FIELD OF THE INVENTION 
     The present invention generally relates to inkjet and other types of printers and more particularly, to a system and method for producing efficient ink drop overlap filled with a pseudo hexagonal grid pattern. 
     BACKGROUND OF THE INVENTION 
     Inkjet printers print dots by ejecting very small drops of ink onto the print media and typically include a movable carriage that supports one or more print cartridges each having a printhead with a nozzle member having ink ejecting nozzles. The carriage traverses over the surface of the print media. For any line of print, the carriage may make more than one traverse and utilize a varying number of nozzles in the array. 
     To complete a full line, the print head passes a specified number of times in a single or multi pass pattern. The print mode may have a number of parameters; the number of passes required to fill the area, and the position of the ink droplets at every pass. To define this feature, a matrix is created that defines each position of each pass in which a drop may print. The matrix is called the printmode mask. 
     Lines, text and graphics are normally printed with all nozzles aligned in the horizontal, or scan, axis. Defects, including, tails, spray drops and spear drops, can result in rough edges, vertical lines, horizontal lines, banding, and changes in hues on the print media. These defects may be due to a number of factors including nozzle alignment, nozzle outs, the firing frequency or the pen or noise. 
     The pattern on the print media is altered due to nozzle outs. A printhead with small drop volumes but utilizing a larger number of nozzles would increase the probability of a nozzle out, but each would have a decrease in visibility. For an unbiased writing system missing nozzle defects would scale linearly for any given color. 
     Printheads may develop mechanical noise. These changes to pen alignment through pen to pen alignment or vibration of the printhead may offset the printing pattern in a regular manner leading to a consistent defect such as banding. To offset this effect, the dots may be printed in a micro-stepping process, a multi-pass process, a process using multiple sized dots and inter-placing these dots, or by utilizing a random or Dithering Pattern. 
     In general, digital printing systems employ a dot placement pattern whereby circular dots are placed on a rectangular co-ordinate system. This pattern is convenient for the calculation of the placement of data. However the circular dots have to be relatively large to completely cover the media with a lot of dot overlap in areas directly between two adjacent dots, and little overlap at the points of the grid that fall between any four neighboring dots. As such, the rectangular system that uses larger drops requires more ink or toner to completely cover the print media. Therefore, what is needed is a printing system that solves the above problems. 
     SUMMARY OF THE INVENTION 
     To overcome the limitations in the prior art described above, and to overcome other limitations that will become apparent upon reading and understanding the present specification, the present invention is embodied in a system and method for producing efficient ink drop overlap filled with a pseudo hexagonal grid pattern. 
     In general, the present invention can include an inkjet printhead assembly that incorporates a preprogrammed correction scheme or schemes [1-n] (herein correction scheme will refer to all applications), for correcting systematic ink drop placement errors of the inkjet printhead. A general correction scheme can be developed for a class of inkjet printhead assemblies during manufacturing of the class of inkjet printhead assemblies. The correction scheme could include general corrections that cover general errors that exist for the entire class of inkjet printheads. Alternatively, individual correction schemes can be developed during manufacturing of each individual inkjet printhead assembly that covers specific errors that exists for each individual printhead. 
     The correction scheme can be controlled by a printer driver as software operating on a computer system that is connected to the inkjet printer or as firmware incorporated into the inter in a controller device. Also, the correction scheme can be encoded on a memory device incorporated into inkjet printhead assembly itself. In this case, the memory device could also store other various printhead specific data. The data can include identification, warranty, characterization usage, systematic ink drop placement errors, etc. Information can be written and stored at the time the printhead assembly is manufactured or during printer operation. The correction scheme can be accessed and applied by the printer driver. 
     In another embodiment, the inkjet printhead assembly includes an image mapping processor that has the ability to apply the correction scheme during printing operations. The image mapping processor can receive the correction scheme from the memory device or from the printer driver. The image mapping processor can make other decisions, such as making its own firing and timing decisions for providing efficient thermal and energy control. For example, it can be preprogrammed to regulate edge errors, depending on the quality of print desired by a user. In addition, the image mapping processor can aid in calibrating the printhead assembly in real time. Further, in another embodiment of the invention, it operates in conjunction with available rasterization engines using commercially viable software products. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention can be further understood by reference to the following description and attached drawings that illustrate the preferred embodiment. Other features and advantages will be apparent from the following detailed description of the preferred embodiment, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the invention. 
     FIG. 1 shows a block diagram of an overall printing system incorporating the present invention. 
     FIG. 2 is an exemplary printer that incorporates the present invention and is shown for purposes of illustration. 
     FIG. 3 shows for illustrative purposes only a perspective view of an exemplary print cartridge incorporating the present invention. 
     FIG. 4 is a schematic cross-sectional partial view taken through section line  4 — 4  of FIG. 3 showing the ink chamber arrangement of the print cartridge of FIGS.  3 . 
     FIG. 5 shows for illustrative purposes only a perspective view of a thermal head assembly, printing ink droplets. 
     FIG. 6 shows for illustrative purposes only a pattern of odd/even ink droplets on a print media. 
     FIG. 7 is a high level flow diagram illustrating the printhead and printing system of the present invention. 
     FIG. 8 is a flow diagram illustrating the image mapping processor of the present invention. 
     FIG. 9A shows a pseudo-hexagonal drop placement pattern for rows shifted a half column incorporated in the present invention. 
     FIG. 9B shows a pseudo-hexagonal drop placement pattern for columns shifted a half row incorporated in the present invention. 
     FIG. 10A illustrates the boundary condition for filling white space using a 1200 dpi with a dot diameter of 1.414 X pitch, rectangular grid writing system. 
     FIG. 10B illustrates the boundary condition for filling white space using a 2400 dpi with a dot diameter of 2.848 X pitch, pseudo-hexagonal grid writing system. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following description of the invention, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration a specific example in which the invention may be practiced. It is to be understood that other embodiments may be utilized and changes may be made without departing from the scope of the present invention. 
     I. General Overview 
     FIG. 1 shows a block diagram of an overall printing system incorporating the present invention. The printing system  100  of the present invention reduces sensitivity to dot placement errors in digital printing systems using pseudo-hexagonal drop placement. The printing system  100  includes a printhead assembly  110 , an ink supply  112  and print media  114 . The printhead assembly  1   10  includes a printhead body  116  and a nozzle system  118 . The printhead body  116  is securely coupled to the nozzle system  118  with an adhesive arrangement. Data to the printhead assembly is supplied through the input data  108  system. 
     During a printing operation, ink is provided from the ink supply  112  to an interior portion (such as an ink reservoir) of the printhead body  116 . The interior portion of the printhead body  116  provides ink through ink channels to the nozzle system  118 . Namely, the printhead assembly  110  receives commands from a processor (not shown) to print ink and form a desired pattern for generating text and images on the print media  114 . Print quality of the desired pattern is dependent on accurate placement of the ink droplets on the print media  114 . 
     In general, the present invention is a printing system that places drops of ink/toner on a geometrically efficient dot grid. The most geometrically efficient system into which circles can be packed to fill an area is the hexagonal close pack system. However, the hexagonal close pack system is computationally complex and would require the development of appropriate software. The present invention also optimizes the addressable grid for dot placement, with an efficient geometry into which circles can be packed to fill an area. In addition, the present invention can create dots on a non-symmetric grid that is not computationally complex and can be supported by available software. 
     Consequently, defects on the print media are minimized, while conserving the use of ink or toner. The system also operates on available rasterization engines so that it would be commercially viable in that it would utilize available software. The system also allows for greater dot misplacement, or allows a balance in dot size for a combination of decreased ink/toner with a decrease in sensitivity to placement error. This system results in a decrease in the white space between lines of print and a decrease in the hue shift banding due to small changes in pen to pen alignment. Further, the ink droplets are ordered in a pattern that will eliminate the random clustering of drops. This will result in a decrease in banding and more consistent color hues in the printed image. 
     II. Exemplary Printing System 
     FIG. 2 is an exemplary high-speed printer that incorporates the invention and is shown for illustrative purposes only. Generally, printer  200  includes printing system  100  for reducing sensitivity to dot placement errors in digital printing systems using pseudo-hexagonal drop placement. The printer  200  includes a tray  222  for holding print media  114  (shown in FIG.  1 ). When a printing operation is initiated, print media  114 , such as a sheet of paper, is fed into printer  200  from tray  222  preferably using a sheet feeder  226 . The sheet then brought around in a U direction and travels in an opposite direction toward output tray  228 . Other paper paths, such as a straight paper path, can also be used. 
     The sheet is stopped in a print zone  230 , and a scanning carriage  234 , supporting one or more print cartridges  236 , is then scanned across the sheet for printing a swath of ink thereon. After a single scan or multiple scans, the sheet is then incrementally shifted using, for example, a stepper motor or paper advance motor  238  and feed rollers to a next position within the print zone  230 . Carriage  234  again scans across the sheet for printing a next swath of ink. The process repeats until the entire sheet has been printed, at which point it is ejected into output tray  228 . 
     The present invention is equally applicable to alternative printing systems (not shown) such as those incorporating grit wheel or drum technology to support and move the print media  114  relative to the printhead assembly  110 . With a grit wheel design, a grit wheel and pinch roller move the media back and forth along one axis while a carriage carrying one or more printheads scans past the media along an orthogonal axis. With a drum printer design, the media is mounted to a rotating drum that is rotated along one axis while a carriage carrying one or more printheads scans past the media along an orthogonal axis. In either the drum or grit wheel designs, the scanning is typically not done in a back and forth manner as is the case for the system depicted in FIG.  2 . 
     The print cartridges  236  may be removeably mounted or permanently mounted to the scanning carriage  234 . Also, the print cartridges  236  can have self-contained ink reservoirs in the body of the printhead as the ink supply  112  (shown in FIG.  1 ). The self-contained ink reservoirs can be refilled with ink for reusing the print cartridges  236 . Alternatively, the print cartridges  236  can be each fluidically coupled, via a flexible conduit  240 , to one of a plurality of fixed or removable ink containers  242  acting as the ink supply  112  (shown in FIG.  1 ). As a further alternative, ink supplies  112  can be one or more ink containers separate or separable from print cartridges  236  and removeably mountable to carriage  234 . The cartridges  236  in this system may be single color, multi color or multi colorant concentration and are not limited to single colors. 
     FIG. 3 shows for illustrative purposes only a perspective view of an exemplary printhead assembly  300  (an example of the printhead assembly  110  of FIG. 1) incorporating the printing system  100  of the present invention for reducing sensitivity to dot placement errors in digital printing systems using pseudo-hexagonal drop placement. A detailed description of the pseudo-hexagonal drop placement system and method of the present invention follows with reference to a typical printhead assembly used with a typical printer, such as printer  200  of FIG. 2 that includes the pseudo-hexagonal drop placement system and method. However, the present invention can be incorporated in any printhead and printer configuration. 
     Referring to FIGS. 1 and 2 along with FIG. 3, the printhead assembly  110  is comprised of a thermal head assembly  302  and a printhead body  116 . The thermal head assembly  302  can be a flexible material commonly referred to as a Tape Automated Bonding (TAB) assembly. The thermal head assembly  302  contains a flexible nozzle member  306  and interconnect contact pads (not shown) and is secured to the printhead assembly  110 . The thermal head assembly  302  can be secured to the print cartridge  236  with suitable adhesives. An integrated circuit chip (not shown) provides feedback to the printer  200  regarding certain parameters of printhead assembly  110 . The contact pads align with, and electrically contact, electrodes (not shown) on carriage  234 . The nozzle member  306  preferably contains plural parallel rows of offset nozzles  310  through the thermal head assembly  302  created by, for example, laser ablation. It should be noted that other nozzle arrangements can be used, such as non-offset parallel rows of nozzles. 
     III. Component and Operation Details 
     FIG. 4 is a cross-sectional schematic taken through section line  4 — 4  of FIG. 3 of the inkjet print cartridge  236  utilizing the present invention. A detailed description of the present invention follows with reference to a typical printhead used with print cartridge  236 . However, the present invention can be incorporated in any printhead configuration. Also, the elements of FIG. 4 are not to scale and are exaggerated for simplification. 
     Referring to FIGS. 1-3 along with FIG. 4, as discussed above, conductors (not shown) are formed on the back of thermal head assembly  302  and terminate in contact pads for contacting electrodes on carriage  234 . The other ends of the conductors are bonded to the printhead  110  via terminals or electrodes (not shown) of a substrate  410 . The substrate  410  has ink ejection elements  416  formed thereon and electrically coupled to the conductors. The integrated circuit chip provides the ink ejection elements  416  with operational electrical signals. A barrier layer  412  is located between the nozzle member  306  and the substrate  410  for insulating conductive elements from the substrate  410 . 
     An ink ejection or vaporization chamber  418  is adjacent to each ink ejection element  416 , as shown in FIG. 4, so that each ink ejection element  416  is located generally behind a single orifice or nozzle  310  of the nozzle member  306 . The nozzles  310  are shown in FIG. 4 to be located near an edge of the substrate  410  for illustrative purposes only. The nozzles  310  can be located in other areas of the nozzle member  306 , such as centered between an edge of the substrate  410  and an interior side of the body  116 . Each ink ejection element  416  acts as ohmic heater when selectively energized by one or more pulses applied sequentially or simultaneously to one or more of the contact pads via the integrated circuit. The ink ejection elements  416  may be heater resistors or piezoelectric elements. The orifices  420  may be of any size, number, and pattern, and the various figures are designed to simply and clearly show features of the invention. The relative dimensions of the various features have been greatly adjusted for the sake of clarity. 
     Referring to FIGS. 1-4, during a printing operation, ink stored in an ink container  242  defined by the printhead body  116  generally flows around the edges of the substrate  410  and into the vaporization chambers  418 . Energization signals are sent to the ink ejection elements  416  and are produced from the electrical connection between the print cartridges  236  and the printer  200 . Upon energization of the ink ejection elements  416 , a thin layer of adjacent ink is superheated to provide explosive vaporization and, consequently, cause a droplet of ink to be ejected through the orifice or nozzle  420 . The vaporization chamber  418  is then refilled by capillary action. This process enables selective deposition of ink on print media  114  to thereby generate text and images. 
     Referring to FIGS. 1-4 and FIG. 5 during the printing process, ink ejection elements  416  in the thermal head assembly  302 , cause ink to be superheated in the vaporization chambers  418 . Ink droplets  520  are forced through the nozzles  310  in the thermal head assembly  302 , onto the print media  114 . All nozzles  310  do not eject simultaneously. The nozzles  310  are divided into rows so that there are odd rows  510  and even rows. 
     FIG. 6 is an illustration showing more ink droplets  520  having been printed on the print media  114 . An odd row  510  is printed adjacent to an even row  512 . In the print swath odd rows  510  are printed next to even rows  512  and between the ink droplets  520  are areas of white space  610 . The present invention employs a system to decrease the white space  610  between ink droplets  520 . 
     FIG. 7 is a block diagram showing elements of the controller devices of the present invention that combine to decrease image defects by reorganizing the drop pattern and therefore decreasing aberrations such as nozzle outs and white space. In particular, the memory device  702  stores the data received from the input data  108 . This data is forwarded to an image mapping processor  706  which would have the relative printmode, print mask and print-media height parameters imbedded in the controller. 
     The correction device  704  would provide the image mapping processor  706  with the adjustments [1-n] to be made to the paper advance motor  720  or to the number of passes, or positions of dots to be printed on the print media  114 . The image mapping processor  706  is a controller for the heater element array  708 . The heater element array  708  causes ink in the chamber array  712  to super heat and expel ink droplets through the nozzles  310  onto the print media  114 . Ink to the chamber array  712  is replaced by capillary action via the ink channels  710 . 
     The print media  114  is advanced by the sheet feeder  722  under the control of the paper advance motor  720 . The advance is the print media height and could factor the number of nozzles  310  used in each pass of the printmode system referred to below in FIG.  8 . 
     FIG. 8 is a block diagram showing some of the components of the printmode system  800  in the image mapping processor  706 . The printmode system  800  is that part of the controller that regulates the number of passes, 1-n, through the passes 1-n controller  802 . The image mapping processor  706 , also calculates the position of each ink droplet through a drop position controller  804 . The data from the passes 1-n controller  802  and the drop position controller  804  are used by the printmode mask  806  to calculate the position of each ink droplet  520  to be printed to the print media  114  through the electronic stimulation of the heater array element  708 . 
     Simultaneously the line calculator  810  utilizes information from the printmode mask  806  and the passes 1-n controller  802 , to determine the printmode height  812 . This information is utilized to advance the print media  114  through the paper advance motor  720 . As noise, either mechanical or electrical or other, can effect the accuracy of ink droplet  506  placement, an embodiment of the present invention is to artificially shift the media advance through the sheet feeder  722 . In odd rows  510  the media advance is increased a ½ nozzle spacing distance, and in the next even row  512  the media advance is decreased a ½ nozzle spacing distance. The correction factor in the printmode mask  806  providing an under/over advance tends to hide errors from the mechanical parts. 
     FIG. 9A is a diagram illustrating a pattern of ink droplets  506  where the rows have been offset ½ column pseudo-hex grid rows shift half column  900 , and FIG. 9B shows a similar pattern of ink droplets  506  where the columns have been vertically offset ½ a row pseudo-hex grid columns shift half row  910 . The rasterization engine, not shown, treats each case as if it where not offset. This maintains maximum simplicity for the purposes of calculating the data and enables the utilization of standard engines and software. This process can introduce intentional noise, horizontal or vertical offsetting, through the correction device  704 . This is achieved through the selection of one or the other pseudo-hex grid. This noise would then decrease image defects such as banding. These patterns, pseudo-hex grid rows shift half column  900  and pseudo-hex grid columns shift half row achieve the effects of over/under advance illustrated in FIG. 8, or by having sufficient native resolution to selectively place drops on a specified grid location in a single pass. 
     These effects are further illustrated in FIG.  10 . FIG. 10A shows the overlap resulting from printing drops on a standard grid. FIG. 10B is an image from drops on a pseudo-hex grid using the same oversize drops as FIG.  10 A. 
     Therefore, in conclusion, the correction device  702  and the image mapping processor  706  are embodiments in the present invention that minimize defects on the print media  114  and/or conserve ink  112  or toner. This is achieved by employing a pseudo-hex format of ink drop placement  900 ,  910 . 
     Basically, two factors are involved in the embodiment of the present invention, dot size and the eventual addressable grid location of each dot. Utilizing these factors in an embodiment of the present invention, three possibilities may arise. The device could be programmed to incorporate a multi-pass mode incorporating a higher grid resolution that can be addressed in a single pass, the nozzle density could be doubled, or the system could incorporate double the number of columns using a suitable technique. 
     As one example, if the data input [page rasterization resolution], was N×N, and the dots were sized approximately for N×N, firing a single drop on each N×N grid location would result in an addressable resolution of double being added to either columns or rows. That is, if the data was input at 600 dots per inch, dots would be approximated in size for 600 dots per inch. The system could then add an addressable resolution of 1200 columns per inch or 1200 rows per inch, and selectively shift subsets of drops to the specific subsets of the higher resolution grid location, such that the drop placement pattern was a pseudo-hexagonal pattern. The system therefore provides for various options in the production of the grid pattern. 
     In addition, the correction device  702  allows the rasterization engine to interpret the data as not offset allowing the system to operate on standard rasterization engines as well as employing standard software. The overall result is a process employing the efficiency benefits of calculating data on a standard square plus the dot overlap benefits of a hexagonal close pack grid. 
     The foregoing has described the principles, preferred embodiments and modes of operation of the present invention. However, the invention should not be construed as being limited to the particular embodiments discussed. As an example, the above-described inventions can be used in conjunction with inkjet printers that are not of the thermal type, piezo, digital printing process etc., as well as inkjet printers that are of the thermal type. Thus, the above-described embodiments should be regarded as illustrative rather than restrictive, and it should be appreciated that variations may be made in those embodiments by workers skilled in the art without departing from the scope of the present invention as defined by the following claims. 
     IV. Conclusion 
     The present invention minimizes defects on the print media but conserves the use of ink or toner. The system also operates on available rasterization engines so that it is commercially viable in that it utilizes available software. The system also allows for greater dot misplacement, or allows a balance in dot size for a combination of decreased ink/toner with a decrease in sensitivity to placement error. This results in a decrease in the white space between lines of print and a decrease in the hue shift banding due to small changes in pen to pen alignment. This will result in a decrease in banding and more consistent color hues in the printed image. 
     As the invention addresses both dot size and addressable grid location, the system can be manipulated on the basis of number of passes, nozzle density, and number of columns. 
     The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. Therefore, the foregoing description should not be taken as limiting the scope of the invention defined by the appended claims. 
     The foregoing has described the principles, preferred embodiments and modes of operation of the present invention. However, the invention should not be construed as being limited to the particular embodiments discussed. As an example, the above-described inventions can be used in conjunction with inkjet printers that are not of the thermal type, as well as inkjet printers that are of the thermal type. Thus, the above-described embodiments should be regarded as illustrative rather than restrictive, and it should be appreciated that variations may be made in those embodiments by workers skilled in the art without departing from the scope of the present invention as defined by the following claims.
The present invention is embodied in a system and method for producing efficient ink drop overlap filled with a pseudo hexagonal grid pattern. In general, the present invention can include an inkjet printhead assembly that incorporates a preprogrammed correction scheme or schemes [1-n] (herein correction scheme will refer to all applications), for correcting systematic ink drop placement errors of the inkjet printhead. The printing system of the present invention uses a unique ink dot pattern, called a pseudo-hexagonal close pack system. The present invention optimizes the addressable grid for dot placement, pseudo hexagonal close pack system, with an efficient geometry for packing circles to fill an area, similar to the hexagonal close pack system. However, the present invention in creating dots on a non-symmetric grid is supported by available software and is not computationally complex.