Patent Publication Number: US-8542410-B2

Title: Least squares based exposure modulation for banding compensation

Description:
CROSS REFERENCES 
     U.S. patent application Ser. No. 12/555,308 filed on Sep. 8, 2009, entitled “LEAST SQUARES BASED COHERENT MULTIPAGE ANALYSIS OF PRINTER BANDING FOR DIAGNOSTICS AND COMPENSATION,” by Ramesh et al.; 
     U.S. patent application Ser. No. 12/555,275 filed on Sep. 8, 2009, entitled “BANDING PROFILE ESTIMATION USING SPLINE INTERPOLATION,” by Ramesh et al.; and 
     U.S. Patent Application Pub. No. 2009/0002724, entitled “BANDING PROFILES ESTIMATOR USING MULTIPLE SAMPLING INTERVALS,” by Paul et al., each of which herein incorporated by reference in its entirety. 
     FIELD 
     The present disclosure relates to a method, system and computer program product for estimating an exposure modulation in an image printing system. 
     BACKGROUND 
     An electrophotographic, or xerographic, image printing system employs an image bearing surface, such as a photoreceptor drum or belt, which is charged to a substantially uniform potential so as to sensitize the surface thereof. The charged portion of the image bearing surface is exposed to a light image of an original document being reproduced. Exposure of the charged image bearing surface selectively discharges the charge thereon in the irradiated areas to record an electrostatic latent image on the image bearing surface corresponding to the image contained within the original document. The location of the electrical charge forming the latent image is usually optically controlled. More specifically, in a digital xerographic system, the formation of the latent image is controlled by a raster output scanning device, usually a laser or LED source. 
     After the electrostatic latent image is recorded on the image bearing surface, the latent image is developed by bringing a developer material into contact therewith. Generally, the electrostatic latent image is developed with dry developer material comprising carrier granules having toner particles adhering triboelectrically thereto. However, a liquid developer material may be used as well. The toner particles are attracted to the latent image, forming a visible powder image on the image bearing surface. After the electrostatic latent image is developed with the toner particles, the toner powder image is transferred to a media, such as sheets, paper or other substrate sheets, using pressure and heat to fuse the toner image to the media to form a print. 
     The image printing system generally has two important dimensions: a process (or a slow scan) direction and a cross-process (or a fast scan) direction. The direction in which an image bearing surface moves is referred to as the process (or the slow scan) direction, and the direction perpendicular to the process (or the slow scan) direction is referred to as the cross-process (or the fast scan) direction. 
     Electrophotographic image printing systems of this type may produce color prints using a plurality of stations. Each station has a charging device for charging the image bearing surface, an exposing device for selectively illuminating the charged portions of the image bearings surface to record an electrostatic latent image thereon, and a developer unit for developing the electrostatic latent image with toner particles. Each developer unit deposits different color toner particles on the respective electrostatic latent image. The images are developed, at least partially in superimposed registration with one another, to form a multi-color toner powder image. The resultant multi-color powder image is subsequently transferred to a media. The transferred multicolor image is then permanently fused to the media forming the color print. 
     Banding generally refers to periodic defects on an image caused by a one-dimensional density variation in the process (slow scan) direction. Various sources of banding exist in a image printing system and the frequencies of these sources are typically known from a mechanical design of the image printing system. Bands can result due to many different types of variations within components and/or subsystems, such as roll run out (variations in roll or drum diameter) in a developer roll or photoreceptor drum, wobble in the polygon mirror of the laser raster optical scanner (ROS), and the like. 
     Banding compensation may be performed by modulating the power or intensity of one or more exposing devices, where exposure power is modulated for each scan line based on the banding profile. For examples of methods and systems for modulating exposure power or intensity, see, e.g., U.S. Pat. Nos. 7,492,381, 6,359,641, 5,818,507, 5,659,414, 5,251,058, 5,165,074 and 4,400,740 and U.S. Patent Application Pub. No. 2003/0063183, each of which herein incorporated by reference in its entirety. 
     To modulate the exposure power for banding compensation, a banding profile may be determined and analyzed. For example, see U.S. Patent Pub. Nos. 2009/0002724 and 2007/0236747, each of which herein incorporated by reference in its entirety, for examples of systems and methods for measuring the frequency, amplitude, and/or phase of bands. Banding profiles analyses may involve printing several pages of uniform halftone image, and measuring the prints using an offline or inline spectrophotometer, scanner, or density sensor. The image data is averaged in the cross process direction to obtain one-dimensional profiles in the process direction which are then analyzed for banding. 
     An exposure correction determined from the banding profile may be applied to a Tone Reproduction Curve (TRC). For examples of TRCs, see, e.g., U.S. Pat. Nos. 5,963,244 and 6,694,109, each of which herein incorporated by reference in its entirety. However, the resulting performance can be unsatisfactory as certain parts of the TRC may be undercompensated and certain parts overcompensated. 
     SUMMARY 
     In an embodiment, a method for estimating an exposure modulation in an image printing system to correct for banding is disclosed. The image printing system comprises at least one marking engine, the at least one marking engine comprising a charging device for charging the image bearing surface, an exposing device for irradiating and discharging the image bearing surface to form a latent discharged image, and a developer unit for developing toner to the discharged portion of the image bearing surface. The method includes determining a banding profile for an image printing system by a processor; determining an adjusted exposure modulation profile based on the banding profile using a least squares estimation by the processor; and printing an output based on the adjusted exposure modulation profile. 
     In another embodiment, a system for estimating an exposure modulation in an image printing system is disclosed. The system includes a marking engine; a sensor configured to obtain image data across multiple measurement intervals; an exposing device; and a processor. The processor is configured to determine a banding profile. The processor is also configured to determine an adjusted exposure modulation profile based on the banding profile using a least squares estimation. 
     In another embodiment, a computer program product, comprising a machine-readable medium having a machine-readable program embodied therein, said machine-readable program adapted to implement a method for estimating an exposure modulation in an image printing system is disclosed. The method includes determining a banding profile for an image printing system; and determining an adjusted exposure modulation profile based on the banding profile using a least squares estimation. 
     Other aspects, features, and advantages will become apparent from the following detailed description, and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various embodiments will now be disclosed, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, in which 
         FIG. 1  illustrates an image printing system incorporating an embodiment; 
         FIG. 2  illustrates an example of a banding calibration target for different area coverages; 
         FIG. 3  illustrates a timing diagram; 
         FIG. 4  illustrates a graph indicating a variation in color (scanner reflectance) due to change in exposure level for the various area coverages 
         FIG. 5  illustrates an adjusted exposure modulation profile; 
         FIGS. 6A-6C  illustrates expected performance of the adjusted exposure modulation profile for 25%, 50% and 75% area coverages, respectively; 
         FIG. 7  illustrates an embodiment of a method for determining the adjusted exposure profile using least squares estimation; and 
         FIG. 8  illustrates an embodiment of the step of estimating a banding profile. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure addresses the issue of optimizing exposure modulation. The present disclosure proposes a method for optimizing exposure modulation for banding correction using least squares estimation for improved performance across a tone reproduction curve (TRC) having at least two steps. First, a banding profile is determined for an image printing system at several area coverages on the TRC. Second, an adjusted exposure modulation profile is determined based on the banding profile using a least squares estimation. An output print may reflect the adjusted exposure modulation profile. 
       FIG. 1  illustrates a schematic perspective view of an image printing system  102  in accordance with an embodiment. The image forming apparatus includes plural (in this exemplary embodiment, four) marking engines  10 , an intermediate transfer belt  20 , a secondary transfer device  30 , a sheet carrying device  40 , and a fixing device  50 . The image forming apparatus further includes a controller  100  and a processor  90 . A controller  100  may be provided to control the various elements and sequence of operations of the image printing system  102 . In some implementations, the controller  100  and/or processor  90  may be dedicated hardware like ASICs or FPGAs, software (firmware), or a combination of dedicated hardware and software. Processor  90  may include one processor or one or more sub-processors. For the different applications of the embodiments disclosed herein, the programming and/or configuration may vary. Specifically, there is shown an “intermediate-belt-transfer” xerographic color image printing system, in which successive primary-color (e.g., C, M, Y, K) images are accumulated on image bearing surfaces  11 . Each image bearing surface  11  in turn transfers the images to an intermediate transfer member  30 . However, it should be appreciated that any image printing machine, such as monochrome machines using any technology, machines that print on photosensitive substrates, xerographic machines with multiple photoreceptors, “image-on-image” xerographic color image printing systems (e.g., U.S. Pat. No. 7,177,585, herein incorporated by reference in its entirety), Tightly Integrated Parallel Printing (TIPP) systems (e.g. U.S. Pat. Nos. 7,024,152 and 7,136,616, each of which herein incorporated by reference in its entirety), or ink-jet-based machines, may utilize the present disclosure as well. 
     The marking engine  10  includes a yellow unit  10 Y for forming a yellow image, a magenta unit  10 M for forming a magenta image, a cyan unit  10 C for forming a cyan image, and a black unit  10 K for forming a black image. The yellow unit  10 Y, the magenta unit  10 M, the cyan unit  10 C and the black unit  10 K form toner images of respective color components as images, by the electrophotography system. 
     The marking engines  10 Y,  10 M,  10 C and  10 K, which may serve as an image forming section, have the same configuration except colors of the used toner. Accordingly, for example, the yellow unit  10 Y will be described below. The yellow unit  10 Y includes an image bearing surface  11 , a charging device  12 , an exposure device  13 , a developing device  14 , a primary transfer device  15  and a drum cleaner  16 . The charging device  12  charges the image bearing surface  11  to a predetermined potential. The exposure device  13  exposes the charged image bearing surface  11  to form an electrostatic latent image. The developing device  14  receives each color component toner (in the yellow unit  10 Y, yellow toner) and develops the electrostatic latent image formed on the image bearing surface  11  with the toner. The primary transfer device  15 , for example, includes a roll member (primary transfer roll) which is in pressure-contact with the image bearing surface  11  via the intermediate transfer belt  20  with the intermediate transfer belt interposed between the primary transfer device  15  (roll member) and the image bearing surface  11 . The primary transfer device  15  applies a predetermined transfer bias between the image bearing surface  11  and the primary transfer roll to primarily transfer the toner image formed on the image bearing surface  11  onto the intermediate transfer belt  20 . The drum cleaner  16  removes remaining toner on the image bearing surface  11  after the primary transfer. 
     The intermediate transfer belt  20 , which serves as a recording material, may be wound on a driving roll  21 , a driven roll  22  and a backup roll  23 . Among them, the driving roll  21  may be rotatable, and may stretch the intermediate transfer belt  20  and transmit a driving force to the intermediate transfer belt  20 . The driven roll  22  may be rotatable, and may stretch the intermediate transfer belt  20  and may be rotated as the intermediate transfer belt  20  rotates. The backup roll  23  may be rotatable, and may stretch the intermediate transfer belt  20  and may serve as a constituent component of the secondary transfer device  30  as described below. A belt cleaner  24  for removing the remaining toner on the intermediate transfer belt  20  after secondary transfer may be provided so as to face a part of the intermediate transfer belt  20  wound on the driving roll  21 . 
     The secondary transfer device  30  includes a secondary transfer roll  31  that is rotatable and that is in pressure-contact with a surface, on a side where the toner image is carried, of the intermediate transfer belt  20 . The secondary transfer device  30  also includes a backup roll  23  disposed on the rear surface of the intermediate transfer belt  20  to form an opposite electrode for the secondary transfer roll  31 . A predetermined secondary transfer bias is applied between the secondary transfer roll  31  and the backup roll  23  such that the toner image on the intermediate transfer belt  20  is secondarily transferred onto a sheet of paper P. For example, a roll cleaner  32  for removing the toner transferred from the intermediate transfer belt  20  to the secondary transfer roll  31  is mounted on the secondary transfer roll  31 . 
     Image printing system  102  includes sensors  60  and  62  that are configured to provide image data (e.g., reflectance of the image in the process and/or cross-process direction) to the processor  104 . The sensor  60  may be configured to sense images created on the intermediate transfer belt  20  and/or to scan test patterns. Sensor  62  may be configured to sense images created in output prints, including paper prints. It should be appreciated that any number of sensors may be provided, and may be placed anywhere in the image printing system as needed, not just in the locations illustrated. 
     It should be appreciated that sensors  60  and  62  may be Automatic Density Control (ADC) sensors. For an example of an ADC sensor, see, e.g., U.S. Pat. No. 5,680,541, which is incorporated herein by reference in its entirety. Sensors  60  and  62  also may be a Full Width Array (FWA) or Enhanced Toner Area Coverage (ETAC). See, e.g., U.S. Pat. Nos. 6,975,949 and 6,462,821, each of which herein incorporated by reference in its entirety, for an example of a FWA sensor and an example of a ETAC sensor, respectively. Sensors  60  and  62  may include a spectrophotometer, color sensors, or color sensing systems. For example, see, e.g., U.S. Pat. Nos. 6,567,170; 6,621,576; 5,519,514; and 5,550,653, each of which herein is incorporated by reference in its entirety. It is should be appreciated that that other linear array sensors may also be used, such as contact image sensors, CMOS array sensors or CCD array sensors. 
     Processor  90  is configured to receive reflectance of the image, or image data, in the process and/or cross-process direction sensed by sensors  60  and/or  62 . The processor  90  is configured to generate a reflectance profile data and send the data to the controller  100 . Processor  90  may also be configured to augment image data with timing data from a signal that is synchronous with the banding source, as disclosed in U.S. Patent Application Pub. No. 2007/0236747, herein incorporated by reference in its entirety. 
     The sheet carrying device  40  includes a sheet accommodating section  41 , a pickup roll  42 , a separation roll  43 , a preregistration roll  44 , a registration roll  45  and an ejection roll  46 . The sheet accommodating section  41  has an opening at its upper part, has a rectangular shape and accommodates the sheet P therein. The pickup roll  42  is provided above the sheet accommodating section  41  to continuously feed an uppermost sheet P of the stack of sheets P accommodated in the sheet accommodating section  41 . The separation roll  43  separates and carries the sheets P, which are continuously fed by the pickup roll  42 , one by one. The preregistration roll  44  carries the sheet P carried through the separation roll  43  downstream and forms a loop together with the registration roll  45 . The registration roll  45  pauses the carrying of the sheet P and resumes the rotation at a predetermined timing so as to feed the sheet P while controlling the registration with respect to the secondary transfer device  30 . The ejection roll  46  carries the sheet P, on which the toner image is transferred by passing through the secondary transfer device  30  and is fused by passing through the fixing device  50 , toward a not-shown ejection section. 
     The fixing device  50  includes a heating roll  51  which has a heating source therein and which is rotatable. The fixing device  50  also includes a pressing roll  52  which is in contact with the heating roll  51  and rotates as the heating roll  51  rotates. 
     In one embodiment, processor  90  may be configured obtain timing information and combine timing information with image data. For example, while printing, the page timing information, such as the page synchronization signal, and the banding source timing information, such as the photoreceptor one around signal, may be obtained. The page synchronization signal may be a signal internally generated by controller  100  (shown in  FIG. 2 ), for example, as is well known in the art. See U.S. Pat. No. 6,342,963,  FIGS. 13A and 13B  and corresponding discussion, herein incorporated by reference in its entirety, for examples of page synchronization signals. The page synchronization signal may indicate the beginning and end of a page of an output image. The photoreceptor once-around may indicate the beginning and end of one photoreceptor cycle, wherein a cycle begins and ends at the same point on the photoreceptor. The photoreceptor once-around signal may be generated by a optical sensor or encoder mounted on the rotating shaft of the photoreceptor drum, as is well known in the art. For more details about obtaining timing information and combining timing information with image data, see, e.g., U.S. Patent Application Pub. No. 2009/002724 and 2007/0236747, each of which herein incorporated by reference in its entirety. 
     In another embodiment, processor  90  may be configured to determine a banding profile. For example, for each area coverage, the printed pages may be scanned using an offline or inline scanner or spectrophotometer or density sensor, such as sensors  60  and  62 , and averaged in the cross process direction to obtain the one-dimensional page profiles in the process direction. Using the page timing information, the banding profile data across multiple pages may be combined into a coherent signal, as is well known in the art. Processor  90  also may be configured to estimate the aperiodic components of the coherent signal for each area coverage. Processor  90  also may be configured to use a least squares estimation or weighted least square estimation, to determine an exposure modulation profile needed to correct for the periodic components optimally across all area coverages. The weights for the select area coverages can be preset in the factory or dynamically adjusted based on a customer image or user input. For example, assuming that the area coverages (AC) in the banding calibration target are [25%, 50% 75%], as shown in  FIG. 2 , by choosing weights of [1, 1, 1], wherein each AC is given full weight, an exposure modulation profile that is optimal across the entire TRC (0 to 100%) may be obtained. However, if the customer image is mostly 50% AC, then a better choice of weights may be [0, 1, 0]. In general, weights can be chosen based on information of spatial AC distribution on the output image page. This information might be available when the page is being Raster Image Processed (ripped). 
       FIG. 2  illustrates an example of a banding calibration target consisting of P pages of uniform halftone at a few select area coverages (i ac =1 . . . n ac ) may be printed. As shown, several bands are present across multiple pages for different area coverages. 
       FIG. 3  illustrates an example of a timing diagram used for banding profile estimation. t p (i ac ) is the page synchronization time for page p for area coverage i ac . t 1  is the time between the page synchronization and start of an image on a page. t 2  is the time between start of an image on a page and start of measured profile on the page. Both t 1  and t 2  are fixed for a particular target image. t 0   p  is the time between the page synchronization for page p and the most recent once around signal. T 0  is the once around period of the banding source. The banding source frequency is f 0 =1/T 0 . The lines  302  represent the once around sensor signal. The lines  304  are the page synchronization signals. The line  306  indicates the beginning of an image on a page. Dotted line  310  indicates the beginning of a profile, while dotted line  312  indicates the end of the profile on the page. 
     For example, a point q in the page profile for page p, is located at a distance x q  from the beginning of the profile. The time at q from the beginning of the page profile is t q =x q /v, where v is the process speed. The banding source once around time at location q on page p is given by t pq =Mod(t n   p +t 1 +t 2 +t q ,T 0 ). Function y(i ac ,p,q) may represent characteristic of a color, including but not limited to luminance, color difference, or scanner grayscale value at location q on page p as measured by an offline or inline spectrophotometer or scanner or density sensor for halftone density i ac . 
     The aperiodic components from the signal for each area coverage may be accounted for first. The aperiodic components can arise from page to page drift and paper lead edge to trail edge variation. For example, a model ŷ 1 (i ac , p, q)=g 1 (i ac , p)+g 2 (i ac ,q), where g 1 (p) refers to the page to page drift, g 2 (q) refers to the lead edge to trail edge variation may model aperiodic components. Assuming that g 1  and g 2  can be expressed as polynomials: 
                   g   1     ⁡     (       i   ac     ,   p     )       =         ∑     k   =   0       n   1       ⁢         a   k     ⁡     (     i   ac     )       ⁢         t   p     ⁡     (     i   ac     )       k     ⁢           ⁢   and   ⁢           ⁢       g   2     ⁡     (       i   ac     ,   q     )           =       ∑     k   =   1       n   2       ⁢         b   k     ⁡     (     i   ac     )       ⁢     t   q   k             ,         
where n 1  and n 2  are the order of the polynomial for g 1  and g 2 , respectively, using Lease Squares Estimation, a k (i ac ) and b k (i ac ) may be solved for according to the following formula:
 
                 Min   [       ∑     p   =   1     P     ⁢       ∑     q   =   1     Q     ⁢       (       y   ⁡     (       i   ac     ,   p   ,   q     )       -         y   ^     1     ⁡     (       i   ac     ,   p   ,   q     )         )     2         ]     ⁢           ⁢   for   ⁢           ⁢     i   ac       =     1   ⁢           ⁢   …   ⁢           ⁢     n   ac             
Where P may be the number of pages and Q is the number of samples per page. The residual profile y 2 (i ac , p, q)=y(i ac , p, q)−ŷ(i ac ,p,q) may be used to obtain the periodic banding signature, or banding profile.
 
       FIG. 4  illustrates a graph indicating a variation in color (scanner reflectance) due to change in exposure level for the various area coverages. For small changes in exposure levels, the variation may be linear. Impact of the exposure may be represented with the slope, 
               s   ⁡     (     i   ac     )       =         ⅆ       L   *     ⁡     (     i   ac     )           ⅆ   e       .             FIG. 4  also shows that slope is steepest at 50% Area Coverage and is more shallow at 25% and 75% Area Coverage.
 
     To determine the adjusted exposure modulation profile, function z(t), for example, may represent the adjusted exposure modulation profile across all area coverages (i ac =1 . . . n ac ) where t is the once around time of the banding source (e.g. PR drum). z(t) may be expressed using sinusoidal bases functions at the source frequency and its harmonics 
               z   ⁡     (   t   )       =       ∑     k   =   1       n   h       ⁢       (         c   k     ⁢     Cos   ⁡     (     2   ⁢   π   ⁢           ⁢     kf   0     ⁢   t     )         +       d   k     ⁢     Sin   ⁡     (     2   ⁢   π   ⁢           ⁢     kf   0     ⁢   t     )           )     .             
The coefficients c k  and d k  can be obtained from Weighted Least Squares Estimation:
 
             Min   [       ∑       i   ac     =   1       n   ac       ⁢       ∑     p   =   1     P     ⁢       ∑     q   =   1     Q     ⁢       w   ⁡     (     i   ac     )       ⁢       (         1     s   ⁡     (     i   ac     )         ⁢       y   2     ⁡     (       i   ac     ,   p   ,   q     )         -     z   ⁡     (       t   pq     ⁡     (     i   ac     )       )         )     2             ]         
w(i ac ) are the weights ([0,1]) assigned to the various area coverages. These weights can be preassigned or determined from the customer image content or from user specified values. The adjusted exposure modulation profile may be applied by controller  100  to modulate exposing devices  13 , as is known in the art. For examples of methods and systems for modulating the power or intensity of exposing devices, see, e.g., U.S. Pat. Nos. 7,492,381, 6,359,641, 5,818,507, 5,835,121, 5,659,414, 5,251,058, 5,165,074 and 4,400,740 and U.S. Patent Application Pub. No. 2003/0063183, each of which herein incorporated by reference in its entirety.
 
       FIG. 5  illustrates curve  502  representing a adjusted exposure modulation profile for image photoreceptor one around banding correction obtained using the method of the present disclosure on a Xerox DocuColor 250®. Data representing three are coverages 25%, 50%, and 75% is shown. The weights w(i ac ) is assumed to equal one (=1) for all three area coverages. 
       FIGS. 6A ,  6 B, and  6 C illustrate expected performance of the adjusted exposure modulation profile for 25%, 50% and 75% area coverages, respectively, on lines  604 . As shown in  FIGS. 6A ,  6 B, and  6 C, applying the adjusted exposure modulation profile, as shown in lines  604 , significantly reduces the within page variation compared to the case where the banding defects are uncorrected, as shown in lines  602 .  FIGS. 6A ,  6 B, and  6 C each also show the best case scenario where the exposure profile is individually tuned to each area coverage on lines  606 . As shown, the performance of the adjusted exposure modulation profile appears to approximate the best case scenario. 
       FIG. 7  illustrates an embodiment of a method for determining the adjusted exposure profile using least squares estimation. In step  702 , a banding profile is determined. The banding profile may be estimated by processor  90  for example. In step  704 , an adjusted exposure modulation profile is estimated using least squares estimation. Both steps  702  and  704  may be performed by processor  90  for example. Optionally, in step  706 , an output in printed based on the adjusted exposure modulation profile. In some embodiment, the adjusted exposure modulation profile may be applied across a TRC. The adjusted modulation profile may be applied across the TRC by controller  100  (shown in  FIG. 1 ) for example. Applying the adjusted exposure modulation profile may involve modulating the power or intensity of exposing devices  13  (shown in  FIG. 1 ) for example. 
       FIG. 8  illustrates one embodiment of step  702  (shown in  FIG. 7 ) for estimating a banding profile. In step  702 A, image data across multiple measurement intervals is obtained by a sensor, such as sensors  60  and/or  62 . The measurement intervals may represent printed pages, interdocument zones, or customer image zones. In step  702 B, the image data across multiple measurement intervals is combined into a coherent signal. In process step  702 C, the signal is analyzed for periodic and aperiodic components, wherein the periodic components represent a banding profile. 
     These embodiments may also be advantageously used for tightly integrated parallel printing (TIPP) systems. Such systems are known where multiple printers are controlled to output a single print job, as disclosed in U.S. Pat. Nos. 7,136,616 and 7,024,152, each of which herein is incorporated by reference in its entirety. In TIPP systems, each printer may have defects in one or more components that cause banding. Each printer may have one or more exposing devices that may be modulated to compensate for banding. It should be appreciated that the adjusted exposure modulation profile may be calculated for each exposing device in each printer. 
     Embodiments may be made in hardware, firmware, software, or various combinations thereof. Embodiments may also be implemented as instructions stored on a machine-readable medium, which may be read and executed using one or more processing devices. In one embodiment, the machine-readable medium may include various mechanisms for storing and/or transmitting information in a form that can be read by a machine (e.g., a computing device). For example, a machine-readable storage medium may include read only memory, random access memory, magnetic disk storage media, optical storage media, flash memory devices, and other media for storing information, and a machine-readable transmission media may include forms of propagated signals, including carrier waves, infrared signals, digital signals, and other media for transmitting information. While firmware, software, routines, or instructions may be described in the above disclosure in terms of specific exemplary aspects and implementations performing certain actions, it will be apparent that such descriptions are merely for the sake of convenience and that such actions in fact result from computing devices, processing devices, processors, controllers, or other devices or machines executing the firmware, software, routines, or instructions. 
     The word “image printing system” as used herein encompasses any device, such as a copier, bookmaking machine, facsimile machine, or a multi-function machine. In addition, the word “image printing system” may include ink jet, laser or other pure printers, which performs a print outputting function for any purpose. 
     While the present disclosure has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that it is capable of further modifications and is not to be limited to the disclosed embodiment, and this application is intended to cover any variations, uses, equivalent arrangements or adaptations of the present disclosure following, in general, the principles of the present disclosure and including such departures from the present disclosure as come within known or customary practice in the art to which the present disclosure pertains, and as may be applied to the essential features hereinbefore set forth and followed in the spirit and scope of the appended claims.