative to the drop ejectors. Similar to the discussion above relative to  FIG. 11B , after waiting for time delay Δt after firing the first drop ejector of the first group, second drop ejectors  112  from group  121  in bank  131  are enabled to be fired in a second printing cycle (not shown) to form second dot  412  ( FIG. 15B ). The distance between first odd dot  411  and second odd dot  412  printed during the first odd stroke is equal to the spacing between drop ejectors  111  and  112  minus the distance that the recording medium has moved during the time Δt, i.e. 2p 2 =X 1 −VΔt. During the third through eighth printing cycles in the first odd stroke, odd dots  413 ,  414 ,  415 ,  416 ,  417  and  418  are printed by drop ejectors  113 ,  114 ,  115 ,  116 ,  117  and  118  respectively. 
     In  FIG. 15B  at an initial time t 1 (E 1 ) for a first even stroke, drop ejector  111  from group  121  is enabled to fire during a first printing cycle to form first even dot  421  on the recording medium. In order to interlace the printed dots at a scan direction pitch p 2 , the recording medium is allowed to travel a distance 3p 2  between the first printing cycle of the first odd stroke ( FIG. 15A ) and the first printing cycle of the first even stroke ( FIG. 15B ). In other words, during a time 3p 2 /V between the start of the first odd stroke (when drop ejector  111  prints first odd dot  411 ) and the start of the first even stroke (when drop ejector  111  prints first even dot  421 ) the recording medium moves relative to the drop ejectors by 3p 2  in the scan direction  56 . More generally for double interlacing, if there are N 1  drop ejectors in each group and N 1  is an even number, the time between the start of the first odd stroke and the start of the first even stroke is equal to (N 1 −1)*p 2 /V. First even dot  421  is represented by a filled X, while allowable dot positions that have not yet been enabled for printing in the first even stroke are represented by unfilled X&#39;s. 
     In  FIG. 15C  at an initial time t 1 (O 2 ) for a second odd stroke, drop ejector  111  from group  121  is enabled to fire during a first printing cycle to form first odd dot  431  on the recording medium. In order to provide a constant scan direction pitch p 2 , the recording medium must move relative to the drop ejectors by a total of 8p 2  between the first printing cycle of the first odd stroke ( FIG. 15A ) and the first printing cycle of the second odd stroke ( FIG. 15C ). Equivalently, the recording medium must move relative to the drop ejectors by 5p 2  between the first printing cycle of the first even stroke ( FIG. 15B ) and the first printing cycle of the second odd stroke ( FIG. 15C ). More generally for double interlacing, if there are N 1  drop ejectors in each group and N 1  is an even number, the time between the start of the first even stroke and the start of the second odd stroke is equal to (N 1 +1)*p 2 /V. First odd dot  431  is represented by a filled triangle, while allowable dot positions that have not yet been enabled for printing in the second odd stroke are represented by unfilled triangles. 
     In  FIG. 15D  at an initial time t 1 (E 2 ) for a second even stroke, drop ejector  111  from group  121  is enabled to fire during a first printing cycle to form first even dot  441  on the recording medium. In order to interlace the printed dots at a scan direction pitch p 2 , the recording medium is allowed to travel a distance 3p 2  between the first printing cycle of the second odd stroke ( FIG. 15C ) and the first printing cycle of the second even stroke ( FIG. 15D ). First even dot  441  is represented by a filled star, while allowable dot positions that have not yet been enabled for printing in the second even stroke are represented by unfilled stars. 
     Near the upper right-hand portion of  FIG. 15D  the sequence of consecutively enabled dots in line  352  is shown. Beginning at dot  433  and going upward: dot  433  is printed on the second odd stroke by drop ejector  113 ; dot  421  is printed on the first even stroke by drop ejector  111 ; dot  434  is printed on the second odd stroke by drop ejector  114 ; dot  422  is printed on the first even stroke by drop ejector  112 ; dot  411  is printed on the first odd stroke by drop ejector  111 ; dot  423  is printed on the first even stroke by drop ejector  113 ; dot  412  is printed on the first odd stroke by drop ejector  112 ; dot  424  is printed on the first even stroke by drop ejector  114 ; and dot  413  is printed on the first odd stroke by drop ejector  113 . In other words, unlike non-interlaced printing where consecutive dots printed in a line along scan direction  56  are printed by consecutive drop ejectors in a group as described above, in interlaced printing, consecutive dots printed in a line along scan direction  56  are not printed by consecutive drop ejectors in a group. In the particular example for the portion of line  352  described above in this paragraph, the consecutive dots are printed by drop ejectors in the following order:  113 ,  111 ,  114 ,  112 ,  111 ,  113 ,  112 ,  114 ,  113 . 
     In the example described above with reference to  FIGS. 15A through 15D  the time between the start of the first odd stroke and the start of the first even stroke is equal to 3p 2 /V, or more generally (N 1 −1)*p 2 /V, and the time between the start of the first even stroke and the start of the second odd stroke is equal to 5p 2 /V, or more generally (N 1 +1)*p 2 /V, in order to properly position the dots for double interlacing. Alternatively, the time between the start of the first odd stroke and the start of the first even stroke can be equal to 5p 2 /V, or more generally (N 1 +1)*p 2 /V, and the time between the start of the first even stroke and the start of the second odd stroke can be equal to 3p 2 /V, or more generally (N 1 −1)*p 2 /V. Another way to look at this is that it is arbitrary whether one designates the first odd stroke as the first stroke and the first even stroke as the subsequent stroke that immediately follows the first stroke. Equally well one could designate the first even stroke as the first stroke and the second odd stroke as the subsequent stroke that immediately follows the first stroke. 
     In double-interlaced printing, the scan direction pitch p 2  is less than can be achieved for non-interlaced printing, but it cannot be made arbitrarily small. The time between printing cycles in a stroke for double-interlaced printing is Δt=(X 1 −2p 2 )/V. Consider the example shown in  FIGS. 15A through 15D  where the number of drop ejectors per group is N 1 =4 and the number of groups per bank is N 2 =2. The time in a stroke required for firing all 8 drop ejectors  111  through  118  is 8(X 1 −2p 2 )/V. The distance the recording medium moves at velocity V along scan direction  56  relative to the drop ejectors during this time is 8(X 1 −2p 2 ). This distance needs to be less than or equal to 3p 2 , so that there are no gaps between clusters of pixels. Therefore, 
       8( X   1 −2 p   2 )≦3 p   2 , so 8 X   1 ≦19 p   2 .   (4)
 
     As a result, the minimum value of scan direction pitch for double-interlaced printing in the example of  FIGS. 15A through 15D  is 
         p   2 min =8 X   1 /19,   (5)
 
     which is less than half of X 1 . 
     In order to print at even higher scan direction resolution with the drop ejector array arrangement described above with reference to  FIG. 7 , it is necessary to use higher-order interlaced printing as described below.  FIGS. 16A through 16E  illustrate a method of triple-interlaced printing at higher resolution by using triple the number of strokes. Conventions for drop ejectors and dots are similar to  FIGS. 15A through 15D . Less individual labeling is used in  FIGS. 16A through 16E  so as not to unnecessarily clutter these more compact figures. The first printing cycles of each of five consecutive strokes A 1 , A 2 , A 3 , B 1  and B 2  are shown in  FIGS. 16A through 16E . For the triple-interlaced example, p 3  is the scan direction pitch. In  FIG. 16A  at an initial time t 1 (A 1 ) for a first stroke, an endmost drop ejector from a first group is enabled to fire during a first printing cycle to form a first dot (represented as a filled circle) on the recording medium. Unfilled circles in  FIG. 16A  represent allowable dot positions from stroke A 1  that have not yet been enabled for printing. Spacing between allowable dot positions printed during stroke A 1  is 3p 3 , i.e. three times the scan direction pitch p 3 . During the printing of the first stroke A 1 , the recording medium moves at velocity V in the scan direction  56  relative to the drop ejectors. Similar to the discussion above relative to  FIG. 15A , after waiting for time delay Δt after firing the first drop ejector of the first group, successive drop ejectors from the first group are enabled to be fired in a successive printing cycles (not shown) to form successive dots represented by filled circles in  FIG. 16B . The distance between consecutive dots printed during stroke A 1  is equal to the spacing between adjacent drop ejectors minus the distance that the recording medium has moved relative to the drop ejectors during the time Δt, i.e. 3p 3 =X 1 −VΔt. 
     In  FIG. 16B  at an initial time t 1 (A 2 ) for a second stroke, an endmost drop ejector from the first group is enabled to fire during a first printing cycle to form a first dot (represented as a filled X) on the recording medium. In order to interlace the printed dots at a scan direction pitch p 3 , the recording medium is allowed to travel relative to the drop ejectors a distance 4p 3  between the first printing cycle of the first stroke A 1  ( FIG. 16A ) and the first printing cycle of the second stroke A 2  ( FIG. 16B ). In other words, during a time 4p 3 /V between the start of the first stroke A 1  and the start of the second stroke A 2  the recording medium moves relative to the drop ejectors by 4p 3  in the scan direction  56 . More generally for triple-interlacing, if there are N 1  drop ejectors in each group and if N 1  is not a multiple of 3, the time between the start of the first stroke and the start of the second stroke is equal to N 1 *p 3 /V. Unfilled X&#39;s in  FIG. 16B  represent allowable dot positions from stroke A 2  that have not yet been enabled for printing. 
     In  FIG. 16C  at an initial time t 1 (A 3 ) for a third stroke, an endmost drop ejector from the first group is enabled to fire during a first printing cycle to form a first dot (represented as a filled square) on the recording medium. In other respects, printing in third stroke A 3  is similar to that described above for  FIGS. 16A and 16B . 
     In  FIG. 16D  at an initial time t 1 (B 1 ) for a fourth stroke, an endmost drop ejector from the first group is enabled to fire during a first printing cycle to form a first dot (represented as a filled triangle) on the recording medium. In other respects, printing in fourth stroke B 1  is similar to that described above for  FIGS. 16A through 16C . 
     In  FIG. 16E  at an initial time t 1 (B 2 ) for a fifth stroke, an endmost drop ejector from the first group is enabled to fire during a first printing cycle to form a first dot (represented as a filled star) on the recording medium. In other respects, printing in fifth stroke B 2  is similar to that described above for  FIGS. 16A through 16D . 
     In triple-interlaced printing, the scan direction pitch p 3  is less than can be achieved for double-interlaced printing, but it cannot be made arbitrarily small. The time between printing cycles in a stroke for triple-interlaced printing is Δt=(X 1 −3p 3 )/V. Consider the example shown in  FIGS. 16A through 16E  where the number of drop ejectors per group is N 1 =4 and the number of groups per bank is N 2 =2. The time in a stroke required for firing all 8 drop ejectors is 8(X 1 −3p 3 )/V. The distance the recording medium moves at velocity V along scan direction  56  relative to the drop ejectors during this time is 8(X 1 −3p 3 ). This distance needs to be less than or equal to 4p 3 , so that there are no gaps between clusters of pixels printed by each group of drop ejectors. Therefore, 
       8( X   1 −3 p   3 )≦4 p   3 , so 8 X   1 ≦28 p   2 .   (6)
 
     As a result, the minimum value of scan direction pitch for triple-interlaced printing in the example of  FIGS. 16A through 16E  is 
         p   3 min =2 X   1 /7,   (7)
 
     which is less than a third of X 1 . 
     In order to print at even higher scan direction resolution with the drop ejector array arrangement described above with reference to  FIG. 7 , it is necessary to use higher-order interlaced printing. Multiple-interlacing is referred to herein as M-interlacing, where M=2 for double-interlacing and M=3 for triple-interlacing. In general for M-interlacing (and as illustrated above for M=2 and M=3), each stroke in a series of (M−1) consecutive subsequent strokes following the first stroke is timed relative to the first stroke such that subsequent-stroke dots formed on the recording medium by drops ejected from at least one drop ejector in each group during each of the subsequent strokes in the series of (M−1) consecutive subsequent strokes are disposed in interlacing fashion in the scan direction between allowable first-stroke dot locations on the recording medium. 
     For the example of double-interlacing described above with reference to  FIGS. 15A through 15D , scan direction pitch p 2 =(X 1 −VΔt)/2. For the example of triple-interlacing described above with reference to  FIGS. 16A through 16E , scan direction pitch p 3 =(X 1 −VΔt)/3. In general for M-interlacing for embodiments where a direction from the first-fired drop ejector of the first group to the second-fired drop ejector of the first group is the same as the scan direction, scan direction pitch p M =(X 1 −VΔt)/M. More simply, p=(X 1 −VΔt)/M, where the scan direction pitch for M-interlacing is generically denoted as p. 
     For the example of double-interlaced printing as described above with reference to  FIGS. 15A through 15D , the time between the start of the first odd stroke and the start of the first even stroke is equal to 3p 2 /V, or more generally (N 1 −1)*p/V where N 1  is even, and the time between the start of the first even stroke and the start of the second odd stroke is equal to 5p/V, or more generally (N 1 +1)*p/V, in order to properly position the dots for double interlacing. More generally for M-interlacing where a least common multiple of N 1  and M is less than N 1 *M, it can be shown that the time between the start of the first stroke and the start of the subsequent stroke immediately following the first stroke is equal to (N 1 1)*p/V, and the time between the start of the Mth subsequent stroke and the start of a stroke immediately following the Mth stroke is equal to (N 1 +1)*p/V. In addition, for M greater than 2, it can be shown that for each of the M strokes except the first stroke and the Mth stroke, a time between the start of each stroke and the start of the immediately following stroke is equal to N 1 *p/V. Also, as observed above for the double-interlacing example, since the sequence of strokes is repetitive, it is somewhat arbitrary which stroke is denoted as the first stroke, i.e. whether the time between strokes (N 1 −1)*p/V is considered to occur before or after the time between strokes (N 1 +1)*p/V. 
     For the example of triple-interlaced printing as described above with reference to  FIGS. 16A through 16E , the time between the start of each stroke and the start of the immediately following stroke is equal to 4p 3 /V, or more generally N 1 *p/V, where N 1 =4 and M=3. It can be shown in general that for embodiments where a least common multiple of N 1  and M is equal to N 1 *M, the time between the start of each of the M strokes, including the first stroke, and the start of an immediately following stroke is equal to N 1 *p/V. 
     In the interlacing examples described above, the advantage has been described in terms of higher scan direction resolution, i.e. an increased number of dots per inch along the scan direction  56 . In some embodiments, as in piezo inkjet, a fairly wide range of drop volumes can be ejected by a given drop ejector. In such embodiments the drop volume can be controlled by adjusting the electrical pulses from electrical pulse source  5  ( FIG. 6 ) such that smaller dots can be printed when using interlacing than when not using interlacing. In this way the overall ink coverage can be kept substantially constant. In other embodiments, as in thermal inkjet, a given drop ejector can eject only a fairly narrow range of drop volumes. In some instances interlacing is used in increasing the addressability along the scan direction  56  without greatly increasing the number of dots per inch that are printed. In other words, not every allowable pixel location on the pixel grid would be printed for the image. Instead, interlacing would be used to make fine adjustments on the positions of dots to be printed. For example, a diagonal line that is not parallel to either the array direction  54  or the scan direction  56  can have a jagged appearance if the scan direction pitch p is about equal to the cross-track pitch Y 1  ( FIG. 6 ). By printing in interlaced fashion, the dot position along the scan direction  56  can be adjusted in fine increments by controllably printing a particular interlaced dot rather than an adjacent interlaced dot, thereby smoothing the appearance of lines or other features in the image. 
     In some embodiments it can be advantageous to print multiple drops of ink on the same pixel location to increase ink coverage and enlarge the color gamut.  FIGS. 17A through 17D  illustrate the printing of up to two drops per pixel by doubling the number of strokes and timing the strokes appropriately using the drop ejector array arrangement described above with reference to  FIG. 7 . As was the case for  FIGS. 15A through 16E ,  FIGS. 17A through 17D  show only the drop ejectors and dot locations corresponding to groups  121  and  122  of bank  131  for simplicity. In  FIG. 17A  at an initial time t 1 (A 1 ) for a first stroke, an endmost drop ejector  111  from a first group  121  is enabled to fire during a first printing cycle to form a first dot  451  (represented as a filled circle) on the recording medium. Unfilled circles in  FIG. 17A  represent allowable dot positions from stroke A 1  that have not yet been enabled for printing. Spacing between allowable dot positions for first stroke A 1  is the scan direction pitch p. During the printing of the first stroke A 1 , the recording medium moves at velocity V in the scan direction  56  relative to the drop ejectors. Similar to the discussion above relative to  FIG. 15A , after waiting for time delay Δt after firing the first drop ejector of the first group, successive drop ejectors from the first group are enabled to be fired in a successive printing cycles (not shown) to form successive dots represented by filled circles in  FIG. 17B . The distance between consecutive dots printed during stroke A 1  is equal to the spacing between adjacent drop ejectors minus the distance that the recording medium has moved relative to the drop ejectors during the time Δt, i.e. p=X 1 −VΔt. 
     In  FIG. 17B  at an initial time t 1 (A 2 ) for a second stroke, the endmost drop ejector  111  from the first group  121  is enabled to fire during a first printing cycle to form a first dot  461  (represented as a filled star) on the recording medium. In order to allow drops of ink printed during successive strokes to land on the same location, the recording medium is allowed to travel relative to the drop ejectors a distance 2p between the first printing cycle of the first stroke A 1  ( FIG. 17A ) and the first printing cycle of the second stroke A 2  ( FIG. 17B ). In other words, during a time 2p/V between the start of the first stroke A 1  and the start of the second stroke A 2  the recording medium moves relative to the drop ejectors by 2p in the scan direction  56 . Unfilled stars in  FIG. 17B  represent allowable dot positions from stroke A 2  that have not yet been enabled for printing. 
     In  FIG. 17C  at an initial time t 1 (B 1 ) for a third stroke, the endmost drop ejector  111  from the first group  121  is enabled to fire during a first printing cycle to form a first dot  471  (represented as a filled triangle) on the recording medium. In order to allow drops of ink printed during successive strokes to land on the same location, the recording medium is allowed to travel relative to the drop ejectors a distance 2p between the first printing cycle of the second stroke A 2  ( FIG. 17B ) and the first printing cycle of the third stroke B 1  ( FIG. 17C ). In other words, during a time 2p/V between the start of the first stroke A 1  and the start of the second stroke A 2  the recording medium moves relative to the drop ejectors by 2p in the scan direction  56 . Unfilled triangles in  FIG. 17C  represent allowable dot positions from stroke B 1  that have not yet been enabled for printing.  FIG. 17C  also shows printed dots that have landed in the same location on the recording medium. For example, dot  463  (represented as a filled star) that was printed as the third dot by drop ejector  113  during the second stroke has landed on top of dot  451  (represented as a filled circle) that was printed by drop ejector  111  as the first dot during the first stroke. Similarly, dot  464  (represented as a filled star) that was printed as the fourth dot by drop ejector  114  during the second stroke has landed on top of dot  452  (represented as a filled circle) that was printed by drop ejector  112  as the second dot during the first stroke. 
     In  FIG. 17D  at an initial time t 1 (B 2 ) for a fourth stroke, the endmost drop ejector  111  from the first group  121  is enabled to fire during a first printing cycle to form a first dot  481  (represented as a filled X) on the recording medium. In order to allow drops of ink printed during successive strokes to land in the same location, the recording medium is allowed to travel relative to the drop ejectors a distance 2p between the first printing cycle of the second stroke B 1  ( FIG. 17C ) and the first printing cycle of the fourth stroke B 2  ( FIG. 17D ). Unfilled X&#39;s in  FIG. 17D  represent allowable dot positions from stroke B 2  that have not yet been enabled for printing.  FIG. 17D  also shows additional printed dots from successive strokes that have landed in the same location on the recording medium. For example, dot  473  (represented as a filled triangle) that was printed by drop ejector  113  in the first group  121  as the third dot during the third stroke has landed on top of dot  461  (represented as a filled star) that was printed by drop ejector  111  in the first group  121  as the first dot during the second stroke. In addition, dot  477  (represented as a filled triangle) that was printed by drop ejector  117  in the second group  122  as the seventh dot during the third stroke has landed on top of dot  465  (represented as a filled star) that was printed by drop ejector  115  in the second group  122  as the fifth dot during the second stroke. Successive strokes beyond the fourth stroke allow each allowable pixel position in a pixel grid to be printed with up to two drops of ink in this example. 
     More generally, M drops can be printed on the same locations in M successive strokes, where M is not greater than the number N 1  of drop ejectors per group. Each stroke in a series of (M−1) consecutive subsequent strokes following the first stroke is timed relative to the first stroke such that subsequent-stroke dots formed on the recording medium by drops ejected from at least one drop ejector in each group during each of the subsequent strokes in the series of (M−1) consecutive subsequent strokes are disposed on allowable first-stroke dot locations on the recording medium. 
     In the example shown in  FIG. 17C  the first stroke and the second stroke jointly printed two drops of ink at allowable image dot locations on the recording medium. As described above, a first pair of dots  451  and  463  was jointly printed by the first stroke and the second stroke in one allowable image dot location. A second pair of dots  452  and  464  was jointly printed by the first stroke and the second stroke in another allowable image dot location. In general, the first stroke and at least one subsequent stroke in a series of (M−1) subsequent strokes can be controlled to enable jointly printing more than one drop of ink at allowable image dot locations on the recording medium. 
     An alternative usage of the capability of printing dots from different strokes at a same location is to provide printing redundancy, so that if one drop ejector fails, its dots can be printed by a different drop ejector during single pass printing. In a carriage printer (as described above in the background) multi-pass printing can be used to allow printing at particular locations on the recording medium using different drop ejectors after the recording medium is advanced along the array direction. However, multi-pass printing is significantly slower than single pass printing. By having a plurality of drop ejectors aligned along the scan direction  56  as shown in  FIG. 7 , printing redundancy can be provided in single-pass printing. As described earlier with reference to  FIG. 8 , if a single drop ejector in a group fails, it does not result in a white streak along the scan direction  56  due to the multiple drop ejectors in a group that cooperatively print the dots in a line along the scan direction. However, a failed drop ejector would result in isolated white dots in the image. Using redundant drop ejector printing, the isolated white dots corresponding to a failed drop ejector can be reduced or even eliminated. 
     For redundant drop ejector printing, the difference in printing method relative to the multiple-drops per pixel method described above with reference to  FIGS. 17A through 17D  is that in the redundant drop ejector printing method, only one of the strokes is used to print a given dot location. In other words, the first stroke and the at least one subsequent stroke in the series of (M−1) subsequent strokes are controlled to enable jointly printing up to one drop of ink at allowable image dot locations on the recording medium. Such control can be done routinely by alternating which stroke has responsibility for printing a dot in a line of dots along the scan direction. In this way, the number of isolated white dots corresponding to a failed drop ejector is reduced. Alternatively, the control can be done in response to an identified print defect. An identified defective drop ejector can be disabled and its printing data assigned to a corresponding functioning drop ejector that can print the dots instead. In such a way white dots can be eliminated and printing high quality images can be performed with high reliability, even if one or more drop ejectors fail. 
     In the various printing method embodiments described above, a direction  127  ( FIG. 11B ) from the first drop ejector  111  enabled to be fired in the first group  121  to the second drop ejector  112  enabled to be fired in the first group  121  is same as the recording medium travel direction (scan direction  56 ) relative to the drop ejectors. In such embodiments the scan direction pitch p is less than the spacing X 1  between drop ejectors along the scan direction  56 . In other printing method embodiments a direction from the first drop ejector enabled to be fired in the first group to the second drop ejector enabled to be fired in the first group is opposite to the recording medium travel direction (scan direction  56 ) relative to the drop ejectors. In such embodiments the scan direction pitch p is greater than the spacing X 1  between drop ejectors along the scan direction  56 . 
       FIGS. 18A through 18D  are analogous to  FIGS. 11A and 11C through 11E  respectively and show the same configuration of drop ejectors ( 111 - 118 ), groups ( 121 - 124 ) and banks ( 131 - 132 ). The recording medium travels along the scan direction  56  relative to the drop ejectors as in  FIGS. 11A through 11E . What is different in the print stroke illustrated in  FIGS. 18A through 18D  is that the order of firing the drop ejectors  111 - 118  is reversed. Rather than enabling firing the drop ejectors in the order  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  117  and  118 , in  FIGS. 18A through 18D , the firing order is  118 ,  117 ,  116 ,  115 ,  114 ,  113 ,  112  and  111 . The direction  128  between the first drop ejector  118  enabled for firing in a group and the second drop ejector  117  enabled for firing in the group is in the opposite direction as the scan direction  56  relative to the drop ejectors. 
     At t=t 1    FIG. 18A  shows the dots  501  printed by drop ejectors  118  in banks  131  and  132  during a first print cycle of the print stroke. At t=t 4    FIG. 18B  shows the dots printed by the end of the fourth print cycle after drop ejectors  118 ,  117 ,  116  and  115  in banks  131  and  132  have been fired. During each print cycle the recording medium moves a distance VΔt relative to the drop ejectors along scan direction  56 . The distance between dot  501  printed by drop ejector  118  during the first print cycle and dot  502  printed by drop ejector  117  during the second print cycle is scan direction pitch p=X 1 +VΔt. Stated another way, Δt=(p−X 1 )/V. At t=t 8    FIG. 18C  shows the dots printed by the end of the eighth printing cycles after all eight drop ejectors  118  through  111  in each bank  131  and  132  have been fired. At t=t S    FIG. 18D  shows the position of the dots relative to the drop ejectors when the next stroke is ready to begin. Similar to the discussion with reference to  FIGS. 11D and 11E , in order for the scan direction pitch p to remain constant along the scan direction  56 , the recording medium must move a total distance of N 1 *p between the start of the first stroke at time t 1  and the start of the next stroke at time t S , as illustrated in  FIG. 11E  where N 1 *p=4p. In  FIG. 18C  at t=t 8 , the recording medium has moved by 7VΔt=(N 1 *N 2 −1)VΔt relative to its first position in  FIG. 18A . The extra distance that the recording medium needs to move between t 8  ( FIG. 18C ) and t S  ( FIG. 18D ) is N 1 *p−(N 1 *N 2 −1)VΔt=N 1 *p−(N 1 *N 2 −1)*(p−X 1 ). Thus there needs to be a delay time τ 3 =t S −t 8 =(N 1 *p−(N 1 *N 2 −1)*(p−X 1 ))/V after all N 1 *N 2  drop ejectors in each bank have been fired in a first stroke before the second stroke begins. 
     An alternative way (not shown) to have the direction from the first enabled drop ejector of the first group to the second enabled drop ejector of the first group be opposite the scan direction  56  is to keep the firing order the same as in  FIG. 11B  (direction  127 ), but reverse the direction of the relative travel of the recording medium. As described above with reference to  FIG. 10 , a sequencer  175  can be used to reverse the firing order and that is typically easier than reversing the medium travel direction, especially for single-pass printing. 
     An advantage of having the direction from the first enabled drop ejector of the first group to the second enabled drop ejector of the first group be opposite the scan direction  56 , so that the scan direction pitch p is greater than the drop ejector spacing X 1  is that ink coverage is reduced. In other words, a higher resolution print mode can be provided by having the firing order and recording medium travel direction as described with reference to  FIGS. 11A through 11E , and an ink-saver print mode can be provided by reversing the firing order as described with reference to  FIGS. 18A through 18D . Furthermore, ink spreads differently on different types of recording medium. For a low ink-spread recording medium it can be advantageous to cause the dots to be printed closer together along scan direction  56  by having the firing order and recording medium travel direction as described with reference to  FIGS. 11A through 11E . For a high ink-spread medium it can be advantageous to cause the dots to be printed farther apart along scan direction  56  by reversing the firing order as described with reference to  FIGS. 18A through 18D . 
     In addition, it is contemplated that interlacing modes can be used with reversed firing order, although such embodiments are not described in detail herein. Such interlaced modes with reversed firing order can provide scan direction pitches that are different from the scan direction pitches that are achievable using the interlacing modes described above with reference to  FIGS. 15A through 16E . 
     In the printing method embodiments described above, drop ejectors in each bank in each column are simultaneously fired. In other embodiments (not shown) drop ejectors in different groups in different columns are simultaneously fired, but no other drop ejectors within the same column are fired simultaneously. Additionally in the embodiments described above, groups of drop ejectors within a bank are fired sequentially in a left to right direction across the bank of groups. In other embodiments (not shown) groups of drop ejectors within a column can be fired in nonsequential order across the column. 
     A more general way to describe a printing method using the inkjet printing system  1  of  FIG. 6  including a printhead  50  having a two-dimensional array  150  of drop ejectors  212  that are fluidically connected to a common ink source  290 , where the two-dimensional array  150  includes spatially offset groups  120  of drop ejectors  212 , each group having a plurality of drop ejectors  212  that are aligned substantially along the scan direction  56  is as follows: Image data is provided to inkjet printhead  50  from image data source  2  via image processing unit  3  and controller  4 , which use the image data to control whether or not a drop ejector  212  is fired when it is enabled. During the ejection of ink drops, transport mechanism  6  continuously advances the recording medium  62  relative to the printhead  50  along the scan direction. Controller  4  and addressing circuitry  170  ( FIG. 9 ) enable simultaneous firing of drop ejectors  212  that are corresponding members of a first set of groups  120 . Controller  4  and addressing circuitry  170  ( FIG. 9 ) enable sequential firing of individual drop ejectors  212  within each group  120  of the first set of groups until each member of each group has had opportunity to fire. Controller  4  and addressing circuitry  170  ( FIG. 9 ) enable simultaneous firing of drop ejectors  212  that are corresponding members of a second set of groups  120 . Controller  4  and addressing circuitry  170  ( FIG. 9 ) enable sequential firing of individual drop ejectors  212  within each group  120  of the second set of groups. Controller  4  and addressing circuitry  170  ( FIG. 9 ) successively enable likewise firing of any additional groups  120  in the two-dimensional array  150  until all drop ejectors in the two-dimensional array  150  have had opportunity to fire during a first stroke. The process of enabling the firing of drop ejectors  212  of the two-dimensional array continues in subsequent strokes similar to the first stroke as the recording medium  62  is moved relative to the printhead  50  along the scan direction  56  until printing of the image with ink from the common ink source  290  according to the image data is completed. 
     Printhead die  215  described above relative to  FIGS. 6-9  includes a single two-dimensional array  150  of nominally identical drop ejectors and is part of inkjet printhead  50  ( FIG. 6 ). Such a printhead die  215  is capable of monochrome printing of ink from first ink source  290 .  FIG. 19  shows a printhead die  216  that can be included in inkjet printhead  50  in other embodiments. Printhead die  215  includes a first two-dimensional array  150  of first drop ejectors and a second two-dimensional array  151  of second drop ejectors that is separated from the first two-dimensional array  150  by an array spacing S along the first direction, i.e. along the scan direction  56 . In some embodiments the second two-dimensional array  151  is in fluidic communication with a second ink source  291  that is different from the first ink source  290 . For example, for a printhead die  216  to be used for color printing, ink source  290  can be cyan ink and ink source  291  can be magenta ink. Inkjet printhead  50  can also include additional two-dimensional arrays (not shown) that are in fluidic communication with corresponding additional ink sources (not shown), such as yellow ink and black ink. These additional two-dimensional arrays can be included on the same printhead die  216  or on a separate printhead die. 
     Second two-dimensional array  151  has a similar configuration of columns, banks and groups of second drop ejectors  213  as first two-dimensional array  150  of first drop ejectors  212 . Second drop ejectors  213  in the second two-dimensional array  151  are fired in similar stroke fashion as the first drop ejectors  212  of the first two-dimensional array  150 , as described above for the various printing methods. Strokes for firing the second drop ejectors  213  of the second array  151  are delayed relative to corresponding strokes for firing the first drop ejectors  212  by a delay time S/V, where the recording medium moves at velocity V along the scan direction  56  relative to the printhead die  216 . In this way, drops ejected from second two-dimensional array  151  can land on the same pixel grid of dot locations as drops ejected from first two-dimensional array  150  corresponding to image data from image source  2  ( FIG. 6 ) in order to form color print images. 
     In order to provide the desired nominal drop volume for different inks it can be advantageous for the second drop ejectors  213  in the second two-dimensional array  151  that are in fluidic communication with second ink source  291  to have a different structure than the first drop ejectors  212  in the first two-dimensional array  151  that are in fluidic communication with the first ink source  290 . For example the nozzle diameters can be different, the pressure chamber geometries can be different or the actuator sizes can be different for drop ejectors  212  and  213 . 
     As described above with reference to  FIG. 6 , two-dimensional arrays  150  and  151  have a width W along the scan direction  56  and a length L along the array direction  54 , where L is greater than W. It is advantageous for the length L along a direction perpendicular to scan direction  56  to be long, in order to allow printing a large area of the recording medium  62  with ink drops from both ink sources  290  and  291  in a single pass or in a single swath. In a color printhead one can determine from the drop ejector array configuration which dimension of the two-dimensional array corresponds to the scan axis X and which dimension of the two-dimensional array corresponds to the array axis Y. In order for different two-dimensional arrays to print drops in the same location on the recording medium, they must be separated from each other along the scan axis X. Therefore, for a color printhead (even without looking at the transport mechanism for providing relative motion of the recording medium and the printhead) one can determine that the width dimension W (that is shorter than the length dimension L) of the two-dimensional arrays extends along the scan direction  56 . 
     In the prior art there are various two-dimensional array configurations of drop ejectors. Prior art  FIG. 20  shows the drop ejector array of U.S. Pat. No. 6,991,318 as depicted in FIG. 85 of that patent (where array direction  54 , scan direction  56 , length L and width W have been added to  FIG. 20 ). A portion  360  of an array of ink ejection nozzle sets  361 - 363  is shown with each set providing separate color output (cyan, magenta and yellow) for color printing. Address circuitry  364  and bond pads  365  are also shown. Each set of color nozzles  361 - 363  contains two spaced apart rows of ink ejection nozzles  368 . At first glance the drop ejector arrangement in a given nozzle set (such as nozzle set  361 ) appears similar to the arrangement shown in  FIG. 7 . In each of the two nozzle rows of nozzle set  361  in array portion  360  there are three groupings of five nozzles, where the groupings are offset from one other. However nozzle sets  361 - 363  correspond to different colors so as discussed above, they are separated from each other along the scan direction  56 . Therefore the three nozzle groupings of five nozzles in each row do not extend along the scan direction  56 , but rather along the array direction  54 . (The width W of each nozzle set does not extend along the scan direction  56 , but rather along array direction  54 .) As such, the drop ejectors in each of the groupings cannot cooperatively print a line of dots along the scan direction  56 , but rather a single nozzle  368  in each grouping is responsible for printing all dots in a line that is printed along the scan direction  56 . The purpose of the two staggered rows of nozzles  368  in each nozzle set  361 - 363  is to provide higher resolution printing along the array direction  54  as can be seen more clearly in FIG. 87 of U.S. Pat. No. 6,991,318. 
     With reference again to  FIG. 19 , in some embodiments, second ink source  291  is the same as first ink source  290  and the drop ejectors  212  and  213  have different structures to provide different drop sizes for the same ink. In other words, in order to print in gray scale, first drop ejectors  212  can be configured to print small dots and second drop ejectors  213  can be configured to print larger dots. 
     In some embodiments, especially for pagewidth printheads, it is impractical to provide on a single printhead die all the required drop ejectors in a two-dimensional array that is long enough to extend across a recording medium.  FIG. 21  shows a first printhead die  215  and a substantially identical second printhead die  217  that is displaced along the array direction  54  from the first printhead die  215  and butted end to end along butting edges  214 . Note: the term “butted end to end” is meant herein to describe close adjacency of the two printhead die without necessarily implying physical contact at the butting edges  214 . The two-dimensional array  152  of drop ejectors  212  includes a first two-dimensional array  153  disposed on the first printhead die  215  and a substantially identical two-dimensional array  154  of drop ejectors disposed on the second printhead die  217 . Both two-dimensional array  153  and two-dimensional array  154  are configured to be in fluidic communication with the first ink source  290 . In the example shown in  FIG. 21 , in order to maintain a consistent spacing between groups along the array direction  54 , adjacent groups  120  within each bank  130  are substantially evenly spaced apart by first offset Y 1  along array direction  54 ; and a first endmost group  191  of the first two-dimensional array  153  and a second endmost group  192  of the substantially identical two-dimensional array  154  are spaced apart along the array direction  54  by a distance that is substantially equal to the first offset Y 1 . 
       FIG. 22  shows a first printhead die  215  and a substantially identical second printhead die  217  that is displaced along the array direction  54  from the first printhead die  215  and is spaced apart from the first printhead die  215  by a distance Y 0 . The two-dimensional array  152  of drop ejectors  212  includes a first two-dimensional array  153  disposed on the first printhead die  215  and a substantially identical two-dimensional array  154  of drop ejectors disposed on the second printhead die  217 . The drop ejectors  212  on the first printhead die  215  includes an ink inlet that is configured to be in fluidic communication with the first ink source  290  and the drop ejectors  212  on the substantially identical second printhead die  217  includes an ink inlet that is configured to be in fluidic communication with a second ink source  291  that is different from the first ink source. The separation Y 0  provides necessary area required to seal and separate the ink supply to the first printhead die  215  and the ink supply to the second printhead die  217 . 
       FIG. 23  shows a pair of printhead die  218  and  219  that are butted end to end along butting edges  214  similar to  FIG. 21 . Printhead die  218  and  219  each include a first two-dimensional array  150  of first drop ejectors and a second two-dimensional array  151  of second drop ejectors that is separated from the first two-dimensional array  150  along the first direction, i.e. along the scan direction  56 . The first two-dimensional array  150  in each printhead die  218  and  219  is in fluidic communication with a first ink source  290 . The second two-dimensional array  151  in each printhead die  218  and  219  is in fluidic communication with a second ink source  291  that is different from the first ink source  290 . The butting edges  214  of printhead die  218  and printhead die  219  include stepped features that facilitate maintaining the spacing Y 1  between endmost drop ejector groups of two-dimensional array  150  and two-dimensional array  151 . 
       FIG. 24A  shows a pair of printhead die  511  and  512  that are butted end to end at butting edges  214 . The drop ejector configuration on both printhead die  511  and  512  is similar to that shown in  FIG. 7 . In the lowermost groups in columns  141 ,  142 ,  143  and  144 , the lowermost drop ejectors  111  are all aligned along the array direction  54 . There is a gap spacing G 1  between outermost portions of nearest neighbor drop ejectors on printhead die  511  and printhead die  512 . It is desirable to increase gap spacing G 1  while still maintaining the spacing Y 1  between endmost adjacent drop ejector groups on the two printhead die  511  and  512  in order to provide room for any electronics or other components near butting edges  214 , as well as to allow a small spacing between adjacent butting edges  214 . 
       FIG. 24B  shows a pair of printhead die  521  and  522  that are butted end to end at butting edges  214 . In the two-dimensional array of drop ejectors formed on each printhead die  521  and  522 , adjacent columns of drop ejectors are displaced along scan direction  56  by a distance X 1 . As a result, drop ejector  112  in column  141  is aligned with drop ejector  111  in column  142 ; drop ejector  112  in column  142  is aligned with drop ejector  111  in column  143 ; and drop ejector  112  in column  143  is aligned with drop ejector  111  in column  144 . A distance X 6  along scan direction  56  between drop ejector  111  in first column  141  and corresponding drop ejector  111  in last column  144  is X 6 =3X 1 =(N 4 −1)*X 1 . It can be seen in  FIG. 24B  that the gap spacing G 2  between outermost portions of nearest neighbor drop ejectors on printhead die  521  and printhead die  522  is larger than the gap spacing G 1  between outermost portions of nearest neighbor drop ejectors on printhead die  511  and printhead die  512  in  FIG. 24A . Gap G 2  increases as X 6  increases. Although the difference between G 1  and G 2  does not seem large in the example shown in  FIGS. 24A and 24B  where the number of columns N 4 =4, the difference is larger for printhead die having a larger number of displaced columns. In addition, the displacement of adjacent columns in  FIG. 24B  is X 1 . More generally the displacement of adjacent columns can be m*X 1 , where m is an integer, and X 6 =m*(N 4 −1)*X 1 . 
       FIG. 25  illustrates a pair of printhead die  531  and  532  that are butted end to end at butting edges  533  and  534  respectively. Unlike examples described above where butting edges  214  are straight, butting edges  533  and  534  include steps  536  and  535  respectively. Each printhead die  531  and  532  has a left-side butting edge  534  having steps  535  that project outwardly toward the left by a step width w, and a right-side butting edge  533  having steps  536  that project inwardly toward the left by a step width w. The steps  536  of butting edge  533  of printhead die  531  and butting edge  534  of printhead die  532  can be positioned in substantially complementary fashion at the point of adjacency of printhead die  531  and  532 . In this way maintaining the spacing Y 1  between endmost drop ejector groups on the two printhead die  531  and  532  is facilitated. Although the steps  535  and  536  are shown in  FIG. 25  are shown as having sharp corners, in practice the corners of steps can be rounded in order to avoid the occurrence of stress concentrators that can result in structural weakness. 
     Many printhead die are typically fabricated together on a single wafer of silicon, for example. After wafer processing is completed, it is necessary to separate the individual printhead die from the wafer. For printhead die having straight edges, the printhead die can be separated from the wafer by dicing. However, if the edges of printhead die are stepped, as in the example shown in  FIGS. 23 and 25 , portions of such steps would be cut through during dicing. One way to precisely form the steps  535  and  536  is to use an etching process, such as deep reactive ion etching, which can provide feature delineation through the wafer with accuracy on the order of one micron. Another way to precisely form the steps  535  and  536  is to use a laser cutting process. 
       FIG. 26  schematically shows an example of a roll-to-roll printing system  80  that can be used with a printhead  50  having one or more two-dimensional arrays of drop ejectors as described in embodiments above. A stationary inkjet printhead  50  is in fluidic communication with a first ink source  290 . A web of recording medium  62  is advanced from a source roll  81  to a take-up roll  82  along scan direction  56  and is guided by one or more rollers  83 . The direction of relative motion between the recording medium  62  and the printhead  50  remains constant throughout the printing process. If a color printhead with multiple two-dimensional arrays in fluidic communication with different ink sources is used as described above with reference to  FIG. 22 , the constant direction of relative motion between the recording medium  62  and the printhead  50  means that the order of printing of different colors always remains the same during single-pass printing. For example, the drop ejectors in two dimensional array  150  always print ink from first ink source  290  before drop ejectors in two dimensional array  151  print ink from second ink source  291 . Maintaining the same order of color laydown helps to provide a more consistent image appearance. Printhead  50  is long enough to span the web of recording medium  62 , or at least the portion of recording medium  62  that is to be printed. 
       FIG. 27  schematically shows an example of a carriage printing system  90  that can be used with a printhead  50  having one or more two-dimensional arrays of drop ejectors as described in embodiments above. The two-dimensional array has a length L along array direction  54  as described above. A carriage (not shown) moves printhead  50  along a carriage path  91 . In a first pass, the carriage moves printhead  50  in forward direction  92  as the drop ejectors print a first swath on the recording medium  62 . At the end of the swath the recording medium  62  is advanced as represented by media advance  94 . In a second pass the carriage moves printhead  50  in a reverse direction  93  as the drop ejectors print a second swath. In successive bidirectional printing swaths the image is printed on recording medium  62 . In bidirectional printing the scan direction reverses for each successive swath. As described above with reference to  FIGS. 11A-11E and 18A-18D , whether the scan direction pitch p is greater than or less than the ejector spacing X 1  depends on whether the firing order is such that the direction  127  between the first ejector and the second ejector in a group enabled for firing is the same as the scan direction, or such that the direction  128  between the first ejector and the second ejector in a group enabled for firing is opposite to the scan direction. In order to keep the scan direction pitch constant from swath to swath in a bidirectional carriage printing system  90 , it is necessary to reverse the firing order on each successive swath. Optionally the successive swaths can be partially overlapping. An advantage of using two-dimensional arrays of the types described in embodiments above is that multiple nozzles in each group cooperatively print the pixels in any given line across the recording medium  62  parallel to the carriage path  91 . Therefore, extensive overlap between adjacent swaths is not necessary for disguising printing defects. Optionally a small overlap in swaths can be used to disguise variations in the media advance  94 . Having a smaller swath overlap enables faster printing throughput relative to prior art carriage printing systems that use multi-pass printing to achieve high quality printing. 
     If a color printhead such as the printhead shown in  FIG. 23  is used in a bidirectional inkjet printing system  90 , it can be necessary to adjust the image to correct for color shift due different orders of color laydown in adjacent swaths as the carriage moves the printhead  50  in the forward direction  92  and then in the reverse direction  93 . For example, cyan dots can be printed over magenta dots in forward direction  92 , and magenta dots can be printed over cyan dots in reverse direction  93  providing a different appearance. Some prior art printheads have had mirror-symmetric arrangements of color drop ejectors. For example, a three-color mirror symmetric printhead can have five drop ejector arrays, including a central yellow array that is bordered on either side by two magenta arrays and having outer cyan arrays. An embodiment of the drop ejector configuration of  FIG. 7  is contemplated where the distance X 5  between two adjacent banks of drop ejectors is not on the order of 2X 1 , but rather is large enough to accommodate a drop ejector array for printing a second color ink between drop ejector banks that both print a first color ink. 
     If a color printhead such as the printhead shown in  FIG. 22  is used in a bidirectional inkjet printing system  90 , it is not necessary to adjust the image to correct for color shift because the orders of color laydown in adjacent swaths is unchanged as the carriage moves the printhead  50  in the forward direction  92  and then in the reverse direction  93 . 
     At least some of the examples above have been described and shown in idealized forms. For example, in  FIG. 7  drop ejectors  111 - 114  in group  121  have been shown as being perfectly aligned along scan direction  56 . In the real world small deviation from perfect alignment is contemplated when it is said herein that the drop ejectors within each group are aligned substantially along the scan direction. Similar to  FIG. 7 ,  FIG. 28A  shows a group  121  of drop ejectors  111 - 114  and a group  122  of drop ejectors  115 - 118  that are perfectly aligned along the scan direction  56 . In other words, a line  551  along scan direction  56  passes through the centers of all drop ejectors  111 - 114  of group  121 , and a line  552  along scan direction  56  passes through the centers of all drop ejectors  115 - 118  of group  122 . Line  552  is spaced apart from line  551  by first offset Y 1  along array direction  54 .  FIG. 28B  shows a group  121  of drop ejectors  111 - 114  that are perfectly aligned along the scan direction  56  and a group  122  of drop ejectors  115 - 118  that are not perfectly aligned along the scan direction  56 . A best-fit line  550  along scan direction  56  passes through the centers of drop ejectors  115  and  117 . However, the center of drop ejector  118  is offset to the left of best-fit line  550  by displacement Y D  along the scan direction  56 , and the center of drop ejector  116  is similarly offset to the right of best-fit line  550 . Such displacement can be related to manufacturing tolerances or they can be intentionally designed to occur. Drop ejectors that are fabricated using photolithography and microelectronic fabrication methods can have placement accuracies on the order of one micron in some embodiments. First offset Y 1  in some embodiments can be 1/1200 of an inch or about 21 microns. In such embodiments manufacturing tolerances permit alignment of drop ejectors along scan direction  56  to within 10% of first offset Y 1 . In other embodiments some amount of drop ejector misalignment is designed in order to disguise the effects of misdirectionality, i.e. the deviation of ejected drops from their intended courses such that even perfectly aligned drop ejectors do not provide perfectly aligned dots on the recording media  62 . Herein it is said that the drop ejectors in a group are substantially aligned along the scan direction when the maximum displacement Y D  along the array direction of a drop ejector in the group from the best-fit line is less than half the first offset Y 1 . Since the straightness of lines such as line  351  in  FIG. 14  partly depends on having a small maximum displacement, in some embodiments it is preferred for the maximum displacement Y D  to be less than 0.3Y 1 , and in other embodiments it is more preferred for the maximum displacement Y D  to be less than 0.2Y 1 . So-called best-fit lines in general may be calculated in a variety of ways, such as by linear regression by least square fitting for example.  FIG. 28C  shows a linear regression line  553  that passes through the centers of two drop ejectors  554  and  555 . Linear regression line  553  is not what is meant herein by a best-fit line along scan direction  56  because linear regression line  553  is not parallel to scan direction  56 . Best-fit line  550  in  FIG. 28C  extends along scan direction  56 . In addition, the best-fit line  550  is defined herein such that the sum of displacements of drop ejectors from best-fit line  550  is zero. In the simple example shown in  FIG. 28C , the center of drop ejector  554  has a displacement of −Y D  from best-fit line  550  and the center of drop ejector  555  has a displacement of +Y D  from best-fit line  550 , so that the sum of displacements is 0. 
     Other uses of the word “substantially” herein will next be described. When it is said herein that the drop ejectors within each group are substantially evenly spaced by a distance X 1  along the scan direction  56 , it is meant that adjacent drop ejectors within the group are spaced by a distance within a range X 1 ±20%. When it is said herein that adjacent groups within each bank are substantially evenly spaced apart by first offset Y 1  along array direction  54 , it is meant that the adjacent groups are spaced by a distance within a range Y 1 ±20%. Similarly, when it is said herein that a first endmost group of a first two-dimensional array and a second endmost group of a second two-dimensional array are spaced apart along the array direction by a distance that is substantially equal to the first offset Y 1 , it is meant that they are spaced by a distance within a range Y 1 ±20%. 
     When it is said herein that a first printhead die and a second printhead die are substantially identical, it is meant that their design is the same, but they can have differences due to manufacturing tolerances. Similarly when it is said herein that a two-dimensional array is substantially identical to another two-dimensional array it is meant that their design is the same, but they can have differences due to manufacturing tolerances. When it is said that the steps on a first edge of a first printhead die and the steps on an adjacent edge of an adjacent second printhead die are positioned in substantially complementary fashion, it is meant deviations from a complementary fitting of the two edges are less than 20% of a width w of the step feature. 
     When it is said herein that the recording media is moved relative to the printhead along the scan direction at a substantially constant velocity V, it is meant that during the ejection of drops, either the recording medium is moved past a stationary printhead at a velocity within a range V±20%, or the printhead is moved past a stationary recording medium at a velocity within a range V±20%. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
     PARTS LIST 
     
         
           1  inkjet printing system 
           2  image data source 
           3  image processing unit 
           4  controller 
           5  electrical pulse source 
           6  transport mechanism 
           7  transport control unit 
           8  ejection control unit 
           10  base plate 
           18  nozzle 
           20  partition wall 
           22  pressure chamber 
           24  ink inlet 
           30  nozzle plate 
           32  nozzle 
           35  heater (actuator) 
           40  half-sized dots 
           42  overlapping dots 
           50  printhead 
           52  linear array 
           54  array direction 
           56  scan direction 
           57   a  reference line (parallel to scan direction) 
           57   b  reference line (parallel to scan direction) 
           57   c  reference line (parallel to scan direction) 
           57   d  reference line (parallel to scan direction) 
           60  drop ejector 
           62  recording medium 
           64  pixel grid 
           66  allowable dot location 
           68  pixel row 
           70  pixel column 
           80  roll-to-roll printing system 
           81  source roll 
           82  take up roll 
           83  roller 
           90  carriage printing system 
           91  carriage path 
           92  forward direction 
           93  reverse direction 
           94  media advance 
           100 - kl  nozzle 
           102  pressure chamber 
           111  drop ejector 
           112  drop ejector 
           113  drop ejector 
           114  drop ejector 
           115  drop ejector 
           116  drop ejector 
           117  drop ejector 
           118  drop ejector 
           120  group 
           121  group 
           122  group 
           123  group 
           124  group 
           125  lower drop ejector 
           126  upper drop ejector 
           127  direction 
           128  direction 
           130  bank 
           131  bank 
           132  bank 
           140  column 
           141  column 
           142  column 
           143  column 
           144  column 
           150  two-dimensional array 
           151  two-dimensional array 
           152  two-dimensional array 
           153  two-dimensional array 
           154  two-dimensional array 
           160  driver circuitry 
           161  driver transistor 
           170  addressing circuitry 
           171  address line 
           172  address line 
           173  address line 
           174  address line 
           175  sequencer 
           180  electrical lead 
           191  first endmost group 
           192  second endmost group 
           201  substrate 
           202  top side 
           203  bottom side 
           209  non-butting edge 
           210  printhead module 
           211  array 
           212  first drop ejector 
           213  second drop ejector 
           214  butting edge 
           215  printhead die 
           216  printhead die 
           217  second printhead die 
           220  ink feed 
           221  slot 
           230  electrical circuitry 
           240  electrical contact 
           250  pixel grid 
           251  boundary line 
           290  first ink source 
           291  second ink source 
           300  pixel location 
           301  first dot 
           302  second dot 
           303  third dot 
           304  fourth dot 
           308  eighth dot. 
           311  first position (first stroke) 
           312  second position (first stroke) 
           318  eighth position (first stroke) 
           351  line of dots 
           352  line of dots 
           353  line of dots 
           354  line of dots 
           360  portion of array 
           361  nozzle set (cyan) 
           362  nozzle set (magenta) 
           363  nozzle set (yellow) 
           364  address circuitry 
           365  bond pads 
           368  nozzle 
           401  allowable dot positions (first odd stroke) 
           411  first odd dot (first odd stroke) 
           412  second odd dot (first odd stroke) 
           413  third odd dot (first odd stroke) 
           414  fourth odd dot (first odd stroke) 
           415  fifth odd dot (first odd stroke) 
           416  sixth odd dot (first odd stroke) 
           417  seventh odd dot (first odd stroke) 
           418  eighth odd dot (first odd stroke) 
           421  first even dot (first even stroke) 
           422  second even dot (first even stroke) 
           423  third even dot (first even stroke) 
           424  fourth even dot (first even stroke) 
           431  first odd dot (second odd stroke) 
           432  second odd dot (second odd stroke) 
           433  third odd dot (second odd stroke) 
           434  fourth odd dot (second odd stroke) 
           441  first even dot (second even stroke) 
           451  first dot (first stroke) 
           452  second dot (first stroke) 
           461  first dot (second stroke) 
           463  third dot (second stroke) 
           464  fourth dot (second stroke) 
           465  fifth dot (second stroke) 
           471  first dot (third stroke) 
           473  third dot (third stroke) 
           477  seventh dot (third stroke) 
           481  first dot (fourth stroke) 
           501  first dot 
           502  second dot 
           511  printhead die 
           512  printhead die 
           521  printhead die 
           522  printhead die 
           531  printhead die 
           532  printhead die 
           533  butting edge 
           534  butting edge 
           535  step 
           536  step 
           550  best fit line along scan direction 
           551  line 
           552  line 
           553  linear regression line 
           554  drop ejector 
           555  drop ejector 
         D x  pixel grid spacing in scan direction 
         D y  drop ejector spacing 
         f drop ejection frequency 
         G gap spacing 
         L length 
         P dot spacing 
         p scan direction pitch 
         R x  resolution in the scan direction 
         R y  resolution in the array direction 
         S array spacing 
         t n  time at the start of the nth printing cycle 
         t S  time at the start of the next stroke 
         V velocity 
         W width 
         w step width 
         X scan axis 
         X 1  drop ejector spacing along scan direction 
         Y array axis 
         Y 1  first offset 
         Y D  displacement