PRINTING METHOD WITH AN INK JET PRINTER USING AN IMPROVED HORIZONTAL RESOLUTION
BACKGROUND OF THE INVENTION Field of the Invention The present invention relates to ink jet printers and, more particularly, to a method of printing with an ink jet printer using an improved horizontal resolution. Description of Related Art An ink jet printer includes a print head having a plurality of holes that emit ink therein (Figure 1). For a multi-color inkjet printer, the orifices that emit ink in the print head are typically isolated in separate arrays of ink-emitting orifices, each order corresponding to an ink of different color to be injected into a printing medium . A plurality of ink jet heaters that are associated with the respective orifices that emit ink are selectively operated to inject the ink from the ink-emitting orifices, in a known manner. The print head is typically mounted and carried by a mobile carriage installation. The printing medium is movable in a forward direction within the printer and the carriage installation is movable in a transverse or orthogonal direction relative to the advancing direction. An image area that overlaps the printing medium is defined. The image area includes a plurality of rows and columns of pixel locations. Each separate pixel location corresponds to a placement location of the ink spot in the printing medium. Resolution or center-to-center spacing between the pixel locations is typically predefined in both the vertical (ie, forward) and horizontal (ie, transverse) directions. The vertical resolution of the pixel locations is defined by the center-to-center spacing between the orifices that emit ink. The horizontal resolution of the pixel locations is defined by the frequency response limitations associated with the print head. For example, the ink feed channel and the nozzle section associated with each ink ejecting hole require a certain amount of time to be filled after the associated ink jet heater is operated during printing. The transverse resolution of the pixel locations can be a function of the ink filling time by the holes in the print head. A typical print head used in an ink jet printer places ink dots in an image area on a print medium at a forward resolution of 300 dpi and a transverse resolution of 300 dpi. However, the frequency response limitations of a print head that can define the actual horizontal resolution of the pixel locations in an image area, the print head can actually have an addressable resolution in the transverse direction that is larger than the actual resolution of the pixel locations in the transverse direction. More particularly, the carriage installation carrying the print head is typically driven by a stepper motor which gradually moves the carriage installation through the printing medium in the transverse directions in progressive steps. The stepper motor has a minimum stage distance corresponding to the addressable resolution of the printhead in the transverse direction. For example, the actual transverse resolution of the print head can be set to 300 dots per inch (dpi) due to the frequency response limitations associated with the print head, while the addressable resolution of the print head in the direction Cross section can correspond to 600 dpi. With such an example, the addressable resolution of the print head is actually twice the actual transverse resolution of the print head. It is known, to provide improved print quality in a monochromatic ink jet printer (ie, a single color) by taking advantage of the addressable, transverse resolution of the print head. For example, the US patent. No. 5,480,240 assigned to the assignee of the present invention, discloses a method for providing improved print quality by improving the resolution of the printed image along the horizontal axis. The print data that is stored in a lower resolution grid format is changed to a finer resolution grid format associated with the addressability of the print head in the horizontal direction. The center of the locations of the ink dot placement and the size of the ink dots can vary using the finer resolution grid to provide the improved print quality. Printing with a multi-color ink jet printer typically uses a half tone process to determine the relative frequency of the ink spots and their arrangement in the print image to produce colors not of the primary color set. A threshold matrix of a predetermined size includes a plurality of rows and columns of cells, each cell corresponding to a pixel location in the image area. Each cell is assigned a threshold value that is proportionally graduated to normalize the colors to the size of the matrix used. As the print image is analyzed, the position of a cell within the threshold matrix is used to determine the threshold value for that particular cell. A color value is assigned to each of the primary colors. If the color value for the primary color is greater than the threshold value within a cell of the threshold array, the ink is injected to a corresponding pixel location in the image area. Referring to Figure 2, an example of a threshold matrix to be used during a half tone process during color printing is shown. The threshold matrix includes four columns and four rows, with a total of sixteen cells. Each cell corresponds to one of the pixel locations in the image area and is assigned a threshold value as indicated. A color value of 8 is assigned to the primary cyan color; the magenta is assigned a color value of 4; and a color value of 12 is assigned to yellow. The cyan ink would thus be printed at pixel locations corresponding to the substantially full cells indicated by the cyan color printing plane. It should be noted that the color values assigned to each primary color can generally be considered as corresponding to a percentage of that particular primary color ink to be injected into the printing medium within a portion of the image area corresponding to the threshold matrix. That is, for the example shown, the threshold matrix includes sixteen cells in total and the color ink .cian is assigned a color value of eight. In this way, approximately eight of sixteen cells (ie, approximately 50%) of the cells are assigned a cyan color value. This correspondingly means that approximately 50% of the pixel locations corresponding to the threshold matrix cells receive cyan-colored ink in the same manner. Similarly, the yellow ink would be placed at approximately 12/16 or 75% of the pixel locations for the threshold matrix in the corresponding portion of the image area. The threshold matrix can thus be considered as a frequency distribution of the various color ink points within a predefined and corresponding portion of the image area. What is needed in the art is a method for providing improved resolution along the horizontal axis with a color ink jet printer, without adversely affecting the technique of printing half tones. SUMMARY OF THE INVENTION The present invention provides a printing method with a multi-color inkjet printer in which the printing resolution in the transverse direction is improved by expanding a threshold matrix in the transverse direction so that each column it is placed adjacent to at least one other column with identical threshold values. The threshold matrix expands in the transverse direction depending on the addressable resolution of the print head in the transverse direction (e.g., the minimum gradual distance of a stepper motor driving a carriage installation carrying the printhead ). The invention comprises, in a form thereof, a method of printing an image on a printing medium with at least one color ink using an ink jet printer. The printing medium is movable in a forward direction in the inkjet printer. The print head has a plurality of orifices that emit ink to inject ink into the printing medium, the ink-emitting orifices being spaced in the direction of travel at a common distance. The print head is movable in a direction transverse to the direction of advance in progressive stages, the progressive stages having a minimum stage distance. An image area has a plurality of rows of pixel locations and a plurality of columns of pixel locations, the pixel locations corresponding to ink spot placement locations in the printing medium. Columns of pixel locations have a pixel advance resolution that depends on the common distance. The rows of pixel locations have a transverse pixel resolution that depends on the minimum stage distance. A color value is assigned to at least one color ink. A threshold array is defined with a plurality of rows of cells and a plurality of columns of cells, each cell corresponding to one of the pixel locations in the image area. A threshold value is assigned to each individual cell within the threshold matrix. A transition matrix is defined by having the same number of rows as the threshold matrix and a greater number of columns than the threshold matrix. The largest number of columns is equal to the product of an integer multiplier with the number of columns in the threshold matrix. - The whole multiplier depends on the minimum stage distance. A threshold value is assigned to each individual cell within the transition matrix. Each column of the transition matrix has cells with threshold values that correspond to one of the columns of the threshold matrix, and placed adjacent to at least one other column with cells with identically assigned threshold values. The printing medium is printed with at least one color ink depending on the color value of at least one color ink and the threshold values of the transition matrix. An advantage of the present invention is that the transverse pixel resolution in a multi-color inkjet printer can be improved without affecting the attributes of half tones such as hue, saturation and / or brightness. Another advantage is that the printing method of the present invention can be used with other print quality improvement techniques that improve the resolution of the print image along the horizontal axis. BRIEF DESCRIPTION OF THE DRAWINGS Other advantages and features of the invention may be understood by reference to the drawings and detailed description of the invention that follows. Figure 1 is a schematic illustration of a print head that can be used with the method of the present invention and a portion of an image area in relation to the print head; Figure 2 is an example of a threshold matrix used during a process of printing half tones with a multicolored print head; Figures 3, 4, 5 illustrate a method for defining a transition matrix by duplicating the threshold matrix of Figure 2 in the transverse direction and thereby altering the pixel resolution in the transverse direction; and Figures 6, 7 and 8 illustrate one embodiment of the method of the present invention that defines a transition matrix by expanding the threshold matrix of Figure 2 in the transverse direction and thereby improving pixel resolution in the transverse direction. The corresponding reference characters indicate corresponding parts through all the various views. The exemplification set forth herein illustrates a preferred embodiment of the invention, in one form and such exemplification should not be construed as limiting the scope of the invention in any way. Detailed Description of the Invention Referring now to the drawings and more particularly to Figure 1, there is shown a schematic illustration of a tricolor printing head 18 that can be used with the method of the present invention. The print head 18 includes a plurality of holes emitting cyan-colored ink 20, holes emitting magenta ink 22 and orifices emitting yellow ink 24, with each arrangement of holes corresponding to a different color ink to be injected into the medium of the ink. printing, such as paper 26. The print head 18 is shown in fragmentary form in Figure 1, for the sake of simplicity with only four holes emitting ink 20, 22 and 24 for each respective color ink. However, each ordering of the ink-emitting holes actually includes more than four holes that emit ink. A plurality of ink jet heaters (not shown) associated with the respective ink-emitting orifices 20, 22 and 24 are selectively driven to inject the ink from the orifices emitting ink 20, 22 and 24. The print head 18 is assembled and carried by a mobile carriage installation (not shown). The paper 26 is movable in an advancing direction 28 within the printer and the carriage installation is movable in a transverse direction 30 relative to the advancing direction 28. An image area 32 that is superimposed on the paper 26 is defined. The image area 32 includes a plurality of rows and columns of pixel locations. Each separate pixel location corresponds to a location of ink spot placement in the printing medium. The image area 32 has a vertical or forward resolution VR corresponding to the center-to-center spacing between the holes emitting ink 20, 22 and 24. In the embodiment shown, the advance resolution VR corresponds to a resolution of 300 dpi . The image area 32 also has a horizontal or transverse resolution HR which depends on the frequency response constraints associated with the print head, as described above. In the embodiment shown, the image area 32 has a transverse resolution HR of approximately 300 dpi. The print head 18 has an addressable resolution AR in the transverse direction 30 which is less than the transverse resolution HR of the image area 32. The addressable resolution AR of the print head 18 is equal to or less than the minimum gradual distance of the print head 18 through paper 26 in transverse directions 30. In the embodiment shown, the addressable resolution AR in the horizontal direction is 600 dpi. Referring now to Figures 3-5, there is shown a method of defining a transition matrix 34 by duplicating the threshold array 36 of Figure 2 in the transverse direction 30 and thereby altering the pixel resolution in the transverse direction 30. It is assumed that the method shown in Figures 3-5 is carried out using the tricolor printing head 18 which includes the holes that emit cyan-colored ink., the orifices that emit magenta ink 22, and the orifices that emit yellow ink 24. The transition matrix 34 (figure 3) is defined to include twice the number of columns as the threshold matrix 36, but the same number of rows that the threshold matrix 36. In the embodiment shown, the transition matrix 34 has a pixel advance resolution of 300 dpi and a pixel transverse resolution of 600 dpi. The pixel transverse resolution of 600 dpi corresponds to the maximum addressable resolution of the print head 18 (example the minimum step distance of the stepper motor driving the print head). As shown, the four columns on the left of the transition matrix 34 include sixteen cells that are identical to the sixteen cells shown in the threshold array 36. Likewise, the four columns on the right of the transition matrix 34 they include sixteen cells that are identical to the cells of the threshold array 36. The transition matrix 34 thus includes two arrays that are placed adjacent and are identical to one another. Figure 4 illustrates the different color image planes corresponding to the transition matrix 34 shown in Figure 3 the three primary colors of the tricolor print head. The four columns in - 1 '
The left side of each matrix are identical to the four columns on the right side of each matrix for each respective color. For the color image plane, all the cells within the transition matrix 34 that have a value of less than 8 correspond to locations in which the ink points can theoretically be placed, regardless of the frequency response limitations of the print head 18. Similarly, the arrangements for the magenta image plane and the yellow image plane also include theoretical ink spot placement locations in which ink dots can be placed if the threshold value assigned to each individual cell is smaller than the color value assigned for magenta and yellow inks. In the example shown, magenta is assigned a color value of 4 and yellow is assigned a color value of 12, which indicates that approximately 25% of the magenta ink points (4/16 = 25%) and approximately 75% of the yellow dots (12/16 = 75%) must be placed within the respective image planes. Figure 5 illustrates the different color printing planes with actual ink spot placement locations associated with the data points shown in Figure 4, based on the actual cross-sectional resolution HR of the print head. The ink points are thus shown as filling a cell of 300 dpi X 300 dpi in general. The center of each ink spot placement location is based on the leading edge of one or more ink dots shown in Figure 4. Thus, where a single ink dot is shown in Figure 4 with an empty cell at the Right of the same, the placement location of the corresponding ink spot in Figure 5 covers both the filled cell and the unfilled cell on the right. It is apparent from observing the positioning locations of the ink spot in Figure 4 that the method of producing a transition matrix 34 with an altered horizontal resolution, described above, is not effective in placing the different color inks on the printing medium. so that physical characteristics such as color, tone, brightness, etc., are preserved. For example, the original threshold matrix 36 includes sixteen cells and the cyan color is assigned a color value of 8 in the previous example. Thus, about 1/2 of the ink spot placement locations must correspond to the cyan ink to retain the properties of the desired color. However, when reviewing the arrangement in Figure 5 the cyan-colored printing plane labeled in, it will be noted that fourteen of sixteen cells are full corresponding to fourteen ink spot placement locations in the image area. The approximate percentage of cyan ink coverage for the image area is thus 15/16 or approximately 94% coverage by cyan ink. It is thus apparent that the color and tone properties that such a half tone process uses can be substantially different since about 38% more than desired of the image area corresponding to the threshold matrix 36 is covered by cyan ink. Similarly, it is noted that the percentages of ink spot placement locations within the magenta image plane and the yellow image plane are also substantially different from those desired for magenta and yellow ink. Referring now to Figures 6, 7 and 8, there is shown an illustration of one embodiment of the method of the present invention of defining a transition matrix 38 by expanding the threshold matrix 36 of Figure 2 in the transverse direction and thus improving the pixel resolution in the transverse direction 30 without perniciously affecting the color, tone, brightness, etc., of the print image. Figure 6 illustrates a transition matrix 38 having four rows and eight columns. The four rows correspond to a pixel advance resolution of 300 dpi and the eight columns correspond to a transverse pixel resolution of 600 dpi as indicated above. Instead of including two adjacent arrays of four columns each that are identical to the threshold array 36 shown in Figure 2, the transition matrix 38 includes columns that have been duplicated and that are identical to at least one adjacent horizontal column. For example, the two columns on the left side of the transition matrix 38 correspond to the only column on the left side of the threshold array 36.; and the two columns on the right side of the transition matrix 38 correspond to the only column on the right side of the threshold array 36. The number of columns of the transition matrix 38 corresponds to a product of an integer multiplier with the number of columns of the threshold array 36. The entire multiplier may depend on the minimum addressable resolution of the print head in the transverse direction. More particularly the entire multiplier may depend on the minimum stage distance of a stepper motor used to drive the carriage installation carrying the print head 18. In the embodiment shown, the threshold array 36 has a transverse pixel resolution of 300 dpi based on the frequency response limitations of the print head, and the transition matrix 38 has a transverse resolution of 600 dpi corresponding to the addressable resolution of the print head in the transverse direction. The entire multiplier, therefore, can not exceed a value of 2 (600 dpi / 300 dpi = 2). If the addressable resolution of the print head was greater than 600 dpi, the number of horizontally adjacent columns could also be increased. For example, if the addressable pixel resolution of the print head in the horizontal direction was 1200 dpi, the transition matrix could include four times the number of columns compared to the original threshold matrix. Thus configured, there would be four groups of four horizontally adjacent columns each group having columns with identical threshold values therein. With an AR addressable resolution of 1200 dpi and a transverse resolution HR of 300 dpi, the entire multiplier can not exceed a value of four (1200 dpi / 300 dpi = 4). Referring now to Figure 7, the ink spot placement locations for the transition matrix 38 are shown. Since each column is placed adjacent to an identical column, the points are grouped in even numbers along a horizontal axis which extends through each image plane. For example, referring to the cyan-colored image plane, second row from the top, two pairs of ink dots are placed to the left of the row and a pair of ink dots is placed to the right of the row. Since each column is arranged horizontally adjacent to an identical column, an even number of pairs is always given along the horizontal axis of each row, thereby eliminating the possibility of a non-number of horizontally adjacent ink points. Figure 8 illustrates the actual placement pattern of the ink dots for each color ink when the transition matrix 38 is used. The center of each location ink dot placement corresponds to the center of each pair of points of horizontally adjacent columns which are shown in Figure 7. There is a direct correspondence between the number of pairs of points shown in Figure 7 and the number of ink spot placement locations shown in Figure 8. The number of point placement locations The ink shown in Figure 8 is substantially different from the number and location of the ink spot placement locations for each color printing plane shown in Figure 5. For the cyan color printing plane shown in Figure 8, There are eight ink spot placement locations. These are the eight of the sixteen desired ink spot placement locations for cyan ink when compared to the fifteen ink spot placement locations for the cyan color printing plane shown in FIG. 5. In addition, there are four ink location locations. ink spot placement for the magenta printing plane shown in Figure 8. Again, these are the four of the sixteen desired ink spot placement locations for the magenta ink compared to the eight ink spot placement locations for the magenta printing plane shown in Figure 5. The method of the present invention to create a transition matrix by expanding the threshold matrix in the transverse direction is, therefore, much more effective in preserving the desired proportions of the different color inks in the print image, as compared to the method of creating a transition matrix shown in Figures 3-5. Using the transition matrix 38 shown in Figure 6 the ink is injected from the selected ink-emitting holes 20, 22 and 24 on the printing medium with pixel locations selected from the image area if the value of the cyan-colored ink, magenta and yellow is less than the threshold value of a corresponding cell of the transition matrix 38. Although the present invention has been described with reference to the preferred embodiments, those skilled in the art will recognize that changes can be made in form and detail without depart from the spirit and scope of the following claims.