Abstract:
A method of printing with an electrophotographic machine includes providing a first optical sensor for sensing a start-of-scan position of a laser beam produced by a scanning laser printhead and transmitting a first position signal indicative thereof A second optical sensor senses an end-of-scan position of the laser beam produced by the scanning laser printhead and transmits a second position signal indicative thereof A temperature of the scanning laser printhead is measured with a temperature sensing device. A plurality of positions of each of the first optical sensor and the second optical sensor are empirically determined at each of a plurality of values of the temperature of the scanning laser beam printhead. The modulation or position of the laser beam produced by the scanning laser printhead is adjusted based upon the first position signal, the second position signal, the measured temperature of the laser printhead, and the empirically determined positions of the first optical sensor and the second optical sensor and the second optical sensor. A single optical sensor and a single thermal sensor constitute the minimum hardware embodiment to perform print line position correction based upon stored empirical relationship.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to electrophotographic machines, and, more particularly, to a method of controlling laser printhead registration in an electrophotographic machine. 
     2. Description of the Related Art. 
     Scanning lasers have significant advantages over light emitting diode (LED) printheads in both monochrome and multi-color printers. These advantages include uniformity of radiant energy across a scan line, uniformity of spot size, a resolution determined by laser diode modulation rather than physical spacings, comparatively low power consumption and resulting low heat generation, optics spaced from the source of toner contamination, and comparatively lower cost. 
     Although scanning lasers have the above-described advantages, single-pass color electrophotographic printers using scanning laser printheads present registration difficulties not found in printer designs using LED printheads. Initial laser spot position in scan and process directions, line length, skew and bow are all expected variations which affect registration of color planes. Temperature changes of the printhead and its mounting are the major source of change in registration. 
     A color-to-color image registration problem arises in single-pass laser printers that have more than one laser imaging source. The registration problem is largely attributable to thermally induced changes in scanning laser beam profile and position, laser start-of-scan sensor position, and laser end-of-scan sensor position. Thermally induced changes in the shape and mounting of optical elements, thermally induced changes in the size of the mounting surface, and a relatively long optical path length can contribute to produce line length, skew, and bow scanning spot position changes at the imaging plane of one or more picture elements (pels). The width of a pel is approximately 42.3 μm at 600 dots per inch (dpi). Differences in heating among multiple laser imaging sources then contributes to misregistration of color planes in a composite image. Print quality is generally judged as unacceptable when color plane misregistration exceeds 100 μm. 
     What is needed in the art is a method of registering a printhead in both the scan and cross-scan directions over a range of printhead operating temperatures. 
     SUMMARY OF THE INVENTION 
     The present invention provides a method of using temperature sensing in conjunction with optical sensors and electronic feedback to control registration of a scanning laser printhead suited for single-pass EP printing. 
     The invention comprises, in one form thereof, a method of printing with an electrophotographic machine. A first optical sensor senses a start-of-scan position of a laser beam produced by a scanning laser printhead and transmits a first position signal indicative thereof. A second optical sensor senses an end-of-scan position of the laser beam produced by the scanning laser printhead and transmits a second position signal indicative thereof. A temperature of the scanning laser printhead is measured with a temperature-sensing device. A plurality of positions of each of the first optical sensor and the second optical sensor are empirically determined at each of a plurality of values of the temperature of the scanning laser beam printhead. The modulation or position of the laser beam produced by the scanning laser printhead is adjusted based upon the first position signal, the second position signal, the measured temperature of the laser printhead, and the empirically determined positions of the first optical sensor and the second optical sensor. 
     The invention comprises, in another form thereof, a method of printing with an electrophotographic machine. A desired scan line length is determined. A plurality of temperatures associated with the electrophotographic machine are measured at respective points in time. A plurality of calibration scan line lengths are empirically determined at a plurality of values of the temperatures associated with the electrophotographic machine. The calibration scan line lengths are used to calculate a scan line length thermal expansion as a function of the temperature associated with the electrophotographic machine. A number of slices in a scan line to be printed is adjusted. The adjusting is dependent upon a current one of the measured temperatures and the scan line length thermal expansion such that a length of the scan line to be printed is substantially equal to the desired scan line length. 
     An advantage of the present invention is that thermally induced changes in printhead registration can be compensated for. 
     Another advantage is that thermally induced shifts in the positions of a start-of-scan sensor and an end-of-scan sensor can be compensated for. 
     Yet another advantage is that the resulting scanning laser printhead has registration performance similar to a modular LED printhead. 
     A further advantage is that the method of the present invention is applicable to laser printheads in which a single scanning polygon is shared among multiple laser sources to produce multiple scanning laser beams. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention will be better understood by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, wherein: 
     FIG. 1 is a partial, schematic, side view of one embodiment of a laser printer in which the method of the present invention may be used; 
     FIG. 2 is a top view of one of the laser printheads of FIG. 1; 
     FIG. 3 is a schematic, side view of the laser printhead of FIG. 2 with an end-of-scan sensor and the corresponding photoconductive drum; 
     FIG. 4 is a schematic, side view of the laser printhead of FIG. 2 with a start-of-scan sensor and the corresponding photoconductive drum; 
     FIG. 5 is a plot of the laser scan position of the printhead of FIG. 2 in the scan direction and the cross-scan direction at two different operating temperatures; 
     FIG. 6 is a plot of the position of the start-of-scan sensor of FIG. 4 at the two different operating temperatures of FIG. 5; 
     FIG. 7 is a plot of the position of the end-of-scan sensor of FIG. 3 at the two different operating temperatures of FIG. 5; 
     FIG. 8 is an exemplary plot of the bow in the laser scan position of the printhead of FIG. 2 at four different operating temperatures; 
     FIG. 9 is a plot of discrete approximations of the four bow characteristics of FIG. 8; 
     FIG. 10 is an exemplary plot of the bow and skew in the laser scan position of the printhead of FIG. 2 at four different operating temperatures; 
     FIG. 11 is a plot of discrete approximations of the four bow and skew characteristics of FIG. 10; and 
     FIG. 12 is a plot of the misregistration in the scan direction of cyan, magenta and yellow versus printhead temperature, without compensation; and 
     FIG. 13 is a plot of the temperatures of the printheads over the course of a 5000 page run. 
     Corresponding reference characters indicate corresponding parts throughout the several views. The exemplification set out herein illustrates one preferred embodiment of the invention, in one form, and such exemplification is not to be construed as limiting the scope of the invention in any manner. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention provides temperature sensing at each imaging source to provide augmentation to start-of-scan and end-of-scan optical sensors, as well as to provide correction of thermally induced errors in the sensors&#39; output signals, which are input signals to a controller. The controller produces electronic corrections to correct spot position for bow, skew, line-length, and start-of-scan timing based upon these sensor inputs. The electronic corrections may include controlling a time at which a scan of a laser printhead begins, or controlling a data rate of the scanning laser printhead. With this electronic control, the resulting modular imaging source possesses spot location accuracy that is suitable for color image registration in a single-pass EP printer. 
     Referring now to the drawings, and, more particularly, to FIG. 1, there is shown one embodiment of a multicolor laser printer  10  including laser printheads  12 ,  14 ,  16 ,  18 , toner cartridges  20 ,  22 ,  24 ,  26 , photoconductive drums  28 ,  30 ,  32 ,  34 , an intermediate transfer member belt  36 , microcontroller  37  and memory device  39 . 
     Each of laser printheads  12 ,  14 ,  16  and  18  can control printing in a respective color, such as cyan, magenta, yellow or black. Each of laser printheads  12 ,  14 ,  16  and  18  scans a respective one of laser beams  38 ,  40 ,  42  and  44  in a scan direction, perpendicular to the plane of FIG. 1, across a respective one of photoconductive drums  28 ,  30 ,  32  and  34 . Photoconductive drums  28 ,  30 ,  32 ,  34  are mounted to a steel frame  52  of printer  10  via a corresponding set of V-shaped notches  54 ,  56 ,  58  and  60 , respectively. Each of photoconductive drums  28 ,  30 ,  32  and  34  is negatively charged to approximately −950 volts and is subsequently discharged to a level of approximately −300 volts in the areas of its peripheral surface that are impinged by a respective one of laser beams  38 ,  40 ,  42  and  44 . During each scan of a laser beam across a photoconductive drum, each of photoconductive drums  28 ,  30 ,  32  and  34  is continuously rotated, clockwise in the embodiment shown, in a process or “cross-scan” direction indicated by direction arrow  46 . The scanning of laser beams  38 ,  40 ,  42  and  44  across the peripheral surfaces of the photoconductive drums is cyclically repeated, thereby discharging the areas of the peripheral surfaces on which the laser beams impinge. 
     The toner in each of toner cartridges  20 ,  22 ,  24  and  26  is negatively charged and is doctored onto a developer roll with shaft potential of approximately −600 volts. Thus, when the toner from cartridges  20 ,  22 ,  24  and  26  is brought into contact with a respective one of photoconductive drums  28 ,  30 ,  32  and  34 , the toner is electrostatically attracted to and adheres to the portions of the peripheral surfaces of the drums that have been discharged to −300 volts by the laser beams. As belt  36  rotates in the direction indicated by arrow  48 , the toner from each of drums  28 ,  30 ,  32  and  34  is transferred to the outside surface of belt  36 . As a print medium, such as paper (not shown), travels along a paper path, the toner is transferred from belt  36  to the surface of the print medium in a nip between opposing rollers. 
     Printheads  12 ,  14 ,  16 ,  18  are structurally substantially identical. Accordingly, to simplify the discussion and for ease of understanding the invention, only the structure of printhead  12  will be described in detail below in relation to FIGS. 2-4. However, it is to be understood that the discussion that follows with respect to printhead  12  also applies to each of printheads  14 ,  16  and  18 . 
     Referring to FIGS. 1 and 2, single-pass printer  10  includes a respective thermal sensor  50  (FIG.  2 ), and the feedback control enabled thereby, in laser printhead  12 . Steel frame  52  of electrophotographic printer  10  accurately locates individual printhead  12  to color photoconductive drum  28  in a print cartridge. Photoconductive drum  28  is precision located in V-notch  54 , which is machined into heavy gauge steel rails that are riveted, welded, or otherwise permanently affixed to steel frame  52 . As shown in FIG. 2, printhead  12  is mounted, such as by screws  62 ,  64 ,  66 , to a steel channel  68  that is similarly riveted, welded or otherwise permanently affixed to the steel frame  52  in precision registration to the steel V-notch  54  which supports cartridge photoconductive drum  28 . 
     Printhead  12  includes a body  70  which is designed and mounted to allow predictable thermal expansion of body  70  in scan direction  72  relative to an anchor point  74 . Anchor point  74  is located near end-of-scan position sensor  76 . Symmetry in the mounting and printhead design minimizes thermally induced skew in cross-scan direction  46 . Printhead  12  includes a polygon mirror  80 , indicated only schematically in FIG. 2, off of which laser beam  38  is reflected. Lens  82  is biased against a stop  84  in the end-of-scan side of printhead body  70 , thereby also allowing predictable thermal expansion. 
     End-of-scan sensor  76  (FIG. 3) is an optical position-sensitive detector, and is positioned to detect scanning laser beam  38  at the end-of-scan. End-of-scan sensor  76  has signal outputs related to both scan direction  72  (x-axis) and cross-scan direction  46  (y-axis). End-of-scan sensor  76  is rigidly and mechanically connected to and supported by steel frame  52  for accurate and precise positioning. End-of-scan sensor  76  is positioned coincident with printhead anchor point  74 . Further, end-of-scan sensor  76  is positioned to receive scanning laser beam  38  after printhead lens  82  and near the image plane within a focal point zone following reflection from a mirror  86  located on the rigid mechanical support. Alternatively, end-of-scan sensor  76  can be located on steel frame  52  in proximity to photoconductive drum  28  at the end-of-scan. End-of-scan sensor  76  is mounted for accurate positioning relative to a fixed datum in the form of anchor point  74 . 
     With the three-point mounting of FIG. 2, the end-of-scan side of printhead  12  is anchored, and thermal expansion is channeled for growth in scan direction  72  toward the start-of-scan side of printhead  12 . Printhead  12  is designed for symmetrical growth with thermal expansion in cross-scan direction  46  to avoid thermally induced skew. 
     Start-of-scan sensor  88  (FIG. 4) is a position sensitive detector, and is mounted within printhead body  70  to detect scanning laser beam  38  at the start-of-scan. Start-of-scan sensor  88  can have both scan direction  72  and cross-scan direction  46  signal outputs. Alternatively, start-of-scan sensor  88  can have only a scan direction  72  signal output. Start-of-scan sensor  88  is mounted within printhead body  70  in order to provide an integral start-of-scan sensor for testing printhead  12  as a module at the time of manufacture. Further, start-of-scan sensor  88  is positioned to receive scanning laser beam  38  after printhead lens  82  and near the image plane within the focal point zone following reflection from a start-of-scan mirror  90  located on the printhead support surface. 
     Errors in laser imaging position that result from printhead temperature changes are illustrated in FIG. 5, which is a plot of laser spot position at the image plane relative to a fixed datum, for example, photoconductive drum V-notch  54 . The scans shown correspond to a fixed rate of angular rotation of printhead polygon mirror  80  and are plotted at two different operating temperatures. The x-axis, labeled “Image Plane x”, indicates laser scan position in scan direction  72 . The y-axis, labeled “Image Plane y”, indicates laser scan position in cross-scan direction  46 . 
     Five types of scan position errors are illustrated at each of the two temperatures. Data related to the magnitudes of these errors at various temperatures can be empirically determined and stored in memory device  39 . Microcontroller  37  can then adjust the modulation or physical position of laser printhead  12  based upon these error characteristics and a present temperature as measured by thermistor  50 . 
     A first of the five types of scan position errors is a DC Offset Position in cross-scan direction  46 . FIG. 5 shows a shift from −11 μm at 22° C. to +29 μm 42° C. for the average scan position change with temperature (horizontal scan lines), using a position of 160 mm along the x axis, as the reference for both 22° C. and  42 ° C. Thus, the shift is 2 μm per degree C. 
     The second type of scan position error is skew in cross-scan direction  46 . A skew rotation point is shown at 160 mm at both 22° C. and 42° C. The skew has a magnitude of 10 μm over the image width at 22° C., and 30 μm over the image width at 42° C. Thus, the change in slope over the image width of 215.9 mm is 1 μm per degree C. 
     The third type of scan position error is the bow in cross-scan direction  46 . There is a change in the magnitude of the bow from 10 μm at 22° C. to 30 μm at 42° C. Thus, the change in magnitude is approximately 1.0 μm per degree C. The illustrated shape is a ½ cycle sine function, but other shapes of bow may result from a particular printhead design or adjustment. 
     The fourth type of scan position error is magnification in scan direction  72 . FIG. 6 illustrates an expanded scale at start-of-scan, and FIG. 7 illustrates an expanded scale at end-of-scan. FIG. 6 shows the image starting position −14 mm at 22° C. and −14.3 mm at 42° C. FIG. 7 shows the image ending at position 229.9 at 22° C. and 229.7 at 42° C. This indicates that the line length had grown from 243.9 mm to 244 mm. The fifth type of scan position error is a start-of-scan offset in scan direction  72 . 
     End-of-scan sensor  76  and start-of-scan sensor  88  can be used to detect and correct, via electronic feedback, for the majority of changes in x-y laser scan position at the image plane. Because the optical detector positions are also subject to change with temperature, the resulting corrections may be erroneous unless detector position is corrected for temperature. End-of-scan sensor  76  and start-of-scan sensor  88  change position with respect to the datum as a result of thermal expansion of the mounting surfaces, lenses, and mirrors in the sensor optical path. 
     Thermistor  50 , which may also be any type of temperature-measuring transducer, is positioned within the printhead enclosure to sense the temperature of the printhead structure and lenses. For example, sensing thermistor  50  can be located on the start-of-scan sensor printhead circuit board (not shown) to share the printhead circuit card and connector. However, thermistor  50  is intentionally not mounted on the motor driver card heat source in order to avoid measuring a temperature that is artificially high and not representative of a temperature affecting printhead thermal expansion. 
     Thermal sensor  50  in scanning laser printhead  12  enables correction of position measurements made using end-of-scan sensor  76  and start-of-scan sensor  88 . The movements of end-of-scan sensor  76  and start-of-scan sensor  88  produced by thermal expansion is significant compared to allowable misregistration. Temperature sensing provides a tool for estimating detector movement and correcting the corresponding position measurements. The resulting thermally-corrected optical measurements of scanning laser position enable accurate electronic feedback to correct start-of-scan (single x-axis sensor), line length (dual x-axis sensors), cross-scan location (at least one y-axis sensor), and skew (dual y-axis sensors). 
     Thermal sensor  50  in scanning laser printhead  12  also enables estimation of skew and bow errors which are not measured optically. The characteristics for skew and bow are measured and recorded for the particular printhead design. Skew is modeled and stored as a linear equation in which slope (and optionally rotation point) is a function of temperature. Bow is modeled as a polynomial and stored as a table which scales with temperature, or as an equation that includes a function of temperature. Skew is then compensated for by using a single y-sensor rather than two y-sensors. Bow can also be compensated for by using a single y-sensor, rather than a sensor array. 
     The present invention provides a model for optical sensor position as a function of measured printhead temperature using the printhead mounted thermistor  50  for thermal feedback. Optical sensor location is characterized and results in a position change with respect to the image plane as illustrated in FIGS. 6 and 7. 
     Start-of-scan sensor  88  can be mounted to printhead body  70 , far from printhead anchor point  74 . As a result, the change in sensor position, as compared to the image plane datum, is large. This is shown in FIG. 6 where the (x, y) location of start-of-scan sensor  88  is (−14000, 0) μm at 22° C. and (−14070, 35) μm at 42° C. Thus, without thermal compensation, the optical sensor location error would be −70 μm in the x-direction and 35 μm in the y-direction at 42° C. With thermal compensation, using a stored value of 3.5 μm per degree C. in the x direction and −1.75 μm per degree C. in the y direction, the location of start-of-scan sensor  88  is corrected and minimized as a source of error. The absolute position of the scanning laser in reference to the datum is determined to a higher degree of accuracy so that color registration errors are minimized. 
     End-of-scan sensor  76  can be mounted on a metal bracket  92  (FIG. 3) near anchor point  74 . As a result, the change in sensor position, as compared to the image plane datum, is very small. This is shown in FIG. 7 where the end-of-scan sensor (x, y) location is (229900, 0) μm at 22° C. and (229890, 5) μm at 42° C. Thus, without thermal compensation, the optical sensor location error would be −10 μm in the x-direction and 5 μm in the y-direction at 42° C. This error magnitude is small enough that it can be ignored such that the position of end-of-scan sensor  76  is not thermally corrected. However, a correction equivalent to that used at start-of-scan sensor  88  would, if implemented, use a stored value of 0.5 μm per degree C. in the x direction and −0.25 μm per degree C. in the y-direction. 
     Start-of-scan x-y sensor  88  and end-of-scan x-y sensor  76  would both be needed to generate and transmit a feedback signal to microcontroller  37  in order to correct for the first, second, fourth and fifth types of scan position errors discussed above. If start-of-scan sensor  88  provides position information in scan direction  72  only, then sensors  76  and  88  can be used to generate and transmit a feedback signal to microcontroller  37  in order to correct for the first, fourth and fifth types of scan position errors discussed above. 
     A y-direction measurement is needed at both ends of the scan in order to directly measure skew. Thus, if start-of-scan sensor  88  has only scan direction  72  measurement capability, skew cannot be measured directly. 
     The present invention uses printhead thermistor sensor  50 , in combination with a particular printhead design and mounting, to calculate skew based upon a stored model. The y direction laser spot position is treated as a linear function of the x scan position as: y sk =A(T)[x−x int (T)] μm. A(T) is the skew slope as a function of temperature. The function x int (T) sets the x intercept value corresponding to the skew rotation point (y sk =0) as a function of temperature. In the example of FIG. 5, with T in ° C., 
     
       
           A ( T )=( T ×1 μm/degree C.−12 μm)/215.9 mm; and x int ( T )=160 mm=constant. 
       
     
     The end-of-scan y-direction value attributable to skew needs to be accounted for in DC offset correction, which is based upon a single end-of-scan y optical measurement at end-of-scan sensor  76 . If y sk =0 μm at x=229.9 mm (end-of-scan sensor  76  location), x int (T)=229.9 mm=constant and y sk =A(T)(x−229.9) μm. Print controller  37  uses this information to produce electronic or electromechanical adjustments to correct the individual printhead for this thermally induced skew. 
     Printhead  12  is designed for minimal bow and includes a setup adjustment at the time of manufacture to further minimize bow. This printhead characteristic is not readily measured in a machine since even the simplest measurement of bow requires three sensors with y direction measurement capability. However, it is possible that only end-of-scan sensor  76  provides measurement in the y direction. 
     Printhead thermistor sensor  50  can be used to calculate bow based upon a stored model. The bow magnitude is treated as a linear (or other) function of temperature. The shape of the required bow correction is stored as either a polynomial or as a table that is a discrete, step-wise approximation of the y correction required at fixed x locations along the scan. The polynomial or table values are then scaled with temperature and provided as input to print controller  37  to electronically correct the individual printhead for this thermally induced bow. FIG. 8 is a plot of printhead bow versus temperature. FIG. 9 is a twenty-segment plot representing the bow profile. The resulting discrete corrections are rounded to the nearest ½ picture element (pel) increments at a resolution of 600 dots per inch (dpi). Bow magnitude is given by A bow (T)=2T−12 μm, where T is in ° C. Image data can be moved (raster-image-processed with hardware assist) in 0, +/−½ pel (600 dpi) increments in y-position at nominally twenty segments along a writing line; and in 0, +/−½ pel (1200 dpi) increments in y-position at nominally forty segments along a writing line. 
     Microcontroller  37 , in order to produce a composite electronic correction, combines bow and skew corrections as a function of temperature and x-scan position. FIG. 9 illustrates an example of composite skew and bow correction. Skew is 1 μm/degree C./215.9 mm with x int =229.9 mm and 0 skew at 12° C. Bow is the same as shown in FIG.  8 . 
     Individual printhead sensing and control yields acceptable color registration via correction of cyan, magenta, yellow and black printheads to an absolute datum. However, in another embodiment, it is possible to sense black printhead laser spot position optically and thermally, but to electronically correct only cyan, magenta and yellow printheads relative to black. This has the advantage that black printing is not subject to any artifacts associated with electronic line-length, skew, or bow correction methods. 
     In this alternative embodiment, all five registration parameters discussed above can be left unchanged for the black printhead as a function of temperature. The three color printheads are corrected based upon the difference between the absolute black position (determined based upon black start-of-scan sensor  88 , black end-of-scan sensor  76  and black printhead temperature) and absolute color position (determined based upon individual color start-of-scan sensor  88 , color end-of-scan sensor  76  and color printhead temperature). All four printheads are sensed identically and individually with respect to a datum. However, in this alternative embodiment, electronic feedback is to color printheads only, based upon differences between calculated black and color spot positions. 
     Another embodiment addresses the problem of misregistration in scan direction  72  as printhead temperatures vary. FIG. 12 illustrates the misregistration of the magenta, cyan and yellow scan lines in scan direction  72  as referenced to black as a function of printhead temperature. The misregistration is caused by thermal expansion of the optical system, such as the f-theta lens  94 , and thermal expansion of printhead bodies or housings  70 . FIG. 13 illustrates the variation in temperature of each of printheads  12 ,  14 ,  16  and  18  over the course of a 5000 page run. As can be seen, there are substantial differences in temperatures between the printheads over the course of the run. Hence, misregistration in scan direction  72  must be corrected for each of printheads  12 ,  14 ,  16  and  18  individually. 
     Pel (picture element) slices are added or removed from scan lines based on inputs from thermal sensors  50  such that each scan line in each color plane has a desired length over a range of operating temperatures. At factory calibration the length of the black scan line is set by adjusting the rotational velocity of the polygon mirror  80  such that the scan line length is equal to the width of the print medium and is registered therewith. Assuming a page width of 8.5 inches, a print resolution of 600 dots per inch, and 12 slices per pel, there are approximately 61,200 slices per scan line. Pel slices are also added or subtracted from each of the magenta, cyan and yellow scan lines such that each of these scan lines has a length equal to that of the black scan line, i.e., the desired scan line length. Each of the magenta, cyan and yellow scan lines is aligned to black. The number of pel slices per scan line, as well as the printhead temperature at calibration, is stored for each of printheads  12 ,  14 ,  16  and  18  in memory  39 . 
     Data relating to the amount of thermal expansion of each of the four scan line lengths as a function of the four printhead temperatures is collected either during calibration or beforehand in the laboratory. The data includes scan line lengths empirically determined at a plurality of measured temperatures of respective printheads  12 ,  14 ,  16  and  18  at respective points in time. A percentage change in the scan line length per degree of temperature change, i.e., a coefficient of thermal expansion, is calculated for each of printheads  12 ,  14 ,  16  and  18  and stored in memory  39 . If the data is collected and the coefficients of thermal expansion are calculated in the laboratory, they can be assumed to apply to all printheads of the same color that are made in production. 
     When printer  10  is operating in the field, i.e., by a consumer, printhead temperatures are measured by sensors  50  at the start of a print job, and the number of pel slices per scan line is adjusted dependent upon a current printhead temperature, the printhead temperature at calibration, and the stored coefficient of scan line length thermal expansion. The number of pel slices per scan line is adjusted such that the printed scan line length is equal to the desired scan line length determined at calibration. 
     For example, assume a desired scan line length was achieved by a magenta scan line having 61,200 slices at a calibration temperature of 30° C. Also assume that the coefficient of thermal expansion of the magenta scan line was determined to be 0.010% /° C. If, at the start of a print job, the temperature of the magenta printhead were measured to be 25° C., the number of slices in the magenta scan line would be adjusted to be 61,200*[1+((30° C.−25° C.)*0.00010/° C.)]=61,231 slices. This adjustment in the number of slices per scan line results in the magenta scan line having the same desired length at 25° C. as was achieved by 61,200 slices per scan line at 30° C. 
     As described above, the processes of empirically determining the calibration scan line lengths, calculating the scan line length coefficients of thermal expansion, and adjusting the number of slices in a scan line are performed separately for each of printheads  12 ,  14 ,  16  and  18 . 
     The scan line length has been described herein as changing linearly with temperature. However, it is to be understood that it is possible in the present invention to adjust scan line length using a non-linear model for the thermal expansion of a scan line as a function of printhead temperature. For example, the following equation may be used as a model for the thermal expansion of a scan line length: 
     
       
         Thermnal expansion=(1+alpha (Δ T ))/(1+beta(Δ T )) 
       
     
     wherein alpha is the change in scan line length per ° C. due to the thermal expansion of f-theta lens  94 , beta is the change in scan line length per ° C. due to the thermal expansion of printhead housing  70 , and ΔT is the change in temperature. 
     While this invention has been described as having a preferred design, the present invention can be further modified within the spirit and scope of this disclosure. This application is therefore intended to cover any variations, uses, or adaptions of the invention using its general principles. Further, this application is intended to cover such departures from the present disclosure as come within know or customary practice in the art to which this invention pertains and which falls within the limits of the appended claims.