Abstract:
An apparatus for correcting beam-to-beam spacing error on an image plane of a photoreceptor includes a controller which generates beam-to-beam spacing error corrections signals, a plurality of optical elements, each of which is adjustable and responsive to beam-to-beam spacing error correction signal and a gray level measurement device. The controller performs the beam-to-beam spacing error correction analysis, determining whether or not a correction is necessary, and if so, which optical element to adjust and the magnitude of adjustment. Enhanced toner area coverage sensors are used to detect the gray level of a toned area of raster scan line patterns at various locations across the photoreceptor image plane. By repeatedly evaluating the beam-to-beam spacing error during operation, the apparatus of the invention is able to correct beam-to-beam spacing errors that may develop during operation and does not permit residual errors to persist even after an initial correction has been implemented.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     This invention is generally related to an image forming apparatus which uses multi-beam raster output scanners (ROS) to form images on a medium. 
     2. Description of Related Art 
     Prealigned dual and quad laser diodes are very expensive. While prealigned dual laser diodes are desirable in xerographic based electronic printers and copiers, due to cost considerations, individual laser diodes are normally used. FIGS. 1 and 2 illustrate top and side views, respectively, of a conventional rotating polygon-based optical system  100  and a known rotating polygon  140 . It should be appreciated that the functions described below equally apply to most rotating polygon-based systems, independently of the number of light sources used. 
     As shown in FIGS. 1 and 2, the ROS optical system  100  includes a pair of sagittally offset laser diodes  102  and  103  that emit laser beams  121  and  123 , respectively. The laser beams  121  and  123  emitted by the laser diodes  102  and  103  are collimated by a collimator lens  110 . A sagittal aperture stop  120  is placed in a position where the laser beams  121  and  123  cross the system optical axis  500 , to control the aperture size, which in turn controls the spot size on the photoreceptor image plane  182 . The input cylinder optical elements  130  and  131  focus the laser beams  121  and  123  on the surface of the current polygon facet  144  of the rotating polygon  140 . After reflecting from the current polygon facet  144 , the laser beams  121  and  123  pass through the Fθ lens  150 . The Fθ lens  150 , in general, has relatively low power in the tangential meridian. The Fθ lens  150  focuses the laser beams  121  and  123  in the tangential meridian to control the scan linearity in terms of uniform spot displacement per unit angle of polygon rotation. A sagittal aperture stop  160  is placed in a position where laser beams  121  and  123  again cross the system optical axis  500 . 
     A motion compensating optical element (MCO)  170  then reimages the focused laser beams  121  and  123  from the current polygon facet  144  onto the photoreceptor image plane  182  at a predetermined position, independently of the polygon angle error or tilt of the current facet  144 . Such compensation is possible because the focused laser beams  121  and  123  are stationary “objects” before the Fθ lens  150  and the motion compensating optical (MCO) element  170 . Although, due to a polygon tilt or wobble, the laser beams  121  and  123  are reflected to different positions of the post polygon optics aperture for each different facet of the rotating polygon, the beams  121  and  123  are imaged to the same position on the photoreceptor image plane  182 . 
     SUMMARY OF THE INVENTION 
     In rotating polygon, ROS-based xerographic copiers and printers, distortions occur from several sources of beam spacing errors. The sources of beam spacing errors in multi-beam rotating polygon based optical systems illustrated in FIG. 2 are optical and/or mechanical in nature. Beam spacing errors fall into one of the following categories: residual errors in the nominal design, thermal effects, vibration, and fabrication and wear errors in the various optical and mechanical components in the system. 
     Nominal differential bow is a source of residual beam spacing error. Even if the components were perfectly fabricated and assembled, beam-to-beam differential bow error will be present because the optical design cannot completely eliminate image distortion, as illustrated in FIGS. 3 and 4. Variations in ambient temperature produce changes in the refractive index, position, and thickness of optical components. These changes cause differences in scan line shape and position, as shown in FIGS. 5 and 6. Mechanical vibrations result in changes in scan line position, which can lead to beam spacing error. 
     FIGS. 3-6 illustrate the various types of errors which can be introduced by differential scan line bow. FIG. 3 shows a barrel type bow distortion. Specifically, FIG. 3 shows the center of curvatures of a pair of bowed scan lines  185  and  187  located on opposite sides of an ideal scan line  189  in such a fashion that the bowed scan lines create a barrel distortion. This occurs whether the bowed scan lines  185  and  187  have the same or different radius of curvature. 
     FIG. 4 shows a pin cushion type bow distortion. Specifically, FIG. 4 shows the center of curvature of the bowed scan lines  185  and  187  are also on the opposite side of the ideal scan line  189  (with the same or different radii). However, the arrangement of the bowed scan lines  185  and  187  relative to each other forms a pin cushion distortion. Again, this occurs whether the bowed scan lines  185  and  187  have the same or different radii of curvature. 
     FIG. 5 shows the ideal scan line  189  as a dashed line. In FIG. 5, first bowed scan line  187  has a first radius of curvature which is different from the radius of curvature of the second bowed scan line  185 . 
     FIG. 6 shows bowed scan line  185  superimposed over the bowed scan line  187 . As shown in FIG. 6, the bowed scan line  185  has a center of curvature which is on the opposite side of the ideal scan line  189  from the center of curvature of the bowed scan line  187 . As can be seen from FIGS. 3-6, the bow appears as a displacement of a scan line in the process direction as the line extends in the fast scan direction. 
     As shown in FIG. 7, there are shown a plurality of dashed lines representing ideal raster scan line paths  175  across a photoreceptor. The scan line spots  121 ′ and  123 ′ and  121 ″ and  123 ″, are shown with respect to each other and with respect to the ideal scan line path  175 . Ideally, the raster scan line spots  121 ′,  123 ′,  121 ″ and  123 ″ travel across the photoreceptor within the corresponding ideal scan line paths  175 . However, due to the factors discussed above, the raster scan line spots  121 ′,  121 ″,  123 ′, and  123 ″ often, if not usually, do not travel within the ideal scan line paths  175 . 
     As can be seen on the left side of FIG. 7, the raster scan spots  121 ″ and  123 ″ are separated from each other by a distance Y and do not lie within ideal scan line paths  175 . On the right side of FIG. 7, the raster scan spots  121 ′ and  123 ′ overlap by a distance X. It should be appreciated that, due to bow and the like, as the raster scan spots  121 ′, 121 ″, 123 ′, and  123 ″ move across the photoreceptor, the distortions shown in FIGS. 3-6 develop. 
     Fabrication variations in material parameters, component geometry, and assembly, manifested in misalignment, improper beam conditioning and defocusing, result in both uniform and non-uniform variation of the beam spacing across the image plane. Local variations in the photoreceptor and tilt errors among the various facets  141 - 148  of the polygon mirror  140 , for example, produce variation in process direction beam position from scan to scan. Curvature error in the lenses can produce either a widening or narrowing of the distance between scanning beams. All of the optical elements of a multi-beam rotating polygon-based optical system  100  may therefore introduce a degree of beam-to-beam spacing error. The combination of errors creates an error unique to each machine, and is commonly referred to as the constant beam-to-beam spacing error. 
     It also should be appreciated, however, that the constant beam-to-beam spacing error is constant over a limited time period, such as that of several scans to that of hours, days or even longer. That is, the constant beam-to-beam spacing error slowly changes over time. The component parts of the multi-beam rotating polygon-based optical system  100  and the assembly tolerances of those parts tend to slowly deteriorate over time, thus imparting a variable quality to the otherwise constant beam-to-beam spacing error. Consequently, it is more accurate to describe the constant beam-to-beam spacing error as a semi-static beam-to-beam spacing error. 
     Thus, in the conventional multi-beam rotating polygon-based optical system  100  described above, the scan lines usually either improperly overlap or are excessively spaced apart. The raster scan shown in FIG. 7, illustrates beam-to-beam spacing and overlap errors for two different sets of dual laser diodes resulting from either differential scan line bow and/or the constant or semi-static errors. Optical system designs can incorporate compensators or adjustments to correct for this error type, but in many cases residual errors persist even after correction has been implemented. 
     This invention provides systems and methods for detecting beam-to-beam spacing errors on the image plane of a photoreceptor during operation of a xerographic based electronic printer. 
     This invention separately provides systems and methods for automatically adjusting for beam-to-beam spacing errors on the image plane of a photoreceptor during operation of a xerographic based electronic printer. 
     This invention separately provides systems and methods for measuring average density variations in test patterns representative of raster scan line spacing errors on the image plane of a photoreceptor during operation of a xerographic based electronic printer. 
     This invention separately provides systems and methods to enable a xerographic printer user to obtain an image without objectionable banding artifacts. 
     In various exemplary embodiments, the systems and methods of the invention provide for specific beam-to-beam spacing error adjustments so that residual errors do not remain even after adjustments have been made. If a first adjustment is not sufficient to fully correct the beam-to-beam spacing errors, in various exemplary embodiments, the systems and methods of the invention are designed to reevaluate the beam-to-beam spacing errors to reduce, or ideally remove, such residual errors. 
     In various other exemplary embodiments, the systems and methods of this invention use a conventional rotating polygon based optical system, gray level measurement devices, a controller and means to measure and possibly adjust for beam-to-beam spacing errors. 
     In various exemplary embodiments, the apparatus of this invention uses a conventional rotating polygon-based optical system having two or more light sources and several optical elements. One or more of the various light sources and/or optical elements are adjustable in response to an error signal generated by the controller in view of signals received from one or more gray level measurement devices. 
     In various exemplary embodiments, two or more sensors of a gray level measurement device are located at fixed positions along the axial length of the photoreceptor. In various other exemplary embodiments, the apparatus includes a single gray level measurement device that is movable along between the ends of the photoreceptor. The movable sensor of the gray level measurement device can detect developed mass per unit areas for the full width of the photoreceptor. In various other exemplary embodiments, the gray level measurement device includes two sensors located relative to the width of the photoreceptor. In this case, each sensor can be moved over a portion of the photoreceptor. Each sensor detects a developed mass per unit area of a viewed area on the photoreceptor. Each sensor generates a signal corresponding to the developed mass per unit area in the viewed area and sends the signal to the controller. 
     The controller generates a beam-to-beam spacing error signal based on the sensor signals and determines which optical element or laser diode can be adjusted to adjust for the error that occurs in the viewed area. The controller signal is then sent to one or more appropriate optical elements and/or light sources, implementing the adjustment. 
     In various exemplary embodiments, the gray level measurement devices are implemented using enhanced toner area coverage sensors. 
     In various other exemplary embodiments, the apparatus includes a conventional polygon-based optical system having four light sources and several optical elements. The four light sources may be implemented as a combination of 4 single light sources or 2 double light sources. In various other exemplary embodiments, the apparatus includes a conventional polygon-based optical system having 2 single light sources and several optical elements. 
     In various other exemplary embodiments, the apparatus includes more than gray level measurement devices. 
     These and other features and advantages of this invention are described in or are apparent from the following detailed description of various exemplary embodiments of the systems and methods according to this invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various exemplary embodiments of this invention will be described in detail with respect to the following drawings, in which like reference numerals indicate like elements, and wherein: 
     FIG. 1 shows a top plan view of the conventional polygon ROS image forming device; 
     FIG. 2 shows a side plan view of one exemplary embodiment of an optical configuration of an ROS image forming device using two single laser diodes; 
     FIG. 3 shows a barrel distortion between a pair of bowed scan lines having centers of curvature on opposite sides with the same or different radii; 
     FIG. 4 shows a pin cushion distortion between a pair of bowed scan lines having centers of curvature on opposite sides with the same or different radii; 
     FIG. 5 shows a pair of bowed scan lines having the center of curvatures on the same side of the optical axis but with different radii of curvatures; 
     FIG. 6 shows a pair of bowed scan lines having centers of curvature on opposite sides of the optical axis with the same or different radii; 
     FIG. 7 shows first and second sets of spots created by laser beams on a photoreceptor, showing a gap between spots and an overlap between spots. 
     FIG. 8 shows a top plan view of one exemplary embodiment of a polygon ROS image forming device with a pair of gray level measurement devices and a controller according to this invention; 
     FIG. 9 shows a side elevation view of one exemplary embodiment of an optical configuration of an ROS image forming device according to this invention using two single laser diodes; 
     FIG. 10 illustrates a set of patterns usable to determine beam spacing offset between raster lines on the photoreceptor device produced by dual laser diodes, according to this invention; 
     FIG. 11 is a block diagram outlining in greater detail a first exemplary embodiment of the controller of FIG. 8; 
     FIG. 12 is a block diagram outlining in greater detail a second exemplary embodiment of the controller of FIG. 8; 
     FIG. 13 shows a side elevation view of one exemplary embodiment of an ROS image forming device according to this invention using two prealigned dual laser diodes according to this invention; 
     FIG. 14 shows a side elevation view of one exemplary embodiment of an ROS image forming device according to this invention using four single laser diodes; 
     FIG. 15 illustrates a set of patterns usable to determine beam spacing offset between raster lines on the photoreceptor device produced by quad laser diodes, according to this invention; 
     FIG. 16 illustrates one exemplary embodiment of three sensors mounted over the width of a photoreceptor usable as the gray level measurement device of FIG. 8; 
     FIG. 17 illustrates one exemplary embodiment of a movable sensor mounted on a lead screw usable as the gray level measurement device of FIG. 8; 
     FIG. 18 illustrates one exemplary embodiment of a differential sensor usable as the gray level measurement device of FIG. 8; 
     FIG. 19 shows a side plan view of an image forming apparatus comprising an ROS image exposure station and at least one sensor according to this invention; 
     FIGS. 20A and 20B are a flowchart outlining one exemplary embodiment of a method for reducing beam-to-beam spacing errors; and 
     FIG. 21 is a flowchart outlining one exemplary embodiment of a method for determining beam-to-beam spacing errors. 
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     FIGS. 8 and 9 show a first exemplary embodiment of the optical system  200  used to measure and/or reduce beam-to-beam spacing errors according to this invention. The optical system  200  includes a polygon scanning raster output scanner  240  (polygon ROS) and a pair of light sources  202  and  203  emitting light beams  221  and  223 , respectively. 
     It should be further appreciated that each light source  202  and  203  can each emit the corresponding light beams  221  and  223  at a wavelength different from the wavelengths of the light beam  221  or  223  emitted by the other light source  202  or  203 . In various exemplary embodiments, the light sources  202  and  203  are laser diodes. However, the optical system  200  is not limited to using laser diodes. Any known light emitting device, such as any solid state laser, gas laser, liquid laser or semiconductor laser can be used. Further, a light emitting diode or the like can be used, so long as the emitted light beam can be modulated, either as the light beam is output, or by an intervening optical, opto-electronic, opto-mechanical or opto-acoustic device. 
     The light beams  221  and  223  pass through a series of optical elements to form scanning spots  221 ′ and  223 ′, respectively, on an image plane  282  of a photoreceptor  280 . The optical elements of the optical system  200  as described herein, include, but are not limited to, one or more of collimator lenses, sagittal aperture stops, cylindrical lenses, polygon facet surfaces, and motion compensated optics (MCO). 
     For example, in the exemplary embodiment shown in FIGS. 8 and 9, the light beams  221  and  223  first pass through a collimator lens  210  and cross the system optical axis  500  at a sagittal aperture stop  220 . The light beams  221  and  223  then pass through a input cylindrical lens  230  and are focused onto a polygon facet  244  of the rotating polygon  240 . The rotation of the polygon facet  244  causes the light beams  221  and  223  to be scanned across the image plane  282  of the photoreceptor  280 . After being reflected by the polygon facet  244 , the light beams  221  and  223  pass through an Fθ scan lens  250  and again cross the system axis  500  at the image of the sagittal aperture stop  260 . This is also the back focal plane of the anamorphic motion compensating optics (MCO)  270 . It should be noted that, in this case, the image of the sagittal aperture stop  260  is not only in front of the image plane  282 , but is also in front of the MCO  270 . In various exemplary embodiments, the MCO  270  comprises a cylindrical lens or cylindrical mirror. 
     After passing through (or being reflected by) the MCO  270 , the light beams  221  and  223  are focused onto the image plane  282  to form the scanning spots  221 ′ and  223 ′, respectively. In general, after passing through the MCO  270 , the light beams  221  and  223  are parallel to the system axis  500 . That is, light beams  221  and  223  are typically designed to be telecentric or near telecentric between the MCO  270  and the image plane  282 . It should be appreciated that either element of the output optics can have a toroidal surface. In addition, the toroidal surface can have a uniform or non-uniform radius, in either the sagittal or tangential direction. The scanning spots  221 ′ and  223 ′ move across the image plane  282  to form the scan lines  175 . The scan lines  175  thus formed have the previously described beam-to-beam spacing errors, and can include bow line distortions and/or semi-static errors. Additionally, a number of sets of the scan lines  175  may be produced to define scan line patterns. Different scan line patterns are defined by turning one and then the other of the light sources  202  and  203  on and off. Alternatively, both laser diodes  202  and  203  may be on and off together. FIG. 10 shows examples of two scan line patterns formed in a test patch that can be created on the photoreceptor  280 . 
     As shown in FIGS. 8 and 9, a gray level measurement system  290  is located near the photoreceptor  280  and sends a signal to a beam spacing error system  400  corresponding to a gray level detected in a test patch formed on the photoreceptor  280  using the optical system  200 . In various exemplary embodiments, the gray level measurement system  290  includes at least one densitometer. However, the gray level measurement system  290  can use any type of sensor that can generate an output signal that is representative of an amount of toned area in the test patch. In the exemplary embodiment shown in FIGS. 8 and 9, the gray level measurement system  290  includes two densitometers  291  and  293 . Particularly, the densitometers  291  and  293  used in this first exemplary embodiment are enhanced toner area coverage sensors (also referred to as an ETAC sensor or an ETACS), which are process controlled sensors utilized in a xerographic process to measure the developed mass per unit area (DMA) of scan line patterns developed on the photoreceptor  280 , such as the scan line patterns  310  and  320  shown in FIG.  10  and discussed below in greater detail. Enhanced toner area coverage sensors have one or both of two possible output signals, a specular reflection signal and a diffuse reflection signal. 
     The specular reflection output signal is a measure of the specular reflection from the developed test patch formed on the photoreceptor  280 . The enhanced toner area coverage sensor is calibrated by increasing the radiance of the sensor&#39;s infrared emitter until a predetermined voltage is reached. As the amount of toner developed onto a test patch increases, the specular (mirror-like) reflection from the underlying reflective photoreceptor decreases while the diffuse reflection from the toner particles increases. As a result, the specular output signal decreases. Once a continuous layer of toner has been developed onto the surface of the photoreceptor  280 , the specular signal is essentially gone and the diffuse output is saturated. 
     The other output is a measure of the diffuse reflection from the surface of the substrate being measured. When a clean area is measured, a generally low signal is obtained, proportional to the base diffuse reflectance of the photoreceptor  280 . Since color toners are generally diffusely reflective, as the amount of toner developed onto the photoreceptor increases, the output of the diffuse signal increases. The range of the diffuse signal is greater than that of the specular signal since, as the depth of the toner layer increases, less light is lost to specular reflection, absorption or transmission and is instead converted into diffuse radiation. The diffuse output has a measurement range of approximately 0-1.5 mg/cm 2  with 7 micrometer toners. Diffuse reflection is thus able to measure in regions better suited for control of the color process. The diffuse signal does not work with black toners. These toners absorb incident radiation. Thus, the signal will decrease when measuring test patches developed using black toners. 
     The rotating polygon based optical system  200  and rotating polygon multi-beam raster output scanner  240  shown in FIGS. 8 and 9 also includes the beam spacing error system  400 . The beam spacing error system  400  receives the one or more signals generated by each of the one or more densitometers  291  and  293  of the gray level measurement system  290  over one or more signal lines  299 . In various exemplary embodiments, based on one or more signals from the gray level measurement system  290 , the beam spacing error system  400  determines the beam-to-beam spacing error. 
     In various other exemplary embodiments, the beam spacing error system  400  determines, based on the one or more signals from the gray level measurement system  290 , when an adjustment to one or more optical elements that will reduce the beam-to-beam spacing error is indicated. The values of the one or more signals from the gray level measurement system  290  are used by the beam spacing error system  400  to adjust one or more optical elements to lessen the beam-to-beam spacing error until the value of the gray level difference value ΔG indicated by the one or more signals from the gray level measurement system  290  is at least within a desired tolerance around zero. The beam spacing error system  400  can output adjustment signals for one or more optical elements to be adjusted to the appropriate one or more optical of the optical elements  201 ,  210 ,  230 ,  240 ,  250 ,  260  and  270  over the signal lines  412  and the appropriate one or more of the signal lines  205 ,  212 ,  232 ,  249 ,  252  and  272 , respectively. 
     As shown in FIG. 10, the dashed ovals on the far left of the Figure represent the ideal arrangement of the scan spots  221 ′ and  223 ′ into the scan lines  175  at the image plane  282 , for each pass of the light beams  221  and  223 . The scan line pattern  310  represents a pattern where both of the light sources  202  and  203 , having one or more of the above-outlined beam spacing errors, are turned on for a first pass and then both light sources  202  and  203  are turned off for the next pass. As shown in FIG. 10, the scan spots  221 ′ and  223 ′, and thus the resulting scan lines overlap, distorting the desired pattern  310 . 
     The right side of FIG. 10 shows a second scan line pattern  320 . The second scan line pattern  320  represents a pattern where, for each pass of the light beams  221  and  223 , one of the two light sources  202  and  203  is turned off and the other is turned on. Additionally, the scan spots  221 ′ and  223 ′, and thus, the resulting scan lines are spaced apart by a gap between the scan lines, distorting the desired pattern  320 . 
     It should be appreciated that, in various exemplary embodiments, the patterns  310  and  320  extend along the photoreceptor  280  in the direction of travel of the photoreceptor for a non-negligible distance. In this case, the patterns  310  and  320  are repeatedly formed so that the area of the photoreceptor on which the patterns  310  and  320  are formed extends along the direction of travel of the photoreceptor  280 . In various exemplary embodiments, the patterns  310  and  320  can extend for several inches or even longer, such as entirely around the circumference of the photoreceptor  280 . 
     The patterns  310  and  320  extend in a non-negligible distance because, in various exemplary embodiments, the gray level measurement system  290  uses low-bandwidth sensors, such as the enhanced toner area coverage sensors, that are designed to determine an average toner amount over an appreciable area, rather than determining if any specific location contains toner. 
     It should be appreciated that, if there is no spacing error in the positions of the light beams  221  and  223  on the image plane  282 , the two scan line patterns  310  and  320  would be identical in the relative size of the toned to untoned areas but out of phase. Thus, the toned area  312  and the clear area  319  would be the same size and would not be broken up into sub-areas, as in the scan line pattern  320  shown in FIG.  10 . 
     FIG. 10 shows a hatched area  314  which represents the clear portion  319  that should be part of the toner portion  312 . The hatched area  314  has a height  316 . Additionally, the size of the toned area portion  312 , which should be part of the clear portion  319 , has a height  318 . 
     It should also be appreciated that, in the exemplary embodiment shown in FIG. 10, the light beams  221  and  223  overlap due to the beam spacing errors. In contrast, the light beams  221  and  223  could be spaced apart due to the beam spacing errors. In this case, the resulting test patches obtained from the pattern  310  of turning the light beams on together and the pattern  320  of alternately turning on the light beams would be reversed from the test patches shown in FIG.  10 . 
     It should be appreciated that any number of possible scan line patterns using the single light sources  202  and  203  can be generated, and that the scan line patterns are not limited to the patterns  310  and  320  shown in FIG.  10 . 
     FIG. 11 is a block diagram outlining a first exemplary embodiment of the beam spacing error system  400 . As shown in FIG. 11, in this first exemplary embodiment, the beam spacing error system  400  includes an input/output circuit or software interface  410 , a controller  420 , a memory  430 , a pattern output circuit or routine  440 , a gray level difference determining circuit or routine  450 , a gray level differential determining circuit or routine  460 , and a spacing error amount determining circuit or routine  470 . The controller  420  coordinates communication between all of the circuits or software routines  430 ,  440 ,  450 ,  460 ,  480 ,  470  during operation. 
     The input/output interface circuit or software interface  410  receives signals sent over the signal lines  299  from the gray level measurement system  290  to the beam spacing error system  400  and outputs one or more signals produced by the beam spacing error system  400 . In various exemplary variations of this first exemplary embodiment, the controller  400  both characterizes the beam spacing error and, based on the characterized beam spacing error, outputs control signals to one or more of the adjustable optical elements of the optical system over the signal lines  412 . In other exemplary embodiments, the beam spacing error system  400  only characterizes the beam-to-beam spacing, but does not directly control any of the adjustable optical elements. In this case, the signal lines  412  from the input/output circuit or software interface  410  can be omitted. The beam spacing error system  400  instead outputs the beam spacing error data to another controller (not shown) over another signal line from the input/output circuit or software interface  410 . 
     As shown in FIG. 11, the memory  430  includes one or more of at least four memory portions, including a spacing error calibration portion  432 , a pattern set portion  434 , a gray level values portion  436 , and a spacing error and location portion  438 . The gray level value calibration portion  432  stores calibration values that relate a measured gray level difference value ΔG to a beam-to-beam spacing error that results in that gray level difference value ΔG. The pattern sets portion  434  contains sets of predetermined scan line patterns usable to measure a gray level of a toned area that is indicative of the beam-to-beam spacing error. In general, there will be at least two such sets of patterns which generate inverse images of each other. The gray level values portion  436  stores the determined differential gray level values ΔG 1  and ΔG 2  corresponding to the test patch areas detected on the photoreceptor  280 . The spacing error and location portion  438  stores each determined spacing error and the location along the width of the photoreceptor where that spacing error occurred. 
     The memory  430  can be implemented using any appropriate combination of alterable, volatile or non-volatile memory or non-alterable, or fixed, memory. The alterable memory, whether volatile or non-volatile, can be implemented using any one or more of static or dynamic RAM, a floppy disk and disk drive, a writeable or re-writeable optical disk and disk drive. A hard drive, flash memory or the like. Similarly, the non-alterable or fixed memory can be implemented using any one or more of ROM, PROM, EPROM, EEPROM, an optical ROM disk, such as a CD-ROM or DVD-ROM disk, and disk drive or the like. 
     The pattern output circuit or software routine  440  provides control signals for driving the rotating polygon based optical system  200  to form scan line patterns on the photoreceptor  280 . These signals are based on a pattern set selected by the controller  420  or the pattern output circuit or software routine  440  from those stored in the pattern set portion  434 . 
     The gray level difference determining circuit or software routine  450  determines the differential gray level values ΔG 1  and ΔG 2  between the scan line patterns formed at a particular location of the photoreceptor  280  based on measured gray level values, such as, for example, the measured gray level values G 1A , G 1B , G 2A , and G 2B , resulting from the test patches shown in FIG.  10 . The differential gray level values between G 1A  and G 1B  at a first portion and between G 2A  and G 2B  at a second portion of the photoreceptor  280  are denoted as ΔG 1  and ΔG 2 , respectively. That is, ΔG 1 =G 1A −G 1B  and ΔG 2 =G 2A −G 2B . It should be appreciated that, as the length of the patterns  310  and  320  used to generate the values G 1A , G 1B , G 2A , and G 2B  increases on the photoreceptor along the direction of travel of the photoreceptor, i.e., as the patterns  310  and  320  are duplicated repeatedly along the direction of travel of the photoreceptor, the signal-to-noise ratio for these values increases. 
     It should be appreciated that, in various exemplary embodiments, the gray level difference determining circuit or software routine  450  can be omitted from the beam spacing error system  400 . In this case, its functions are incorporated into the gray level measurement system  290 . That is, in these exemplary embodiments, the gray level measurement system  290 , rather than outputting the measured gray level values G 1A , G 1B , G 2A  and G 2B , outputs the differential gray level values ΔG, and ΔG 2 . 
     As shown in FIG. 11, the gray level difference determining circuit or software routine  460  determines the gray level difference value ΔG between the differential gray level values ΔG 1  and ΔG 2 , using the relationship ΔG=(ΔG 1 −ΔG 2 )/2. The spacing error amount determining circuit or software routine  470  determines the magnitude of the beam-to-beam spacing error based on the gray level difference value ΔG and the calibration values stored in the spacing error calibration portion  436 . The spacing error amount determining circuit or software routine  470  stores the determined beam spacing error and the location along the width of the photoreceptor  280  where that error occurs in the spacing error and location portion  438 . 
     The adjustments made to one or more of the adjustable optical elements in view of the determined beam spacing errors and location information for those errors are made using any appropriate methods and systems. Several types of methods and systems for adjusting the various optical elements are commercially available. Particularly, in various exemplary embodiments, the methods and systems described in U.S. Pat. No. 5,287,125 and 5,469,290, each incorporated herein by reference in its entirety, are used to implement the adjustments to the optical system  200  based on the determined beam-to-beam spacing error and location information stored in the spacing error and location portion  438 . 
     It should be appreciated that, in various exemplary variations of this first exemplary embodiment, such adjustments can be made by adding an optical element adjustment signal generating circuit or routine  475  to the beam spacing error system  400  shown in FIG.  11 . In this case, the optical element adjustment signal generating circuit or routine  475  inputs the beam spacing error and location information stored in the spacing error and location portion  438 , and uses that information to generate control signals to one or more of the adjustable optical elements. 
     FIG. 12 shows a second exemplary embodiment of the beam spacing error system  400  of the optical system  200  used to reduce, measure or otherwise determine beam-to-beam spacing errors according to the invention. The beam spacing error system  400 , as shown in FIG. 12, can include substantially the same circuits or software routines as the beam spacing error system  400  as shown in FIG. 11 in any of the various combinations discussed above with respect to FIG.  11 . In the second exemplary embodiment of the beam spacing error system  400 , the beam spacing error system  400  also includes an optical element adjusting amount determining circuit  480 , but omits the optical element adjustment signal generating circuit  475 . 
     In this second exemplary embodiment, the memory  430  includes one or more of a position adjustment value portion  433 , the pattern set portion  434 , and the gray level values portion  436 . The position adjustment value portion  433  contains values corresponding to the amount of adjustment required at various locations along the photoreceptor  280  based on a determined value for ΔG. The pattern set portion  434  contains sets of predetermined scan line patterns. The gray level values portion  436  stores the measured gray level values G 1A , G 2A , G 1B , and G 2B  corresponding to the test patch areas formed on the photoreceptor  280 . 
     The optical element adjusting amount determining circuit or routine  480  first determines if the gray level difference value ΔG is zero or at least within a desired tolerance around zero. Alternatively, and essentially equivalently, the optical element adjusting amount determining circuit or routine  480  can determine if the differential gray level values ΔG 1  and ΔG 2  are both equal to zero, or are at least both within a desired tolerance around zero. If so, in either case, no further adjustments to any of the adjustable optical elements needs to be made. In this case, under control of the controller  420 , the optical element adjusting amount determining circuit or routine  480  stores the current location along the width of the photoreceptor  280  and the values(s) of the current control signal(s), which was used to adjust one or more adjusted ones of the adjustable optical elements to reduce the beam spacing error, in the position adjustment value portion  433 . 
     Otherwise, further adjustments to one or more of the adjustable optical elements need to be made. Accordingly, the gray level difference determining circuit or routine  460  determines the gray level difference value ΔG as outlined above. Then, the optical element adjusting amount determining circuit or routine  480  determines a new adjusting amount control signal for each of one or more of the adjustable optical elements based on the determined gray level difference value ΔG. 
     As such, the second exemplary embodiment of the beam spacing error system  400  implements a kind of closed-loop control over the one or more adjustable optical elements. In particular, the differential gray level values ΔG 1  and ΔG 2  represent error signals. The gray level difference value ΔG generally indicates the direction and rough magnitude of the change that the optical element adjusting amount determining circuit or routine  480  must make to one or more of the adjustment signals to one or more of the adjustable optical elements that will tend to reduce the beam spacing error, as represented by the differential gray level values ΔG 1  and ΔG 2 . 
     It should be appreciated that, in this second exemplary embodiment, the actual linear measurement in length units of the beam spacing error is not determined. Rather, the beam spacing error goes to zero as the gray level difference value ΔG goes towards zero. Thus, by making adjustments to one or more adjustable optical elements that move the gray level difference value ΔG towards zero, the net effect is to reduce the actual beam spacing error towards zero, at least for the location across the width of the photoreceptor  280  where the scan line patterns are being formed. 
     The adjustments made by this second exemplary embodiment are made using methods and systems apparent to those of ordinary skill in the art. Several types of methods and systems for adjusting the various optical elements are commercially available. Particularly, in various exemplary embodiments, the methods and systems described in the incorporated 125 and 290 patents can be used to implement the adjustments to the optical system  200 . 
     FIGS. 13 and 14 show third and fourth exemplary embodiments, respectively, of the optical system  200  used to reduce, measure or otherwise determine beam-to-beam spacing errors according to the invention. The optical system  200 , as shown in FIGS. 13 and 14, includes substantially the same optical elements as the optical system  200  shown in FIGS. 8 and 9. A detailed description of the beam-to-beam error adjustments made to the second and third embodiments of the optical system  200  is not provided because the adjustments are substantially the same as those described with respect to the first exemplary embodiment of the optical system  200 . 
     In the third and fourth exemplary embodiments, the optical system  200  includes four light sources  201 ,  202 ,  203 , and  204 . These light sources  201 ,  202 ,  203 , and  204  can be of any of the types of light sources discussed with respect to the first exemplary embodiment shown in FIGS. 8 and 9. In particular, in various exemplary embodiments, the light sources  201 ,  202 ,  203 , and  204  are laser diodes that emit corresponding laser beams as the light beams  222 ,  221 ,  223 , and  224 . 
     As shown in FIG. 13 in the third exemplary embodiment of the optical system  200 , the light sources  201 ,  202 ,  203 , and  204  are implemented using two pre-aligned dual light sources. As shown in FIG. 14, in the fourth exemplary embodiment of the optical system  200 , the light sources  201 ,  202 ,  203  and  204  are implemented using individual light sources. It should be appreciated that two pre-aligned dual light sources require fewer adjustments than using four single light sources. 
     As shown in FIGS. 13 and 14, the light beams  222 ,  221 ,  223 , and  224  pass through the optical elements  210 ,  220 ,  230 ,  240 ,  250 ,  260 , and  270  to form scanning spots  222 ′,  221 ′,  223 ′, and  224 ′, respectively, on the image plane  282 . The scanning spots  222 ′,  221 ′,  223 ′, and  224 ′ move across the image plane  282  to form the nominal scan lines  175 . The scan lines  175  thus formed have the previously-described beam-to-beam spacing errors, which can include bow line distortions and/or semi-static errors. 
     FIG. 15 shows examples of two scan line patterns  330  and  340  formed in a test patch found on a photoreceptor  280 . The scan line patterns  330  and  340  are formed using the two pre-aligned dual light sources of the third exemplary embodiment of the optical system  200  shown in FIG.  13 . 
     FIG. 15 shows a hatched area  314  which represents the clear portion  319  that should be part of the toned area portion  312 . The hatched area  314  has a height  316 . Additionally, the toned area portion  312 , which should be part of the clear portion  319 , has a height  318 . 
     As shown in FIG. 15, the dashed ovals on the far left of the Figure represent the ideal arrangement of the scan spots  221 ′,  222 ′,  223 ′ and  224 ′ into the scan lines  175  at the image plane  282 , for each pass of the light beams  221 ,  222 ,  223  and  224 . The scan line pattern  330  represents a pattern where two of the light sources  202  and  203  of the four light sources  201 ,  202 ,  203 , and  204 , having one or more of the above-outlined beam spacing errors, are turned on for each pass, while the other light sources  201  and  204  are turned off. As shown in FIG. 15, the scan spots  221 ′ and  223 ′, and thus the resulting scan lines overlap and widen the clear portion  319  between passes, distorting the desired pattern  330 . 
     The right side of FIG. 15 shows a second scan line pattern  340 . The second scan line pattern  340  represents a pattern where two other light sources  201  and  204  of the four light sources  201 ,  202 ,  203  and  204 , having one or more of the above-outlined beam spacing errors, are turned on for each pass, while the other light sources  202  and  203  are turned off. As shown in FIG. 15, the scan spots  222 ′ and  224 ′, and thus, the resulting scan lines are spaced apart by a gap, shown as hatched area  314 , between the scan lines due to the overlap between scan spots  221 ′ and  223 ′, distorting the desired pattern  340 . 
     It should be appreciated that, if there is no spacing error in the positions of the light beams  221 ,  222 ,  223  and  224  on the image plane  282 , the two scan line patterns  330  and  340  would be identical in the relative size of the toned to untoned areas but out of phase. Additionally, the toned area  312  and the clear area  319  would be the same size and would not be broken up into sub-areas, as on the scan line patterns  330  and  340  shown in FIG.  15 . 
     It should also be appreciated that, in the third exemplary embodiment shown in FIG. 15, the light beams  221 ,  222 ,  223  and  224  overlap due to the beam spacing errors. In contrast, the light beams  221 ,  222 ,  223  and  224  could be spaced apart due to the beam spacing errors. In this case, the resulting test patches obtained from the pattern  330  and the pattern  340  would be reversed from the test patches shown in FIG.  15 . 
     It should be appreciated that any number of possible scan line patterns using the light sources  201 ,  202 ,  203  and  204  can be generated, using pre-aligned dual light sources of the third exemplary embodiment of the invention or individual light sources of the fourth exemplary embodiment of the invention. Additionally, it should be appreciated that the scan line patterns are not limited to the patterns  330  and  340  shown in FIG.  15 . 
     FIG. 16 shows the gray level measurement system  290  of a fifth exemplary embodiment of the optical system  200  used to measure or otherwise determine beam-to-beam spacing errors according to the invention. The fifth embodiment of the optical system  200  includes substantially the same optical elements as the first, second, third, and fourth exemplary embodiments of the optical system  200 . Consequently, a detailed description of the optical elements comprising the optical system  200  and of the beam-to-beam error adjustment of the fifth exemplary embodiment is not provided, because the optical elements and the adjustments for this fifth exemplary embodiment are substantially the same as the previous embodiments. 
     As shown in FIG. 16, in this fifth exemplary embodiment of the optical system  200 , the gray level measurement system  290  comprises three densitometers  291 ,  292  and  293  located near the photoreceptor  280 . In this embodiment, the three densitometers  291 ,  292  and  293  are located on a lead screw  298 , and thus can be located at different locations along the width of the photoreceptor  280 . In various exemplary embodiments, the densitometers  291 ,  292  and  293  of this fifth exemplary embodiment are also enhanced toner area coverage sensors, as discussed with regard to the first exemplary embodiment of this invention. Accordingly, each of the densitometers  291 ,  292  and  293  detect a gray level of the toned area within their respective viewing areas. The gray level measurement system  290  sends corresponding signals to the controller  300 , so that the beam-to-beam spacing errors may be determined at each location, or so that one or more control signals may be determined that adjust one or more optical elements such that the beam-to-beam spacing error tends towards zero. 
     It should be appreciated that the densitometers  291 ,  292  and  293  may be located with respect to the photoreceptor  280  in any manner and are not required to be mounted on the lead screw  298 , as shown in FIG.  16 . Additionally, it should be appreciated that the densitometers  291 ,  292  and  293  may be located at any set of locations along the length of the photoreceptor  280 , so long as the densitometers  291 ,  292  and  293  are able to detect the toned areas of test patches on the photoreceptor  280 . 
     FIG. 17 shows the gray level measurement system  290  of a sixth exemplary embodiment of the optical system  200  used to measure or otherwise determine beam-to-beam spacing errors according to the invention. The sixth embodiment of the optical system  200  includes substantially the same optical elements as the first, second, third, fourth, and fifth exemplary embodiments of the optical system  200 . Consequently, a detailed description of the optical elements comprising the optical system  200  and the beam-to-beam error adjustment of the sixth exemplary embodiment is not provided because the optical elements and the adjustment for this sixth exemplary embodiment are substantially the same as the previous embodiments. 
     As shown in FIG. 17, in this sixth exemplary embodiment, the gray level measurement system  290  comprises a single movable densitometer  294 . The densitometer  294  is not fixedly located at a specific position along the width of the photoreceptor  280 . Instead, the densitometer  294  moves along the width of photoreceptor  280  and is able to detect toned areas of test patches at different locations over the full width of the photoreceptor  280 . 
     FIG. 17 specifically shows the densitometer  294  movably mounted on the lead screw  298 . The densitometer  294  of this sixth exemplary embodiment is also the same type of enhanced toner area coverage sensor (ETAC sensor) discussed with regard to the first exemplary embodiment of this invention. Accordingly, the densitometer  294  detects the toned areas of test patches on the photoreceptor  280  and the gray level measurement system  290  sends one or more corresponding signals to the controller  300  so that a beam-to-beam adjustment may be implemented. 
     It should be appreciated that the densitometer  294  may be located at any set of one or more positions along the width of the photoreceptor  280  in any manner, so long as the densitometer  294  moves across the width of the photoreceptor  280 . Further, the densitometer  294  does not have to be mounted on the lead screw  298 , as shown in FIG.  17 . Additionally, it should be appreciated that the densitometer  294  may be variously located at any point along the length of the photoreceptor  280 , so long as the densitometer  294  is able to detect the toned areas of test patches on the photoreceptor  280 . 
     FIG. 18 shows the photoreceptor  280  having test patterns formed using the two scan line patterns  330  and  340 . FIG. 18 also shows the orientation of one of the densitometers  291 - 294  of the gray level measurement system  290  with respect to the raster scan line patterns  330  and  340 . As shown in FIG. 18, in various exemplary embodiments, each densitometer  291 - 294  includes a pair of detectors  295  and  296  that are aligned with a set of paired test patch patterns  310  and  320 , or  330  and  340 . That is, each detector  295  and  296  is presented with both of the patterns  310  and  320 , or  330  and  340 , during a single measurement of the beam-to-beam spacing error at a given location. 
     As the detector  295  is presented with the test patch patterns  310  and  320 , or  330  and  340 , the detector  295  outputs analog signals having amplitudes that correspond to the relative gray levels of the toned areas of the patterns  310  or  330 , and  320  or  340 , respectively. These magnitudes correspond to the measured gray level values G 1A  and G 2A , respectively. As the detector  296  is presented with the test patch patterns  320  or  340 , and  310  or  330 , respectively, the detector  296  outputs analog signals having amplitudes that correspond to the relative gray levels of the toned areas of the test patch patterns  320  or  340 , and  310  or  330 , respectively. These magnitudes correspond to the measured gray level values G 1B  and G 2B , respectively. 
     The differential gray level values ΔG 1  and ΔG 2 , between G 1A  and G 1B , and G 2A  and G 2B , respectively, or the gray level difference ΔG derived from ΔG 1 , and ΔG 2 , are used to determine whether an adjustment may be necessary, as outlined above. If either one of the differential gray level values ΔG 1  and ΔG 2  does not equal zero, adjustments to one or more adjustable optical elements may be necessary to reduce the beam spacing error. However, in various exemplary embodiments, if the gray level difference value ΔG is zero, or within a desired tolerance of zero, or equivalently, if both of the differential gray level values ΔG 1  and ΔG 2  are within a predetermined tolerance of zero, as outlined above, then the adjustments to one or more adjustable optical elements are not necessary. 
     It should be appreciated that the greater the number of densitometers  291 ,  292 ,  293  and  294  provided in the gray level measurement system  290 , the better the overall scan line beam-to-beam adjustment will be in reducing or removing the beam spacing error. Consequently, as shown in FIG. 17, the first and third exemplary embodiments may be modified to include a gray level measurement system  290  having three enhanced toner area coverage sensors  291 ,  292 , and  293 , so that better beam-to-beam spacing adjustments can be determined. It should be appreciated that any number of densitometers  291 - 294  may be used and that the number is not limited to that shown in FIG.  17 . 
     FIG. 19 shows an ROS image exposure station having a photoreceptor  280  and a gray level measurement system  290  according to this invention. It should be appreciated that the gray level measurement system  290  of this invention may be located anywhere along the length of the photoreceptor  280 , so long as the gray level measurement system  290  is able to detect the gray level of toned areas on the photoreceptor  280 . 
     FIGS. 20A and 20B are a flowchart outlining one exemplary embodiment of a method for reducing beam-to-beam spacing error according to this invention. Beginning in step S 100 , operation continues to step S 200 , where a first set of raster scan lines are written on the photoreceptor at a first location across the width of the photoreceptor, where the first set of raster lines extends on the photoreceptor along the direction of travel of the photoreceptor. Then, in step S 300 , the measured gray level values G 1A  and G 1B  of the toned areas of each raster scan line pattern are determined. Next, in step S 400 , the differential gray level value ΔG 1 , is determined between the measured gray levels G 1A  and G 1B  of the first set of raster scan lines. Operation then continues to step S 500 . 
     In step S 500 , a second set of raster scan lines are written on the photoreceptor at the first location across the width of the photoreceptor, where the second set of raster lines extends on the photoreceptor along the direction of travel of the photoreceptor. Next, in step S 600 , the measured gray level values G 2A  and G 2B  of the toned areas of each raster scan line pattern are determined. Then, in step S 700 , the differential gray level value ΔG 2  is determined between the measured gray levels G 2A  and G 2B  of the second set of raster scan lines. Operation then continues to step S 800 . 
     In step S 800 , the gray level difference value ΔG between the first and second differential gray level values ΔG 1  and ΔG 2  is determined. It should be appreciated that the absolute values of the first and second differential gray level values ΔG 1  and ΔG 2  should be used so that an accurate average value is calculated. Then, in step S 900 , a determination is made whether the gray level difference value ΔG is equal to zero or within an acceptable tolerance around zero. If not, some beam-to-beam spacing error is considered to exist at this location along the photoreceptor. Accordingly, operation continues to step S 1000 . Otherwise, operation jumps to step S 1100 . 
     In step S 900 , an adjustment is made to at least one optical element to reduce the beam-to-beam spacing. In various exemplary embodiments, this adjustment is made by generating at least one control signal based on the value of the gray level difference value ΔG. The at least one control signal alters the at least one optical element to move the location of at least one of beams of light on the photoreceptor at the current location across the width of the photoreceptor. Operation then returns to step S 200 . The process of steps S 200 -S 1000  is then repeated until at most a predetermined amount of beam spacing error remains. 
     In contrast, in step S 1100 , the current location on the photoreceptor requiring the adjustment and the at least one control signal that alters the at least one optical element to obtain the current adjustment to the location of at least one of beams of light on the photoreceptor at the current location is recorded. Next, in step S 1200 , a determination is made whether another location along the width of the photoreceptor is to be analyzed to determine the at least one control signal for that location that reduces the gray level difference value ΔG to at least within the determined or predetermined tolerance around zero. If not, operation jumps to step S 1400 , where operation of the method ends. In contrast, if another location is to be analyzed, operation continues to step S 1300 . 
     In step S 1300 , a next location across the width of the photoreceptor is selected. It should be appreciated that the next location across the width of the photoreceptor can be selected by moving a current gray level detector element across the width of the photoreceptor, by switching to another gray level detector element that is positioned at a different location across the width of the photoreceptor, or both. Operation then jumps back to step S 200 . 
     FIG. 21 is a flowchart outlining one exemplary embodiment of a method for reducing beam-to-beam spacing error according to this invention. Beginning in step S 2000 , operation continues to step S 2100 , where a first set of raster scan lines are written on the photoreceptor at a first location across the width of the photoreceptor, where the first set of raster lines extends on the photoreceptor along the direction of travel of the photoreceptor. Then, in step S 2200 , the measured gray level values G 1A  and G 1B  of the toned areas of each raster scan line pattern are determined. Next, in step S 2300 , the differential gray level value ΔG 1  is determined between the determined gray levels G 1A  and G 1B  of the first set of raster scan lines. Operation then continues to step S 2400 . 
     In step S 2400 , a second set of raster scan lines are written on the photoreceptor at the first location across the width of the photoreceptor, where the second set of raster lines extends on the photoreceptor along the direction of travel of the photoreceptor. Next, in step S 2500 , the measured gray level values G 2A  and G 2B  of the toned areas of each raster scan line pattern are determined. Then, in step S 2600 , the differential gray level value ΔG 2  is determined between the determined gray levels G 2A  and G 2B  of the second set of raster scan lines. Operation then continues to step S 2700 . 
     In step S 2700 , the gray level difference value ΔG between the first and second differential gray level values ΔG, and ΔG 2  is determined. It should be appreciated that the absolute values of the first and second differential gray level values ΔG 1  and ΔG 2  should be used so that an accurate average value is calculated. Then, in step S 2800 , a determination is made whether the gray level difference value ΔG is equal to zero or within an acceptable tolerance around zero. If so, the beam-to-beam spacing error is considered to be effectively zero at this location along the photoreceptor. Accordingly, operation continues to step S 2900 . Otherwise, operation jumps to step S 3000 . 
     In step S 2900 , the spacing error is set to zero. Operation then jumps to step S 3100 . In contrast, in step S 3000 , the spacing error is determined based on the gray level difference value ΔG. In various exemplary embodiments, a calibration table or equation is used to convert the gray level difference value ΔG to the equivalent beam-to-beam spacing error. Operation then continues to step S 3100 . 
     In step S 3100 , the spacing error and the current location across the width of the photoreceptor are recorded. Next, in step S 3200 , a determination is made whether another location along the width of the photoreceptor is to be analyzed to determine the beam-to-beam spacing error for that location across the width of the photoreceptor. If not, operation jumps to step S 3400 , where operation of the method ends. In contrast, if another location is to be analyzed, operation continues to step S 3300 . 
     In step S 3300 , a next location across the width of the photoreceptor is selected. It should be appreciated that the next location across the width of the photoreceptor can be selected by moving a current gray level detector element across the width of the photoreceptor, by switching to another gray level detector element that is positioned at a different location across the width of the photoreceptor, or both. Operation then jumps back to step S 2100 . 
     The beam spacing error system  400  is, in various exemplary embodiments, implemented on a programmed general purpose compute. However, the beam spacing error system  400  can also be implemented on a special purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit elements, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmable logic device such as a PLD, PLA, FPGA or PAL, or the like. In general, any device, capable of implementing a finite state machine that is in turn capable of implementing the flowcharts shown in FIGS. 20 and 21, can be used to implement the beam spacing error system  400 . 
     Moreover, the beam spacing error system  400  can be implemented as software executing on a programmed general purpose computer, a special purpose computer, a microprocessor or the like. In this case, the beam spacing error system  400  can be implemented as a routine embedded in a printer control system or controller or the like. That is, the beam spacing error system  400  can be implemented by physically incorporating it into a software and/or hardware system, such as the hardware and software systems of a printer or a digital photocopier. 
     It should be appreciated that each of the circuits or routines shown in FIGS. 11 and 12 can be implemented as portions of a suitably programmed general purpose computer. Alternatively, each of the circuits or routines shown in FIGS. 11 and 12 can be implemented as physically distinct hardware circuits within an ASIC, or using a FPGA, a PDL, a PLA, or a PAL, or using discrete logic elements or discrete circuit elements. The particular form each of the circuits shown in FIG. 11 will take is a design choice and will be obvious and predictable to those skilled in the art. 
     While the invention has been described with reference to specific embodiments, the description of the specific embodiments is illustrative only and is not to be construed as limiting the scope of the invention. Various other modifications and changes may occur to those skilled in the art without departing from the spirit and scope of the invention.