Abstract:
A laser scanning assembly generates a laser beam and scans the laser beam through a plurality of scan lines to form desired dots. Each scan line is positioned to overlap an adjacent scan line and each dot includes a plurality of segments. The scanning assembly scans the laser beam through multiple scan lines to fully discharge each segment of each dot. The laser scanner assembly would typically be part of a laser printer.

Description:
BACKGROUND OF THE INVENTION  
       [0001]      FIG. 1  shows a typical laser printer  10  including a movable photoreceptor  12 , typically a revolving drum or cylinder. This drum  12  is made out of a highly photoconductive material that is discharged by light photons. Initially, the photoreceptor drum  12  is given a total positive charge by a charging electrode  14 , typically a wire or roller having a current running through it. As the drum  12  revolves, the printer  10  uses a laser unit  16  (such as a laser diode) to shine a laser beam  18  across the surface of the drum  12 to discharge certain points. In this manner, the laser beam  18  “draws” the text and images to be printed as a pattern of electrical discharges (an electrostatic image) on the drum  12 . If the laser beam  18  is modulated, resulting variations in charge on the drum  12  will ultimately be translated to proportionate amounts of toner deposited on a sheet of paper  21 .  
         [0002]     After the laser beam  18  scans the desired electrostatic pattern on the drum  12 , the printer  10  uses a toner roller  20  to coat the drum  12  with positively charged toner powder. Since the toner has a positive charge, it clings to the negative discharged areas of the drum  12  that have been scanned by the laser beam, but the toner does not cling to the positively charged “background” of the drum. With the toner pattern affixed to the drum  12 , the drum rolls over the sheet of paper  21  traveling below it. Before the paper  21  travels under the drum  12 , the paper is given a negative charge that is stronger than the negative charge of the electrostatic image on the drum  12  so that the paper pulls the toner powder away from the drum  12 . Finally, the printer  10  passes the paper  21  through a fuser  24 , which is typically a pair of heated rollers and as the paper  21  passes through the fuser  24 , the loose toner powder on the paper melts, fusing with the fibers in the paper and forming a permanent image on the paper. After the toner on the drum  12  is transferred to the paper  21 , the drum surface passes a discharge lamp  22  that generates a bright light that exposes the entire photoreceptor surface of the drum  12 , erasing the electrostatic image. The drum surface then passes the charging electrode  14 , which reapplies a positive charge to the surface of the drum  12  in anticipation of the laser beam  18  scanning the next image to be printed onto the drum.  
         [0003]      FIG. 2  is a functional top view of the printer  10  of  FIG. 1  showing a number of dark areas  200  on the drum  12  that represent the negatively discharged areas or dots created by the scanning laser beam  18 .  FIG. 3  shows a perspective view of portions of the laser printer  10  in  FIG. 1  better showing the scanning of the laser beam  18  in a horizontal direction across the drum  12  as indicated by an arrow  300 . Image processing circuitry (not shown) controls the laser unit  16  to modulate the laser beam  18  as the beam scans across the drum  12  in the horizontal direction  300  one line at a time. The image processing circuitry controls the laser unit  16  to turn ON and emit a pulse of light for every dot to be printed in a given horizontal line and to turn OFF where no dots are to be printed in the line.  
         [0004]     In scanning the laser beam  18  across the drum  12 , the laser unit  16  does not actually move the laser beam  18  itself but instead bounces the laser beam  18  off of a movable mirror  26 , such as a rotating mirror or an oscillating mirror. As the mirror  26  moves, it reflects the laser beam  18  through a series of lenses (not shown) and onto the drum  12 . These lenses change characteristics of the light beam  18  to compensate for image distortion that would otherwise be caused by the varying distance between the mirror  26  and points along the drum  12 .  
         [0005]     The laser printer  10  is designed to print pages of paper  21  at a fast rate, meaning the mirror  26  must move at a very fast rate to scan the beam in the horizontal direction and drum  12  must rotate at a fast rate to transfer toner deposited on the drum to the paper. As a result, laser printers with this type of architecture have proven to be extremely sensitive to variations in the rotational speed of the drum  12 . These variations in speed of the drum  12  appear on the paper  21  as increased or decreased spacing between horizontal scan lines of dots or pixels formed by the horizontally scanning laser beam  18  and visually appear on the paper as bands. This undesirable effect is called “banding” with the visually noticeable bands being referred to as “banding artifacts.” 
         [0006]     Banding will now be described in more detail with reference to  FIGS. 4-6 .  FIG. 4  is a diagram of an ideal scan line pattern  400  produced by the laser printer  10  of  FIG. 1  where the rotational speed of the photoconductive drum  12  is constant. The scan line pattern  400  is a pattern of horizontal lines that the laser beam  18  scans along the surface of the drum  12 . In the example of  FIG. 4 , the laser beam  18  scans from left to right in generating each scan line  402 - 406 . In the scan line pattern  400 , as the laser beam  18  scans each line  402 - 406  the laser beam is turned ON and OFF or modulated to generate the desired discharge areas or dots in each scan line. A vertical column of dots including dots  408 - 412  in  FIG. 4  is an example of a discharged area generated by the laser beam  18  as the laser beam traverses the scan lines  402 - 406 . The scan line pattern  400  is ideal in that each scan line  402 - 406  is perfectly positioned adjacent other scan lines so that the dots  40 &amp; 412  may be formed in the consecutive scan lines to print the desired vertical column of dots and the corresponding text and/or images including this vertical column of dots. A vertical line  414  shown in  FIG. 4  extending vertically from the vertical midpoint of scan line  402  and extending to the vertical midpoint of scan line  406  will be discussed in more detail below with reference to  FIG. 6 .  
         [0007]      FIG. 5  is a diagram of scan line pattern  500  produced by the laser printer  10  that includes banding caused by variations in the rotational speed of the photoconductive drum  12 . When the drum  12  rotates too fast, a space or gap G between scan lines  502  and  504  occurs and leads to under development or removal of charge on the drum in this gap, which causes light areas on the paper  21 . In the example of  FIG. 5 , the gap G occurs between scan lines  502  and  504  as shown. A vertical column of dots including dots  508 - 512  being formed in scan lines  502 - 506  is thus shifted downward by the gap G so that no charge in this vertical column is removed in the gap. Ideally the top portion of the dot  510  would be formed in the gap G just under the dot  508  in the scan line  502 , but due to the increase in speed of the drum  12  and resulting gap G there is no discharge in this area. This results in a light horizontal line or “band” between all dots  508  formed in line  502  and dots formed in line  504 . Note that the average rotational speed of the drum  12  is correct due to the operation of control circuitry (not shown) that controls a motor (also not shown) that drives the rotation of the drum. As a result, an increase in rotational speed of the drum  12  will necessarily be followed by a period during which the drum slows down, offseting the increase in velocity so the desired average velocity is realized. As a result of this slowing down of the drum  12 , some scan lines  502 - 506  may overlap. This is shown in  FIG. 5  for scan lines  504  and  506  where the bottom of scan line  504  is shown as dotted since the top of scan line  506  overlaps the bottom of scan line  504  due to the drum  12  slowing down. This overlap results in a region  513  being undesirably scanned twice, once during scan line  504  and once during scan line  506 . Note that this additional scan of this region during scan line  506  does not affect the discharge of this region since the region will have been completely discharged during scan line  504  so the region is unaffected by scan line  506  since there is no additional charge removed. A vertical line  514  shown in  FIG. 5  extending vertically from the vertical midpoint of scan line  502  and extending to the vertical midpoint of scan line  506  will be discussed in more detail below with reference to  FIG. 6 .  
         [0008]      FIG. 6  is a graph showing the variation in the discharge of dots in the vertical columns of dotsin the scan line patterns  400  and  500  of  FIGS. 4 and 5 , respectively. The vertical lines  414  and  514  shown in  FIGS. 4 and 5  represent the vertical axis in  FIG. 6  and represents the scan line number or physical location in the scan lines in the vertical direction. The scan line number  1  on the vertical axis in  FIG. 6  corresponds to the midpoint of the scan lines  402  and and  502 . The dotted line in the graph of  FIG. 6  corresponds to the ideal pattern  400  where consecutive vertically aligned dots  408 - 412  are being formed in scan lines  402 - 406 . The horizontal axis in the graph represents the discharge of these dots  408 - 412 , with 1 being fully discharged and 0 being not discharged at all so no dot will be formed. Thus, ideally each of the dots being formed in scan lines  402 - 406  is completely discharged to 1 as shown by the dotted line in  FIG. 6 . In contrast, where banding occurs there is a gap in this vertical discharge distribution corresponding to the gap G on the drum  12  of  FIG. 5 . The graph shows that in the gap G, which corresponds approximately to line number 1.5 in the graph, the discharge falls to zero meaning there is no discharge at all. The discharge then increases again to 1 at just before line number 2 due to the dot  510  in the scan line  504  after the gap G. The discontinuity in the discharge graphically shows why banding occurs since where there has been no discharge no toner will be attracted to the drum  12  in this region. It should be noted that the example of  FIG. 6  assumes a perfect linear discharge of the drum  12  and a perfectly uniform laser beam  18 . The actual discharge pattern would be different due to nonlinear discharge of regions on the drum  12  and due to a nonuniform intensity profile for the laser beam  18 , which would typically be a Gaussian intensity distribution. All examples discussed herein assume a perfect discharge and perfectly uniform laser beam  18  to simplify the examples and allow the concept of overlapping scan lines to be more easily described under these ideal operating conditions.  
         [0009]     The principle cause of variations in the speed of rotation of the drum  12  and resulting banding is due to gear noise in gears driving the drum. Gear noise results from imperfect spacing of teeth on the gears, variances in flexing of gear teeth, and other intrinsic variations in gear force transfer. Imperfections on the surfaces of the movable mirror  26  and vibration of the laser unit  16  and mirror  26  relative to the drum  12  can also contribute to banding. Accordingly, existing attempts to reduce banding have focused on improving the mechanical components in the printer  10  in attempts to reduce gear noise and to rotate the drum  12  at a more constant velocity. These approaches, however, can add significantly greater expense to the mechanical components of the printer  10  and thus to the overall cost of the printer.  
         [0010]     There is a need for reducing banding in a laser printer without adversely affecting the cost of the laser printer.  
       SUMMARY OF THE INVENTION  
       [0011]     According to one aspect of the present invention, a laser scanning assembly generates a laser beam and scans the laser beam through a plurality of scan lines to form desired dots. Each scan line is positioned to overlap an adjacent scan line and each dot includes a plurality of segments. The scanning assembly scans the laser beam through multiple scan lines to fully discharge each segment of each dot. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]      FIG. 1  is a cross-sectional view showing the primary components of a conventional laser printer.  
         [0013]      FIG. 2  is a top view of the conventional laser printer of  FIG. 1  better illustrating the operation of the photoreceptor drum, laser beam, toner roller, paper, and fuser during operation of the laser printer.  
         [0014]      FIG. 3  is a perspective view of various components of the conventional laser printer of  FIG. 1  that better illustrates the scanning of the laser beam in a horizontal direction across the drum during operation of the laser printer.  
         [0015]      FIG. 4  is a diagram of a scan line pattern produced by the laser printer of  FIG. 1  where the rotational speed of the photoconductive drum is constant.  
         [0016]      FIG. 5  is a diagram of scan line pattern produced by the laser printer of  FIG. 1  that includes banding cause by variations in the rotational speed of the photoconductive drum.  
         [0017]      FIG. 6  is a graph showing the variation in the discharge of dots in each of the scan lines for the scan line patterns of  FIGS. 4 and 5 .  
         [0018]      FIG. 7  is a diagram of an ideal overlapping scan line pattern produced by a laser printer the according to a first embodiment of the present invention.  
         [0019]      FIG. 8  is a diagram showing the effect of an overlapping scan line pattern according to an embodiment of the present invention when the rotational speed of the photoconductive drum varies.  
         [0020]      FIG. 9  is a graph showing the variation in the discharge of dots in the scan line patterns of  FIGS. 7 and 8 .  
         [0021]      FIG. 10  is representation of the surface of the phontoconductive drum of  FIG. 8  showing the various discharged and charged areas resulting from the scanning line pattern of  FIG. 8 . 
     
    
     DESCRIPTION OF THE INVENTION  
       [0022]     The following discussion is presented to enable a person skilled in the art to make and use the invention. Various modifications to the preferred embodiment will be readily apparent to those skilled in the art, and the generic principles herein may be applied to other embodiments and applications without departing from the spirit and scope of the present invention as defined by the appended claims. Thus, the present invention is not intended to be limited to the embodiment shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.  
         [0023]      FIG. 7  is a diagram of an ideal overlapping scan line pattern  700  produced by a laser printer according to a first embodiment of the present invention. The scan line pattern  700  includes a number of scan lines  702 - 710 , with the scan line  704  overlapping the scan lines  702  and  706  and the scan line  708  overlapping the scan lines  706  and  710 . The scan lines  702 - 710  represent the scan lines that a laser beam traverses on a photoconductive surface  712  of a rotating drum  714 . In the example of  FIG. 7 , the surface  712  moves in the direction indicated by an arrow  713  and the laser beam scans from left to right in generating each scan line  702 - 710 , such as would be the case when the beam is reflected by a rotating mirror as previously described with reference to  FIGS. 1-3 . In the scan line pattern  700 , the overlapping scan lines  704  and  708  are in contrast to the conventional nonoverlapping scan line pattern  400  as previously discussed with reference to  FIGS. 4 and 5 . The overlap of the scan lines  702 - 710  makes the resulting discharged areas or dots on the surface  712  less susceptible to variations in the speed of the drum  714  and thereby reduces banding, as will be explained in more detail below.  
         [0024]     The formation of discharged dots with the scan line pattern  700  will now be explained in more detail by way of example. In  FIG. 7 , a vertical column of dots includes dots  716 - 720 , each dot having an upper half designed “U” and a lower half designated “L” as shown for the dot  718  in the scan line  706 . The dot  718  is formed by scanning each of the halves U and L twice in the embodiment of  FIG. 7 . In forming the dot  718 , the laser beam first scans the overlapping scan line  704  which scans the upper half U of the dot  718  a first time to remove a first portion of the charge from this region. The laser beam thereafter scans the scan line  706 , which scans the upper half U of dot  718  a second time to remove a second portion of charge from this region and discharge the region to its desired state. The scanning of line  706  also scans the lower half L of dot  718  a first time to remove a first portion of the charge from this region. Finally, the laser beam scans the overlapping scan line  708  to thereby scan the lower half L of dot  718  a second time and remove a second portion of charge from this region and discharge the region to its desired state. In this way, three scans of the laser beam are required to form a dot  718  in the pattern  700 , with two passes of the laser beam forming each of the upper and lower halves U and L.  
         [0025]     With the overlapping scan line pattern  700 , the modulation of the laser beam as it traverses each scan line  702 - 710  must of course be modified to remove the proper amount of charge. In the embodiment of  FIG. 7 , the intensity of the laser would be half of what it would be in the conventional nonoverlapping scan pattern of  FIG. 4 . This way for each half U and L of the dot  718  and the other dots  716  and  720  in the vertical column of dots being formed, half of the desired charge is removed in the first scan and the other half in the second scan. Also note that in the ideal scan line pattern shown in  FIG. 7 , during the formation of the dot  718  half the full charge is also removed in the half scan lines just above and below the dot. In other words, during the scan line  704  the laser removes not only half the charge in the upper half U of the dot  718  but also removes half the charge in the lower half of the dot  716 . The same is true of the upper half of the dot  720  just below the dot  718 , which has half the charge removed during scanning of the scan line  708 . In the cases where a vertical column of consecutive dots  716 - 720  is being formed, which is the case where banding could occur, these extra areas actually help reduce banding by removing this additional charge. A vertical line  722  shown in  FIG. 7  extending vertically from the vertical midpoint of scan line  702  and extending to the vertical midpoint of scan line  710  will be discussed in more detail below with reference to  FIG. 9 .  
         [0026]     Note the scan line pattern  700  of  FIG. 7  once again assumes a perfect linear discharge of regions on the surface  712  of the drum  714  and a perfectly uniform intensify profile for the laser beam. Actual discharge patterns would be different due to nonlinear discharge of regions on the surface  712  of drum  714  and due to a nonuniform (typically Gaussian) intensity profile for the laser beam, as was mentioned above with regard to conventional laser printers. Details of the physics and the nuances of operation of actual laser printers will be understood by those skilled in the art. Therefore, the present description will only discuss and illustrate ideal operation where discharge is perfectly linear and the intensity profile of the laser beam is perfectly uniform in order to more clearly illustrate the inventive aspects of the present invention.  
         [0027]     Where a given dot is the last dot in a vertical column of dots, the laser beam is modulated differently to create a desired discharge end point, as will be understood by those skilled in the art. For example, assume dot  716  is a white dot, meaning the dot  718  is the last dot in a vertical column of dots. A different laser modulation, the nonlinear discharge of the surface  712 , and nonuniform intensity profile of the laser beam means that half the desired amount of discharge would not actually be removed as described above for the lower half of dot  716  during the scan line  704 . This is true because the shorter amount of laser on-time, the nature of the Gaussian intensity profile of the laser beam and the nonlinear discharge of the surface  712  combine to remove most the charge from the top of scan line  706  (i.e., from the upper half U of dot  718 ) instead of from the lower half of dot  716 . This would result in toner being attracted to the upper half U of dot  718  in scan line  706  and very little toner being attracted to the lower half of dot  716  above the dot  718  as a consequence of scan line  704 .  
         [0028]     The substantially overlapping scan lines  702 - 710  cause the discharged dots  716 -  720  generated on the photoconductive surface  712  to be less sensitive to small variations in speed of the photoconductive drum  714 , which results in less banding. The reason for this will now be described in more detail with reference to  FIG. 8 , which is a diagram showing the effect of an overlapping scan line pattern  800  including a number scan lines  802 - 810 . The figure depicts an example where the rotational speed of a photoconductive surface  812  on a drum  814  varies, which may be caused by imperfections in gears driving the drum, variations in the rotational speed of motor driving the gears, or other factors. The surface  812  travels in the direction indicated by an arrow  813  and a laser beam scans from left to right in generating each scan line  802 - 810 , which would be the case when the laser beam is reflected off a rotating mirror as previously discussed.  
         [0029]     The scan lines  802 - 810  are the scan lines on the surface  812  that result from a temporary increase in the rotational speed of the drum  814 . In the example of  FIG. 8 , after the laser beam traverses the scan lines  802  and  804  the drum  814  speeds up. This increase in speed of the drum  814  results in a gap G between the scan lines  802  and  806  in the same way as previously described with reference to  FIG. 5 . With the overlapping scan line pattern  800 , the laser beam traverses the gap G during the scan line  804 . As a result, a first portion of charge is removed from the gap G where a dot  818  is ideally to be formed. The dot  818  is intended to be a dot formed in the scan line  806  just as was the dot  718  in  FIG. 7 , but due to the gap G the formation of the dot  818  is very different. The gap G has a height that is less than half the height of the scan lines  802 - 810  merely by way of example in  FIG. 8 .  
         [0030]     In the formation of the dot  818 , the laser beam scans an upper half U of the dot as the beam traverses the overlapping scan line  804 . Thus, since each pass of the laser beam is assumed to remove half the desired amount of charge in the embodiment of  FIG. 8 , half the desired amount of charge is removed from the upper half U during the scan line  804 . Next, the laser beam traverses the scan line  806  after the drum  814  has speeded up. As a result, there is the gap G between the bottom of the scan line  802  and the scan line  806 . The height of the gap G in  FIG. 8  is assumed to be equal to the height G of the gap G in  FIG. 5 . This gap G in  FIG. 8  means that the scan line  806  is offset by the height of this gap from the ideal location of the scan line  806 . Therefore, as the laser beam traverses scan line  806  only a portion of the upper half U of the dot  818  is scanned along with all of a lower half L of the dot  818 . At this point, although the full charge should be removed from the upper half U of the dot  818  due to the scan lines  804  and  806 , the full charge is removed only from the portion of the upper half U that the beam traversed during the scan line  806 . The remainder of the upper half U has half the full charge removed. While only half the full charge has been removed from the upper half U in the gap G when ideally the full charge should have been removed, removal of half the charge is better than no removal of charge at all as was the case with the conventional scan line pattern  500  of  FIG. 5 .  
         [0031]     The laser beam next traverses the overlapping scan line  808 . The example of  FIG. 8  includes an additional gap GO between the scan lines  804  and  808 , which may or may not occur depending on mechanical and electrical components (not shown) in the laser printer (not shown) generating the scan pattern  800 . With the gap GO, as the laser beam traverses the scan line  808  just after traversing scan line  806  only a portion of the lower half L of dot  818  is scanned. As a result, the full charge in the lower half L is removed only in the portion scanned by scan lines  806  and  808 . The remainder of the lower half L, which is equal to the height of the lower half minus the height of the additional gap GO, was scanned only once during the scan line  806  and therefore has half the full charge removed. Once again, while ideally the entire lower half L of the dot  816  has been fully discharged at this point, at least a portion of the lower half has been fully discharged notwithstanding the gaps GO and G caused by variations in the speed of the drum  814 . A vertical line  822  shown in  FIG. 8  extending vertically from the vertical midpoint of scan line  802  and extending to the vertical midpoint of scan line  810  will be discussed in more detail below with reference to  FIG. 9 .  
         [0032]     As discussed with reference to  FIG. 7 , under the ideal conditions being assumed in the example of  FIG. 8 , namely perfect discharge of regions on the surface  812  and a perfectly uniform intensity profile for the laser beam, areas above and below the dot  818  have half the full charge removed due to the scan lines  804  and  808 , respectively. In the cases where the vertical column of consecutive dots  816 - 818  is being formed, which is the case where banding could occur, these extra areas actually help reduce banding by removing this additional charge. For example, in the example of  FIG. 8  the scan line  808  removes half the full charge in the area from the bottom-of dot  818 to the bottom of this scan line. When the laser beam traverses scan line  810 , the full charge will be removed from these areas as desired. Note that in  FIG. 8  the lower edge of scan line  806  is shown as a dotted and dashed line. This is done because the scan line  810  overlaps a lower portion of the scan line  806  due to the drum  814  slowing back down to its desired rotational velocity. Thus, the top of the scan line  810  is above the bottom of scan line  806  and the bottom of scan line  806  is represented as a dashed and dotted line. Once again, recall that the average rotational speed of the drum  814  is correct due to the operation of control circuitry (not shown) that controls a motor (also not shown) that drives the rotation of the drum. As a result, an increase in rotational speed of the drum  814  will necessarily be followed by a period during which the drum slows down, offseting the increase in velocity so the average velocity is realized. As a result of this slowing down of the drum  814 , the scan lines  806  and  810  overlap.  
         [0033]     The overlapping scan line pattern  800  reduces banding caused by variations in the rotational speed of the drum  814 . This is true because multiple passes of the laser beam are required to form each desired dot  816  on the surface  812 . As a result, if some of these multiple passes do not occur due to speed variations in the drum  814 , then the other ones of the passes will still discharge a desired dots  816 - 820  albeit not by as much as desired.  
         [0034]      FIG. 9  is a graph showing the variation in the discharge of dots in the vertical colum of dots in the scan line patterns of  FIGS. 7 and 8 . The graph shows the variations in the discharge of the dots  716 - 720  and  816 - 820  in each of the scan lines for the scan line patterns  700  and  800  of  FIGS. 7 and 8 , respectively. The vertical lines  722  and  822  shown in  FIGS. 7 and 8  represent the vertical axis in  FIG. 9  and represent the scan line number or physical location in the scan lines in the vertical direction. The scan line number 1 on the vertical axis in  FIG. 9  corresponds to the midpoint of the scan lines  702  and and  802 . The dotted line in the graph of  FIG. 9  corresponds to the ideal pattern  700  where the consecutive vertically aligned dots  716 - 720  are being formed in scan lines  702 - 710 . The horizontal axis in the graph represents the discharge of the dot, with 1 being fully discharged and 0 being not discharged at all so no dot will be formed.  
         [0035]     Ideally each of the dots being formed in the scan lines  702 - 710  or  802 - 810  is completely discharged to 1 as shown by the dotted line in the graph. The dotted line thus represents the ideal overlapping scan pattern  700 . In contrast, where banding occurs there are gaps in this discharge distribution corresponding to the gaps on the drum  814 . The solid lines thus represent the charge distribution for the scan line pattern  800 . Due to the overlapping scan lines  802 - 810 , regions that ideally should have been completely discharged to 1 are at least partially discharged to ½. This is true because the overlapping scan lines  802 - 810  each scan the same regions on the drum  814 , with the scans collectively forming the desired dots. The first leftward dip the graph results from the gap G while the second dip results from the gap GO. Note that even though these are dips, meaning the regions have not been fully discharged to 1 as desired, the dips are only to ½ since both these gaps gets scanned during one of the scan lines  802 - 810 . As a result, at least some toner will be attracted to the gaps which will provide continous vertical distribution of toner and reduce the visual appearance of banding in the vertical column of dots  816 - 820 .  
         [0036]      FIG. 10  is representation of the surface of the phontoconductive drum  814  of  FIG. 8  showing the various discharged and charged areas in the vertical column of dots  816 - 820  resulting from the scanning line pattern  800 . This figure merely shows what is depicted in the graph of  FIG. 9  in an alternative way. The cross-hatched regions represent areas in a vertical column of dots that have been fully discharged to 1 while the white areas represent areas that have been scanned only once and thus discharged to ½. The scan line number is shown on the left in the figure. Starting from the top, the scan lines  802  and  804  result in the topmost fully discharged region. Next comes the gap G, which is only scanned during the scan line  804  and is thus discharged to ½. Next comes a small fully discharged region scanned during scan lines  804  and  806 , and underneath this region is another region discharged to ½ in the gap GO during the scan line  806 . Next come two fully discharged regions formed during scan lines  806  and  808 . The lower one of these regions is also scanned during scan line  810  and thus this region is indicated as being discharged during scans “806+808+810.” Below this region is another fully discharged region formed during the scanning of lines  808  and  810 . The slowing down of the drum  814  is reflected by the overlap of scan lines  806  and  810  as previously discussed. In the example of  FIG. 10  it is assumed the vertical column of dots  816 - 820  extends above the dot  816  and below the dot  820 . Where a given dot is the last dot in a vertical column of dots, the laser beam is modulated differently to create a desired discharge end point, as will be understood by those skilled in the art.  
         [0037]     Once again, it should be noted that all of  FIGS. 7-10  assume a perfect linear discharge of regions on the surfaces of the rotating drums and also assume a perfectly uniform intensity profile for the laser beam. Actual discharge patterns would be different due to nonlinear discharge of regions on the surfaces of drums and due to nonuniform, typically Gaussian, intensity profiles for the laser beams. As a result of this nonlinear discharge of the surface  712  and nonuniform intensity profile of the laser beam, some of the discussion of removal of charge may not actually occur as dicussed in these ideal examples. Recall, for example, that if the dot  816  is a white dot, meaning the dot  818  is the last dot in a vertical column of dots, then half the desired amount of discharge would not actually be removed from the scan line  702  in  FIG. 7 . Similarly, in the ideal example of  FIG. 10  certain scan lines may not actually discharge regions exactly as described due to the nonlinearities of the discharge on the surface of the drum and the nonuniform intensity profile of the laser beam. These ideal examples are utilized merely to more clearly illustrate inventive aspects of the present invention and to avoid obscurring these inventive aspects with a relativley complex and detailed discussion of the physics and actual operation resulting from these nonlinearities and nonuniformities, which will be understood by those skilled in the art.  
         [0038]     In all the above figures, the photoconductive surface of the drum is moving in what is termed a vertical direction while the scan line pattern is being produced as the laser beam is scanned in a horizontal direction. As a result, the scan lines in each pattern are not actually produced in a perfectly horizontal direction across the photoconductive surface of the drum. Instead, each scan line is angled slightly since the drum is rotating as the laser beam scans across the surface. With the photoconductive surface moving upward in the above example scan line patterns  700  and  800  of  FIGS. 7 and 8 , each scan line would actually be angled downward slightly from left to right across the surface. Although angled downward, the scan lines are all scanned in the same horizontal direction from left to right across the surface and are therefore parallel to each other so that the amount of overlap for adjacent lines stays substantially constant as each line is scanned. As will be understood by those skilled in the art, the rotational axis of the rotational mirror  26  of  FIG. 1  could be adjusted to compensate for this angling of the scan lines.  
         [0039]     Note that in a laser printer that generates a scan line pattern such as the patterns  700  and  800 , the speed at which the laser beam is scanned across the photoconductive drum must be adjusted. In one embodiment, the rotational speed of the drum is slowed down and the horizontal scanning rate of the laser beam is left the same as in a conventional laser printer. In this embodiment, the power of the laser beam is reduced to remove the desired amount of charge on each scan. For example, where two scans of the laser beam are required to fully discharge a region then the power of the laser beam would be adjusted accordingly to remove the required amount of charge on each scan. In another embodiment, the rotational speed of the drum is left the same as in a conventional laser printer and the scanning rate of the laser beam is increased. The increase in the scanning rate depends upon the overlap of the scan lines, or put another way the scanning rate depends on the number of scans required by the laser beam to fully discharge a region. The greater the number of scans, the faster the required scanning rate.  
         [0040]     In the previously described embodiment, a single scan line (or a single pass of the laser beam) does not completely discharge the desired areas on the photoconductor surface. An overlapping scan line is required to completely discharge the areas on the surface of the photoconductor. In such an embodiment, each scan line would overlap the previous scan line by at least 50 percent of the height of the scan line, thus ensuring that each area on the photoconductor surface is ideally scanned twice by the laser. The example embodiment of  FIGS. 7 and 8  includes two scans to fully discharge a region, but other embodiments include more scans. In the situation where the amount of overlap of the scan lines is substantially constant as the laser beam scans across the photoconductive surface, the modulation of the laser beam is relatively simple as described above and the modulation need not be adjusted according to the amount of overlap of the adjacent scan lines.  
         [0041]     A pulse modulation technique similar to resolution doubling may also be used according to another embodiment of the present invention. In resolution doubling, the laser beam is modulated to place partial charges next to each other on different scans of the laser beam in such a way that a new charge can be formed that acts as if there was a scan of the laser beam at a different location. For example, the laser beam is modulated in such a way that charge will be attracted between two scan lines and in this way doubles the resolution of the printer. This technique may be combined with the significantly overlapping scans to allow individual charges to be placed very accurately on the photoconductive surface of a rotating drum.  
         [0042]     Other embodiments of the present invention may be utilized in laser printers that include an oscillating mirror in place of the rotating mirror  26  of  FIG. 1 . In one such embodiment, the oscillating mirror scans the photoconductive drum in both horizontal directions or “bidirectionally,” meaning from left to right and right to left across the drum. Because the speed of the laser beam varies in the horizontal direction with an oscillating mirror, the amount of overlap of consecutive scan lines will also vary as a function of the horizontal position of the laser beam. Also, because the laser beam is scanned in both directions across the drum, consecutive scan lines are not parallel to each other. As a result of consecutive scan lines not being parallel, the amount of overlap of consecutive scan lines changes as the scan line progresses in a given direction. The modulation of the laser beam is modified in these embodiments to remove the desired amount of charge as a function of the horizontal position and scanning direction of the laser beam.  
         [0043]     The amount of overlap of adjacent scan lines varies in different embodiments of the present invention, with the number of multiple passes of the laser beam required to form each dot depending upon the amount of overlap. For different amounts of overlap, the number of segments each dot is divided into and the number of scan lines required to form each dot varies. Assume X is an integer corresponding to the number of equal horizontal segments that each dot is divided into and is defined by the amount of overlap of consecutive scan lines. For an overlap of ½ between consecutive scan lines, there are two segments (X=2) per dot and two scans to fully discharge each segment. In this situation, which corresponds to the above described examples, three scan lines are required to fully form an individual dot. In another example, assume there is an overlap of ⅔ between consecutive scan lines such that there are 3 segments (X=3) per dot, each segment being ⅓ of a dot or pixel. Three scan lines are required to discharge each segment in this example and five scan lines required to fully form an individual dot. In general, where each individual dot is divided into X equal horizontal segments, the overlap of consecutive scan lines equals (X−1)/X and each segment requires X scans to fully discharge that segment. The total number of scan lines required to fully form each dot is equal to (2X−1). Note that X is assumed to be an integer in the above examples, with the more general situation of an arbitrary overlap being a much more difficult situation to generalize. Also note that for an overlap of 0 to just less than ½, some portion or segment of each dot cannot be scanned more than one time. For overlap values between ½ and ⅔, some segments would be scanned two times while other segments would be scanned three times. While this could be done, ideally all of the segments within a given scan line are scanned the same number of times.  
         [0044]     The multiple scans required to form each dot according to embodiments of the present invention make the dots less susceptible to banding since multiple passes are required to fully discharge a given dot. As a result, if variation in the speed of the rotating drum occurs, segments of a given dot will be at least partially discharged and any banding effects reduced or eliminated, at least as far as a corresponding printed image appears to a person.  
         [0045]     From the foregoing it will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. For example, although the beam being utilized to discharge the photoconductive drum has been described as a laser beam, other light generating sources may be used as well if suitable in particular applications. Thus, the term laser beam is not limited to a beam of light generated by a laser but instead should be construed broadly as an image beam that is a suitable electromagnetic beam generated by an suitable means in a given printer application.