Abstract:
Techniques to compensate for random and systematic errors when measuring dot placement errors. Error accumulation due to scan axis irregularities during printhead calibration is minimized by swapping alignment block positions on the print medium from swath to swath. Print media advances during the calibration are minimized by the use of a moving reference instead of a constant reference; adjacent groups of nozzles are used to calibrate the following group. Only a small media advance is needed to print alignment blocks using adjacent nozzle groups one beside the other to be calibrated. To prevent paper slip accumulative errors when using moving references, the order of the groups of nozzles is swapped from one paper advance to the other. This randomizes for small, unavoidable slips when advancing the paper and prevents error accumulation. No further paper advances are used at all for the rest of the dot placement calibration (odd to even columns in a print-head, pen to pen correction and bidirectional correction). When calibrating X-axis position for a group of nozzles, a group of nozzles located at the same Y-axis coordinate is used, so that no paper advances are needed to print them one beside the other.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to co-pending application Ser. No. 09/199,882, entitled ALIGNMENT OF INK DOTS IN AN INKJET PRINTER, filed Nov. 24, 1998, the entire contents of which are incorporated herein by this reference. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     This invention relates to inkjet printers, and particularly to techniques for measuring and correcting for dot placement errors. 
     BACKGROUND OF THE INVENTION 
     Exemplary embodiments of this invention will be described with respect to large format printers, although the invention can also be practiced on other types of printers. 
     Large scale plotters typically support roll-form print media, i.e., a supply of paper or transparent film on a roll. The media is loaded into the printer, and is advanced along a media path to a print area. A swath-type printer includes a carriage mounted for scanning movement along a swath axis, transverse to the media path at the print area. Hereafter, the media path is known as the X-axis, and the scanning or swath axis is the Y-axis. For color printing, the carriage holds a plurality of ink-jet printheads, each for printing a different color ink, typically black, cyan, magenta and yellow. The printer will include a media drive mechanism for moving the media along the media path, and a carriage drive mechanism for scanning the carriage along the scan axis. The printer controller issues print control signals to cause the printheads to eject droplets of ink in a controlled manner to form a desired image or plot on the medium. 
     Ink-jet printing is based on accurate ballistic delivery of small ink droplets to exact locations onto the paper or other media. Typically the droplet placement occurs onto a grid of different resolutions, most common grids being 300×300 dpi or 600×600 dpi, although other solutions are continuously being considered. One key factor for sharp and high quality images stems from the accuracy of the droplet placement. 
     There are several contributors to droplet placement inaccuracies. Some of these arise from the printer and some other from the printhead. They can occur along the scan axis or the media path directions. Some inaccuracies are systematic, while some others follow random patterns. Some of these errors can also affect the correction algorithm itself. 
     Several factors contribute to error in paper movements. The media roll is typically mounted in the printer on an axis or spindle. The spindle is prevented from turning at idle by a friction brake. This creates “back-tension” which helps the media auto-alignment. The media auto-alignment process includes X-axis movements, i.e. movements along the media advance direction, and rotations of the paper to prevent skew and mispositioning of the paper on the print zone. These movements create some undesirable paper slip on the print zone that negatively affect dot placement. These errors affect both printing and also dot placement calibration. 
     Some other movements have been detected when advancing the paper with back-tension. These movements are due to irregularities on the pinch-wheels as well as different pressures between pinch-wheels and roller and media tensions along the X-axis. 
     These factors can create several problems. When calibrating Y-axis directionality, i.e. where Y is the carriage scan axis direction, the back-tension creates large media slips. These movements include advance errors, X-axis displacements and rotations about a vertical (Z) axis. 
     When calibrating scan-axis directionality for the reference printhead, some advances are needed to print and measure dot placement along the printhead length. Some paper slip during these measurements could affect the calibration, causing the dots printed before the paper advance to be in a different X axis coordinate after the paper advance, and therefore measured at an incorrect distance to the next printed dots. 
     SUMMARY OF THE INVENTION 
     A technique to compensate for random and systematic errors when measuring dot placement is described, and results in reduction or elimination of paper movements during the dot placement calibration as well as avoidance of error accumulation. 
     An aspect of the invention is a technique to compensate for random and systematic errors when measuring dot placement errors. One solution for error accumulation due to scan axis irregularities includes swapping alignment block positions on the print medium from swath to swath. The paper advances are minimized by the use of a moving reference instead of a constant reference, i.e. using adjacent groups of nozzles to calibrate the following group. In this technique only a small paper advance, e.g. in an exemplary embodiment, a 64 dot rows advance for a 32 dot primitive at 300 dpi, is needed to print adjacent nozzle groups one beside the other to be calibrated. 
     In accordance with a further aspect of the invention, to prevent paper slip accumulative errors when using moving references, the order of the groups of nozzles is swapped from one paper advance to the other. This randomizes for small, unavoidable slips when advancing the paper and prevents error accumulation. 
     In accordance with a further aspect of the invention, no more paper advances are used at all for the rest of the dot placement calibration (odd to even columns in a print-head, pen to pen correction and bi-directional correction). When calibrating X-axis position for a group of nozzles, a group of nozzles located at the same Y-axis coordinate is used. Therefore no paper advances are needed to print them one beside the other. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     These and other features and advantages of the present invention will become more apparent from the following detailed description of an exemplary embodiment thereof, as illustrated in the accompanying drawings, in which: 
     FIG. 1 is a perspective view of a large format inkjet printer/plotter incorporating the features of the present invention; 
     FIG. 2 is a close-up view of the carriage portion of the printer/plotter of FIG. 1 showing a carriage-mounted optical sensor; 
     FIG. 3 is a close-up view of the platen portion of the printer/plotter of FIG. 1 showing the carriage portion in phantom lines; 
     FIG. 4 is a schematic representation of a top view of a carriage showing offsets between individual printheads in the media advance axis and in the carriage scan axis; 
     FIG. 5 is a front view of the optical components of the sensor unit of FIG. 4; 
     FIGS. 6A and 6B are isometric views respectively looking downwardly and upwardly toward the carriage showing the optical sensor and one print cartridge mounted on the carriage; 
     FIG. 7 schematically shows the nozzle plate of a 600 dpi print carriage having one column of ink-ejection nozzles separated from another column of ink-ejection nozzles; 
     FIG. 8 schematically shows the print cartridge of FIG. 7 in printing position over a print zone. 
     FIG. 9 diagrammatically illustrates SAD error. 
     FIG. 10 diagrammatically illustrates APCS errors in a printhead. 
     FIGS. 11,  11 A, and  11 B show a printhead alignment pattern printed in accordance with aspects of the invention. 
     FIG. 12 is an enlarged view of a portion of the alignment pattern of FIG.  11 . 
     FIG. 13 is a diagrammatic depiction of a printhead and a portion of a first band of the black printhead alignment pattern. 
     FIG. 14 illustrates the first band of FIG. 13 after completion. 
     FIG. 15 illustrates the scanning of the first band of FIG. 14 in successive bidirectional passes of the line sensor. 
     FIG. 16 illustrates the even and odd columns of the black printhead, and the illustrative distances SAD  1 - 2  and SAD  3 - 4 . 
     FIG. 17 is a simplified flow diagram illustrating the general steps of a printhead alignment technique as described with respect to FIGS.  11 - 16 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     This invention provides a method to measure and correct droplet placement errors, and provides robustness to some systematic and random errors when measuring dot placement error, particularly paper skew, paper slip, X axis advance errors (due to roller and/or gears), and paper growth due to ink. 
     A typical embodiment of the invention is exemplified in a large format color inkjet printer/plotter. Commonly assigned U.S. Pat. No. 5,835,108, entitled CALIBRATION TECHNIQUE FOR MISDIRECTED INKJET PRINTHEAD NOZZLES, describes an exemplary device which can employ the recent invention. FIGS. 1-8 and the following description of these figures are generally taken from this patent, the entire contents of which are incorporated herein by this reference. 
     FIG. 1 is a perspective view of an inkjet printer/plotter  10  having a housing  12  mounted on a stand  14 . The housing has left and right drive mechanism enclosures  16  and  18 . A control panel  20  is mounted on the right enclosure  18 . A carriage assembly  30 , illustrated in phantom under a cover  22 , is adapted for reciprocal motion along a carriage bar  24 , also shown in phantom. The position of the carriage assembly  30  in a horizontal or carriage scan axis is determined by a carriage positioning mechanism  31  with respect to an encoder strip  32  (see FIG.  2 ). A print medium  33  such as paper is positioned along a vertical or media axis by a media axis drive mechanism (not shown). As used herein, the media axis is called the X axis denoted as  13 , and the scan axis is called the Y axis denoted as  15 . 
     FIG. 2 is a perspective view of the carriage assembly  30 , the carriage positioning mechanism  31  and the encoder strip  32 . The carriage positioning mechanism  31  includes a carriage position motor  31 A which has a shaft  31 B which drives a belt  31 C which is secured by idler  31 D and which is attached to the carriage  30 . 
     The position of the carriage assembly in the scan axis is determined precisely by the encoder strip  32 . The encoder strip  32  is secured by a first stanchion  34 A on one end and a second stanchion  34 B on the other end. An optical reader (not shown) is disposed on the carriage assembly and provides carriage position signals which are utilized by the invention to achieve image registration in the manner described below. 
     FIG. 3 is a perspective view of a simplified representation of a media positioning system  35  which can be utilized in the inventive printer. The media positioning system  35  includes a motor  35 A which is normal to and drives a media roller  35 B. The position of the media roller  35 B is determined by a media position encoder  35 C on the motor. An optical reader  35 D senses the position of the encoder  35 C and provides a plurality of output pulses which indirectly determines the position of the roller  35 B and, therefore, the position of the media  33  in the Y axis. 
     The media and carriage position information is provided to a processor on a circuit board  36  disposed on the carriage assembly  30  for use in connection with printhead alignment techniques of the present invention. 
     The printer  10  has four inkjet print cartridges  38 ,  40 ,  42 , and  44  that store ink of different colors, e.g., black, magenta, cyan and yellow ink, respectively. As the carriage assembly  30  translates relative to the medium  33  along the X and Y axes, selected nozzles in the inkjet print cartridges are activated and ink is applied to the medium  33 . The colors from the three color cartridges are mixed to obtain any other particular color. Sample lines  46  are typically printed on the media  33  prior to doing an actual printout in order to allow the optical sensor  50  to pass over and scan across the lines as part of the initial calibration. 
     The carriage assembly  30  positions the inkjet print cartridges and holds the circuitry required for interface to the ink firing circuits in the print cartridges. The carriage assembly  30  includes a carriage  31  adapted for reciprocal motion on front and rear slider rods. 
     As mentioned above, full color printing and plotting requires that the colors from the individual print cartridges be precisely applied to the media. This requires precise alignment of the print cartridges in the carriage. Unfortunately, paper slippage, paper skew, and mechanical misalignment of the print cartridge results in offsets in the X direction (in the media advance axis) and the Y direction (in the carriage or axis) as well as angular theta offsets. This misalignment causes misregistration of the print images/graphics formed by the individual ink drops in the media. This is generally unacceptable as multi-color printing can typically require image registration accuracy from each of the printheads to within {fraction (1/2400)} inch. 
     FIG. 4 shows a presently preferred embodiment of printheads  38 ,  40 ,  42 ,  44  each having two groups of nozzles with a column offset  41 . By comparing the relative positions of corresponding nozzles in different printheads along the Y axis, it is possible to determine an actual horizontal offset  41 A between two printheads, and by comparison with a nominal default offset  41 B determine an actual offset  41 C in the carriage scan axis. This is repeated for all of the different printheads while they remain on the carriage. 
     Similarly, by comparing the relative positions of corresponding nozzles in different printheads along the X axis, it is possible to determine an actual vertical offset  41 D in the media advance axis. This is also repeated for all of the different printheads while they remain on the carriage. 
     In order to accurately scan across a test pattern line, the optical sensor  50  is designed for precise positioning of all of its optical components. Referring to FIGS. 5,  6 A and  6 B, the sensor unit includes a photocell  50 A, holder  50 B, cover  50 C, lens  50 D; and light source such as two LEDs  50 E,  50 F. A protective casing  50 G which also acts as an ESD shield for sensor components is provided for attachment to the carriage. 
     Additional details of the function of a preferred optical sensor system and related printing system are disclosed in corresponding application Ser. No. 08/551,022 filed Oct. 31, 1995 entitled OPTICAL PATH OPTIMIZATION FOR LIGHT TRANSMISSION AND REFLECTION IN A CARRIAGE-MOUNTED INKJET PRINTER SENSOR, which application is assigned to the assignee of the present application, and is hereby incorporated by reference. 
     The optical sensor in this exemplary embodiment includes two LEDs, one green and one blue. The green LED is used to scan all of the patterns except the patterns used to obtain information from the yellow ink printhead. 
     The signal read from the optical sensor is processed and entered to an analog-to-digital converter. 
     The printhead alignment techniques in accordance with this invention are now described in detail. 
     Before starting the calibration process a certain length of paper is pulled from the roll and after is pushed back behind, hanging below the roller. This deactivates the media roll “back-tension” which acts as a brake for the paper advance and produces some errors described above. This method is applied before measuring dot placement on paper-axis and also before measuring dot placement in scan-axis for the reference printhead. 
     Pen primitives (or also called physical primitives) are groups of nozzles in the same pen column that can be fired in advance or delay with respect to the firing pulse, due to a ‘quarter dot correction’ or other correction with the purpose of correcting for scan axis directionality (SAD) or adjacent primitive centroid separation (APCS) problems. Pen primitives are described in detail in pending application Ser No. 09/199,882, referenced above, and illustrated in FIG. 3 thereof. SAD errors, also sometimes known as column separation errors, consist in perpendicularity errors of the drop ejection direction with the respect to the nozzle plate in the plane YZ. SAD errors often manifest themselves symmetrically in the two nozzle columns of the printheads. SAD errors are measured as a column to column offset; two nozzles that are a distance d apart from each other in the printhead eject two droplets that fall on the print medium with an offset d′. This is illustrated in FIG. 9, wherein printhead  38  with corresponding nozzles of nozzle columns  38 A,  38 B spaced apart by distance d eject droplets that fall on the print medium a distance d′ apart. 
     APCS errors, also sometimes known as column straightness errors, consist in perpendicularity errors of the drop ejection direction with respect to the nozzle plate in the plane XY. These errors refer to the straightness of one single printhead nozzle column. APCS errors are measured as offsets in the Y axis between groups of droplets from two adjacent primitives. This is illustrated in FIG. 10, wherein P 1  and P 2  are groups of droplets ejected by respective primitives of printhead  38 . G 1  and G 2  represent the respective centroids of the groups of droplets. The offset between the two centroids is the APCS error. 
     In an exemplary embodiment, the pen primitives are groups of 16 nozzles, and the printer electronics and firmware use logical primitives which include 32 nozzles (less at the ends of the printhead depending on the paper axis correction). The logical primitives can be fired in advance or with delay to their nominal firing time. This is described more fully in application Ser. No. 09/199,882, entitled ALIGNMENT OF INK DOTS IN AN INKJET PRINTER, referenced above. 
     In this example, for simplicity, the word ‘primitive’ refers to primitives of 32 nozzles each, so each printhead column will have 8 primitives (32 nozzles each). The printhead has two columns, the odd column and the even column. The odd column contains even primitive numbers; the even column contains correspondingly odd primitive numbers. When reference is made to nozzles or primitives, i.e., “first primitive of the odd column”, this means the first 32 usable odd nozzles after the pen to pen in media axis alignment. A dot row is used as an equivalent for a pixel, in this example {fraction (1/600)} of an inch or 42 microns. When, e.g., a column printed with the odd column is 448 dot rows tall, that means that there are 224 droplets (each column of the pen is at 300 dpi). 
     To accomplish a printhead alignment procedure in accordance with the invention, a set  300  of printhead patterns, sometime referred to herein as a “blanket, ” are printed. This alignment procedure is typically performed at printhead replacement, either immediately after the replacement, or after a power up and a new printhead is detected. Alternatively, the printhead alignment procedure can be manually triggered by the user through a printer front panel input. FIG. 11 illustrates an exemplary blanket  300 . The printhead alignment patterns include a number of color blocks printed on the print medium, e.g. paper, to be scanned using the printer&#39;s line sensor. Subsequent to scanning, distances between blocks are measured, and corrections are calculated comparing the measured distances with the targeted distances between blocks. 
     The upper side of the blanket  300  is adjacent the leading edge of the print medium in FIG. 11, and so the printer carriage would be located at the bottom of the illustration. Therefore, a forward movement of the paper refers to a displacement in the up direction in the context of FIG. 11, and a backward movement of the paper refers to a displacement in the down direction. 
     In an exemplary implementation on a large format printer, the size of the blanket  300  is 15 cm by 55 cm, and about 6 minutes are used to print and scan the blanket, including the dry times. The invention can be implemented by first printing the blanket in its entirety before any scanning. However, in the following description, the invention is described as implemented with partial blanket printing, then partial scanning, then partial printing, scanning, etc. Either technique may be employed in practicing the invention. 
     The sizes and spacing of the blocks respond to the line sensor field of view, which is approximately 47 dot rows (1.6 mm) in this embodiment. A desired width of the blocks for the scan axis measurements (36 dots) corresponds to an optimum for the centroid search algorithm. This algorithm analyzes the line sensor signal and determines the centroids of the blocks by adjusting a cosenoidal waveform to each peak in the waveform. Centroid search algorithms are well known in the art, and include fitting the cosenoidal curve to the scanned signal data, using a “minimum squares fit” method. 
     The blocks for the media axis (X-axis) measurements are also 36 dots high (they are scanned in the media axis direction) but their spacing is bigger (512/5-36), since it has to be an entire number of blocks every swath, and with an approximately equal spacing between swaths. The block spacing for this exemplary embodiment is determined in the following manner. A block is at least 36 dot rows thick for signal reasons. The minimum spacing is 55 dot rows for field of view reasons. Therefore the spacing between blocks for the X-axis measurements is (36+55+margin)*n =512, where 512 is the swath height (printhead height) and n must be an integer number. So the margin is 11, except in the space between swaths where it is 13. 
     Several paper movements or wait times correspond to dry times, before moving the media backwards, again under the pinch wheels of the media drive system. This will allow the ink to dry before a portion of a printed pattern is reversed in movement, taking it under the output pinch wheels, to minimize smearing the pattern. 
     The pen servicing procedures are important for the repeatability of the pen alignment procedure. These parameters include, in an exemplary embodiment, warming the printhead at an appropriate temperature by means of supplying short electrical pulses to the nozzles, to ensure optimum drop weight. Other exemplary pen servicing parameters include firing a certain number of drops per nozzle before printing the alignment patterns to ensure optimum drop directionality and drop stability, and eliminating dry ink from the nozzle bores. These procedures will preferably be performed before a printhead alignment procedure is conducted in accordance with the invention. 
     Prior to the printhead alignment being conducted, in the exemplary large format printer, several calibrations will have been performed. These include service station calibration which determines the distance between the optical center of the line sensor with respect to the center of the black printhead. A media advance calibration corrects the eccentricity, worm, gear and other periodic errors in the paper advance. Color-to-color calibration determines the chassis straightness effect on dot placement errors and introduces an offset (if necessary) in the color-to-color calculations performed by the pen alignment, and is described in further detail in pending application Ser. No. 09/253,694, entitled COLOR TO COLOR CALIBRATION, the entire contents of which are incorporated herein by this reference. A theta-X calibration technique can be used to determine the amount of theta-X errors induced by pen to paper relative rotations and to modify theta-X corrections for the reverse directions, as described in further detail in European Patent Application 99103185.7.A mark encoder calibration determines the absolute zero in the media axis encoder. A pen-to-media spacing calibration also corrects for pen-to-media spacing variations along the scan axis (mainly noticeable in bi-directional printing at high carriage speeds), and is described in further detail in pending U.S. application Ser. No. 09/259,070, entitled PEN TO PAPER SPACING. 
     There are five main areas in the blanket  300 , which will now be described in more detail. 
     First Area  310   
     Line Sensor Calibration. Four blocks or solid tiles  312 ,  314 ,  316 ,  318  are printed, one for each printhead, e.g. black tile  312 , yellow tile  314 , magenta tile  316  and cyan tile  318 , having areas at least as big as the line sensor field of view. The line sensor scans these tiles, obtaining the maximum and minimum signal level. An algorithm chooses for each line sensor LED, the best gain channel, offset and LED intensity targeting to maximize the signal range. 
     Second Area  320   
     Pen-to-Pen In Media (X) Axis and Pad Factor. Eight vertical stripes  322 - 336  with 20 rectangles each are printed in consecutive swaths using a mask of 50% density, i.e. wherein each nozzle only prints one pixel in every two pixel. This means that the rectangles are printed using both odd and even nozzles of each printhead and, in this example, at a firing frequency of 6 Khz. This firing frequency is for a carriage speed of 20 inches per second, the pen firing one of every two pixels on the media (equivalent to fill half the cells on a 600 dpi grid.) The media advance error has first been calibrated, by the aforementioned calibrations conducted before commencing the printhead alignment procedure. The reference printhead for this calibration, i.e. the pen-to-pen calibration in the X axis direction, is the magenta pen. For each pen there are two stripes (to gain repetitions); each of the stripes has a length of four swaths. 
     For each swath used to print the stripes comprising area  320 , the magenta printhead is used to print the center block, and the other blocks for a swath in a given stripe printed by a printhead of a different color. Thus, stripes  322  and  326  mostly printed with yellow but with four blocks of magenta interleaved along the length of the stripes, the magenta blocks being the central block printed in a the respective four swaths. Similarly, stripes  324  and  334  are mostly printed with cyan but with four blocks of magenta printed as the central block in each swath. Stripes  328  and  332  are mostly printed with black but with four blocks of magenta printed as the central block for each swath used to print the respective stripe. Stripes  328  and  330  are printed with all magenta blocks. This use of the magenta printhead to print the central block allows for measurement of pen-to-pen alignment along the media axis, with the magenta printhead being used as the reference, allowing calculation of the offset between printheads along the media axis. 
     Two measurements are done in the same pattern. The first measurement, pen-to-pen in the media axis (X-axis) direction, is made swath by swath, i.e., every five blocks. The central block is always printed by the magenta printhead (the reference printhead). The four blocks (two upper and two lower) adjacent the central block of each swath are used to calculate the center of the referenced pen. Misalignments between the center of the magenta block and the center of the referenced printhead are corrected with a resolution of 1 dot row. This is achieved by using only 512 of the 524 nozzles in one exemplary pen. The magenta pen always uses its 512 central nozzles, whereas in the other printheads, the 512 nozzles selected for use (out of 524 nozzles) can shift plus/minus six dot rows. In other words, to compensate vertical (X axis) mispositionings and/or misplacements of the printheads, a choice is made of which 512 nozzles are going to be used, and since there are 524 nozzles in the vertical direction, there is a choice of rows shifted plus/minus six dot rows. This procedure results in printhead to printhead alignment, so that the printheads are aligned with respect to the X axis. 
     A second measurement is the pad factor determination. The two blocks in each swath which are furthest apart are included in the calibration. The measured swath height is the distance between the upper block to the lower block in each swath, extrapolated over the whole printhead height, i.e. in this example this measured distance between the upper block and the lower block in each swath multiplied by 512. The pad factor is the ratio between the theoretical swath height (512 dot rows) and the measured swath height. The pad factor is applied to over-advance or under-advance the print media to achieve an optimum area filling without overlapping or gaps between the passes. 
     Third Area  340   
     Calibration of the Black Pen In The Scan (Y) Axis. This area is used to calibrate the black pen or printhead. The black printhead is more completely calibrated that the other printheads, so that it will have the most accurate dot placement of any of the printheads. This is done because the black printhead receives heaviest use during most applications including CAD applications, and dot placement errors are most noticeable for the black droplets. The third area  340  includes two horizontal bands  342 ,  344 , printed by the black pen. Each band has two regions (one on the left and the other on the right), with 46 rectangles or blocks each. Thus, band  342  includes left region  342 A and right region  342 B. The left and right regions can not be distinguished by eye (unless there are nozzles out). The APCS error is measured using the left regions of the bands. The SAD error, i.e. the odd to even primitive centroid separation, is measured using the left regions of the bands. 
     All the measurements could be done only in the first band, adding one 64 dot row band for the first primitive swath, but it was chosen to do it in two bands with the purpose of swapping positions on the print medium between adjacent primitives. This is illustrated in FIGS. 13 and 14. The advantages of swapping position on the print medium between adjacent primitives include minimizing the contribution of sudden carriage velocity variations due to ink tube drag and other causes as well as carriage encoder errors or media errors. 
     FIG. 13 shows in schematic form a black pen printhead nozzle plate  400 , with two columns of nozzles, the odd column  402 A and the even column  402 B. To print the first band  342 , a set  342 C of 23 blocks is initially printed in a first pass using the last 7 primitives (224 bottom nozzles from 256) of the black pen, all from the odd column  402 A, as shown in FIG. 13 (see height h of the printhead in FIG.  13 ). The set  342 C is printed within the left side  342 A of the first band. The spacing between the blocks of this set  342 C is 146 dots in this example. These spaces will be filled with another set of 23 blocks printed in the second pass, after some print medium (X-axis) advance. The right region  342 B will be filled with blocks forming the same kind of pattern in the second pass, i.e. with a total of 46 spaced blocks. 
     The 23+46 blocks of the second pass are printed after moving the print medium forward along the X-axis for a distance of 64 dot rows, i.e. by a distance equal to the height of one primitive. These blocks include the 46 blocks  342 D printed in the right region  342 B, and 23 block printed in the left region in the gaps between the blocks  342 C printed in the first pass. For clarity, only one ( 342 E) of the blocks printed in the second pass in the left region  342 A is shown in FIG.  14 . 
     The first 23 blocks of the second pass are printed in the left region  342 A using the  224  top nozzles (starting in primitive  1 ) of the black pen  402 , also from the odd column  402 A. The other 46 blocks (in the right region) are printed alternatively with odd and with even nozzles. 
     The purpose of this procedure, for the left region, is to locate adjacent odd primitives side by side in alternate blocks on the print medium in the left region  342 A. This is achieved with a single media advance of 64 dot rows which introduces very small advance-skew errors. The left region pattern therefore contains 7 (out of 8) primitives from the odd column positioned side by side laterally every couple, i.e.,the first and second primitives of the odd column are printed side by side in the scan axis, at the same X position due to a media advance. In this example, then, adjacent pairs of the blocks will position blocks printed by the second odd black primitive adjacent the first primitive, and so on, i.e. third primitive adjacent the second primitive, fourth primitive adjacent the third primitive, fifth primitive adjacent the fourth primitive, seventh primitive adjacent the sixth primitive, and eight primitive adjacent the seventh primitive. 
     In the right region  342 B, blocks printed with the odd and with the even columns alternatively allow the measurement of the distance between odd nozzles to their corresponding even nozzles in the other column of the printhead, i.e. to measure the SAD error. 
     The pattern  342  is then scanned with the line sensor. Three metrics are obtained, the magnitude of APCS for the odd column of the black printhead, the magnitude of SAD (odd to even distance), and the magnitude of APCS error for the even column of the black printhead. When measuring the odd to even distance, two magnitudes can be considered, the APCS profile of each of the pen columns, and the mean distance between them. FIG. 16 illustrates the even and odd columns of the black printhead, and the illustrative distances SAD  1 - 2  and SAD  3 - 4 . 
     This exemplary technique does not differentiate between SAD and APCS of the even column of the black printhead, but it is not necessary to determine each separately but only their addition, i.e. the sum of SAD and APCS of the even column, since the correction of their addition ensures that odd and even droplets will reach their target position on the print medium. 
     Scanning with the line sensor is done bi-directionally to reduce scan time. Each block is 448 dot rows tall in this example (7 primitives). Thus, seven passes are needed to completely scan the pattern. This is illustrated in FIG. 15, with arrows  343  indicating the seven scanning passes. 
     The scanning begins at the top of the band  342 A, immediately after printing the second pass. The print medium is first moved backwards (in the X axis) to position the line sensor on the first 64 dot rows of the blocks. 
     Although the line sensor covers the whole length of the band when scanning all 7 passes, the data corresponding to the left region is alternatively discarded. FIG. 15 illustrates the scanning data used in the first pass, and the scanning data used in the second pass; the third pass data is analogous to the first and so successively. Thus, the data saved from scanning the left region is a measurement of distance between blocks printed by the second and first primitives, the fourth and third primitives, the sixth and fifth primitives and the eight and seventh primitives, all of the odd nozzle column of the black pen. The reason for saving only this half of the data is that the other half of the data will be measured in the second band  344 , as is discussed below. 
     For the right region  342 B, all the data is used. Therefore, after scanning the first band, the distance between odd and even columns  402 A and  402 B of the black printhead is almost characterized except for one primitive (the eighth primitive). The APCS of the odd column is known only for five primitives (second to first, fourth to third, sixth to fifth and eighth to seventh). The remaining measurements will be obtained when the second band is printed as explained more fully below. 
     The second band  344  is printed and scanned using a procedure akin to that used for the first band  342 . In the first print pass, half (23) of the blocks in the left region are printed using the odd column  402 A of the black printhead  400 . In this pass the second to the seventh primitives of the printhead are used (384 dot row tall blocks). 
     Then, before printing the second pass, the print medium is moved backwards in the X axis. The third to eighth primitives are then used to print 23 blocks in the gaps between the 23 blocks printed in the left region during the first pass. For the left region, adjacent portions of pairs of the blocks are printed with second and third primitives, the third and fourth primitives, the fourth and fifth primitives, the fifth and sixth primitives, the sixth and seventh primitives, and the seventh and eighth primitives. Similar to the procedure for printing the first band, the right region is printed during the second pass with blocks printed alternatively with the odd and with the even columns  402 A and  402 B of the black printhead  400 . 
     Scanning of the second band  344  with the line sensor is also done bidirectionally to reduce scan time. Each block is 384 dot rows tall (6 primitives). But only four passes are needed to scan the pattern to obtain the desired measurements. The scanning begins at the top of the band, after printing the second pass. Before scanning, the print medium is first moved backwards to position the line sensor on the first 64 dot rows of the blocks. Only the data in the left region is used now except the last scan. 
     The four scans are done on the whole length of the second band  344 . Starting with the first 64 dot rows of the band and continuing, the distances between adjacent block portions printed by the second and third primitives, by the fourth and fifth primitives, and by the sixth and seventh primitives are measured. The data for the right region is not used except the last row which includes the odd-even pattern which was not printed in the first band  342  (corresponding to the eighth primitive of the odd and the even columns). 
     The data from the left region of the second band is used, with the data from the left region of the first band, to characterize the distances between each adjacent pair of left column primitives of the black pen. The media (X) axis position of the pairs to be measured is the opposite to the position they had in the first band. For example, if in the first band primitive  2  is in the same scan axis position as primitive  3 , with primitive  2  to the left of primitive  3 , then in the second band primitive  3  is in the same media (X) axis position as primitive  2 , with primitive  3  now to the left of primitive  2 . Thus, the positions of primitive  2  and primitive  3  are swapped in the second band, relative to their positions in the first band. By swapping the positions from the first band to the second band, if encoder errors or scan axis errors had created errors in the measurement of the first band, now due to the swapping of positions of the primitives, these errors have the opposite sign, avoiding error accumulation. 
     Fourth Area  350   
     Color-to-Color In Scan (Y) Axis and Color SAD/APCS. The fourth area  350  has three bands  352 ,  354 ,  356  (FIG.  12 ), each band having a left region and a right region as discussed above regarding the bands  342 ,  344  for area  340 . The first band  352  is used to measure the relative errors in the magenta pen with respect to the black one. The second and third bands  354  and  356  respectively use the magenta pen as reference for the cyan and yellow colors respectively. Each band is printed and scanned before proceeding to the following one in this exemplary embodiment. 
     The left region of each band  352 ,  354 ,  356  is used for the SAD/APCS measurement for the corresponding color. The blocks in the left region are alternatively printed with odd and even nozzles of the pen. The right region of each band  352 ,  354 ,  356  is used for the APCS/Color to Color measurement for each color. The blocks in the right region are alternatively printed with odd reference nozzles and odd referred nozzles of the pen being measured and the reference pen. 
     Eight scans (8×64 dot rows each) are performed bi-directionally, and similarly to the scans for the black printhead. For the magenta color, the APCS and Color-to-Color measurements are translated into only APCS by subtracting the APCS value of the black printhead odd column from the measured distances between Magenta odd and Black odd. The value of the magenta odd column to black odd column offset is stored to apply to the first primitive of the magenta pen, which acts as the reference for the yellow and cyan measurements. The procedure is similar for the cyan and yellow printheads, with the only difference that the magenta printhead is here used as a reference instead of the black printhead. The SAD value is again unnecessary, and only the addition of SAD plus APCS for the even column are stored for each printhead after measuring the left region of each band. 
     The left region  352 A of band  352  has 46 blocks, alternatively printed with the nozzles of the odd column and the even column of the magenta printhead. The right region  352 B of band  352  has 46 blocks, alternatively printed with the nozzles of the odd column of the black printhead and the nozzles of the odd column of the magenta printhead. This is illustrated in FIG. 12, wherein the blocks printed by the reference printhead, i.e. the black printhead, are shown in solid form, and the blocks printed by the printhead to be measured, i.e. the magenta printhead, are show in shaded form. 
     During scanning, the distances between the blocks printed by the odd column and the even column of the magenta printhead are measured, using the left area  352 A blocks. The distances between the blocks printed by the reference printhead and the printhead under measurement are measured using the right area  352 B blocks. 
     The left region  354 A of band  354  has 46 blocks, alternatively printed with the nozzles of the odd column and the even column of the cyan printhead. The right region  354 B of band  354  has 46 blocks, alternatively printed with the nozzles of the odd column of the magenta printhead and the nozzles of the odd column of the cyan printhead. This is illustrated in FIG. 12, wherein the blocks in left area  354 B printed by the reference printhead, i.e. the magenta printhead, are shown in solid form, and the blocks printed by the printhead to be measured, i.e. the cyan printhead, are show in shaded form. 
     During scanning, the distances between the blocks printed by the odd column and the even column of the cyan printhead are measured, using the left area  354 A blocks. The distances between the blocks printed by the reference printhead and the printhead under measurement are measured using the right area  354 B blocks. 
     The left region  356 A of band  356  has 46 blocks, alternatively printed with the nozzles of the odd column and the even column of the yellow printhead. The right region  356 B of band  356  has 46 blocks, alternatively printed with the nozzles of the odd column of the magenta printhead and the nozzles of the odd column of the yellow printhead. This is illustrated in FIG. 12, wherein the blocks in left area  356 B printed by the reference printhead, i.e. the magenta printhead, are shown in solid form, and the blocks printed by the printhead to be measured, i.e. the yellow printhead, are show in shaded form. 
     During scanning, the distances between the blocks printed by the odd column and the even column of the yellow printhead are measured, using the left area  356 A blocks. The distances between the blocks printed by the reference printhead and the printhead under measurement are measured using the right area  356 B blocks. 
     The SAD, APCS and color to color corrections are calculated from the obtained measurements. At this point, if the printer had performed any previous calibrations, e.g.,chassis straightness, some re-calculations will be applied on the corrections to achieve the optimum corrections. A “minimax” algorithm is used to minimize the maximum remaining error. Minimax algorithms are well known in the art, and are used to solve equation systems with discretization errors. This type of algorithm chooses the solution with the smallest maximum amount of error. Minimax algorithms are described, e.g., in “Numerical Recipes in C, The Art of Scientific Computing,” by William H. Press et al., Cambridge University Press, at pages 204-205, 1996. 
     Fifth Area  370   
     Bi-Directional Alignment. In this area  370 , ten bands are printed bi-directionally. Each band is only 64 dot rows tall; and 100% dense, this is because both odd and even nozzles are firing at the same time and no print mask is used. 
     For the black printhead, two bands  374 ,  376  are printed at a carriage velocity of 20 inches per second (ips) and two bands  378 ,  380  are printed at 40 ips. The first band is formed with blocks printed in the forward and reverse directions alternatively with the top primitives of the printhead (odd and even together). The second band uses the same method but the bottom primitives (odd and even together). The third and fourth are equivalent to the first and second but printed at 50% density (40 ips). 
     The color bands are printed only at 20 ips using top and bottom primitives of the printhead in a similar way. Thus, bands  382 ,  384  are printed with the cyan printhead in this example, bands  386 , 388  with the magenta printhead, and bands  390 ,  392  with the yellow printhead. The results from the bi-directional scanning affect the calculation for the pen to pen alignment values obtained in area  350 . The pen-to-pen alignment values in the scan axis reverse direction are determined, by adding an offset to the pen-to-pen alignment values in the forward direction to provide the reverse direction alignment values. The offset is equal to the bi-directional error. 
     The number of blocks is 66 (greater than the 46 in the SAD measurements) to slightly increase the repeatability of the measurement. 
     These patterns  370  include warm-up areas indicated as areas  372 A,  372 B at the left and right edges, respectively because in bi-directional printing decap problems could appear as a consequence of dried ink on the orifices, typically occurring when the printhead has been sweeping a long time above the paper without firing drops. 
     FIG. 17 is a simplified flow diagram illustrating the general steps of a printhead alignment technique  600  as described with respect to FIGS. 11-16. At step  602 , the printhead alignment procedure is initiated, typically through a printhead change or by the user triggering the alignment through a menu selection. The line sensor is calibrated at  604 , by printing the first pattern area  310 , scanning the pattern with the sensor, and determining sensor calibration values to be applied. 
     At  606 , pen-to-pen errors along the X-axis are measured, by printing and analyzing the second pattern area  320 . As noted above, the black, cyan and yellow printheads can be aligned relative to the magenta printhead to correct the X-axis errors measured in this step. 
     At  608 , the black pen is used to print the third pattern area  340 , comprising horizontal bands of blocks. By scanning and analyzing the third pattern area, the black printhead SAD and APCS errors in the Y-axis direction are determined. 
     At  610 , the four pens are used to print the fourth pattern area, and to determine the color-to-color errors in the Y-axis direction. The black pen is used as a fixed reference for measuring the magenta Y-axis errors, and then the magenta printhead is used as the reference for measuring the yellow and cyan printhead Y-axis errors. 
     The measured errors are then utilized at  612  to calculate corrections to compensate the measured errors. These corrections can take the form of determining which 512 nozzles of the black, cyan and yellow pens to use to compensate the X-axis errors relative to the magenta pen, and for determining delays or advances in the firing for the logical primitives with respect to their nominal firing times, as described more fully with respect to application Ser. No. 09/199,882, entitled ALIGNMENT OF INK DOTS IN AN INKJET PRINTER, referenced above. 
     The bi-directional alignment is performed at  614 , and operation then returns to the main program flow for the printer. 
     It is understood that the above-described embodiments are merely illustrative of the possible specific embodiments which may represent principles of the present invention. Other arrangements may readily be devised in accordance with these principles by those skilled in the art without departing from the scope and spirit of the invention.